LAPACK  3.6.0
LAPACK: Linear Algebra PACKage
Collaboration diagram for double:

Functions

program dchkaa
 DCHKAA More...
 
program dchkab
 DCHKAB More...
 
subroutine dchkeq (THRESH, NOUT)
 DCHKEQ More...
 
subroutine dchkgb (DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NNS, NSVAL, THRESH, TSTERR, A, LA, AFAC, LAFAC, B, X, XACT, WORK, RWORK, IWORK, NOUT)
 DCHKGB More...
 
subroutine dchkge (DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
 DCHKGE More...
 
subroutine dchkgt (DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR, A, AF, B, X, XACT, WORK, RWORK, IWORK, NOUT)
 DCHKGT More...
 
subroutine dchklq (DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NXVAL, NRHS, THRESH, TSTERR, NMAX, A, AF, AQ, AL, AC, B, X, XACT, TAU, WORK, RWORK, NOUT)
 DCHKLQ More...
 
subroutine dchkpb (DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
 DCHKPB More...
 
subroutine dchkpo (DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
 DCHKPO More...
 
subroutine dchkpp (DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
 DCHKPP More...
 
subroutine dchkps (DOTYPE, NN, NVAL, NNB, NBVAL, NRANK, RANKVAL, THRESH, TSTERR, NMAX, A, AFAC, PERM, PIV, WORK, RWORK, NOUT)
 DCHKPS More...
 
subroutine dchkpt (DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR, A, D, E, B, X, XACT, WORK, RWORK, NOUT)
 DCHKPT More...
 
subroutine dchkq3 (DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NXVAL, THRESH, A, COPYA, S, TAU, WORK, IWORK, NOUT)
 DCHKQ3 More...
 
subroutine dchkql (DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NXVAL, NRHS, THRESH, TSTERR, NMAX, A, AF, AQ, AL, AC, B, X, XACT, TAU, WORK, RWORK, NOUT)
 DCHKQL More...
 
subroutine dchkqr (DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NXVAL, NRHS, THRESH, TSTERR, NMAX, A, AF, AQ, AR, AC, B, X, XACT, TAU, WORK, RWORK, IWORK, NOUT)
 DCHKQR More...
 
subroutine dchkqrt (THRESH, TSTERR, NM, MVAL, NN, NVAL, NNB, NBVAL, NOUT)
 DCHKQRT More...
 
subroutine dchkqrtp (THRESH, TSTERR, NM, MVAL, NN, NVAL, NNB, NBVAL, NOUT)
 DCHKQRTP More...
 
program dchkrfp
 DCHKRFP More...
 
subroutine dchkrq (DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NXVAL, NRHS, THRESH, TSTERR, NMAX, A, AF, AQ, AR, AC, B, X, XACT, TAU, WORK, RWORK, IWORK, NOUT)
 DCHKRQ More...
 
subroutine dchksp (DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
 DCHKSP More...
 
subroutine dchksy (DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
 DCHKSY More...
 
subroutine dchksy_rook (DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
 DCHKSY_ROOK More...
 
subroutine dchktb (DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, AB, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
 DCHKTB More...
 
subroutine dchktp (DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, AP, AINVP, B, X, XACT, WORK, RWORK, IWORK, NOUT)
 DCHKTP More...
 
subroutine dchktr (DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, A, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
 DCHKTR More...
 
subroutine dchktz (DOTYPE, NM, MVAL, NN, NVAL, THRESH, TSTERR, A, COPYA, S, TAU, WORK, NOUT)
 DCHKTZ More...
 
subroutine ddrvab (DOTYPE, NM, MVAL, NNS, NSVAL, THRESH, NMAX, A, AFAC, B, X, WORK, RWORK, SWORK, IWORK, NOUT)
 DDRVAB More...
 
subroutine ddrvac (DOTYPE, NM, MVAL, NNS, NSVAL, THRESH, NMAX, A, AFAC, B, X, WORK, RWORK, SWORK, NOUT)
 DDRVAC More...
 
subroutine ddrvgb (DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, A, LA, AFB, LAFB, ASAV, B, BSAV, X, XACT, S, WORK, RWORK, IWORK, NOUT)
 DDRVGB More...
 
subroutine ddrvge (DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, A, AFAC, ASAV, B, BSAV, X, XACT, S, WORK, RWORK, IWORK, NOUT)
 DDRVGE More...
 
subroutine ddrvgt (DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, A, AF, B, X, XACT, WORK, RWORK, IWORK, NOUT)
 DDRVGT More...
 
subroutine ddrvls (DOTYPE, NM, MVAL, NN, NVAL, NNS, NSVAL, NNB, NBVAL, NXVAL, THRESH, TSTERR, A, COPYA, B, COPYB, C, S, COPYS, WORK, IWORK, NOUT)
 DDRVLS More...
 
subroutine ddrvpb (DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, A, AFAC, ASAV, B, BSAV, X, XACT, S, WORK, RWORK, IWORK, NOUT)
 DDRVPB More...
 
subroutine ddrvpo (DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, A, AFAC, ASAV, B, BSAV, X, XACT, S, WORK, RWORK, IWORK, NOUT)
 DDRVPO More...
 
subroutine ddrvpp (DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, A, AFAC, ASAV, B, BSAV, X, XACT, S, WORK, RWORK, IWORK, NOUT)
 DDRVPP More...
 
subroutine ddrvpt (DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, A, D, E, B, X, XACT, WORK, RWORK, NOUT)
 DDRVPT More...
 
subroutine ddrvrf1 (NOUT, NN, NVAL, THRESH, A, LDA, ARF, WORK)
 DDRVRF1 More...
 
subroutine ddrvrf2 (NOUT, NN, NVAL, A, LDA, ARF, AP, ASAV)
 DDRVRF2 More...
 
subroutine ddrvrf3 (NOUT, NN, NVAL, THRESH, A, LDA, ARF, B1, B2, D_WORK_DLANGE, D_WORK_DGEQRF, TAU)
 DDRVRF3 More...
 
subroutine ddrvrf4 (NOUT, NN, NVAL, THRESH, C1, C2, LDC, CRF, A, LDA, D_WORK_DLANGE)
 DDRVRF4 More...
 
subroutine ddrvrfp (NOUT, NN, NVAL, NNS, NSVAL, NNT, NTVAL, THRESH, A, ASAV, AFAC, AINV, B, BSAV, XACT, X, ARF, ARFINV, D_WORK_DLATMS, D_WORK_DPOT01, D_TEMP_DPOT02, D_TEMP_DPOT03, D_WORK_DLANSY, D_WORK_DPOT02, D_WORK_DPOT03)
 DDRVRFP More...
 
subroutine ddrvsp (DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
 DDRVSP More...
 
subroutine ddrvsy (DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
 DDRVSY More...
 
subroutine ddrvsy_rook (DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
 DDRVSY_ROOK More...
 
subroutine debchvxx (THRESH, PATH)
 DEBCHVXX More...
 
subroutine derrab (NUNIT)
 DERRAB More...
 
subroutine derrac (NUNIT)
 DERRAC More...
 
subroutine derrge (PATH, NUNIT)
 DERRGE More...
 
subroutine derrgt (PATH, NUNIT)
 DERRGT More...
 
subroutine derrlq (PATH, NUNIT)
 DERRLQ More...
 
subroutine derrls (PATH, NUNIT)
 DERRLS More...
 
subroutine derrpo (PATH, NUNIT)
 DERRPO More...
 
subroutine derrps (PATH, NUNIT)
 DERRPS More...
 
subroutine derrql (PATH, NUNIT)
 DERRQL More...
 
subroutine derrqp (PATH, NUNIT)
 DERRQP More...
 
subroutine derrqr (PATH, NUNIT)
 DERRQR More...
 
subroutine derrqrt (PATH, NUNIT)
 DERRQRT More...
 
subroutine derrqrtp (PATH, NUNIT)
 DERRQRTP More...
 
subroutine derrrfp (NUNIT)
 DERRRFP More...
 
subroutine derrrq (PATH, NUNIT)
 DERRRQ More...
 
subroutine derrsy (PATH, NUNIT)
 DERRSY More...
 
subroutine derrtr (PATH, NUNIT)
 DERRTR More...
 
subroutine derrtz (PATH, NUNIT)
 DERRTZ More...
 
subroutine derrvx (PATH, NUNIT)
 DERRVX More...
 
subroutine dgbt01 (M, N, KL, KU, A, LDA, AFAC, LDAFAC, IPIV, WORK, RESID)
 DGBT01 More...
 
subroutine dgbt02 (TRANS, M, N, KL, KU, NRHS, A, LDA, X, LDX, B, LDB, RESID)
 DGBT02 More...
 
subroutine dgbt05 (TRANS, N, KL, KU, NRHS, AB, LDAB, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
 DGBT05 More...
 
subroutine dgelqs (M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK, INFO)
 DGELQS More...
 
logical function dgennd (M, N, A, LDA)
 DGENND More...
 
subroutine dgeqls (M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK, INFO)
 DGEQLS More...
 
subroutine dgeqrs (M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK, INFO)
 DGEQRS More...
 
subroutine dgerqs (M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK, INFO)
 DGERQS More...
 
subroutine dget01 (M, N, A, LDA, AFAC, LDAFAC, IPIV, RWORK, RESID)
 DGET01 More...
 
subroutine dget02 (TRANS, M, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
 DGET02 More...
 
subroutine dget03 (N, A, LDA, AINV, LDAINV, WORK, LDWORK, RWORK, RCOND, RESID)
 DGET03 More...
 
subroutine dget04 (N, NRHS, X, LDX, XACT, LDXACT, RCOND, RESID)
 DGET04 More...
 
double precision function dget06 (RCOND, RCONDC)
 DGET06 More...
 
subroutine dget07 (TRANS, N, NRHS, A, LDA, B, LDB, X, LDX, XACT, LDXACT, FERR, CHKFERR, BERR, RESLTS)
 DGET07 More...
 
subroutine dget08 (TRANS, M, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
 DGET08 More...
 
subroutine dgtt01 (N, DL, D, DU, DLF, DF, DUF, DU2, IPIV, WORK, LDWORK, RWORK, RESID)
 DGTT01 More...
 
subroutine dgtt02 (TRANS, N, NRHS, DL, D, DU, X, LDX, B, LDB, RESID)
 DGTT02 More...
 
subroutine dgtt05 (TRANS, N, NRHS, DL, D, DU, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
 DGTT05 More...
 
subroutine dlahilb (N, NRHS, A, LDA, X, LDX, B, LDB, WORK, INFO)
 DLAHILB More...
 
subroutine dlaord (JOB, N, X, INCX)
 DLAORD More...
 
subroutine dlaptm (N, NRHS, ALPHA, D, E, X, LDX, BETA, B, LDB)
 DLAPTM More...
 
subroutine dlarhs (PATH, XTYPE, UPLO, TRANS, M, N, KL, KU, NRHS, A, LDA, X, LDX, B, LDB, ISEED, INFO)
 DLARHS More...
 
subroutine dlatb4 (PATH, IMAT, M, N, TYPE, KL, KU, ANORM, MODE, CNDNUM, DIST)
 DLATB4 More...
 
subroutine dlatb5 (PATH, IMAT, N, TYPE, KL, KU, ANORM, MODE, CNDNUM, DIST)
 DLATB5 More...
 
subroutine dlattb (IMAT, UPLO, TRANS, DIAG, ISEED, N, KD, AB, LDAB, B, WORK, INFO)
 DLATTB More...
 
subroutine dlattp (IMAT, UPLO, TRANS, DIAG, ISEED, N, A, B, WORK, INFO)
 DLATTP More...
 
subroutine dlattr (IMAT, UPLO, TRANS, DIAG, ISEED, N, A, LDA, B, WORK, INFO)
 DLATTR More...
 
subroutine dlavsp (UPLO, TRANS, DIAG, N, NRHS, A, IPIV, B, LDB, INFO)
 DLAVSP More...
 
subroutine dlavsy (UPLO, TRANS, DIAG, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
 DLAVSY More...
 
subroutine dlavsy_rook (UPLO, TRANS, DIAG, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
 DLAVSY_ROOK More...
 
subroutine dlqt01 (M, N, A, AF, Q, L, LDA, TAU, WORK, LWORK, RWORK, RESULT)
 DLQT01 More...
 
subroutine dlqt02 (M, N, K, A, AF, Q, L, LDA, TAU, WORK, LWORK, RWORK, RESULT)
 DLQT02 More...
 
subroutine dlqt03 (M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK, RWORK, RESULT)
 DLQT03 More...
 
subroutine dpbt01 (UPLO, N, KD, A, LDA, AFAC, LDAFAC, RWORK, RESID)
 DPBT01 More...
 
subroutine dpbt02 (UPLO, N, KD, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
 DPBT02 More...
 
subroutine dpbt05 (UPLO, N, KD, NRHS, AB, LDAB, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
 DPBT05 More...
 
subroutine dpot01 (UPLO, N, A, LDA, AFAC, LDAFAC, RWORK, RESID)
 DPOT01 More...
 
subroutine dpot02 (UPLO, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
 DPOT02 More...
 
subroutine dpot03 (UPLO, N, A, LDA, AINV, LDAINV, WORK, LDWORK, RWORK, RCOND, RESID)
 DPOT03 More...
 
subroutine dpot05 (UPLO, N, NRHS, A, LDA, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
 DPOT05 More...
 
subroutine dpot06 (UPLO, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
 DPOT06 More...
 
subroutine dppt01 (UPLO, N, A, AFAC, RWORK, RESID)
 DPPT01 More...
 
subroutine dppt02 (UPLO, N, NRHS, A, X, LDX, B, LDB, RWORK, RESID)
 DPPT02 More...
 
subroutine dppt03 (UPLO, N, A, AINV, WORK, LDWORK, RWORK, RCOND, RESID)
 DPPT03 More...
 
subroutine dppt05 (UPLO, N, NRHS, AP, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
 DPPT05 More...
 
subroutine dpst01 (UPLO, N, A, LDA, AFAC, LDAFAC, PERM, LDPERM, PIV, RWORK, RESID, RANK)
 DPST01 More...
 
subroutine dptt01 (N, D, E, DF, EF, WORK, RESID)
 DPTT01 More...
 
subroutine dptt02 (N, NRHS, D, E, X, LDX, B, LDB, RESID)
 DPTT02 More...
 
subroutine dptt05 (N, NRHS, D, E, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
 DPTT05 More...
 
subroutine dqlt01 (M, N, A, AF, Q, L, LDA, TAU, WORK, LWORK, RWORK, RESULT)
 DQLT01 More...
 
subroutine dqlt02 (M, N, K, A, AF, Q, L, LDA, TAU, WORK, LWORK, RWORK, RESULT)
 DQLT02 More...
 
subroutine dqlt03 (M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK, RWORK, RESULT)
 DQLT03 More...
 
double precision function dqpt01 (M, N, K, A, AF, LDA, TAU, JPVT, WORK, LWORK)
 DQPT01 More...
 
subroutine dqrt01 (M, N, A, AF, Q, R, LDA, TAU, WORK, LWORK, RWORK, RESULT)
 DQRT01 More...
 
subroutine dqrt01p (M, N, A, AF, Q, R, LDA, TAU, WORK, LWORK, RWORK, RESULT)
 DQRT01P More...
 
subroutine dqrt02 (M, N, K, A, AF, Q, R, LDA, TAU, WORK, LWORK, RWORK, RESULT)
 DQRT02 More...
 
subroutine dqrt03 (M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK, RWORK, RESULT)
 DQRT03 More...
 
subroutine dqrt04 (M, N, NB, RESULT)
 DQRT04 More...
 
subroutine dqrt05 (M, N, L, NB, RESULT)
 DQRT05 More...
 
double precision function dqrt11 (M, K, A, LDA, TAU, WORK, LWORK)
 DQRT11 More...
 
double precision function dqrt12 (M, N, A, LDA, S, WORK, LWORK)
 DQRT12 More...
 
subroutine dqrt13 (SCALE, M, N, A, LDA, NORMA, ISEED)
 DQRT13 More...
 
double precision function dqrt14 (TRANS, M, N, NRHS, A, LDA, X, LDX, WORK, LWORK)
 DQRT14 More...
 
subroutine dqrt15 (SCALE, RKSEL, M, N, NRHS, A, LDA, B, LDB, S, RANK, NORMA, NORMB, ISEED, WORK, LWORK)
 DQRT15 More...
 
subroutine dqrt16 (TRANS, M, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
 DQRT16 More...
 
double precision function dqrt17 (TRANS, IRESID, M, N, NRHS, A, LDA, X, LDX, B, LDB, C, WORK, LWORK)
 DQRT17 More...
 
subroutine drqt01 (M, N, A, AF, Q, R, LDA, TAU, WORK, LWORK, RWORK, RESULT)
 DRQT01 More...
 
subroutine drqt02 (M, N, K, A, AF, Q, R, LDA, TAU, WORK, LWORK, RWORK, RESULT)
 DRQT02 More...
 
subroutine drqt03 (M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK, RWORK, RESULT)
 DRQT03 More...
 
double precision function drzt01 (M, N, A, AF, LDA, TAU, WORK, LWORK)
 DRZT01 More...
 
double precision function drzt02 (M, N, AF, LDA, TAU, WORK, LWORK)
 DRZT02 More...
 
subroutine dspt01 (UPLO, N, A, AFAC, IPIV, C, LDC, RWORK, RESID)
 DSPT01 More...
 
subroutine dsyt01 (UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, LDC, RWORK, RESID)
 DSYT01 More...
 
subroutine dsyt01_rook (UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, LDC, RWORK, RESID)
 DSYT01_ROOK More...
 
subroutine dtbt02 (UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, X, LDX, B, LDB, WORK, RESID)
 DTBT02 More...
 
subroutine dtbt03 (UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, SCALE, CNORM, TSCAL, X, LDX, B, LDB, WORK, RESID)
 DTBT03 More...
 
subroutine dtbt05 (UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
 DTBT05 More...
 
subroutine dtbt06 (RCOND, RCONDC, UPLO, DIAG, N, KD, AB, LDAB, WORK, RAT)
 DTBT06 More...
 
subroutine dtpt01 (UPLO, DIAG, N, AP, AINVP, RCOND, WORK, RESID)
 DTPT01 More...
 
subroutine dtpt02 (UPLO, TRANS, DIAG, N, NRHS, AP, X, LDX, B, LDB, WORK, RESID)
 DTPT02 More...
 
subroutine dtpt03 (UPLO, TRANS, DIAG, N, NRHS, AP, SCALE, CNORM, TSCAL, X, LDX, B, LDB, WORK, RESID)
 DTPT03 More...
 
subroutine dtpt05 (UPLO, TRANS, DIAG, N, NRHS, AP, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
 DTPT05 More...
 
subroutine dtpt06 (RCOND, RCONDC, UPLO, DIAG, N, AP, WORK, RAT)
 DTPT06 More...
 
subroutine dtrt01 (UPLO, DIAG, N, A, LDA, AINV, LDAINV, RCOND, WORK, RESID)
 DTRT01 More...
 
subroutine dtrt02 (UPLO, TRANS, DIAG, N, NRHS, A, LDA, X, LDX, B, LDB, WORK, RESID)
 DTRT02 More...
 
subroutine dtrt03 (UPLO, TRANS, DIAG, N, NRHS, A, LDA, SCALE, CNORM, TSCAL, X, LDX, B, LDB, WORK, RESID)
 DTRT03 More...
 
subroutine dtrt05 (UPLO, TRANS, DIAG, N, NRHS, A, LDA, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
 DTRT05 More...
 
subroutine dtrt06 (RCOND, RCONDC, UPLO, DIAG, N, A, LDA, WORK, RAT)
 DTRT06 More...
 
subroutine sdrvsy_rook (DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
 SDRVSY_ROOK More...
 

Detailed Description

This is the group of double LAPACK TESTING LIN routines.

Function Documentation

program dchkaa ( )

DCHKAA

Purpose:
 DCHKAA is the main test program for the DOUBLE PRECISION LAPACK
 linear equation routines

 The program must be driven by a short data file. The first 15 records
 (not including the first comment  line) specify problem dimensions
 and program options using list-directed input. The remaining lines
 specify the LAPACK test paths and the number of matrix types to use
 in testing.  An annotated example of a data file can be obtained by
 deleting the first 3 characters from the following 40 lines:
 Data file for testing DOUBLE PRECISION LAPACK linear eqn. routines
 7                      Number of values of M
 0 1 2 3 5 10 16        Values of M (row dimension)
 7                      Number of values of N
 0 1 2 3 5 10 16        Values of N (column dimension)
 1                      Number of values of NRHS
 2                      Values of NRHS (number of right hand sides)
 5                      Number of values of NB
 1 3 3 3 20             Values of NB (the blocksize)
 1 0 5 9 1              Values of NX (crossover point)
 3                      Number of values of RANK
 30 50 90               Values of rank (as a % of N)
 20.0                   Threshold value of test ratio
 T                      Put T to test the LAPACK routines
 T                      Put T to test the driver routines
 T                      Put T to test the error exits
 DGE   11               List types on next line if 0 < NTYPES < 11
 DGB    8               List types on next line if 0 < NTYPES <  8
 DGT   12               List types on next line if 0 < NTYPES < 12
 DPO    9               List types on next line if 0 < NTYPES <  9
 DPS    9               List types on next line if 0 < NTYPES <  9
 DPP    9               List types on next line if 0 < NTYPES <  9
 DPB    8               List types on next line if 0 < NTYPES <  8
 DPT   12               List types on next line if 0 < NTYPES < 12
 DSY   10               List types on next line if 0 < NTYPES < 10
 DSR   10               List types on next line if 0 < NTYPES < 10
 DSP   10               List types on next line if 0 < NTYPES < 10
 DTR   18               List types on next line if 0 < NTYPES < 18
 DTP   18               List types on next line if 0 < NTYPES < 18
 DTB   17               List types on next line if 0 < NTYPES < 17
 DQR    8               List types on next line if 0 < NTYPES <  8
 DRQ    8               List types on next line if 0 < NTYPES <  8
 DLQ    8               List types on next line if 0 < NTYPES <  8
 DQL    8               List types on next line if 0 < NTYPES <  8
 DQP    6               List types on next line if 0 < NTYPES <  6
 DTZ    3               List types on next line if 0 < NTYPES <  3
 DLS    6               List types on next line if 0 < NTYPES <  6
 DEQ
 DQT
 DQX
  NMAX    INTEGER
          The maximum allowable value for M and N.

  MAXIN   INTEGER
          The number of different values that can be used for each of
          M, N, NRHS, NB, NX and RANK

  MAXRHS  INTEGER
          The maximum number of right hand sides

  MATMAX  INTEGER
          The maximum number of matrix types to use for testing

  NIN     INTEGER
          The unit number for input

  NOUT    INTEGER
          The unit number for output
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
April 2012
program dchkab ( )

DCHKAB

Purpose:
 DCHKAB is the test program for the DOUBLE PRECISION LAPACK
 DSGESV/DSPOSV routine

 The program must be driven by a short data file. The first 5 records
 specify problem dimensions and program options using list-directed
 input. The remaining lines specify the LAPACK test paths and the
 number of matrix types to use in testing.  An annotated example of a
 data file can be obtained by deleting the first 3 characters from the
 following 10 lines:
 Data file for testing DOUBLE PRECISION LAPACK DSGESV
 7                      Number of values of M
 0 1 2 3 5 10 16        Values of M (row dimension)
 1                      Number of values of NRHS
 2                      Values of NRHS (number of right hand sides)
 20.0                   Threshold value of test ratio
 T                      Put T to test the LAPACK routines
 T                      Put T to test the error exits 
 DGE    11              List types on next line if 0 < NTYPES < 11
 DPO    9               List types on next line if 0 < NTYPES <  9
  NMAX    INTEGER
          The maximum allowable value for N

  MAXIN   INTEGER
          The number of different values that can be used for each of
          M, N, NRHS, NB, and NX

  MAXRHS  INTEGER
          The maximum number of right hand sides

  NIN     INTEGER
          The unit number for input

  NOUT    INTEGER
          The unit number for output
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
April 2012
subroutine dchkeq ( double precision  THRESH,
integer  NOUT 
)

DCHKEQ

Purpose:
 DCHKEQ tests DGEEQU, DGBEQU, DPOEQU, DPPEQU and DPBEQU
Parameters
[in]THRESH
          THRESH is DOUBLE PRECISION
          Threshold for testing routines. Should be between 2 and 10.
[in]NOUT
          NOUT is INTEGER
          The unit number for output.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dchkgb ( logical, dimension( * )  DOTYPE,
integer  NM,
integer, dimension( * )  MVAL,
integer  NN,
integer, dimension( * )  NVAL,
integer  NNB,
integer, dimension( * )  NBVAL,
integer  NNS,
integer, dimension( * )  NSVAL,
double precision  THRESH,
logical  TSTERR,
double precision, dimension( * )  A,
integer  LA,
double precision, dimension( * )  AFAC,
integer  LAFAC,
double precision, dimension( * )  B,
double precision, dimension( * )  X,
double precision, dimension( * )  XACT,
double precision, dimension( * )  WORK,
double precision, dimension( * )  RWORK,
integer, dimension( * )  IWORK,
integer  NOUT 
)

DCHKGB

Purpose:
 DCHKGB tests DGBTRF, -TRS, -RFS, and -CON
Parameters
[in]DOTYPE
          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
[in]NM
          NM is INTEGER
          The number of values of M contained in the vector MVAL.
[in]MVAL
          MVAL is INTEGER array, dimension (NM)
          The values of the matrix row dimension M.
[in]NN
          NN is INTEGER
          The number of values of N contained in the vector NVAL.
[in]NVAL
          NVAL is INTEGER array, dimension (NN)
          The values of the matrix column dimension N.
[in]NNB
          NNB is INTEGER
          The number of values of NB contained in the vector NBVAL.
[in]NBVAL
          NBVAL is INTEGER array, dimension (NNB)
          The values of the blocksize NB.
[in]NNS
          NNS is INTEGER
          The number of values of NRHS contained in the vector NSVAL.
[in]NSVAL
          NSVAL is INTEGER array, dimension (NNS)
          The values of the number of right hand sides NRHS.
[in]THRESH
          THRESH is DOUBLE PRECISION
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.
[in]TSTERR
          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.
[out]A
          A is DOUBLE PRECISION array, dimension (LA)
[in]LA
          LA is INTEGER
          The length of the array A.  LA >= (KLMAX+KUMAX+1)*NMAX
          where KLMAX is the largest entry in the local array KLVAL,
                KUMAX is the largest entry in the local array KUVAL and
                NMAX is the largest entry in the input array NVAL.
[out]AFAC
          AFAC is DOUBLE PRECISION array, dimension (LAFAC)
[in]LAFAC
          LAFAC is INTEGER
          The length of the array AFAC. LAFAC >= (2*KLMAX+KUMAX+1)*NMAX
          where KLMAX is the largest entry in the local array KLVAL,
                KUMAX is the largest entry in the local array KUVAL and
                NMAX is the largest entry in the input array NVAL.
[out]B
          B is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
          where NSMAX is the largest entry in NSVAL.
[out]X
          X is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
[out]XACT
          XACT is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
[out]WORK
          WORK is DOUBLE PRECISION array, dimension
                      (NMAX*max(3,NSMAX,NMAX))
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension
                      (max(NMAX,2*NSMAX))
[out]IWORK
          IWORK is INTEGER array, dimension (2*NMAX)
[in]NOUT
          NOUT is INTEGER
          The unit number for output.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dchkge ( logical, dimension( * )  DOTYPE,
integer  NM,
integer, dimension( * )  MVAL,
integer  NN,
integer, dimension( * )  NVAL,
integer  NNB,
integer, dimension( * )  NBVAL,
integer  NNS,
integer, dimension( * )  NSVAL,
double precision  THRESH,
logical  TSTERR,
integer  NMAX,
double precision, dimension( * )  A,
double precision, dimension( * )  AFAC,
double precision, dimension( * )  AINV,
double precision, dimension( * )  B,
double precision, dimension( * )  X,
double precision, dimension( * )  XACT,
double precision, dimension( * )  WORK,
double precision, dimension( * )  RWORK,
integer, dimension( * )  IWORK,
integer  NOUT 
)

DCHKGE

Purpose:
 DCHKGE tests DGETRF, -TRI, -TRS, -RFS, and -CON.
Parameters
[in]DOTYPE
          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
[in]NM
          NM is INTEGER
          The number of values of M contained in the vector MVAL.
[in]MVAL
          MVAL is INTEGER array, dimension (NM)
          The values of the matrix row dimension M.
[in]NN
          NN is INTEGER
          The number of values of N contained in the vector NVAL.
[in]NVAL
          NVAL is INTEGER array, dimension (NN)
          The values of the matrix column dimension N.
[in]NNB
          NNB is INTEGER
          The number of values of NB contained in the vector NBVAL.
[in]NBVAL
          NBVAL is INTEGER array, dimension (NBVAL)
          The values of the blocksize NB.
[in]NNS
          NNS is INTEGER
          The number of values of NRHS contained in the vector NSVAL.
[in]NSVAL
          NSVAL is INTEGER array, dimension (NNS)
          The values of the number of right hand sides NRHS.
[in]THRESH
          THRESH is DOUBLE PRECISION
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.
[in]TSTERR
          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.
[in]NMAX
          NMAX is INTEGER
          The maximum value permitted for M or N, used in dimensioning
          the work arrays.
[out]A
          A is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]AFAC
          AFAC is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]AINV
          AINV is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]B
          B is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
          where NSMAX is the largest entry in NSVAL.
[out]X
          X is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
[out]XACT
          XACT is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
[out]WORK
          WORK is DOUBLE PRECISION array, dimension
                      (NMAX*max(3,NSMAX))
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension
                      (max(2*NMAX,2*NSMAX+NWORK))
[out]IWORK
          IWORK is INTEGER array, dimension (2*NMAX)
[in]NOUT
          NOUT is INTEGER
          The unit number for output.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dchkgt ( logical, dimension( * )  DOTYPE,
integer  NN,
integer, dimension( * )  NVAL,
integer  NNS,
integer, dimension( * )  NSVAL,
double precision  THRESH,
logical  TSTERR,
double precision, dimension( * )  A,
double precision, dimension( * )  AF,
double precision, dimension( * )  B,
double precision, dimension( * )  X,
double precision, dimension( * )  XACT,
double precision, dimension( * )  WORK,
double precision, dimension( * )  RWORK,
integer, dimension( * )  IWORK,
integer  NOUT 
)

DCHKGT

Purpose:
 DCHKGT tests DGTTRF, -TRS, -RFS, and -CON
Parameters
[in]DOTYPE
          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
[in]NN
          NN is INTEGER
          The number of values of N contained in the vector NVAL.
[in]NVAL
          NVAL is INTEGER array, dimension (NN)
          The values of the matrix dimension N.
[in]NNS
          NNS is INTEGER
          The number of values of NRHS contained in the vector NSVAL.
[in]NSVAL
          NSVAL is INTEGER array, dimension (NNS)
          The values of the number of right hand sides NRHS.
[in]THRESH
          THRESH is DOUBLE PRECISION
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.
[in]TSTERR
          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.
[out]A
          A is DOUBLE PRECISION array, dimension (NMAX*4)
[out]AF
          AF is DOUBLE PRECISION array, dimension (NMAX*4)
[out]B
          B is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
          where NSMAX is the largest entry in NSVAL.
[out]X
          X is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
[out]XACT
          XACT is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
[out]WORK
          WORK is DOUBLE PRECISION array, dimension
                      (NMAX*max(3,NSMAX))
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension
                      (max(NMAX,2*NSMAX))
[out]IWORK
          IWORK is INTEGER array, dimension (2*NMAX)
[in]NOUT
          NOUT is INTEGER
          The unit number for output.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dchklq ( logical, dimension( * )  DOTYPE,
integer  NM,
integer, dimension( * )  MVAL,
integer  NN,
integer, dimension( * )  NVAL,
integer  NNB,
integer, dimension( * )  NBVAL,
integer, dimension( * )  NXVAL,
integer  NRHS,
double precision  THRESH,
logical  TSTERR,
integer  NMAX,
double precision, dimension( * )  A,
double precision, dimension( * )  AF,
double precision, dimension( * )  AQ,
double precision, dimension( * )  AL,
double precision, dimension( * )  AC,
double precision, dimension( * )  B,
double precision, dimension( * )  X,
double precision, dimension( * )  XACT,
double precision, dimension( * )  TAU,
double precision, dimension( * )  WORK,
double precision, dimension( * )  RWORK,
integer  NOUT 
)

DCHKLQ

Purpose:
 DCHKLQ tests DGELQF, DORGLQ and DORMLQ.
Parameters
[in]DOTYPE
          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
[in]NM
          NM is INTEGER
          The number of values of M contained in the vector MVAL.
[in]MVAL
          MVAL is INTEGER array, dimension (NM)
          The values of the matrix row dimension M.
[in]NN
          NN is INTEGER
          The number of values of N contained in the vector NVAL.
[in]NVAL
          NVAL is INTEGER array, dimension (NN)
          The values of the matrix column dimension N.
[in]NNB
          NNB is INTEGER
          The number of values of NB and NX contained in the
          vectors NBVAL and NXVAL.  The blocking parameters are used
          in pairs (NB,NX).
[in]NBVAL
          NBVAL is INTEGER array, dimension (NNB)
          The values of the blocksize NB.
[in]NXVAL
          NXVAL is INTEGER array, dimension (NNB)
          The values of the crossover point NX.
[in]NRHS
          NRHS is INTEGER
          The number of right hand side vectors to be generated for
          each linear system.
[in]THRESH
          THRESH is DOUBLE PRECISION
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.
[in]TSTERR
          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.
[in]NMAX
          NMAX is INTEGER
          The maximum value permitted for M or N, used in dimensioning
          the work arrays.
[out]A
          A is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]AF
          AF is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]AQ
          AQ is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]AL
          AL is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]AC
          AC is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]B
          B is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]X
          X is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]XACT
          XACT is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]TAU
          TAU is DOUBLE PRECISION array, dimension (NMAX)
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension (NMAX)
[in]NOUT
          NOUT is INTEGER
          The unit number for output.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dchkpb ( logical, dimension( * )  DOTYPE,
integer  NN,
integer, dimension( * )  NVAL,
integer  NNB,
integer, dimension( * )  NBVAL,
integer  NNS,
integer, dimension( * )  NSVAL,
double precision  THRESH,
logical  TSTERR,
integer  NMAX,
double precision, dimension( * )  A,
double precision, dimension( * )  AFAC,
double precision, dimension( * )  AINV,
double precision, dimension( * )  B,
double precision, dimension( * )  X,
double precision, dimension( * )  XACT,
double precision, dimension( * )  WORK,
double precision, dimension( * )  RWORK,
integer, dimension( * )  IWORK,
integer  NOUT 
)

DCHKPB

Purpose:
 DCHKPB tests DPBTRF, -TRS, -RFS, and -CON.
Parameters
[in]DOTYPE
          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
[in]NN
          NN is INTEGER
          The number of values of N contained in the vector NVAL.
[in]NVAL
          NVAL is INTEGER array, dimension (NN)
          The values of the matrix dimension N.
[in]NNB
          NNB is INTEGER
          The number of values of NB contained in the vector NBVAL.
[in]NBVAL
          NBVAL is INTEGER array, dimension (NBVAL)
          The values of the blocksize NB.
[in]NNS
          NNS is INTEGER
          The number of values of NRHS contained in the vector NSVAL.
[in]NSVAL
          NSVAL is INTEGER array, dimension (NNS)
          The values of the number of right hand sides NRHS.
[in]THRESH
          THRESH is DOUBLE PRECISION
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.
[in]TSTERR
          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.
[in]NMAX
          NMAX is INTEGER
          The maximum value permitted for N, used in dimensioning the
          work arrays.
[out]A
          A is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]AFAC
          AFAC is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]AINV
          AINV is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]B
          B is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
          where NSMAX is the largest entry in NSVAL.
[out]X
          X is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
[out]XACT
          XACT is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
[out]WORK
          WORK is DOUBLE PRECISION array, dimension
                      (NMAX*max(3,NSMAX))
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension
                      (max(NMAX,2*NSMAX))
[out]IWORK
          IWORK is INTEGER array, dimension (NMAX)
[in]NOUT
          NOUT is INTEGER
          The unit number for output.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dchkpo ( logical, dimension( * )  DOTYPE,
integer  NN,
integer, dimension( * )  NVAL,
integer  NNB,
integer, dimension( * )  NBVAL,
integer  NNS,
integer, dimension( * )  NSVAL,
double precision  THRESH,
logical  TSTERR,
integer  NMAX,
double precision, dimension( * )  A,
double precision, dimension( * )  AFAC,
double precision, dimension( * )  AINV,
double precision, dimension( * )  B,
double precision, dimension( * )  X,
double precision, dimension( * )  XACT,
double precision, dimension( * )  WORK,
double precision, dimension( * )  RWORK,
integer, dimension( * )  IWORK,
integer  NOUT 
)

DCHKPO

Purpose:
 DCHKPO tests DPOTRF, -TRI, -TRS, -RFS, and -CON
Parameters
[in]DOTYPE
          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
[in]NN
          NN is INTEGER
          The number of values of N contained in the vector NVAL.
[in]NVAL
          NVAL is INTEGER array, dimension (NN)
          The values of the matrix dimension N.
[in]NNB
          NNB is INTEGER
          The number of values of NB contained in the vector NBVAL.
[in]NBVAL
          NBVAL is INTEGER array, dimension (NBVAL)
          The values of the blocksize NB.
[in]NNS
          NNS is INTEGER
          The number of values of NRHS contained in the vector NSVAL.
[in]NSVAL
          NSVAL is INTEGER array, dimension (NNS)
          The values of the number of right hand sides NRHS.
[in]THRESH
          THRESH is DOUBLE PRECISION
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.
[in]TSTERR
          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.
[in]NMAX
          NMAX is INTEGER
          The maximum value permitted for N, used in dimensioning the
          work arrays.
[out]A
          A is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]AFAC
          AFAC is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]AINV
          AINV is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]B
          B is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
          where NSMAX is the largest entry in NSVAL.
[out]X
          X is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
[out]XACT
          XACT is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
[out]WORK
          WORK is DOUBLE PRECISION array, dimension
                      (NMAX*max(3,NSMAX))
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension
                      (max(NMAX,2*NSMAX))
[out]IWORK
          IWORK is INTEGER array, dimension (NMAX)
[in]NOUT
          NOUT is INTEGER
          The unit number for output.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dchkpp ( logical, dimension( * )  DOTYPE,
integer  NN,
integer, dimension( * )  NVAL,
integer  NNS,
integer, dimension( * )  NSVAL,
double precision  THRESH,
logical  TSTERR,
integer  NMAX,
double precision, dimension( * )  A,
double precision, dimension( * )  AFAC,
double precision, dimension( * )  AINV,
double precision, dimension( * )  B,
double precision, dimension( * )  X,
double precision, dimension( * )  XACT,
double precision, dimension( * )  WORK,
double precision, dimension( * )  RWORK,
integer, dimension( * )  IWORK,
integer  NOUT 
)

DCHKPP

Purpose:
 DCHKPP tests DPPTRF, -TRI, -TRS, -RFS, and -CON
Parameters
[in]DOTYPE
          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
[in]NN
          NN is INTEGER
          The number of values of N contained in the vector NVAL.
[in]NVAL
          NVAL is INTEGER array, dimension (NN)
          The values of the matrix dimension N.
[in]NNS
          NNS is INTEGER
          The number of values of NRHS contained in the vector NSVAL.
[in]NSVAL
          NSVAL is INTEGER array, dimension (NNS)
          The values of the number of right hand sides NRHS.
[in]THRESH
          THRESH is DOUBLE PRECISION
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.
[in]TSTERR
          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.
[in]NMAX
          NMAX is INTEGER
          The maximum value permitted for N, used in dimensioning the
          work arrays.
[out]A
          A is DOUBLE PRECISION array, dimension
                      (NMAX*(NMAX+1)/2)
[out]AFAC
          AFAC is DOUBLE PRECISION array, dimension
                      (NMAX*(NMAX+1)/2)
[out]AINV
          AINV is DOUBLE PRECISION array, dimension
                      (NMAX*(NMAX+1)/2)
[out]B
          B is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
          where NSMAX is the largest entry in NSVAL.
[out]X
          X is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
[out]XACT
          XACT is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
[out]WORK
          WORK is DOUBLE PRECISION array, dimension
                      (NMAX*max(3,NSMAX))
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension
                      (max(NMAX,2*NSMAX))
[out]IWORK
          IWORK is INTEGER array, dimension (NMAX)
[in]NOUT
          NOUT is INTEGER
          The unit number for output.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dchkps ( logical, dimension( * )  DOTYPE,
integer  NN,
integer, dimension( * )  NVAL,
integer  NNB,
integer, dimension( * )  NBVAL,
integer  NRANK,
integer, dimension( * )  RANKVAL,
double precision  THRESH,
logical  TSTERR,
integer  NMAX,
double precision, dimension( * )  A,
double precision, dimension( * )  AFAC,
double precision, dimension( * )  PERM,
integer, dimension( * )  PIV,
double precision, dimension( * )  WORK,
double precision, dimension( * )  RWORK,
integer  NOUT 
)

DCHKPS

Purpose:
 DCHKPS tests DPSTRF.
Parameters
[in]DOTYPE
          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
[in]NN
          NN is INTEGER
          The number of values of N contained in the vector NVAL.
[in]NVAL
          NVAL is INTEGER array, dimension (NN)
          The values of the matrix dimension N.
[in]NNB
          NNB is INTEGER
          The number of values of NB contained in the vector NBVAL.
[in]NBVAL
          NBVAL is INTEGER array, dimension (NBVAL)
          The values of the block size NB.
[in]NRANK
          NRANK is INTEGER
          The number of values of RANK contained in the vector RANKVAL.
[in]RANKVAL
          RANKVAL is INTEGER array, dimension (NBVAL)
          The values of the block size NB.
[in]THRESH
          THRESH is DOUBLE PRECISION
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.
[in]TSTERR
          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.
[in]NMAX
          NMAX is INTEGER
          The maximum value permitted for N, used in dimensioning the
          work arrays.
[out]A
          A is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]AFAC
          AFAC is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]PERM
          PERM is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]PIV
          PIV is INTEGER array, dimension (NMAX)
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (NMAX*3)
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension (NMAX)
[in]NOUT
          NOUT is INTEGER
          The unit number for output.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dchkpt ( logical, dimension( * )  DOTYPE,
integer  NN,
integer, dimension( * )  NVAL,
integer  NNS,
integer, dimension( * )  NSVAL,
double precision  THRESH,
logical  TSTERR,
double precision, dimension( * )  A,
double precision, dimension( * )  D,
double precision, dimension( * )  E,
double precision, dimension( * )  B,
double precision, dimension( * )  X,
double precision, dimension( * )  XACT,
double precision, dimension( * )  WORK,
double precision, dimension( * )  RWORK,
integer  NOUT 
)

DCHKPT

Purpose:
 DCHKPT tests DPTTRF, -TRS, -RFS, and -CON
Parameters
[in]DOTYPE
          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
[in]NN
          NN is INTEGER
          The number of values of N contained in the vector NVAL.
[in]NVAL
          NVAL is INTEGER array, dimension (NN)
          The values of the matrix dimension N.
[in]NNS
          NNS is INTEGER
          The number of values of NRHS contained in the vector NSVAL.
[in]NSVAL
          NSVAL is INTEGER array, dimension (NNS)
          The values of the number of right hand sides NRHS.
[in]THRESH
          THRESH is DOUBLE PRECISION
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.
[in]TSTERR
          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.
[out]A
          A is DOUBLE PRECISION array, dimension (NMAX*2)
[out]D
          D is DOUBLE PRECISION array, dimension (NMAX*2)
[out]E
          E is DOUBLE PRECISION array, dimension (NMAX*2)
[out]B
          B is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
          where NSMAX is the largest entry in NSVAL.
[out]X
          X is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
[out]XACT
          XACT is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
[out]WORK
          WORK is DOUBLE PRECISION array, dimension
                      (NMAX*max(3,NSMAX))
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension
                      (max(NMAX,2*NSMAX))
[in]NOUT
          NOUT is INTEGER
          The unit number for output.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dchkq3 ( logical, dimension( * )  DOTYPE,
integer  NM,
integer, dimension( * )  MVAL,
integer  NN,
integer, dimension( * )  NVAL,
integer  NNB,
integer, dimension( * )  NBVAL,
integer, dimension( * )  NXVAL,
double precision  THRESH,
double precision, dimension( * )  A,
double precision, dimension( * )  COPYA,
double precision, dimension( * )  S,
double precision, dimension( * )  TAU,
double precision, dimension( * )  WORK,
integer, dimension( * )  IWORK,
integer  NOUT 
)

DCHKQ3

Purpose:
 DCHKQ3 tests DGEQP3.
Parameters
[in]DOTYPE
          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
[in]NM
          NM is INTEGER
          The number of values of M contained in the vector MVAL.
[in]MVAL
          MVAL is INTEGER array, dimension (NM)
          The values of the matrix row dimension M.
[in]NN
          NN is INTEGER
          The number of values of N contained in the vector NVAL.
[in]NVAL
          NVAL is INTEGER array, dimension (NN)
          The values of the matrix column dimension N.
[in]NNB
          NNB is INTEGER
          The number of values of NB and NX contained in the
          vectors NBVAL and NXVAL.  The blocking parameters are used
          in pairs (NB,NX).
[in]NBVAL
          NBVAL is INTEGER array, dimension (NNB)
          The values of the blocksize NB.
[in]NXVAL
          NXVAL is INTEGER array, dimension (NNB)
          The values of the crossover point NX.
[in]THRESH
          THRESH is DOUBLE PRECISION
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.
[out]A
          A is DOUBLE PRECISION array, dimension (MMAX*NMAX)
          where MMAX is the maximum value of M in MVAL and NMAX is the
          maximum value of N in NVAL.
[out]COPYA
          COPYA is DOUBLE PRECISION array, dimension (MMAX*NMAX)
[out]S
          S is DOUBLE PRECISION array, dimension
                      (min(MMAX,NMAX))
[out]TAU
          TAU is DOUBLE PRECISION array, dimension (MMAX)
[out]WORK
          WORK is DOUBLE PRECISION array, dimension
                      (MMAX*NMAX + 4*NMAX + MMAX)
[out]IWORK
          IWORK is INTEGER array, dimension (2*NMAX)
[in]NOUT
          NOUT is INTEGER
          The unit number for output.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dchkql ( logical, dimension( * )  DOTYPE,
integer  NM,
integer, dimension( * )  MVAL,
integer  NN,
integer, dimension( * )  NVAL,
integer  NNB,
integer, dimension( * )  NBVAL,
integer, dimension( * )  NXVAL,
integer  NRHS,
double precision  THRESH,
logical  TSTERR,
integer  NMAX,
double precision, dimension( * )  A,
double precision, dimension( * )  AF,
double precision, dimension( * )  AQ,
double precision, dimension( * )  AL,
double precision, dimension( * )  AC,
double precision, dimension( * )  B,
double precision, dimension( * )  X,
double precision, dimension( * )  XACT,
double precision, dimension( * )  TAU,
double precision, dimension( * )  WORK,
double precision, dimension( * )  RWORK,
integer  NOUT 
)

DCHKQL

Purpose:
 DCHKQL tests DGEQLF, DORGQL and DORMQL.
Parameters
[in]DOTYPE
          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
[in]NM
          NM is INTEGER
          The number of values of M contained in the vector MVAL.
[in]MVAL
          MVAL is INTEGER array, dimension (NM)
          The values of the matrix row dimension M.
[in]NN
          NN is INTEGER
          The number of values of N contained in the vector NVAL.
[in]NVAL
          NVAL is INTEGER array, dimension (NN)
          The values of the matrix column dimension N.
[in]NNB
          NNB is INTEGER
          The number of values of NB and NX contained in the
          vectors NBVAL and NXVAL.  The blocking parameters are used
          in pairs (NB,NX).
[in]NBVAL
          NBVAL is INTEGER array, dimension (NNB)
          The values of the blocksize NB.
[in]NXVAL
          NXVAL is INTEGER array, dimension (NNB)
          The values of the crossover point NX.
[in]NRHS
          NRHS is INTEGER
          The number of right hand side vectors to be generated for
          each linear system.
[in]THRESH
          THRESH is DOUBLE PRECISION
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.
[in]TSTERR
          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.
[in]NMAX
          NMAX is INTEGER
          The maximum value permitted for M or N, used in dimensioning
          the work arrays.
[out]A
          A is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]AF
          AF is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]AQ
          AQ is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]AL
          AL is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]AC
          AC is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]B
          B is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]X
          X is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]XACT
          XACT is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]TAU
          TAU is DOUBLE PRECISION array, dimension (NMAX)
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension (NMAX)
[in]NOUT
          NOUT is INTEGER
          The unit number for output.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2015
subroutine dchkqr ( logical, dimension( * )  DOTYPE,
integer  NM,
integer, dimension( * )  MVAL,
integer  NN,
integer, dimension( * )  NVAL,
integer  NNB,
integer, dimension( * )  NBVAL,
integer, dimension( * )  NXVAL,
integer  NRHS,
double precision  THRESH,
logical  TSTERR,
integer  NMAX,
double precision, dimension( * )  A,
double precision, dimension( * )  AF,
double precision, dimension( * )  AQ,
double precision, dimension( * )  AR,
double precision, dimension( * )  AC,
double precision, dimension( * )  B,
double precision, dimension( * )  X,
double precision, dimension( * )  XACT,
double precision, dimension( * )  TAU,
double precision, dimension( * )  WORK,
double precision, dimension( * )  RWORK,
integer, dimension( * )  IWORK,
integer  NOUT 
)

DCHKQR

Purpose:
 DCHKQR tests DGEQRF, DORGQR and DORMQR.
Parameters
[in]DOTYPE
          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
[in]NM
          NM is INTEGER
          The number of values of M contained in the vector MVAL.
[in]MVAL
          MVAL is INTEGER array, dimension (NM)
          The values of the matrix row dimension M.
[in]NN
          NN is INTEGER
          The number of values of N contained in the vector NVAL.
[in]NVAL
          NVAL is INTEGER array, dimension (NN)
          The values of the matrix column dimension N.
[in]NNB
          NNB is INTEGER
          The number of values of NB and NX contained in the
          vectors NBVAL and NXVAL.  The blocking parameters are used
          in pairs (NB,NX).
[in]NBVAL
          NBVAL is INTEGER array, dimension (NNB)
          The values of the blocksize NB.
[in]NXVAL
          NXVAL is INTEGER array, dimension (NNB)
          The values of the crossover point NX.
[in]NRHS
          NRHS is INTEGER
          The number of right hand side vectors to be generated for
          each linear system.
[in]THRESH
          THRESH is DOUBLE PRECISION
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.
[in]TSTERR
          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.
[in]NMAX
          NMAX is INTEGER
          The maximum value permitted for M or N, used in dimensioning
          the work arrays.
[out]A
          A is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]AF
          AF is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]AQ
          AQ is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]AR
          AR is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]AC
          AC is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]B
          B is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]X
          X is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]XACT
          XACT is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]TAU
          TAU is DOUBLE PRECISION array, dimension (NMAX)
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension (NMAX)
[out]IWORK
          IWORK is INTEGER array, dimension (NMAX)
[in]NOUT
          NOUT is INTEGER
          The unit number for output.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2015
subroutine dchkqrt ( double precision  THRESH,
logical  TSTERR,
integer  NM,
integer, dimension( * )  MVAL,
integer  NN,
integer, dimension( * )  NVAL,
integer  NNB,
integer, dimension( * )  NBVAL,
integer  NOUT 
)

DCHKQRT

Purpose:
 DCHKQRT tests DGEQRT and DGEMQRT.
Parameters
[in]THRESH
          THRESH is DOUBLE PRECISION
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.
[in]TSTERR
          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.
[in]NM
          NM is INTEGER
          The number of values of M contained in the vector MVAL.
[in]MVAL
          MVAL is INTEGER array, dimension (NM)
          The values of the matrix row dimension M.
[in]NN
          NN is INTEGER
          The number of values of N contained in the vector NVAL.
[in]NVAL
          NVAL is INTEGER array, dimension (NN)
          The values of the matrix column dimension N.
[in]NNB
          NNB is INTEGER
          The number of values of NB contained in the vector NBVAL.
[in]NBVAL
          NBVAL is INTEGER array, dimension (NBVAL)
          The values of the blocksize NB.
[in]NOUT
          NOUT is INTEGER
          The unit number for output.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dchkqrtp ( double precision  THRESH,
logical  TSTERR,
integer  NM,
integer, dimension( * )  MVAL,
integer  NN,
integer, dimension( * )  NVAL,
integer  NNB,
integer, dimension( * )  NBVAL,
integer  NOUT 
)

DCHKQRTP

Purpose:
 DCHKQRTP tests DTPQRT and DTPMQRT.
Parameters
[in]THRESH
          THRESH is DOUBLE PRECISION
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.
[in]TSTERR
          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.
[in]NM
          NM is INTEGER
          The number of values of M contained in the vector MVAL.
[in]MVAL
          MVAL is INTEGER array, dimension (NM)
          The values of the matrix row dimension M.
[in]NN
          NN is INTEGER
          The number of values of N contained in the vector NVAL.
[in]NVAL
          NVAL is INTEGER array, dimension (NN)
          The values of the matrix column dimension N.
[in]NNB
          NNB is INTEGER
          The number of values of NB contained in the vector NBVAL.
[in]NBVAL
          NBVAL is INTEGER array, dimension (NBVAL)
          The values of the blocksize NB.
[in]NOUT
          NOUT is INTEGER
          The unit number for output.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
program dchkrfp ( )

DCHKRFP

Purpose:
 DCHKRFP is the main test program for the DOUBLE PRECISION linear
 equation routines with RFP storage format
  MAXIN   INTEGER
          The number of different values that can be used for each of
          M, N, or NB

  MAXRHS  INTEGER
          The maximum number of right hand sides

  NTYPES  INTEGER

  NMAX    INTEGER
          The maximum allowable value for N.

  NIN     INTEGER
          The unit number for input

  NOUT    INTEGER
          The unit number for output
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
April 2012
subroutine dchkrq ( logical, dimension( * )  DOTYPE,
integer  NM,
integer, dimension( * )  MVAL,
integer  NN,
integer, dimension( * )  NVAL,
integer  NNB,
integer, dimension( * )  NBVAL,
integer, dimension( * )  NXVAL,
integer  NRHS,
double precision  THRESH,
logical  TSTERR,
integer  NMAX,
double precision, dimension( * )  A,
double precision, dimension( * )  AF,
double precision, dimension( * )  AQ,
double precision, dimension( * )  AR,
double precision, dimension( * )  AC,
double precision, dimension( * )  B,
double precision, dimension( * )  X,
double precision, dimension( * )  XACT,
double precision, dimension( * )  TAU,
double precision, dimension( * )  WORK,
double precision, dimension( * )  RWORK,
integer, dimension( * )  IWORK,
integer  NOUT 
)

DCHKRQ

Purpose:
 DCHKRQ tests DGERQF, DORGRQ and DORMRQ.
Parameters
[in]DOTYPE
          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
[in]NM
          NM is INTEGER
          The number of values of M contained in the vector MVAL.
[in]MVAL
          MVAL is INTEGER array, dimension (NM)
          The values of the matrix row dimension M.
[in]NN
          NN is INTEGER
          The number of values of N contained in the vector NVAL.
[in]NVAL
          NVAL is INTEGER array, dimension (NN)
          The values of the matrix column dimension N.
[in]NNB
          NNB is INTEGER
          The number of values of NB and NX contained in the
          vectors NBVAL and NXVAL.  The blocking parameters are used
          in pairs (NB,NX).
[in]NBVAL
          NBVAL is INTEGER array, dimension (NNB)
          The values of the blocksize NB.
[in]NXVAL
          NXVAL is INTEGER array, dimension (NNB)
          The values of the crossover point NX.
[in]NRHS
          NRHS is INTEGER
          The number of right hand side vectors to be generated for
          each linear system.
[in]THRESH
          THRESH is DOUBLE PRECISION
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.
[in]TSTERR
          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.
[in]NMAX
          NMAX is INTEGER
          The maximum value permitted for M or N, used in dimensioning
          the work arrays.
[out]A
          A is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]AF
          AF is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]AQ
          AQ is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]AR
          AR is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]AC
          AC is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]B
          B is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]X
          X is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]XACT
          XACT is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]TAU
          TAU is DOUBLE PRECISION array, dimension (NMAX)
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension (NMAX)
[out]IWORK
          IWORK is INTEGER array, dimension (NMAX)
[in]NOUT
          NOUT is INTEGER
          The unit number for output.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dchksp ( logical, dimension( * )  DOTYPE,
integer  NN,
integer, dimension( * )  NVAL,
integer  NNS,
integer, dimension( * )  NSVAL,
double precision  THRESH,
logical  TSTERR,
integer  NMAX,
double precision, dimension( * )  A,
double precision, dimension( * )  AFAC,
double precision, dimension( * )  AINV,
double precision, dimension( * )  B,
double precision, dimension( * )  X,
double precision, dimension( * )  XACT,
double precision, dimension( * )  WORK,
double precision, dimension( * )  RWORK,
integer, dimension( * )  IWORK,
integer  NOUT 
)

DCHKSP

Purpose:
 DCHKSP tests DSPTRF, -TRI, -TRS, -RFS, and -CON
Parameters
[in]DOTYPE
          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
[in]NN
          NN is INTEGER
          The number of values of N contained in the vector NVAL.
[in]NVAL
          NVAL is INTEGER array, dimension (NN)
          The values of the matrix dimension N.
[in]NNS
          NNS is INTEGER
          The number of values of NRHS contained in the vector NSVAL.
[in]NSVAL
          NSVAL is INTEGER array, dimension (NNS)
          The values of the number of right hand sides NRHS.
[in]THRESH
          THRESH is DOUBLE PRECISION
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.
[in]TSTERR
          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.
[in]NMAX
          NMAX is INTEGER
          The maximum value permitted for N, used in dimensioning the
          work arrays.
[out]A
          A is DOUBLE PRECISION array, dimension
                      (NMAX*(NMAX+1)/2)
[out]AFAC
          AFAC is DOUBLE PRECISION array, dimension
                      (NMAX*(NMAX+1)/2)
[out]AINV
          AINV is DOUBLE PRECISION array, dimension
                      (NMAX*(NMAX+1)/2)
[out]B
          B is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
          where NSMAX is the largest entry in NSVAL.
[out]X
          X is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
[out]XACT
          XACT is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
[out]WORK
          WORK is DOUBLE PRECISION array, dimension
                      (NMAX*max(2,NSMAX))
[out]RWORK
          RWORK is DOUBLE PRECISION array,
                                 dimension (NMAX+2*NSMAX)
[out]IWORK
          IWORK is INTEGER array, dimension (2*NMAX)
[in]NOUT
          NOUT is INTEGER
          The unit number for output.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dchksy ( logical, dimension( * )  DOTYPE,
integer  NN,
integer, dimension( * )  NVAL,
integer  NNB,
integer, dimension( * )  NBVAL,
integer  NNS,
integer, dimension( * )  NSVAL,
double precision  THRESH,
logical  TSTERR,
integer  NMAX,
double precision, dimension( * )  A,
double precision, dimension( * )  AFAC,
double precision, dimension( * )  AINV,
double precision, dimension( * )  B,
double precision, dimension( * )  X,
double precision, dimension( * )  XACT,
double precision, dimension( * )  WORK,
double precision, dimension( * )  RWORK,
integer, dimension( * )  IWORK,
integer  NOUT 
)

DCHKSY

Purpose:
 DCHKSY tests DSYTRF, -TRI2, -TRS, -TRS2, -RFS, and -CON.
Parameters
[in]DOTYPE
          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
[in]NN
          NN is INTEGER
          The number of values of N contained in the vector NVAL.
[in]NVAL
          NVAL is INTEGER array, dimension (NN)
          The values of the matrix dimension N.
[in]NNB
          NNB is INTEGER
          The number of values of NB contained in the vector NBVAL.
[in]NBVAL
          NBVAL is INTEGER array, dimension (NBVAL)
          The values of the blocksize NB.
[in]NNS
          NNS is INTEGER
          The number of values of NRHS contained in the vector NSVAL.
[in]NSVAL
          NSVAL is INTEGER array, dimension (NNS)
          The values of the number of right hand sides NRHS.
[in]THRESH
          THRESH is DOUBLE PRECISION
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.
[in]TSTERR
          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.
[in]NMAX
          NMAX is INTEGER
          The maximum value permitted for N, used in dimensioning the
          work arrays.
[out]A
          A is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]AFAC
          AFAC is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]AINV
          AINV is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]B
          B is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
          where NSMAX is the largest entry in NSVAL.
[out]X
          X is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
[out]XACT
          XACT is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (NMAX*max(3,NSMAX))
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension (max(NMAX,2*NSMAX))
[out]IWORK
          IWORK is INTEGER array, dimension (2*NMAX)
[in]NOUT
          NOUT is INTEGER
          The unit number for output.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2013
subroutine dchksy_rook ( logical, dimension( * )  DOTYPE,
integer  NN,
integer, dimension( * )  NVAL,
integer  NNB,
integer, dimension( * )  NBVAL,
integer  NNS,
integer, dimension( * )  NSVAL,
double precision  THRESH,
logical  TSTERR,
integer  NMAX,
double precision, dimension( * )  A,
double precision, dimension( * )  AFAC,
double precision, dimension( * )  AINV,
double precision, dimension( * )  B,
double precision, dimension( * )  X,
double precision, dimension( * )  XACT,
double precision, dimension( * )  WORK,
double precision, dimension( * )  RWORK,
integer, dimension( * )  IWORK,
integer  NOUT 
)

DCHKSY_ROOK

Purpose:
 DCHKSY_ROOK tests DSYTRF_ROOK, -TRI_ROOK, -TRS_ROOK,
 and -CON_ROOK.
Parameters
[in]DOTYPE
          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
[in]NN
          NN is INTEGER
          The number of values of N contained in the vector NVAL.
[in]NVAL
          NVAL is INTEGER array, dimension (NN)
          The values of the matrix dimension N.
[in]NNB
          NNB is INTEGER
          The number of values of NB contained in the vector NBVAL.
[in]NBVAL
          NBVAL is INTEGER array, dimension (NBVAL)
          The values of the blocksize NB.
[in]NNS
          NNS is INTEGER
          The number of values of NRHS contained in the vector NSVAL.
[in]NSVAL
          NSVAL is INTEGER array, dimension (NNS)
          The values of the number of right hand sides NRHS.
[in]THRESH
          THRESH is DOUBLE PRECISION
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.
[in]TSTERR
          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.
[in]NMAX
          NMAX is INTEGER
          The maximum value permitted for N, used in dimensioning the
          work arrays.
[out]A
          A is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]AFAC
          AFAC is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]AINV
          AINV is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]B
          B is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
          where NSMAX is the largest entry in NSVAL.
[out]X
          X is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
[out]XACT
          XACT is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (NMAX*max(3,NSMAX))
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension (max(NMAX,2*NSMAX))
[out]IWORK
          IWORK is INTEGER array, dimension (2*NMAX)
[in]NOUT
          NOUT is INTEGER
          The unit number for output.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2015
subroutine dchktb ( logical, dimension( * )  DOTYPE,
integer  NN,
integer, dimension( * )  NVAL,
integer  NNS,
integer, dimension( * )  NSVAL,
double precision  THRESH,
logical  TSTERR,
integer  NMAX,
double precision, dimension( * )  AB,
double precision, dimension( * )  AINV,
double precision, dimension( * )  B,
double precision, dimension( * )  X,
double precision, dimension( * )  XACT,
double precision, dimension( * )  WORK,
double precision, dimension( * )  RWORK,
integer, dimension( * )  IWORK,
integer  NOUT 
)

DCHKTB

Purpose:
 DCHKTB tests DTBTRS, -RFS, and -CON, and DLATBS.
Parameters
[in]DOTYPE
          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
[in]NN
          NN is INTEGER
          The number of values of N contained in the vector NVAL.
[in]NVAL
          NVAL is INTEGER array, dimension (NN)
          The values of the matrix column dimension N.
[in]NNS
          NNS is INTEGER
          The number of values of NRHS contained in the vector NSVAL.
[in]NSVAL
          NSVAL is INTEGER array, dimension (NNS)
          The values of the number of right hand sides NRHS.
[in]THRESH
          THRESH is DOUBLE PRECISION
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.
[in]TSTERR
          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.
[in]NMAX
          NMAX is INTEGER
          The leading dimension of the work arrays.
          NMAX >= the maximum value of N in NVAL.
[out]AB
          AB is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]AINV
          AINV is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]B
          B is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
          where NSMAX is the largest entry in NSVAL.
[out]X
          X is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
[out]XACT
          XACT is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
[out]WORK
          WORK is DOUBLE PRECISION array, dimension
                      (NMAX*max(3,NSMAX))
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension
                      (max(NMAX,2*NSMAX))
[out]IWORK
          IWORK is INTEGER array, dimension (NMAX)
[in]NOUT
          NOUT is INTEGER
          The unit number for output.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dchktp ( logical, dimension( * )  DOTYPE,
integer  NN,
integer, dimension( * )  NVAL,
integer  NNS,
integer, dimension( * )  NSVAL,
double precision  THRESH,
logical  TSTERR,
integer  NMAX,
double precision, dimension( * )  AP,
double precision, dimension( * )  AINVP,
double precision, dimension( * )  B,
double precision, dimension( * )  X,
double precision, dimension( * )  XACT,
double precision, dimension( * )  WORK,
double precision, dimension( * )  RWORK,
integer, dimension( * )  IWORK,
integer  NOUT 
)

DCHKTP

Purpose:
 DCHKTP tests DTPTRI, -TRS, -RFS, and -CON, and DLATPS
Parameters
[in]DOTYPE
          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
[in]NN
          NN is INTEGER
          The number of values of N contained in the vector NVAL.
[in]NVAL
          NVAL is INTEGER array, dimension (NN)
          The values of the matrix column dimension N.
[in]NNS
          NNS is INTEGER
          The number of values of NRHS contained in the vector NSVAL.
[in]NSVAL
          NSVAL is INTEGER array, dimension (NNS)
          The values of the number of right hand sides NRHS.
[in]THRESH
          THRESH is DOUBLE PRECISION
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.
[in]TSTERR
          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.
[in]NMAX
          NMAX is INTEGER
          The leading dimension of the work arrays.  NMAX >= the
          maximumm value of N in NVAL.
[out]AP
          AP is DOUBLE PRECISION array, dimension
                      (NMAX*(NMAX+1)/2)
[out]AINVP
          AINVP is DOUBLE PRECISION array, dimension
                      (NMAX*(NMAX+1)/2)
[out]B
          B is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
          where NSMAX is the largest entry in NSVAL.
[out]X
          X is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
[out]XACT
          XACT is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
[out]WORK
          WORK is DOUBLE PRECISION array, dimension
                      (NMAX*max(3,NSMAX))
[out]IWORK
          IWORK is INTEGER array, dimension (NMAX)
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension
                      (max(NMAX,2*NSMAX))
[in]NOUT
          NOUT is INTEGER
          The unit number for output.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dchktr ( logical, dimension( * )  DOTYPE,
integer  NN,
integer, dimension( * )  NVAL,
integer  NNB,
integer, dimension( * )  NBVAL,
integer  NNS,
integer, dimension( * )  NSVAL,
double precision  THRESH,
logical  TSTERR,
integer  NMAX,
double precision, dimension( * )  A,
double precision, dimension( * )  AINV,
double precision, dimension( * )  B,
double precision, dimension( * )  X,
double precision, dimension( * )  XACT,
double precision, dimension( * )  WORK,
double precision, dimension( * )  RWORK,
integer, dimension( * )  IWORK,
integer  NOUT 
)

DCHKTR

Purpose:
 DCHKTR tests DTRTRI, -TRS, -RFS, and -CON, and DLATRS
Parameters
[in]DOTYPE
          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
[in]NN
          NN is INTEGER
          The number of values of N contained in the vector NVAL.
[in]NVAL
          NVAL is INTEGER array, dimension (NN)
          The values of the matrix column dimension N.
[in]NNB
          NNB is INTEGER
          The number of values of NB contained in the vector NBVAL.
[in]NBVAL
          NBVAL is INTEGER array, dimension (NNB)
          The values of the blocksize NB.
[in]NNS
          NNS is INTEGER
          The number of values of NRHS contained in the vector NSVAL.
[in]NSVAL
          NSVAL is INTEGER array, dimension (NNS)
          The values of the number of right hand sides NRHS.
[in]THRESH
          THRESH is DOUBLE PRECISION
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.
[in]TSTERR
          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.
[in]NMAX
          NMAX is INTEGER
          The leading dimension of the work arrays.
          NMAX >= the maximum value of N in NVAL.
[out]A
          A is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]AINV
          AINV is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]B
          B is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
          where NSMAX is the largest entry in NSVAL.
[out]X
          X is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
[out]XACT
          XACT is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
[out]WORK
          WORK is DOUBLE PRECISION array, dimension
                      (NMAX*max(3,NSMAX))
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension
                      (max(NMAX,2*NSMAX))
[out]IWORK
          IWORK is INTEGER array, dimension (NMAX)
[in]NOUT
          NOUT is INTEGER
          The unit number for output.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dchktz ( logical, dimension( * )  DOTYPE,
integer  NM,
integer, dimension( * )  MVAL,
integer  NN,
integer, dimension( * )  NVAL,
double precision  THRESH,
logical  TSTERR,
double precision, dimension( * )  A,
double precision, dimension( * )  COPYA,
double precision, dimension( * )  S,
double precision, dimension( * )  TAU,
double precision, dimension( * )  WORK,
integer  NOUT 
)

DCHKTZ

Purpose:
 DCHKTZ tests DTZRZF.
Parameters
[in]DOTYPE
          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
[in]NM
          NM is INTEGER
          The number of values of M contained in the vector MVAL.
[in]MVAL
          MVAL is INTEGER array, dimension (NM)
          The values of the matrix row dimension M.
[in]NN
          NN is INTEGER
          The number of values of N contained in the vector NVAL.
[in]NVAL
          NVAL is INTEGER array, dimension (NN)
          The values of the matrix column dimension N.
[in]THRESH
          THRESH is DOUBLE PRECISION
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.
[in]TSTERR
          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.
[out]A
          A is DOUBLE PRECISION array, dimension (MMAX*NMAX)
          where MMAX is the maximum value of M in MVAL and NMAX is the
          maximum value of N in NVAL.
[out]COPYA
          COPYA is DOUBLE PRECISION array, dimension (MMAX*NMAX)
[out]S
          S is DOUBLE PRECISION array, dimension
                      (min(MMAX,NMAX))
[out]TAU
          TAU is DOUBLE PRECISION array, dimension (MMAX)
[out]WORK
          WORK is DOUBLE PRECISION array, dimension
                      (MMAX*NMAX + 4*NMAX + MMAX)
[in]NOUT
          NOUT is INTEGER
          The unit number for output.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2015
subroutine ddrvab ( logical, dimension( * )  DOTYPE,
integer  NM,
integer, dimension( * )  MVAL,
integer  NNS,
integer, dimension( * )  NSVAL,
double precision  THRESH,
integer  NMAX,
double precision, dimension( * )  A,
double precision, dimension( * )  AFAC,
double precision, dimension( * )  B,
double precision, dimension( * )  X,
double precision, dimension( * )  WORK,
double precision, dimension( * )  RWORK,
real, dimension(*)  SWORK,
integer, dimension( * )  IWORK,
integer  NOUT 
)

DDRVAB

Purpose:
 DDRVAB tests DSGESV
Parameters
[in]DOTYPE
          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
[in]NM
          NM is INTEGER
          The number of values of M contained in the vector MVAL.
[in]MVAL
          MVAL is INTEGER array, dimension (NM)
          The values of the matrix row dimension M.
[in]NNS
          NNS is INTEGER
          The number of values of NRHS contained in the vector NSVAL.
[in]NSVAL
          NSVAL is INTEGER array, dimension (NNS)
          The values of the number of right hand sides NRHS.
[in]THRESH
          THRESH is DOUBLE PRECISION
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.
[in]NMAX
          NMAX is INTEGER
          The maximum value permitted for M or N, used in dimensioning
          the work arrays.
[out]A
          A is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]AFAC
          AFAC is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]B
          B is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
          where NSMAX is the largest entry in NSVAL.
[out]X
          X is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
[out]WORK
          WORK is DOUBLE PRECISION array, dimension
                      (NMAX*max(3,NSMAX))
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension
                      (max(2*NMAX,2*NSMAX+NWORK))
[out]SWORK
          SWORK is REAL array, dimension
                      (NMAX*(NSMAX+NMAX))
[out]IWORK
          IWORK is INTEGER array, dimension
                      NMAX
[in]NOUT
          NOUT is INTEGER
          The unit number for output.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine ddrvac ( logical, dimension( * )  DOTYPE,
integer  NM,
integer, dimension( * )  MVAL,
integer  NNS,
integer, dimension( * )  NSVAL,
double precision  THRESH,
integer  NMAX,
double precision, dimension( * )  A,
double precision, dimension( * )  AFAC,
double precision, dimension( * )  B,
double precision, dimension( * )  X,
double precision, dimension( * )  WORK,
double precision, dimension( * )  RWORK,
real, dimension(*)  SWORK,
integer  NOUT 
)

DDRVAC

Purpose:
 DDRVAC tests DSPOSV.
Parameters
[in]DOTYPE
          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
[in]NM
          NM is INTEGER
          The number of values of N contained in the vector MVAL.
[in]MVAL
          MVAL is INTEGER array, dimension (NM)
          The values of the matrix dimension N.
[in]NNS
          NNS is INTEGER
          The number of values of NRHS contained in the vector NSVAL.
[in]NSVAL
          NSVAL is INTEGER array, dimension (NNS)
          The values of the number of right hand sides NRHS.
[in]THRESH
          THRESH is DOUBLE PRECISION
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.
[in]NMAX
          NMAX is INTEGER
          The maximum value permitted for N, used in dimensioning the
          work arrays.
[out]A
          A is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]AFAC
          AFAC is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]B
          B is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
[out]X
          X is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
[out]WORK
          WORK is DOUBLE PRECISION array, dimension
                      (NMAX*max(3,NSMAX))
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension
                      (max(2*NMAX,2*NSMAX+NWORK))
[out]SWORK
          SWORK is REAL array, dimension
                      (NMAX*(NSMAX+NMAX))
[in]NOUT
          NOUT is INTEGER
          The unit number for output.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine ddrvgb ( logical, dimension( * )  DOTYPE,
integer  NN,
integer, dimension( * )  NVAL,
integer  NRHS,
double precision  THRESH,
logical  TSTERR,
double precision, dimension( * )  A,
integer  LA,
double precision, dimension( * )  AFB,
integer  LAFB,
double precision, dimension( * )  ASAV,
double precision, dimension( * )  B,
double precision, dimension( * )  BSAV,
double precision, dimension( * )  X,
double precision, dimension( * )  XACT,
double precision, dimension( * )  S,
double precision, dimension( * )  WORK,
double precision, dimension( * )  RWORK,
integer, dimension( * )  IWORK,
integer  NOUT 
)

DDRVGB

DDRVGBX

Purpose:
 DDRVGB tests the driver routines DGBSV and -SVX.
Parameters
[in]DOTYPE
          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
[in]NN
          NN is INTEGER
          The number of values of N contained in the vector NVAL.
[in]NVAL
          NVAL is INTEGER array, dimension (NN)
          The values of the matrix column dimension N.
[in]NRHS
          NRHS is INTEGER
          The number of right hand side vectors to be generated for
          each linear system.
[in]THRESH
          THRESH is DOUBLE PRECISION
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.
[in]TSTERR
          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.
[out]A
          A is DOUBLE PRECISION array, dimension (LA)
[in]LA
          LA is INTEGER
          The length of the array A.  LA >= (2*NMAX-1)*NMAX
          where NMAX is the largest entry in NVAL.
[out]AFB
          AFB is DOUBLE PRECISION array, dimension (LAFB)
[in]LAFB
          LAFB is INTEGER
          The length of the array AFB.  LAFB >= (3*NMAX-2)*NMAX
          where NMAX is the largest entry in NVAL.
[out]ASAV
          ASAV is DOUBLE PRECISION array, dimension (LA)
[out]B
          B is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]BSAV
          BSAV is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]X
          X is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]XACT
          XACT is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]S
          S is DOUBLE PRECISION array, dimension (2*NMAX)
[out]WORK
          WORK is DOUBLE PRECISION array, dimension
                      (NMAX*max(3,NRHS,NMAX))
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension
                      (max(NMAX,2*NRHS))
[out]IWORK
          IWORK is INTEGER array, dimension (2*NMAX)
[in]NOUT
          NOUT is INTEGER
          The unit number for output.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2015
Purpose:
 DDRVGB tests the driver routines DGBSV, -SVX, and -SVXX.

 Note that this file is used only when the XBLAS are available,
 otherwise ddrvgb.f defines this subroutine.
Parameters
[in]DOTYPE
          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
[in]NN
          NN is INTEGER
          The number of values of N contained in the vector NVAL.
[in]NVAL
          NVAL is INTEGER array, dimension (NN)
          The values of the matrix column dimension N.
[in]NRHS
          NRHS is INTEGER
          The number of right hand side vectors to be generated for
          each linear system.
[in]THRESH
          THRESH is DOUBLE PRECISION
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.
[in]TSTERR
          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.
[out]A
          A is DOUBLE PRECISION array, dimension (LA)
[in]LA
          LA is INTEGER
          The length of the array A.  LA >= (2*NMAX-1)*NMAX
          where NMAX is the largest entry in NVAL.
[out]AFB
          AFB is DOUBLE PRECISION array, dimension (LAFB)
[in]LAFB
          LAFB is INTEGER
          The length of the array AFB.  LAFB >= (3*NMAX-2)*NMAX
          where NMAX is the largest entry in NVAL.
[out]ASAV
          ASAV is DOUBLE PRECISION array, dimension (LA)
[out]B
          B is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]BSAV
          BSAV is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]X
          X is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]XACT
          XACT is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]S
          S is DOUBLE PRECISION array, dimension (2*NMAX)
[out]WORK
          WORK is DOUBLE PRECISION array, dimension
                      (NMAX*max(3,NRHS,NMAX))
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension
                      (max(NMAX,2*NRHS))
[out]IWORK
          IWORK is INTEGER array, dimension (2*NMAX)
[in]NOUT
          NOUT is INTEGER
          The unit number for output.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine ddrvge ( logical, dimension( * )  DOTYPE,
integer  NN,
integer, dimension( * )  NVAL,
integer  NRHS,
double precision  THRESH,
logical  TSTERR,
integer  NMAX,
double precision, dimension( * )  A,
double precision, dimension( * )  AFAC,
double precision, dimension( * )  ASAV,
double precision, dimension( * )  B,
double precision, dimension( * )  BSAV,
double precision, dimension( * )  X,
double precision, dimension( * )  XACT,
double precision, dimension( * )  S,
double precision, dimension( * )  WORK,
double precision, dimension( * )  RWORK,
integer, dimension( * )  IWORK,
integer  NOUT 
)

DDRVGE

DDRVGEX

Purpose:
 DDRVGE tests the driver routines DGESV and -SVX.
Parameters
[in]DOTYPE
          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
[in]NN
          NN is INTEGER
          The number of values of N contained in the vector NVAL.
[in]NVAL
          NVAL is INTEGER array, dimension (NN)
          The values of the matrix column dimension N.
[in]NRHS
          NRHS is INTEGER
          The number of right hand side vectors to be generated for
          each linear system.
[in]THRESH
          THRESH is DOUBLE PRECISION
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.
[in]TSTERR
          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.
[in]NMAX
          NMAX is INTEGER
          The maximum value permitted for N, used in dimensioning the
          work arrays.
[out]A
          A is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]AFAC
          AFAC is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]ASAV
          ASAV is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]B
          B is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]BSAV
          BSAV is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]X
          X is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]XACT
          XACT is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]S
          S is DOUBLE PRECISION array, dimension (2*NMAX)
[out]WORK
          WORK is DOUBLE PRECISION array, dimension
                      (NMAX*max(3,NRHS))
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension (2*NRHS+NMAX)
[out]IWORK
          IWORK is INTEGER array, dimension (2*NMAX)
[in]NOUT
          NOUT is INTEGER
          The unit number for output.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2015
Purpose:
 DDRVGE tests the driver routines DGESV, -SVX, and -SVXX.

 Note that this file is used only when the XBLAS are available,
 otherwise ddrvge.f defines this subroutine.
Parameters
[in]DOTYPE
          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
[in]NN
          NN is INTEGER
          The number of values of N contained in the vector NVAL.
[in]NVAL
          NVAL is INTEGER array, dimension (NN)
          The values of the matrix column dimension N.
[in]NRHS
          NRHS is INTEGER
          The number of right hand side vectors to be generated for
          each linear system.
[in]THRESH
          THRESH is DOUBLE PRECISION
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.
[in]TSTERR
          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.
[in]NMAX
          NMAX is INTEGER
          The maximum value permitted for N, used in dimensioning the
          work arrays.
[out]A
          A is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]AFAC
          AFAC is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]ASAV
          ASAV is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]B
          B is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]BSAV
          BSAV is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]X
          X is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]XACT
          XACT is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]S
          S is DOUBLE PRECISION array, dimension (2*NMAX)
[out]WORK
          WORK is DOUBLE PRECISION array, dimension
                      (NMAX*max(3,NRHS))
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension (2*NRHS+NMAX)
[out]IWORK
          IWORK is INTEGER array, dimension (2*NMAX)
[in]NOUT
          NOUT is INTEGER
          The unit number for output.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
April 2012
subroutine ddrvgt ( logical, dimension( * )  DOTYPE,
integer  NN,
integer, dimension( * )  NVAL,
integer  NRHS,
double precision  THRESH,
logical  TSTERR,
double precision, dimension( * )  A,
double precision, dimension( * )  AF,
double precision, dimension( * )  B,
double precision, dimension( * )  X,
double precision, dimension( * )  XACT,
double precision, dimension( * )  WORK,
double precision, dimension( * )  RWORK,
integer, dimension( * )  IWORK,
integer  NOUT 
)

DDRVGT

Purpose:
 DDRVGT tests DGTSV and -SVX.
Parameters
[in]DOTYPE
          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
[in]NN
          NN is INTEGER
          The number of values of N contained in the vector NVAL.
[in]NVAL
          NVAL is INTEGER array, dimension (NN)
          The values of the matrix dimension N.
[in]NRHS
          NRHS is INTEGER
          The number of right hand sides, NRHS >= 0.
[in]THRESH
          THRESH is DOUBLE PRECISION
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.
[in]TSTERR
          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.
[out]A
          A is DOUBLE PRECISION array, dimension (NMAX*4)
[out]AF
          AF is DOUBLE PRECISION array, dimension (NMAX*4)
[out]B
          B is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]X
          X is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]XACT
          XACT is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]WORK
          WORK is DOUBLE PRECISION array, dimension
                      (NMAX*max(3,NRHS))
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension
                      (max(NMAX,2*NRHS))
[out]IWORK
          IWORK is INTEGER array, dimension (2*NMAX)
[in]NOUT
          NOUT is INTEGER
          The unit number for output.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine ddrvls ( logical, dimension( * )  DOTYPE,
integer  NM,
integer, dimension( * )  MVAL,
integer  NN,
integer, dimension( * )  NVAL,
integer  NNS,
integer, dimension( * )  NSVAL,
integer  NNB,
integer, dimension( * )  NBVAL,
integer, dimension( * )  NXVAL,
double precision  THRESH,
logical  TSTERR,
double precision, dimension( * )  A,
double precision, dimension( * )  COPYA,
double precision, dimension( * )  B,
double precision, dimension( * )  COPYB,
double precision, dimension( * )  C,
double precision, dimension( * )  S,
double precision, dimension( * )  COPYS,
double precision, dimension( * )  WORK,
integer, dimension( * )  IWORK,
integer  NOUT 
)

DDRVLS

Purpose:
 DDRVLS tests the least squares driver routines DGELS, DGELSS, DGELSY,
 and DGELSD.
Parameters
[in]DOTYPE
          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
          The matrix of type j is generated as follows:
          j=1: A = U*D*V where U and V are random orthogonal matrices
               and D has random entries (> 0.1) taken from a uniform 
               distribution (0,1). A is full rank.
          j=2: The same of 1, but A is scaled up.
          j=3: The same of 1, but A is scaled down.
          j=4: A = U*D*V where U and V are random orthogonal matrices
               and D has 3*min(M,N)/4 random entries (> 0.1) taken
               from a uniform distribution (0,1) and the remaining
               entries set to 0. A is rank-deficient. 
          j=5: The same of 4, but A is scaled up.
          j=6: The same of 5, but A is scaled down.
[in]NM
          NM is INTEGER
          The number of values of M contained in the vector MVAL.
[in]MVAL
          MVAL is INTEGER array, dimension (NM)
          The values of the matrix row dimension M.
[in]NN
          NN is INTEGER
          The number of values of N contained in the vector NVAL.
[in]NVAL
          NVAL is INTEGER array, dimension (NN)
          The values of the matrix column dimension N.
[in]NNS
          NNS is INTEGER
          The number of values of NRHS contained in the vector NSVAL.
[in]NSVAL
          NSVAL is INTEGER array, dimension (NNS)
          The values of the number of right hand sides NRHS.
[in]NNB
          NNB is INTEGER
          The number of values of NB and NX contained in the
          vectors NBVAL and NXVAL.  The blocking parameters are used
          in pairs (NB,NX).
[in]NBVAL
          NBVAL is INTEGER array, dimension (NNB)
          The values of the blocksize NB.
[in]NXVAL
          NXVAL is INTEGER array, dimension (NNB)
          The values of the crossover point NX.
[in]THRESH
          THRESH is DOUBLE PRECISION
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.
[in]TSTERR
          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.
[out]A
          A is DOUBLE PRECISION array, dimension (MMAX*NMAX)
          where MMAX is the maximum value of M in MVAL and NMAX is the
          maximum value of N in NVAL.
[out]COPYA
          COPYA is DOUBLE PRECISION array, dimension (MMAX*NMAX)
[out]B
          B is DOUBLE PRECISION array, dimension (MMAX*NSMAX)
          where MMAX is the maximum value of M in MVAL and NSMAX is the
          maximum value of NRHS in NSVAL.
[out]COPYB
          COPYB is DOUBLE PRECISION array, dimension (MMAX*NSMAX)
[out]C
          C is DOUBLE PRECISION array, dimension (MMAX*NSMAX)
[out]S
          S is DOUBLE PRECISION array, dimension
                      (min(MMAX,NMAX))
[out]COPYS
          COPYS is DOUBLE PRECISION array, dimension
                      (min(MMAX,NMAX))
[out]WORK
          WORK is DOUBLE PRECISION array,
                      dimension (MMAX*NMAX + 4*NMAX + MMAX).
[out]IWORK
          IWORK is INTEGER array, dimension (15*NMAX)
[in]NOUT
          NOUT is INTEGER
          The unit number for output.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2015
subroutine ddrvpb ( logical, dimension( * )  DOTYPE,
integer  NN,
integer, dimension( * )  NVAL,
integer  NRHS,
double precision  THRESH,
logical  TSTERR,
integer  NMAX,
double precision, dimension( * )  A,
double precision, dimension( * )  AFAC,
double precision, dimension( * )  ASAV,
double precision, dimension( * )  B,
double precision, dimension( * )  BSAV,
double precision, dimension( * )  X,
double precision, dimension( * )  XACT,
double precision, dimension( * )  S,
double precision, dimension( * )  WORK,
double precision, dimension( * )  RWORK,
integer, dimension( * )  IWORK,
integer  NOUT 
)

DDRVPB

Purpose:
 DDRVPB tests the driver routines DPBSV and -SVX.
Parameters
[in]DOTYPE
          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
[in]NN
          NN is INTEGER
          The number of values of N contained in the vector NVAL.
[in]NVAL
          NVAL is INTEGER array, dimension (NN)
          The values of the matrix dimension N.
[in]NRHS
          NRHS is INTEGER
          The number of right hand side vectors to be generated for
          each linear system.
[in]THRESH
          THRESH is DOUBLE PRECISION
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.
[in]TSTERR
          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.
[in]NMAX
          NMAX is INTEGER
          The maximum value permitted for N, used in dimensioning the
          work arrays.
[out]A
          A is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]AFAC
          AFAC is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]ASAV
          ASAV is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]B
          B is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]BSAV
          BSAV is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]X
          X is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]XACT
          XACT is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]S
          S is DOUBLE PRECISION array, dimension (NMAX)
[out]WORK
          WORK is DOUBLE PRECISION array, dimension
                      (NMAX*max(3,NRHS))
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension (NMAX+2*NRHS)
[out]IWORK
          IWORK is INTEGER array, dimension (NMAX)
[in]NOUT
          NOUT is INTEGER
          The unit number for output.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine ddrvpo ( logical, dimension( * )  DOTYPE,
integer  NN,
integer, dimension( * )  NVAL,
integer  NRHS,
double precision  THRESH,
logical  TSTERR,
integer  NMAX,
double precision, dimension( * )  A,
double precision, dimension( * )  AFAC,
double precision, dimension( * )  ASAV,
double precision, dimension( * )  B,
double precision, dimension( * )  BSAV,
double precision, dimension( * )  X,
double precision, dimension( * )  XACT,
double precision, dimension( * )  S,
double precision, dimension( * )  WORK,
double precision, dimension( * )  RWORK,
integer, dimension( * )  IWORK,
integer  NOUT 
)

DDRVPO

DDRVPOX

Purpose:
 DDRVPO tests the driver routines DPOSV and -SVX.
Parameters
[in]DOTYPE
          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
[in]NN
          NN is INTEGER
          The number of values of N contained in the vector NVAL.
[in]NVAL
          NVAL is INTEGER array, dimension (NN)
          The values of the matrix dimension N.
[in]NRHS
          NRHS is INTEGER
          The number of right hand side vectors to be generated for
          each linear system.
[in]THRESH
          THRESH is DOUBLE PRECISION
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.
[in]TSTERR
          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.
[in]NMAX
          NMAX is INTEGER
          The maximum value permitted for N, used in dimensioning the
          work arrays.
[out]A
          A is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]AFAC
          AFAC is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]ASAV
          ASAV is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]B
          B is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]BSAV
          BSAV is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]X
          X is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]XACT
          XACT is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]S
          S is DOUBLE PRECISION array, dimension (NMAX)
[out]WORK
          WORK is DOUBLE PRECISION array, dimension
                      (NMAX*max(3,NRHS))
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension (NMAX+2*NRHS)
[out]IWORK
          IWORK is INTEGER array, dimension (NMAX)
[in]NOUT
          NOUT is INTEGER
          The unit number for output.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
Purpose:
 DDRVPO tests the driver routines DPOSV, -SVX, and -SVXX.

 Note that this file is used only when the XBLAS are available,
 otherwise ddrvpo.f defines this subroutine.
Parameters
[in]DOTYPE
          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
[in]NN
          NN is INTEGER
          The number of values of N contained in the vector NVAL.
[in]NVAL
          NVAL is INTEGER array, dimension (NN)
          The values of the matrix dimension N.
[in]NRHS
          NRHS is INTEGER
          The number of right hand side vectors to be generated for
          each linear system.
[in]THRESH
          THRESH is DOUBLE PRECISION
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.
[in]TSTERR
          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.
[in]NMAX
          NMAX is INTEGER
          The maximum value permitted for N, used in dimensioning the
          work arrays.
[out]A
          A is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]AFAC
          AFAC is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]ASAV
          ASAV is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]B
          B is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]BSAV
          BSAV is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]X
          X is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]XACT
          XACT is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]S
          S is DOUBLE PRECISION array, dimension (NMAX)
[out]WORK
          WORK is DOUBLE PRECISION array, dimension
                      (NMAX*max(3,NRHS))
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension (NMAX+2*NRHS)
[out]IWORK
          IWORK is INTEGER array, dimension (NMAX)
[in]NOUT
          NOUT is INTEGER
          The unit number for output.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2013
subroutine ddrvpp ( logical, dimension( * )  DOTYPE,
integer  NN,
integer, dimension( * )  NVAL,
integer  NRHS,
double precision  THRESH,
logical  TSTERR,
integer  NMAX,
double precision, dimension( * )  A,
double precision, dimension( * )  AFAC,
double precision, dimension( * )  ASAV,
double precision, dimension( * )  B,
double precision, dimension( * )  BSAV,
double precision, dimension( * )  X,
double precision, dimension( * )  XACT,
double precision, dimension( * )  S,
double precision, dimension( * )  WORK,
double precision, dimension( * )  RWORK,
integer, dimension( * )  IWORK,
integer  NOUT 
)

DDRVPP

Purpose:
 DDRVPP tests the driver routines DPPSV and -SVX.
Parameters
[in]DOTYPE
          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
[in]NN
          NN is INTEGER
          The number of values of N contained in the vector NVAL.
[in]NVAL
          NVAL is INTEGER array, dimension (NN)
          The values of the matrix dimension N.
[in]NRHS
          NRHS is INTEGER
          The number of right hand side vectors to be generated for
          each linear system.
[in]THRESH
          THRESH is DOUBLE PRECISION
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.
[in]TSTERR
          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.
[in]NMAX
          NMAX is INTEGER
          The maximum value permitted for N, used in dimensioning the
          work arrays.
[out]A
          A is DOUBLE PRECISION array, dimension
                      (NMAX*(NMAX+1)/2)
[out]AFAC
          AFAC is DOUBLE PRECISION array, dimension
                      (NMAX*(NMAX+1)/2)
[out]ASAV
          ASAV is DOUBLE PRECISION array, dimension
                      (NMAX*(NMAX+1)/2)
[out]B
          B is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]BSAV
          BSAV is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]X
          X is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]XACT
          XACT is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]S
          S is DOUBLE PRECISION array, dimension (NMAX)
[out]WORK
          WORK is DOUBLE PRECISION array, dimension
                      (NMAX*max(3,NRHS))
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension (NMAX+2*NRHS)
[out]IWORK
          IWORK is INTEGER array, dimension (NMAX)
[in]NOUT
          NOUT is INTEGER
          The unit number for output.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine ddrvpt ( logical, dimension( * )  DOTYPE,
integer  NN,
integer, dimension( * )  NVAL,
integer  NRHS,
double precision  THRESH,
logical  TSTERR,
double precision, dimension( * )  A,
double precision, dimension( * )  D,
double precision, dimension( * )  E,
double precision, dimension( * )  B,
double precision, dimension( * )  X,
double precision, dimension( * )  XACT,
double precision, dimension( * )  WORK,
double precision, dimension( * )  RWORK,
integer  NOUT 
)

DDRVPT

Purpose:
 DDRVPT tests DPTSV and -SVX.
Parameters
[in]DOTYPE
          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
[in]NN
          NN is INTEGER
          The number of values of N contained in the vector NVAL.
[in]NVAL
          NVAL is INTEGER array, dimension (NN)
          The values of the matrix dimension N.
[in]NRHS
          NRHS is INTEGER
          The number of right hand side vectors to be generated for
          each linear system.
[in]THRESH
          THRESH is DOUBLE PRECISION
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.
[in]TSTERR
          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.
[out]A
          A is DOUBLE PRECISION array, dimension (NMAX*2)
[out]D
          D is DOUBLE PRECISION array, dimension (NMAX*2)
[out]E
          E is DOUBLE PRECISION array, dimension (NMAX*2)
[out]B
          B is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]X
          X is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]XACT
          XACT is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]WORK
          WORK is DOUBLE PRECISION array, dimension
                      (NMAX*max(3,NRHS))
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension
                      (max(NMAX,2*NRHS))
[in]NOUT
          NOUT is INTEGER
          The unit number for output.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine ddrvrf1 ( integer  NOUT,
integer  NN,
integer, dimension( nn )  NVAL,
double precision  THRESH,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( * )  ARF,
double precision, dimension( * )  WORK 
)

DDRVRF1

Purpose:
 DDRVRF1 tests the LAPACK RFP routines:
     DLANSF
Parameters
[in]NOUT
          NOUT is INTEGER
                The unit number for output.
[in]NN
          NN is INTEGER
                The number of values of N contained in the vector NVAL.
[in]NVAL
          NVAL is INTEGER array, dimension (NN)
                The values of the matrix dimension N.
[in]THRESH
          THRESH is DOUBLE PRECISION
                The threshold value for the test ratios.  A result is
                included in the output file if RESULT >= THRESH.  To have
                every test ratio printed, use THRESH = 0.
[out]A
          A is DOUBLE PRECISION array, dimension (LDA,NMAX)
[in]LDA
          LDA is INTEGER
                The leading dimension of the array A.  LDA >= max(1,NMAX).
[out]ARF
          ARF is DOUBLE PRECISION array, dimension ((NMAX*(NMAX+1))/2).
[out]WORK
          WORK is DOUBLE PRECISION array, dimension ( NMAX )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine ddrvrf2 ( integer  NOUT,
integer  NN,
integer, dimension( nn )  NVAL,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( * )  ARF,
double precision, dimension(*)  AP,
double precision, dimension( lda, * )  ASAV 
)

DDRVRF2

Purpose:
 DDRVRF2 tests the LAPACK RFP convertion routines.
Parameters
[in]NOUT
          NOUT is INTEGER
                The unit number for output.
[in]NN
          NN is INTEGER
                The number of values of N contained in the vector NVAL.
[in]NVAL
          NVAL is INTEGER array, dimension (NN)
                The values of the matrix dimension N.
[out]A
          A is DOUBLE PRECISION array, dimension (LDA,NMAX)
[in]LDA
          LDA is INTEGER
                The leading dimension of the array A.  LDA >= max(1,NMAX).
[out]ARF
          ARF is DOUBLE PRECISION array, dimension ((NMAX*(NMAX+1))/2).
[out]AP
          AP is DOUBLE PRECISION array, dimension ((NMAX*(NMAX+1))/2).
[out]ASAV
          ASAV is DOUBLE PRECISION array, dimension (LDA,NMAX)
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine ddrvrf3 ( integer  NOUT,
integer  NN,
integer, dimension( nn )  NVAL,
double precision  THRESH,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( * )  ARF,
double precision, dimension( lda, * )  B1,
double precision, dimension( lda, * )  B2,
double precision, dimension( * )  D_WORK_DLANGE,
double precision, dimension( * )  D_WORK_DGEQRF,
double precision, dimension( * )  TAU 
)

DDRVRF3

Purpose:
 DDRVRF3 tests the LAPACK RFP routines:
     DTFSM
Parameters
[in]NOUT
          NOUT is INTEGER
                The unit number for output.
[in]NN
          NN is INTEGER
                The number of values of N contained in the vector NVAL.
[in]NVAL
          NVAL is INTEGER array, dimension (NN)
                The values of the matrix dimension N.
[in]THRESH
          THRESH is DOUBLE PRECISION
                The threshold value for the test ratios.  A result is
                included in the output file if RESULT >= THRESH.  To have
                every test ratio printed, use THRESH = 0.
[out]A
          A is DOUBLE PRECISION array, dimension (LDA,NMAX)
[in]LDA
          LDA is INTEGER
                The leading dimension of the array A.  LDA >= max(1,NMAX).
[out]ARF
          ARF is DOUBLE PRECISION array, dimension ((NMAX*(NMAX+1))/2).
[out]B1
          B1 is DOUBLE PRECISION array, dimension (LDA,NMAX)
[out]B2
          B2 is DOUBLE PRECISION array, dimension (LDA,NMAX)
[out]D_WORK_DLANGE
          D_WORK_DLANGE is DOUBLE PRECISION array, dimension (NMAX)
[out]D_WORK_DGEQRF
          D_WORK_DGEQRF is DOUBLE PRECISION array, dimension (NMAX)
[out]TAU
          TAU is DOUBLE PRECISION array, dimension (NMAX)
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine ddrvrf4 ( integer  NOUT,
integer  NN,
integer, dimension( nn )  NVAL,
double precision  THRESH,
double precision, dimension( ldc, * )  C1,
double precision, dimension( ldc, *)  C2,
integer  LDC,
double precision, dimension( * )  CRF,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( * )  D_WORK_DLANGE 
)

DDRVRF4

Purpose:
 DDRVRF4 tests the LAPACK RFP routines:
     DSFRK
Parameters
[in]NOUT
          NOUT is INTEGER
                The unit number for output.
[in]NN
          NN is INTEGER
                The number of values of N contained in the vector NVAL.
[in]NVAL
          NVAL is INTEGER array, dimension (NN)
                The values of the matrix dimension N.
[in]THRESH
          THRESH is DOUBLE PRECISION
                The threshold value for the test ratios.  A result is
                included in the output file if RESULT >= THRESH.  To
                have every test ratio printed, use THRESH = 0.
[out]C1
          C1 is DOUBLE PRECISION array,
                dimension (LDC,NMAX)
[out]C2
          C2 is DOUBLE PRECISION array,
                dimension (LDC,NMAX)
[in]LDC
          LDC is INTEGER
                The leading dimension of the array A.
                LDA >= max(1,NMAX).
[out]CRF
          CRF is DOUBLE PRECISION array,
                dimension ((NMAX*(NMAX+1))/2).
[out]A
          A is DOUBLE PRECISION array,
                dimension (LDA,NMAX)
[in]LDA
          LDA is INTEGER
                The leading dimension of the array A.  LDA >= max(1,NMAX).
[out]D_WORK_DLANGE
          D_WORK_DLANGE is DOUBLE PRECISION array, dimension (NMAX)
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine ddrvrfp ( integer  NOUT,
integer  NN,
integer, dimension( nn )  NVAL,
integer  NNS,
integer, dimension( nns )  NSVAL,
integer  NNT,
integer, dimension( nnt )  NTVAL,
double precision  THRESH,
double precision, dimension( * )  A,
double precision, dimension( * )  ASAV,
double precision, dimension( * )  AFAC,
double precision, dimension( * )  AINV,
double precision, dimension( * )  B,
double precision, dimension( * )  BSAV,
double precision, dimension( * )  XACT,
double precision, dimension( * )  X,
double precision, dimension( * )  ARF,
double precision, dimension( * )  ARFINV,
double precision, dimension( * )  D_WORK_DLATMS,
double precision, dimension( * )  D_WORK_DPOT01,
double precision, dimension( * )  D_TEMP_DPOT02,
double precision, dimension( * )  D_TEMP_DPOT03,
double precision, dimension( * )  D_WORK_DLANSY,
double precision, dimension( * )  D_WORK_DPOT02,
double precision, dimension( * )  D_WORK_DPOT03 
)

DDRVRFP

Purpose:
 DDRVRFP tests the LAPACK RFP routines:
     DPFTRF, DPFTRS, and DPFTRI.

 This testing routine follow the same tests as DDRVPO (test for the full
 format Symmetric Positive Definite solver).

 The tests are performed in Full Format, convertion back and forth from
 full format to RFP format are performed using the routines DTRTTF and
 DTFTTR.

 First, a specific matrix A of size N is created. There is nine types of 
 different matrixes possible.
  1. Diagonal                        6. Random, CNDNUM = sqrt(0.1/EPS)
  2. Random, CNDNUM = 2              7. Random, CNDNUM = 0.1/EPS
 *3. First row and column zero       8. Scaled near underflow
 *4. Last row and column zero        9. Scaled near overflow
 *5. Middle row and column zero
 (* - tests error exits from DPFTRF, no test ratios are computed)
 A solution XACT of size N-by-NRHS is created and the associated right
 hand side B as well. Then DPFTRF is called to compute L (or U), the
 Cholesky factor of A. Then L (or U) is used to solve the linear system
 of equations AX = B. This gives X. Then L (or U) is used to compute the
 inverse of A, AINV. The following four tests are then performed:
 (1) norm( L*L' - A ) / ( N * norm(A) * EPS ) or
     norm( U'*U - A ) / ( N * norm(A) * EPS ),
 (2) norm(B - A*X) / ( norm(A) * norm(X) * EPS ),
 (3) norm( I - A*AINV ) / ( N * norm(A) * norm(AINV) * EPS ),
 (4) ( norm(X-XACT) * RCOND ) / ( norm(XACT) * EPS ),
 where EPS is the machine precision, RCOND the condition number of A, and
 norm( . ) the 1-norm for (1,2,3) and the inf-norm for (4).
 Errors occur when INFO parameter is not as expected. Failures occur when
 a test ratios is greater than THRES.
Parameters
[in]NOUT
          NOUT is INTEGER
                The unit number for output.
[in]NN
          NN is INTEGER
                The number of values of N contained in the vector NVAL.
[in]NVAL
          NVAL is INTEGER array, dimension (NN)
                The values of the matrix dimension N.
[in]NNS
          NNS is INTEGER
                The number of values of NRHS contained in the vector NSVAL.
[in]NSVAL
          NSVAL is INTEGER array, dimension (NNS)
                The values of the number of right-hand sides NRHS.
[in]NNT
          NNT is INTEGER
                The number of values of MATRIX TYPE contained in the vector NTVAL.
[in]NTVAL
          NTVAL is INTEGER array, dimension (NNT)
                The values of matrix type (between 0 and 9 for PO/PP/PF matrices).
[in]THRESH
          THRESH is DOUBLE PRECISION
                The threshold value for the test ratios.  A result is
                included in the output file if RESULT >= THRESH.  To have
                every test ratio printed, use THRESH = 0.
[out]A
          A is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]ASAV
          ASAV is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]AFAC
          AFAC is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]AINV
          AINV is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]B
          B is DOUBLE PRECISION array, dimension (NMAX*MAXRHS)
[out]BSAV
          BSAV is DOUBLE PRECISION array, dimension (NMAX*MAXRHS)
[out]XACT
          XACT is DOUBLE PRECISION array, dimension (NMAX*MAXRHS)
[out]X
          X is DOUBLE PRECISION array, dimension (NMAX*MAXRHS)
[out]ARF
          ARF is DOUBLE PRECISION array, dimension ((NMAX*(NMAX+1))/2)
[out]ARFINV
          ARFINV is DOUBLE PRECISION array, dimension ((NMAX*(NMAX+1))/2)
[out]D_WORK_DLATMS
          D_WORK_DLATMS is DOUBLE PRECISION array, dimension ( 3*NMAX )
[out]D_WORK_DPOT01
          D_WORK_DPOT01 is DOUBLE PRECISION array, dimension ( NMAX )
[out]D_TEMP_DPOT02
          D_TEMP_DPOT02 is DOUBLE PRECISION array, dimension ( NMAX*MAXRHS )
[out]D_TEMP_DPOT03
          D_TEMP_DPOT03 is DOUBLE PRECISION array, dimension ( NMAX*NMAX )
[out]D_WORK_DLATMS
          D_WORK_DLATMS is DOUBLE PRECISION array, dimension ( NMAX )
[out]D_WORK_DLANSY
          D_WORK_DLANSY is DOUBLE PRECISION array, dimension ( NMAX )
[out]D_WORK_DPOT02
          D_WORK_DPOT02 is DOUBLE PRECISION array, dimension ( NMAX )
[out]D_WORK_DPOT03
          D_WORK_DPOT03 is DOUBLE PRECISION array, dimension ( NMAX )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2013
subroutine ddrvsp ( logical, dimension( * )  DOTYPE,
integer  NN,
integer, dimension( * )  NVAL,
integer  NRHS,
double precision  THRESH,
logical  TSTERR,
integer  NMAX,
double precision, dimension( * )  A,
double precision, dimension( * )  AFAC,
double precision, dimension( * )  AINV,
double precision, dimension( * )  B,
double precision, dimension( * )  X,
double precision, dimension( * )  XACT,
double precision, dimension( * )  WORK,
double precision, dimension( * )  RWORK,
integer, dimension( * )  IWORK,
integer  NOUT 
)

DDRVSP

Purpose:
 DDRVSP tests the driver routines DSPSV and -SVX.
Parameters
[in]DOTYPE
          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
[in]NN
          NN is INTEGER
          The number of values of N contained in the vector NVAL.
[in]NVAL
          NVAL is INTEGER array, dimension (NN)
          The values of the matrix dimension N.
[in]NRHS
          NRHS is INTEGER
          The number of right hand side vectors to be generated for
          each linear system.
[in]THRESH
          THRESH is DOUBLE PRECISION
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.
[in]TSTERR
          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.
[in]NMAX
          NMAX is INTEGER
          The maximum value permitted for N, used in dimensioning the
          work arrays.
[out]A
          A is DOUBLE PRECISION array, dimension
                      (NMAX*(NMAX+1)/2)
[out]AFAC
          AFAC is DOUBLE PRECISION array, dimension
                      (NMAX*(NMAX+1)/2)
[out]AINV
          AINV is DOUBLE PRECISION array, dimension
                      (NMAX*(NMAX+1)/2)
[out]B
          B is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]X
          X is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]XACT
          XACT is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]WORK
          WORK is DOUBLE PRECISION array, dimension
                      (NMAX*max(2,NRHS))
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension (NMAX+2*NRHS)
[out]IWORK
          IWORK is INTEGER array, dimension (2*NMAX)
[in]NOUT
          NOUT is INTEGER
          The unit number for output.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine ddrvsy ( logical, dimension( * )  DOTYPE,
integer  NN,
integer, dimension( * )  NVAL,
integer  NRHS,
double precision  THRESH,
logical  TSTERR,
integer  NMAX,
double precision, dimension( * )  A,
double precision, dimension( * )  AFAC,
double precision, dimension( * )  AINV,
double precision, dimension( * )  B,
double precision, dimension( * )  X,
double precision, dimension( * )  XACT,
double precision, dimension( * )  WORK,
double precision, dimension( * )  RWORK,
integer, dimension( * )  IWORK,
integer  NOUT 
)

DDRVSY

DDRVSYX

Purpose:
 DDRVSY tests the driver routines DSYSV and -SVX.
Parameters
[in]DOTYPE
          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
[in]NN
          NN is INTEGER
          The number of values of N contained in the vector NVAL.
[in]NVAL
          NVAL is INTEGER array, dimension (NN)
          The values of the matrix dimension N.
[in]NRHS
          NRHS is INTEGER
          The number of right hand side vectors to be generated for
          each linear system.
[in]THRESH
          THRESH is DOUBLE PRECISION
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.
[in]TSTERR
          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.
[in]NMAX
          NMAX is INTEGER
          The maximum value permitted for N, used in dimensioning the
          work arrays.
[out]A
          A is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]AFAC
          AFAC is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]AINV
          AINV is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]B
          B is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]X
          X is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]XACT
          XACT is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (NMAX*max(2,NRHS))
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension (NMAX+2*NRHS)
[out]IWORK
          IWORK is INTEGER array, dimension (2*NMAX)
[in]NOUT
          NOUT is INTEGER
          The unit number for output.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2013
Purpose:
 DDRVSY tests the driver routines DSYSV, -SVX, and -SVXX.

 Note that this file is used only when the XBLAS are available,
 otherwise ddrvsy.f defines this subroutine.
Parameters
[in]DOTYPE
          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
[in]NN
          NN is INTEGER
          The number of values of N contained in the vector NVAL.
[in]NVAL
          NVAL is INTEGER array, dimension (NN)
          The values of the matrix dimension N.
[in]NRHS
          NRHS is INTEGER
          The number of right hand side vectors to be generated for
          each linear system.
[in]THRESH
          THRESH is DOUBLE PRECISION
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.
[in]TSTERR
          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.
[in]NMAX
          NMAX is INTEGER
          The maximum value permitted for N, used in dimensioning the
          work arrays.
[out]A
          A is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]AFAC
          AFAC is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]AINV
          AINV is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]B
          B is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]X
          X is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]XACT
          XACT is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]WORK
          WORK is DOUBLE PRECISION array, dimension
                      (NMAX*max(2,NRHS))
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension (NMAX+2*NRHS)
[out]IWORK
          IWORK is INTEGER array, dimension (2*NMAX)
[in]NOUT
          NOUT is INTEGER
          The unit number for output.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine ddrvsy_rook ( logical, dimension( * )  DOTYPE,
integer  NN,
integer, dimension( * )  NVAL,
integer  NRHS,
double precision  THRESH,
logical  TSTERR,
integer  NMAX,
double precision, dimension( * )  A,
double precision, dimension( * )  AFAC,
double precision, dimension( * )  AINV,
double precision, dimension( * )  B,
double precision, dimension( * )  X,
double precision, dimension( * )  XACT,
double precision, dimension( * )  WORK,
double precision, dimension( * )  RWORK,
integer, dimension( * )  IWORK,
integer  NOUT 
)

DDRVSY_ROOK

Purpose:
 DDRVSY_ROOK tests the driver routines DSYSV_ROOK.
Parameters
[in]DOTYPE
          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
[in]NN
          NN is INTEGER
          The number of values of N contained in the vector NVAL.
[in]NVAL
          NVAL is INTEGER array, dimension (NN)
          The values of the matrix dimension N.
[in]NRHS
          NRHS is INTEGER
          The number of right hand side vectors to be generated for
          each linear system.
[in]THRESH
          THRESH is DOUBLE PRECISION
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.
[in]TSTERR
          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.
[in]NMAX
          NMAX is INTEGER
          The maximum value permitted for N, used in dimensioning the
          work arrays.
[out]A
          A is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]AFAC
          AFAC is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]AINV
          AINV is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]B
          B is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]X
          X is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]XACT
          XACT is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (NMAX*max(2,NRHS))
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension (NMAX+2*NRHS)
[out]IWORK
          IWORK is INTEGER array, dimension (2*NMAX)
[in]NOUT
          NOUT is INTEGER
          The unit number for output.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2013
subroutine debchvxx ( double precision  THRESH,
character*3  PATH 
)

DEBCHVXX

Purpose:
  DEBCHVXX will run D**SVXX on a series of Hilbert matrices and then
  compare the error bounds returned by D**SVXX to see if the returned
  answer indeed falls within those bounds.

  Eight test ratios will be computed.  The tests will pass if they are .LT.
  THRESH.  There are two cases that are determined by 1 / (SQRT( N ) * EPS).
  If that value is .LE. to the component wise reciprocal condition number,
  it uses the guaranteed case, other wise it uses the unguaranteed case.

  Test ratios:
     Let Xc be X_computed and Xt be X_truth.
     The norm used is the infinity norm.

     Let A be the guaranteed case and B be the unguaranteed case.

       1. Normwise guaranteed forward error bound.
       A: norm ( abs( Xc - Xt ) / norm ( Xt ) .LE. ERRBND( *, nwise_i, bnd_i ) and
          ERRBND( *, nwise_i, bnd_i ) .LE. MAX(SQRT(N),10) * EPS.
          If these conditions are met, the test ratio is set to be
          ERRBND( *, nwise_i, bnd_i ) / MAX(SQRT(N), 10).  Otherwise it is 1/EPS.
       B: For this case, CGESVXX should just return 1.  If it is less than
          one, treat it the same as in 1A.  Otherwise it fails. (Set test
          ratio to ERRBND( *, nwise_i, bnd_i ) * THRESH?)

       2. Componentwise guaranteed forward error bound.
       A: norm ( abs( Xc(j) - Xt(j) ) ) / norm (Xt(j)) .LE. ERRBND( *, cwise_i, bnd_i )
          for all j .AND. ERRBND( *, cwise_i, bnd_i ) .LE. MAX(SQRT(N), 10) * EPS.
          If these conditions are met, the test ratio is set to be
          ERRBND( *, cwise_i, bnd_i ) / MAX(SQRT(N), 10).  Otherwise it is 1/EPS.
       B: Same as normwise test ratio.

       3. Backwards error.
       A: The test ratio is set to BERR/EPS.
       B: Same test ratio.

       4. Reciprocal condition number.
       A: A condition number is computed with Xt and compared with the one
          returned from CGESVXX.  Let RCONDc be the RCOND returned by D**SVXX
          and RCONDt be the RCOND from the truth value.  Test ratio is set to
          MAX(RCONDc/RCONDt, RCONDt/RCONDc).
       B: Test ratio is set to 1 / (EPS * RCONDc).

       5. Reciprocal normwise condition number.
       A: The test ratio is set to
          MAX(ERRBND( *, nwise_i, cond_i ) / NCOND, NCOND / ERRBND( *, nwise_i, cond_i )).
       B: Test ratio is set to 1 / (EPS * ERRBND( *, nwise_i, cond_i )).

       6. Reciprocal componentwise condition number.
       A: Test ratio is set to
          MAX(ERRBND( *, cwise_i, cond_i ) / CCOND, CCOND / ERRBND( *, cwise_i, cond_i )).
       B: Test ratio is set to 1 / (EPS * ERRBND( *, cwise_i, cond_i )).

     .. Parameters ..
     NMAX is determined by the largest number in the inverse of the hilbert
     matrix.  Precision is exhausted when the largest entry in it is greater
     than 2 to the power of the number of bits in the fraction of the data
     type used plus one, which is 24 for single precision.
     NMAX should be 6 for single and 11 for double.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine derrab ( integer  NUNIT)

DERRAB

Purpose:
 DERRAB tests the error exits for DSGESV.
Parameters
[in]NUNIT
          NUNIT is INTEGER
          The unit number for output.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine derrac ( integer  NUNIT)

DERRAC

Purpose:
 DERRAC tests the error exits for DSPOSV.
Parameters
[in]NUNIT
          NUNIT is INTEGER
          The unit number for output.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine derrge ( character*3  PATH,
integer  NUNIT 
)

DERRGE

DERRGEX

Purpose:
 DERRGE tests the error exits for the DOUBLE PRECISION routines
 for general matrices.
Parameters
[in]PATH
          PATH is CHARACTER*3
          The LAPACK path name for the routines to be tested.
[in]NUNIT
          NUNIT is INTEGER
          The unit number for output.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
Purpose:
 DERRGE tests the error exits for the DOUBLE PRECISION routines
 for general matrices.

 Note that this file is used only when the XBLAS are available,
 otherwise derrge.f defines this subroutine.
Parameters
[in]PATH
          PATH is CHARACTER*3
          The LAPACK path name for the routines to be tested.
[in]NUNIT
          NUNIT is INTEGER
          The unit number for output.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine derrgt ( character*3  PATH,
integer  NUNIT 
)

DERRGT

Purpose:
 DERRGT tests the error exits for the DOUBLE PRECISION tridiagonal
 routines.
Parameters
[in]PATH
          PATH is CHARACTER*3
          The LAPACK path name for the routines to be tested.
[in]NUNIT
          NUNIT is INTEGER
          The unit number for output.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine derrlq ( character*3  PATH,
integer  NUNIT 
)

DERRLQ

Purpose:
 DERRLQ tests the error exits for the DOUBLE PRECISION routines
 that use the LQ decomposition of a general matrix.
Parameters
[in]PATH
          PATH is CHARACTER*3
          The LAPACK path name for the routines to be tested.
[in]NUNIT
          NUNIT is INTEGER
          The unit number for output.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine derrls ( character*3  PATH,
integer  NUNIT 
)

DERRLS

Purpose:
 DERRLS tests the error exits for the DOUBLE PRECISION least squares
 driver routines (DGELS, SGELSS, SGELSY, SGELSD).
Parameters
[in]PATH
          PATH is CHARACTER*3
          The LAPACK path name for the routines to be tested.
[in]NUNIT
          NUNIT is INTEGER
          The unit number for output.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2015
subroutine derrpo ( character*3  PATH,
integer  NUNIT 
)

DERRPO

DERRPOX

Purpose:
 DERRPO tests the error exits for the DOUBLE PRECISION routines
 for symmetric positive definite matrices.
Parameters
[in]PATH
          PATH is CHARACTER*3
          The LAPACK path name for the routines to be tested.
[in]NUNIT
          NUNIT is INTEGER
          The unit number for output.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
Purpose:
 DERRPO tests the error exits for the DOUBLE PRECISION routines
 for symmetric positive definite matrices.

 Note that this file is used only when the XBLAS are available,
 otherwise derrpo.f defines this subroutine.
Parameters
[in]PATH
          PATH is CHARACTER*3
          The LAPACK path name for the routines to be tested.
[in]NUNIT
          NUNIT is INTEGER
          The unit number for output.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2015
subroutine derrps ( character*3  PATH,
integer  NUNIT 
)

DERRPS

Purpose:
 DERRPS tests the error exits for the DOUBLE PRECISION routines
 for DPSTRF.
Parameters
[in]PATH
          PATH is CHARACTER*3
          The LAPACK path name for the routines to be tested.
[in]NUNIT
          NUNIT is INTEGER
          The unit number for output.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine derrql ( character*3  PATH,
integer  NUNIT 
)

DERRQL

Purpose:
 DERRQL tests the error exits for the DOUBLE PRECISION routines
 that use the QL decomposition of a general matrix.
Parameters
[in]PATH
          PATH is CHARACTER*3
          The LAPACK path name for the routines to be tested.
[in]NUNIT
          NUNIT is INTEGER
          The unit number for output.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine derrqp ( character*3  PATH,
integer  NUNIT 
)

DERRQP

Purpose:
 DERRQP tests the error exits for DGEQP3.
Parameters
[in]PATH
          PATH is CHARACTER*3
          The LAPACK path name for the routines to be tested.
[in]NUNIT
          NUNIT is INTEGER
          The unit number for output.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2015
subroutine derrqr ( character*3  PATH,
integer  NUNIT 
)

DERRQR

Purpose:
 DERRQR tests the error exits for the DOUBLE PRECISION routines
 that use the QR decomposition of a general matrix.
Parameters
[in]PATH
          PATH is CHARACTER*3
          The LAPACK path name for the routines to be tested.
[in]NUNIT
          NUNIT is INTEGER
          The unit number for output.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine derrqrt ( character*3  PATH,
integer  NUNIT 
)

DERRQRT

Purpose:
 DERRQRT tests the error exits for the DOUBLE PRECISION routines
 that use the QRT decomposition of a general matrix.
Parameters
[in]PATH
          PATH is CHARACTER*3
          The LAPACK path name for the routines to be tested.
[in]NUNIT
          NUNIT is INTEGER
          The unit number for output.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine derrqrtp ( character*3  PATH,
integer  NUNIT 
)

DERRQRTP

Purpose:
 DERRQRTP tests the error exits for the REAL routines
 that use the QRT decomposition of a triangular-pentagonal matrix.
Parameters
[in]PATH
          PATH is CHARACTER*3
          The LAPACK path name for the routines to be tested.
[in]NUNIT
          NUNIT is INTEGER
          The unit number for output.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine derrrfp ( integer  NUNIT)

DERRRFP

Purpose:
 DERRRFP tests the error exits for the DOUBLE PRECISION driver routines
 for solving linear systems of equations.

 DDRVRFP tests the DOUBLE PRECISION LAPACK RFP routines:
     DTFSM, DTFTRI, DSFRK, DTFTTP, DTFTTR, DPFTRF, DPFTRS, DTPTTF,
     DTPTTR, DTRTTF, and DTRTTP
Parameters
[in]NUNIT
          NUNIT is INTEGER
          The unit number for output.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine derrrq ( character*3  PATH,
integer  NUNIT 
)

DERRRQ

Purpose:
 DERRRQ tests the error exits for the DOUBLE PRECISION routines
 that use the RQ decomposition of a general matrix.
Parameters
[in]PATH
          PATH is CHARACTER*3
          The LAPACK path name for the routines to be tested.
[in]NUNIT
          NUNIT is INTEGER
          The unit number for output.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine derrsy ( character*3  PATH,
integer  NUNIT 
)

DERRSY

DERRSYX

Purpose:
 DERRSY tests the error exits for the DOUBLE PRECISION routines
 for symmetric indefinite matrices.
Parameters
[in]PATH
          PATH is CHARACTER*3
          The LAPACK path name for the routines to be tested.
[in]NUNIT
          NUNIT is INTEGER
          The unit number for output.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2015
Purpose:
 DERRSY tests the error exits for the DOUBLE PRECISION routines
 for symmetric indefinite matrices.

 Note that this file is used only when the XBLAS are available,
 otherwise derrsy.f defines this subroutine.
Parameters
[in]PATH
          PATH is CHARACTER*3
          The LAPACK path name for the routines to be tested.
[in]NUNIT
          NUNIT is INTEGER
          The unit number for output.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2015
subroutine derrtr ( character*3  PATH,
integer  NUNIT 
)

DERRTR

Purpose:
 DERRTR tests the error exits for the DOUBLE PRECISION triangular
 routines.
Parameters
[in]PATH
          PATH is CHARACTER*3
          The LAPACK path name for the routines to be tested.
[in]NUNIT
          NUNIT is INTEGER
          The unit number for output.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine derrtz ( character*3  PATH,
integer  NUNIT 
)

DERRTZ

Purpose:
 DERRTZ tests the error exits for STZRZF.
Parameters
[in]PATH
          PATH is CHARACTER*3
          The LAPACK path name for the routines to be tested.
[in]NUNIT
          NUNIT is INTEGER
          The unit number for output.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2015
subroutine derrvx ( character*3  PATH,
integer  NUNIT 
)

DERRVX

DERRVXX

Purpose:
 DERRVX tests the error exits for the DOUBLE PRECISION driver routines
 for solving linear systems of equations.
Parameters
[in]PATH
          PATH is CHARACTER*3
          The LAPACK path name for the routines to be tested.
[in]NUNIT
          NUNIT is INTEGER
          The unit number for output.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
April 2012
Purpose:
 DERRVX tests the error exits for the DOUBLE PRECISION driver routines
 for solving linear systems of equations.
Parameters
[in]PATH
          PATH is CHARACTER*3
          The LAPACK path name for the routines to be tested.
[in]NUNIT
          NUNIT is INTEGER
          The unit number for output.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2015
subroutine dgbt01 ( integer  M,
integer  N,
integer  KL,
integer  KU,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( ldafac, * )  AFAC,
integer  LDAFAC,
integer, dimension( * )  IPIV,
double precision, dimension( * )  WORK,
double precision  RESID 
)

DGBT01

Purpose:
 DGBT01 reconstructs a band matrix  A  from its L*U factorization and
 computes the residual:
    norm(L*U - A) / ( N * norm(A) * EPS ),
 where EPS is the machine epsilon.

 The expression L*U - A is computed one column at a time, so A and
 AFAC are not modified.
Parameters
[in]M
          M is INTEGER
          The number of rows of the matrix A.  M >= 0.
[in]N
          N is INTEGER
          The number of columns of the matrix A.  N >= 0.
[in]KL
          KL is INTEGER
          The number of subdiagonals within the band of A.  KL >= 0.
[in]KU
          KU is INTEGER
          The number of superdiagonals within the band of A.  KU >= 0.
[in,out]A
          A is DOUBLE PRECISION array, dimension (LDA,N)
          The original matrix A in band storage, stored in rows 1 to
          KL+KU+1.
[in]LDA
          LDA is INTEGER.
          The leading dimension of the array A.  LDA >= max(1,KL+KU+1).
[in]AFAC
          AFAC is DOUBLE PRECISION array, dimension (LDAFAC,N)
          The factored form of the matrix A.  AFAC contains the banded
          factors L and U from the L*U factorization, as computed by
          DGBTRF.  U is stored as an upper triangular band matrix with
          KL+KU superdiagonals in rows 1 to KL+KU+1, and the
          multipliers used during the factorization are stored in rows
          KL+KU+2 to 2*KL+KU+1.  See DGBTRF for further details.
[in]LDAFAC
          LDAFAC is INTEGER
          The leading dimension of the array AFAC.
          LDAFAC >= max(1,2*KL*KU+1).
[in]IPIV
          IPIV is INTEGER array, dimension (min(M,N))
          The pivot indices from DGBTRF.
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (2*KL+KU+1)
[out]RESID
          RESID is DOUBLE PRECISION
          norm(L*U - A) / ( N * norm(A) * EPS )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dgbt02 ( character  TRANS,
integer  M,
integer  N,
integer  KL,
integer  KU,
integer  NRHS,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( ldx, * )  X,
integer  LDX,
double precision, dimension( ldb, * )  B,
integer  LDB,
double precision  RESID 
)

DGBT02

Purpose:
 DGBT02 computes the residual for a solution of a banded system of
 equations  A*x = b  or  A'*x = b:
    RESID = norm( B - A*X ) / ( norm(A) * norm(X) * EPS).
 where EPS is the machine precision.
Parameters
[in]TRANS
          TRANS is CHARACTER*1
          Specifies the form of the system of equations:
          = 'N':  A *x = b
          = 'T':  A'*x = b, where A' is the transpose of A
          = 'C':  A'*x = b, where A' is the transpose of A
[in]M
          M is INTEGER
          The number of rows of the matrix A.  M >= 0.
[in]N
          N is INTEGER
          The number of columns of the matrix A.  N >= 0.
[in]KL
          KL is INTEGER
          The number of subdiagonals within the band of A.  KL >= 0.
[in]KU
          KU is INTEGER
          The number of superdiagonals within the band of A.  KU >= 0.
[in]NRHS
          NRHS is INTEGER
          The number of columns of B.  NRHS >= 0.
[in]A
          A is DOUBLE PRECISION array, dimension (LDA,N)
          The original matrix A in band storage, stored in rows 1 to
          KL+KU+1.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,KL+KU+1).
[in]X
          X is DOUBLE PRECISION array, dimension (LDX,NRHS)
          The computed solution vectors for the system of linear
          equations.
[in]LDX
          LDX is INTEGER
          The leading dimension of the array X.  If TRANS = 'N',
          LDX >= max(1,N); if TRANS = 'T' or 'C', LDX >= max(1,M).
[in,out]B
          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
          On entry, the right hand side vectors for the system of
          linear equations.
          On exit, B is overwritten with the difference B - A*X.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B.  IF TRANS = 'N',
          LDB >= max(1,M); if TRANS = 'T' or 'C', LDB >= max(1,N).
[out]RESID
          RESID is DOUBLE PRECISION
          The maximum over the number of right hand sides of
          norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dgbt05 ( character  TRANS,
integer  N,
integer  KL,
integer  KU,
integer  NRHS,
double precision, dimension( ldab, * )  AB,
integer  LDAB,
double precision, dimension( ldb, * )  B,
integer  LDB,
double precision, dimension( ldx, * )  X,
integer  LDX,
double precision, dimension( ldxact, * )  XACT,
integer  LDXACT,
double precision, dimension( * )  FERR,
double precision, dimension( * )  BERR,
double precision, dimension( * )  RESLTS 
)

DGBT05

Purpose:
 DGBT05 tests the error bounds from iterative refinement for the
 computed solution to a system of equations op(A)*X = B, where A is a
 general band matrix of order n with kl subdiagonals and ku
 superdiagonals and op(A) = A or A**T, depending on TRANS.

 RESLTS(1) = test of the error bound
           = norm(X - XACT) / ( norm(X) * FERR )

 A large value is returned if this ratio is not less than one.

 RESLTS(2) = residual from the iterative refinement routine
           = the maximum of BERR / ( NZ*EPS + (*) ), where
             (*) = NZ*UNFL / (min_i (abs(op(A))*abs(X) +abs(b))_i )
             and NZ = max. number of nonzeros in any row of A, plus 1
Parameters
[in]TRANS
          TRANS is CHARACTER*1
          Specifies the form of the system of equations.
          = 'N':  A * X = B     (No transpose)
          = 'T':  A**T * X = B  (Transpose)
          = 'C':  A**H * X = B  (Conjugate transpose = Transpose)
[in]N
          N is INTEGER
          The number of rows of the matrices X, B, and XACT, and the
          order of the matrix A.  N >= 0.
[in]KL
          KL is INTEGER
          The number of subdiagonals within the band of A.  KL >= 0.
[in]KU
          KU is INTEGER
          The number of superdiagonals within the band of A.  KU >= 0.
[in]NRHS
          NRHS is INTEGER
          The number of columns of the matrices X, B, and XACT.
          NRHS >= 0.
[in]AB
          AB is DOUBLE PRECISION array, dimension (LDAB,N)
          The original band matrix A, stored in rows 1 to KL+KU+1.
          The j-th column of A is stored in the j-th column of the
          array AB as follows:
          AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).
[in]LDAB
          LDAB is INTEGER
          The leading dimension of the array AB.  LDAB >= KL+KU+1.
[in]B
          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
          The right hand side vectors for the system of linear
          equations.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).
[in]X
          X is DOUBLE PRECISION array, dimension (LDX,NRHS)
          The computed solution vectors.  Each vector is stored as a
          column of the matrix X.
[in]LDX
          LDX is INTEGER
          The leading dimension of the array X.  LDX >= max(1,N).
[in]XACT
          XACT is DOUBLE PRECISION array, dimension (LDX,NRHS)
          The exact solution vectors.  Each vector is stored as a
          column of the matrix XACT.
[in]LDXACT
          LDXACT is INTEGER
          The leading dimension of the array XACT.  LDXACT >= max(1,N).
[in]FERR
          FERR is DOUBLE PRECISION array, dimension (NRHS)
          The estimated forward error bounds for each solution vector
          X.  If XTRUE is the true solution, FERR bounds the magnitude
          of the largest entry in (X - XTRUE) divided by the magnitude
          of the largest entry in X.
[in]BERR
          BERR is DOUBLE PRECISION array, dimension (NRHS)
          The componentwise relative backward error of each solution
          vector (i.e., the smallest relative change in any entry of A
          or B that makes X an exact solution).
[out]RESLTS
          RESLTS is DOUBLE PRECISION array, dimension (2)
          The maximum over the NRHS solution vectors of the ratios:
          RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
          RESLTS(2) = BERR / ( NZ*EPS + (*) )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dgelqs ( integer  M,
integer  N,
integer  NRHS,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( * )  TAU,
double precision, dimension( ldb, * )  B,
integer  LDB,
double precision, dimension( lwork )  WORK,
integer  LWORK,
integer  INFO 
)

DGELQS

Purpose:
 Compute a minimum-norm solution
     min || A*X - B ||
 using the LQ factorization
     A = L*Q
 computed by DGELQF.
Parameters
[in]M
          M is INTEGER
          The number of rows of the matrix A.  M >= 0.
[in]N
          N is INTEGER
          The number of columns of the matrix A.  N >= M >= 0.
[in]NRHS
          NRHS is INTEGER
          The number of columns of B.  NRHS >= 0.
[in]A
          A is DOUBLE PRECISION array, dimension (LDA,N)
          Details of the LQ factorization of the original matrix A as
          returned by DGELQF.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= M.
[in]TAU
          TAU is DOUBLE PRECISION array, dimension (M)
          Details of the orthogonal matrix Q.
[in,out]B
          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
          On entry, the m-by-nrhs right hand side matrix B.
          On exit, the n-by-nrhs solution matrix X.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B. LDB >= N.
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (LWORK)
[in]LWORK
          LWORK is INTEGER
          The length of the array WORK.  LWORK must be at least NRHS,
          and should be at least NRHS*NB, where NB is the block size
          for this environment.
[out]INFO
          INFO is INTEGER
          = 0: successful exit
          < 0: if INFO = -i, the i-th argument had an illegal value
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
logical function dgennd ( integer  M,
integer  N,
double precision, dimension( lda, * )  A,
integer  LDA 
)

DGENND

Purpose:
    DGENND tests that its argument has a non-negative diagonal.
Parameters
[in]M
          M is INTEGER
          The number of rows in A.
[in]N
          N is INTEGER
          The number of columns in A.
[in]A
          A is DOUBLE PRECISION array, dimension (LDA, N)
          The matrix.
[in]LDA
          LDA is INTEGER
          Leading dimension of A.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dgeqls ( integer  M,
integer  N,
integer  NRHS,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( * )  TAU,
double precision, dimension( ldb, * )  B,
integer  LDB,
double precision, dimension( lwork )  WORK,
integer  LWORK,
integer  INFO 
)

DGEQLS

Purpose:
 Solve the least squares problem
     min || A*X - B ||
 using the QL factorization
     A = Q*L
 computed by DGEQLF.
Parameters
[in]M
          M is INTEGER
          The number of rows of the matrix A.  M >= 0.
[in]N
          N is INTEGER
          The number of columns of the matrix A.  M >= N >= 0.
[in]NRHS
          NRHS is INTEGER
          The number of columns of B.  NRHS >= 0.
[in]A
          A is DOUBLE PRECISION array, dimension (LDA,N)
          Details of the QL factorization of the original matrix A as
          returned by DGEQLF.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= M.
[in]TAU
          TAU is DOUBLE PRECISION array, dimension (N)
          Details of the orthogonal matrix Q.
[in,out]B
          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
          On entry, the m-by-nrhs right hand side matrix B.
          On exit, the n-by-nrhs solution matrix X, stored in rows
          m-n+1:m.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B. LDB >= M.
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (LWORK)
[in]LWORK
          LWORK is INTEGER
          The length of the array WORK.  LWORK must be at least NRHS,
          and should be at least NRHS*NB, where NB is the block size
          for this environment.
[out]INFO
          INFO is INTEGER
          = 0: successful exit
          < 0: if INFO = -i, the i-th argument had an illegal value
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dgeqrs ( integer  M,
integer  N,
integer  NRHS,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( * )  TAU,
double precision, dimension( ldb, * )  B,
integer  LDB,
double precision, dimension( lwork )  WORK,
integer  LWORK,
integer  INFO 
)

DGEQRS

Purpose:
 Solve the least squares problem
     min || A*X - B ||
 using the QR factorization
     A = Q*R
 computed by DGEQRF.
Parameters
[in]M
          M is INTEGER
          The number of rows of the matrix A.  M >= 0.
[in]N
          N is INTEGER
          The number of columns of the matrix A.  M >= N >= 0.
[in]NRHS
          NRHS is INTEGER
          The number of columns of B.  NRHS >= 0.
[in]A
          A is DOUBLE PRECISION array, dimension (LDA,N)
          Details of the QR factorization of the original matrix A as
          returned by DGEQRF.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= M.
[in]TAU
          TAU is DOUBLE PRECISION array, dimension (N)
          Details of the orthogonal matrix Q.
[in,out]B
          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
          On entry, the m-by-nrhs right hand side matrix B.
          On exit, the n-by-nrhs solution matrix X.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B. LDB >= M.
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (LWORK)
[in]LWORK
          LWORK is INTEGER
          The length of the array WORK.  LWORK must be at least NRHS,
          and should be at least NRHS*NB, where NB is the block size
          for this environment.
[out]INFO
          INFO is INTEGER
          = 0: successful exit
          < 0: if INFO = -i, the i-th argument had an illegal value
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dgerqs ( integer  M,
integer  N,
integer  NRHS,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( * )  TAU,
double precision, dimension( ldb, * )  B,
integer  LDB,
double precision, dimension( lwork )  WORK,
integer  LWORK,
integer  INFO 
)

DGERQS

Purpose:
 Compute a minimum-norm solution
     min || A*X - B ||
 using the RQ factorization
     A = R*Q
 computed by DGERQF.
Parameters
[in]M
          M is INTEGER
          The number of rows of the matrix A.  M >= 0.
[in]N
          N is INTEGER
          The number of columns of the matrix A.  N >= M >= 0.
[in]NRHS
          NRHS is INTEGER
          The number of columns of B.  NRHS >= 0.
[in]A
          A is DOUBLE PRECISION array, dimension (LDA,N)
          Details of the RQ factorization of the original matrix A as
          returned by DGERQF.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= M.
[in]TAU
          TAU is DOUBLE PRECISION array, dimension (M)
          Details of the orthogonal matrix Q.
[in,out]B
          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
          On entry, the right hand side vectors for the linear system.
          On exit, the solution vectors X.  Each solution vector
          is contained in rows 1:N of a column of B.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B. LDB >= max(1,N).
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (LWORK)
[in]LWORK
          LWORK is INTEGER
          The length of the array WORK.  LWORK must be at least NRHS,
          and should be at least NRHS*NB, where NB is the block size
          for this environment.
[out]INFO
          INFO is INTEGER
          = 0: successful exit
          < 0: if INFO = -i, the i-th argument had an illegal value
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dget01 ( integer  M,
integer  N,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( ldafac, * )  AFAC,
integer  LDAFAC,
integer, dimension( * )  IPIV,
double precision, dimension( * )  RWORK,
double precision  RESID 
)

DGET01

Purpose:
 DGET01 reconstructs a matrix A from its L*U factorization and
 computes the residual
    norm(L*U - A) / ( N * norm(A) * EPS ),
 where EPS is the machine epsilon.
Parameters
[in]M
          M is INTEGER
          The number of rows of the matrix A.  M >= 0.
[in]N
          N is INTEGER
          The number of columns of the matrix A.  N >= 0.
[in]A
          A is DOUBLE PRECISION array, dimension (LDA,N)
          The original M x N matrix A.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,M).
[in,out]AFAC
          AFAC is DOUBLE PRECISION array, dimension (LDAFAC,N)
          The factored form of the matrix A.  AFAC contains the factors
          L and U from the L*U factorization as computed by DGETRF.
          Overwritten with the reconstructed matrix, and then with the
          difference L*U - A.
[in]LDAFAC
          LDAFAC is INTEGER
          The leading dimension of the array AFAC.  LDAFAC >= max(1,M).
[in]IPIV
          IPIV is INTEGER array, dimension (N)
          The pivot indices from DGETRF.
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension (M)
[out]RESID
          RESID is DOUBLE PRECISION
          norm(L*U - A) / ( N * norm(A) * EPS )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dget02 ( character  TRANS,
integer  M,
integer  N,
integer  NRHS,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( ldx, * )  X,
integer  LDX,
double precision, dimension( ldb, * )  B,
integer  LDB,
double precision, dimension( * )  RWORK,
double precision  RESID 
)

DGET02

Purpose:
 DGET02 computes the residual for a solution of a system of linear
 equations  A*x = b  or  A'*x = b:
    RESID = norm(B - A*X) / ( norm(A) * norm(X) * EPS ),
 where EPS is the machine epsilon.
Parameters
[in]TRANS
          TRANS is CHARACTER*1
          Specifies the form of the system of equations:
          = 'N':  A *x = b
          = 'T':  A'*x = b, where A' is the transpose of A
          = 'C':  A'*x = b, where A' is the transpose of A
[in]M
          M is INTEGER
          The number of rows of the matrix A.  M >= 0.
[in]N
          N is INTEGER
          The number of columns of the matrix A.  N >= 0.
[in]NRHS
          NRHS is INTEGER
          The number of columns of B, the matrix of right hand sides.
          NRHS >= 0.
[in]A
          A is DOUBLE PRECISION array, dimension (LDA,N)
          The original M x N matrix A.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,M).
[in]X
          X is DOUBLE PRECISION array, dimension (LDX,NRHS)
          The computed solution vectors for the system of linear
          equations.
[in]LDX
          LDX is INTEGER
          The leading dimension of the array X.  If TRANS = 'N',
          LDX >= max(1,N); if TRANS = 'T' or 'C', LDX >= max(1,M).
[in,out]B
          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
          On entry, the right hand side vectors for the system of
          linear equations.
          On exit, B is overwritten with the difference B - A*X.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B.  IF TRANS = 'N',
          LDB >= max(1,M); if TRANS = 'T' or 'C', LDB >= max(1,N).
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension (M)
[out]RESID
          RESID is DOUBLE PRECISION
          The maximum over the number of right hand sides of
          norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2015
subroutine dget03 ( integer  N,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( ldainv, * )  AINV,
integer  LDAINV,
double precision, dimension( ldwork, * )  WORK,
integer  LDWORK,
double precision, dimension( * )  RWORK,
double precision  RCOND,
double precision  RESID 
)

DGET03

Purpose:
 DGET03 computes the residual for a general matrix times its inverse:
    norm( I - AINV*A ) / ( N * norm(A) * norm(AINV) * EPS ),
 where EPS is the machine epsilon.
Parameters
[in]N
          N is INTEGER
          The number of rows and columns of the matrix A.  N >= 0.
[in]A
          A is DOUBLE PRECISION array, dimension (LDA,N)
          The original N x N matrix A.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).
[in]AINV
          AINV is DOUBLE PRECISION array, dimension (LDAINV,N)
          The inverse of the matrix A.
[in]LDAINV
          LDAINV is INTEGER
          The leading dimension of the array AINV.  LDAINV >= max(1,N).
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (LDWORK,N)
[in]LDWORK
          LDWORK is INTEGER
          The leading dimension of the array WORK.  LDWORK >= max(1,N).
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension (N)
[out]RCOND
          RCOND is DOUBLE PRECISION
          The reciprocal of the condition number of A, computed as
          ( 1/norm(A) ) / norm(AINV).
[out]RESID
          RESID is DOUBLE PRECISION
          norm(I - AINV*A) / ( N * norm(A) * norm(AINV) * EPS )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dget04 ( integer  N,
integer  NRHS,
double precision, dimension( ldx, * )  X,
integer  LDX,
double precision, dimension( ldxact, * )  XACT,
integer  LDXACT,
double precision  RCOND,
double precision  RESID 
)

DGET04

Purpose:
 DGET04 computes the difference between a computed solution and the
 true solution to a system of linear equations.

 RESID =  ( norm(X-XACT) * RCOND ) / ( norm(XACT) * EPS ),
 where RCOND is the reciprocal of the condition number and EPS is the
 machine epsilon.
Parameters
[in]N
          N is INTEGER
          The number of rows of the matrices X and XACT.  N >= 0.
[in]NRHS
          NRHS is INTEGER
          The number of columns of the matrices X and XACT.  NRHS >= 0.
[in]X
          X is DOUBLE PRECISION array, dimension (LDX,NRHS)
          The computed solution vectors.  Each vector is stored as a
          column of the matrix X.
[in]LDX
          LDX is INTEGER
          The leading dimension of the array X.  LDX >= max(1,N).
[in]XACT
          XACT is DOUBLE PRECISION array, dimension( LDX, NRHS )
          The exact solution vectors.  Each vector is stored as a
          column of the matrix XACT.
[in]LDXACT
          LDXACT is INTEGER
          The leading dimension of the array XACT.  LDXACT >= max(1,N).
[in]RCOND
          RCOND is DOUBLE PRECISION
          The reciprocal of the condition number of the coefficient
          matrix in the system of equations.
[out]RESID
          RESID is DOUBLE PRECISION
          The maximum over the NRHS solution vectors of
          ( norm(X-XACT) * RCOND ) / ( norm(XACT) * EPS )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
double precision function dget06 ( double precision  RCOND,
double precision  RCONDC 
)

DGET06

Purpose:
 DGET06 computes a test ratio to compare two values for RCOND.
Parameters
[in]RCOND
          RCOND is DOUBLE PRECISION
          The estimate of the reciprocal of the condition number of A,
          as computed by DGECON.
[in]RCONDC
          RCONDC is DOUBLE PRECISION
          The reciprocal of the condition number of A, computed as
          ( 1/norm(A) ) / norm(inv(A)).
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dget07 ( character  TRANS,
integer  N,
integer  NRHS,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( ldb, * )  B,
integer  LDB,
double precision, dimension( ldx, * )  X,
integer  LDX,
double precision, dimension( ldxact, * )  XACT,
integer  LDXACT,
double precision, dimension( * )  FERR,
logical  CHKFERR,
double precision, dimension( * )  BERR,
double precision, dimension( * )  RESLTS 
)

DGET07

Purpose:
 DGET07 tests the error bounds from iterative refinement for the
 computed solution to a system of equations op(A)*X = B, where A is a
 general n by n matrix and op(A) = A or A**T, depending on TRANS.

 RESLTS(1) = test of the error bound
           = norm(X - XACT) / ( norm(X) * FERR )

 A large value is returned if this ratio is not less than one.

 RESLTS(2) = residual from the iterative refinement routine
           = the maximum of BERR / ( (n+1)*EPS + (*) ), where
             (*) = (n+1)*UNFL / (min_i (abs(op(A))*abs(X) +abs(b))_i )
Parameters
[in]TRANS
          TRANS is CHARACTER*1
          Specifies the form of the system of equations.
          = 'N':  A * X = B     (No transpose)
          = 'T':  A**T * X = B  (Transpose)
          = 'C':  A**H * X = B  (Conjugate transpose = Transpose)
[in]N
          N is INTEGER
          The number of rows of the matrices X and XACT.  N >= 0.
[in]NRHS
          NRHS is INTEGER
          The number of columns of the matrices X and XACT.  NRHS >= 0.
[in]A
          A is DOUBLE PRECISION array, dimension (LDA,N)
          The original n by n matrix A.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).
[in]B
          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
          The right hand side vectors for the system of linear
          equations.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).
[in]X
          X is DOUBLE PRECISION array, dimension (LDX,NRHS)
          The computed solution vectors.  Each vector is stored as a
          column of the matrix X.
[in]LDX
          LDX is INTEGER
          The leading dimension of the array X.  LDX >= max(1,N).
[in]XACT
          XACT is DOUBLE PRECISION array, dimension (LDX,NRHS)
          The exact solution vectors.  Each vector is stored as a
          column of the matrix XACT.
[in]LDXACT
          LDXACT is INTEGER
          The leading dimension of the array XACT.  LDXACT >= max(1,N).
[in]FERR
          FERR is DOUBLE PRECISION array, dimension (NRHS)
          The estimated forward error bounds for each solution vector
          X.  If XTRUE is the true solution, FERR bounds the magnitude
          of the largest entry in (X - XTRUE) divided by the magnitude
          of the largest entry in X.
[in]CHKFERR
          CHKFERR is LOGICAL
          Set to .TRUE. to check FERR, .FALSE. not to check FERR.
          When the test system is ill-conditioned, the "true"
          solution in XACT may be incorrect.
[in]BERR
          BERR is DOUBLE PRECISION array, dimension (NRHS)
          The componentwise relative backward error of each solution
          vector (i.e., the smallest relative change in any entry of A
          or B that makes X an exact solution).
[out]RESLTS
          RESLTS is DOUBLE PRECISION array, dimension (2)
          The maximum over the NRHS solution vectors of the ratios:
          RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
          RESLTS(2) = BERR / ( (n+1)*EPS + (*) )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dget08 ( character  TRANS,
integer  M,
integer  N,
integer  NRHS,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( ldx, * )  X,
integer  LDX,
double precision, dimension( ldb, * )  B,
integer  LDB,
double precision, dimension( * )  RWORK,
double precision  RESID 
)

DGET08

Purpose:
 DGET08 computes the residual for a solution of a system of linear
 equations  A*x = b  or  A'*x = b:
    RESID = norm(B - A*X,inf) / ( norm(A,inf) * norm(X,inf) * EPS ),
 where EPS is the machine epsilon.
Parameters
[in]TRANS
          TRANS is CHARACTER*1
          Specifies the form of the system of equations:
          = 'N':  A *x = b
          = 'T':  A'*x = b, where A' is the transpose of A
          = 'C':  A'*x = b, where A' is the transpose of A
[in]M
          M is INTEGER
          The number of rows of the matrix A.  M >= 0.
[in]N
          N is INTEGER
          The number of columns of the matrix A.  N >= 0.
[in]NRHS
          NRHS is INTEGER
          The number of columns of B, the matrix of right hand sides.
          NRHS >= 0.
[in]A
          A is DOUBLE PRECISION array, dimension (LDA,N)
          The original M x N matrix A.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,M).
[in]X
          X is DOUBLE PRECISION array, dimension (LDX,NRHS)
          The computed solution vectors for the system of linear
          equations.
[in]LDX
          LDX is INTEGER
          The leading dimension of the array X.  If TRANS = 'N',
          LDX >= max(1,N); if TRANS = 'T' or 'C', LDX >= max(1,M).
[in,out]B
          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
          On entry, the right hand side vectors for the system of
          linear equations.
          On exit, B is overwritten with the difference B - A*X.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B.  IF TRANS = 'N',
          LDB >= max(1,M); if TRANS = 'T' or 'C', LDB >= max(1,N).
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension (M)
[out]RESID
          RESID is DOUBLE PRECISION
          The maximum over the number of right hand sides of
          norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dgtt01 ( integer  N,
double precision, dimension( * )  DL,
double precision, dimension( * )  D,
double precision, dimension( * )  DU,
double precision, dimension( * )  DLF,
double precision, dimension( * )  DF,
double precision, dimension( * )  DUF,
double precision, dimension( * )  DU2,
integer, dimension( * )  IPIV,
double precision, dimension( ldwork, * )  WORK,
integer  LDWORK,
double precision, dimension( * )  RWORK,
double precision  RESID 
)

DGTT01

Purpose:
 DGTT01 reconstructs a tridiagonal matrix A from its LU factorization
 and computes the residual
    norm(L*U - A) / ( norm(A) * EPS ),
 where EPS is the machine epsilon.
Parameters
[in]N
          N is INTEGTER
          The order of the matrix A.  N >= 0.
[in]DL
          DL is DOUBLE PRECISION array, dimension (N-1)
          The (n-1) sub-diagonal elements of A.
[in]D
          D is DOUBLE PRECISION array, dimension (N)
          The diagonal elements of A.
[in]DU
          DU is DOUBLE PRECISION array, dimension (N-1)
          The (n-1) super-diagonal elements of A.
[in]DLF
          DLF is DOUBLE PRECISION array, dimension (N-1)
          The (n-1) multipliers that define the matrix L from the
          LU factorization of A.
[in]DF
          DF is DOUBLE PRECISION array, dimension (N)
          The n diagonal elements of the upper triangular matrix U from
          the LU factorization of A.
[in]DUF
          DUF is DOUBLE PRECISION array, dimension (N-1)
          The (n-1) elements of the first super-diagonal of U.
[in]DU2
          DU2 is DOUBLE PRECISION array, dimension (N-2)
          The (n-2) elements of the second super-diagonal of U.
[in]IPIV
          IPIV is INTEGER array, dimension (N)
          The pivot indices; for 1 <= i <= n, row i of the matrix was
          interchanged with row IPIV(i).  IPIV(i) will always be either
          i or i+1; IPIV(i) = i indicates a row interchange was not
          required.
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (LDWORK,N)
[in]LDWORK
          LDWORK is INTEGER
          The leading dimension of the array WORK.  LDWORK >= max(1,N).
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension (N)
[out]RESID
          RESID is DOUBLE PRECISION
          The scaled residual:  norm(L*U - A) / (norm(A) * EPS)
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dgtt02 ( character  TRANS,
integer  N,
integer  NRHS,
double precision, dimension( * )  DL,
double precision, dimension( * )  D,
double precision, dimension( * )  DU,
double precision, dimension( ldx, * )  X,
integer  LDX,
double precision, dimension( ldb, * )  B,
integer  LDB,
double precision  RESID 
)

DGTT02

Purpose:
 DGTT02 computes the residual for the solution to a tridiagonal
 system of equations:
    RESID = norm(B - op(A)*X) / (norm(A) * norm(X) * EPS),
 where EPS is the machine epsilon.
Parameters
[in]TRANS
          TRANS is CHARACTER
          Specifies the form of the residual.
          = 'N':  B - A * X  (No transpose)
          = 'T':  B - A'* X  (Transpose)
          = 'C':  B - A'* X  (Conjugate transpose = Transpose)
[in]N
          N is INTEGTER
          The order of the matrix A.  N >= 0.
[in]NRHS
          NRHS is INTEGER
          The number of right hand sides, i.e., the number of columns
          of the matrices B and X.  NRHS >= 0.
[in]DL
          DL is DOUBLE PRECISION array, dimension (N-1)
          The (n-1) sub-diagonal elements of A.
[in]D
          D is DOUBLE PRECISION array, dimension (N)
          The diagonal elements of A.
[in]DU
          DU is DOUBLE PRECISION array, dimension (N-1)
          The (n-1) super-diagonal elements of A.
[in]X
          X is DOUBLE PRECISION array, dimension (LDX,NRHS)
          The computed solution vectors X.
[in]LDX
          LDX is INTEGER
          The leading dimension of the array X.  LDX >= max(1,N).
[in,out]B
          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
          On entry, the right hand side vectors for the system of
          linear equations.
          On exit, B is overwritten with the difference B - op(A)*X.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).
[out]RESID
          RESID is DOUBLE PRECISION
          norm(B - op(A)*X) / (norm(A) * norm(X) * EPS)
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dgtt05 ( character  TRANS,
integer  N,
integer  NRHS,
double precision, dimension( * )  DL,
double precision, dimension( * )  D,
double precision, dimension( * )  DU,
double precision, dimension( ldb, * )  B,
integer  LDB,
double precision, dimension( ldx, * )  X,
integer  LDX,
double precision, dimension( ldxact, * )  XACT,
integer  LDXACT,
double precision, dimension( * )  FERR,
double precision, dimension( * )  BERR,
double precision, dimension( * )  RESLTS 
)

DGTT05

Purpose:
 DGTT05 tests the error bounds from iterative refinement for the
 computed solution to a system of equations A*X = B, where A is a
 general tridiagonal matrix of order n and op(A) = A or A**T,
 depending on TRANS.

 RESLTS(1) = test of the error bound
           = norm(X - XACT) / ( norm(X) * FERR )

 A large value is returned if this ratio is not less than one.

 RESLTS(2) = residual from the iterative refinement routine
           = the maximum of BERR / ( NZ*EPS + (*) ), where
             (*) = NZ*UNFL / (min_i (abs(op(A))*abs(X) +abs(b))_i )
             and NZ = max. number of nonzeros in any row of A, plus 1
Parameters
[in]TRANS
          TRANS is CHARACTER*1
          Specifies the form of the system of equations.
          = 'N':  A * X = B     (No transpose)
          = 'T':  A**T * X = B  (Transpose)
          = 'C':  A**H * X = B  (Conjugate transpose = Transpose)
[in]N
          N is INTEGER
          The number of rows of the matrices X and XACT.  N >= 0.
[in]NRHS
          NRHS is INTEGER
          The number of columns of the matrices X and XACT.  NRHS >= 0.
[in]DL
          DL is DOUBLE PRECISION array, dimension (N-1)
          The (n-1) sub-diagonal elements of A.
[in]D
          D is DOUBLE PRECISION array, dimension (N)
          The diagonal elements of A.
[in]DU
          DU is DOUBLE PRECISION array, dimension (N-1)
          The (n-1) super-diagonal elements of A.
[in]B
          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
          The right hand side vectors for the system of linear
          equations.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).
[in]X
          X is DOUBLE PRECISION array, dimension (LDX,NRHS)
          The computed solution vectors.  Each vector is stored as a
          column of the matrix X.
[in]LDX
          LDX is INTEGER
          The leading dimension of the array X.  LDX >= max(1,N).
[in]XACT
          XACT is DOUBLE PRECISION array, dimension (LDX,NRHS)
          The exact solution vectors.  Each vector is stored as a
          column of the matrix XACT.
[in]LDXACT
          LDXACT is INTEGER
          The leading dimension of the array XACT.  LDXACT >= max(1,N).
[in]FERR
          FERR is DOUBLE PRECISION array, dimension (NRHS)
          The estimated forward error bounds for each solution vector
          X.  If XTRUE is the true solution, FERR bounds the magnitude
          of the largest entry in (X - XTRUE) divided by the magnitude
          of the largest entry in X.
[in]BERR
          BERR is DOUBLE PRECISION array, dimension (NRHS)
          The componentwise relative backward error of each solution
          vector (i.e., the smallest relative change in any entry of A
          or B that makes X an exact solution).
[out]RESLTS
          RESLTS is DOUBLE PRECISION array, dimension (2)
          The maximum over the NRHS solution vectors of the ratios:
          RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
          RESLTS(2) = BERR / ( NZ*EPS + (*) )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dlahilb ( integer  N,
integer  NRHS,
double precision, dimension(lda, n)  A,
integer  LDA,
double precision, dimension(ldx, nrhs)  X,
integer  LDX,
double precision, dimension(ldb, nrhs)  B,
integer  LDB,
double precision, dimension(n)  WORK,
integer  INFO 
)

DLAHILB

Purpose:
 DLAHILB generates an N by N scaled Hilbert matrix in A along with
 NRHS right-hand sides in B and solutions in X such that A*X=B.

 The Hilbert matrix is scaled by M = LCM(1, 2, ..., 2*N-1) so that all
 entries are integers.  The right-hand sides are the first NRHS 
 columns of M * the identity matrix, and the solutions are the 
 first NRHS columns of the inverse Hilbert matrix.

 The condition number of the Hilbert matrix grows exponentially with
 its size, roughly as O(e ** (3.5*N)).  Additionally, the inverse
 Hilbert matrices beyond a relatively small dimension cannot be
 generated exactly without extra precision.  Precision is exhausted
 when the largest entry in the inverse Hilbert matrix is greater than
 2 to the power of the number of bits in the fraction of the data type
 used plus one, which is 24 for single precision.  

 In single, the generated solution is exact for N <= 6 and has
 small componentwise error for 7 <= N <= 11.
Parameters
[in]N
          N is INTEGER
          The dimension of the matrix A.
[in]NRHS
          NRHS is NRHS
          The requested number of right-hand sides.
[out]A
          A is DOUBLE PRECISION array, dimension (LDA, N)
          The generated scaled Hilbert matrix.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= N.
[out]X
          X is DOUBLE PRECISION array, dimension (LDX, NRHS)
          The generated exact solutions.  Currently, the first NRHS
          columns of the inverse Hilbert matrix.
[in]LDX
          LDX is INTEGER
          The leading dimension of the array X.  LDX >= N.
[out]B
          B is DOUBLE PRECISION array, dimension (LDB, NRHS)
          The generated right-hand sides.  Currently, the first NRHS
          columns of LCM(1, 2, ..., 2*N-1) * the identity matrix.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B.  LDB >= N.
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (N)
[out]INFO
          INFO is INTEGER
          = 0: successful exit
          = 1: N is too large; the data is still generated but may not
               be not exact.
          < 0: if INFO = -i, the i-th argument had an illegal value
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dlaord ( character  JOB,
integer  N,
double precision, dimension( * )  X,
integer  INCX 
)

DLAORD

Purpose:
 DLAORD sorts the elements of a vector x in increasing or decreasing
 order.
Parameters
[in]JOB
          JOB is CHARACTER
          = 'I':  Sort in increasing order
          = 'D':  Sort in decreasing order
[in]N
          N is INTEGER
          The length of the vector X.
[in,out]X
          X is DOUBLE PRECISION array, dimension
                         (1+(N-1)*INCX)
          On entry, the vector of length n to be sorted.
          On exit, the vector x is sorted in the prescribed order.
[in]INCX
          INCX is INTEGER
          The spacing between successive elements of X.  INCX >= 0.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dlaptm ( integer  N,
integer  NRHS,
double precision  ALPHA,
double precision, dimension( * )  D,
double precision, dimension( * )  E,
double precision, dimension( ldx, * )  X,
integer  LDX,
double precision  BETA,
double precision, dimension( ldb, * )  B,
integer  LDB 
)

DLAPTM

Purpose:
 DLAPTM multiplies an N by NRHS matrix X by a symmetric tridiagonal
 matrix A and stores the result in a matrix B.  The operation has the
 form

    B := alpha * A * X + beta * B

 where alpha may be either 1. or -1. and beta may be 0., 1., or -1.
Parameters
[in]N
          N is INTEGER
          The order of the matrix A.  N >= 0.
[in]NRHS
          NRHS is INTEGER
          The number of right hand sides, i.e., the number of columns
          of the matrices X and B.
[in]ALPHA
          ALPHA is DOUBLE PRECISION
          The scalar alpha.  ALPHA must be 1. or -1.; otherwise,
          it is assumed to be 0.
[in]D
          D is DOUBLE PRECISION array, dimension (N)
          The n diagonal elements of the tridiagonal matrix A.
[in]E
          E is DOUBLE PRECISION array, dimension (N-1)
          The (n-1) subdiagonal or superdiagonal elements of A.
[in]X
          X is DOUBLE PRECISION array, dimension (LDX,NRHS)
          The N by NRHS matrix X.
[in]LDX
          LDX is INTEGER
          The leading dimension of the array X.  LDX >= max(N,1).
[in]BETA
          BETA is DOUBLE PRECISION
          The scalar beta.  BETA must be 0., 1., or -1.; otherwise,
          it is assumed to be 1.
[in,out]B
          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
          On entry, the N by NRHS matrix B.
          On exit, B is overwritten by the matrix expression
          B := alpha * A * X + beta * B.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(N,1).
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dlarhs ( character*3  PATH,
character  XTYPE,
character  UPLO,
character  TRANS,
integer  M,
integer  N,
integer  KL,
integer  KU,
integer  NRHS,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( ldx, * )  X,
integer  LDX,
double precision, dimension( ldb, * )  B,
integer  LDB,
integer, dimension( 4 )  ISEED,
integer  INFO 
)

DLARHS

Purpose:
 DLARHS chooses a set of NRHS random solution vectors and sets
 up the right hand sides for the linear system
    op( A ) * X = B,
 where op( A ) may be A or A' (transpose of A).
Parameters
[in]PATH
          PATH is CHARACTER*3
          The type of the real matrix A.  PATH may be given in any
          combination of upper and lower case.  Valid types include
             xGE:  General m x n matrix
             xGB:  General banded matrix
             xPO:  Symmetric positive definite, 2-D storage
             xPP:  Symmetric positive definite packed
             xPB:  Symmetric positive definite banded
             xSY:  Symmetric indefinite, 2-D storage
             xSP:  Symmetric indefinite packed
             xSB:  Symmetric indefinite banded
             xTR:  Triangular
             xTP:  Triangular packed
             xTB:  Triangular banded
             xQR:  General m x n matrix
             xLQ:  General m x n matrix
             xQL:  General m x n matrix
             xRQ:  General m x n matrix
          where the leading character indicates the precision.
[in]XTYPE
          XTYPE is CHARACTER*1
          Specifies how the exact solution X will be determined:
          = 'N':  New solution; generate a random X.
          = 'C':  Computed; use value of X on entry.
[in]UPLO
          UPLO is CHARACTER*1
          Specifies whether the upper or lower triangular part of the
          matrix A is stored, if A is symmetric.
          = 'U':  Upper triangular
          = 'L':  Lower triangular
[in]TRANS
          TRANS is CHARACTER*1
          Specifies the operation applied to the matrix A.
          = 'N':  System is  A * x = b
          = 'T':  System is  A'* x = b
          = 'C':  System is  A'* x = b
[in]M
          M is INTEGER
          The number or rows of the matrix A.  M >= 0.
[in]N
          N is INTEGER
          The number of columns of the matrix A.  N >= 0.
[in]KL
          KL is INTEGER
          Used only if A is a band matrix; specifies the number of
          subdiagonals of A if A is a general band matrix or if A is
          symmetric or triangular and UPLO = 'L'; specifies the number
          of superdiagonals of A if A is symmetric or triangular and
          UPLO = 'U'.  0 <= KL <= M-1.
[in]KU
          KU is INTEGER
          Used only if A is a general band matrix or if A is
          triangular.

          If PATH = xGB, specifies the number of superdiagonals of A,
          and 0 <= KU <= N-1.

          If PATH = xTR, xTP, or xTB, specifies whether or not the
          matrix has unit diagonal:
          = 1:  matrix has non-unit diagonal (default)
          = 2:  matrix has unit diagonal
[in]NRHS
          NRHS is INTEGER
          The number of right hand side vectors in the system A*X = B.
[in]A
          A is DOUBLE PRECISION array, dimension (LDA,N)
          The test matrix whose type is given by PATH.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.
          If PATH = xGB, LDA >= KL+KU+1.
          If PATH = xPB, xSB, xHB, or xTB, LDA >= KL+1.
          Otherwise, LDA >= max(1,M).
[in,out]X
          X is or output) DOUBLE PRECISION array, dimension(LDX,NRHS)
          On entry, if XTYPE = 'C' (for 'Computed'), then X contains
          the exact solution to the system of linear equations.
          On exit, if XTYPE = 'N' (for 'New'), then X is initialized
          with random values.
[in]LDX
          LDX is INTEGER
          The leading dimension of the array X.  If TRANS = 'N',
          LDX >= max(1,N); if TRANS = 'T', LDX >= max(1,M).
[out]B
          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
          The right hand side vector(s) for the system of equations,
          computed from B = op(A) * X, where op(A) is determined by
          TRANS.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B.  If TRANS = 'N',
          LDB >= max(1,M); if TRANS = 'T', LDB >= max(1,N).
[in,out]ISEED
          ISEED is INTEGER array, dimension (4)
          The seed vector for the random number generator (used in
          DLATMS).  Modified on exit.
[out]INFO
          INFO is INTEGER
          = 0: successful exit
          < 0: if INFO = -i, the i-th argument had an illegal value
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dlatb4 ( character*3  PATH,
integer  IMAT,
integer  M,
integer  N,
character  TYPE,
integer  KL,
integer  KU,
double precision  ANORM,
integer  MODE,
double precision  CNDNUM,
character  DIST 
)

DLATB4

Purpose:
 DLATB4 sets parameters for the matrix generator based on the type of
 matrix to be generated.
Parameters
[in]PATH
          PATH is CHARACTER*3
          The LAPACK path name.
[in]IMAT
          IMAT is INTEGER
          An integer key describing which matrix to generate for this
          path.
[in]M
          M is INTEGER
          The number of rows in the matrix to be generated.
[in]N
          N is INTEGER
          The number of columns in the matrix to be generated.
[out]TYPE
          TYPE is CHARACTER*1
          The type of the matrix to be generated:
          = 'S':  symmetric matrix
          = 'P':  symmetric positive (semi)definite matrix
          = 'N':  nonsymmetric matrix
[out]KL
          KL is INTEGER
          The lower band width of the matrix to be generated.
[out]KU
          KU is INTEGER
          The upper band width of the matrix to be generated.
[out]ANORM
          ANORM is DOUBLE PRECISION
          The desired norm of the matrix to be generated.  The diagonal
          matrix of singular values or eigenvalues is scaled by this
          value.
[out]MODE
          MODE is INTEGER
          A key indicating how to choose the vector of eigenvalues.
[out]CNDNUM
          CNDNUM is DOUBLE PRECISION
          The desired condition number.
[out]DIST
          DIST is CHARACTER*1
          The type of distribution to be used by the random number
          generator.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dlatb5 ( character*3  PATH,
integer  IMAT,
integer  N,
character  TYPE,
integer  KL,
integer  KU,
double precision  ANORM,
integer  MODE,
double precision  CNDNUM,
character  DIST 
)

DLATB5

Purpose:
 DLATB5 sets parameters for the matrix generator based on the type
 of matrix to be generated.
Parameters
[in]PATH
          PATH is CHARACTER*3
          The LAPACK path name.
[in]IMAT
          IMAT is INTEGER
          An integer key describing which matrix to generate for this
          path.
[in]N
          N is INTEGER
          The number of rows and columns in the matrix to be generated.
[out]TYPE
          TYPE is CHARACTER*1
          The type of the matrix to be generated:
          = 'S':  symmetric matrix
          = 'P':  symmetric positive (semi)definite matrix
          = 'N':  nonsymmetric matrix
[out]KL
          KL is INTEGER
          The lower band width of the matrix to be generated.
[out]KU
          KU is INTEGER
          The upper band width of the matrix to be generated.
[out]ANORM
          ANORM is DOUBLE PRECISION
          The desired norm of the matrix to be generated.  The diagonal
          matrix of singular values or eigenvalues is scaled by this
          value.
[out]MODE
          MODE is INTEGER
          A key indicating how to choose the vector of eigenvalues.
[out]CNDNUM
          CNDNUM is DOUBLE PRECISION
          The desired condition number.
[out]DIST
          DIST is CHARACTER*1
          The type of distribution to be used by the random number
          generator.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dlattb ( integer  IMAT,
character  UPLO,
character  TRANS,
character  DIAG,
integer, dimension( 4 )  ISEED,
integer  N,
integer  KD,
double precision, dimension( ldab, * )  AB,
integer  LDAB,
double precision, dimension( * )  B,
double precision, dimension( * )  WORK,
integer  INFO 
)

DLATTB

Purpose:
 DLATTB generates a triangular test matrix in 2-dimensional storage.
 IMAT and UPLO uniquely specify the properties of the test matrix,
 which is returned in the array A.
Parameters
[in]IMAT
          IMAT is INTEGER
          An integer key describing which matrix to generate for this
          path.
[in]UPLO
          UPLO is CHARACTER*1
          Specifies whether the matrix A will be upper or lower
          triangular.
          = 'U':  Upper triangular
          = 'L':  Lower triangular
[in]TRANS
          TRANS is CHARACTER*1
          Specifies whether the matrix or its transpose will be used.
          = 'N':  No transpose
          = 'T':  Transpose
          = 'C':  Conjugate transpose (= transpose)
[out]DIAG
          DIAG is CHARACTER*1
          Specifies whether or not the matrix A is unit triangular.
          = 'N':  Non-unit triangular
          = 'U':  Unit triangular
[in,out]ISEED
          ISEED is INTEGER array, dimension (4)
          The seed vector for the random number generator (used in
          DLATMS).  Modified on exit.
[in]N
          N is INTEGER
          The order of the matrix to be generated.
[in]KD
          KD is INTEGER
          The number of superdiagonals or subdiagonals of the banded
          triangular matrix A.  KD >= 0.
[out]AB
          AB is DOUBLE PRECISION array, dimension (LDAB,N)
          The upper or lower triangular banded matrix A, stored in the
          first KD+1 rows of AB.  Let j be a column of A, 1<=j<=n.
          If UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j.
          If UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
[in]LDAB
          LDAB is INTEGER
          The leading dimension of the array AB.  LDAB >= KD+1.
[out]B
          B is DOUBLE PRECISION array, dimension (N)
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (2*N)
[out]INFO
          INFO is INTEGER
          = 0:  successful exit
          < 0: if INFO = -k, the k-th argument had an illegal value
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dlattp ( integer  IMAT,
character  UPLO,
character  TRANS,
character  DIAG,
integer, dimension( 4 )  ISEED,
integer  N,
double precision, dimension( * )  A,
double precision, dimension( * )  B,
double precision, dimension( * )  WORK,
integer  INFO 
)

DLATTP

Purpose:
 DLATTP generates a triangular test matrix in packed storage.
 IMAT and UPLO uniquely specify the properties of the test
 matrix, which is returned in the array AP.
Parameters
[in]IMAT
          IMAT is INTEGER
          An integer key describing which matrix to generate for this
          path.
[in]UPLO
          UPLO is CHARACTER*1
          Specifies whether the matrix A will be upper or lower
          triangular.
          = 'U':  Upper triangular
          = 'L':  Lower triangular
[in]TRANS
          TRANS is CHARACTER*1
          Specifies whether the matrix or its transpose will be used.
          = 'N':  No transpose
          = 'T':  Transpose
          = 'C':  Conjugate transpose (= Transpose)
[out]DIAG
          DIAG is CHARACTER*1
          Specifies whether or not the matrix A is unit triangular.
          = 'N':  Non-unit triangular
          = 'U':  Unit triangular
[in,out]ISEED
          ISEED is INTEGER array, dimension (4)
          The seed vector for the random number generator (used in
          DLATMS).  Modified on exit.
[in]N
          N is INTEGER
          The order of the matrix to be generated.
[out]A
          A is DOUBLE PRECISION array, dimension (N*(N+1)/2)
          The upper or lower triangular matrix A, packed columnwise in
          a linear array.  The j-th column of A is stored in the array
          AP as follows:
          if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j;
          if UPLO = 'L',
             AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n.
[out]B
          B is DOUBLE PRECISION array, dimension (N)
          The right hand side vector, if IMAT > 10.
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (3*N)
[out]INFO
          INFO is INTEGER
          = 0:  successful exit
          < 0: if INFO = -k, the k-th argument had an illegal value
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dlattr ( integer  IMAT,
character  UPLO,
character  TRANS,
character  DIAG,
integer, dimension( 4 )  ISEED,
integer  N,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( * )  B,
double precision, dimension( * )  WORK,
integer  INFO 
)

DLATTR

Purpose:
 DLATTR generates a triangular test matrix.
 IMAT and UPLO uniquely specify the properties of the test
 matrix, which is returned in the array A.
Parameters
[in]IMAT
          IMAT is INTEGER
          An integer key describing which matrix to generate for this
          path.
[in]UPLO
          UPLO is CHARACTER*1
          Specifies whether the matrix A will be upper or lower
          triangular.
          = 'U':  Upper triangular
          = 'L':  Lower triangular
[in]TRANS
          TRANS is CHARACTER*1
          Specifies whether the matrix or its transpose will be used.
          = 'N':  No transpose
          = 'T':  Transpose
          = 'C':  Conjugate transpose (= Transpose)
[out]DIAG
          DIAG is CHARACTER*1
          Specifies whether or not the matrix A is unit triangular.
          = 'N':  Non-unit triangular
          = 'U':  Unit triangular
[in,out]ISEED
          ISEED is INTEGER array, dimension (4)
          The seed vector for the random number generator (used in
          DLATMS).  Modified on exit.
[in]N
          N is INTEGER
          The order of the matrix to be generated.
[out]A
          A is DOUBLE PRECISION array, dimension (LDA,N)
          The triangular matrix A.  If UPLO = 'U', the leading n by n
          upper triangular part of the array A contains the upper
          triangular matrix, and the strictly lower triangular part of
          A is not referenced.  If UPLO = 'L', the leading n by n lower
          triangular part of the array A contains the lower triangular
          matrix, and the strictly upper triangular part of A is not
          referenced.  If DIAG = 'U', the diagonal elements of A are
          set so that A(k,k) = k for 1 <= k <= n.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).
[out]B
          B is DOUBLE PRECISION array, dimension (N)
          The right hand side vector, if IMAT > 10.
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (3*N)
[out]INFO
          INFO is INTEGER
          = 0:  successful exit
          < 0: if INFO = -k, the k-th argument had an illegal value
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dlavsp ( character  UPLO,
character  TRANS,
character  DIAG,
integer  N,
integer  NRHS,
double precision, dimension( * )  A,
integer, dimension( * )  IPIV,
double precision, dimension( ldb, * )  B,
integer  LDB,
integer  INFO 
)

DLAVSP

Purpose:
 DLAVSP  performs one of the matrix-vector operations
    x := A*x  or  x := A'*x,
 where x is an N element vector and  A is one of the factors
 from the block U*D*U' or L*D*L' factorization computed by DSPTRF.

 If TRANS = 'N', multiplies by U  or U * D  (or L  or L * D)
 If TRANS = 'T', multiplies by U' or D * U' (or L' or D * L' )
 If TRANS = 'C', multiplies by U' or D * U' (or L' or D * L' )
Parameters
[in]UPLO
          UPLO is CHARACTER*1
          Specifies whether the factor stored in A is upper or lower
          triangular.
          = 'U':  Upper triangular
          = 'L':  Lower triangular
[in]TRANS
          TRANS is CHARACTER*1
          Specifies the operation to be performed:
          = 'N':  x := A*x
          = 'T':  x := A'*x
          = 'C':  x := A'*x
[in]DIAG
          DIAG is CHARACTER*1
          Specifies whether or not the diagonal blocks are unit
          matrices.  If the diagonal blocks are assumed to be unit,
          then A = U or A = L, otherwise A = U*D or A = L*D.
          = 'U':  Diagonal blocks are assumed to be unit matrices.
          = 'N':  Diagonal blocks are assumed to be non-unit matrices.
[in]N
          N is INTEGER
          The number of rows and columns of the matrix A.  N >= 0.
[in]NRHS
          NRHS is INTEGER
          The number of right hand sides, i.e., the number of vectors
          x to be multiplied by A.  NRHS >= 0.
[in]A
          A is DOUBLE PRECISION array, dimension (N*(N+1)/2)
          The block diagonal matrix D and the multipliers used to
          obtain the factor U or L, stored as a packed triangular
          matrix as computed by DSPTRF.
[in]IPIV
          IPIV is INTEGER array, dimension (N)
          The pivot indices from DSPTRF.
[in,out]B
          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
          On entry, B contains NRHS vectors of length N.
          On exit, B is overwritten with the product A * B.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).
[out]INFO
          INFO is INTEGER
          = 0: successful exit
          < 0: if INFO = -k, the k-th argument had an illegal value
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dlavsy ( character  UPLO,
character  TRANS,
character  DIAG,
integer  N,
integer  NRHS,
double precision, dimension( lda, * )  A,
integer  LDA,
integer, dimension( * )  IPIV,
double precision, dimension( ldb, * )  B,
integer  LDB,
integer  INFO 
)

DLAVSY

Purpose:
 DLAVSY  performs one of the matrix-vector operations
    x := A*x  or  x := A'*x,
 where x is an N element vector and A is one of the factors
 from the block U*D*U' or L*D*L' factorization computed by DSYTRF.

 If TRANS = 'N', multiplies by U  or U * D  (or L  or L * D)
 If TRANS = 'T', multiplies by U' or D * U' (or L' or D * L')
 If TRANS = 'C', multiplies by U' or D * U' (or L' or D * L')
Parameters
[in]UPLO
          UPLO is CHARACTER*1
          Specifies whether the factor stored in A is upper or lower
          triangular.
          = 'U':  Upper triangular
          = 'L':  Lower triangular
[in]TRANS
          TRANS is CHARACTER*1
          Specifies the operation to be performed:
          = 'N':  x := A*x
          = 'T':  x := A'*x
          = 'C':  x := A'*x
[in]DIAG
          DIAG is CHARACTER*1
          Specifies whether or not the diagonal blocks are unit
          matrices.  If the diagonal blocks are assumed to be unit,
          then A = U or A = L, otherwise A = U*D or A = L*D.
          = 'U':  Diagonal blocks are assumed to be unit matrices.
          = 'N':  Diagonal blocks are assumed to be non-unit matrices.
[in]N
          N is INTEGER
          The number of rows and columns of the matrix A.  N >= 0.
[in]NRHS
          NRHS is INTEGER
          The number of right hand sides, i.e., the number of vectors
          x to be multiplied by A.  NRHS >= 0.
[in]A
          A is DOUBLE PRECISION array, dimension (LDA,N)
          The block diagonal matrix D and the multipliers used to
          obtain the factor U or L as computed by DSYTRF.
          Stored as a 2-D triangular matrix.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).
[in]IPIV
          IPIV is INTEGER array, dimension (N)
          Details of the interchanges and the block structure of D,
          as determined by DSYTRF.

          If UPLO = 'U':
               If IPIV(k) > 0, then rows and columns k and IPIV(k)
               were interchanged and D(k,k) is a 1-by-1 diagonal block.
               (If IPIV( k ) = k, no interchange was done).

               If IPIV(k) = IPIV(k-1) < 0, then rows and
               columns k-1 and -IPIV(k) were interchanged,
               D(k-1:k,k-1:k) is a 2-by-2 diagonal block.

          If UPLO = 'L':
               If IPIV(k) > 0, then rows and columns k and IPIV(k)
               were interchanged and D(k,k) is a 1-by-1 diagonal block.
               (If IPIV( k ) = k, no interchange was done).

               If IPIV(k) = IPIV(k+1) < 0, then rows and
               columns k+1 and -IPIV(k) were interchanged,
               D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
[in,out]B
          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
          On entry, B contains NRHS vectors of length N.
          On exit, B is overwritten with the product A * B.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).
[out]INFO
          INFO is INTEGER
          = 0: successful exit
          < 0: if INFO = -k, the k-th argument had an illegal value
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2013
subroutine dlavsy_rook ( character  UPLO,
character  TRANS,
character  DIAG,
integer  N,
integer  NRHS,
double precision, dimension( lda, * )  A,
integer  LDA,
integer, dimension( * )  IPIV,
double precision, dimension( ldb, * )  B,
integer  LDB,
integer  INFO 
)

DLAVSY_ROOK

Purpose:
 DLAVSY_ROOK  performs one of the matrix-vector operations
    x := A*x  or  x := A'*x,
 where x is an N element vector and A is one of the factors
 from the block U*D*U' or L*D*L' factorization computed by DSYTRF_ROOK.

 If TRANS = 'N', multiplies by U  or U * D  (or L  or L * D)
 If TRANS = 'T', multiplies by U' or D * U' (or L' or D * L')
 If TRANS = 'C', multiplies by U' or D * U' (or L' or D * L')
Parameters
[in]UPLO
          UPLO is CHARACTER*1
          Specifies whether the factor stored in A is upper or lower
          triangular.
          = 'U':  Upper triangular
          = 'L':  Lower triangular
[in]TRANS
          TRANS is CHARACTER*1
          Specifies the operation to be performed:
          = 'N':  x := A*x
          = 'T':  x := A'*x
          = 'C':  x := A'*x
[in]DIAG
          DIAG is CHARACTER*1
          Specifies whether or not the diagonal blocks are unit
          matrices.  If the diagonal blocks are assumed to be unit,
          then A = U or A = L, otherwise A = U*D or A = L*D.
          = 'U':  Diagonal blocks are assumed to be unit matrices.
          = 'N':  Diagonal blocks are assumed to be non-unit matrices.
[in]N
          N is INTEGER
          The number of rows and columns of the matrix A.  N >= 0.
[in]NRHS
          NRHS is INTEGER
          The number of right hand sides, i.e., the number of vectors
          x to be multiplied by A.  NRHS >= 0.
[in]A
          A is DOUBLE PRECISION array, dimension (LDA,N)
          The block diagonal matrix D and the multipliers used to
          obtain the factor U or L as computed by DSYTRF_ROOK.
          Stored as a 2-D triangular matrix.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).
[in]IPIV
          IPIV is INTEGER array, dimension (N)
          Details of the interchanges and the block structure of D,
          as determined by DSYTRF_ROOK.

          If UPLO = 'U':
               If IPIV(k) > 0, then rows and columns k and IPIV(k)
               were interchanged and D(k,k) is a 1-by-1 diagonal block.
               (If IPIV( k ) = k, no interchange was done).

               If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and
               columns k and -IPIV(k) were interchanged and rows and
               columns k-1 and -IPIV(k-1) were inerchaged,
               D(k-1:k,k-1:k) is a 2-by-2 diagonal block.

          If UPLO = 'L':
               If IPIV(k) > 0, then rows and columns k and IPIV(k)
               were interchanged and D(k,k) is a 1-by-1 diagonal block.
               (If IPIV( k ) = k, no interchange was done).

               If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and
               columns k and -IPIV(k) were interchanged and rows and
               columns k+1 and -IPIV(k+1) were inerchaged,
               D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
[in,out]B
          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
          On entry, B contains NRHS vectors of length N.
          On exit, B is overwritten with the product A * B.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).
[out]INFO
          INFO is INTEGER
          = 0: successful exit
          < 0: if INFO = -k, the k-th argument had an illegal value
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2013
subroutine dlqt01 ( integer  M,
integer  N,
double precision, dimension( lda, * )  A,
double precision, dimension( lda, * )  AF,
double precision, dimension( lda, * )  Q,
double precision, dimension( lda, * )  L,
integer  LDA,
double precision, dimension( * )  TAU,
double precision, dimension( lwork )  WORK,
integer  LWORK,
double precision, dimension( * )  RWORK,
double precision, dimension( * )  RESULT 
)

DLQT01

Purpose:
 DLQT01 tests DGELQF, which computes the LQ factorization of an m-by-n
 matrix A, and partially tests DORGLQ which forms the n-by-n
 orthogonal matrix Q.

 DLQT01 compares L with A*Q', and checks that Q is orthogonal.
Parameters
[in]M
          M is INTEGER
          The number of rows of the matrix A.  M >= 0.
[in]N
          N is INTEGER
          The number of columns of the matrix A.  N >= 0.
[in]A
          A is DOUBLE PRECISION array, dimension (LDA,N)
          The m-by-n matrix A.
[out]AF
          AF is DOUBLE PRECISION array, dimension (LDA,N)
          Details of the LQ factorization of A, as returned by DGELQF.
          See DGELQF for further details.
[out]Q
          Q is DOUBLE PRECISION array, dimension (LDA,N)
          The n-by-n orthogonal matrix Q.
[out]L
          L is DOUBLE PRECISION array, dimension (LDA,max(M,N))
[in]LDA
          LDA is INTEGER
          The leading dimension of the arrays A, AF, Q and L.
          LDA >= max(M,N).
[out]TAU
          TAU is DOUBLE PRECISION array, dimension (min(M,N))
          The scalar factors of the elementary reflectors, as returned
          by DGELQF.
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (LWORK)
[in]LWORK
          LWORK is INTEGER
          The dimension of the array WORK.
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension (max(M,N))
[out]RESULT
          RESULT is DOUBLE PRECISION array, dimension (2)
          The test ratios:
          RESULT(1) = norm( L - A*Q' ) / ( N * norm(A) * EPS )
          RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dlqt02 ( integer  M,
integer  N,
integer  K,
double precision, dimension( lda, * )  A,
double precision, dimension( lda, * )  AF,
double precision, dimension( lda, * )  Q,
double precision, dimension( lda, * )  L,
integer  LDA,
double precision, dimension( * )  TAU,
double precision, dimension( lwork )  WORK,
integer  LWORK,
double precision, dimension( * )  RWORK,
double precision, dimension( * )  RESULT 
)

DLQT02

Purpose:
 DLQT02 tests DORGLQ, which generates an m-by-n matrix Q with
 orthonornmal rows that is defined as the product of k elementary
 reflectors.

 Given the LQ factorization of an m-by-n matrix A, DLQT02 generates
 the orthogonal matrix Q defined by the factorization of the first k
 rows of A; it compares L(1:k,1:m) with A(1:k,1:n)*Q(1:m,1:n)', and
 checks that the rows of Q are orthonormal.
Parameters
[in]M
          M is INTEGER
          The number of rows of the matrix Q to be generated.  M >= 0.
[in]N
          N is INTEGER
          The number of columns of the matrix Q to be generated.
          N >= M >= 0.
[in]K
          K is INTEGER
          The number of elementary reflectors whose product defines the
          matrix Q. M >= K >= 0.
[in]A
          A is DOUBLE PRECISION array, dimension (LDA,N)
          The m-by-n matrix A which was factorized by DLQT01.
[in]AF
          AF is DOUBLE PRECISION array, dimension (LDA,N)
          Details of the LQ factorization of A, as returned by DGELQF.
          See DGELQF for further details.
[out]Q
          Q is DOUBLE PRECISION array, dimension (LDA,N)
[out]L
          L is DOUBLE PRECISION array, dimension (LDA,M)
[in]LDA
          LDA is INTEGER
          The leading dimension of the arrays A, AF, Q and L. LDA >= N.
[in]TAU
          TAU is DOUBLE PRECISION array, dimension (M)
          The scalar factors of the elementary reflectors corresponding
          to the LQ factorization in AF.
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (LWORK)
[in]LWORK
          LWORK is INTEGER
          The dimension of the array WORK.
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension (M)
[out]RESULT
          RESULT is DOUBLE PRECISION array, dimension (2)
          The test ratios:
          RESULT(1) = norm( L - A*Q' ) / ( N * norm(A) * EPS )
          RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dlqt03 ( integer  M,
integer  N,
integer  K,
double precision, dimension( lda, * )  AF,
double precision, dimension( lda, * )  C,
double precision, dimension( lda, * )  CC,
double precision, dimension( lda, * )  Q,
integer  LDA,
double precision, dimension( * )  TAU,
double precision, dimension( lwork )  WORK,
integer  LWORK,
double precision, dimension( * )  RWORK,
double precision, dimension( * )  RESULT 
)

DLQT03

Purpose:
 DLQT03 tests DORMLQ, which computes Q*C, Q'*C, C*Q or C*Q'.

 DLQT03 compares the results of a call to DORMLQ with the results of
 forming Q explicitly by a call to DORGLQ and then performing matrix
 multiplication by a call to DGEMM.
Parameters
[in]M
          M is INTEGER
          The number of rows or columns of the matrix C; C is n-by-m if
          Q is applied from the left, or m-by-n if Q is applied from
          the right.  M >= 0.
[in]N
          N is INTEGER
          The order of the orthogonal matrix Q.  N >= 0.
[in]K
          K is INTEGER
          The number of elementary reflectors whose product defines the
          orthogonal matrix Q.  N >= K >= 0.
[in]AF
          AF is DOUBLE PRECISION array, dimension (LDA,N)
          Details of the LQ factorization of an m-by-n matrix, as
          returned by DGELQF. See SGELQF for further details.
[out]C
          C is DOUBLE PRECISION array, dimension (LDA,N)
[out]CC
          CC is DOUBLE PRECISION array, dimension (LDA,N)
[out]Q
          Q is DOUBLE PRECISION array, dimension (LDA,N)
[in]LDA
          LDA is INTEGER
          The leading dimension of the arrays AF, C, CC, and Q.
[in]TAU
          TAU is DOUBLE PRECISION array, dimension (min(M,N))
          The scalar factors of the elementary reflectors corresponding
          to the LQ factorization in AF.
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (LWORK)
[in]LWORK
          LWORK is INTEGER
          The length of WORK.  LWORK must be at least M, and should be
          M*NB, where NB is the blocksize for this environment.
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension (M)
[out]RESULT
          RESULT is DOUBLE PRECISION array, dimension (4)
          The test ratios compare two techniques for multiplying a
          random matrix C by an n-by-n orthogonal matrix Q.
          RESULT(1) = norm( Q*C - Q*C )  / ( N * norm(C) * EPS )
          RESULT(2) = norm( C*Q - C*Q )  / ( N * norm(C) * EPS )
          RESULT(3) = norm( Q'*C - Q'*C )/ ( N * norm(C) * EPS )
          RESULT(4) = norm( C*Q' - C*Q' )/ ( N * norm(C) * EPS )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dpbt01 ( character  UPLO,
integer  N,
integer  KD,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( ldafac, * )  AFAC,
integer  LDAFAC,
double precision, dimension( * )  RWORK,
double precision  RESID 
)

DPBT01

Purpose:
 DPBT01 reconstructs a symmetric positive definite band matrix A from
 its L*L' or U'*U factorization and computes the residual
    norm( L*L' - A ) / ( N * norm(A) * EPS ) or
    norm( U'*U - A ) / ( N * norm(A) * EPS ),
 where EPS is the machine epsilon, L' is the conjugate transpose of
 L, and U' is the conjugate transpose of U.
Parameters
[in]UPLO
          UPLO is CHARACTER*1
          Specifies whether the upper or lower triangular part of the
          symmetric matrix A is stored:
          = 'U':  Upper triangular
          = 'L':  Lower triangular
[in]N
          N is INTEGER
          The number of rows and columns of the matrix A.  N >= 0.
[in]KD
          KD is INTEGER
          The number of super-diagonals of the matrix A if UPLO = 'U',
          or the number of sub-diagonals if UPLO = 'L'.  KD >= 0.
[in]A
          A is DOUBLE PRECISION array, dimension (LDA,N)
          The original symmetric band matrix A.  If UPLO = 'U', the
          upper triangular part of A is stored as a band matrix; if
          UPLO = 'L', the lower triangular part of A is stored.  The
          columns of the appropriate triangle are stored in the columns
          of A and the diagonals of the triangle are stored in the rows
          of A.  See DPBTRF for further details.
[in]LDA
          LDA is INTEGER.
          The leading dimension of the array A.  LDA >= max(1,KD+1).
[in]AFAC
          AFAC is DOUBLE PRECISION array, dimension (LDAFAC,N)
          The factored form of the matrix A.  AFAC contains the factor
          L or U from the L*L' or U'*U factorization in band storage
          format, as computed by DPBTRF.
[in]LDAFAC
          LDAFAC is INTEGER
          The leading dimension of the array AFAC.
          LDAFAC >= max(1,KD+1).
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension (N)
[out]RESID
          RESID is DOUBLE PRECISION
          If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS )
          If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dpbt02 ( character  UPLO,
integer  N,
integer  KD,
integer  NRHS,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( ldx, * )  X,
integer  LDX,
double precision, dimension( ldb, * )  B,
integer  LDB,
double precision, dimension( * )  RWORK,
double precision  RESID 
)

DPBT02

Purpose:
 DPBT02 computes the residual for a solution of a symmetric banded
 system of equations  A*x = b:
    RESID = norm( B - A*X ) / ( norm(A) * norm(X) * EPS)
 where EPS is the machine precision.
Parameters
[in]UPLO
          UPLO is CHARACTER*1
          Specifies whether the upper or lower triangular part of the
          symmetric matrix A is stored:
          = 'U':  Upper triangular
          = 'L':  Lower triangular
[in]N
          N is INTEGER
          The number of rows and columns of the matrix A.  N >= 0.
[in]KD
          KD is INTEGER
          The number of super-diagonals of the matrix A if UPLO = 'U',
          or the number of sub-diagonals if UPLO = 'L'.  KD >= 0.
[in]NRHS
          NRHS is INTEGER
          The number of right hand sides. NRHS >= 0.
[in]A
          A is DOUBLE PRECISION array, dimension (LDA,N)
          The original symmetric band matrix A.  If UPLO = 'U', the
          upper triangular part of A is stored as a band matrix; if
          UPLO = 'L', the lower triangular part of A is stored.  The
          columns of the appropriate triangle are stored in the columns
          of A and the diagonals of the triangle are stored in the rows
          of A.  See DPBTRF for further details.
[in]LDA
          LDA is INTEGER.
          The leading dimension of the array A.  LDA >= max(1,KD+1).
[in]X
          X is DOUBLE PRECISION array, dimension (LDX,NRHS)
          The computed solution vectors for the system of linear
          equations.
[in]LDX
          LDX is INTEGER
          The leading dimension of the array X.   LDX >= max(1,N).
[in,out]B
          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
          On entry, the right hand side vectors for the system of
          linear equations.
          On exit, B is overwritten with the difference B - A*X.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension (N)
[out]RESID
          RESID is DOUBLE PRECISION
          The maximum over the number of right hand sides of
          norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dpbt05 ( character  UPLO,
integer  N,
integer  KD,
integer  NRHS,
double precision, dimension( ldab, * )  AB,
integer  LDAB,
double precision, dimension( ldb, * )  B,
integer  LDB,
double precision, dimension( ldx, * )  X,
integer  LDX,
double precision, dimension( ldxact, * )  XACT,
integer  LDXACT,
double precision, dimension( * )  FERR,
double precision, dimension( * )  BERR,
double precision, dimension( * )  RESLTS 
)

DPBT05

Purpose:
 DPBT05 tests the error bounds from iterative refinement for the
 computed solution to a system of equations A*X = B, where A is a
 symmetric band matrix.

 RESLTS(1) = test of the error bound
           = norm(X - XACT) / ( norm(X) * FERR )

 A large value is returned if this ratio is not less than one.

 RESLTS(2) = residual from the iterative refinement routine
           = the maximum of BERR / ( NZ*EPS + (*) ), where
             (*) = NZ*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
             and NZ = max. number of nonzeros in any row of A, plus 1
Parameters
[in]UPLO
          UPLO is CHARACTER*1
          Specifies whether the upper or lower triangular part of the
          symmetric matrix A is stored.
          = 'U':  Upper triangular
          = 'L':  Lower triangular
[in]N
          N is INTEGER
          The number of rows of the matrices X, B, and XACT, and the
          order of the matrix A.  N >= 0.
[in]KD
          KD is INTEGER
          The number of super-diagonals of the matrix A if UPLO = 'U',
          or the number of sub-diagonals if UPLO = 'L'.  KD >= 0.
[in]NRHS
          NRHS is INTEGER
          The number of columns of the matrices X, B, and XACT.
          NRHS >= 0.
[in]AB
          AB is DOUBLE PRECISION array, dimension (LDAB,N)
          The upper or lower triangle of the symmetric band matrix A,
          stored in the first KD+1 rows of the array.  The j-th column
          of A is stored in the j-th column of the array AB as follows:
          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
[in]LDAB
          LDAB is INTEGER
          The leading dimension of the array AB.  LDAB >= KD+1.
[in]B
          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
          The right hand side vectors for the system of linear
          equations.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).
[in]X
          X is DOUBLE PRECISION array, dimension (LDX,NRHS)
          The computed solution vectors.  Each vector is stored as a
          column of the matrix X.
[in]LDX
          LDX is INTEGER
          The leading dimension of the array X.  LDX >= max(1,N).
[in]XACT
          XACT is DOUBLE PRECISION array, dimension (LDX,NRHS)
          The exact solution vectors.  Each vector is stored as a
          column of the matrix XACT.
[in]LDXACT
          LDXACT is INTEGER
          The leading dimension of the array XACT.  LDXACT >= max(1,N).
[in]FERR
          FERR is DOUBLE PRECISION array, dimension (NRHS)
          The estimated forward error bounds for each solution vector
          X.  If XTRUE is the true solution, FERR bounds the magnitude
          of the largest entry in (X - XTRUE) divided by the magnitude
          of the largest entry in X.
[in]BERR
          BERR is DOUBLE PRECISION array, dimension (NRHS)
          The componentwise relative backward error of each solution
          vector (i.e., the smallest relative change in any entry of A
          or B that makes X an exact solution).
[out]RESLTS
          RESLTS is DOUBLE PRECISION array, dimension (2)
          The maximum over the NRHS solution vectors of the ratios:
          RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
          RESLTS(2) = BERR / ( NZ*EPS + (*) )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dpot01 ( character  UPLO,
integer  N,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( ldafac, * )  AFAC,
integer  LDAFAC,
double precision, dimension( * )  RWORK,
double precision  RESID 
)

DPOT01

Purpose:
 DPOT01 reconstructs a symmetric positive definite matrix  A  from
 its L*L' or U'*U factorization and computes the residual
    norm( L*L' - A ) / ( N * norm(A) * EPS ) or
    norm( U'*U - A ) / ( N * norm(A) * EPS ),
 where EPS is the machine epsilon.
Parameters
[in]UPLO
          UPLO is CHARACTER*1
          Specifies whether the upper or lower triangular part of the
          symmetric matrix A is stored:
          = 'U':  Upper triangular
          = 'L':  Lower triangular
[in]N
          N is INTEGER
          The number of rows and columns of the matrix A.  N >= 0.
[in]A
          A is DOUBLE PRECISION array, dimension (LDA,N)
          The original symmetric matrix A.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N)
[in,out]AFAC
          AFAC is DOUBLE PRECISION array, dimension (LDAFAC,N)
          On entry, the factor L or U from the L*L' or U'*U
          factorization of A.
          Overwritten with the reconstructed matrix, and then with the
          difference L*L' - A (or U'*U - A).
[in]LDAFAC
          LDAFAC is INTEGER
          The leading dimension of the array AFAC.  LDAFAC >= max(1,N).
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension (N)
[out]RESID
          RESID is DOUBLE PRECISION
          If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS )
          If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dpot02 ( character  UPLO,
integer  N,
integer  NRHS,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( ldx, * )  X,
integer  LDX,
double precision, dimension( ldb, * )  B,
integer  LDB,
double precision, dimension( * )  RWORK,
double precision  RESID 
)

DPOT02

Purpose:
 DPOT02 computes the residual for the solution of a symmetric system
 of linear equations  A*x = b:

    RESID = norm(B - A*X) / ( norm(A) * norm(X) * EPS ),

 where EPS is the machine epsilon.
Parameters
[in]UPLO
          UPLO is CHARACTER*1
          Specifies whether the upper or lower triangular part of the
          symmetric matrix A is stored:
          = 'U':  Upper triangular
          = 'L':  Lower triangular
[in]N
          N is INTEGER
          The number of rows and columns of the matrix A.  N >= 0.
[in]NRHS
          NRHS is INTEGER
          The number of columns of B, the matrix of right hand sides.
          NRHS >= 0.
[in]A
          A is DOUBLE PRECISION array, dimension (LDA,N)
          The original symmetric matrix A.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N)
[in]X
          X is DOUBLE PRECISION array, dimension (LDX,NRHS)
          The computed solution vectors for the system of linear
          equations.
[in]LDX
          LDX is INTEGER
          The leading dimension of the array X.   LDX >= max(1,N).
[in,out]B
          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
          On entry, the right hand side vectors for the system of
          linear equations.
          On exit, B is overwritten with the difference B - A*X.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension (N)
[out]RESID
          RESID is DOUBLE PRECISION
          The maximum over the number of right hand sides of
          norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dpot03 ( character  UPLO,
integer  N,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( ldainv, * )  AINV,
integer  LDAINV,
double precision, dimension( ldwork, * )  WORK,
integer  LDWORK,
double precision, dimension( * )  RWORK,
double precision  RCOND,
double precision  RESID 
)

DPOT03

Purpose:
 DPOT03 computes the residual for a symmetric matrix times its
 inverse:
    norm( I - A*AINV ) / ( N * norm(A) * norm(AINV) * EPS ),
 where EPS is the machine epsilon.
Parameters
[in]UPLO
          UPLO is CHARACTER*1
          Specifies whether the upper or lower triangular part of the
          symmetric matrix A is stored:
          = 'U':  Upper triangular
          = 'L':  Lower triangular
[in]N
          N is INTEGER
          The number of rows and columns of the matrix A.  N >= 0.
[in]A
          A is DOUBLE PRECISION array, dimension (LDA,N)
          The original symmetric matrix A.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N)
[in,out]AINV
          AINV is DOUBLE PRECISION array, dimension (LDAINV,N)
          On entry, the inverse of the matrix A, stored as a symmetric
          matrix in the same format as A.
          In this version, AINV is expanded into a full matrix and
          multiplied by A, so the opposing triangle of AINV will be
          changed; i.e., if the upper triangular part of AINV is
          stored, the lower triangular part will be used as work space.
[in]LDAINV
          LDAINV is INTEGER
          The leading dimension of the array AINV.  LDAINV >= max(1,N).
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (LDWORK,N)
[in]LDWORK
          LDWORK is INTEGER
          The leading dimension of the array WORK.  LDWORK >= max(1,N).
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension (N)
[out]RCOND
          RCOND is DOUBLE PRECISION
          The reciprocal of the condition number of A, computed as
          ( 1/norm(A) ) / norm(AINV).
[out]RESID
          RESID is DOUBLE PRECISION
          norm(I - A*AINV) / ( N * norm(A) * norm(AINV) * EPS )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dpot05 ( character  UPLO,
integer  N,
integer  NRHS,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( ldb, * )  B,
integer  LDB,
double precision, dimension( ldx, * )  X,
integer  LDX,
double precision, dimension( ldxact, * )  XACT,
integer  LDXACT,
double precision, dimension( * )  FERR,
double precision, dimension( * )  BERR,
double precision, dimension( * )  RESLTS 
)

DPOT05

Purpose:
 DPOT05 tests the error bounds from iterative refinement for the
 computed solution to a system of equations A*X = B, where A is a
 symmetric n by n matrix.

 RESLTS(1) = test of the error bound
           = norm(X - XACT) / ( norm(X) * FERR )

 A large value is returned if this ratio is not less than one.

 RESLTS(2) = residual from the iterative refinement routine
           = the maximum of BERR / ( (n+1)*EPS + (*) ), where
             (*) = (n+1)*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
Parameters
[in]UPLO
          UPLO is CHARACTER*1
          Specifies whether the upper or lower triangular part of the
          symmetric matrix A is stored.
          = 'U':  Upper triangular
          = 'L':  Lower triangular
[in]N
          N is INTEGER
          The number of rows of the matrices X, B, and XACT, and the
          order of the matrix A.  N >= 0.
[in]NRHS
          NRHS is INTEGER
          The number of columns of the matrices X, B, and XACT.
          NRHS >= 0.
[in]A
          A is DOUBLE PRECISION array, dimension (LDA,N)
          The symmetric matrix A.  If UPLO = 'U', the leading n by n
          upper triangular part of A contains the upper triangular part
          of the matrix A, and the strictly lower triangular part of A
          is not referenced.  If UPLO = 'L', the leading n by n lower
          triangular part of A contains the lower triangular part of
          the matrix A, and the strictly upper triangular part of A is
          not referenced.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).
[in]B
          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
          The right hand side vectors for the system of linear
          equations.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).
[in]X
          X is DOUBLE PRECISION array, dimension (LDX,NRHS)
          The computed solution vectors.  Each vector is stored as a
          column of the matrix X.
[in]LDX
          LDX is INTEGER
          The leading dimension of the array X.  LDX >= max(1,N).
[in]XACT
          XACT is DOUBLE PRECISION array, dimension (LDX,NRHS)
          The exact solution vectors.  Each vector is stored as a
          column of the matrix XACT.
[in]LDXACT
          LDXACT is INTEGER
          The leading dimension of the array XACT.  LDXACT >= max(1,N).
[in]FERR
          FERR is DOUBLE PRECISION array, dimension (NRHS)
          The estimated forward error bounds for each solution vector
          X.  If XTRUE is the true solution, FERR bounds the magnitude
          of the largest entry in (X - XTRUE) divided by the magnitude
          of the largest entry in X.
[in]BERR
          BERR is DOUBLE PRECISION array, dimension (NRHS)
          The componentwise relative backward error of each solution
          vector (i.e., the smallest relative change in any entry of A
          or B that makes X an exact solution).
[out]RESLTS
          RESLTS is DOUBLE PRECISION array, dimension (2)
          The maximum over the NRHS solution vectors of the ratios:
          RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
          RESLTS(2) = BERR / ( (n+1)*EPS + (*) )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dpot06 ( character  UPLO,
integer  N,
integer  NRHS,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( ldx, * )  X,
integer  LDX,
double precision, dimension( ldb, * )  B,
integer  LDB,
double precision, dimension( * )  RWORK,
double precision  RESID 
)

DPOT06

Purpose:
 DPOT06 computes the residual for a solution of a system of linear
 equations  A*x = b :
    RESID = norm(B - A*X,inf) / ( norm(A,inf) * norm(X,inf) * EPS ),
 where EPS is the machine epsilon.
Parameters
[in]UPLO
          UPLO is CHARACTER*1
          Specifies whether the upper or lower triangular part of the
          symmetric matrix A is stored:
          = 'U':  Upper triangular
          = 'L':  Lower triangular
[in]N
          N is INTEGER
          The number of rows and columns of the matrix A.  N >= 0.
[in]NRHS
          NRHS is INTEGER
          The number of columns of B, the matrix of right hand sides.
          NRHS >= 0.
[in]A
          A is DOUBLE PRECISION array, dimension (LDA,N)
          The original M x N matrix A.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).
[in]X
          X is DOUBLE PRECISION array, dimension (LDX,NRHS)
          The computed solution vectors for the system of linear
          equations.
[in]LDX
          LDX is INTEGER
          The leading dimension of the array X.  If TRANS = 'N',
          LDX >= max(1,N); if TRANS = 'T' or 'C', LDX >= max(1,N).
[in,out]B
          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
          On entry, the right hand side vectors for the system of
          linear equations.
          On exit, B is overwritten with the difference B - A*X.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B.  IF TRANS = 'N',
          LDB >= max(1,M); if TRANS = 'T' or 'C', LDB >= max(1,N).
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension (N)
[out]RESID
          RESID is DOUBLE PRECISION
          The maximum over the number of right hand sides of
          norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dppt01 ( character  UPLO,
integer  N,
double precision, dimension( * )  A,
double precision, dimension( * )  AFAC,
double precision, dimension( * )  RWORK,
double precision  RESID 
)

DPPT01

Purpose:
 DPPT01 reconstructs a symmetric positive definite packed matrix A
 from its L*L' or U'*U factorization and computes the residual
    norm( L*L' - A ) / ( N * norm(A) * EPS ) or
    norm( U'*U - A ) / ( N * norm(A) * EPS ),
 where EPS is the machine epsilon.
Parameters
[in]UPLO
          UPLO is CHARACTER*1
          Specifies whether the upper or lower triangular part of the
          symmetric matrix A is stored:
          = 'U':  Upper triangular
          = 'L':  Lower triangular
[in]N
          N is INTEGER
          The number of rows and columns of the matrix A.  N >= 0.
[in]A
          A is DOUBLE PRECISION array, dimension (N*(N+1)/2)
          The original symmetric matrix A, stored as a packed
          triangular matrix.
[in,out]AFAC
          AFAC is DOUBLE PRECISION array, dimension (N*(N+1)/2)
          On entry, the factor L or U from the L*L' or U'*U
          factorization of A, stored as a packed triangular matrix.
          Overwritten with the reconstructed matrix, and then with the
          difference L*L' - A (or U'*U - A).
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension (N)
[out]RESID
          RESID is DOUBLE PRECISION
          If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS )
          If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dppt02 ( character  UPLO,
integer  N,
integer  NRHS,
double precision, dimension( * )  A,
double precision, dimension( ldx, * )  X,
integer  LDX,
double precision, dimension( ldb, * )  B,
integer  LDB,
double precision, dimension( * )  RWORK,
double precision  RESID 
)

DPPT02

Purpose:
 DPPT02 computes the residual in the solution of a symmetric system
 of linear equations  A*x = b  when packed storage is used for the
 coefficient matrix.  The ratio computed is

    RESID = norm(B - A*X) / ( norm(A) * norm(X) * EPS),

 where EPS is the machine precision.
Parameters
[in]UPLO
          UPLO is CHARACTER*1
          Specifies whether the upper or lower triangular part of the
          symmetric matrix A is stored:
          = 'U':  Upper triangular
          = 'L':  Lower triangular
[in]N
          N is INTEGER
          The number of rows and columns of the matrix A.  N >= 0.
[in]NRHS
          NRHS is INTEGER
          The number of columns of B, the matrix of right hand sides.
          NRHS >= 0.
[in]A
          A is DOUBLE PRECISION array, dimension (N*(N+1)/2)
          The original symmetric matrix A, stored as a packed
          triangular matrix.
[in]X
          X is DOUBLE PRECISION array, dimension (LDX,NRHS)
          The computed solution vectors for the system of linear
          equations.
[in]LDX
          LDX is INTEGER
          The leading dimension of the array X.   LDX >= max(1,N).
[in,out]B
          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
          On entry, the right hand side vectors for the system of
          linear equations.
          On exit, B is overwritten with the difference B - A*X.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension (N)
[out]RESID
          RESID is DOUBLE PRECISION
          The maximum over the number of right hand sides of
          norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dppt03 ( character  UPLO,
integer  N,
double precision, dimension( * )  A,
double precision, dimension( * )  AINV,
double precision, dimension( ldwork, * )  WORK,
integer  LDWORK,
double precision, dimension( * )  RWORK,
double precision  RCOND,
double precision  RESID 
)

DPPT03

Purpose:
 DPPT03 computes the residual for a symmetric packed matrix times its
 inverse:
    norm( I - A*AINV ) / ( N * norm(A) * norm(AINV) * EPS ),
 where EPS is the machine epsilon.
Parameters
[in]UPLO
          UPLO is CHARACTER*1
          Specifies whether the upper or lower triangular part of the
          symmetric matrix A is stored:
          = 'U':  Upper triangular
          = 'L':  Lower triangular
[in]N
          N is INTEGER
          The number of rows and columns of the matrix A.  N >= 0.
[in]A
          A is DOUBLE PRECISION array, dimension (N*(N+1)/2)
          The original symmetric matrix A, stored as a packed
          triangular matrix.
[in]AINV
          AINV is DOUBLE PRECISION array, dimension (N*(N+1)/2)
          The (symmetric) inverse of the matrix A, stored as a packed
          triangular matrix.
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (LDWORK,N)
[in]LDWORK
          LDWORK is INTEGER
          The leading dimension of the array WORK.  LDWORK >= max(1,N).
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension (N)
[out]RCOND
          RCOND is DOUBLE PRECISION
          The reciprocal of the condition number of A, computed as
          ( 1/norm(A) ) / norm(AINV).
[out]RESID
          RESID is DOUBLE PRECISION
          norm(I - A*AINV) / ( N * norm(A) * norm(AINV) * EPS )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dppt05 ( character  UPLO,
integer  N,
integer  NRHS,
double precision, dimension( * )  AP,
double precision, dimension( ldb, * )  B,
integer  LDB,
double precision, dimension( ldx, * )  X,
integer  LDX,
double precision, dimension( ldxact, * )  XACT,
integer  LDXACT,
double precision, dimension( * )  FERR,
double precision, dimension( * )  BERR,
double precision, dimension( * )  RESLTS 
)

DPPT05

Purpose:
 DPPT05 tests the error bounds from iterative refinement for the
 computed solution to a system of equations A*X = B, where A is a
 symmetric matrix in packed storage format.

 RESLTS(1) = test of the error bound
           = norm(X - XACT) / ( norm(X) * FERR )

 A large value is returned if this ratio is not less than one.

 RESLTS(2) = residual from the iterative refinement routine
           = the maximum of BERR / ( (n+1)*EPS + (*) ), where
             (*) = (n+1)*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
Parameters
[in]UPLO
          UPLO is CHARACTER*1
          Specifies whether the upper or lower triangular part of the
          symmetric matrix A is stored.
          = 'U':  Upper triangular
          = 'L':  Lower triangular
[in]N
          N is INTEGER
          The number of rows of the matrices X, B, and XACT, and the
          order of the matrix A.  N >= 0.
[in]NRHS
          NRHS is INTEGER
          The number of columns of the matrices X, B, and XACT.
          NRHS >= 0.
[in]AP
          AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
          The upper or lower triangle of the symmetric matrix A, packed
          columnwise in a linear array.  The j-th column of A is stored
          in the array AP as follows:
          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
[in]B
          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
          The right hand side vectors for the system of linear
          equations.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).
[in]X
          X is DOUBLE PRECISION array, dimension (LDX,NRHS)
          The computed solution vectors.  Each vector is stored as a
          column of the matrix X.
[in]LDX
          LDX is INTEGER
          The leading dimension of the array X.  LDX >= max(1,N).
[in]XACT
          XACT is DOUBLE PRECISION array, dimension (LDX,NRHS)
          The exact solution vectors.  Each vector is stored as a
          column of the matrix XACT.
[in]LDXACT
          LDXACT is INTEGER
          The leading dimension of the array XACT.  LDXACT >= max(1,N).
[in]FERR
          FERR is DOUBLE PRECISION array, dimension (NRHS)
          The estimated forward error bounds for each solution vector
          X.  If XTRUE is the true solution, FERR bounds the magnitude
          of the largest entry in (X - XTRUE) divided by the magnitude
          of the largest entry in X.
[in]BERR
          BERR is DOUBLE PRECISION array, dimension (NRHS)
          The componentwise relative backward error of each solution
          vector (i.e., the smallest relative change in any entry of A
          or B that makes X an exact solution).
[out]RESLTS
          RESLTS is DOUBLE PRECISION array, dimension (2)
          The maximum over the NRHS solution vectors of the ratios:
          RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
          RESLTS(2) = BERR / ( (n+1)*EPS + (*) )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dpst01 ( character  UPLO,
integer  N,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( ldafac, * )  AFAC,
integer  LDAFAC,
double precision, dimension( ldperm, * )  PERM,
integer  LDPERM,
integer, dimension( * )  PIV,
double precision, dimension( * )  RWORK,
double precision  RESID,
integer  RANK 
)

DPST01

Purpose:
 DPST01 reconstructs a symmetric positive semidefinite matrix A
 from its L or U factors and the permutation matrix P and computes
 the residual
    norm( P*L*L'*P' - A ) / ( N * norm(A) * EPS ) or
    norm( P*U'*U*P' - A ) / ( N * norm(A) * EPS ),
 where EPS is the machine epsilon.
Parameters
[in]UPLO
          UPLO is CHARACTER*1
          Specifies whether the upper or lower triangular part of the
          symmetric matrix A is stored:
          = 'U':  Upper triangular
          = 'L':  Lower triangular
[in]N
          N is INTEGER
          The number of rows and columns of the matrix A.  N >= 0.
[in]A
          A is DOUBLE PRECISION array, dimension (LDA,N)
          The original symmetric matrix A.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N)
[in]AFAC
          AFAC is DOUBLE PRECISION array, dimension (LDAFAC,N)
          The factor L or U from the L*L' or U'*U
          factorization of A.
[in]LDAFAC
          LDAFAC is INTEGER
          The leading dimension of the array AFAC.  LDAFAC >= max(1,N).
[out]PERM
          PERM is DOUBLE PRECISION array, dimension (LDPERM,N)
          Overwritten with the reconstructed matrix, and then with the
          difference P*L*L'*P' - A (or P*U'*U*P' - A)
[in]LDPERM
          LDPERM is INTEGER
          The leading dimension of the array PERM.
          LDAPERM >= max(1,N).
[in]PIV
          PIV is INTEGER array, dimension (N)
          PIV is such that the nonzero entries are
          P( PIV( K ), K ) = 1.
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension (N)
[out]RESID
          RESID is DOUBLE PRECISION
          If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS )
          If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS )
[in]RANK
          RANK is INTEGER
          number of nonzero singular values of A.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dptt01 ( integer  N,
double precision, dimension( * )  D,
double precision, dimension( * )  E,
double precision, dimension( * )  DF,
double precision, dimension( * )  EF,
double precision, dimension( * )  WORK,
double precision  RESID 
)

DPTT01

Purpose:
 DPTT01 reconstructs a tridiagonal matrix A from its L*D*L'
 factorization and computes the residual
    norm(L*D*L' - A) / ( n * norm(A) * EPS ),
 where EPS is the machine epsilon.
Parameters
[in]N
          N is INTEGTER
          The order of the matrix A.
[in]D
          D is DOUBLE PRECISION array, dimension (N)
          The n diagonal elements of the tridiagonal matrix A.
[in]E
          E is DOUBLE PRECISION array, dimension (N-1)
          The (n-1) subdiagonal elements of the tridiagonal matrix A.
[in]DF
          DF is DOUBLE PRECISION array, dimension (N)
          The n diagonal elements of the factor L from the L*D*L'
          factorization of A.
[in]EF
          EF is DOUBLE PRECISION array, dimension (N-1)
          The (n-1) subdiagonal elements of the factor L from the
          L*D*L' factorization of A.
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (2*N)
[out]RESID
          RESID is DOUBLE PRECISION
          norm(L*D*L' - A) / (n * norm(A) * EPS)
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dptt02 ( integer  N,
integer  NRHS,
double precision, dimension( * )  D,
double precision, dimension( * )  E,
double precision, dimension( ldx, * )  X,
integer  LDX,
double precision, dimension( ldb, * )  B,
integer  LDB,
double precision  RESID 
)

DPTT02

Purpose:
 DPTT02 computes the residual for the solution to a symmetric
 tridiagonal system of equations:
    RESID = norm(B - A*X) / (norm(A) * norm(X) * EPS),
 where EPS is the machine epsilon.
Parameters
[in]N
          N is INTEGTER
          The order of the matrix A.
[in]NRHS
          NRHS is INTEGER
          The number of right hand sides, i.e., the number of columns
          of the matrices B and X.  NRHS >= 0.
[in]D
          D is DOUBLE PRECISION array, dimension (N)
          The n diagonal elements of the tridiagonal matrix A.
[in]E
          E is DOUBLE PRECISION array, dimension (N-1)
          The (n-1) subdiagonal elements of the tridiagonal matrix A.
[in]X
          X is DOUBLE PRECISION array, dimension (LDX,NRHS)
          The n by nrhs matrix of solution vectors X.
[in]LDX
          LDX is INTEGER
          The leading dimension of the array X.  LDX >= max(1,N).
[in,out]B
          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
          On entry, the n by nrhs matrix of right hand side vectors B.
          On exit, B is overwritten with the difference B - A*X.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).
[out]RESID
          RESID is DOUBLE PRECISION
          norm(B - A*X) / (norm(A) * norm(X) * EPS)
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dptt05 ( integer  N,
integer  NRHS,
double precision, dimension( * )  D,
double precision, dimension( * )  E,
double precision, dimension( ldb, * )  B,
integer  LDB,
double precision, dimension( ldx, * )  X,
integer  LDX,
double precision, dimension( ldxact, * )  XACT,
integer  LDXACT,
double precision, dimension( * )  FERR,
double precision, dimension( * )  BERR,
double precision, dimension( * )  RESLTS 
)

DPTT05

Purpose:
 DPTT05 tests the error bounds from iterative refinement for the
 computed solution to a system of equations A*X = B, where A is a
 symmetric tridiagonal matrix of order n.

 RESLTS(1) = test of the error bound
           = norm(X - XACT) / ( norm(X) * FERR )

 A large value is returned if this ratio is not less than one.

 RESLTS(2) = residual from the iterative refinement routine
           = the maximum of BERR / ( NZ*EPS + (*) ), where
             (*) = NZ*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
             and NZ = max. number of nonzeros in any row of A, plus 1
Parameters
[in]N
          N is INTEGER
          The number of rows of the matrices X, B, and XACT, and the
          order of the matrix A.  N >= 0.
[in]NRHS
          NRHS is INTEGER
          The number of columns of the matrices X, B, and XACT.
          NRHS >= 0.
[in]D
          D is DOUBLE PRECISION array, dimension (N)
          The n diagonal elements of the tridiagonal matrix A.
[in]E
          E is DOUBLE PRECISION array, dimension (N-1)
          The (n-1) subdiagonal elements of the tridiagonal matrix A.
[in]B
          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
          The right hand side vectors for the system of linear
          equations.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).
[in]X
          X is DOUBLE PRECISION array, dimension (LDX,NRHS)
          The computed solution vectors.  Each vector is stored as a
          column of the matrix X.
[in]LDX
          LDX is INTEGER
          The leading dimension of the array X.  LDX >= max(1,N).
[in]XACT
          XACT is DOUBLE PRECISION array, dimension (LDX,NRHS)
          The exact solution vectors.  Each vector is stored as a
          column of the matrix XACT.
[in]LDXACT
          LDXACT is INTEGER
          The leading dimension of the array XACT.  LDXACT >= max(1,N).
[in]FERR
          FERR is DOUBLE PRECISION array, dimension (NRHS)
          The estimated forward error bounds for each solution vector
          X.  If XTRUE is the true solution, FERR bounds the magnitude
          of the largest entry in (X - XTRUE) divided by the magnitude
          of the largest entry in X.
[in]BERR
          BERR is DOUBLE PRECISION array, dimension (NRHS)
          The componentwise relative backward error of each solution
          vector (i.e., the smallest relative change in any entry of A
          or B that makes X an exact solution).
[out]RESLTS
          RESLTS is DOUBLE PRECISION array, dimension (2)
          The maximum over the NRHS solution vectors of the ratios:
          RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
          RESLTS(2) = BERR / ( NZ*EPS + (*) )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dqlt01 ( integer  M,
integer  N,
double precision, dimension( lda, * )  A,
double precision, dimension( lda, * )  AF,
double precision, dimension( lda, * )  Q,
double precision, dimension( lda, * )  L,
integer  LDA,
double precision, dimension( * )  TAU,
double precision, dimension( lwork )  WORK,
integer  LWORK,
double precision, dimension( * )  RWORK,
double precision, dimension( * )  RESULT 
)

DQLT01

Purpose:
 DQLT01 tests DGEQLF, which computes the QL factorization of an m-by-n
 matrix A, and partially tests DORGQL which forms the m-by-m
 orthogonal matrix Q.

 DQLT01 compares L with Q'*A, and checks that Q is orthogonal.
Parameters
[in]M
          M is INTEGER
          The number of rows of the matrix A.  M >= 0.
[in]N
          N is INTEGER
          The number of columns of the matrix A.  N >= 0.
[in]A
          A is DOUBLE PRECISION array, dimension (LDA,N)
          The m-by-n matrix A.
[out]AF
          AF is DOUBLE PRECISION array, dimension (LDA,N)
          Details of the QL factorization of A, as returned by DGEQLF.
          See DGEQLF for further details.
[out]Q
          Q is DOUBLE PRECISION array, dimension (LDA,M)
          The m-by-m orthogonal matrix Q.
[out]L
          L is DOUBLE PRECISION array, dimension (LDA,max(M,N))
[in]LDA
          LDA is INTEGER
          The leading dimension of the arrays A, AF, Q and R.
          LDA >= max(M,N).
[out]TAU
          TAU is DOUBLE PRECISION array, dimension (min(M,N))
          The scalar factors of the elementary reflectors, as returned
          by DGEQLF.
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (LWORK)
[in]LWORK
          LWORK is INTEGER
          The dimension of the array WORK.
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension (M)
[out]RESULT
          RESULT is DOUBLE PRECISION array, dimension (2)
          The test ratios:
          RESULT(1) = norm( L - Q'*A ) / ( M * norm(A) * EPS )
          RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dqlt02 ( integer  M,
integer  N,
integer  K,
double precision, dimension( lda, * )  A,
double precision, dimension( lda, * )  AF,
double precision, dimension( lda, * )  Q,
double precision, dimension( lda, * )  L,
integer  LDA,
double precision, dimension( * )  TAU,
double precision, dimension( lwork )  WORK,
integer  LWORK,
double precision, dimension( * )  RWORK,
double precision, dimension( * )  RESULT 
)

DQLT02

Purpose:
 DQLT02 tests DORGQL, which generates an m-by-n matrix Q with
 orthonornmal columns that is defined as the product of k elementary
 reflectors.

 Given the QL factorization of an m-by-n matrix A, DQLT02 generates
 the orthogonal matrix Q defined by the factorization of the last k
 columns of A; it compares L(m-n+1:m,n-k+1:n) with
 Q(1:m,m-n+1:m)'*A(1:m,n-k+1:n), and checks that the columns of Q are
 orthonormal.
Parameters
[in]M
          M is INTEGER
          The number of rows of the matrix Q to be generated.  M >= 0.
[in]N
          N is INTEGER
          The number of columns of the matrix Q to be generated.
          M >= N >= 0.
[in]K
          K is INTEGER
          The number of elementary reflectors whose product defines the
          matrix Q. N >= K >= 0.
[in]A
          A is DOUBLE PRECISION array, dimension (LDA,N)
          The m-by-n matrix A which was factorized by DQLT01.
[in]AF
          AF is DOUBLE PRECISION array, dimension (LDA,N)
          Details of the QL factorization of A, as returned by DGEQLF.
          See DGEQLF for further details.
[out]Q
          Q is DOUBLE PRECISION array, dimension (LDA,N)
[out]L
          L is DOUBLE PRECISION array, dimension (LDA,N)
[in]LDA
          LDA is INTEGER
          The leading dimension of the arrays A, AF, Q and L. LDA >= M.
[in]TAU
          TAU is DOUBLE PRECISION array, dimension (N)
          The scalar factors of the elementary reflectors corresponding
          to the QL factorization in AF.
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (LWORK)
[in]LWORK
          LWORK is INTEGER
          The dimension of the array WORK.
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension (M)
[out]RESULT
          RESULT is DOUBLE PRECISION array, dimension (2)
          The test ratios:
          RESULT(1) = norm( L - Q'*A ) / ( M * norm(A) * EPS )
          RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dqlt03 ( integer  M,
integer  N,
integer  K,
double precision, dimension( lda, * )  AF,
double precision, dimension( lda, * )  C,
double precision, dimension( lda, * )  CC,
double precision, dimension( lda, * )  Q,
integer  LDA,
double precision, dimension( * )  TAU,
double precision, dimension( lwork )  WORK,
integer  LWORK,
double precision, dimension( * )  RWORK,
double precision, dimension( * )  RESULT 
)

DQLT03

Purpose:
 DQLT03 tests DORMQL, which computes Q*C, Q'*C, C*Q or C*Q'.

 DQLT03 compares the results of a call to DORMQL with the results of
 forming Q explicitly by a call to DORGQL and then performing matrix
 multiplication by a call to DGEMM.
Parameters
[in]M
          M is INTEGER
          The order of the orthogonal matrix Q.  M >= 0.
[in]N
          N is INTEGER
          The number of rows or columns of the matrix C; C is m-by-n if
          Q is applied from the left, or n-by-m if Q is applied from
          the right.  N >= 0.
[in]K
          K is INTEGER
          The number of elementary reflectors whose product defines the
          orthogonal matrix Q.  M >= K >= 0.
[in]AF
          AF is DOUBLE PRECISION array, dimension (LDA,N)
          Details of the QL factorization of an m-by-n matrix, as
          returned by DGEQLF. See SGEQLF for further details.
[out]C
          C is DOUBLE PRECISION array, dimension (LDA,N)
[out]CC
          CC is DOUBLE PRECISION array, dimension (LDA,N)
[out]Q
          Q is DOUBLE PRECISION array, dimension (LDA,M)
[in]LDA
          LDA is INTEGER
          The leading dimension of the arrays AF, C, CC, and Q.
[in]TAU
          TAU is DOUBLE PRECISION array, dimension (min(M,N))
          The scalar factors of the elementary reflectors corresponding
          to the QL factorization in AF.
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (LWORK)
[in]LWORK
          LWORK is INTEGER
          The length of WORK.  LWORK must be at least M, and should be
          M*NB, where NB is the blocksize for this environment.
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension (M)
[out]RESULT
          RESULT is DOUBLE PRECISION array, dimension (4)
          The test ratios compare two techniques for multiplying a
          random matrix C by an m-by-m orthogonal matrix Q.
          RESULT(1) = norm( Q*C - Q*C )  / ( M * norm(C) * EPS )
          RESULT(2) = norm( C*Q - C*Q )  / ( M * norm(C) * EPS )
          RESULT(3) = norm( Q'*C - Q'*C )/ ( M * norm(C) * EPS )
          RESULT(4) = norm( C*Q' - C*Q' )/ ( M * norm(C) * EPS )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
double precision function dqpt01 ( integer  M,
integer  N,
integer  K,
double precision, dimension( lda, * )  A,
double precision, dimension( lda, * )  AF,
integer  LDA,
double precision, dimension( * )  TAU,
integer, dimension( * )  JPVT,
double precision, dimension( lwork )  WORK,
integer  LWORK 
)

DQPT01

Purpose:
 DQPT01 tests the QR-factorization with pivoting of a matrix A.  The
 array AF contains the (possibly partial) QR-factorization of A, where
 the upper triangle of AF(1:k,1:k) is a partial triangular factor,
 the entries below the diagonal in the first k columns are the
 Householder vectors, and the rest of AF contains a partially updated
 matrix.

 This function returns ||A*P - Q*R||/(||norm(A)||*eps*M)
Parameters
[in]M
          M is INTEGER
          The number of rows of the matrices A and AF.
[in]N
          N is INTEGER
          The number of columns of the matrices A and AF.
[in]K
          K is INTEGER
          The number of columns of AF that have been reduced
          to upper triangular form.
[in]A
          A is DOUBLE PRECISION array, dimension (LDA, N)
          The original matrix A.
[in]AF
          AF is DOUBLE PRECISION array, dimension (LDA,N)
          The (possibly partial) output of DGEQPF.  The upper triangle
          of AF(1:k,1:k) is a partial triangular factor, the entries
          below the diagonal in the first k columns are the Householder
          vectors, and the rest of AF contains a partially updated
          matrix.
[in]LDA
          LDA is INTEGER
          The leading dimension of the arrays A and AF.
[in]TAU
          TAU is DOUBLE PRECISION array, dimension (K)
          Details of the Householder transformations as returned by
          DGEQPF.
[in]JPVT
          JPVT is INTEGER array, dimension (N)
          Pivot information as returned by DGEQPF.
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (LWORK)
[in]LWORK
          LWORK is INTEGER
          The length of the array WORK.  LWORK >= M*N+N.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dqrt01 ( integer  M,
integer  N,
double precision, dimension( lda, * )  A,
double precision, dimension( lda, * )  AF,
double precision, dimension( lda, * )  Q,
double precision, dimension( lda, * )  R,
integer  LDA,
double precision, dimension( * )  TAU,
double precision, dimension( lwork )  WORK,
integer  LWORK,
double precision, dimension( * )  RWORK,
double precision, dimension( * )  RESULT 
)

DQRT01

Purpose:
 DQRT01 tests DGEQRF, which computes the QR factorization of an m-by-n
 matrix A, and partially tests DORGQR which forms the m-by-m
 orthogonal matrix Q.

 DQRT01 compares R with Q'*A, and checks that Q is orthogonal.
Parameters
[in]M
          M is INTEGER
          The number of rows of the matrix A.  M >= 0.
[in]N
          N is INTEGER
          The number of columns of the matrix A.  N >= 0.
[in]A
          A is DOUBLE PRECISION array, dimension (LDA,N)
          The m-by-n matrix A.
[out]AF
          AF is DOUBLE PRECISION array, dimension (LDA,N)
          Details of the QR factorization of A, as returned by DGEQRF.
          See DGEQRF for further details.
[out]Q
          Q is DOUBLE PRECISION array, dimension (LDA,M)
          The m-by-m orthogonal matrix Q.
[out]R
          R is DOUBLE PRECISION array, dimension (LDA,max(M,N))
[in]LDA
          LDA is INTEGER
          The leading dimension of the arrays A, AF, Q and R.
          LDA >= max(M,N).
[out]TAU
          TAU is DOUBLE PRECISION array, dimension (min(M,N))
          The scalar factors of the elementary reflectors, as returned
          by DGEQRF.
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (LWORK)
[in]LWORK
          LWORK is INTEGER
          The dimension of the array WORK.
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension (M)
[out]RESULT
          RESULT is DOUBLE PRECISION array, dimension (2)
          The test ratios:
          RESULT(1) = norm( R - Q'*A ) / ( M * norm(A) * EPS )
          RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dqrt01p ( integer  M,
integer  N,
double precision, dimension( lda, * )  A,
double precision, dimension( lda, * )  AF,
double precision, dimension( lda, * )  Q,
double precision, dimension( lda, * )  R,
integer  LDA,
double precision, dimension( * )  TAU,
double precision, dimension( lwork )  WORK,
integer  LWORK,
double precision, dimension( * )  RWORK,
double precision, dimension( * )  RESULT 
)

DQRT01P

Purpose:
 DQRT01P tests DGEQRFP, which computes the QR factorization of an m-by-n
 matrix A, and partially tests DORGQR which forms the m-by-m
 orthogonal matrix Q.

 DQRT01P compares R with Q'*A, and checks that Q is orthogonal.
Parameters
[in]M
          M is INTEGER
          The number of rows of the matrix A.  M >= 0.
[in]N
          N is INTEGER
          The number of columns of the matrix A.  N >= 0.
[in]A
          A is DOUBLE PRECISION array, dimension (LDA,N)
          The m-by-n matrix A.
[out]AF
          AF is DOUBLE PRECISION array, dimension (LDA,N)
          Details of the QR factorization of A, as returned by DGEQRFP.
          See DGEQRFP for further details.
[out]Q
          Q is DOUBLE PRECISION array, dimension (LDA,M)
          The m-by-m orthogonal matrix Q.
[out]R
          R is DOUBLE PRECISION array, dimension (LDA,max(M,N))
[in]LDA
          LDA is INTEGER
          The leading dimension of the arrays A, AF, Q and R.
          LDA >= max(M,N).
[out]TAU
          TAU is DOUBLE PRECISION array, dimension (min(M,N))
          The scalar factors of the elementary reflectors, as returned
          by DGEQRFP.
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (LWORK)
[in]LWORK
          LWORK is INTEGER
          The dimension of the array WORK.
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension (M)
[out]RESULT
          RESULT is DOUBLE PRECISION array, dimension (2)
          The test ratios:
          RESULT(1) = norm( R - Q'*A ) / ( M * norm(A) * EPS )
          RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dqrt02 ( integer  M,
integer  N,
integer  K,
double precision, dimension( lda, * )  A,
double precision, dimension( lda, * )  AF,
double precision, dimension( lda, * )  Q,
double precision, dimension( lda, * )  R,
integer  LDA,
double precision, dimension( * )  TAU,
double precision, dimension( lwork )  WORK,
integer  LWORK,
double precision, dimension( * )  RWORK,
double precision, dimension( * )  RESULT 
)

DQRT02

Purpose:
 DQRT02 tests DORGQR, which generates an m-by-n matrix Q with
 orthonornmal columns that is defined as the product of k elementary
 reflectors.

 Given the QR factorization of an m-by-n matrix A, DQRT02 generates
 the orthogonal matrix Q defined by the factorization of the first k
 columns of A; it compares R(1:n,1:k) with Q(1:m,1:n)'*A(1:m,1:k),
 and checks that the columns of Q are orthonormal.
Parameters
[in]M
          M is INTEGER
          The number of rows of the matrix Q to be generated.  M >= 0.
[in]N
          N is INTEGER
          The number of columns of the matrix Q to be generated.
          M >= N >= 0.
[in]K
          K is INTEGER
          The number of elementary reflectors whose product defines the
          matrix Q. N >= K >= 0.
[in]A
          A is DOUBLE PRECISION array, dimension (LDA,N)
          The m-by-n matrix A which was factorized by DQRT01.
[in]AF
          AF is DOUBLE PRECISION array, dimension (LDA,N)
          Details of the QR factorization of A, as returned by DGEQRF.
          See DGEQRF for further details.
[out]Q
          Q is DOUBLE PRECISION array, dimension (LDA,N)
[out]R
          R is DOUBLE PRECISION array, dimension (LDA,N)
[in]LDA
          LDA is INTEGER
          The leading dimension of the arrays A, AF, Q and R. LDA >= M.
[in]TAU
          TAU is DOUBLE PRECISION array, dimension (N)
          The scalar factors of the elementary reflectors corresponding
          to the QR factorization in AF.
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (LWORK)
[in]LWORK
          LWORK is INTEGER
          The dimension of the array WORK.
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension (M)
[out]RESULT
          RESULT is DOUBLE PRECISION array, dimension (2)
          The test ratios:
          RESULT(1) = norm( R - Q'*A ) / ( M * norm(A) * EPS )
          RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dqrt03 ( integer  M,
integer  N,
integer  K,
double precision, dimension( lda, * )  AF,
double precision, dimension( lda, * )  C,
double precision, dimension( lda, * )  CC,
double precision, dimension( lda, * )  Q,
integer  LDA,
double precision, dimension( * )  TAU,
double precision, dimension( lwork )  WORK,
integer  LWORK,
double precision, dimension( * )  RWORK,
double precision, dimension( * )  RESULT 
)

DQRT03

Purpose:
 DQRT03 tests DORMQR, which computes Q*C, Q'*C, C*Q or C*Q'.

 DQRT03 compares the results of a call to DORMQR with the results of
 forming Q explicitly by a call to DORGQR and then performing matrix
 multiplication by a call to DGEMM.
Parameters
[in]M
          M is INTEGER
          The order of the orthogonal matrix Q.  M >= 0.
[in]N
          N is INTEGER
          The number of rows or columns of the matrix C; C is m-by-n if
          Q is applied from the left, or n-by-m if Q is applied from
          the right.  N >= 0.
[in]K
          K is INTEGER
          The number of elementary reflectors whose product defines the
          orthogonal matrix Q.  M >= K >= 0.
[in]AF
          AF is DOUBLE PRECISION array, dimension (LDA,N)
          Details of the QR factorization of an m-by-n matrix, as
          returned by DGEQRF. See DGEQRF for further details.
[out]C
          C is DOUBLE PRECISION array, dimension (LDA,N)
[out]CC
          CC is DOUBLE PRECISION array, dimension (LDA,N)
[out]Q
          Q is DOUBLE PRECISION array, dimension (LDA,M)
[in]LDA
          LDA is INTEGER
          The leading dimension of the arrays AF, C, CC, and Q.
[in]TAU
          TAU is DOUBLE PRECISION array, dimension (min(M,N))
          The scalar factors of the elementary reflectors corresponding
          to the QR factorization in AF.
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (LWORK)
[in]LWORK
          LWORK is INTEGER
          The length of WORK.  LWORK must be at least M, and should be
          M*NB, where NB is the blocksize for this environment.
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension (M)
[out]RESULT
          RESULT is DOUBLE PRECISION array, dimension (4)
          The test ratios compare two techniques for multiplying a
          random matrix C by an m-by-m orthogonal matrix Q.
          RESULT(1) = norm( Q*C - Q*C )  / ( M * norm(C) * EPS )
          RESULT(2) = norm( C*Q - C*Q )  / ( M * norm(C) * EPS )
          RESULT(3) = norm( Q'*C - Q'*C )/ ( M * norm(C) * EPS )
          RESULT(4) = norm( C*Q' - C*Q' )/ ( M * norm(C) * EPS )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2015
subroutine dqrt04 ( integer  M,
integer  N,
integer  NB,
double precision, dimension(6)  RESULT 
)

DQRT04

Purpose:
 DQRT04 tests DGEQRT and DGEMQRT.
Parameters
[in]M
          M is INTEGER
          Number of rows in test matrix.
[in]N
          N is INTEGER
          Number of columns in test matrix.
[in]NB
          NB is INTEGER
          Block size of test matrix.  NB <= Min(M,N).
[out]RESULT
          RESULT is DOUBLE PRECISION array, dimension (6)
          Results of each of the six tests below.

          RESULT(1) = | A - Q R |
          RESULT(2) = | I - Q^H Q |
          RESULT(3) = | Q C - Q C |
          RESULT(4) = | Q^H C - Q^H C |
          RESULT(5) = | C Q - C Q | 
          RESULT(6) = | C Q^H - C Q^H |
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
April 2012
subroutine dqrt05 ( integer  M,
integer  N,
integer  L,
integer  NB,
double precision, dimension(6)  RESULT 
)

DQRT05

Purpose:
 DQRT05 tests DTPQRT and DTPMQRT.
Parameters
[in]M
          M is INTEGER
          Number of rows in lower part of the test matrix.
[in]N
          N is INTEGER
          Number of columns in test matrix.
[in]L
          L is INTEGER
          The number of rows of the upper trapezoidal part the
          lower test matrix.  0 <= L <= M.
[in]NB
          NB is INTEGER
          Block size of test matrix.  NB <= N.
[out]RESULT
          RESULT is DOUBLE PRECISION array, dimension (6)
          Results of each of the six tests below.

          RESULT(1) = | A - Q R |
          RESULT(2) = | I - Q^H Q |
          RESULT(3) = | Q C - Q C |
          RESULT(4) = | Q^H C - Q^H C |
          RESULT(5) = | C Q - C Q | 
          RESULT(6) = | C Q^H - C Q^H |
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
April 2012
double precision function dqrt11 ( integer  M,
integer  K,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( * )  TAU,
double precision, dimension( lwork )  WORK,
integer  LWORK 
)

DQRT11

Purpose:
 DQRT11 computes the test ratio

       || Q'*Q - I || / (eps * m)

 where the orthogonal matrix Q is represented as a product of
 elementary transformations.  Each transformation has the form

    H(k) = I - tau(k) v(k) v(k)'

 where tau(k) is stored in TAU(k) and v(k) is an m-vector of the form
 [ 0 ... 0 1 x(k) ]', where x(k) is a vector of length m-k stored
 in A(k+1:m,k).
Parameters
[in]M
          M is INTEGER
          The number of rows of the matrix A.
[in]K
          K is INTEGER
          The number of columns of A whose subdiagonal entries
          contain information about orthogonal transformations.
[in]A
          A is DOUBLE PRECISION array, dimension (LDA,K)
          The (possibly partial) output of a QR reduction routine.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.
[in]TAU
          TAU is DOUBLE PRECISION array, dimension (K)
          The scaling factors tau for the elementary transformations as
          computed by the QR factorization routine.
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (LWORK)
[in]LWORK
          LWORK is INTEGER
          The length of the array WORK.  LWORK >= M*M + M.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
double precision function dqrt12 ( integer  M,
integer  N,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( * )  S,
double precision, dimension( lwork )  WORK,
integer  LWORK 
)

DQRT12

Purpose:
 DQRT12 computes the singular values `svlues' of the upper trapezoid
 of A(1:M,1:N) and returns the ratio

      || s - svlues||/(||svlues||*eps*max(M,N))
Parameters
[in]M
          M is INTEGER
          The number of rows of the matrix A.
[in]N
          N is INTEGER
          The number of columns of the matrix A.
[in]A
          A is DOUBLE PRECISION array, dimension (LDA,N)
          The M-by-N matrix A. Only the upper trapezoid is referenced.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.
[in]S
          S is DOUBLE PRECISION array, dimension (min(M,N))
          The singular values of the matrix A.
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (LWORK)
[in]LWORK
          LWORK is INTEGER
          The length of the array WORK. LWORK >= max(M*N + 4*min(M,N) +
          max(M,N), M*N+2*MIN( M, N )+4*N).
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dqrt13 ( integer  SCALE,
integer  M,
integer  N,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision  NORMA,
integer, dimension( 4 )  ISEED 
)

DQRT13

Purpose:
 DQRT13 generates a full-rank matrix that may be scaled to have large
 or small norm.
Parameters
[in]SCALE
          SCALE is INTEGER
          SCALE = 1: normally scaled matrix
          SCALE = 2: matrix scaled up
          SCALE = 3: matrix scaled down
[in]M
          M is INTEGER
          The number of rows of the matrix A.
[in]N
          N is INTEGER
          The number of columns of A.
[out]A
          A is DOUBLE PRECISION array, dimension (LDA,N)
          The M-by-N matrix A.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.
[out]NORMA
          NORMA is DOUBLE PRECISION
          The one-norm of A.
[in,out]ISEED
          ISEED is integer array, dimension (4)
          Seed for random number generator
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
double precision function dqrt14 ( character  TRANS,
integer  M,
integer  N,
integer  NRHS,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( ldx, * )  X,
integer  LDX,
double precision, dimension( lwork )  WORK,
integer  LWORK 
)

DQRT14

Purpose:
 DQRT14 checks whether X is in the row space of A or A'.  It does so
 by scaling both X and A such that their norms are in the range
 [sqrt(eps), 1/sqrt(eps)], then computing a QR factorization of [A,X]
 (if TRANS = 'T') or an LQ factorization of [A',X]' (if TRANS = 'N'),
 and returning the norm of the trailing triangle, scaled by
 MAX(M,N,NRHS)*eps.
Parameters
[in]TRANS
          TRANS is CHARACTER*1
          = 'N':  No transpose, check for X in the row space of A
          = 'T':  Transpose, check for X in the row space of A'.
[in]M
          M is INTEGER
          The number of rows of the matrix A.
[in]N
          N is INTEGER
          The number of columns of the matrix A.
[in]NRHS
          NRHS is INTEGER
          The number of right hand sides, i.e., the number of columns
          of X.
[in]A
          A is DOUBLE PRECISION array, dimension (LDA,N)
          The M-by-N matrix A.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.
[in]X
          X is DOUBLE PRECISION array, dimension (LDX,NRHS)
          If TRANS = 'N', the N-by-NRHS matrix X.
          IF TRANS = 'T', the M-by-NRHS matrix X.
[in]LDX
          LDX is INTEGER
          The leading dimension of the array X.
[out]WORK
          WORK is DOUBLE PRECISION array dimension (LWORK)
[in]LWORK
          LWORK is INTEGER
          length of workspace array required
          If TRANS = 'N', LWORK >= (M+NRHS)*(N+2);
          if TRANS = 'T', LWORK >= (N+NRHS)*(M+2).
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dqrt15 ( integer  SCALE,
integer  RKSEL,
integer  M,
integer  N,
integer  NRHS,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( ldb, * )  B,
integer  LDB,
double precision, dimension( * )  S,
integer  RANK,
double precision  NORMA,
double precision  NORMB,
integer, dimension( 4 )  ISEED,
double precision, dimension( lwork )  WORK,
integer  LWORK 
)

DQRT15

Purpose:
 DQRT15 generates a matrix with full or deficient rank and of various
 norms.
Parameters
[in]SCALE
          SCALE is INTEGER
          SCALE = 1: normally scaled matrix
          SCALE = 2: matrix scaled up
          SCALE = 3: matrix scaled down
[in]RKSEL
          RKSEL is INTEGER
          RKSEL = 1: full rank matrix
          RKSEL = 2: rank-deficient matrix
[in]M
          M is INTEGER
          The number of rows of the matrix A.
[in]N
          N is INTEGER
          The number of columns of A.
[in]NRHS
          NRHS is INTEGER
          The number of columns of B.
[out]A
          A is DOUBLE PRECISION array, dimension (LDA,N)
          The M-by-N matrix A.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.
[out]B
          B is DOUBLE PRECISION array, dimension (LDB, NRHS)
          A matrix that is in the range space of matrix A.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B.
[out]S
          S is DOUBLE PRECISION array, dimension MIN(M,N)
          Singular values of A.
[out]RANK
          RANK is INTEGER
          number of nonzero singular values of A.
[out]NORMA
          NORMA is DOUBLE PRECISION
          one-norm of A.
[out]NORMB
          NORMB is DOUBLE PRECISION
          one-norm of B.
[in,out]ISEED
          ISEED is integer array, dimension (4)
          seed for random number generator.
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (LWORK)
[in]LWORK
          LWORK is INTEGER
          length of work space required.
          LWORK >= MAX(M+MIN(M,N),NRHS*MIN(M,N),2*N+M)
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dqrt16 ( character  TRANS,
integer  M,
integer  N,
integer  NRHS,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( ldx, * )  X,
integer  LDX,
double precision, dimension( ldb, * )  B,
integer  LDB,
double precision, dimension( * )  RWORK,
double precision  RESID 
)

DQRT16

Purpose:
 DQRT16 computes the residual for a solution of a system of linear
 equations  A*x = b  or  A'*x = b:
    RESID = norm(B - A*X) / ( max(m,n) * norm(A) * norm(X) * EPS ),
 where EPS is the machine epsilon.
Parameters
[in]TRANS
          TRANS is CHARACTER*1
          Specifies the form of the system of equations:
          = 'N':  A *x = b
          = 'T':  A'*x = b, where A' is the transpose of A
          = 'C':  A'*x = b, where A' is the transpose of A
[in]M
          M is INTEGER
          The number of rows of the matrix A.  M >= 0.
[in]N
          N is INTEGER
          The number of columns of the matrix A.  N >= 0.
[in]NRHS
          NRHS is INTEGER
          The number of columns of B, the matrix of right hand sides.
          NRHS >= 0.
[in]A
          A is DOUBLE PRECISION array, dimension (LDA,N)
          The original M x N matrix A.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,M).
[in]X
          X is DOUBLE PRECISION array, dimension (LDX,NRHS)
          The computed solution vectors for the system of linear
          equations.
[in]LDX
          LDX is INTEGER
          The leading dimension of the array X.  If TRANS = 'N',
          LDX >= max(1,N); if TRANS = 'T' or 'C', LDX >= max(1,M).
[in,out]B
          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
          On entry, the right hand side vectors for the system of
          linear equations.
          On exit, B is overwritten with the difference B - A*X.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B.  IF TRANS = 'N',
          LDB >= max(1,M); if TRANS = 'T' or 'C', LDB >= max(1,N).
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension (M)
[out]RESID
          RESID is DOUBLE PRECISION
          The maximum over the number of right hand sides of
          norm(B - A*X) / ( max(m,n) * norm(A) * norm(X) * EPS ).
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
double precision function dqrt17 ( character  TRANS,
integer  IRESID,
integer  M,
integer  N,
integer  NRHS,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( ldx, * )  X,
integer  LDX,
double precision, dimension( ldb, * )  B,
integer  LDB,
double precision, dimension( ldb, * )  C,
double precision, dimension( lwork )  WORK,
integer  LWORK 
)

DQRT17

Purpose:
 DQRT17 computes the ratio

    || R'*op(A) ||/(||A||*alpha*max(M,N,NRHS)*eps)

 where R = op(A)*X - B, op(A) is A or A', and

    alpha = ||B|| if IRESID = 1 (zero-residual problem)
    alpha = ||R|| if IRESID = 2 (otherwise).
Parameters
[in]TRANS
          TRANS is CHARACTER*1
          Specifies whether or not the transpose of A is used.
          = 'N':  No transpose, op(A) = A.
          = 'T':  Transpose, op(A) = A'.
[in]IRESID
          IRESID is INTEGER
          IRESID = 1 indicates zero-residual problem.
          IRESID = 2 indicates non-zero residual.
[in]M
          M is INTEGER
          The number of rows of the matrix A.
          If TRANS = 'N', the number of rows of the matrix B.
          If TRANS = 'T', the number of rows of the matrix X.
[in]N
          N is INTEGER
          The number of columns of the matrix  A.
          If TRANS = 'N', the number of rows of the matrix X.
          If TRANS = 'T', the number of rows of the matrix B.
[in]NRHS
          NRHS is INTEGER
          The number of columns of the matrices X and B.
[in]A
          A is DOUBLE PRECISION array, dimension (LDA,N)
          The m-by-n matrix A.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A. LDA >= M.
[in]X
          X is DOUBLE PRECISION array, dimension (LDX,NRHS)
          If TRANS = 'N', the n-by-nrhs matrix X.
          If TRANS = 'T', the m-by-nrhs matrix X.
[in]LDX
          LDX is INTEGER
          The leading dimension of the array X.
          If TRANS = 'N', LDX >= N.
          If TRANS = 'T', LDX >= M.
[in]B
          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
          If TRANS = 'N', the m-by-nrhs matrix B.
          If TRANS = 'T', the n-by-nrhs matrix B.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B.
          If TRANS = 'N', LDB >= M.
          If TRANS = 'T', LDB >= N.
[out]C
          C is DOUBLE PRECISION array, dimension (LDB,NRHS)
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (LWORK)
[in]LWORK
          LWORK is INTEGER
          The length of the array WORK.  LWORK >= NRHS*(M+N).
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2015
subroutine drqt01 ( integer  M,
integer  N,
double precision, dimension( lda, * )  A,
double precision, dimension( lda, * )  AF,
double precision, dimension( lda, * )  Q,
double precision, dimension( lda, * )  R,
integer  LDA,
double precision, dimension( * )  TAU,
double precision, dimension( lwork )  WORK,
integer  LWORK,
double precision, dimension( * )  RWORK,
double precision, dimension( * )  RESULT 
)

DRQT01

Purpose:
 DRQT01 tests DGERQF, which computes the RQ factorization of an m-by-n
 matrix A, and partially tests DORGRQ which forms the n-by-n
 orthogonal matrix Q.

 DRQT01 compares R with A*Q', and checks that Q is orthogonal.
Parameters
[in]M
          M is INTEGER
          The number of rows of the matrix A.  M >= 0.
[in]N
          N is INTEGER
          The number of columns of the matrix A.  N >= 0.
[in]A
          A is DOUBLE PRECISION array, dimension (LDA,N)
          The m-by-n matrix A.
[out]AF
          AF is DOUBLE PRECISION array, dimension (LDA,N)
          Details of the RQ factorization of A, as returned by DGERQF.
          See DGERQF for further details.
[out]Q
          Q is DOUBLE PRECISION array, dimension (LDA,N)
          The n-by-n orthogonal matrix Q.
[out]R
          R is DOUBLE PRECISION array, dimension (LDA,max(M,N))
[in]LDA
          LDA is INTEGER
          The leading dimension of the arrays A, AF, Q and L.
          LDA >= max(M,N).
[out]TAU
          TAU is DOUBLE PRECISION array, dimension (min(M,N))
          The scalar factors of the elementary reflectors, as returned
          by DGERQF.
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (LWORK)
[in]LWORK
          LWORK is INTEGER
          The dimension of the array WORK.
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension (max(M,N))
[out]RESULT
          RESULT is DOUBLE PRECISION array, dimension (2)
          The test ratios:
          RESULT(1) = norm( R - A*Q' ) / ( N * norm(A) * EPS )
          RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine drqt02 ( integer  M,
integer  N,
integer  K,
double precision, dimension( lda, * )  A,
double precision, dimension( lda, * )  AF,
double precision, dimension( lda, * )  Q,
double precision, dimension( lda, * )  R,
integer  LDA,
double precision, dimension( * )  TAU,
double precision, dimension( lwork )  WORK,
integer  LWORK,
double precision, dimension( * )  RWORK,
double precision, dimension( * )  RESULT 
)

DRQT02

Purpose:
 DRQT02 tests DORGRQ, which generates an m-by-n matrix Q with
 orthonornmal rows that is defined as the product of k elementary
 reflectors.

 Given the RQ factorization of an m-by-n matrix A, DRQT02 generates
 the orthogonal matrix Q defined by the factorization of the last k
 rows of A; it compares R(m-k+1:m,n-m+1:n) with
 A(m-k+1:m,1:n)*Q(n-m+1:n,1:n)', and checks that the rows of Q are
 orthonormal.
Parameters
[in]M
          M is INTEGER
          The number of rows of the matrix Q to be generated.  M >= 0.
[in]N
          N is INTEGER
          The number of columns of the matrix Q to be generated.
          N >= M >= 0.
[in]K
          K is INTEGER
          The number of elementary reflectors whose product defines the
          matrix Q. M >= K >= 0.
[in]A
          A is DOUBLE PRECISION array, dimension (LDA,N)
          The m-by-n matrix A which was factorized by DRQT01.
[in]AF
          AF is DOUBLE PRECISION array, dimension (LDA,N)
          Details of the RQ factorization of A, as returned by DGERQF.
          See DGERQF for further details.
[out]Q
          Q is DOUBLE PRECISION array, dimension (LDA,N)
[out]R
          R is DOUBLE PRECISION array, dimension (LDA,M)
[in]LDA
          LDA is INTEGER
          The leading dimension of the arrays A, AF, Q and L. LDA >= N.
[in]TAU
          TAU is DOUBLE PRECISION array, dimension (M)
          The scalar factors of the elementary reflectors corresponding
          to the RQ factorization in AF.
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (LWORK)
[in]LWORK
          LWORK is INTEGER
          The dimension of the array WORK.
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension (M)
[out]RESULT
          RESULT is DOUBLE PRECISION array, dimension (2)
          The test ratios:
          RESULT(1) = norm( R - A*Q' ) / ( N * norm(A) * EPS )
          RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine drqt03 ( integer  M,
integer  N,
integer  K,
double precision, dimension( lda, * )  AF,
double precision, dimension( lda, * )  C,
double precision, dimension( lda, * )  CC,
double precision, dimension( lda, * )  Q,
integer  LDA,
double precision, dimension( * )  TAU,
double precision, dimension( lwork )  WORK,
integer  LWORK,
double precision, dimension( * )  RWORK,
double precision, dimension( * )  RESULT 
)

DRQT03

Purpose:
 DRQT03 tests DORMRQ, which computes Q*C, Q'*C, C*Q or C*Q'.

 DRQT03 compares the results of a call to DORMRQ with the results of
 forming Q explicitly by a call to DORGRQ and then performing matrix
 multiplication by a call to DGEMM.
Parameters
[in]M
          M is INTEGER
          The number of rows or columns of the matrix C; C is n-by-m if
          Q is applied from the left, or m-by-n if Q is applied from
          the right.  M >= 0.
[in]N
          N is INTEGER
          The order of the orthogonal matrix Q.  N >= 0.
[in]K
          K is INTEGER
          The number of elementary reflectors whose product defines the
          orthogonal matrix Q.  N >= K >= 0.
[in]AF
          AF is DOUBLE PRECISION array, dimension (LDA,N)
          Details of the RQ factorization of an m-by-n matrix, as
          returned by DGERQF. See SGERQF for further details.
[out]C
          C is DOUBLE PRECISION array, dimension (LDA,N)
[out]CC
          CC is DOUBLE PRECISION array, dimension (LDA,N)
[out]Q
          Q is DOUBLE PRECISION array, dimension (LDA,N)
[in]LDA
          LDA is INTEGER
          The leading dimension of the arrays AF, C, CC, and Q.
[in]TAU
          TAU is DOUBLE PRECISION array, dimension (min(M,N))
          The scalar factors of the elementary reflectors corresponding
          to the RQ factorization in AF.
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (LWORK)
[in]LWORK
          LWORK is INTEGER
          The length of WORK.  LWORK must be at least M, and should be
          M*NB, where NB is the blocksize for this environment.
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension (M)
[out]RESULT
          RESULT is DOUBLE PRECISION array, dimension (4)
          The test ratios compare two techniques for multiplying a
          random matrix C by an n-by-n orthogonal matrix Q.
          RESULT(1) = norm( Q*C - Q*C )  / ( N * norm(C) * EPS )
          RESULT(2) = norm( C*Q - C*Q )  / ( N * norm(C) * EPS )
          RESULT(3) = norm( Q'*C - Q'*C )/ ( N * norm(C) * EPS )
          RESULT(4) = norm( C*Q' - C*Q' )/ ( N * norm(C) * EPS )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
double precision function drzt01 ( integer  M,
integer  N,
double precision, dimension( lda, * )  A,
double precision, dimension( lda, * )  AF,
integer  LDA,
double precision, dimension( * )  TAU,
double precision, dimension( lwork )  WORK,
integer  LWORK 
)

DRZT01

Purpose:
 DRZT01 returns
      || A - R*Q || / ( M * eps * ||A|| )
 for an upper trapezoidal A that was factored with DTZRZF.
Parameters
[in]M
          M is INTEGER
          The number of rows of the matrices A and AF.
[in]N
          N is INTEGER
          The number of columns of the matrices A and AF.
[in]A
          A is DOUBLE PRECISION array, dimension (LDA,N)
          The original upper trapezoidal M by N matrix A.
[in]AF
          AF is DOUBLE PRECISION array, dimension (LDA,N)
          The output of DTZRZF for input matrix A.
          The lower triangle is not referenced.
[in]LDA
          LDA is INTEGER
          The leading dimension of the arrays A and AF.
[in]TAU
          TAU is DOUBLE PRECISION array, dimension (M)
          Details of the Householder transformations as returned by
          DTZRZF.
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (LWORK)
[in]LWORK
          LWORK is INTEGER
          The length of the array WORK.  LWORK >= m*n + m*nb.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
double precision function drzt02 ( integer  M,
integer  N,
double precision, dimension( lda, * )  AF,
integer  LDA,
double precision, dimension( * )  TAU,
double precision, dimension( lwork )  WORK,
integer  LWORK 
)

DRZT02

Purpose:
 DRZT02 returns
      || I - Q'*Q || / ( M * eps)
 where the matrix Q is defined by the Householder transformations
 generated by DTZRZF.
Parameters
[in]M
          M is INTEGER
          The number of rows of the matrix AF.
[in]N
          N is INTEGER
          The number of columns of the matrix AF.
[in]AF
          AF is DOUBLE PRECISION array, dimension (LDA,N)
          The output of DTZRZF.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array AF.
[in]TAU
          TAU is DOUBLE PRECISION array, dimension (M)
          Details of the Householder transformations as returned by
          DTZRZF.
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (LWORK)
[in]LWORK
          LWORK is INTEGER
          length of WORK array. LWORK >= N*N+N*NB.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dspt01 ( character  UPLO,
integer  N,
double precision, dimension( * )  A,
double precision, dimension( * )  AFAC,
integer, dimension( * )  IPIV,
double precision, dimension( ldc, * )  C,
integer  LDC,
double precision, dimension( * )  RWORK,
double precision  RESID 
)

DSPT01

Purpose:
 DSPT01 reconstructs a symmetric indefinite packed matrix A from its
 block L*D*L' or U*D*U' factorization and computes the residual
      norm( C - A ) / ( N * norm(A) * EPS ),
 where C is the reconstructed matrix and EPS is the machine epsilon.
Parameters
[in]UPLO
          UPLO is CHARACTER*1
          Specifies whether the upper or lower triangular part of the
          symmetric matrix A is stored:
          = 'U':  Upper triangular
          = 'L':  Lower triangular
[in]N
          N is INTEGER
          The number of rows and columns of the matrix A.  N >= 0.
[in]A
          A is DOUBLE PRECISION array, dimension (N*(N+1)/2)
          The original symmetric matrix A, stored as a packed
          triangular matrix.
[in]AFAC
          AFAC is DOUBLE PRECISION array, dimension (N*(N+1)/2)
          The factored form of the matrix A, stored as a packed
          triangular matrix.  AFAC contains the block diagonal matrix D
          and the multipliers used to obtain the factor L or U from the
          block L*D*L' or U*D*U' factorization as computed by DSPTRF.
[in]IPIV
          IPIV is INTEGER array, dimension (N)
          The pivot indices from DSPTRF.
[out]C
          C is DOUBLE PRECISION array, dimension (LDC,N)
[in]LDC
          LDC is INTEGER
          The leading dimension of the array C.  LDC >= max(1,N).
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension (N)
[out]RESID
          RESID is DOUBLE PRECISION
          If UPLO = 'L', norm(L*D*L' - A) / ( N * norm(A) * EPS )
          If UPLO = 'U', norm(U*D*U' - A) / ( N * norm(A) * EPS )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dsyt01 ( character  UPLO,
integer  N,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( ldafac, * )  AFAC,
integer  LDAFAC,
integer, dimension( * )  IPIV,
double precision, dimension( ldc, * )  C,
integer  LDC,
double precision, dimension( * )  RWORK,
double precision  RESID 
)

DSYT01

Purpose:
 DSYT01 reconstructs a symmetric indefinite matrix A from its
 block L*D*L' or U*D*U' factorization and computes the residual
    norm( C - A ) / ( N * norm(A) * EPS ),
 where C is the reconstructed matrix and EPS is the machine epsilon.
Parameters
[in]UPLO
          UPLO is CHARACTER*1
          Specifies whether the upper or lower triangular part of the
          symmetric matrix A is stored:
          = 'U':  Upper triangular
          = 'L':  Lower triangular
[in]N
          N is INTEGER
          The number of rows and columns of the matrix A.  N >= 0.
[in]A
          A is DOUBLE PRECISION array, dimension (LDA,N)
          The original symmetric matrix A.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N)
[in]AFAC
          AFAC is DOUBLE PRECISION array, dimension (LDAFAC,N)
          The factored form of the matrix A.  AFAC contains the block
          diagonal matrix D and the multipliers used to obtain the
          factor L or U from the block L*D*L' or U*D*U' factorization
          as computed by DSYTRF.
[in]LDAFAC
          LDAFAC is INTEGER
          The leading dimension of the array AFAC.  LDAFAC >= max(1,N).
[in]IPIV
          IPIV is INTEGER array, dimension (N)
          The pivot indices from DSYTRF.
[out]C
          C is DOUBLE PRECISION array, dimension (LDC,N)
[in]LDC
          LDC is INTEGER
          The leading dimension of the array C.  LDC >= max(1,N).
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension (N)
[out]RESID
          RESID is DOUBLE PRECISION
          If UPLO = 'L', norm(L*D*L' - A) / ( N * norm(A) * EPS )
          If UPLO = 'U', norm(U*D*U' - A) / ( N * norm(A) * EPS )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2013
subroutine dsyt01_rook ( character  UPLO,
integer  N,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( ldafac, * )  AFAC,
integer  LDAFAC,
integer, dimension( * )  IPIV,
double precision, dimension( ldc, * )  C,
integer  LDC,
double precision, dimension( * )  RWORK,
double precision  RESID 
)

DSYT01_ROOK

Purpose:
 DSYT01_ROOK reconstructs a symmetric indefinite matrix A from its
 block L*D*L' or U*D*U' factorization and computes the residual
    norm( C - A ) / ( N * norm(A) * EPS ),
 where C is the reconstructed matrix and EPS is the machine epsilon.
Parameters
[in]UPLO
          UPLO is CHARACTER*1
          Specifies whether the upper or lower triangular part of the
          symmetric matrix A is stored:
          = 'U':  Upper triangular
          = 'L':  Lower triangular
[in]N
          N is INTEGER
          The number of rows and columns of the matrix A.  N >= 0.
[in]A
          A is DOUBLE PRECISION array, dimension (LDA,N)
          The original symmetric matrix A.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N)
[in]AFAC
          AFAC is DOUBLE PRECISION array, dimension (LDAFAC,N)
          The factored form of the matrix A.  AFAC contains the block
          diagonal matrix D and the multipliers used to obtain the
          factor L or U from the block L*D*L' or U*D*U' factorization
          as computed by DSYTRF_ROOK.
[in]LDAFAC
          LDAFAC is INTEGER
          The leading dimension of the array AFAC.  LDAFAC >= max(1,N).
[in]IPIV
          IPIV is INTEGER array, dimension (N)
          The pivot indices from DSYTRF_ROOK.
[out]C
          C is DOUBLE PRECISION array, dimension (LDC,N)
[in]LDC
          LDC is INTEGER
          The leading dimension of the array C.  LDC >= max(1,N).
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension (N)
[out]RESID
          RESID is DOUBLE PRECISION
          If UPLO = 'L', norm(L*D*L' - A) / ( N * norm(A) * EPS )
          If UPLO = 'U', norm(U*D*U' - A) / ( N * norm(A) * EPS )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2013
subroutine dtbt02 ( character  UPLO,
character  TRANS,
character  DIAG,
integer  N,
integer  KD,
integer  NRHS,
double precision, dimension( ldab, * )  AB,
integer  LDAB,
double precision, dimension( ldx, * )  X,
integer  LDX,
double precision, dimension( ldb, * )  B,
integer  LDB,
double precision, dimension( * )  WORK,
double precision  RESID 
)

DTBT02

Purpose:
 DTBT02 computes the residual for the computed solution to a
 triangular system of linear equations  A*x = b  or  A' *x = b when
 A is a triangular band matrix.  Here A' is the transpose of A and
 x and b are N by NRHS matrices.  The test ratio is the maximum over
 the number of right hand sides of
    norm(b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
 where op(A) denotes A or A' and EPS is the machine epsilon.
Parameters
[in]UPLO
          UPLO is CHARACTER*1
          Specifies whether the matrix A is upper or lower triangular.
          = 'U':  Upper triangular
          = 'L':  Lower triangular
[in]TRANS
          TRANS is CHARACTER*1
          Specifies the operation applied to A.
          = 'N':  A *x = b  (No transpose)
          = 'T':  A'*x = b  (Transpose)
          = 'C':  A'*x = b  (Conjugate transpose = Transpose)
[in]DIAG
          DIAG is CHARACTER*1
          Specifies whether or not the matrix A is unit triangular.
          = 'N':  Non-unit triangular
          = 'U':  Unit triangular
[in]N
          N is INTEGER
          The order of the matrix A.  N >= 0.
[in]KD
          KD is INTEGER
          The number of superdiagonals or subdiagonals of the
          triangular band matrix A.  KD >= 0.
[in]NRHS
          NRHS is INTEGER
          The number of right hand sides, i.e., the number of columns
          of the matrices X and B.  NRHS >= 0.
[in]AB
          AB is DOUBLE PRECISION array, dimension (LDAB,N)
          The upper or lower triangular band matrix A, stored in the
          first kd+1 rows of the array. The j-th column of A is stored
          in the j-th column of the array AB as follows:
          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
[in]LDAB
          LDAB is INTEGER
          The leading dimension of the array AB.  LDAB >= KD+1.
[in]X
          X is DOUBLE PRECISION array, dimension (LDX,NRHS)
          The computed solution vectors for the system of linear
          equations.
[in]LDX
          LDX is INTEGER
          The leading dimension of the array X.  LDX >= max(1,N).
[in]B
          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
          The right hand side vectors for the system of linear
          equations.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (N)
[out]RESID
          RESID is DOUBLE PRECISION
          The maximum over the number of right hand sides of
          norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ).
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dtbt03 ( character  UPLO,
character  TRANS,
character  DIAG,
integer  N,
integer  KD,
integer  NRHS,
double precision, dimension( ldab, * )  AB,
integer  LDAB,
double precision  SCALE,
double precision, dimension( * )  CNORM,
double precision  TSCAL,
double precision, dimension( ldx, * )  X,
integer  LDX,
double precision, dimension( ldb, * )  B,
integer  LDB,
double precision, dimension( * )  WORK,
double precision  RESID 
)

DTBT03

Purpose:
 DTBT03 computes the residual for the solution to a scaled triangular
 system of equations  A*x = s*b  or  A'*x = s*b  when A is a
 triangular band matrix. Here A' is the transpose of A, s is a scalar,
 and x and b are N by NRHS matrices.  The test ratio is the maximum
 over the number of right hand sides of
    norm(s*b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
 where op(A) denotes A or A' and EPS is the machine epsilon.
Parameters
[in]UPLO
          UPLO is CHARACTER*1
          Specifies whether the matrix A is upper or lower triangular.
          = 'U':  Upper triangular
          = 'L':  Lower triangular
[in]TRANS
          TRANS is CHARACTER*1
          Specifies the operation applied to A.
          = 'N':  A *x = b  (No transpose)
          = 'T':  A'*x = b  (Transpose)
          = 'C':  A'*x = b  (Conjugate transpose = Transpose)
[in]DIAG
          DIAG is CHARACTER*1
          Specifies whether or not the matrix A is unit triangular.
          = 'N':  Non-unit triangular
          = 'U':  Unit triangular
[in]N
          N is INTEGER
          The order of the matrix A.  N >= 0.
[in]KD
          KD is INTEGER
          The number of superdiagonals or subdiagonals of the
          triangular band matrix A.  KD >= 0.
[in]NRHS
          NRHS is INTEGER
          The number of right hand sides, i.e., the number of columns
          of the matrices X and B.  NRHS >= 0.
[in]AB
          AB is DOUBLE PRECISION array, dimension (LDAB,N)
          The upper or lower triangular band matrix A, stored in the
          first kd+1 rows of the array. The j-th column of A is stored
          in the j-th column of the array AB as follows:
          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
[in]LDAB
          LDAB is INTEGER
          The leading dimension of the array AB.  LDAB >= KD+1.
[in]SCALE
          SCALE is DOUBLE PRECISION
          The scaling factor s used in solving the triangular system.
[in]CNORM
          CNORM is DOUBLE PRECISION array, dimension (N)
          The 1-norms of the columns of A, not counting the diagonal.
[in]TSCAL
          TSCAL is DOUBLE PRECISION
          The scaling factor used in computing the 1-norms in CNORM.
          CNORM actually contains the column norms of TSCAL*A.
[in]X
          X is DOUBLE PRECISION array, dimension (LDX,NRHS)
          The computed solution vectors for the system of linear
          equations.
[in]LDX
          LDX is INTEGER
          The leading dimension of the array X.  LDX >= max(1,N).
[in]B
          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
          The right hand side vectors for the system of linear
          equations.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (N)
[out]RESID
          RESID is DOUBLE PRECISION
          The maximum over the number of right hand sides of
          norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ).
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dtbt05 ( character  UPLO,
character  TRANS,
character  DIAG,
integer  N,
integer  KD,
integer  NRHS,
double precision, dimension( ldab, * )  AB,
integer  LDAB,
double precision, dimension( ldb, * )  B,
integer  LDB,
double precision, dimension( ldx, * )  X,
integer  LDX,
double precision, dimension( ldxact, * )  XACT,
integer  LDXACT,
double precision, dimension( * )  FERR,
double precision, dimension( * )  BERR,
double precision, dimension( * )  RESLTS 
)

DTBT05

Purpose:
 DTBT05 tests the error bounds from iterative refinement for the
 computed solution to a system of equations A*X = B, where A is a
 triangular band matrix.

 RESLTS(1) = test of the error bound
           = norm(X - XACT) / ( norm(X) * FERR )

 A large value is returned if this ratio is not less than one.

 RESLTS(2) = residual from the iterative refinement routine
           = the maximum of BERR / ( NZ*EPS + (*) ), where
             (*) = NZ*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
             and NZ = max. number of nonzeros in any row of A, plus 1
Parameters
[in]UPLO
          UPLO is CHARACTER*1
          Specifies whether the matrix A is upper or lower triangular.
          = 'U':  Upper triangular
          = 'L':  Lower triangular
[in]TRANS
          TRANS is CHARACTER*1
          Specifies the form of the system of equations.
          = 'N':  A * X = B  (No transpose)
          = 'T':  A'* X = B  (Transpose)
          = 'C':  A'* X = B  (Conjugate transpose = Transpose)
[in]DIAG
          DIAG is CHARACTER*1
          Specifies whether or not the matrix A is unit triangular.
          = 'N':  Non-unit triangular
          = 'U':  Unit triangular
[in]N
          N is INTEGER
          The number of rows of the matrices X, B, and XACT, and the
          order of the matrix A.  N >= 0.
[in]KD
          KD is INTEGER
          The number of super-diagonals of the matrix A if UPLO = 'U',
          or the number of sub-diagonals if UPLO = 'L'.  KD >= 0.
[in]NRHS
          NRHS is INTEGER
          The number of columns of the matrices X, B, and XACT.
          NRHS >= 0.
[in]AB
          AB is DOUBLE PRECISION array, dimension (LDAB,N)
          The upper or lower triangular band matrix A, stored in the
          first kd+1 rows of the array. The j-th column of A is stored
          in the j-th column of the array AB as follows:
          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
          If DIAG = 'U', the diagonal elements of A are not referenced
          and are assumed to be 1.
[in]LDAB
          LDAB is INTEGER
          The leading dimension of the array AB.  LDAB >= KD+1.
[in]B
          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
          The right hand side vectors for the system of linear
          equations.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).
[in]X
          X is DOUBLE PRECISION array, dimension (LDX,NRHS)
          The computed solution vectors.  Each vector is stored as a
          column of the matrix X.
[in]LDX
          LDX is INTEGER
          The leading dimension of the array X.  LDX >= max(1,N).
[in]XACT
          XACT is DOUBLE PRECISION array, dimension (LDX,NRHS)
          The exact solution vectors.  Each vector is stored as a
          column of the matrix XACT.
[in]LDXACT
          LDXACT is INTEGER
          The leading dimension of the array XACT.  LDXACT >= max(1,N).
[in]FERR
          FERR is DOUBLE PRECISION array, dimension (NRHS)
          The estimated forward error bounds for each solution vector
          X.  If XTRUE is the true solution, FERR bounds the magnitude
          of the largest entry in (X - XTRUE) divided by the magnitude
          of the largest entry in X.
[in]BERR
          BERR is DOUBLE PRECISION array, dimension (NRHS)
          The componentwise relative backward error of each solution
          vector (i.e., the smallest relative change in any entry of A
          or B that makes X an exact solution).
[out]RESLTS
          RESLTS is DOUBLE PRECISION array, dimension (2)
          The maximum over the NRHS solution vectors of the ratios:
          RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
          RESLTS(2) = BERR / ( NZ*EPS + (*) )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dtbt06 ( double precision  RCOND,
double precision  RCONDC,
character  UPLO,
character  DIAG,
integer  N,
integer  KD,
double precision, dimension( ldab, * )  AB,
integer  LDAB,
double precision, dimension( * )  WORK,
double precision  RAT 
)

DTBT06

Purpose:
 DTBT06 computes a test ratio comparing RCOND (the reciprocal
 condition number of a triangular matrix A) and RCONDC, the estimate
 computed by DTBCON.  Information about the triangular matrix A is
 used if one estimate is zero and the other is non-zero to decide if
 underflow in the estimate is justified.
Parameters
[in]RCOND
          RCOND is DOUBLE PRECISION
          The estimate of the reciprocal condition number obtained by
          forming the explicit inverse of the matrix A and computing
          RCOND = 1/( norm(A) * norm(inv(A)) ).
[in]RCONDC
          RCONDC is DOUBLE PRECISION
          The estimate of the reciprocal condition number computed by
          DTBCON.
[in]UPLO
          UPLO is CHARACTER
          Specifies whether the matrix A is upper or lower triangular.
          = 'U':  Upper triangular
          = 'L':  Lower triangular
[in]DIAG
          DIAG is CHARACTER
          Specifies whether or not the matrix A is unit triangular.
          = 'N':  Non-unit triangular
          = 'U':  Unit triangular
[in]N
          N is INTEGER
          The order of the matrix A.  N >= 0.
[in]KD
          KD is INTEGER
          The number of superdiagonals or subdiagonals of the
          triangular band matrix A.  KD >= 0.
[in]AB
          AB is DOUBLE PRECISION array, dimension (LDAB,N)
          The upper or lower triangular band matrix A, stored in the
          first kd+1 rows of the array. The j-th column of A is stored
          in the j-th column of the array AB as follows:
          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
[in]LDAB
          LDAB is INTEGER
          The leading dimension of the array AB.  LDAB >= KD+1.
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (N)
[out]RAT
          RAT is DOUBLE PRECISION
          The test ratio.  If both RCOND and RCONDC are nonzero,
             RAT = MAX( RCOND, RCONDC )/MIN( RCOND, RCONDC ) - 1.
          If RAT = 0, the two estimates are exactly the same.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dtpt01 ( character  UPLO,
character  DIAG,
integer  N,
double precision, dimension( * )  AP,
double precision, dimension( * )  AINVP,
double precision  RCOND,
double precision, dimension( * )  WORK,
double precision  RESID 
)

DTPT01

Purpose:
 DTPT01 computes the residual for a triangular matrix A times its
 inverse when A is stored in packed format:
    RESID = norm(A*AINV - I) / ( N * norm(A) * norm(AINV) * EPS ),
 where EPS is the machine epsilon.
Parameters
[in]UPLO
          UPLO is CHARACTER*1
          Specifies whether the matrix A is upper or lower triangular.
          = 'U':  Upper triangular
          = 'L':  Lower triangular
[in]DIAG
          DIAG is CHARACTER*1
          Specifies whether or not the matrix A is unit triangular.
          = 'N':  Non-unit triangular
          = 'U':  Unit triangular
[in]N
          N is INTEGER
          The order of the matrix A.  N >= 0.
[in]AP
          AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
          The original upper or lower triangular matrix A, packed
          columnwise in a linear array.  The j-th column of A is stored
          in the array AP as follows:
          if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j;
          if UPLO = 'L',
             AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n.
[in,out]AINVP
          AINVP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
          On entry, the (triangular) inverse of the matrix A, packed
          columnwise in a linear array as in AP.
          On exit, the contents of AINVP are destroyed.
[out]RCOND
          RCOND is DOUBLE PRECISION
          The reciprocal condition number of A, computed as
          1/(norm(A) * norm(AINV)).
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (N)
[out]RESID
          RESID is DOUBLE PRECISION
          norm(A*AINV - I) / ( N * norm(A) * norm(AINV) * EPS )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dtpt02 ( character  UPLO,
character  TRANS,
character  DIAG,
integer  N,
integer  NRHS,
double precision, dimension( * )  AP,
double precision, dimension( ldx, * )  X,
integer  LDX,
double precision, dimension( ldb, * )  B,
integer  LDB,
double precision, dimension( * )  WORK,
double precision  RESID 
)

DTPT02

Purpose:
 DTPT02 computes the residual for the computed solution to a
 triangular system of linear equations  A*x = b  or  A'*x = b  when
 the triangular matrix A is stored in packed format.  Here A' is the
 transpose of A and x and b are N by NRHS matrices.  The test ratio is
 the maximum over the number of right hand sides of
    norm(b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
 where op(A) denotes A or A' and EPS is the machine epsilon.
Parameters
[in]UPLO
          UPLO is CHARACTER*1
          Specifies whether the matrix A is upper or lower triangular.
          = 'U':  Upper triangular
          = 'L':  Lower triangular
[in]TRANS
          TRANS is CHARACTER*1
          Specifies the operation applied to A.
          = 'N':  A *x = b  (No transpose)
          = 'T':  A'*x = b  (Transpose)
          = 'C':  A'*x = b  (Conjugate transpose = Transpose)
[in]DIAG
          DIAG is CHARACTER*1
          Specifies whether or not the matrix A is unit triangular.
          = 'N':  Non-unit triangular
          = 'U':  Unit triangular
[in]N
          N is INTEGER
          The order of the matrix A.  N >= 0.
[in]NRHS
          NRHS is INTEGER
          The number of right hand sides, i.e., the number of columns
          of the matrices X and B.  NRHS >= 0.
[in]AP
          AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
          The upper or lower triangular matrix A, packed columnwise in
          a linear array.  The j-th column of A is stored in the array
          AP as follows:
          if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j;
          if UPLO = 'L',
             AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n.
[in]X
          X is DOUBLE PRECISION array, dimension (LDX,NRHS)
          The computed solution vectors for the system of linear
          equations.
[in]LDX
          LDX is INTEGER
          The leading dimension of the array X.  LDX >= max(1,N).
[in]B
          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
          The right hand side vectors for the system of linear
          equations.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (N)
[out]RESID
          RESID is DOUBLE PRECISION
          The maximum over the number of right hand sides of
          norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ).
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dtpt03 ( character  UPLO,
character  TRANS,
character  DIAG,
integer  N,
integer  NRHS,
double precision, dimension( * )  AP,
double precision  SCALE,
double precision, dimension( * )  CNORM,
double precision  TSCAL,
double precision, dimension( ldx, * )  X,
integer  LDX,
double precision, dimension( ldb, * )  B,
integer  LDB,
double precision, dimension( * )  WORK,
double precision  RESID 
)

DTPT03

Purpose:
 DTPT03 computes the residual for the solution to a scaled triangular
 system of equations A*x = s*b  or  A'*x = s*b  when the triangular
 matrix A is stored in packed format.  Here A' is the transpose of A,
 s is a scalar, and x and b are N by NRHS matrices.  The test ratio is
 the maximum over the number of right hand sides of
    norm(s*b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
 where op(A) denotes A or A' and EPS is the machine epsilon.
Parameters
[in]UPLO
          UPLO is CHARACTER*1
          Specifies whether the matrix A is upper or lower triangular.
          = 'U':  Upper triangular
          = 'L':  Lower triangular
[in]TRANS
          TRANS is CHARACTER*1
          Specifies the operation applied to A.
          = 'N':  A *x = s*b  (No transpose)
          = 'T':  A'*x = s*b  (Transpose)
          = 'C':  A'*x = s*b  (Conjugate transpose = Transpose)
[in]DIAG
          DIAG is CHARACTER*1
          Specifies whether or not the matrix A is unit triangular.
          = 'N':  Non-unit triangular
          = 'U':  Unit triangular
[in]N
          N is INTEGER
          The order of the matrix A.  N >= 0.
[in]NRHS
          NRHS is INTEGER
          The number of right hand sides, i.e., the number of columns
          of the matrices X and B.  NRHS >= 0.
[in]AP
          AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
          The upper or lower triangular matrix A, packed columnwise in
          a linear array.  The j-th column of A is stored in the array
          AP as follows:
          if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j;
          if UPLO = 'L',
             AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n.
[in]SCALE
          SCALE is DOUBLE PRECISION
          The scaling factor s used in solving the triangular system.
[in]CNORM
          CNORM is DOUBLE PRECISION array, dimension (N)
          The 1-norms of the columns of A, not counting the diagonal.
[in]TSCAL
          TSCAL is DOUBLE PRECISION
          The scaling factor used in computing the 1-norms in CNORM.
          CNORM actually contains the column norms of TSCAL*A.
[in]X
          X is DOUBLE PRECISION array, dimension (LDX,NRHS)
          The computed solution vectors for the system of linear
          equations.
[in]LDX
          LDX is INTEGER
          The leading dimension of the array X.  LDX >= max(1,N).
[in]B
          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
          The right hand side vectors for the system of linear
          equations.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (N)
[out]RESID
          RESID is DOUBLE PRECISION
          The maximum over the number of right hand sides of
          norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ).
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dtpt05 ( character  UPLO,
character  TRANS,
character  DIAG,
integer  N,
integer  NRHS,
double precision, dimension( * )  AP,
double precision, dimension( ldb, * )  B,
integer  LDB,
double precision, dimension( ldx, * )  X,
integer  LDX,
double precision, dimension( ldxact, * )  XACT,
integer  LDXACT,
double precision, dimension( * )  FERR,
double precision, dimension( * )  BERR,
double precision, dimension( * )  RESLTS 
)

DTPT05

Purpose:
 DTPT05 tests the error bounds from iterative refinement for the
 computed solution to a system of equations A*X = B, where A is a
 triangular matrix in packed storage format.

 RESLTS(1) = test of the error bound
           = norm(X - XACT) / ( norm(X) * FERR )

 A large value is returned if this ratio is not less than one.

 RESLTS(2) = residual from the iterative refinement routine
           = the maximum of BERR / ( (n+1)*EPS + (*) ), where
             (*) = (n+1)*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
Parameters
[in]UPLO
          UPLO is CHARACTER*1
          Specifies whether the matrix A is upper or lower triangular.
          = 'U':  Upper triangular
          = 'L':  Lower triangular
[in]TRANS
          TRANS is CHARACTER*1
          Specifies the form of the system of equations.
          = 'N':  A * X = B  (No transpose)
          = 'T':  A'* X = B  (Transpose)
          = 'C':  A'* X = B  (Conjugate transpose = Transpose)
[in]DIAG
          DIAG is CHARACTER*1
          Specifies whether or not the matrix A is unit triangular.
          = 'N':  Non-unit triangular
          = 'U':  Unit triangular
[in]N
          N is INTEGER
          The number of rows of the matrices X, B, and XACT, and the
          order of the matrix A.  N >= 0.
[in]NRHS
          NRHS is INTEGER
          The number of columns of the matrices X, B, and XACT.
          NRHS >= 0.
[in]AP
          AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
          The upper or lower triangular matrix A, packed columnwise in
          a linear array.  The j-th column of A is stored in the array
          AP as follows:
          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
          If DIAG = 'U', the diagonal elements of A are not referenced
          and are assumed to be 1.
[in]B
          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
          The right hand side vectors for the system of linear
          equations.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).
[in]X
          X is DOUBLE PRECISION array, dimension (LDX,NRHS)
          The computed solution vectors.  Each vector is stored as a
          column of the matrix X.
[in]LDX
          LDX is INTEGER
          The leading dimension of the array X.  LDX >= max(1,N).
[in]XACT
          XACT is DOUBLE PRECISION array, dimension (LDX,NRHS)
          The exact solution vectors.  Each vector is stored as a
          column of the matrix XACT.
[in]LDXACT
          LDXACT is INTEGER
          The leading dimension of the array XACT.  LDXACT >= max(1,N).
[in]FERR
          FERR is DOUBLE PRECISION array, dimension (NRHS)
          The estimated forward error bounds for each solution vector
          X.  If XTRUE is the true solution, FERR bounds the magnitude
          of the largest entry in (X - XTRUE) divided by the magnitude
          of the largest entry in X.
[in]BERR
          BERR is DOUBLE PRECISION array, dimension (NRHS)
          The componentwise relative backward error of each solution
          vector (i.e., the smallest relative change in any entry of A
          or B that makes X an exact solution).
[out]RESLTS
          RESLTS is DOUBLE PRECISION array, dimension (2)
          The maximum over the NRHS solution vectors of the ratios:
          RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
          RESLTS(2) = BERR / ( (n+1)*EPS + (*) )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dtpt06 ( double precision  RCOND,
double precision  RCONDC,
character  UPLO,
character  DIAG,
integer  N,
double precision, dimension( * )  AP,
double precision, dimension( * )  WORK,
double precision  RAT 
)

DTPT06

Purpose:
 DTPT06 computes a test ratio comparing RCOND (the reciprocal
 condition number of a triangular matrix A) and RCONDC, the estimate
 computed by DTPCON.  Information about the triangular matrix A is
 used if one estimate is zero and the other is non-zero to decide if
 underflow in the estimate is justified.
Parameters
[in]RCOND
          RCOND is DOUBLE PRECISION
          The estimate of the reciprocal condition number obtained by
          forming the explicit inverse of the matrix A and computing
          RCOND = 1/( norm(A) * norm(inv(A)) ).
[in]RCONDC
          RCONDC is DOUBLE PRECISION
          The estimate of the reciprocal condition number computed by
          DTPCON.
[in]UPLO
          UPLO is CHARACTER
          Specifies whether the matrix A is upper or lower triangular.
          = 'U':  Upper triangular
          = 'L':  Lower triangular
[in]DIAG
          DIAG is CHARACTER
          Specifies whether or not the matrix A is unit triangular.
          = 'N':  Non-unit triangular
          = 'U':  Unit triangular
[in]N
          N is INTEGER
          The order of the matrix A.  N >= 0.
[in]AP
          AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
          The upper or lower triangular matrix A, packed columnwise in
          a linear array.  The j-th column of A is stored in the array
          AP as follows:
          if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j;
          if UPLO = 'L',
             AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n.
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (N)
[out]RAT
          RAT is DOUBLE PRECISION
          The test ratio.  If both RCOND and RCONDC are nonzero,
             RAT = MAX( RCOND, RCONDC )/MIN( RCOND, RCONDC ) - 1.
          If RAT = 0, the two estimates are exactly the same.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dtrt01 ( character  UPLO,
character  DIAG,
integer  N,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( ldainv, * )  AINV,
integer  LDAINV,
double precision  RCOND,
double precision, dimension( * )  WORK,
double precision  RESID 
)

DTRT01

Purpose:
 DTRT01 computes the residual for a triangular matrix A times its
 inverse:
    RESID = norm( A*AINV - I ) / ( N * norm(A) * norm(AINV) * EPS ),
 where EPS is the machine epsilon.
Parameters
[in]UPLO
          UPLO is CHARACTER*1
          Specifies whether the matrix A is upper or lower triangular.
          = 'U':  Upper triangular
          = 'L':  Lower triangular
[in]DIAG
          DIAG is CHARACTER*1
          Specifies whether or not the matrix A is unit triangular.
          = 'N':  Non-unit triangular
          = 'U':  Unit triangular
[in]N
          N is INTEGER
          The order of the matrix A.  N >= 0.
[in]A
          A is DOUBLE PRECISION array, dimension (LDA,N)
          The triangular matrix A.  If UPLO = 'U', the leading n by n
          upper triangular part of the array A contains the upper
          triangular matrix, and the strictly lower triangular part of
          A is not referenced.  If UPLO = 'L', the leading n by n lower
          triangular part of the array A contains the lower triangular
          matrix, and the strictly upper triangular part of A is not
          referenced.  If DIAG = 'U', the diagonal elements of A are
          also not referenced and are assumed to be 1.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).
[in,out]AINV
          AINV is DOUBLE PRECISION array, dimension (LDAINV,N)
          On entry, the (triangular) inverse of the matrix A, in the
          same storage format as A.
          On exit, the contents of AINV are destroyed.
[in]LDAINV
          LDAINV is INTEGER
          The leading dimension of the array AINV.  LDAINV >= max(1,N).
[out]RCOND
          RCOND is DOUBLE PRECISION
          The reciprocal condition number of A, computed as
          1/(norm(A) * norm(AINV)).
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (N)
[out]RESID
          RESID is DOUBLE PRECISION
          norm(A*AINV - I) / ( N * norm(A) * norm(AINV) * EPS )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dtrt02 ( character  UPLO,
character  TRANS,
character  DIAG,
integer  N,
integer  NRHS,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( ldx, * )  X,
integer  LDX,
double precision, dimension( ldb, * )  B,
integer  LDB,
double precision, dimension( * )  WORK,
double precision  RESID 
)

DTRT02

Purpose:
 DTRT02 computes the residual for the computed solution to a
 triangular system of linear equations  A*x = b  or  A'*x = b.
 Here A is a triangular matrix, A' is the transpose of A, and x and b
 are N by NRHS matrices.  The test ratio is the maximum over the
 number of right hand sides of
    norm(b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
 where op(A) denotes A or A' and EPS is the machine epsilon.
Parameters
[in]UPLO
          UPLO is CHARACTER*1
          Specifies whether the matrix A is upper or lower triangular.
          = 'U':  Upper triangular
          = 'L':  Lower triangular
[in]TRANS
          TRANS is CHARACTER*1
          Specifies the operation applied to A.
          = 'N':  A *x = b  (No transpose)
          = 'T':  A'*x = b  (Transpose)
          = 'C':  A'*x = b  (Conjugate transpose = Transpose)
[in]DIAG
          DIAG is CHARACTER*1
          Specifies whether or not the matrix A is unit triangular.
          = 'N':  Non-unit triangular
          = 'U':  Unit triangular
[in]N
          N is INTEGER
          The order of the matrix A.  N >= 0.
[in]NRHS
          NRHS is INTEGER
          The number of right hand sides, i.e., the number of columns
          of the matrices X and B.  NRHS >= 0.
[in]A
          A is DOUBLE PRECISION array, dimension (LDA,N)
          The triangular matrix A.  If UPLO = 'U', the leading n by n
          upper triangular part of the array A contains the upper
          triangular matrix, and the strictly lower triangular part of
          A is not referenced.  If UPLO = 'L', the leading n by n lower
          triangular part of the array A contains the lower triangular
          matrix, and the strictly upper triangular part of A is not
          referenced.  If DIAG = 'U', the diagonal elements of A are
          also not referenced and are assumed to be 1.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).
[in]X
          X is DOUBLE PRECISION array, dimension (LDX,NRHS)
          The computed solution vectors for the system of linear
          equations.
[in]LDX
          LDX is INTEGER
          The leading dimension of the array X.  LDX >= max(1,N).
[in]B
          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
          The right hand side vectors for the system of linear
          equations.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (N)
[out]RESID
          RESID is DOUBLE PRECISION
          The maximum over the number of right hand sides of
          norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ).
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dtrt03 ( character  UPLO,
character  TRANS,
character  DIAG,
integer  N,
integer  NRHS,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision  SCALE,
double precision, dimension( * )  CNORM,
double precision  TSCAL,
double precision, dimension( ldx, * )  X,
integer  LDX,
double precision, dimension( ldb, * )  B,
integer  LDB,
double precision, dimension( * )  WORK,
double precision  RESID 
)

DTRT03

Purpose:
 DTRT03 computes the residual for the solution to a scaled triangular
 system of equations A*x = s*b  or  A'*x = s*b.
 Here A is a triangular matrix, A' is the transpose of A, s is a
 scalar, and x and b are N by NRHS matrices.  The test ratio is the
 maximum over the number of right hand sides of
    norm(s*b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
 where op(A) denotes A or A' and EPS is the machine epsilon.
Parameters
[in]UPLO
          UPLO is CHARACTER*1
          Specifies whether the matrix A is upper or lower triangular.
          = 'U':  Upper triangular
          = 'L':  Lower triangular
[in]TRANS
          TRANS is CHARACTER*1
          Specifies the operation applied to A.
          = 'N':  A *x = s*b  (No transpose)
          = 'T':  A'*x = s*b  (Transpose)
          = 'C':  A'*x = s*b  (Conjugate transpose = Transpose)
[in]DIAG
          DIAG is CHARACTER*1
          Specifies whether or not the matrix A is unit triangular.
          = 'N':  Non-unit triangular
          = 'U':  Unit triangular
[in]N
          N is INTEGER
          The order of the matrix A.  N >= 0.
[in]NRHS
          NRHS is INTEGER
          The number of right hand sides, i.e., the number of columns
          of the matrices X and B.  NRHS >= 0.
[in]A
          A is DOUBLE PRECISION array, dimension (LDA,N)
          The triangular matrix A.  If UPLO = 'U', the leading n by n
          upper triangular part of the array A contains the upper
          triangular matrix, and the strictly lower triangular part of
          A is not referenced.  If UPLO = 'L', the leading n by n lower
          triangular part of the array A contains the lower triangular
          matrix, and the strictly upper triangular part of A is not
          referenced.  If DIAG = 'U', the diagonal elements of A are
          also not referenced and are assumed to be 1.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).
[in]SCALE
          SCALE is DOUBLE PRECISION
          The scaling factor s used in solving the triangular system.
[in]CNORM
          CNORM is DOUBLE PRECISION array, dimension (N)
          The 1-norms of the columns of A, not counting the diagonal.
[in]TSCAL
          TSCAL is DOUBLE PRECISION
          The scaling factor used in computing the 1-norms in CNORM.
          CNORM actually contains the column norms of TSCAL*A.
[in]X
          X is DOUBLE PRECISION array, dimension (LDX,NRHS)
          The computed solution vectors for the system of linear
          equations.
[in]LDX
          LDX is INTEGER
          The leading dimension of the array X.  LDX >= max(1,N).
[in]B
          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
          The right hand side vectors for the system of linear
          equations.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (N)
[out]RESID
          RESID is DOUBLE PRECISION
          The maximum over the number of right hand sides of
          norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ).
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dtrt05 ( character  UPLO,
character  TRANS,
character  DIAG,
integer  N,
integer  NRHS,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( ldb, * )  B,
integer  LDB,
double precision, dimension( ldx, * )  X,
integer  LDX,
double precision, dimension( ldxact, * )  XACT,
integer  LDXACT,
double precision, dimension( * )  FERR,
double precision, dimension( * )  BERR,
double precision, dimension( * )  RESLTS 
)

DTRT05

Purpose:
 DTRT05 tests the error bounds from iterative refinement for the
 computed solution to a system of equations A*X = B, where A is a
 triangular n by n matrix.

 RESLTS(1) = test of the error bound
           = norm(X - XACT) / ( norm(X) * FERR )

 A large value is returned if this ratio is not less than one.

 RESLTS(2) = residual from the iterative refinement routine
           = the maximum of BERR / ( (n+1)*EPS + (*) ), where
             (*) = (n+1)*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
Parameters
[in]UPLO
          UPLO is CHARACTER*1
          Specifies whether the matrix A is upper or lower triangular.
          = 'U':  Upper triangular
          = 'L':  Lower triangular
[in]TRANS
          TRANS is CHARACTER*1
          Specifies the form of the system of equations.
          = 'N':  A * X = B  (No transpose)
          = 'T':  A'* X = B  (Transpose)
          = 'C':  A'* X = B  (Conjugate transpose = Transpose)
[in]DIAG
          DIAG is CHARACTER*1
          Specifies whether or not the matrix A is unit triangular.
          = 'N':  Non-unit triangular
          = 'U':  Unit triangular
[in]N
          N is INTEGER
          The number of rows of the matrices X, B, and XACT, and the
          order of the matrix A.  N >= 0.
[in]NRHS
          NRHS is INTEGER
          The number of columns of the matrices X, B, and XACT.
          NRHS >= 0.
[in]A
          A is DOUBLE PRECISION array, dimension (LDA,N)
          The triangular matrix A.  If UPLO = 'U', the leading n by n
          upper triangular part of the array A contains the upper
          triangular matrix, and the strictly lower triangular part of
          A is not referenced.  If UPLO = 'L', the leading n by n lower
          triangular part of the array A contains the lower triangular
          matrix, and the strictly upper triangular part of A is not
          referenced.  If DIAG = 'U', the diagonal elements of A are
          also not referenced and are assumed to be 1.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).
[in]B
          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
          The right hand side vectors for the system of linear
          equations.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).
[in]X
          X is DOUBLE PRECISION array, dimension (LDX,NRHS)
          The computed solution vectors.  Each vector is stored as a
          column of the matrix X.
[in]LDX
          LDX is INTEGER
          The leading dimension of the array X.  LDX >= max(1,N).
[in]XACT
          XACT is DOUBLE PRECISION array, dimension (LDX,NRHS)
          The exact solution vectors.  Each vector is stored as a
          column of the matrix XACT.
[in]LDXACT
          LDXACT is INTEGER
          The leading dimension of the array XACT.  LDXACT >= max(1,N).
[in]FERR
          FERR is DOUBLE PRECISION array, dimension (NRHS)
          The estimated forward error bounds for each solution vector
          X.  If XTRUE is the true solution, FERR bounds the magnitude
          of the largest entry in (X - XTRUE) divided by the magnitude
          of the largest entry in X.
[in]BERR
          BERR is DOUBLE PRECISION array, dimension (NRHS)
          The componentwise relative backward error of each solution
          vector (i.e., the smallest relative change in any entry of A
          or B that makes X an exact solution).
[out]RESLTS
          RESLTS is DOUBLE PRECISION array, dimension (2)
          The maximum over the NRHS solution vectors of the ratios:
          RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
          RESLTS(2) = BERR / ( (n+1)*EPS + (*) )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine dtrt06 ( double precision  RCOND,
double precision  RCONDC,
character  UPLO,
character  DIAG,
integer  N,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( * )  WORK,
double precision  RAT 
)

DTRT06

Purpose:
 DTRT06 computes a test ratio comparing RCOND (the reciprocal
 condition number of a triangular matrix A) and RCONDC, the estimate
 computed by DTRCON.  Information about the triangular matrix A is
 used if one estimate is zero and the other is non-zero to decide if
 underflow in the estimate is justified.
Parameters
[in]RCOND
          RCOND is DOUBLE PRECISION
          The estimate of the reciprocal condition number obtained by
          forming the explicit inverse of the matrix A and computing
          RCOND = 1/( norm(A) * norm(inv(A)) ).
[in]RCONDC
          RCONDC is DOUBLE PRECISION
          The estimate of the reciprocal condition number computed by
          DTRCON.
[in]UPLO
          UPLO is CHARACTER
          Specifies whether the matrix A is upper or lower triangular.
          = 'U':  Upper triangular
          = 'L':  Lower triangular
[in]DIAG
          DIAG is CHARACTER
          Specifies whether or not the matrix A is unit triangular.
          = 'N':  Non-unit triangular
          = 'U':  Unit triangular
[in]N
          N is INTEGER
          The order of the matrix A.  N >= 0.
[in]A
          A is DOUBLE PRECISION array, dimension (LDA,N)
          The triangular matrix A.  If UPLO = 'U', the leading n by n
          upper triangular part of the array A contains the upper
          triangular matrix, and the strictly lower triangular part of
          A is not referenced.  If UPLO = 'L', the leading n by n lower
          triangular part of the array A contains the lower triangular
          matrix, and the strictly upper triangular part of A is not
          referenced.  If DIAG = 'U', the diagonal elements of A are
          also not referenced and are assumed to be 1.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (N)
[out]RAT
          RAT is DOUBLE PRECISION
          The test ratio.  If both RCOND and RCONDC are nonzero,
             RAT = MAX( RCOND, RCONDC )/MIN( RCOND, RCONDC ) - 1.
          If RAT = 0, the two estimates are exactly the same.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
subroutine sdrvsy_rook ( logical, dimension( * )  DOTYPE,
integer  NN,
integer, dimension( * )  NVAL,
integer  NRHS,
real  THRESH,
logical  TSTERR,
integer  NMAX,
real, dimension( * )  A,
real, dimension( * )  AFAC,
real, dimension( * )  AINV,
real, dimension( * )  B,
real, dimension( * )  X,
real, dimension( * )  XACT,
real, dimension( * )  WORK,
real, dimension( * )  RWORK,
integer, dimension( * )  IWORK,
integer  NOUT 
)

SDRVSY_ROOK

Purpose:
 SDRVSY_ROOK tests the driver routines SSYSV_ROOK.
Parameters
[in]DOTYPE
          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
[in]NN
          NN is INTEGER
          The number of values of N contained in the vector NVAL.
[in]NVAL
          NVAL is INTEGER array, dimension (NN)
          The values of the matrix dimension N.
[in]NRHS
          NRHS is INTEGER
          The number of right hand side vectors to be generated for
          each linear system.
[in]THRESH
          THRESH is DOUBLE PRECISION
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.
[in]TSTERR
          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.
[in]NMAX
          NMAX is INTEGER
          The maximum value permitted for N, used in dimensioning the
          work arrays.
[out]A
          A is REAL array, dimension (NMAX*NMAX)
[out]AFAC
          AFAC is REAL array, dimension (NMAX*NMAX)
[out]AINV
          AINV is REAL array, dimension (NMAX*NMAX)
[out]B
          B is REAL array, dimension (NMAX*NRHS)
[out]X
          X is REAL array, dimension (NMAX*NRHS)
[out]XACT
          XACT is REAL array, dimension (NMAX*NRHS)
[out]WORK
          WORK is REAL array, dimension
                      (NMAX*max(2,NRHS))
[out]RWORK
          RWORK is REAL array, dimension (NMAX+2*NRHS)
[out]IWORK
          IWORK is INTEGER array, dimension (2*NMAX)
[in]NOUT
          NOUT is INTEGER
          The unit number for output.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2013