LAPACK
3.4.2
LAPACK: Linear Algebra PACKage
|
Functions/Subroutines | |
program | dchkaa |
DCHKAA | |
program | dchkab |
DCHKAB | |
subroutine | dchkeq (THRESH, NOUT) |
DCHKEQ | |
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 | |
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 | |
subroutine | dchkgt (DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR, A, AF, B, X, XACT, WORK, RWORK, IWORK, NOUT) |
DCHKGT | |
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 | |
subroutine | dchkpb (DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT) |
DCHKPB | |
subroutine | dchkpo (DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT) |
DCHKPO | |
subroutine | dchkpp (DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT) |
DCHKPP | |
subroutine | dchkps (DOTYPE, NN, NVAL, NNB, NBVAL, NRANK, RANKVAL, THRESH, TSTERR, NMAX, A, AFAC, PERM, PIV, WORK, RWORK, NOUT) |
DCHKPS | |
subroutine | dchkpt (DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR, A, D, E, B, X, XACT, WORK, RWORK, NOUT) |
DCHKPT | |
subroutine | dchkq3 (DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NXVAL, THRESH, A, COPYA, S, TAU, WORK, IWORK, NOUT) |
DCHKQ3 | |
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, IWORK, NOUT) |
DCHKQL | |
subroutine | dchkqp (DOTYPE, NM, MVAL, NN, NVAL, THRESH, TSTERR, A, COPYA, S, TAU, WORK, IWORK, NOUT) |
DCHKQP | |
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 | |
subroutine | dchkqrt (THRESH, TSTERR, NM, MVAL, NN, NVAL, NNB, NBVAL, NOUT) |
DCHKQRT | |
subroutine | dchkqrtp (THRESH, TSTERR, NM, MVAL, NN, NVAL, NNB, NBVAL, NOUT) |
DCHKQRTP | |
program | dchkrfp |
DCHKRFP | |
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 | |
subroutine | dchksp (DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT) |
DCHKSP | |
subroutine | dchksy (DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT) |
DCHKSY | |
subroutine | dchktb (DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, AB, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT) |
DCHKTB | |
subroutine | dchktp (DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, AP, AINVP, B, X, XACT, WORK, RWORK, IWORK, NOUT) |
DCHKTP | |
subroutine | dchktr (DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, A, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT) |
DCHKTR | |
subroutine | dchktz (DOTYPE, NM, MVAL, NN, NVAL, THRESH, TSTERR, A, COPYA, S, TAU, WORK, NOUT) |
DCHKTZ | |
subroutine | ddrvab (DOTYPE, NM, MVAL, NNS, NSVAL, THRESH, NMAX, A, AFAC, B, X, WORK, RWORK, SWORK, IWORK, NOUT) |
DDRVAB | |
subroutine | ddrvac (DOTYPE, NM, MVAL, NNS, NSVAL, THRESH, NMAX, A, AFAC, B, X, WORK, RWORK, SWORK, NOUT) |
DDRVAC | |
subroutine | ddrvgb (DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, A, LA, AFB, LAFB, ASAV, B, BSAV, X, XACT, S, WORK, RWORK, IWORK, NOUT) |
DDRVGB | |
subroutine | ddrvge (DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, A, AFAC, ASAV, B, BSAV, X, XACT, S, WORK, RWORK, IWORK, NOUT) |
DDRVGE | |
subroutine | ddrvgt (DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, A, AF, B, X, XACT, WORK, RWORK, IWORK, NOUT) |
DDRVGT | |
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 | |
subroutine | ddrvpb (DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, A, AFAC, ASAV, B, BSAV, X, XACT, S, WORK, RWORK, IWORK, NOUT) |
DDRVPB | |
subroutine | ddrvpo (DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, A, AFAC, ASAV, B, BSAV, X, XACT, S, WORK, RWORK, IWORK, NOUT) |
DDRVPO | |
subroutine | ddrvpp (DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, A, AFAC, ASAV, B, BSAV, X, XACT, S, WORK, RWORK, IWORK, NOUT) |
DDRVPP | |
subroutine | ddrvpt (DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, A, D, E, B, X, XACT, WORK, RWORK, NOUT) |
DDRVPT | |
subroutine | ddrvrf1 (NOUT, NN, NVAL, THRESH, A, LDA, ARF, WORK) |
DDRVRF1 | |
subroutine | ddrvrf2 (NOUT, NN, NVAL, A, LDA, ARF, AP, ASAV) |
DDRVRF2 | |
subroutine | ddrvrf3 (NOUT, NN, NVAL, THRESH, A, LDA, ARF, B1, B2, D_WORK_DLANGE, D_WORK_DGEQRF, TAU) |
DDRVRF3 | |
subroutine | ddrvrf4 (NOUT, NN, NVAL, THRESH, C1, C2, LDC, CRF, A, LDA, D_WORK_DLANGE) |
DDRVRF4 | |
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 | |
subroutine | ddrvsp (DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT) |
DDRVSP | |
subroutine | ddrvsy (DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT) |
DDRVSY | |
subroutine | debchvxx (THRESH, PATH) |
DEBCHVXX | |
subroutine | derrab (NUNIT) |
DERRAB | |
subroutine | derrac (NUNIT) |
DERRAC | |
subroutine | derrge (PATH, NUNIT) |
DERRGE | |
subroutine | derrgt (PATH, NUNIT) |
DERRGT | |
subroutine | derrlq (PATH, NUNIT) |
DERRLQ | |
subroutine | derrls (PATH, NUNIT) |
DERRLS | |
subroutine | derrpo (PATH, NUNIT) |
DERRPO | |
subroutine | derrps (PATH, NUNIT) |
DERRPS | |
subroutine | derrql (PATH, NUNIT) |
DERRQL | |
subroutine | derrqp (PATH, NUNIT) |
DERRQP | |
subroutine | derrqr (PATH, NUNIT) |
DERRQR | |
subroutine | derrqrt (PATH, NUNIT) |
DERRQRT | |
subroutine | derrqrtp (PATH, NUNIT) |
DERRQRTP | |
subroutine | derrrfp (NUNIT) |
DERRRFP | |
subroutine | derrrq (PATH, NUNIT) |
DERRRQ | |
subroutine | derrsy (PATH, NUNIT) |
DERRSY | |
subroutine | derrtr (PATH, NUNIT) |
DERRTR | |
subroutine | derrtz (PATH, NUNIT) |
DERRTZ | |
subroutine | derrvx (PATH, NUNIT) |
DERRVX | |
subroutine | dgbt01 (M, N, KL, KU, A, LDA, AFAC, LDAFAC, IPIV, WORK, RESID) |
DGBT01 | |
subroutine | dgbt02 (TRANS, M, N, KL, KU, NRHS, A, LDA, X, LDX, B, LDB, RESID) |
DGBT02 | |
subroutine | dgbt05 (TRANS, N, KL, KU, NRHS, AB, LDAB, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS) |
DGBT05 | |
subroutine | dgelqs (M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK, INFO) |
DGELQS | |
LOGICAL function | dgennd (M, N, A, LDA) |
DGENND | |
subroutine | dgeqls (M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK, INFO) |
DGEQLS | |
subroutine | dgeqrs (M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK, INFO) |
DGEQRS | |
subroutine | dgerqs (M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK, INFO) |
DGERQS | |
subroutine | dget01 (M, N, A, LDA, AFAC, LDAFAC, IPIV, RWORK, RESID) |
DGET01 | |
subroutine | dget02 (TRANS, M, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID) |
DGET02 | |
subroutine | dget03 (N, A, LDA, AINV, LDAINV, WORK, LDWORK, RWORK, RCOND, RESID) |
DGET03 | |
subroutine | dget04 (N, NRHS, X, LDX, XACT, LDXACT, RCOND, RESID) |
DGET04 | |
DOUBLE PRECISION function | dget06 (RCOND, RCONDC) |
DGET06 | |
subroutine | dget07 (TRANS, N, NRHS, A, LDA, B, LDB, X, LDX, XACT, LDXACT, FERR, CHKFERR, BERR, RESLTS) |
DGET07 | |
subroutine | dget08 (TRANS, M, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID) |
DGET08 | |
subroutine | dgtt01 (N, DL, D, DU, DLF, DF, DUF, DU2, IPIV, WORK, LDWORK, RWORK, RESID) |
DGTT01 | |
subroutine | dgtt02 (TRANS, N, NRHS, DL, D, DU, X, LDX, B, LDB, RESID) |
DGTT02 | |
subroutine | dgtt05 (TRANS, N, NRHS, DL, D, DU, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS) |
DGTT05 | |
subroutine | dlahilb (N, NRHS, A, LDA, X, LDX, B, LDB, WORK, INFO) |
DLAHILB | |
subroutine | dlaord (JOB, N, X, INCX) |
DLAORD | |
subroutine | dlaptm (N, NRHS, ALPHA, D, E, X, LDX, BETA, B, LDB) |
DLAPTM | |
subroutine | dlarhs (PATH, XTYPE, UPLO, TRANS, M, N, KL, KU, NRHS, A, LDA, X, LDX, B, LDB, ISEED, INFO) |
DLARHS | |
subroutine | dlatb4 (PATH, IMAT, M, N, TYPE, KL, KU, ANORM, MODE, CNDNUM, DIST) |
DLATB4 | |
subroutine | dlatb5 (PATH, IMAT, N, TYPE, KL, KU, ANORM, MODE, CNDNUM, DIST) |
DLATB5 | |
subroutine | dlattb (IMAT, UPLO, TRANS, DIAG, ISEED, N, KD, AB, LDAB, B, WORK, INFO) |
DLATTB | |
subroutine | dlattp (IMAT, UPLO, TRANS, DIAG, ISEED, N, A, B, WORK, INFO) |
DLATTP | |
subroutine | dlattr (IMAT, UPLO, TRANS, DIAG, ISEED, N, A, LDA, B, WORK, INFO) |
DLATTR | |
subroutine | dlavsp (UPLO, TRANS, DIAG, N, NRHS, A, IPIV, B, LDB, INFO) |
DLAVSP | |
subroutine | dlavsy (UPLO, TRANS, DIAG, N, NRHS, A, LDA, IPIV, B, LDB, INFO) |
DLAVSY | |
subroutine | dlqt01 (M, N, A, AF, Q, L, LDA, TAU, WORK, LWORK, RWORK, RESULT) |
DLQT01 | |
subroutine | dlqt02 (M, N, K, A, AF, Q, L, LDA, TAU, WORK, LWORK, RWORK, RESULT) |
DLQT02 | |
subroutine | dlqt03 (M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK, RWORK, RESULT) |
DLQT03 | |
subroutine | dpbt01 (UPLO, N, KD, A, LDA, AFAC, LDAFAC, RWORK, RESID) |
DPBT01 | |
subroutine | dpbt02 (UPLO, N, KD, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID) |
DPBT02 | |
subroutine | dpbt05 (UPLO, N, KD, NRHS, AB, LDAB, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS) |
DPBT05 | |
subroutine | dpot01 (UPLO, N, A, LDA, AFAC, LDAFAC, RWORK, RESID) |
DPOT01 | |
subroutine | dpot02 (UPLO, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID) |
DPOT02 | |
subroutine | dpot03 (UPLO, N, A, LDA, AINV, LDAINV, WORK, LDWORK, RWORK, RCOND, RESID) |
DPOT03 | |
subroutine | dpot05 (UPLO, N, NRHS, A, LDA, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS) |
DPOT05 | |
subroutine | dpot06 (UPLO, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID) |
DPOT06 | |
subroutine | dppt01 (UPLO, N, A, AFAC, RWORK, RESID) |
DPPT01 | |
subroutine | dppt02 (UPLO, N, NRHS, A, X, LDX, B, LDB, RWORK, RESID) |
DPPT02 | |
subroutine | dppt03 (UPLO, N, A, AINV, WORK, LDWORK, RWORK, RCOND, RESID) |
DPPT03 | |
subroutine | dppt05 (UPLO, N, NRHS, AP, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS) |
DPPT05 | |
subroutine | dpst01 (UPLO, N, A, LDA, AFAC, LDAFAC, PERM, LDPERM, PIV, RWORK, RESID, RANK) |
DPST01 | |
subroutine | dptt01 (N, D, E, DF, EF, WORK, RESID) |
DPTT01 | |
subroutine | dptt02 (N, NRHS, D, E, X, LDX, B, LDB, RESID) |
DPTT02 | |
subroutine | dptt05 (N, NRHS, D, E, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS) |
DPTT05 | |
subroutine | dqlt01 (M, N, A, AF, Q, L, LDA, TAU, WORK, LWORK, RWORK, RESULT) |
DQLT01 | |
subroutine | dqlt02 (M, N, K, A, AF, Q, L, LDA, TAU, WORK, LWORK, RWORK, RESULT) |
DQLT02 | |
subroutine | dqlt03 (M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK, RWORK, RESULT) |
DQLT03 | |
DOUBLE PRECISION function | dqpt01 (M, N, K, A, AF, LDA, TAU, JPVT, WORK, LWORK) |
DQPT01 | |
subroutine | dqrt01 (M, N, A, AF, Q, R, LDA, TAU, WORK, LWORK, RWORK, RESULT) |
DQRT01 | |
subroutine | dqrt01p (M, N, A, AF, Q, R, LDA, TAU, WORK, LWORK, RWORK, RESULT) |
DQRT01P | |
subroutine | dqrt02 (M, N, K, A, AF, Q, R, LDA, TAU, WORK, LWORK, RWORK, RESULT) |
DQRT02 | |
subroutine | dqrt03 (M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK, RWORK, RESULT) |
DQRT03 | |
subroutine | dqrt04 (M, N, NB, RESULT) |
DQRT04 | |
subroutine | dqrt05 (M, N, L, NB, RESULT) |
DQRT05 | |
DOUBLE PRECISION function | dqrt11 (M, K, A, LDA, TAU, WORK, LWORK) |
DQRT11 | |
DOUBLE PRECISION function | dqrt12 (M, N, A, LDA, S, WORK, LWORK) |
DQRT12 | |
subroutine | dqrt13 (SCALE, M, N, A, LDA, NORMA, ISEED) |
DQRT13 | |
DOUBLE PRECISION function | dqrt14 (TRANS, M, N, NRHS, A, LDA, X, LDX, WORK, LWORK) |
DQRT14 | |
subroutine | dqrt15 (SCALE, RKSEL, M, N, NRHS, A, LDA, B, LDB, S, RANK, NORMA, NORMB, ISEED, WORK, LWORK) |
DQRT15 | |
subroutine | dqrt16 (TRANS, M, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID) |
DQRT16 | |
DOUBLE PRECISION function | dqrt17 (TRANS, IRESID, M, N, NRHS, A, LDA, X, LDX, B, LDB, C, WORK, LWORK) |
DQRT17 | |
subroutine | drqt01 (M, N, A, AF, Q, R, LDA, TAU, WORK, LWORK, RWORK, RESULT) |
DRQT01 | |
subroutine | drqt02 (M, N, K, A, AF, Q, R, LDA, TAU, WORK, LWORK, RWORK, RESULT) |
DRQT02 | |
subroutine | drqt03 (M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK, RWORK, RESULT) |
DRQT03 | |
DOUBLE PRECISION function | drzt01 (M, N, A, AF, LDA, TAU, WORK, LWORK) |
DRZT01 | |
DOUBLE PRECISION function | drzt02 (M, N, AF, LDA, TAU, WORK, LWORK) |
DRZT02 | |
subroutine | dspt01 (UPLO, N, A, AFAC, IPIV, C, LDC, RWORK, RESID) |
DSPT01 | |
subroutine | dsyt01 (UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, LDC, RWORK, RESID) |
DSYT01 | |
subroutine | dtbt02 (UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, X, LDX, B, LDB, WORK, RESID) |
DTBT02 | |
subroutine | dtbt03 (UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, SCALE, CNORM, TSCAL, X, LDX, B, LDB, WORK, RESID) |
DTBT03 | |
subroutine | dtbt05 (UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS) |
DTBT05 | |
subroutine | dtbt06 (RCOND, RCONDC, UPLO, DIAG, N, KD, AB, LDAB, WORK, RAT) |
DTBT06 | |
subroutine | dtpt01 (UPLO, DIAG, N, AP, AINVP, RCOND, WORK, RESID) |
DTPT01 | |
subroutine | dtpt02 (UPLO, TRANS, DIAG, N, NRHS, AP, X, LDX, B, LDB, WORK, RESID) |
DTPT02 | |
subroutine | dtpt03 (UPLO, TRANS, DIAG, N, NRHS, AP, SCALE, CNORM, TSCAL, X, LDX, B, LDB, WORK, RESID) |
DTPT03 | |
subroutine | dtpt05 (UPLO, TRANS, DIAG, N, NRHS, AP, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS) |
DTPT05 | |
subroutine | dtpt06 (RCOND, RCONDC, UPLO, DIAG, N, AP, WORK, RAT) |
DTPT06 | |
subroutine | dtrt01 (UPLO, DIAG, N, A, LDA, AINV, LDAINV, RCOND, WORK, RESID) |
DTRT01 | |
subroutine | dtrt02 (UPLO, TRANS, DIAG, N, NRHS, A, LDA, X, LDX, B, LDB, WORK, RESID) |
DTRT02 | |
subroutine | dtrt03 (UPLO, TRANS, DIAG, N, NRHS, A, LDA, SCALE, CNORM, TSCAL, X, LDX, B, LDB, WORK, RESID) |
DTRT03 | |
subroutine | dtrt05 (UPLO, TRANS, DIAG, N, NRHS, A, LDA, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS) |
DTRT05 | |
subroutine | dtrt06 (RCOND, RCONDC, UPLO, DIAG, N, A, LDA, WORK, RAT) |
DTRT06 | |
DOUBLE PRECISION function | dtzt01 (M, N, A, AF, LDA, TAU, WORK, LWORK) |
DTZT01 | |
DOUBLE PRECISION function | dtzt02 (M, N, AF, LDA, TAU, WORK, LWORK) |
DTZT02 |
This is the group of double LAPACK TESTING LIN routines.
program dchkaa | ( | ) |
DCHKAA
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
Definition at line 107 of file dchkaa.f.
program dchkab | ( | ) |
DCHKAB
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
Definition at line 74 of file dchkab.f.
subroutine dchkeq | ( | double precision | THRESH, |
integer | NOUT | ||
) |
DCHKEQ
DCHKEQ tests DGEEQU, DGBEQU, DPOEQU, DPPEQU and DPBEQU
[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. |
Definition at line 55 of file dchkeq.f.
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
DCHKGB tests DGBTRF, -TRS, -RFS, and -CON
[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. |
Definition at line 190 of file dchkgb.f.
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
DCHKGE tests DGETRF, -TRI, -TRS, -RFS, and -CON.
[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. |
Definition at line 184 of file dchkge.f.
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
DCHKGT tests DGTTRF, -TRS, -RFS, and -CON
[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. |
Definition at line 146 of file dchkgt.f.
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
DCHKLQ tests DGELQF, DORGLQ and DORMLQ.
[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. |
Definition at line 195 of file dchklq.f.
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
DCHKPB tests DPBTRF, -TRS, -RFS, and -CON.
[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. |
Definition at line 171 of file dchkpb.f.
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
DCHKPO tests DPOTRF, -TRI, -TRS, -RFS, and -CON
[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. |
Definition at line 171 of file dchkpo.f.
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
DCHKPP tests DPPTRF, -TRI, -TRS, -RFS, and -CON
[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. |
Definition at line 162 of file dchkpp.f.
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
DCHKPS tests DPSTRF.
[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. |
Definition at line 153 of file dchkps.f.
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
DCHKPT tests DPTTRF, -TRS, -RFS, and -CON
[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. |
Definition at line 146 of file dchkpt.f.
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
DCHKQ3 tests DGEQP3.
[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. |
Definition at line 152 of file dchkq3.f.
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, dimension( * ) | IWORK, | ||
integer | NOUT | ||
) |
DCHKQL
DCHKQL tests DGEQLF, DORGQL and DORMQL.
[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) |
[out] | IWORK | IWORK is INTEGER array, dimension (NMAX) |
[in] | NOUT | NOUT is INTEGER The unit number for output. |
Definition at line 200 of file dchkql.f.
subroutine dchkqp | ( | 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, dimension( * ) | IWORK, | ||
integer | NOUT | ||
) |
DCHKQP
DCHKQP tests DGEQPF.
[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) |
[out] | IWORK | IWORK is INTEGER array, dimension (NMAX) |
[in] | NOUT | NOUT is INTEGER The unit number for output. |
Definition at line 137 of file dchkqp.f.
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
DCHKQR tests DGEQRF, DORGQR and DORMQR.
[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. |
Definition at line 200 of file dchkqr.f.
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
DCHKQRT tests DGEQRT and DGEMQRT.
[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. |
Definition at line 102 of file dchkqrt.f.
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
DCHKQRTP tests DTPQRT and DTPMQRT.
[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. |
Definition at line 102 of file dchkqrtp.f.
program dchkrfp | ( | ) |
DCHKRFP
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
Definition at line 60 of file dchkrfp.f.
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
DCHKRQ tests DGERQF, DORGRQ and DORMRQ.
[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. |
Definition at line 200 of file dchkrq.f.
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
DCHKSP tests DSPTRF, -TRI, -TRS, -RFS, and -CON
[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. |
Definition at line 162 of file dchksp.f.
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
DCHKSY tests DSYTRF, -TRI2, -TRS, -TRS2, -RFS, and -CON.
[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. |
Definition at line 171 of file dchksy.f.
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
DCHKTB tests DTBTRS, -RFS, and -CON, and DLATBS.
[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. |
Definition at line 154 of file dchktb.f.
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
DCHKTP tests DTPTRI, -TRS, -RFS, and -CON, and DLATPS
[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. |
Definition at line 156 of file dchktp.f.
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
DCHKTR tests DTRTRI, -TRS, -RFS, and -CON, and DLATRS
[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. |
Definition at line 166 of file dchktr.f.
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
DCHKTZ tests DTZRQF and STZRZF.
[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. |
Definition at line 132 of file dchktz.f.
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
DDRVAB tests DSGESV
[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. |
Definition at line 150 of file ddrvab.f.
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
DDRVAC tests DSPOSV.
[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. |
Definition at line 143 of file ddrvac.f.
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
DDRVGB tests the driver routines DGBSV and -SVX.
[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. |
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.
[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. |
Definition at line 171 of file ddrvgb.f.
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
DDRVGE tests the driver routines DGESV and -SVX.
[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. |
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.
[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. |
Definition at line 163 of file ddrvge.f.
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
DDRVGT tests DGTSV and -SVX.
[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. |
Definition at line 139 of file ddrvgt.f.
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
DDRVLS tests the least squares driver routines DGELS, DGELSS, DGELSX, DGELSY and DGELSD.
[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. |
Definition at line 202 of file ddrvls.f.
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
DDRVPB tests the driver routines DPBSV and -SVX.
[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. |
Definition at line 163 of file ddrvpb.f.
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
DDRVPO tests the driver routines DPOSV and -SVX.
[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. |
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.
[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. |
Definition at line 163 of file ddrvpo.f.
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
DDRVPP tests the driver routines DPPSV and -SVX.
[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. |
Definition at line 166 of file ddrvpp.f.
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
DDRVPT tests DPTSV and -SVX.
[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. |
Definition at line 140 of file ddrvpt.f.
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
DDRVRF1 tests the LAPACK RFP routines: DLANSF
[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 ) |
Definition at line 95 of file ddrvrf1.f.
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
DDRVRF2 tests the LAPACK RFP convertion routines.
[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) |
Definition at line 90 of file ddrvrf2.f.
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
DDRVRF3 tests the LAPACK RFP routines: DTFSM
[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) |
Definition at line 118 of file ddrvrf3.f.
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
DDRVRF4 tests the LAPACK RFP routines: DSFRK
[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) |
Definition at line 118 of file ddrvrf4.f.
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
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.
[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 ) |
Definition at line 239 of file ddrvrfp.f.
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
DDRVSP tests the driver routines DSPSV and -SVX.
[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. |
Definition at line 155 of file ddrvsp.f.
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
DDRVSY tests the driver routines DSYSV and -SVX.
[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. |
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.
[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. |
Definition at line 152 of file ddrvsy.f.
subroutine debchvxx | ( | double precision | THRESH, |
character*3 | PATH | ||
) |
DEBCHVXX
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.
Definition at line 97 of file debchvxx.f.
subroutine derrab | ( | integer | NUNIT | ) |
subroutine derrac | ( | integer | NUNIT | ) |
subroutine derrge | ( | character*3 | PATH, |
integer | NUNIT | ||
) |
DERRGE
DERRGEX
DERRGE tests the error exits for the DOUBLE PRECISION routines for general matrices.
[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. |
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.
[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. |
Definition at line 56 of file derrge.f.
subroutine derrgt | ( | character*3 | PATH, |
integer | NUNIT | ||
) |
DERRGT
DERRGT tests the error exits for the DOUBLE PRECISION tridiagonal routines.
[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. |
Definition at line 56 of file derrgt.f.
subroutine derrlq | ( | character*3 | PATH, |
integer | NUNIT | ||
) |
DERRLQ
DERRLQ tests the error exits for the DOUBLE PRECISION routines that use the LQ decomposition of a general matrix.
[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. |
Definition at line 56 of file derrlq.f.
subroutine derrls | ( | character*3 | PATH, |
integer | NUNIT | ||
) |
DERRLS
DERRLS tests the error exits for the DOUBLE PRECISION least squares driver routines (DGELS, SGELSS, SGELSX, SGELSY, SGELSD).
[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. |
Definition at line 56 of file derrls.f.
subroutine derrpo | ( | character*3 | PATH, |
integer | NUNIT | ||
) |
DERRPO
DERRPOX
DERRPO tests the error exits for the DOUBLE PRECISION routines for symmetric positive definite matrices.
[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. |
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.
[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. |
Definition at line 56 of file derrpo.f.
subroutine derrps | ( | character*3 | PATH, |
integer | NUNIT | ||
) |
DERRPS
DERRPS tests the error exits for the DOUBLE PRECISION routines for DPSTRF.
[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. |
Definition at line 56 of file derrps.f.
subroutine derrql | ( | character*3 | PATH, |
integer | NUNIT | ||
) |
DERRQL
DERRQL tests the error exits for the DOUBLE PRECISION routines that use the QL decomposition of a general matrix.
[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. |
Definition at line 56 of file derrql.f.
subroutine derrqp | ( | character*3 | PATH, |
integer | NUNIT | ||
) |
DERRQP
DERRQP tests the error exits for DGEQPF and DGEQP3.
[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. |
Definition at line 55 of file derrqp.f.
subroutine derrqr | ( | character*3 | PATH, |
integer | NUNIT | ||
) |
DERRQR
DERRQR tests the error exits for the DOUBLE PRECISION routines that use the QR decomposition of a general matrix.
[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. |
Definition at line 56 of file derrqr.f.
subroutine derrqrt | ( | character*3 | PATH, |
integer | NUNIT | ||
) |
DERRQRT
DERRQRT tests the error exits for the DOUBLE PRECISION routines that use the QRT decomposition of a general matrix.
[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. |
Definition at line 56 of file derrqrt.f.
subroutine derrqrtp | ( | character*3 | PATH, |
integer | NUNIT | ||
) |
DERRQRTP
DERRQRTP tests the error exits for the REAL routines that use the QRT decomposition of a triangular-pentagonal matrix.
[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. |
Definition at line 56 of file derrqrtp.f.
subroutine derrrfp | ( | integer | NUNIT | ) |
DERRRFP
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
[in] | NUNIT | NUNIT is INTEGER The unit number for output. |
Definition at line 53 of file derrrfp.f.
subroutine derrrq | ( | character*3 | PATH, |
integer | NUNIT | ||
) |
DERRRQ
DERRRQ tests the error exits for the DOUBLE PRECISION routines that use the RQ decomposition of a general matrix.
[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. |
Definition at line 56 of file derrrq.f.
subroutine derrsy | ( | character*3 | PATH, |
integer | NUNIT | ||
) |
DERRSY
DERRSYX
DERRSY tests the error exits for the DOUBLE PRECISION routines for symmetric indefinite matrices.
[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. |
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.
[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. |
Definition at line 56 of file derrsy.f.
subroutine derrtr | ( | character*3 | PATH, |
integer | NUNIT | ||
) |
DERRTR
DERRTR tests the error exits for the DOUBLE PRECISION triangular routines.
[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. |
Definition at line 56 of file derrtr.f.
subroutine derrtz | ( | character*3 | PATH, |
integer | NUNIT | ||
) |
DERRTZ
DERRTZ tests the error exits for DTZRQF and STZRZF.
[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. |
Definition at line 55 of file derrtz.f.
subroutine derrvx | ( | character*3 | PATH, |
integer | NUNIT | ||
) |
DERRVX
DERRVXX
DERRVX tests the error exits for the DOUBLE PRECISION driver routines for solving linear systems of equations.
[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. |
DERRVX tests the error exits for the DOUBLE PRECISION driver routines for solving linear systems of equations.
[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. |
Definition at line 56 of file derrvx.f.
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
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.
[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 ) |
Definition at line 126 of file dgbt01.f.
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
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.
[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 ). |
Definition at line 139 of file dgbt02.f.
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
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
[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 + (*) ) |
Definition at line 176 of file dgbt05.f.
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
Compute a minimum-norm solution min || A*X - B || using the LQ factorization A = L*Q computed by DGELQF.
[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 |
Definition at line 121 of file dgelqs.f.
LOGICAL function dgennd | ( | integer | M, |
integer | N, | ||
double precision, dimension( lda, * ) | A, | ||
integer | LDA | ||
) |
DGENND
DGENND tests that its argument has a non-negative diagonal.
[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. |
Definition at line 69 of file dgennd.f.
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
Solve the least squares problem min || A*X - B || using the QL factorization A = Q*L computed by DGEQLF.
[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 |
Definition at line 122 of file dgeqls.f.
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
Solve the least squares problem min || A*X - B || using the QR factorization A = Q*R computed by DGEQRF.
[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 |
Definition at line 121 of file dgeqrs.f.
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
Compute a minimum-norm solution min || A*X - B || using the RQ factorization A = R*Q computed by DGERQF.
[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 |
Definition at line 122 of file dgerqs.f.
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
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.
[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 ) |
Definition at line 107 of file dget01.f.
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
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.
[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 ). |
Definition at line 133 of file dget02.f.
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
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.
[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 ) |
Definition at line 109 of file dget03.f.
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
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.
[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 ) |
Definition at line 103 of file dget04.f.
DOUBLE PRECISION function dget06 | ( | double precision | RCOND, |
double precision | RCONDC | ||
) |
DGET06
DGET06 computes a test ratio to compare two values for RCOND.
[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)). |
Definition at line 56 of file dget06.f.
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
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 )
[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 + (*) ) |
Definition at line 165 of file dget07.f.
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
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.
[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 ). |
Definition at line 133 of file dget08.f.
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
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.
[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) |
Definition at line 134 of file dgtt01.f.
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
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.
[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) |
Definition at line 124 of file dgtt02.f.
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
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
[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 + (*) ) |
Definition at line 165 of file dgtt05.f.
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
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.
[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 |
Definition at line 125 of file dlahilb.f.
subroutine dlaord | ( | character | JOB, |
integer | N, | ||
double precision, dimension( * ) | X, | ||
integer | INCX | ||
) |
DLAORD
DLAORD sorts the elements of a vector x in increasing or decreasing order.
[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. |
Definition at line 74 of file dlaord.f.
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
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.
[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). |
Definition at line 117 of file dlaptm.f.
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
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).
[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 |
Definition at line 204 of file dlarhs.f.
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
DLATB4 sets parameters for the matrix generator based on the type of matrix to be generated.
[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. |
Definition at line 120 of file dlatb4.f.
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
DLATB5 sets parameters for the matrix generator based on the type of matrix to be generated.
[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. |
Definition at line 114 of file dlatb5.f.
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
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.
[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 |
Definition at line 135 of file dlattb.f.
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
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.
[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 |
Definition at line 125 of file dlattp.f.
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
DLATTR generates a triangular test matrix. IMAT and UPLO uniquely specify the properties of the test matrix, which is returned in the array A.
[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 |
Definition at line 133 of file dlattr.f.
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
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' )
[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 |
Definition at line 130 of file dlavsp.f.
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
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')
[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. |
[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 |
Definition at line 154 of file dlavsy.f.
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
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.
[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 ) |
Definition at line 126 of file dlqt01.f.
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
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.
[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 ) |
Definition at line 135 of file dlqt02.f.
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
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.
[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 ) |
Definition at line 136 of file dlqt03.f.
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
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.
[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 ) |
Definition at line 119 of file dpbt01.f.
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
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.
[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 ). |
Definition at line 136 of file dpbt02.f.
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
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
[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 + (*) ) |
Definition at line 171 of file dpbt05.f.
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
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.
[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 ) |
Definition at line 105 of file dpot01.f.
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
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.
[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 ). |
Definition at line 127 of file dpot02.f.
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
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.
[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 ) |
Definition at line 125 of file dpot03.f.
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
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 )
[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 + (*) ) |
Definition at line 164 of file dpot05.f.
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
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.
[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 ). |
Definition at line 127 of file dpot06.f.
subroutine dppt01 | ( | character | UPLO, |
integer | N, | ||
double precision, dimension( * ) | A, | ||
double precision, dimension( * ) | AFAC, | ||
double precision, dimension( * ) | RWORK, | ||
double precision | RESID | ||
) |
DPPT01
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.
[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 ) |
Definition at line 94 of file dppt01.f.
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
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.
[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 ). |
Definition at line 122 of file dppt02.f.
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
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.
[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 ) |
Definition at line 110 of file dppt03.f.
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
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 )
[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 + (*) ) |
Definition at line 156 of file dppt05.f.
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
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.
[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. |
Definition at line 134 of file dpst01.f.
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
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.
[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) |
Definition at line 92 of file dptt01.f.
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
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.
[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) |
Definition at line 105 of file dptt02.f.
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
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
[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 + (*) ) |
Definition at line 150 of file dptt05.f.
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
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.
[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 ) |
Definition at line 126 of file dqlt01.f.
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
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.
[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 ) |
Definition at line 136 of file dqlt02.f.
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
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.
[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 ) |
Definition at line 136 of file dqlt03.f.
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
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)
[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. |
Definition at line 120 of file dqpt01.f.
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
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.
[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 ) |
Definition at line 126 of file dqrt01.f.
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
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.
[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 ) |
Definition at line 126 of file dqrt01p.f.
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
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.
[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 ) |
Definition at line 135 of file dqrt02.f.
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
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.
[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 returnedby DGEQRF. See SGEQRF 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 ) |
Definition at line 136 of file dqrt03.f.
subroutine dqrt04 | ( | integer | M, |
integer | N, | ||
integer | NB, | ||
double precision, dimension(6) | RESULT | ||
) |
DQRT04
DQRT04 tests DGEQRT and DGEMQRT.
[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 | |
Definition at line 74 of file dqrt04.f.
subroutine dqrt05 | ( | integer | M, |
integer | N, | ||
integer | L, | ||
integer | NB, | ||
double precision, dimension(6) | RESULT | ||
) |
DQRT05
DQRT05 tests DTPQRT and DTPMQRT.
[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 | |
Definition at line 81 of file dqrt05.f.
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
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).
[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. |
Definition at line 99 of file dqrt11.f.
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
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))
[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). |
Definition at line 90 of file dqrt12.f.
subroutine dqrt13 | ( | integer | SCALE, |
integer | M, | ||
integer | N, | ||
double precision, dimension( lda, * ) | A, | ||
integer | LDA, | ||
double precision | NORMA, | ||
integer, dimension( 4 ) | ISEED | ||
) |
DQRT13
DQRT13 generates a full-rank matrix that may be scaled to have large or small norm.
[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 |
Definition at line 92 of file dqrt13.f.
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
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.
[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). |
Definition at line 116 of file dqrt14.f.
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
DQRT15 generates a matrix with full or deficient rank and of various norms.
[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) |
Definition at line 148 of file dqrt15.f.
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
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.
[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 ). |
Definition at line 133 of file dqrt16.f.
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
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).
[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). |
Definition at line 150 of file dqrt17.f.
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
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.
[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 ) |
Definition at line 126 of file drqt01.f.
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
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.
[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 ) |
Definition at line 136 of file drqt02.f.
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
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.
[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 ) |
Definition at line 136 of file drqt03.f.
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
DRZT01 returns || A - R*Q || / ( M * eps * ||A|| ) for an upper trapezoidal A that was factored with DTZRZF.
[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. |
Definition at line 98 of file drzt01.f.
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
DRZT02 returns || I - Q'*Q || / ( M * eps) where the matrix Q is defined by the Householder transformations generated by DTZRZF.
[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. |
Definition at line 91 of file drzt02.f.
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
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.
[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 ) |
Definition at line 111 of file dspt01.f.
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
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.
[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 ) |
Definition at line 124 of file dsyt01.f.
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
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.
[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 ). |
Definition at line 154 of file dtbt02.f.
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
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.
[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 ). |
Definition at line 174 of file dtbt03.f.
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
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
[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 + (*) ) |
Definition at line 189 of file dtbt05.f.
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
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.
[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. |
Definition at line 125 of file dtbt06.f.
subroutine dtpt01 | ( | character | UPLO, |
character | DIAG, | ||
integer | N, | ||