Collaboration diagram for double:

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

Detailed Description

This is the group of double LAPACK TESTING LIN routines.

Function/Subroutine Documentation

program dchkaa ( )

DCHKAA

Purpose:

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

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

  NMAX    INTEGER
          The maximum allowable value for M and N.

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

  MAXRHS  INTEGER
          The maximum number of right hand sides

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

  NIN     INTEGER
          The unit number for input

  NOUT    INTEGER
          The unit number for output

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: April 2012

Definition at line 107 of file dchkaa.f.

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program dchkab ( )

DCHKAB

Purpose:

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

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

  NMAX    INTEGER
          The maximum allowable value for N

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

  MAXRHS  INTEGER
          The maximum number of right hand sides

  NIN     INTEGER
          The unit number for input

  NOUT    INTEGER
          The unit number for output

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: April 2012

Definition at line 74 of file dchkab.f.

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subroutine dchkeq	(	double precision	THRESH,
		integer	NOUT
	)

DCHKEQ

Purpose:

 DCHKEQ tests DGEEQU, DGBEQU, DPOEQU, DPPEQU and DPBEQU

Parameters:

[in]	THRESH	THRESH is DOUBLE PRECISION Threshold for testing routines. Should be between 2 and 10.
[in]	NOUT	NOUT is INTEGER The unit number for output.

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 55 of file dchkeq.f.

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subroutine dchkgb	(	logical, dimension( * )	DOTYPE,
		integer	NM,
		integer, dimension( * )	MVAL,
		integer	NN,
		integer, dimension( * )	NVAL,
		integer	NNB,
		integer, dimension( * )	NBVAL,
		integer	NNS,
		integer, dimension( * )	NSVAL,
		double precision	THRESH,
		logical	TSTERR,
		double precision, dimension( * )	A,
		integer	LA,
		double precision, dimension( * )	AFAC,
		integer	LAFAC,
		double precision, dimension( * )	B,
		double precision, dimension( * )	X,
		double precision, dimension( * )	XACT,
		double precision, dimension( * )	WORK,
		double precision, dimension( * )	RWORK,
		integer, dimension( * )	IWORK,
		integer	NOUT
	)

DCHKGB

Purpose:

 DCHKGB tests DGBTRF, -TRS, -RFS, and -CON

Parameters:

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

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 190 of file dchkgb.f.

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subroutine dchkge	(	logical, dimension( * )	DOTYPE,
		integer	NM,
		integer, dimension( * )	MVAL,
		integer	NN,
		integer, dimension( * )	NVAL,
		integer	NNB,
		integer, dimension( * )	NBVAL,
		integer	NNS,
		integer, dimension( * )	NSVAL,
		double precision	THRESH,
		logical	TSTERR,
		integer	NMAX,
		double precision, dimension( * )	A,
		double precision, dimension( * )	AFAC,
		double precision, dimension( * )	AINV,
		double precision, dimension( * )	B,
		double precision, dimension( * )	X,
		double precision, dimension( * )	XACT,
		double precision, dimension( * )	WORK,
		double precision, dimension( * )	RWORK,
		integer, dimension( * )	IWORK,
		integer	NOUT
	)

DCHKGE

Purpose:

 DCHKGE tests DGETRF, -TRI, -TRS, -RFS, and -CON.

Parameters:

[in]	DOTYPE	DOTYPE is LOGICAL array, dimension (NTYPES) The matrix types to be used for testing. Matrices of type j (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) = .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
[in]	NM	NM is INTEGER The number of values of M contained in the vector MVAL.
[in]	MVAL	MVAL is INTEGER array, dimension (NM) The values of the matrix row dimension M.
[in]	NN	NN is INTEGER The number of values of N contained in the vector NVAL.
[in]	NVAL	NVAL is INTEGER array, dimension (NN) The values of the matrix column dimension N.
[in]	NNB	NNB is INTEGER The number of values of NB contained in the vector NBVAL.
[in]	NBVAL	NBVAL is INTEGER array, dimension (NBVAL) The values of the blocksize NB.
[in]	NNS	NNS is INTEGER The number of values of NRHS contained in the vector NSVAL.
[in]	NSVAL	NSVAL is INTEGER array, dimension (NNS) The values of the number of right hand sides NRHS.
[in]	THRESH	THRESH is DOUBLE PRECISION The threshold value for the test ratios. A result is included in the output file if RESULT >= THRESH. To have every test ratio printed, use THRESH = 0.
[in]	TSTERR	TSTERR is LOGICAL Flag that indicates whether error exits are to be tested.
[in]	NMAX	NMAX is INTEGER The maximum value permitted for M or N, used in dimensioning the work arrays.
[out]	A	A is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]	AFAC	AFAC is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]	AINV	AINV is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]	B	B is DOUBLE PRECISION array, dimension (NMAX*NSMAX) where NSMAX is the largest entry in NSVAL.
[out]	X	X is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
[out]	XACT	XACT is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (NMAX*max(3,NSMAX))
[out]	RWORK	RWORK is DOUBLE PRECISION array, dimension (max(2NMAX,2NSMAX+NWORK))
[out]	IWORK	IWORK is INTEGER array, dimension (2*NMAX)
[in]	NOUT	NOUT is INTEGER The unit number for output.

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 184 of file dchkge.f.

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subroutine dchkgt	(	logical, dimension( * )	DOTYPE,
		integer	NN,
		integer, dimension( * )	NVAL,
		integer	NNS,
		integer, dimension( * )	NSVAL,
		double precision	THRESH,
		logical	TSTERR,
		double precision, dimension( * )	A,
		double precision, dimension( * )	AF,
		double precision, dimension( * )	B,
		double precision, dimension( * )	X,
		double precision, dimension( * )	XACT,
		double precision, dimension( * )	WORK,
		double precision, dimension( * )	RWORK,
		integer, dimension( * )	IWORK,
		integer	NOUT
	)

DCHKGT

Purpose:

 DCHKGT tests DGTTRF, -TRS, -RFS, and -CON

Parameters:

[in]	DOTYPE	DOTYPE is LOGICAL array, dimension (NTYPES) The matrix types to be used for testing. Matrices of type j (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) = .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
[in]	NN	NN is INTEGER The number of values of N contained in the vector NVAL.
[in]	NVAL	NVAL is INTEGER array, dimension (NN) The values of the matrix dimension N.
[in]	NNS	NNS is INTEGER The number of values of NRHS contained in the vector NSVAL.
[in]	NSVAL	NSVAL is INTEGER array, dimension (NNS) The values of the number of right hand sides NRHS.
[in]	THRESH	THRESH is DOUBLE PRECISION The threshold value for the test ratios. A result is included in the output file if RESULT >= THRESH. To have every test ratio printed, use THRESH = 0.
[in]	TSTERR	TSTERR is LOGICAL Flag that indicates whether error exits are to be tested.
[out]	A	A is DOUBLE PRECISION array, dimension (NMAX*4)
[out]	AF	AF is DOUBLE PRECISION array, dimension (NMAX*4)
[out]	B	B is DOUBLE PRECISION array, dimension (NMAX*NSMAX) where NSMAX is the largest entry in NSVAL.
[out]	X	X is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
[out]	XACT	XACT is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (NMAX*max(3,NSMAX))
[out]	RWORK	RWORK is DOUBLE PRECISION array, dimension (max(NMAX,2*NSMAX))
[out]	IWORK	IWORK is INTEGER array, dimension (2*NMAX)
[in]	NOUT	NOUT is INTEGER The unit number for output.

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 146 of file dchkgt.f.

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subroutine dchklq	(	logical, dimension( * )	DOTYPE,
		integer	NM,
		integer, dimension( * )	MVAL,
		integer	NN,
		integer, dimension( * )	NVAL,
		integer	NNB,
		integer, dimension( * )	NBVAL,
		integer, dimension( * )	NXVAL,
		integer	NRHS,
		double precision	THRESH,
		logical	TSTERR,
		integer	NMAX,
		double precision, dimension( * )	A,
		double precision, dimension( * )	AF,
		double precision, dimension( * )	AQ,
		double precision, dimension( * )	AL,
		double precision, dimension( * )	AC,
		double precision, dimension( * )	B,
		double precision, dimension( * )	X,
		double precision, dimension( * )	XACT,
		double precision, dimension( * )	TAU,
		double precision, dimension( * )	WORK,
		double precision, dimension( * )	RWORK,
		integer	NOUT
	)

DCHKLQ

Purpose:

 DCHKLQ tests DGELQF, DORGLQ and DORMLQ.

Parameters:

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

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 195 of file dchklq.f.

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subroutine dchkpb	(	logical, dimension( * )	DOTYPE,
		integer	NN,
		integer, dimension( * )	NVAL,
		integer	NNB,
		integer, dimension( * )	NBVAL,
		integer	NNS,
		integer, dimension( * )	NSVAL,
		double precision	THRESH,
		logical	TSTERR,
		integer	NMAX,
		double precision, dimension( * )	A,
		double precision, dimension( * )	AFAC,
		double precision, dimension( * )	AINV,
		double precision, dimension( * )	B,
		double precision, dimension( * )	X,
		double precision, dimension( * )	XACT,
		double precision, dimension( * )	WORK,
		double precision, dimension( * )	RWORK,
		integer, dimension( * )	IWORK,
		integer	NOUT
	)

DCHKPB

Purpose:

 DCHKPB tests DPBTRF, -TRS, -RFS, and -CON.

Parameters:

[in]	DOTYPE	DOTYPE is LOGICAL array, dimension (NTYPES) The matrix types to be used for testing. Matrices of type j (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) = .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
[in]	NN	NN is INTEGER The number of values of N contained in the vector NVAL.
[in]	NVAL	NVAL is INTEGER array, dimension (NN) The values of the matrix dimension N.
[in]	NNB	NNB is INTEGER The number of values of NB contained in the vector NBVAL.
[in]	NBVAL	NBVAL is INTEGER array, dimension (NBVAL) The values of the blocksize NB.
[in]	NNS	NNS is INTEGER The number of values of NRHS contained in the vector NSVAL.
[in]	NSVAL	NSVAL is INTEGER array, dimension (NNS) The values of the number of right hand sides NRHS.
[in]	THRESH	THRESH is DOUBLE PRECISION The threshold value for the test ratios. A result is included in the output file if RESULT >= THRESH. To have every test ratio printed, use THRESH = 0.
[in]	TSTERR	TSTERR is LOGICAL Flag that indicates whether error exits are to be tested.
[in]	NMAX	NMAX is INTEGER The maximum value permitted for N, used in dimensioning the work arrays.
[out]	A	A is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]	AFAC	AFAC is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]	AINV	AINV is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]	B	B is DOUBLE PRECISION array, dimension (NMAX*NSMAX) where NSMAX is the largest entry in NSVAL.
[out]	X	X is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
[out]	XACT	XACT is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (NMAX*max(3,NSMAX))
[out]	RWORK	RWORK is DOUBLE PRECISION array, dimension (max(NMAX,2*NSMAX))
[out]	IWORK	IWORK is INTEGER array, dimension (NMAX)
[in]	NOUT	NOUT is INTEGER The unit number for output.

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 171 of file dchkpb.f.

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subroutine dchkpo	(	logical, dimension( * )	DOTYPE,
		integer	NN,
		integer, dimension( * )	NVAL,
		integer	NNB,
		integer, dimension( * )	NBVAL,
		integer	NNS,
		integer, dimension( * )	NSVAL,
		double precision	THRESH,
		logical	TSTERR,
		integer	NMAX,
		double precision, dimension( * )	A,
		double precision, dimension( * )	AFAC,
		double precision, dimension( * )	AINV,
		double precision, dimension( * )	B,
		double precision, dimension( * )	X,
		double precision, dimension( * )	XACT,
		double precision, dimension( * )	WORK,
		double precision, dimension( * )	RWORK,
		integer, dimension( * )	IWORK,
		integer	NOUT
	)

DCHKPO

Purpose:

 DCHKPO tests DPOTRF, -TRI, -TRS, -RFS, and -CON

Parameters:

[in]	DOTYPE	DOTYPE is LOGICAL array, dimension (NTYPES) The matrix types to be used for testing. Matrices of type j (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) = .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
[in]	NN	NN is INTEGER The number of values of N contained in the vector NVAL.
[in]	NVAL	NVAL is INTEGER array, dimension (NN) The values of the matrix dimension N.
[in]	NNB	NNB is INTEGER The number of values of NB contained in the vector NBVAL.
[in]	NBVAL	NBVAL is INTEGER array, dimension (NBVAL) The values of the blocksize NB.
[in]	NNS	NNS is INTEGER The number of values of NRHS contained in the vector NSVAL.
[in]	NSVAL	NSVAL is INTEGER array, dimension (NNS) The values of the number of right hand sides NRHS.
[in]	THRESH	THRESH is DOUBLE PRECISION The threshold value for the test ratios. A result is included in the output file if RESULT >= THRESH. To have every test ratio printed, use THRESH = 0.
[in]	TSTERR	TSTERR is LOGICAL Flag that indicates whether error exits are to be tested.
[in]	NMAX	NMAX is INTEGER The maximum value permitted for N, used in dimensioning the work arrays.
[out]	A	A is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]	AFAC	AFAC is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]	AINV	AINV is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]	B	B is DOUBLE PRECISION array, dimension (NMAX*NSMAX) where NSMAX is the largest entry in NSVAL.
[out]	X	X is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
[out]	XACT	XACT is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (NMAX*max(3,NSMAX))
[out]	RWORK	RWORK is DOUBLE PRECISION array, dimension (max(NMAX,2*NSMAX))
[out]	IWORK	IWORK is INTEGER array, dimension (NMAX)
[in]	NOUT	NOUT is INTEGER The unit number for output.

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 171 of file dchkpo.f.

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subroutine dchkpp	(	logical, dimension( * )	DOTYPE,
		integer	NN,
		integer, dimension( * )	NVAL,
		integer	NNS,
		integer, dimension( * )	NSVAL,
		double precision	THRESH,
		logical	TSTERR,
		integer	NMAX,
		double precision, dimension( * )	A,
		double precision, dimension( * )	AFAC,
		double precision, dimension( * )	AINV,
		double precision, dimension( * )	B,
		double precision, dimension( * )	X,
		double precision, dimension( * )	XACT,
		double precision, dimension( * )	WORK,
		double precision, dimension( * )	RWORK,
		integer, dimension( * )	IWORK,
		integer	NOUT
	)

DCHKPP

Purpose:

 DCHKPP tests DPPTRF, -TRI, -TRS, -RFS, and -CON

Parameters:

[in]	DOTYPE	DOTYPE is LOGICAL array, dimension (NTYPES) The matrix types to be used for testing. Matrices of type j (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) = .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
[in]	NN	NN is INTEGER The number of values of N contained in the vector NVAL.
[in]	NVAL	NVAL is INTEGER array, dimension (NN) The values of the matrix dimension N.
[in]	NNS	NNS is INTEGER The number of values of NRHS contained in the vector NSVAL.
[in]	NSVAL	NSVAL is INTEGER array, dimension (NNS) The values of the number of right hand sides NRHS.
[in]	THRESH	THRESH is DOUBLE PRECISION The threshold value for the test ratios. A result is included in the output file if RESULT >= THRESH. To have every test ratio printed, use THRESH = 0.
[in]	TSTERR	TSTERR is LOGICAL Flag that indicates whether error exits are to be tested.
[in]	NMAX	NMAX is INTEGER The maximum value permitted for N, used in dimensioning the work arrays.
[out]	A	A is DOUBLE PRECISION array, dimension (NMAX*(NMAX+1)/2)
[out]	AFAC	AFAC is DOUBLE PRECISION array, dimension (NMAX*(NMAX+1)/2)
[out]	AINV	AINV is DOUBLE PRECISION array, dimension (NMAX*(NMAX+1)/2)
[out]	B	B is DOUBLE PRECISION array, dimension (NMAX*NSMAX) where NSMAX is the largest entry in NSVAL.
[out]	X	X is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
[out]	XACT	XACT is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (NMAX*max(3,NSMAX))
[out]	RWORK	RWORK is DOUBLE PRECISION array, dimension (max(NMAX,2*NSMAX))
[out]	IWORK	IWORK is INTEGER array, dimension (NMAX)
[in]	NOUT	NOUT is INTEGER The unit number for output.

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 162 of file dchkpp.f.

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subroutine dchkps	(	logical, dimension( * )	DOTYPE,
		integer	NN,
		integer, dimension( * )	NVAL,
		integer	NNB,
		integer, dimension( * )	NBVAL,
		integer	NRANK,
		integer, dimension( * )	RANKVAL,
		double precision	THRESH,
		logical	TSTERR,
		integer	NMAX,
		double precision, dimension( * )	A,
		double precision, dimension( * )	AFAC,
		double precision, dimension( * )	PERM,
		integer, dimension( * )	PIV,
		double precision, dimension( * )	WORK,
		double precision, dimension( * )	RWORK,
		integer	NOUT
	)

DCHKPS

Purpose:

 DCHKPS tests DPSTRF.

Parameters:

[in]	DOTYPE	DOTYPE is LOGICAL array, dimension (NTYPES) The matrix types to be used for testing. Matrices of type j (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) = .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
[in]	NN	NN is INTEGER The number of values of N contained in the vector NVAL.
[in]	NVAL	NVAL is INTEGER array, dimension (NN) The values of the matrix dimension N.
[in]	NNB	NNB is INTEGER The number of values of NB contained in the vector NBVAL.
[in]	NBVAL	NBVAL is INTEGER array, dimension (NBVAL) The values of the block size NB.
[in]	NRANK	NRANK is INTEGER The number of values of RANK contained in the vector RANKVAL.
[in]	RANKVAL	RANKVAL is INTEGER array, dimension (NBVAL) The values of the block size NB.
[in]	THRESH	THRESH is DOUBLE PRECISION The threshold value for the test ratios. A result is included in the output file if RESULT >= THRESH. To have every test ratio printed, use THRESH = 0.
[in]	TSTERR	TSTERR is LOGICAL Flag that indicates whether error exits are to be tested.
[in]	NMAX	NMAX is INTEGER The maximum value permitted for N, used in dimensioning the work arrays.
[out]	A	A is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]	AFAC	AFAC is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]	PERM	PERM is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]	PIV	PIV is INTEGER array, dimension (NMAX)
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (NMAX*3)
[out]	RWORK	RWORK is DOUBLE PRECISION array, dimension (NMAX)
[in]	NOUT	NOUT is INTEGER The unit number for output.

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 153 of file dchkps.f.

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subroutine dchkpt	(	logical, dimension( * )	DOTYPE,
		integer	NN,
		integer, dimension( * )	NVAL,
		integer	NNS,
		integer, dimension( * )	NSVAL,
		double precision	THRESH,
		logical	TSTERR,
		double precision, dimension( * )	A,
		double precision, dimension( * )	D,
		double precision, dimension( * )	E,
		double precision, dimension( * )	B,
		double precision, dimension( * )	X,
		double precision, dimension( * )	XACT,
		double precision, dimension( * )	WORK,
		double precision, dimension( * )	RWORK,
		integer	NOUT
	)

DCHKPT

Purpose:

 DCHKPT tests DPTTRF, -TRS, -RFS, and -CON

Parameters:

[in]	DOTYPE	DOTYPE is LOGICAL array, dimension (NTYPES) The matrix types to be used for testing. Matrices of type j (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) = .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
[in]	NN	NN is INTEGER The number of values of N contained in the vector NVAL.
[in]	NVAL	NVAL is INTEGER array, dimension (NN) The values of the matrix dimension N.
[in]	NNS	NNS is INTEGER The number of values of NRHS contained in the vector NSVAL.
[in]	NSVAL	NSVAL is INTEGER array, dimension (NNS) The values of the number of right hand sides NRHS.
[in]	THRESH	THRESH is DOUBLE PRECISION The threshold value for the test ratios. A result is included in the output file if RESULT >= THRESH. To have every test ratio printed, use THRESH = 0.
[in]	TSTERR	TSTERR is LOGICAL Flag that indicates whether error exits are to be tested.
[out]	A	A is DOUBLE PRECISION array, dimension (NMAX*2)
[out]	D	D is DOUBLE PRECISION array, dimension (NMAX*2)
[out]	E	E is DOUBLE PRECISION array, dimension (NMAX*2)
[out]	B	B is DOUBLE PRECISION array, dimension (NMAX*NSMAX) where NSMAX is the largest entry in NSVAL.
[out]	X	X is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
[out]	XACT	XACT is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (NMAX*max(3,NSMAX))
[out]	RWORK	RWORK is DOUBLE PRECISION array, dimension (max(NMAX,2*NSMAX))
[in]	NOUT	NOUT is INTEGER The unit number for output.

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 146 of file dchkpt.f.

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subroutine dchkq3	(	logical, dimension( * )	DOTYPE,
		integer	NM,
		integer, dimension( * )	MVAL,
		integer	NN,
		integer, dimension( * )	NVAL,
		integer	NNB,
		integer, dimension( * )	NBVAL,
		integer, dimension( * )	NXVAL,
		double precision	THRESH,
		double precision, dimension( * )	A,
		double precision, dimension( * )	COPYA,
		double precision, dimension( * )	S,
		double precision, dimension( * )	TAU,
		double precision, dimension( * )	WORK,
		integer, dimension( * )	IWORK,
		integer	NOUT
	)

DCHKQ3

Purpose:

 DCHKQ3 tests DGEQP3.

Parameters:

[in]	DOTYPE	DOTYPE is LOGICAL array, dimension (NTYPES) The matrix types to be used for testing. Matrices of type j (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) = .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
[in]	NM	NM is INTEGER The number of values of M contained in the vector MVAL.
[in]	MVAL	MVAL is INTEGER array, dimension (NM) The values of the matrix row dimension M.
[in]	NN	NN is INTEGER The number of values of N contained in the vector NVAL.
[in]	NVAL	NVAL is INTEGER array, dimension (NN) The values of the matrix column dimension N.
[in]	NNB	NNB is INTEGER The number of values of NB and NX contained in the vectors NBVAL and NXVAL. The blocking parameters are used in pairs (NB,NX).
[in]	NBVAL	NBVAL is INTEGER array, dimension (NNB) The values of the blocksize NB.
[in]	NXVAL	NXVAL is INTEGER array, dimension (NNB) The values of the crossover point NX.
[in]	THRESH	THRESH is DOUBLE PRECISION The threshold value for the test ratios. A result is included in the output file if RESULT >= THRESH. To have every test ratio printed, use THRESH = 0.
[out]	A	A is DOUBLE PRECISION array, dimension (MMAX*NMAX) where MMAX is the maximum value of M in MVAL and NMAX is the maximum value of N in NVAL.
[out]	COPYA	COPYA is DOUBLE PRECISION array, dimension (MMAX*NMAX)
[out]	S	S is DOUBLE PRECISION array, dimension (min(MMAX,NMAX))
[out]	TAU	TAU is DOUBLE PRECISION array, dimension (MMAX)
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (MMAXNMAX + 4NMAX + MMAX)
[out]	IWORK	IWORK is INTEGER array, dimension (2*NMAX)
[in]	NOUT	NOUT is INTEGER The unit number for output.

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 152 of file dchkq3.f.

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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

Purpose:

 DCHKQL tests DGEQLF, DORGQL and DORMQL.

Parameters:

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

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 200 of file dchkql.f.

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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

Purpose:

 DCHKQP tests DGEQPF.

Parameters:

[in]	DOTYPE	DOTYPE is LOGICAL array, dimension (NTYPES) The matrix types to be used for testing. Matrices of type j (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) = .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
[in]	NM	NM is INTEGER The number of values of M contained in the vector MVAL.
[in]	MVAL	MVAL is INTEGER array, dimension (NM) The values of the matrix row dimension M.
[in]	NN	NN is INTEGER The number of values of N contained in the vector NVAL.
[in]	NVAL	NVAL is INTEGER array, dimension (NN) The values of the matrix column dimension N.
[in]	THRESH	THRESH is DOUBLE PRECISION The threshold value for the test ratios. A result is included in the output file if RESULT >= THRESH. To have every test ratio printed, use THRESH = 0.
[in]	TSTERR	TSTERR is LOGICAL Flag that indicates whether error exits are to be tested.
[out]	A	A is DOUBLE PRECISION array, dimension (MMAX*NMAX) where MMAX is the maximum value of M in MVAL and NMAX is the maximum value of N in NVAL.
[out]	COPYA	COPYA is DOUBLE PRECISION array, dimension (MMAX*NMAX)
[out]	S	S is DOUBLE PRECISION array, dimension (min(MMAX,NMAX))
[out]	TAU	TAU is DOUBLE PRECISION array, dimension (MMAX)
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (MMAXNMAX + 4NMAX + MMAX)
[out]	IWORK	IWORK is INTEGER array, dimension (NMAX)
[in]	NOUT	NOUT is INTEGER The unit number for output.

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 137 of file dchkqp.f.

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subroutine dchkqr	(	logical, dimension( * )	DOTYPE,
		integer	NM,
		integer, dimension( * )	MVAL,
		integer	NN,
		integer, dimension( * )	NVAL,
		integer	NNB,
		integer, dimension( * )	NBVAL,
		integer, dimension( * )	NXVAL,
		integer	NRHS,
		double precision	THRESH,
		logical	TSTERR,
		integer	NMAX,
		double precision, dimension( * )	A,
		double precision, dimension( * )	AF,
		double precision, dimension( * )	AQ,
		double precision, dimension( * )	AR,
		double precision, dimension( * )	AC,
		double precision, dimension( * )	B,
		double precision, dimension( * )	X,
		double precision, dimension( * )	XACT,
		double precision, dimension( * )	TAU,
		double precision, dimension( * )	WORK,
		double precision, dimension( * )	RWORK,
		integer, dimension( * )	IWORK,
		integer	NOUT
	)

DCHKQR

Purpose:

 DCHKQR tests DGEQRF, DORGQR and DORMQR.

Parameters:

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

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 200 of file dchkqr.f.

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subroutine dchkqrt	(	double precision	THRESH,
		logical	TSTERR,
		integer	NM,
		integer, dimension( * )	MVAL,
		integer	NN,
		integer, dimension( * )	NVAL,
		integer	NNB,
		integer, dimension( * )	NBVAL,
		integer	NOUT
	)

DCHKQRT

Purpose:

 DCHKQRT tests DGEQRT and DGEMQRT.

Parameters:

[in]	THRESH	THRESH is DOUBLE PRECISION The threshold value for the test ratios. A result is included in the output file if RESULT >= THRESH. To have every test ratio printed, use THRESH = 0.
[in]	TSTERR	TSTERR is LOGICAL Flag that indicates whether error exits are to be tested.
[in]	NM	NM is INTEGER The number of values of M contained in the vector MVAL.
[in]	MVAL	MVAL is INTEGER array, dimension (NM) The values of the matrix row dimension M.
[in]	NN	NN is INTEGER The number of values of N contained in the vector NVAL.
[in]	NVAL	NVAL is INTEGER array, dimension (NN) The values of the matrix column dimension N.
[in]	NNB	NNB is INTEGER The number of values of NB contained in the vector NBVAL.
[in]	NBVAL	NBVAL is INTEGER array, dimension (NBVAL) The values of the blocksize NB.
[in]	NOUT	NOUT is INTEGER The unit number for output.

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 102 of file dchkqrt.f.

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subroutine dchkqrtp	(	double precision	THRESH,
		logical	TSTERR,
		integer	NM,
		integer, dimension( * )	MVAL,
		integer	NN,
		integer, dimension( * )	NVAL,
		integer	NNB,
		integer, dimension( * )	NBVAL,
		integer	NOUT
	)

DCHKQRTP

Purpose:

 DCHKQRTP tests DTPQRT and DTPMQRT.

Parameters:

[in]	THRESH	THRESH is DOUBLE PRECISION The threshold value for the test ratios. A result is included in the output file if RESULT >= THRESH. To have every test ratio printed, use THRESH = 0.
[in]	TSTERR	TSTERR is LOGICAL Flag that indicates whether error exits are to be tested.
[in]	NM	NM is INTEGER The number of values of M contained in the vector MVAL.
[in]	MVAL	MVAL is INTEGER array, dimension (NM) The values of the matrix row dimension M.
[in]	NN	NN is INTEGER The number of values of N contained in the vector NVAL.
[in]	NVAL	NVAL is INTEGER array, dimension (NN) The values of the matrix column dimension N.
[in]	NNB	NNB is INTEGER The number of values of NB contained in the vector NBVAL.
[in]	NBVAL	NBVAL is INTEGER array, dimension (NBVAL) The values of the blocksize NB.
[in]	NOUT	NOUT is INTEGER The unit number for output.

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 102 of file dchkqrtp.f.

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program dchkrfp ( )

DCHKRFP

Purpose:

 DCHKRFP is the main test program for the DOUBLE PRECISION linear
 equation routines with RFP storage format

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

  MAXRHS  INTEGER
          The maximum number of right hand sides

  NTYPES  INTEGER

  NMAX    INTEGER
          The maximum allowable value for N.

  NIN     INTEGER
          The unit number for input

  NOUT    INTEGER
          The unit number for output

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: April 2012

Definition at line 60 of file dchkrfp.f.

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subroutine dchkrq	(	logical, dimension( * )	DOTYPE,
		integer	NM,
		integer, dimension( * )	MVAL,
		integer	NN,
		integer, dimension( * )	NVAL,
		integer	NNB,
		integer, dimension( * )	NBVAL,
		integer, dimension( * )	NXVAL,
		integer	NRHS,
		double precision	THRESH,
		logical	TSTERR,
		integer	NMAX,
		double precision, dimension( * )	A,
		double precision, dimension( * )	AF,
		double precision, dimension( * )	AQ,
		double precision, dimension( * )	AR,
		double precision, dimension( * )	AC,
		double precision, dimension( * )	B,
		double precision, dimension( * )	X,
		double precision, dimension( * )	XACT,
		double precision, dimension( * )	TAU,
		double precision, dimension( * )	WORK,
		double precision, dimension( * )	RWORK,
		integer, dimension( * )	IWORK,
		integer	NOUT
	)

DCHKRQ

Purpose:

 DCHKRQ tests DGERQF, DORGRQ and DORMRQ.

Parameters:

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

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 200 of file dchkrq.f.

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subroutine dchksp	(	logical, dimension( * )	DOTYPE,
		integer	NN,
		integer, dimension( * )	NVAL,
		integer	NNS,
		integer, dimension( * )	NSVAL,
		double precision	THRESH,
		logical	TSTERR,
		integer	NMAX,
		double precision, dimension( * )	A,
		double precision, dimension( * )	AFAC,
		double precision, dimension( * )	AINV,
		double precision, dimension( * )	B,
		double precision, dimension( * )	X,
		double precision, dimension( * )	XACT,
		double precision, dimension( * )	WORK,
		double precision, dimension( * )	RWORK,
		integer, dimension( * )	IWORK,
		integer	NOUT
	)

DCHKSP

Purpose:

 DCHKSP tests DSPTRF, -TRI, -TRS, -RFS, and -CON

Parameters:

[in]	DOTYPE	DOTYPE is LOGICAL array, dimension (NTYPES) The matrix types to be used for testing. Matrices of type j (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) = .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
[in]	NN	NN is INTEGER The number of values of N contained in the vector NVAL.
[in]	NVAL	NVAL is INTEGER array, dimension (NN) The values of the matrix dimension N.
[in]	NNS	NNS is INTEGER The number of values of NRHS contained in the vector NSVAL.
[in]	NSVAL	NSVAL is INTEGER array, dimension (NNS) The values of the number of right hand sides NRHS.
[in]	THRESH	THRESH is DOUBLE PRECISION The threshold value for the test ratios. A result is included in the output file if RESULT >= THRESH. To have every test ratio printed, use THRESH = 0.
[in]	TSTERR	TSTERR is LOGICAL Flag that indicates whether error exits are to be tested.
[in]	NMAX	NMAX is INTEGER The maximum value permitted for N, used in dimensioning the work arrays.
[out]	A	A is DOUBLE PRECISION array, dimension (NMAX*(NMAX+1)/2)
[out]	AFAC	AFAC is DOUBLE PRECISION array, dimension (NMAX*(NMAX+1)/2)
[out]	AINV	AINV is DOUBLE PRECISION array, dimension (NMAX*(NMAX+1)/2)
[out]	B	B is DOUBLE PRECISION array, dimension (NMAX*NSMAX) where NSMAX is the largest entry in NSVAL.
[out]	X	X is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
[out]	XACT	XACT is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (NMAX*max(2,NSMAX))
[out]	RWORK	RWORK is DOUBLE PRECISION array, dimension (NMAX+2*NSMAX)
[out]	IWORK	IWORK is INTEGER array, dimension (2*NMAX)
[in]	NOUT	NOUT is INTEGER The unit number for output.

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 162 of file dchksp.f.

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subroutine dchksy	(	logical, dimension( * )	DOTYPE,
		integer	NN,
		integer, dimension( * )	NVAL,
		integer	NNB,
		integer, dimension( * )	NBVAL,
		integer	NNS,
		integer, dimension( * )	NSVAL,
		double precision	THRESH,
		logical	TSTERR,
		integer	NMAX,
		double precision, dimension( * )	A,
		double precision, dimension( * )	AFAC,
		double precision, dimension( * )	AINV,
		double precision, dimension( * )	B,
		double precision, dimension( * )	X,
		double precision, dimension( * )	XACT,
		double precision, dimension( * )	WORK,
		double precision, dimension( * )	RWORK,
		integer, dimension( * )	IWORK,
		integer	NOUT
	)

DCHKSY

Purpose:

 DCHKSY tests DSYTRF, -TRI2, -TRS, -TRS2, -RFS, and -CON.

Parameters:

[in]	DOTYPE	DOTYPE is LOGICAL array, dimension (NTYPES) The matrix types to be used for testing. Matrices of type j (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) = .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
[in]	NN	NN is INTEGER The number of values of N contained in the vector NVAL.
[in]	NVAL	NVAL is INTEGER array, dimension (NN) The values of the matrix dimension N.
[in]	NNB	NNB is INTEGER The number of values of NB contained in the vector NBVAL.
[in]	NBVAL	NBVAL is INTEGER array, dimension (NBVAL) The values of the blocksize NB.
[in]	NNS	NNS is INTEGER The number of values of NRHS contained in the vector NSVAL.
[in]	NSVAL	NSVAL is INTEGER array, dimension (NNS) The values of the number of right hand sides NRHS.
[in]	THRESH	THRESH is DOUBLE PRECISION The threshold value for the test ratios. A result is included in the output file if RESULT >= THRESH. To have every test ratio printed, use THRESH = 0.
[in]	TSTERR	TSTERR is LOGICAL Flag that indicates whether error exits are to be tested.
[in]	NMAX	NMAX is INTEGER The maximum value permitted for N, used in dimensioning the work arrays.
[out]	A	A is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]	AFAC	AFAC is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]	AINV	AINV is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]	B	B is DOUBLE PRECISION array, dimension (NMAX*NSMAX) where NSMAX is the largest entry in NSVAL.
[out]	X	X is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
[out]	XACT	XACT is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (NMAX*max(3,NSMAX))
[out]	RWORK	RWORK is DOUBLE PRECISION array, dimension (max(NMAX,2*NSMAX))
[out]	IWORK	IWORK is INTEGER array, dimension (2*NMAX)
[in]	NOUT	NOUT is INTEGER The unit number for output.

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: April 2012

Definition at line 171 of file dchksy.f.

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subroutine dchktb	(	logical, dimension( * )	DOTYPE,
		integer	NN,
		integer, dimension( * )	NVAL,
		integer	NNS,
		integer, dimension( * )	NSVAL,
		double precision	THRESH,
		logical	TSTERR,
		integer	NMAX,
		double precision, dimension( * )	AB,
		double precision, dimension( * )	AINV,
		double precision, dimension( * )	B,
		double precision, dimension( * )	X,
		double precision, dimension( * )	XACT,
		double precision, dimension( * )	WORK,
		double precision, dimension( * )	RWORK,
		integer, dimension( * )	IWORK,
		integer	NOUT
	)

DCHKTB

Purpose:

 DCHKTB tests DTBTRS, -RFS, and -CON, and DLATBS.

Parameters:

[in]	DOTYPE	DOTYPE is LOGICAL array, dimension (NTYPES) The matrix types to be used for testing. Matrices of type j (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) = .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
[in]	NN	NN is INTEGER The number of values of N contained in the vector NVAL.
[in]	NVAL	NVAL is INTEGER array, dimension (NN) The values of the matrix column dimension N.
[in]	NNS	NNS is INTEGER The number of values of NRHS contained in the vector NSVAL.
[in]	NSVAL	NSVAL is INTEGER array, dimension (NNS) The values of the number of right hand sides NRHS.
[in]	THRESH	THRESH is DOUBLE PRECISION The threshold value for the test ratios. A result is included in the output file if RESULT >= THRESH. To have every test ratio printed, use THRESH = 0.
[in]	TSTERR	TSTERR is LOGICAL Flag that indicates whether error exits are to be tested.
[in]	NMAX	NMAX is INTEGER The leading dimension of the work arrays. NMAX >= the maximum value of N in NVAL.
[out]	AB	AB is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]	AINV	AINV is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]	B	B is DOUBLE PRECISION array, dimension (NMAX*NSMAX) where NSMAX is the largest entry in NSVAL.
[out]	X	X is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
[out]	XACT	XACT is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (NMAX*max(3,NSMAX))
[out]	RWORK	RWORK is DOUBLE PRECISION array, dimension (max(NMAX,2*NSMAX))
[out]	IWORK	IWORK is INTEGER array, dimension (NMAX)
[in]	NOUT	NOUT is INTEGER The unit number for output.

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 154 of file dchktb.f.

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subroutine dchktp	(	logical, dimension( * )	DOTYPE,
		integer	NN,
		integer, dimension( * )	NVAL,
		integer	NNS,
		integer, dimension( * )	NSVAL,
		double precision	THRESH,
		logical	TSTERR,
		integer	NMAX,
		double precision, dimension( * )	AP,
		double precision, dimension( * )	AINVP,
		double precision, dimension( * )	B,
		double precision, dimension( * )	X,
		double precision, dimension( * )	XACT,
		double precision, dimension( * )	WORK,
		double precision, dimension( * )	RWORK,
		integer, dimension( * )	IWORK,
		integer	NOUT
	)

DCHKTP

Purpose:

 DCHKTP tests DTPTRI, -TRS, -RFS, and -CON, and DLATPS

Parameters:

[in]	DOTYPE	DOTYPE is LOGICAL array, dimension (NTYPES) The matrix types to be used for testing. Matrices of type j (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) = .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
[in]	NN	NN is INTEGER The number of values of N contained in the vector NVAL.
[in]	NVAL	NVAL is INTEGER array, dimension (NN) The values of the matrix column dimension N.
[in]	NNS	NNS is INTEGER The number of values of NRHS contained in the vector NSVAL.
[in]	NSVAL	NSVAL is INTEGER array, dimension (NNS) The values of the number of right hand sides NRHS.
[in]	THRESH	THRESH is DOUBLE PRECISION The threshold value for the test ratios. A result is included in the output file if RESULT >= THRESH. To have every test ratio printed, use THRESH = 0.
[in]	TSTERR	TSTERR is LOGICAL Flag that indicates whether error exits are to be tested.
[in]	NMAX	NMAX is INTEGER The leading dimension of the work arrays. NMAX >= the maximumm value of N in NVAL.
[out]	AP	AP is DOUBLE PRECISION array, dimension (NMAX*(NMAX+1)/2)
[out]	AINVP	AINVP is DOUBLE PRECISION array, dimension (NMAX*(NMAX+1)/2)
[out]	B	B is DOUBLE PRECISION array, dimension (NMAX*NSMAX) where NSMAX is the largest entry in NSVAL.
[out]	X	X is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
[out]	XACT	XACT is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (NMAX*max(3,NSMAX))
[out]	IWORK	IWORK is INTEGER array, dimension (NMAX)
[out]	RWORK	RWORK is DOUBLE PRECISION array, dimension (max(NMAX,2*NSMAX))
[in]	NOUT	NOUT is INTEGER The unit number for output.

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 156 of file dchktp.f.

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subroutine dchktr	(	logical, dimension( * )	DOTYPE,
		integer	NN,
		integer, dimension( * )	NVAL,
		integer	NNB,
		integer, dimension( * )	NBVAL,
		integer	NNS,
		integer, dimension( * )	NSVAL,
		double precision	THRESH,
		logical	TSTERR,
		integer	NMAX,
		double precision, dimension( * )	A,
		double precision, dimension( * )	AINV,
		double precision, dimension( * )	B,
		double precision, dimension( * )	X,
		double precision, dimension( * )	XACT,
		double precision, dimension( * )	WORK,
		double precision, dimension( * )	RWORK,
		integer, dimension( * )	IWORK,
		integer	NOUT
	)

DCHKTR

Purpose:

 DCHKTR tests DTRTRI, -TRS, -RFS, and -CON, and DLATRS

Parameters:

[in]	DOTYPE	DOTYPE is LOGICAL array, dimension (NTYPES) The matrix types to be used for testing. Matrices of type j (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) = .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
[in]	NN	NN is INTEGER The number of values of N contained in the vector NVAL.
[in]	NVAL	NVAL is INTEGER array, dimension (NN) The values of the matrix column dimension N.
[in]	NNB	NNB is INTEGER The number of values of NB contained in the vector NBVAL.
[in]	NBVAL	NBVAL is INTEGER array, dimension (NNB) The values of the blocksize NB.
[in]	NNS	NNS is INTEGER The number of values of NRHS contained in the vector NSVAL.
[in]	NSVAL	NSVAL is INTEGER array, dimension (NNS) The values of the number of right hand sides NRHS.
[in]	THRESH	THRESH is DOUBLE PRECISION The threshold value for the test ratios. A result is included in the output file if RESULT >= THRESH. To have every test ratio printed, use THRESH = 0.
[in]	TSTERR	TSTERR is LOGICAL Flag that indicates whether error exits are to be tested.
[in]	NMAX	NMAX is INTEGER The leading dimension of the work arrays. NMAX >= the maximum value of N in NVAL.
[out]	A	A is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]	AINV	AINV is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]	B	B is DOUBLE PRECISION array, dimension (NMAX*NSMAX) where NSMAX is the largest entry in NSVAL.
[out]	X	X is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
[out]	XACT	XACT is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (NMAX*max(3,NSMAX))
[out]	RWORK	RWORK is DOUBLE PRECISION array, dimension (max(NMAX,2*NSMAX))
[out]	IWORK	IWORK is INTEGER array, dimension (NMAX)
[in]	NOUT	NOUT is INTEGER The unit number for output.

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 166 of file dchktr.f.

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subroutine dchktz	(	logical, dimension( * )	DOTYPE,
		integer	NM,
		integer, dimension( * )	MVAL,
		integer	NN,
		integer, dimension( * )	NVAL,
		double precision	THRESH,
		logical	TSTERR,
		double precision, dimension( * )	A,
		double precision, dimension( * )	COPYA,
		double precision, dimension( * )	S,
		double precision, dimension( * )	TAU,
		double precision, dimension( * )	WORK,
		integer	NOUT
	)

DCHKTZ

Purpose:

 DCHKTZ tests DTZRQF and STZRZF.

Parameters:

[in]	DOTYPE	DOTYPE is LOGICAL array, dimension (NTYPES) The matrix types to be used for testing. Matrices of type j (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) = .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
[in]	NM	NM is INTEGER The number of values of M contained in the vector MVAL.
[in]	MVAL	MVAL is INTEGER array, dimension (NM) The values of the matrix row dimension M.
[in]	NN	NN is INTEGER The number of values of N contained in the vector NVAL.
[in]	NVAL	NVAL is INTEGER array, dimension (NN) The values of the matrix column dimension N.
[in]	THRESH	THRESH is DOUBLE PRECISION The threshold value for the test ratios. A result is included in the output file if RESULT >= THRESH. To have every test ratio printed, use THRESH = 0.
[in]	TSTERR	TSTERR is LOGICAL Flag that indicates whether error exits are to be tested.
[out]	A	A is DOUBLE PRECISION array, dimension (MMAX*NMAX) where MMAX is the maximum value of M in MVAL and NMAX is the maximum value of N in NVAL.
[out]	COPYA	COPYA is DOUBLE PRECISION array, dimension (MMAX*NMAX)
[out]	S	S is DOUBLE PRECISION array, dimension (min(MMAX,NMAX))
[out]	TAU	TAU is DOUBLE PRECISION array, dimension (MMAX)
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (MMAXNMAX + 4NMAX + MMAX)
[in]	NOUT	NOUT is INTEGER The unit number for output.

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 132 of file dchktz.f.

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subroutine ddrvab	(	logical, dimension( * )	DOTYPE,
		integer	NM,
		integer, dimension( * )	MVAL,
		integer	NNS,
		integer, dimension( * )	NSVAL,
		double precision	THRESH,
		integer	NMAX,
		double precision, dimension( * )	A,
		double precision, dimension( * )	AFAC,
		double precision, dimension( * )	B,
		double precision, dimension( * )	X,
		double precision, dimension( * )	WORK,
		double precision, dimension( * )	RWORK,
		real, dimension(*)	SWORK,
		integer, dimension( * )	IWORK,
		integer	NOUT
	)

DDRVAB

Purpose:

 DDRVAB tests DSGESV

Parameters:

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

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 150 of file ddrvab.f.

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subroutine ddrvac	(	logical, dimension( * )	DOTYPE,
		integer	NM,
		integer, dimension( * )	MVAL,
		integer	NNS,
		integer, dimension( * )	NSVAL,
		double precision	THRESH,
		integer	NMAX,
		double precision, dimension( * )	A,
		double precision, dimension( * )	AFAC,
		double precision, dimension( * )	B,
		double precision, dimension( * )	X,
		double precision, dimension( * )	WORK,
		double precision, dimension( * )	RWORK,
		real, dimension(*)	SWORK,
		integer	NOUT
	)

DDRVAC

Purpose:

 DDRVAC tests DSPOSV.

Parameters:

[in]	DOTYPE	DOTYPE is LOGICAL array, dimension (NTYPES) The matrix types to be used for testing. Matrices of type j (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) = .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
[in]	NM	NM is INTEGER The number of values of N contained in the vector MVAL.
[in]	MVAL	MVAL is INTEGER array, dimension (NM) The values of the matrix dimension N.
[in]	NNS	NNS is INTEGER The number of values of NRHS contained in the vector NSVAL.
[in]	NSVAL	NSVAL is INTEGER array, dimension (NNS) The values of the number of right hand sides NRHS.
[in]	THRESH	THRESH is DOUBLE PRECISION The threshold value for the test ratios. A result is included in the output file if RESULT >= THRESH. To have every test ratio printed, use THRESH = 0.
[in]	NMAX	NMAX is INTEGER The maximum value permitted for N, used in dimensioning the work arrays.
[out]	A	A is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]	AFAC	AFAC is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]	B	B is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
[out]	X	X is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (NMAX*max(3,NSMAX))
[out]	RWORK	RWORK is DOUBLE PRECISION array, dimension (max(2NMAX,2NSMAX+NWORK))
[out]	SWORK	SWORK is REAL array, dimension (NMAX*(NSMAX+NMAX))
[in]	NOUT	NOUT is INTEGER The unit number for output.

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 143 of file ddrvac.f.

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subroutine ddrvgb	(	logical, dimension( * )	DOTYPE,
		integer	NN,
		integer, dimension( * )	NVAL,
		integer	NRHS,
		double precision	THRESH,
		logical	TSTERR,
		double precision, dimension( * )	A,
		integer	LA,
		double precision, dimension( * )	AFB,
		integer	LAFB,
		double precision, dimension( * )	ASAV,
		double precision, dimension( * )	B,
		double precision, dimension( * )	BSAV,
		double precision, dimension( * )	X,
		double precision, dimension( * )	XACT,
		double precision, dimension( * )	S,
		double precision, dimension( * )	WORK,
		double precision, dimension( * )	RWORK,
		integer, dimension( * )	IWORK,
		integer	NOUT
	)

DDRVGB

DDRVGBX

Purpose:

 DDRVGB tests the driver routines DGBSV and -SVX.

Parameters:

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

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Purpose:

 DDRVGB tests the driver routines DGBSV, -SVX, and -SVXX.

 Note that this file is used only when the XBLAS are available,
 otherwise ddrvgb.f defines this subroutine.

Parameters:

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

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 171 of file ddrvgb.f.

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subroutine ddrvge	(	logical, dimension( * )	DOTYPE,
		integer	NN,
		integer, dimension( * )	NVAL,
		integer	NRHS,
		double precision	THRESH,
		logical	TSTERR,
		integer	NMAX,
		double precision, dimension( * )	A,
		double precision, dimension( * )	AFAC,
		double precision, dimension( * )	ASAV,
		double precision, dimension( * )	B,
		double precision, dimension( * )	BSAV,
		double precision, dimension( * )	X,
		double precision, dimension( * )	XACT,
		double precision, dimension( * )	S,
		double precision, dimension( * )	WORK,
		double precision, dimension( * )	RWORK,
		integer, dimension( * )	IWORK,
		integer	NOUT
	)

DDRVGE

DDRVGEX

Purpose:

 DDRVGE tests the driver routines DGESV and -SVX.

Parameters:

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

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Purpose:

 DDRVGE tests the driver routines DGESV, -SVX, and -SVXX.

 Note that this file is used only when the XBLAS are available,
 otherwise ddrvge.f defines this subroutine.

Parameters:

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

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: April 2012

Definition at line 163 of file ddrvge.f.

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subroutine ddrvgt	(	logical, dimension( * )	DOTYPE,
		integer	NN,
		integer, dimension( * )	NVAL,
		integer	NRHS,
		double precision	THRESH,
		logical	TSTERR,
		double precision, dimension( * )	A,
		double precision, dimension( * )	AF,
		double precision, dimension( * )	B,
		double precision, dimension( * )	X,
		double precision, dimension( * )	XACT,
		double precision, dimension( * )	WORK,
		double precision, dimension( * )	RWORK,
		integer, dimension( * )	IWORK,
		integer	NOUT
	)

DDRVGT

Purpose:

 DDRVGT tests DGTSV and -SVX.

Parameters:

[in]	DOTYPE	DOTYPE is LOGICAL array, dimension (NTYPES) The matrix types to be used for testing. Matrices of type j (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) = .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
[in]	NN	NN is INTEGER The number of values of N contained in the vector NVAL.
[in]	NVAL	NVAL is INTEGER array, dimension (NN) The values of the matrix dimension N.
[in]	NRHS	NRHS is INTEGER The number of right hand sides, NRHS >= 0.
[in]	THRESH	THRESH is DOUBLE PRECISION The threshold value for the test ratios. A result is included in the output file if RESULT >= THRESH. To have every test ratio printed, use THRESH = 0.
[in]	TSTERR	TSTERR is LOGICAL Flag that indicates whether error exits are to be tested.
[out]	A	A is DOUBLE PRECISION array, dimension (NMAX*4)
[out]	AF	AF is DOUBLE PRECISION array, dimension (NMAX*4)
[out]	B	B is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]	X	X is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]	XACT	XACT is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (NMAX*max(3,NRHS))
[out]	RWORK	RWORK is DOUBLE PRECISION array, dimension (max(NMAX,2*NRHS))
[out]	IWORK	IWORK is INTEGER array, dimension (2*NMAX)
[in]	NOUT	NOUT is INTEGER The unit number for output.

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 139 of file ddrvgt.f.

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subroutine ddrvls	(	logical, dimension( * )	DOTYPE,
		integer	NM,
		integer, dimension( * )	MVAL,
		integer	NN,
		integer, dimension( * )	NVAL,
		integer	NNS,
		integer, dimension( * )	NSVAL,
		integer	NNB,
		integer, dimension( * )	NBVAL,
		integer, dimension( * )	NXVAL,
		double precision	THRESH,
		logical	TSTERR,
		double precision, dimension( * )	A,
		double precision, dimension( * )	COPYA,
		double precision, dimension( * )	B,
		double precision, dimension( * )	COPYB,
		double precision, dimension( * )	C,
		double precision, dimension( * )	S,
		double precision, dimension( * )	COPYS,
		double precision, dimension( * )	WORK,
		integer, dimension( * )	IWORK,
		integer	NOUT
	)

DDRVLS

Purpose:

 DDRVLS tests the least squares driver routines DGELS, DGELSS, DGELSX,
 DGELSY and DGELSD.

Parameters:

[in]	DOTYPE	DOTYPE is LOGICAL array, dimension (NTYPES) The matrix types to be used for testing. Matrices of type j (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) = .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used. The matrix of type j is generated as follows: j=1: A = UDV 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 = UDV 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 (MMAXNMAX + 4NMAX + MMAX).
[out]	IWORK	IWORK is INTEGER array, dimension (15*NMAX)
[in]	NOUT	NOUT is INTEGER The unit number for output.

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 202 of file ddrvls.f.

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subroutine ddrvpb	(	logical, dimension( * )	DOTYPE,
		integer	NN,
		integer, dimension( * )	NVAL,
		integer	NRHS,
		double precision	THRESH,
		logical	TSTERR,
		integer	NMAX,
		double precision, dimension( * )	A,
		double precision, dimension( * )	AFAC,
		double precision, dimension( * )	ASAV,
		double precision, dimension( * )	B,
		double precision, dimension( * )	BSAV,
		double precision, dimension( * )	X,
		double precision, dimension( * )	XACT,
		double precision, dimension( * )	S,
		double precision, dimension( * )	WORK,
		double precision, dimension( * )	RWORK,
		integer, dimension( * )	IWORK,
		integer	NOUT
	)

DDRVPB

Purpose:

 DDRVPB tests the driver routines DPBSV and -SVX.

Parameters:

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

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 163 of file ddrvpb.f.

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subroutine ddrvpo	(	logical, dimension( * )	DOTYPE,
		integer	NN,
		integer, dimension( * )	NVAL,
		integer	NRHS,
		double precision	THRESH,
		logical	TSTERR,
		integer	NMAX,
		double precision, dimension( * )	A,
		double precision, dimension( * )	AFAC,
		double precision, dimension( * )	ASAV,
		double precision, dimension( * )	B,
		double precision, dimension( * )	BSAV,
		double precision, dimension( * )	X,
		double precision, dimension( * )	XACT,
		double precision, dimension( * )	S,
		double precision, dimension( * )	WORK,
		double precision, dimension( * )	RWORK,
		integer, dimension( * )	IWORK,
		integer	NOUT
	)

DDRVPO

DDRVPOX

Purpose:

 DDRVPO tests the driver routines DPOSV and -SVX.

Parameters:

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

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Purpose:

 DDRVPO tests the driver routines DPOSV, -SVX, and -SVXX.

 Note that this file is used only when the XBLAS are available,
 otherwise ddrvpo.f defines this subroutine.

Parameters:

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

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 163 of file ddrvpo.f.

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subroutine ddrvpp	(	logical, dimension( * )	DOTYPE,
		integer	NN,
		integer, dimension( * )	NVAL,
		integer	NRHS,
		double precision	THRESH,
		logical	TSTERR,
		integer	NMAX,
		double precision, dimension( * )	A,
		double precision, dimension( * )	AFAC,
		double precision, dimension( * )	ASAV,
		double precision, dimension( * )	B,
		double precision, dimension( * )	BSAV,
		double precision, dimension( * )	X,
		double precision, dimension( * )	XACT,
		double precision, dimension( * )	S,
		double precision, dimension( * )	WORK,
		double precision, dimension( * )	RWORK,
		integer, dimension( * )	IWORK,
		integer	NOUT
	)

DDRVPP

Purpose:

 DDRVPP tests the driver routines DPPSV and -SVX.

Parameters:

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

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 166 of file ddrvpp.f.

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subroutine ddrvpt	(	logical, dimension( * )	DOTYPE,
		integer	NN,
		integer, dimension( * )	NVAL,
		integer	NRHS,
		double precision	THRESH,
		logical	TSTERR,
		double precision, dimension( * )	A,
		double precision, dimension( * )	D,
		double precision, dimension( * )	E,
		double precision, dimension( * )	B,
		double precision, dimension( * )	X,
		double precision, dimension( * )	XACT,
		double precision, dimension( * )	WORK,
		double precision, dimension( * )	RWORK,
		integer	NOUT
	)

DDRVPT

Purpose:

 DDRVPT tests DPTSV and -SVX.

Parameters:

[in]	DOTYPE	DOTYPE is LOGICAL array, dimension (NTYPES) The matrix types to be used for testing. Matrices of type j (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) = .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
[in]	NN	NN is INTEGER The number of values of N contained in the vector NVAL.
[in]	NVAL	NVAL is INTEGER array, dimension (NN) The values of the matrix dimension N.
[in]	NRHS	NRHS is INTEGER The number of right hand side vectors to be generated for each linear system.
[in]	THRESH	THRESH is DOUBLE PRECISION The threshold value for the test ratios. A result is included in the output file if RESULT >= THRESH. To have every test ratio printed, use THRESH = 0.
[in]	TSTERR	TSTERR is LOGICAL Flag that indicates whether error exits are to be tested.
[out]	A	A is DOUBLE PRECISION array, dimension (NMAX*2)
[out]	D	D is DOUBLE PRECISION array, dimension (NMAX*2)
[out]	E	E is DOUBLE PRECISION array, dimension (NMAX*2)
[out]	B	B is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]	X	X is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]	XACT	XACT is DOUBLE PRECISION array, dimension (NMAX*NRHS)
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (NMAX*max(3,NRHS))
[out]	RWORK	RWORK is DOUBLE PRECISION array, dimension (max(NMAX,2*NRHS))
[in]	NOUT	NOUT is INTEGER The unit number for output.

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 140 of file ddrvpt.f.

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subroutine ddrvrf1	(	integer	NOUT,
		integer	NN,
		integer, dimension( nn )	NVAL,
		double precision	THRESH,
		double precision, dimension( lda, * )	A,
		integer	LDA,
		double precision, dimension( * )	ARF,
		double precision, dimension( * )	WORK
	)

DDRVRF1

Purpose:

 DDRVRF1 tests the LAPACK RFP routines:
     DLANSF

Parameters:

[in]	NOUT	NOUT is INTEGER The unit number for output.
[in]	NN	NN is INTEGER The number of values of N contained in the vector NVAL.
[in]	NVAL	NVAL is INTEGER array, dimension (NN) The values of the matrix dimension N.
[in]	THRESH	THRESH is DOUBLE PRECISION The threshold value for the test ratios. A result is included in the output file if RESULT >= THRESH. To have every test ratio printed, use THRESH = 0.
[out]	A	A is DOUBLE PRECISION array, dimension (LDA,NMAX)
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= max(1,NMAX).
[out]	ARF	ARF is DOUBLE PRECISION array, dimension ((NMAX*(NMAX+1))/2).
[out]	WORK	WORK is DOUBLE PRECISION array, dimension ( NMAX )

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 95 of file ddrvrf1.f.

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subroutine ddrvrf2	(	integer	NOUT,
		integer	NN,
		integer, dimension( nn )	NVAL,
		double precision, dimension( lda, * )	A,
		integer	LDA,
		double precision, dimension( * )	ARF,
		double precision, dimension(*)	AP,
		double precision, dimension( lda, * )	ASAV
	)

DDRVRF2

Purpose:

 DDRVRF2 tests the LAPACK RFP convertion routines.

Parameters:

[in]	NOUT	NOUT is INTEGER The unit number for output.
[in]	NN	NN is INTEGER The number of values of N contained in the vector NVAL.
[in]	NVAL	NVAL is INTEGER array, dimension (NN) The values of the matrix dimension N.
[out]	A	A is DOUBLE PRECISION array, dimension (LDA,NMAX)
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= max(1,NMAX).
[out]	ARF	ARF is DOUBLE PRECISION array, dimension ((NMAX*(NMAX+1))/2).
[out]	AP	AP is DOUBLE PRECISION array, dimension ((NMAX*(NMAX+1))/2).
[out]	ASAV	ASAV is DOUBLE PRECISION array, dimension (LDA,NMAX)

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 90 of file ddrvrf2.f.

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subroutine ddrvrf3	(	integer	NOUT,
		integer	NN,
		integer, dimension( nn )	NVAL,
		double precision	THRESH,
		double precision, dimension( lda, * )	A,
		integer	LDA,
		double precision, dimension( * )	ARF,
		double precision, dimension( lda, * )	B1,
		double precision, dimension( lda, * )	B2,
		double precision, dimension( * )	D_WORK_DLANGE,
		double precision, dimension( * )	D_WORK_DGEQRF,
		double precision, dimension( * )	TAU
	)

DDRVRF3

Purpose:

 DDRVRF3 tests the LAPACK RFP routines:
     DTFSM

Parameters:

[in]	NOUT	NOUT is INTEGER The unit number for output.
[in]	NN	NN is INTEGER The number of values of N contained in the vector NVAL.
[in]	NVAL	NVAL is INTEGER array, dimension (NN) The values of the matrix dimension N.
[in]	THRESH	THRESH is DOUBLE PRECISION The threshold value for the test ratios. A result is included in the output file if RESULT >= THRESH. To have every test ratio printed, use THRESH = 0.
[out]	A	A is DOUBLE PRECISION array, dimension (LDA,NMAX)
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= max(1,NMAX).
[out]	ARF	ARF is DOUBLE PRECISION array, dimension ((NMAX*(NMAX+1))/2).
[out]	B1	B1 is DOUBLE PRECISION array, dimension (LDA,NMAX)
[out]	B2	B2 is DOUBLE PRECISION array, dimension (LDA,NMAX)
[out]	D_WORK_DLANGE	D_WORK_DLANGE is DOUBLE PRECISION array, dimension (NMAX)
[out]	D_WORK_DGEQRF	D_WORK_DGEQRF is DOUBLE PRECISION array, dimension (NMAX)
[out]	TAU	TAU is DOUBLE PRECISION array, dimension (NMAX)

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 118 of file ddrvrf3.f.

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subroutine ddrvrf4	(	integer	NOUT,
		integer	NN,
		integer, dimension( nn )	NVAL,
		double precision	THRESH,
		double precision, dimension( ldc, * )	C1,
		double precision, dimension( ldc, *)	C2,
		integer	LDC,
		double precision, dimension( * )	CRF,
		double precision, dimension( lda, * )	A,
		integer	LDA,
		double precision, dimension( * )	D_WORK_DLANGE
	)

DDRVRF4

Purpose:

 DDRVRF4 tests the LAPACK RFP routines:
     DSFRK

Parameters:

[in]	NOUT	NOUT is INTEGER The unit number for output.
[in]	NN	NN is INTEGER The number of values of N contained in the vector NVAL.
[in]	NVAL	NVAL is INTEGER array, dimension (NN) The values of the matrix dimension N.
[in]	THRESH	THRESH is DOUBLE PRECISION The threshold value for the test ratios. A result is included in the output file if RESULT >= THRESH. To have every test ratio printed, use THRESH = 0.
[out]	C1	C1 is DOUBLE PRECISION array, dimension (LDC,NMAX)
[out]	C2	C2 is DOUBLE PRECISION array, dimension (LDC,NMAX)
[in]	LDC	LDC is INTEGER The leading dimension of the array A. LDA >= max(1,NMAX).
[out]	CRF	CRF is DOUBLE PRECISION array, dimension ((NMAX*(NMAX+1))/2).
[out]	A	A is DOUBLE PRECISION array, dimension (LDA,NMAX)
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= max(1,NMAX).
[out]	D_WORK_DLANGE	D_WORK_DLANGE is DOUBLE PRECISION array, dimension (NMAX)

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 118 of file ddrvrf4.f.

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subroutine ddrvrfp	(	integer	NOUT,
		integer	NN,
		integer, dimension( nn )	NVAL,
		integer	NNS,
		integer, dimension( nns )	NSVAL,
		integer	NNT,
		integer, dimension( nnt )	NTVAL,
		double precision	THRESH,
		double precision, dimension( * )	A,
		double precision, dimension( * )	ASAV,
		double precision, dimension( * )	AFAC,
		double precision, dimension( * )	AINV,
		double precision, dimension( * )	B,
		double precision, dimension( * )	BSAV,
		double precision, dimension( * )	XACT,
		double precision, dimension( * )	X,
		double precision, dimension( * )	ARF,
		double precision, dimension( * )	ARFINV,
		double precision, dimension( * )	D_WORK_DLATMS,
		double precision, dimension( * )	D_WORK_DPOT01,
		double precision, dimension( * )	D_TEMP_DPOT02,
		double precision, dimension( * )	D_TEMP_DPOT03,
		double precision, dimension( * )	D_WORK_DLANSY,
		double precision, dimension( * )	D_WORK_DPOT02,
		double precision, dimension( * )	D_WORK_DPOT03
	)

DDRVRFP

Purpose:

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

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

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

 First, a specific matrix A of size N is created. There is nine types of 
 different matrixes possible.
  1. Diagonal                        6. Random, CNDNUM = sqrt(0.1/EPS)
  2. Random, CNDNUM = 2              7. Random, CNDNUM = 0.1/EPS
 *3. First row and column zero       8. Scaled near underflow
 *4. Last row and column zero        9. Scaled near overflow
 *5. Middle row and column zero
 (* - tests error exits from DPFTRF, no test ratios are computed)
 A solution XACT of size N-by-NRHS is created and the associated right
 hand side B as well. Then DPFTRF is called to compute L (or U), the
 Cholesky factor of A. Then L (or U) is used to solve the linear system
 of equations AX = B. This gives X. Then L (or U) is used to compute the
 inverse of A, AINV. The following four tests are then performed:
 (1) norm( L*L' - A ) / ( N * norm(A) * EPS ) or
     norm( U'*U - A ) / ( N * norm(A) * EPS ),
 (2) norm(B - A*X) / ( norm(A) * norm(X) * EPS ),
 (3) norm( I - A*AINV ) / ( N * norm(A) * norm(AINV) * EPS ),
 (4) ( norm(X-XACT) * RCOND ) / ( norm(XACT) * EPS ),
 where EPS is the machine precision, RCOND the condition number of A, and
 norm( . ) the 1-norm for (1,2,3) and the inf-norm for (4).
 Errors occur when INFO parameter is not as expected. Failures occur when
 a test ratios is greater than THRES.

Parameters:

[in]	NOUT	NOUT is INTEGER The unit number for output.
[in]	NN	NN is INTEGER The number of values of N contained in the vector NVAL.
[in]	NVAL	NVAL is INTEGER array, dimension (NN) The values of the matrix dimension N.
[in]	NNS	NNS is INTEGER The number of values of NRHS contained in the vector NSVAL.
[in]	NSVAL	NSVAL is INTEGER array, dimension (NNS) The values of the number of right-hand sides NRHS.
[in]	NNT	NNT is INTEGER The number of values of MATRIX TYPE contained in the vector NTVAL.
[in]	NTVAL	NTVAL is INTEGER array, dimension (NNT) The values of matrix type (between 0 and 9 for PO/PP/PF matrices).
[in]	THRESH	THRESH is DOUBLE PRECISION The threshold value for the test ratios. A result is included in the output file if RESULT >= THRESH. To have every test ratio printed, use THRESH = 0.
[out]	A	A is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]	ASAV	ASAV is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]	AFAC	AFAC is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]	AINV	AINV is DOUBLE PRECISION array, dimension (NMAX*NMAX)
[out]	B	B is DOUBLE PRECISION array, dimension (NMAX*MAXRHS)
[out]	BSAV	BSAV is DOUBLE PRECISION array, dimension (NMAX*MAXRHS)
[out]	XACT	XACT is DOUBLE PRECISION array, dimension (NMAX*MAXRHS)
[out]	X	X is DOUBLE PRECISION array, dimension (NMAX*MAXRHS)
[out]	ARF	ARF is DOUBLE PRECISION array, dimension ((NMAX*(NMAX+1))/2)
[out]	ARFINV	ARFINV is DOUBLE PRECISION array, dimension ((NMAX*(NMAX+1))/2)
[out]	D_WORK_DLATMS	D_WORK_DLATMS is DOUBLE PRECISION array, dimension ( 3*NMAX )
[out]	D_WORK_DPOT01	D_WORK_DPOT01 is DOUBLE PRECISION array, dimension ( NMAX )
[out]	D_TEMP_DPOT02	D_TEMP_DPOT02 is DOUBLE PRECISION array, dimension ( NMAX*MAXRHS )
[out]	D_TEMP_DPOT03	D_TEMP_DPOT03 is DOUBLE PRECISION array, dimension ( NMAX*NMAX )
[out]	D_WORK_DLATMS	D_WORK_DLATMS is DOUBLE PRECISION array, dimension ( NMAX )
[out]	D_WORK_DLANSY	D_WORK_DLANSY is DOUBLE PRECISION array, dimension ( NMAX )
[out]	D_WORK_DPOT02	D_WORK_DPOT02 is DOUBLE PRECISION array, dimension ( NMAX )
[out]	D_WORK_DPOT03	D_WORK_DPOT03 is DOUBLE PRECISION array, dimension ( NMAX )

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 239 of file ddrvrfp.f.

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subroutine ddrvsp	(	logical, dimension( * )	DOTYPE,
		integer	NN,
		integer, dimension( * )	NVAL,
		integer	NRHS,
		double precision	THRESH,
		logical	TSTERR,
		integer	NMAX,
		double precision, dimension( * )	A,
		double precision, dimension( * )	AFAC,
		double precision, dimension( * )	AINV,
		double precision, dimension( * )	B,
		double precision, dimension( * )	X,
		double precision, dimension( * )	XACT,
		double precision, dimension( * )	WORK,
		double precision, dimension( * )	RWORK,
		integer, dimension( * )	IWORK,
		integer	NOUT
	)

DDRVSP

Purpose:

 DDRVSP tests the driver routines DSPSV and -SVX.

Parameters:

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

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 155 of file ddrvsp.f.

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subroutine ddrvsy	(	logical, dimension( * )	DOTYPE,
		integer	NN,
		integer, dimension( * )	NVAL,
		integer	NRHS,
		double precision	THRESH,
		logical	TSTERR,
		integer	NMAX,
		double precision, dimension( * )	A,
		double precision, dimension( * )	AFAC,
		double precision, dimension( * )	AINV,
		double precision, dimension( * )	B,
		double precision, dimension( * )	X,
		double precision, dimension( * )	XACT,
		double precision, dimension( * )	WORK,
		double precision, dimension( * )	RWORK,
		integer, dimension( * )	IWORK,
		integer	NOUT
	)

DDRVSY

DDRVSYX

Purpose:

 DDRVSY tests the driver routines DSYSV and -SVX.

Parameters:

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

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Purpose:

 DDRVSY tests the driver routines DSYSV, -SVX, and -SVXX.

 Note that this file is used only when the XBLAS are available,
 otherwise ddrvsy.f defines this subroutine.

Parameters:

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

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 152 of file ddrvsy.f.

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subroutine debchvxx	(	double precision	THRESH,
		character*3	PATH
	)

DEBCHVXX

Purpose:

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

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

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

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

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

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

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

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

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

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

     .. Parameters ..
     NMAX is determined by the largest number in the inverse of the hilbert
     matrix.  Precision is exhausted when the largest entry in it is greater
     than 2 to the power of the number of bits in the fraction of the data
     type used plus one, which is 24 for single precision.
     NMAX should be 6 for single and 11 for double.

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 97 of file debchvxx.f.

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subroutine derrab ( integer NUNIT )

DERRAB

Purpose:

 DERRAB tests the error exits for DSGESV.

Parameters:

[in]

NUNIT

          NUNIT is INTEGER
          The unit number for output.

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 48 of file derrab.f.

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subroutine derrac ( integer NUNIT )

DERRAC

Purpose:

 DERRAC tests the error exits for DSPOSV.

Parameters:

[in]

NUNIT

          NUNIT is INTEGER
          The unit number for output.

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 48 of file derrac.f.

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subroutine derrge	(	character*3	PATH,
		integer	NUNIT
	)

DERRGE

DERRGEX

Purpose:

 DERRGE tests the error exits for the DOUBLE PRECISION routines
 for general matrices.

Parameters:

[in]	PATH	PATH is CHARACTER*3 The LAPACK path name for the routines to be tested.
[in]	NUNIT	NUNIT is INTEGER The unit number for output.

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Purpose:

 DERRGE tests the error exits for the DOUBLE PRECISION routines
 for general matrices.

 Note that this file is used only when the XBLAS are available,
 otherwise derrge.f defines this subroutine.

Parameters:

[in]	PATH	PATH is CHARACTER*3 The LAPACK path name for the routines to be tested.
[in]	NUNIT	NUNIT is INTEGER The unit number for output.

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 56 of file derrge.f.

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subroutine derrgt	(	character*3	PATH,
		integer	NUNIT
	)

DERRGT

Purpose:

 DERRGT tests the error exits for the DOUBLE PRECISION tridiagonal
 routines.

Parameters:

[in]	PATH	PATH is CHARACTER*3 The LAPACK path name for the routines to be tested.
[in]	NUNIT	NUNIT is INTEGER The unit number for output.

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 56 of file derrgt.f.

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subroutine derrlq	(	character*3	PATH,
		integer	NUNIT
	)

DERRLQ

Purpose:

 DERRLQ tests the error exits for the DOUBLE PRECISION routines
 that use the LQ decomposition of a general matrix.

Parameters:

[in]	PATH	PATH is CHARACTER*3 The LAPACK path name for the routines to be tested.
[in]	NUNIT	NUNIT is INTEGER The unit number for output.

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 56 of file derrlq.f.

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subroutine derrls	(	character*3	PATH,
		integer	NUNIT
	)

DERRLS

Purpose:

 DERRLS tests the error exits for the DOUBLE PRECISION least squares
 driver routines (DGELS, SGELSS, SGELSX, SGELSY, SGELSD).

Parameters:

[in]	PATH	PATH is CHARACTER*3 The LAPACK path name for the routines to be tested.
[in]	NUNIT	NUNIT is INTEGER The unit number for output.

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 56 of file derrls.f.

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subroutine derrpo	(	character*3	PATH,
		integer	NUNIT
	)

DERRPO

DERRPOX

Purpose:

 DERRPO tests the error exits for the DOUBLE PRECISION routines
 for symmetric positive definite matrices.

Parameters:

[in]	PATH	PATH is CHARACTER*3 The LAPACK path name for the routines to be tested.
[in]	NUNIT	NUNIT is INTEGER The unit number for output.

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Purpose:

 DERRPO tests the error exits for the DOUBLE PRECISION routines
 for symmetric positive definite matrices.

 Note that this file is used only when the XBLAS are available,
 otherwise derrpo.f defines this subroutine.

Parameters:

[in]	PATH	PATH is CHARACTER*3 The LAPACK path name for the routines to be tested.
[in]	NUNIT	NUNIT is INTEGER The unit number for output.

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 56 of file derrpo.f.

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subroutine derrps	(	character*3	PATH,
		integer	NUNIT
	)

DERRPS

Purpose:

 DERRPS tests the error exits for the DOUBLE PRECISION routines
 for DPSTRF.

Parameters:

[in]	PATH	PATH is CHARACTER*3 The LAPACK path name for the routines to be tested.
[in]	NUNIT	NUNIT is INTEGER The unit number for output.

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 56 of file derrps.f.

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subroutine derrql	(	character*3	PATH,
		integer	NUNIT
	)

DERRQL

Purpose:

 DERRQL tests the error exits for the DOUBLE PRECISION routines
 that use the QL decomposition of a general matrix.

Parameters:

[in]	PATH	PATH is CHARACTER*3 The LAPACK path name for the routines to be tested.
[in]	NUNIT	NUNIT is INTEGER The unit number for output.

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 56 of file derrql.f.

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subroutine derrqp	(	character*3	PATH,
		integer	NUNIT
	)

DERRQP

Purpose:

 DERRQP tests the error exits for DGEQPF and DGEQP3.

Parameters:

[in]	PATH	PATH is CHARACTER*3 The LAPACK path name for the routines to be tested.
[in]	NUNIT	NUNIT is INTEGER The unit number for output.

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 55 of file derrqp.f.

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subroutine derrqr	(	character*3	PATH,
		integer	NUNIT
	)

DERRQR

Purpose:

 DERRQR tests the error exits for the DOUBLE PRECISION routines
 that use the QR decomposition of a general matrix.

Parameters:

[in]	PATH	PATH is CHARACTER*3 The LAPACK path name for the routines to be tested.
[in]	NUNIT	NUNIT is INTEGER The unit number for output.

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 56 of file derrqr.f.

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subroutine derrqrt	(	character*3	PATH,
		integer	NUNIT
	)

DERRQRT

Purpose:

 DERRQRT tests the error exits for the DOUBLE PRECISION routines
 that use the QRT decomposition of a general matrix.

Parameters:

[in]	PATH	PATH is CHARACTER*3 The LAPACK path name for the routines to be tested.
[in]	NUNIT	NUNIT is INTEGER The unit number for output.

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 56 of file derrqrt.f.

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subroutine derrqrtp	(	character*3	PATH,
		integer	NUNIT
	)

DERRQRTP

Purpose:

 DERRQRTP tests the error exits for the REAL routines
 that use the QRT decomposition of a triangular-pentagonal matrix.

Parameters:

[in]	PATH	PATH is CHARACTER*3 The LAPACK path name for the routines to be tested.
[in]	NUNIT	NUNIT is INTEGER The unit number for output.

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 56 of file derrqrtp.f.

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subroutine derrrfp ( integer NUNIT )

DERRRFP

Purpose:

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

 DDRVRFP tests the DOUBLE PRECISION LAPACK RFP routines:
     DTFSM, DTFTRI, DSFRK, DTFTTP, DTFTTR, DPFTRF, DPFTRS, DTPTTF,
     DTPTTR, DTRTTF, and DTRTTP

Parameters:

[in]

NUNIT

          NUNIT is INTEGER
          The unit number for output.

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 53 of file derrrfp.f.

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subroutine derrrq	(	character*3	PATH,
		integer	NUNIT
	)

DERRRQ

Purpose:

 DERRRQ tests the error exits for the DOUBLE PRECISION routines
 that use the RQ decomposition of a general matrix.

Parameters:

[in]	PATH	PATH is CHARACTER*3 The LAPACK path name for the routines to be tested.
[in]	NUNIT	NUNIT is INTEGER The unit number for output.

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 56 of file derrrq.f.

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subroutine derrsy	(	character*3	PATH,
		integer	NUNIT
	)

DERRSY

DERRSYX

Purpose:

 DERRSY tests the error exits for the DOUBLE PRECISION routines
 for symmetric indefinite matrices.

Parameters:

[in]	PATH	PATH is CHARACTER*3 The LAPACK path name for the routines to be tested.
[in]	NUNIT	NUNIT is INTEGER The unit number for output.

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: April 2012

Purpose:

 DERRSY tests the error exits for the DOUBLE PRECISION routines
 for symmetric indefinite matrices.

 Note that this file is used only when the XBLAS are available,
 otherwise derrsy.f defines this subroutine.

Parameters:

[in]	PATH	PATH is CHARACTER*3 The LAPACK path name for the routines to be tested.
[in]	NUNIT	NUNIT is INTEGER The unit number for output.

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 56 of file derrsy.f.

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subroutine derrtr	(	character*3	PATH,
		integer	NUNIT
	)

DERRTR

Purpose:

 DERRTR tests the error exits for the DOUBLE PRECISION triangular
 routines.

Parameters:

[in]	PATH	PATH is CHARACTER*3 The LAPACK path name for the routines to be tested.
[in]	NUNIT	NUNIT is INTEGER The unit number for output.

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 56 of file derrtr.f.

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subroutine derrtz	(	character*3	PATH,
		integer	NUNIT
	)

DERRTZ

Purpose:

 DERRTZ tests the error exits for DTZRQF and STZRZF.

Parameters:

[in]	PATH	PATH is CHARACTER*3 The LAPACK path name for the routines to be tested.
[in]	NUNIT	NUNIT is INTEGER The unit number for output.

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 55 of file derrtz.f.

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subroutine derrvx	(	character*3	PATH,
		integer	NUNIT
	)

DERRVX

DERRVXX

Purpose:

 DERRVX tests the error exits for the DOUBLE PRECISION driver routines
 for solving linear systems of equations.

Parameters:

[in]	PATH	PATH is CHARACTER*3 The LAPACK path name for the routines to be tested.
[in]	NUNIT	NUNIT is INTEGER The unit number for output.

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: April 2012

Purpose:

 DERRVX tests the error exits for the DOUBLE PRECISION driver routines
 for solving linear systems of equations.

Parameters:

[in]	PATH	PATH is CHARACTER*3 The LAPACK path name for the routines to be tested.
[in]	NUNIT	NUNIT is INTEGER The unit number for output.

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 56 of file derrvx.f.

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subroutine dgbt01	(	integer	M,
		integer	N,
		integer	KL,
		integer	KU,
		double precision, dimension( lda, * )	A,
		integer	LDA,
		double precision, dimension( ldafac, * )	AFAC,
		integer	LDAFAC,
		integer, dimension( * )	IPIV,
		double precision, dimension( * )	WORK,
		double precision	RESID
	)

DGBT01

Purpose:

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

 The expression L*U - A is computed one column at a time, so A and
 AFAC are not modified.

Parameters:

[in]	M	M is INTEGER The number of rows of the matrix A. M >= 0.
[in]	N	N is INTEGER The number of columns of the matrix A. N >= 0.
[in]	KL	KL is INTEGER The number of subdiagonals within the band of A. KL >= 0.
[in]	KU	KU is INTEGER The number of superdiagonals within the band of A. KU >= 0.
[in,out]	A	A is DOUBLE PRECISION array, dimension (LDA,N) The original matrix A in band storage, stored in rows 1 to KL+KU+1.
[in]	LDA	LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,KL+KU+1).
[in]	AFAC	AFAC is DOUBLE PRECISION array, dimension (LDAFAC,N) The factored form of the matrix A. AFAC contains the banded factors L and U from the LU 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 2KL+KU+1. See DGBTRF for further details.
[in]	LDAFAC	LDAFAC is INTEGER The leading dimension of the array AFAC. LDAFAC >= max(1,2KLKU+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(LU - A) / ( N norm(A) * EPS )

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 126 of file dgbt01.f.

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subroutine dgbt02	(	character	TRANS,
		integer	M,
		integer	N,
		integer	KL,
		integer	KU,
		integer	NRHS,
		double precision, dimension( lda, * )	A,
		integer	LDA,
		double precision, dimension( ldx, * )	X,
		integer	LDX,
		double precision, dimension( ldb, * )	B,
		integer	LDB,
		double precision	RESID
	)

DGBT02

Purpose:

 DGBT02 computes the residual for a solution of a banded system of
 equations  A*x = b  or  A'*x = b:
    RESID = norm( B - A*X ) / ( norm(A) * norm(X) * EPS).
 where EPS is the machine precision.

Parameters:

[in]	TRANS	TRANS is CHARACTER1 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 - AX) / ( norm(A) norm(X) * EPS ).

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 139 of file dgbt02.f.

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subroutine dgbt05	(	character	TRANS,
		integer	N,
		integer	KL,
		integer	KU,
		integer	NRHS,
		double precision, dimension( ldab, * )	AB,
		integer	LDAB,
		double precision, dimension( ldb, * )	B,
		integer	LDB,
		double precision, dimension( ldx, * )	X,
		integer	LDX,
		double precision, dimension( ldxact, * )	XACT,
		integer	LDXACT,
		double precision, dimension( * )	FERR,
		double precision, dimension( * )	BERR,
		double precision, dimension( * )	RESLTS
	)

DGBT05

Purpose:

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

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

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

 RESLTS(2) = residual from the iterative refinement routine
           = the maximum of BERR / ( NZ*EPS + (*) ), where
             (*) = NZ*UNFL / (min_i (abs(op(A))*abs(X) +abs(b))_i )
             and NZ = max. number of nonzeros in any row of A, plus 1

Parameters:

[in]	TRANS	TRANS is CHARACTER1 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 / ( NZEPS + () )

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 176 of file dgbt05.f.

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subroutine dgelqs	(	integer	M,
		integer	N,
		integer	NRHS,
		double precision, dimension( lda, * )	A,
		integer	LDA,
		double precision, dimension( * )	TAU,
		double precision, dimension( ldb, * )	B,
		integer	LDB,
		double precision, dimension( lwork )	WORK,
		integer	LWORK,
		integer	INFO
	)

DGELQS

Purpose:

 Compute a minimum-norm solution
     min || A*X - B ||
 using the LQ factorization
     A = L*Q
 computed by DGELQF.

Parameters:

[in]	M	M is INTEGER The number of rows of the matrix A. M >= 0.
[in]	N	N is INTEGER The number of columns of the matrix A. N >= M >= 0.
[in]	NRHS	NRHS is INTEGER The number of columns of B. NRHS >= 0.
[in]	A	A is DOUBLE PRECISION array, dimension (LDA,N) Details of the LQ factorization of the original matrix A as returned by DGELQF.
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= M.
[in]	TAU	TAU is DOUBLE PRECISION array, dimension (M) Details of the orthogonal matrix Q.
[in,out]	B	B is DOUBLE PRECISION array, dimension (LDB,NRHS) On entry, the m-by-nrhs right hand side matrix B. On exit, the n-by-nrhs solution matrix X.
[in]	LDB	LDB is INTEGER The leading dimension of the array B. LDB >= N.
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (LWORK)
[in]	LWORK	LWORK is INTEGER The length of the array WORK. LWORK must be at least NRHS, and should be at least NRHS*NB, where NB is the block size for this environment.
[out]	INFO	INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 121 of file dgelqs.f.

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LOGICAL function dgennd	(	integer	M,
		integer	N,
		double precision, dimension( lda, * )	A,
		integer	LDA
	)

DGENND

Purpose:

    DGENND tests that its argument has a non-negative diagonal.

Parameters:

[in]	M	M is INTEGER The number of rows in A.
[in]	N	N is INTEGER The number of columns in A.
[in]	A	A is DOUBLE PRECISION array, dimension (LDA, N) The matrix.
[in]	LDA	LDA is INTEGER Leading dimension of A.

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 69 of file dgennd.f.

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subroutine dgeqls	(	integer	M,
		integer	N,
		integer	NRHS,
		double precision, dimension( lda, * )	A,
		integer	LDA,
		double precision, dimension( * )	TAU,
		double precision, dimension( ldb, * )	B,
		integer	LDB,
		double precision, dimension( lwork )	WORK,
		integer	LWORK,
		integer	INFO
	)

DGEQLS

Purpose:

 Solve the least squares problem
     min || A*X - B ||
 using the QL factorization
     A = Q*L
 computed by DGEQLF.

Parameters:

[in]	M	M is INTEGER The number of rows of the matrix A. M >= 0.
[in]	N	N is INTEGER The number of columns of the matrix A. M >= N >= 0.
[in]	NRHS	NRHS is INTEGER The number of columns of B. NRHS >= 0.
[in]	A	A is DOUBLE PRECISION array, dimension (LDA,N) Details of the QL factorization of the original matrix A as returned by DGEQLF.
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= M.
[in]	TAU	TAU is DOUBLE PRECISION array, dimension (N) Details of the orthogonal matrix Q.
[in,out]	B	B is DOUBLE PRECISION array, dimension (LDB,NRHS) On entry, the m-by-nrhs right hand side matrix B. On exit, the n-by-nrhs solution matrix X, stored in rows m-n+1:m.
[in]	LDB	LDB is INTEGER The leading dimension of the array B. LDB >= M.
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (LWORK)
[in]	LWORK	LWORK is INTEGER The length of the array WORK. LWORK must be at least NRHS, and should be at least NRHS*NB, where NB is the block size for this environment.
[out]	INFO	INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 122 of file dgeqls.f.

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subroutine dgeqrs	(	integer	M,
		integer	N,
		integer	NRHS,
		double precision, dimension( lda, * )	A,
		integer	LDA,
		double precision, dimension( * )	TAU,
		double precision, dimension( ldb, * )	B,
		integer	LDB,
		double precision, dimension( lwork )	WORK,
		integer	LWORK,
		integer	INFO
	)

DGEQRS

Purpose:

 Solve the least squares problem
     min || A*X - B ||
 using the QR factorization
     A = Q*R
 computed by DGEQRF.

Parameters:

[in]	M	M is INTEGER The number of rows of the matrix A. M >= 0.
[in]	N	N is INTEGER The number of columns of the matrix A. M >= N >= 0.
[in]	NRHS	NRHS is INTEGER The number of columns of B. NRHS >= 0.
[in]	A	A is DOUBLE PRECISION array, dimension (LDA,N) Details of the QR factorization of the original matrix A as returned by DGEQRF.
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= M.
[in]	TAU	TAU is DOUBLE PRECISION array, dimension (N) Details of the orthogonal matrix Q.
[in,out]	B	B is DOUBLE PRECISION array, dimension (LDB,NRHS) On entry, the m-by-nrhs right hand side matrix B. On exit, the n-by-nrhs solution matrix X.
[in]	LDB	LDB is INTEGER The leading dimension of the array B. LDB >= M.
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (LWORK)
[in]	LWORK	LWORK is INTEGER The length of the array WORK. LWORK must be at least NRHS, and should be at least NRHS*NB, where NB is the block size for this environment.
[out]	INFO	INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 121 of file dgeqrs.f.

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subroutine dgerqs	(	integer	M,
		integer	N,
		integer	NRHS,
		double precision, dimension( lda, * )	A,
		integer	LDA,
		double precision, dimension( * )	TAU,
		double precision, dimension( ldb, * )	B,
		integer	LDB,
		double precision, dimension( lwork )	WORK,
		integer	LWORK,
		integer	INFO
	)

DGERQS

Purpose:

 Compute a minimum-norm solution
     min || A*X - B ||
 using the RQ factorization
     A = R*Q
 computed by DGERQF.

Parameters:

[in]	M	M is INTEGER The number of rows of the matrix A. M >= 0.
[in]	N	N is INTEGER The number of columns of the matrix A. N >= M >= 0.
[in]	NRHS	NRHS is INTEGER The number of columns of B. NRHS >= 0.
[in]	A	A is DOUBLE PRECISION array, dimension (LDA,N) Details of the RQ factorization of the original matrix A as returned by DGERQF.
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= M.
[in]	TAU	TAU is DOUBLE PRECISION array, dimension (M) Details of the orthogonal matrix Q.
[in,out]	B	B is DOUBLE PRECISION array, dimension (LDB,NRHS) On entry, the right hand side vectors for the linear system. On exit, the solution vectors X. Each solution vector is contained in rows 1:N of a column of B.
[in]	LDB	LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (LWORK)
[in]	LWORK	LWORK is INTEGER The length of the array WORK. LWORK must be at least NRHS, and should be at least NRHS*NB, where NB is the block size for this environment.
[out]	INFO	INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 122 of file dgerqs.f.

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subroutine dget01	(	integer	M,
		integer	N,
		double precision, dimension( lda, * )	A,
		integer	LDA,
		double precision, dimension( ldafac, * )	AFAC,
		integer	LDAFAC,
		integer, dimension( * )	IPIV,
		double precision, dimension( * )	RWORK,
		double precision	RESID
	)

DGET01

Purpose:

 DGET01 reconstructs a matrix A from its L*U factorization and
 computes the residual
    norm(L*U - A) / ( N * norm(A) * EPS ),
 where EPS is the machine epsilon.

Parameters:

[in]	M	M is INTEGER The number of rows of the matrix A. M >= 0.
[in]	N	N is INTEGER The number of columns of the matrix A. N >= 0.
[in]	A	A is DOUBLE PRECISION array, dimension (LDA,N) The original M x N matrix A.
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).
[in,out]	AFAC	AFAC is DOUBLE PRECISION array, dimension (LDAFAC,N) The factored form of the matrix A. AFAC contains the factors L and U from the LU factorization as computed by DGETRF. Overwritten with the reconstructed matrix, and then with the difference LU - 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(LU - A) / ( N norm(A) * EPS )

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 107 of file dget01.f.

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subroutine dget02	(	character	TRANS,
		integer	M,
		integer	N,
		integer	NRHS,
		double precision, dimension( lda, * )	A,
		integer	LDA,
		double precision, dimension( ldx, * )	X,
		integer	LDX,
		double precision, dimension( ldb, * )	B,
		integer	LDB,
		double precision, dimension( * )	RWORK,
		double precision	RESID
	)

DGET02

Purpose:

 DGET02 computes the residual for a solution of a system of linear
 equations  A*x = b  or  A'*x = b:
    RESID = norm(B - A*X) / ( norm(A) * norm(X) * EPS ),
 where EPS is the machine epsilon.

Parameters:

[in]	TRANS	TRANS is CHARACTER1 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 - AX) / ( norm(A) norm(X) * EPS ).

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 133 of file dget02.f.

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subroutine dget03	(	integer	N,
		double precision, dimension( lda, * )	A,
		integer	LDA,
		double precision, dimension( ldainv, * )	AINV,
		integer	LDAINV,
		double precision, dimension( ldwork, * )	WORK,
		integer	LDWORK,
		double precision, dimension( * )	RWORK,
		double precision	RCOND,
		double precision	RESID
	)

DGET03

Purpose:

 DGET03 computes the residual for a general matrix times its inverse:
    norm( I - AINV*A ) / ( N * norm(A) * norm(AINV) * EPS ),
 where EPS is the machine epsilon.

Parameters:

[in]	N	N is INTEGER The number of rows and columns of the matrix A. N >= 0.
[in]	A	A is DOUBLE PRECISION array, dimension (LDA,N) The original N x N matrix A.
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).
[in]	AINV	AINV is DOUBLE PRECISION array, dimension (LDAINV,N) The inverse of the matrix A.
[in]	LDAINV	LDAINV is INTEGER The leading dimension of the array AINV. LDAINV >= max(1,N).
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (LDWORK,N)
[in]	LDWORK	LDWORK is INTEGER The leading dimension of the array WORK. LDWORK >= max(1,N).
[out]	RWORK	RWORK is DOUBLE PRECISION array, dimension (N)
[out]	RCOND	RCOND is DOUBLE PRECISION The reciprocal of the condition number of A, computed as ( 1/norm(A) ) / norm(AINV).
[out]	RESID	RESID is DOUBLE PRECISION norm(I - AINVA) / ( N norm(A) * norm(AINV) * EPS )

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 109 of file dget03.f.

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subroutine dget04	(	integer	N,
		integer	NRHS,
		double precision, dimension( ldx, * )	X,
		integer	LDX,
		double precision, dimension( ldxact, * )	XACT,
		integer	LDXACT,
		double precision	RCOND,
		double precision	RESID
	)

DGET04

Purpose:

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

 RESID =  ( norm(X-XACT) * RCOND ) / ( norm(XACT) * EPS ),
 where RCOND is the reciprocal of the condition number and EPS is the
 machine epsilon.

Parameters:

[in]	N	N is INTEGER The number of rows of the matrices X and XACT. N >= 0.
[in]	NRHS	NRHS is INTEGER The number of columns of the matrices X and XACT. NRHS >= 0.
[in]	X	X is DOUBLE PRECISION array, dimension (LDX,NRHS) The computed solution vectors. Each vector is stored as a column of the matrix X.
[in]	LDX	LDX is INTEGER The leading dimension of the array X. LDX >= max(1,N).
[in]	XACT	XACT is DOUBLE PRECISION array, dimension( LDX, NRHS ) The exact solution vectors. Each vector is stored as a column of the matrix XACT.
[in]	LDXACT	LDXACT is INTEGER The leading dimension of the array XACT. LDXACT >= max(1,N).
[in]	RCOND	RCOND is DOUBLE PRECISION The reciprocal of the condition number of the coefficient matrix in the system of equations.
[out]	RESID	RESID is DOUBLE PRECISION The maximum over the NRHS solution vectors of ( norm(X-XACT) * RCOND ) / ( norm(XACT) * EPS )

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 103 of file dget04.f.

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DOUBLE PRECISION function dget06	(	double precision	RCOND,
		double precision	RCONDC
	)

DGET06

Purpose:

 DGET06 computes a test ratio to compare two values for RCOND.

Parameters:

[in]

RCOND

          RCOND is DOUBLE PRECISION
          The estimate of the reciprocal of the condition number of A,
          as computed by DGECON.

[in]

RCONDC

          RCONDC is DOUBLE PRECISION
          The reciprocal of the condition number of A, computed as
          ( 1/norm(A) ) / norm(inv(A)).

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 56 of file dget06.f.

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subroutine dget07	(	character	TRANS,
		integer	N,
		integer	NRHS,
		double precision, dimension( lda, * )	A,
		integer	LDA,
		double precision, dimension( ldb, * )	B,
		integer	LDB,
		double precision, dimension( ldx, * )	X,
		integer	LDX,
		double precision, dimension( ldxact, * )	XACT,
		integer	LDXACT,
		double precision, dimension( * )	FERR,
		logical	CHKFERR,
		double precision, dimension( * )	BERR,
		double precision, dimension( * )	RESLTS
	)

DGET07

Purpose:

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

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

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

 RESLTS(2) = residual from the iterative refinement routine
           = the maximum of BERR / ( (n+1)*EPS + (*) ), where
             (*) = (n+1)*UNFL / (min_i (abs(op(A))*abs(X) +abs(b))_i )

Parameters:

[in]	TRANS	TRANS is CHARACTER1 Specifies the form of the system of equations. = 'N': A X = B (No transpose) = 'T': A*T X = B (Transpose) = 'C': A*H X = B (Conjugate transpose = Transpose)
[in]	N	N is INTEGER The number of rows of the matrices X and XACT. N >= 0.
[in]	NRHS	NRHS is INTEGER The number of columns of the matrices X and XACT. NRHS >= 0.
[in]	A	A is DOUBLE PRECISION array, dimension (LDA,N) The original n by n matrix A.
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).
[in]	B	B is DOUBLE PRECISION array, dimension (LDB,NRHS) The right hand side vectors for the system of linear equations.
[in]	LDB	LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).
[in]	X	X is DOUBLE PRECISION array, dimension (LDX,NRHS) The computed solution vectors. Each vector is stored as a column of the matrix X.
[in]	LDX	LDX is INTEGER The leading dimension of the array X. LDX >= max(1,N).
[in]	XACT	XACT is DOUBLE PRECISION array, dimension (LDX,NRHS) The exact solution vectors. Each vector is stored as a column of the matrix XACT.
[in]	LDXACT	LDXACT is INTEGER The leading dimension of the array XACT. LDXACT >= max(1,N).
[in]	FERR	FERR is DOUBLE PRECISION array, dimension (NRHS) The estimated forward error bounds for each solution vector X. If XTRUE is the true solution, FERR bounds the magnitude of the largest entry in (X - XTRUE) divided by the magnitude of the largest entry in X.
[in]	CHKFERR	CHKFERR is LOGICAL Set to .TRUE. to check FERR, .FALSE. not to check FERR. When the test system is ill-conditioned, the "true" solution in XACT may be incorrect.
[in]	BERR	BERR is DOUBLE PRECISION array, dimension (NRHS) The componentwise relative backward error of each solution vector (i.e., the smallest relative change in any entry of A or B that makes X an exact solution).
[out]	RESLTS	RESLTS is DOUBLE PRECISION array, dimension (2) The maximum over the NRHS solution vectors of the ratios: RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR ) RESLTS(2) = BERR / ( (n+1)EPS + () )

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 165 of file dget07.f.

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subroutine dget08	(	character	TRANS,
		integer	M,
		integer	N,
		integer	NRHS,
		double precision, dimension( lda, * )	A,
		integer	LDA,
		double precision, dimension( ldx, * )	X,
		integer	LDX,
		double precision, dimension( ldb, * )	B,
		integer	LDB,
		double precision, dimension( * )	RWORK,
		double precision	RESID
	)

DGET08

Purpose:

 DGET08 computes the residual for a solution of a system of linear
 equations  A*x = b  or  A'*x = b:
    RESID = norm(B - A*X,inf) / ( norm(A,inf) * norm(X,inf) * EPS ),
 where EPS is the machine epsilon.

Parameters:

[in]	TRANS	TRANS is CHARACTER1 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 - AX) / ( norm(A) norm(X) * EPS ).

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 133 of file dget08.f.

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subroutine dgtt01	(	integer	N,
		double precision, dimension( * )	DL,
		double precision, dimension( * )	D,
		double precision, dimension( * )	DU,
		double precision, dimension( * )	DLF,
		double precision, dimension( * )	DF,
		double precision, dimension( * )	DUF,
		double precision, dimension( * )	DU2,
		integer, dimension( * )	IPIV,
		double precision, dimension( ldwork, * )	WORK,
		integer	LDWORK,
		double precision, dimension( * )	RWORK,
		double precision	RESID
	)

DGTT01

Purpose:

 DGTT01 reconstructs a tridiagonal matrix A from its LU factorization
 and computes the residual
    norm(L*U - A) / ( norm(A) * EPS ),
 where EPS is the machine epsilon.

Parameters:

[in]	N	N is INTEGTER The order of the matrix A. N >= 0.
[in]	DL	DL is DOUBLE PRECISION array, dimension (N-1) The (n-1) sub-diagonal elements of A.
[in]	D	D is DOUBLE PRECISION array, dimension (N) The diagonal elements of A.
[in]	DU	DU is DOUBLE PRECISION array, dimension (N-1) The (n-1) super-diagonal elements of A.
[in]	DLF	DLF is DOUBLE PRECISION array, dimension (N-1) The (n-1) multipliers that define the matrix L from the LU factorization of A.
[in]	DF	DF is DOUBLE PRECISION array, dimension (N) The n diagonal elements of the upper triangular matrix U from the LU factorization of A.
[in]	DUF	DUF is DOUBLE PRECISION array, dimension (N-1) The (n-1) elements of the first super-diagonal of U.
[in]	DU2	DU2 is DOUBLE PRECISION array, dimension (N-2) The (n-2) elements of the second super-diagonal of U.
[in]	IPIV	IPIV is INTEGER array, dimension (N) The pivot indices; for 1 <= i <= n, row i of the matrix was interchanged with row IPIV(i). IPIV(i) will always be either i or i+1; IPIV(i) = i indicates a row interchange was not required.
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (LDWORK,N)
[in]	LDWORK	LDWORK is INTEGER The leading dimension of the array WORK. LDWORK >= max(1,N).
[out]	RWORK	RWORK is DOUBLE PRECISION array, dimension (N)
[out]	RESID	RESID is DOUBLE PRECISION The scaled residual: norm(LU - A) / (norm(A) EPS)

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 134 of file dgtt01.f.

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subroutine dgtt02	(	character	TRANS,
		integer	N,
		integer	NRHS,
		double precision, dimension( * )	DL,
		double precision, dimension( * )	D,
		double precision, dimension( * )	DU,
		double precision, dimension( ldx, * )	X,
		integer	LDX,
		double precision, dimension( ldb, * )	B,
		integer	LDB,
		double precision	RESID
	)

DGTT02

Purpose:

 DGTT02 computes the residual for the solution to a tridiagonal
 system of equations:
    RESID = norm(B - op(A)*X) / (norm(A) * norm(X) * EPS),
 where EPS is the machine epsilon.

Parameters:

[in]	TRANS	TRANS is CHARACTER Specifies the form of the residual. = 'N': B - A * X (No transpose) = 'T': B - A'* X (Transpose) = 'C': B - A'* X (Conjugate transpose = Transpose)
[in]	N	N is INTEGTER The order of the matrix A. N >= 0.
[in]	NRHS	NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrices B and X. NRHS >= 0.
[in]	DL	DL is DOUBLE PRECISION array, dimension (N-1) The (n-1) sub-diagonal elements of A.
[in]	D	D is DOUBLE PRECISION array, dimension (N) The diagonal elements of A.
[in]	DU	DU is DOUBLE PRECISION array, dimension (N-1) The (n-1) super-diagonal elements of A.
[in]	X	X is DOUBLE PRECISION array, dimension (LDX,NRHS) The computed solution vectors X.
[in]	LDX	LDX is INTEGER The leading dimension of the array X. LDX >= max(1,N).
[in,out]	B	B is DOUBLE PRECISION array, dimension (LDB,NRHS) On entry, the right hand side vectors for the system of linear equations. On exit, B is overwritten with the difference B - op(A)*X.
[in]	LDB	LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).
[out]	RESID	RESID is DOUBLE PRECISION norm(B - op(A)X) / (norm(A) norm(X) * EPS)

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 124 of file dgtt02.f.

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subroutine dgtt05	(	character	TRANS,
		integer	N,
		integer	NRHS,
		double precision, dimension( * )	DL,
		double precision, dimension( * )	D,
		double precision, dimension( * )	DU,
		double precision, dimension( ldb, * )	B,
		integer	LDB,
		double precision, dimension( ldx, * )	X,
		integer	LDX,
		double precision, dimension( ldxact, * )	XACT,
		integer	LDXACT,
		double precision, dimension( * )	FERR,
		double precision, dimension( * )	BERR,
		double precision, dimension( * )	RESLTS
	)

DGTT05

Purpose:

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

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

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

 RESLTS(2) = residual from the iterative refinement routine
           = the maximum of BERR / ( NZ*EPS + (*) ), where
             (*) = NZ*UNFL / (min_i (abs(op(A))*abs(X) +abs(b))_i )
             and NZ = max. number of nonzeros in any row of A, plus 1

Parameters:

[in]	TRANS	TRANS is CHARACTER1 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 / ( NZEPS + () )

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 165 of file dgtt05.f.

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subroutine dlahilb	(	integer	N,
		integer	NRHS,
		double precision, dimension(lda, n)	A,
		integer	LDA,
		double precision, dimension(ldx, nrhs)	X,
		integer	LDX,
		double precision, dimension(ldb, nrhs)	B,
		integer	LDB,
		double precision, dimension(n)	WORK,
		integer	INFO
	)

DLAHILB

Purpose:

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

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

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

 In single, the generated solution is exact for N <= 6 and has
 small componentwise error for 7 <= N <= 11.

Parameters:

[in]	N	N is INTEGER The dimension of the matrix A.
[in]	NRHS	NRHS is NRHS The requested number of right-hand sides.
[out]	A	A is DOUBLE PRECISION array, dimension (LDA, N) The generated scaled Hilbert matrix.
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= N.
[out]	X	X is DOUBLE PRECISION array, dimension (LDX, NRHS) The generated exact solutions. Currently, the first NRHS columns of the inverse Hilbert matrix.
[in]	LDX	LDX is INTEGER The leading dimension of the array X. LDX >= N.
[out]	B	B is DOUBLE PRECISION array, dimension (LDB, NRHS) The generated right-hand sides. Currently, the first NRHS columns of LCM(1, 2, ..., 2N-1) the identity matrix.
[in]	LDB	LDB is INTEGER The leading dimension of the array B. LDB >= N.
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (N)
[out]	INFO	INFO is INTEGER = 0: successful exit = 1: N is too large; the data is still generated but may not be not exact. < 0: if INFO = -i, the i-th argument had an illegal value

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 125 of file dlahilb.f.

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subroutine dlaord	(	character	JOB,
		integer	N,
		double precision, dimension( * )	X,
		integer	INCX
	)

DLAORD

Purpose:

 DLAORD sorts the elements of a vector x in increasing or decreasing
 order.

Parameters:

[in]	JOB	JOB is CHARACTER = 'I': Sort in increasing order = 'D': Sort in decreasing order
[in]	N	N is INTEGER The length of the vector X.
[in,out]	X	X is DOUBLE PRECISION array, dimension (1+(N-1)*INCX) On entry, the vector of length n to be sorted. On exit, the vector x is sorted in the prescribed order.
[in]	INCX	INCX is INTEGER The spacing between successive elements of X. INCX >= 0.

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 74 of file dlaord.f.

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subroutine dlaptm	(	integer	N,
		integer	NRHS,
		double precision	ALPHA,
		double precision, dimension( * )	D,
		double precision, dimension( * )	E,
		double precision, dimension( ldx, * )	X,
		integer	LDX,
		double precision	BETA,
		double precision, dimension( ldb, * )	B,
		integer	LDB
	)

DLAPTM

Purpose:

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

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

 where alpha may be either 1. or -1. and beta may be 0., 1., or -1.

Parameters:

[in]	N	N is INTEGER The order of the matrix A. N >= 0.
[in]	NRHS	NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrices X and B.
[in]	ALPHA	ALPHA is DOUBLE PRECISION The scalar alpha. ALPHA must be 1. or -1.; otherwise, it is assumed to be 0.
[in]	D	D is DOUBLE PRECISION array, dimension (N) The n diagonal elements of the tridiagonal matrix A.
[in]	E	E is DOUBLE PRECISION array, dimension (N-1) The (n-1) subdiagonal or superdiagonal elements of A.
[in]	X	X is DOUBLE PRECISION array, dimension (LDX,NRHS) The N by NRHS matrix X.
[in]	LDX	LDX is INTEGER The leading dimension of the array X. LDX >= max(N,1).
[in]	BETA	BETA is DOUBLE PRECISION The scalar beta. BETA must be 0., 1., or -1.; otherwise, it is assumed to be 1.
[in,out]	B	B is DOUBLE PRECISION array, dimension (LDB,NRHS) On entry, the N by NRHS matrix B. On exit, B is overwritten by the matrix expression B := alpha * A * X + beta * B.
[in]	LDB	LDB is INTEGER The leading dimension of the array B. LDB >= max(N,1).

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 117 of file dlaptm.f.

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subroutine dlarhs	(	character*3	PATH,
		character	XTYPE,
		character	UPLO,
		character	TRANS,
		integer	M,
		integer	N,
		integer	KL,
		integer	KU,
		integer	NRHS,
		double precision, dimension( lda, * )	A,
		integer	LDA,
		double precision, dimension( ldx, * )	X,
		integer	LDX,
		double precision, dimension( ldb, * )	B,
		integer	LDB,
		integer, dimension( 4 )	ISEED,
		integer	INFO
	)

DLARHS

Purpose:

 DLARHS chooses a set of NRHS random solution vectors and sets
 up the right hand sides for the linear system
    op( A ) * X = B,
 where op( A ) may be A or A' (transpose of A).

Parameters:

[in]	PATH	PATH is CHARACTER*3 The type of the real matrix A. PATH may be given in any combination of upper and lower case. Valid types include xGE: General m x n matrix xGB: General banded matrix xPO: Symmetric positive definite, 2-D storage xPP: Symmetric positive definite packed xPB: Symmetric positive definite banded xSY: Symmetric indefinite, 2-D storage xSP: Symmetric indefinite packed xSB: Symmetric indefinite banded xTR: Triangular xTP: Triangular packed xTB: Triangular banded xQR: General m x n matrix xLQ: General m x n matrix xQL: General m x n matrix xRQ: General m x n matrix where the leading character indicates the precision.
[in]	XTYPE	XTYPE is CHARACTER*1 Specifies how the exact solution X will be determined: = 'N': New solution; generate a random X. = 'C': Computed; use value of X on entry.
[in]	UPLO	UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the matrix A is stored, if A is symmetric. = 'U': Upper triangular = 'L': Lower triangular
[in]	TRANS	TRANS is CHARACTER1 Specifies the operation applied to the matrix A. = 'N': System is A x = b = 'T': System is A'* x = b = 'C': System is A'* x = b
[in]	M	M is INTEGER The number or rows of the matrix A. M >= 0.
[in]	N	N is INTEGER The number of columns of the matrix A. N >= 0.
[in]	KL	KL is INTEGER Used only if A is a band matrix; specifies the number of subdiagonals of A if A is a general band matrix or if A is symmetric or triangular and UPLO = 'L'; specifies the number of superdiagonals of A if A is symmetric or triangular and UPLO = 'U'. 0 <= KL <= M-1.
[in]	KU	KU is INTEGER Used only if A is a general band matrix or if A is triangular. If PATH = xGB, specifies the number of superdiagonals of A, and 0 <= KU <= N-1. If PATH = xTR, xTP, or xTB, specifies whether or not the matrix has unit diagonal: = 1: matrix has non-unit diagonal (default) = 2: matrix has unit diagonal
[in]	NRHS	NRHS is INTEGER The number of right hand side vectors in the system A*X = B.
[in]	A	A is DOUBLE PRECISION array, dimension (LDA,N) The test matrix whose type is given by PATH.
[in]	LDA	LDA is INTEGER The leading dimension of the array A. If PATH = xGB, LDA >= KL+KU+1. If PATH = xPB, xSB, xHB, or xTB, LDA >= KL+1. Otherwise, LDA >= max(1,M).
[in,out]	X	X is or output) DOUBLE PRECISION array, dimension(LDX,NRHS) On entry, if XTYPE = 'C' (for 'Computed'), then X contains the exact solution to the system of linear equations. On exit, if XTYPE = 'N' (for 'New'), then X is initialized with random values.
[in]	LDX	LDX is INTEGER The leading dimension of the array X. If TRANS = 'N', LDX >= max(1,N); if TRANS = 'T', LDX >= max(1,M).
[out]	B	B is DOUBLE PRECISION array, dimension (LDB,NRHS) The right hand side vector(s) for the system of equations, computed from B = op(A) * X, where op(A) is determined by TRANS.
[in]	LDB	LDB is INTEGER The leading dimension of the array B. If TRANS = 'N', LDB >= max(1,M); if TRANS = 'T', LDB >= max(1,N).
[in,out]	ISEED	ISEED is INTEGER array, dimension (4) The seed vector for the random number generator (used in DLATMS). Modified on exit.
[out]	INFO	INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 204 of file dlarhs.f.

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subroutine dlatb4	(	character*3	PATH,
		integer	IMAT,
		integer	M,
		integer	N,
		character	TYPE,
		integer	KL,
		integer	KU,
		double precision	ANORM,
		integer	MODE,
		double precision	CNDNUM,
		character	DIST
	)

DLATB4

Purpose:

 DLATB4 sets parameters for the matrix generator based on the type of
 matrix to be generated.

Parameters:

[in]	PATH	PATH is CHARACTER*3 The LAPACK path name.
[in]	IMAT	IMAT is INTEGER An integer key describing which matrix to generate for this path.
[in]	M	M is INTEGER The number of rows in the matrix to be generated.
[in]	N	N is INTEGER The number of columns in the matrix to be generated.
[out]	TYPE	TYPE is CHARACTER*1 The type of the matrix to be generated: = 'S': symmetric matrix = 'P': symmetric positive (semi)definite matrix = 'N': nonsymmetric matrix
[out]	KL	KL is INTEGER The lower band width of the matrix to be generated.
[out]	KU	KU is INTEGER The upper band width of the matrix to be generated.
[out]	ANORM	ANORM is DOUBLE PRECISION The desired norm of the matrix to be generated. The diagonal matrix of singular values or eigenvalues is scaled by this value.
[out]	MODE	MODE is INTEGER A key indicating how to choose the vector of eigenvalues.
[out]	CNDNUM	CNDNUM is DOUBLE PRECISION The desired condition number.
[out]	DIST	DIST is CHARACTER*1 The type of distribution to be used by the random number generator.

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 120 of file dlatb4.f.

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subroutine dlatb5	(	character*3	PATH,
		integer	IMAT,
		integer	N,
		character	TYPE,
		integer	KL,
		integer	KU,
		double precision	ANORM,
		integer	MODE,
		double precision	CNDNUM,
		character	DIST
	)

DLATB5

Purpose:

 DLATB5 sets parameters for the matrix generator based on the type
 of matrix to be generated.

Parameters:

[in]	PATH	PATH is CHARACTER*3 The LAPACK path name.
[in]	IMAT	IMAT is INTEGER An integer key describing which matrix to generate for this path.
[in]	N	N is INTEGER The number of rows and columns in the matrix to be generated.
[out]	TYPE	TYPE is CHARACTER*1 The type of the matrix to be generated: = 'S': symmetric matrix = 'P': symmetric positive (semi)definite matrix = 'N': nonsymmetric matrix
[out]	KL	KL is INTEGER The lower band width of the matrix to be generated.
[out]	KU	KU is INTEGER The upper band width of the matrix to be generated.
[out]	ANORM	ANORM is DOUBLE PRECISION The desired norm of the matrix to be generated. The diagonal matrix of singular values or eigenvalues is scaled by this value.
[out]	MODE	MODE is INTEGER A key indicating how to choose the vector of eigenvalues.
[out]	CNDNUM	CNDNUM is DOUBLE PRECISION The desired condition number.
[out]	DIST	DIST is CHARACTER*1 The type of distribution to be used by the random number generator.

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 114 of file dlatb5.f.

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subroutine dlattb	(	integer	IMAT,
		character	UPLO,
		character	TRANS,
		character	DIAG,
		integer, dimension( 4 )	ISEED,
		integer	N,
		integer	KD,
		double precision, dimension( ldab, * )	AB,
		integer	LDAB,
		double precision, dimension( * )	B,
		double precision, dimension( * )	WORK,
		integer	INFO
	)

DLATTB

Purpose:

 DLATTB generates a triangular test matrix in 2-dimensional storage.
 IMAT and UPLO uniquely specify the properties of the test matrix,
 which is returned in the array A.

Parameters:

[in]	IMAT	IMAT is INTEGER An integer key describing which matrix to generate for this path.
[in]	UPLO	UPLO is CHARACTER*1 Specifies whether the matrix A will be upper or lower triangular. = 'U': Upper triangular = 'L': Lower triangular
[in]	TRANS	TRANS is CHARACTER*1 Specifies whether the matrix or its transpose will be used. = 'N': No transpose = 'T': Transpose = 'C': Conjugate transpose (= transpose)
[out]	DIAG	DIAG is CHARACTER*1 Specifies whether or not the matrix A is unit triangular. = 'N': Non-unit triangular = 'U': Unit triangular
[in,out]	ISEED	ISEED is INTEGER array, dimension (4) The seed vector for the random number generator (used in DLATMS). Modified on exit.
[in]	N	N is INTEGER The order of the matrix to be generated.
[in]	KD	KD is INTEGER The number of superdiagonals or subdiagonals of the banded triangular matrix A. KD >= 0.
[out]	AB	AB is DOUBLE PRECISION array, dimension (LDAB,N) The upper or lower triangular banded matrix A, stored in the first KD+1 rows of AB. Let j be a column of A, 1<=j<=n. If UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j. If UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
[in]	LDAB	LDAB is INTEGER The leading dimension of the array AB. LDAB >= KD+1.
[out]	B	B is DOUBLE PRECISION array, dimension (N)
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (2*N)
[out]	INFO	INFO is INTEGER = 0: successful exit < 0: if INFO = -k, the k-th argument had an illegal value

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 135 of file dlattb.f.

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subroutine dlattp	(	integer	IMAT,
		character	UPLO,
		character	TRANS,
		character	DIAG,
		integer, dimension( 4 )	ISEED,
		integer	N,
		double precision, dimension( * )	A,
		double precision, dimension( * )	B,
		double precision, dimension( * )	WORK,
		integer	INFO
	)

DLATTP

Purpose:

 DLATTP generates a triangular test matrix in packed storage.
 IMAT and UPLO uniquely specify the properties of the test
 matrix, which is returned in the array AP.

Parameters:

[in]	IMAT	IMAT is INTEGER An integer key describing which matrix to generate for this path.
[in]	UPLO	UPLO is CHARACTER*1 Specifies whether the matrix A will be upper or lower triangular. = 'U': Upper triangular = 'L': Lower triangular
[in]	TRANS	TRANS is CHARACTER*1 Specifies whether the matrix or its transpose will be used. = 'N': No transpose = 'T': Transpose = 'C': Conjugate transpose (= Transpose)
[out]	DIAG	DIAG is CHARACTER*1 Specifies whether or not the matrix A is unit triangular. = 'N': Non-unit triangular = 'U': Unit triangular
[in,out]	ISEED	ISEED is INTEGER array, dimension (4) The seed vector for the random number generator (used in DLATMS). Modified on exit.
[in]	N	N is INTEGER The order of the matrix to be generated.
[out]	A	A is DOUBLE PRECISION array, dimension (N(N+1)/2) The upper or lower triangular matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP((j-1)j/2 + i) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP((j-1)(n-j) + j(j+1)/2 + i-j) = A(i,j) for j<=i<=n.
[out]	B	B is DOUBLE PRECISION array, dimension (N) The right hand side vector, if IMAT > 10.
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (3*N)
[out]	INFO	INFO is INTEGER = 0: successful exit < 0: if INFO = -k, the k-th argument had an illegal value

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 125 of file dlattp.f.

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subroutine dlattr	(	integer	IMAT,
		character	UPLO,
		character	TRANS,
		character	DIAG,
		integer, dimension( 4 )	ISEED,
		integer	N,
		double precision, dimension( lda, * )	A,
		integer	LDA,
		double precision, dimension( * )	B,
		double precision, dimension( * )	WORK,
		integer	INFO
	)

DLATTR

Purpose:

 DLATTR generates a triangular test matrix.
 IMAT and UPLO uniquely specify the properties of the test
 matrix, which is returned in the array A.

Parameters:

[in]	IMAT	IMAT is INTEGER An integer key describing which matrix to generate for this path.
[in]	UPLO	UPLO is CHARACTER*1 Specifies whether the matrix A will be upper or lower triangular. = 'U': Upper triangular = 'L': Lower triangular
[in]	TRANS	TRANS is CHARACTER*1 Specifies whether the matrix or its transpose will be used. = 'N': No transpose = 'T': Transpose = 'C': Conjugate transpose (= Transpose)
[out]	DIAG	DIAG is CHARACTER*1 Specifies whether or not the matrix A is unit triangular. = 'N': Non-unit triangular = 'U': Unit triangular
[in,out]	ISEED	ISEED is INTEGER array, dimension (4) The seed vector for the random number generator (used in DLATMS). Modified on exit.
[in]	N	N is INTEGER The order of the matrix to be generated.
[out]	A	A is DOUBLE PRECISION array, dimension (LDA,N) The triangular matrix A. If UPLO = 'U', the leading n by n upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading n by n lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. If DIAG = 'U', the diagonal elements of A are set so that A(k,k) = k for 1 <= k <= n.
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).
[out]	B	B is DOUBLE PRECISION array, dimension (N) The right hand side vector, if IMAT > 10.
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (3*N)
[out]	INFO	INFO is INTEGER = 0: successful exit < 0: if INFO = -k, the k-th argument had an illegal value

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 133 of file dlattr.f.

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subroutine dlavsp	(	character	UPLO,
		character	TRANS,
		character	DIAG,
		integer	N,
		integer	NRHS,
		double precision, dimension( * )	A,
		integer, dimension( * )	IPIV,
		double precision, dimension( ldb, * )	B,
		integer	LDB,
		integer	INFO
	)

DLAVSP

Purpose:

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

 If TRANS = 'N', multiplies by U  or U * D  (or L  or L * D)
 If TRANS = 'T', multiplies by U' or D * U' (or L' or D * L' )
 If TRANS = 'C', multiplies by U' or D * U' (or L' or D * L' )

Parameters:

[in]	UPLO	UPLO is CHARACTER*1 Specifies whether the factor stored in A is upper or lower triangular. = 'U': Upper triangular = 'L': Lower triangular
[in]	TRANS	TRANS is CHARACTER1 Specifies the operation to be performed: = 'N': x := Ax = 'T': x := A'x = 'C': x := A'x
[in]	DIAG	DIAG is CHARACTER1 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 = UD or A = L*D. = 'U': Diagonal blocks are assumed to be unit matrices. = 'N': Diagonal blocks are assumed to be non-unit matrices.
[in]	N	N is INTEGER The number of rows and columns of the matrix A. N >= 0.
[in]	NRHS	NRHS is INTEGER The number of right hand sides, i.e., the number of vectors x to be multiplied by A. NRHS >= 0.
[in]	A	A is DOUBLE PRECISION array, dimension (N*(N+1)/2) The block diagonal matrix D and the multipliers used to obtain the factor U or L, stored as a packed triangular matrix as computed by DSPTRF.
[in]	IPIV	IPIV is INTEGER array, dimension (N) The pivot indices from DSPTRF.
[in,out]	B	B is DOUBLE PRECISION array, dimension (LDB,NRHS) On entry, B contains NRHS vectors of length N. On exit, B is overwritten with the product A * B.
[in]	LDB	LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).
[out]	INFO	INFO is INTEGER = 0: successful exit < 0: if INFO = -k, the k-th argument had an illegal value

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 130 of file dlavsp.f.

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subroutine dlavsy	(	character	UPLO,
		character	TRANS,
		character	DIAG,
		integer	N,
		integer	NRHS,
		double precision, dimension( lda, * )	A,
		integer	LDA,
		integer, dimension( * )	IPIV,
		double precision, dimension( ldb, * )	B,
		integer	LDB,
		integer	INFO
	)

DLAVSY

Purpose:

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

 If TRANS = 'N', multiplies by U  or U * D  (or L  or L * D)
 If TRANS = 'T', multiplies by U' or D * U' (or L' or D * L')
 If TRANS = 'C', multiplies by U' or D * U' (or L' or D * L')

Parameters:

[in]	UPLO	UPLO is CHARACTER*1 Specifies whether the factor stored in A is upper or lower triangular. = 'U': Upper triangular = 'L': Lower triangular
[in]	TRANS	TRANS is CHARACTER1 Specifies the operation to be performed: = 'N': x := Ax = 'T': x := A'x = 'C': x := A'x
[in]	DIAG	DIAG is CHARACTER1 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 = UD 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

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: April 2012

Definition at line 154 of file dlavsy.f.

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subroutine dlqt01	(	integer	M,
		integer	N,
		double precision, dimension( lda, * )	A,
		double precision, dimension( lda, * )	AF,
		double precision, dimension( lda, * )	Q,
		double precision, dimension( lda, * )	L,
		integer	LDA,
		double precision, dimension( * )	TAU,
		double precision, dimension( lwork )	WORK,
		integer	LWORK,
		double precision, dimension( * )	RWORK,
		double precision, dimension( * )	RESULT
	)

DLQT01

Purpose:

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

 DLQT01 compares L with A*Q', and checks that Q is orthogonal.

Parameters:

[in]	M	M is INTEGER The number of rows of the matrix A. M >= 0.
[in]	N	N is INTEGER The number of columns of the matrix A. N >= 0.
[in]	A	A is DOUBLE PRECISION array, dimension (LDA,N) The m-by-n matrix A.
[out]	AF	AF is DOUBLE PRECISION array, dimension (LDA,N) Details of the LQ factorization of A, as returned by DGELQF. See DGELQF for further details.
[out]	Q	Q is DOUBLE PRECISION array, dimension (LDA,N) The n-by-n orthogonal matrix Q.
[out]	L	L is DOUBLE PRECISION array, dimension (LDA,max(M,N))
[in]	LDA	LDA is INTEGER The leading dimension of the arrays A, AF, Q and L. LDA >= max(M,N).
[out]	TAU	TAU is DOUBLE PRECISION array, dimension (min(M,N)) The scalar factors of the elementary reflectors, as returned by DGELQF.
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (LWORK)
[in]	LWORK	LWORK is INTEGER The dimension of the array WORK.
[out]	RWORK	RWORK is DOUBLE PRECISION array, dimension (max(M,N))
[out]	RESULT	RESULT is DOUBLE PRECISION array, dimension (2) The test ratios: RESULT(1) = norm( L - AQ' ) / ( N norm(A) * EPS ) RESULT(2) = norm( I - QQ' ) / ( N EPS )

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 126 of file dlqt01.f.

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subroutine dlqt02	(	integer	M,
		integer	N,
		integer	K,
		double precision, dimension( lda, * )	A,
		double precision, dimension( lda, * )	AF,
		double precision, dimension( lda, * )	Q,
		double precision, dimension( lda, * )	L,
		integer	LDA,
		double precision, dimension( * )	TAU,
		double precision, dimension( lwork )	WORK,
		integer	LWORK,
		double precision, dimension( * )	RWORK,
		double precision, dimension( * )	RESULT
	)

DLQT02

Purpose:

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

 Given the LQ factorization of an m-by-n matrix A, DLQT02 generates
 the orthogonal matrix Q defined by the factorization of the first k
 rows of A; it compares L(1:k,1:m) with A(1:k,1:n)*Q(1:m,1:n)', and
 checks that the rows of Q are orthonormal.

Parameters:

[in]	M	M is INTEGER The number of rows of the matrix Q to be generated. M >= 0.
[in]	N	N is INTEGER The number of columns of the matrix Q to be generated. N >= M >= 0.
[in]	K	K is INTEGER The number of elementary reflectors whose product defines the matrix Q. M >= K >= 0.
[in]	A	A is DOUBLE PRECISION array, dimension (LDA,N) The m-by-n matrix A which was factorized by DLQT01.
[in]	AF	AF is DOUBLE PRECISION array, dimension (LDA,N) Details of the LQ factorization of A, as returned by DGELQF. See DGELQF for further details.
[out]	Q	Q is DOUBLE PRECISION array, dimension (LDA,N)
[out]	L	L is DOUBLE PRECISION array, dimension (LDA,M)
[in]	LDA	LDA is INTEGER The leading dimension of the arrays A, AF, Q and L. LDA >= N.
[in]	TAU	TAU is DOUBLE PRECISION array, dimension (M) The scalar factors of the elementary reflectors corresponding to the LQ factorization in AF.
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (LWORK)
[in]	LWORK	LWORK is INTEGER The dimension of the array WORK.
[out]	RWORK	RWORK is DOUBLE PRECISION array, dimension (M)
[out]	RESULT	RESULT is DOUBLE PRECISION array, dimension (2) The test ratios: RESULT(1) = norm( L - AQ' ) / ( N norm(A) * EPS ) RESULT(2) = norm( I - QQ' ) / ( N EPS )

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 135 of file dlqt02.f.

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subroutine dlqt03	(	integer	M,
		integer	N,
		integer	K,
		double precision, dimension( lda, * )	AF,
		double precision, dimension( lda, * )	C,
		double precision, dimension( lda, * )	CC,
		double precision, dimension( lda, * )	Q,
		integer	LDA,
		double precision, dimension( * )	TAU,
		double precision, dimension( lwork )	WORK,
		integer	LWORK,
		double precision, dimension( * )	RWORK,
		double precision, dimension( * )	RESULT
	)

DLQT03

Purpose:

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

 DLQT03 compares the results of a call to DORMLQ with the results of
 forming Q explicitly by a call to DORGLQ and then performing matrix
 multiplication by a call to DGEMM.

Parameters:

[in]	M	M is INTEGER The number of rows or columns of the matrix C; C is n-by-m if Q is applied from the left, or m-by-n if Q is applied from the right. M >= 0.
[in]	N	N is INTEGER The order of the orthogonal matrix Q. N >= 0.
[in]	K	K is INTEGER The number of elementary reflectors whose product defines the orthogonal matrix Q. N >= K >= 0.
[in]	AF	AF is DOUBLE PRECISION array, dimension (LDA,N) Details of the LQ factorization of an m-by-n matrix, as returned by DGELQF. See SGELQF for further details.
[out]	C	C is DOUBLE PRECISION array, dimension (LDA,N)
[out]	CC	CC is DOUBLE PRECISION array, dimension (LDA,N)
[out]	Q	Q is DOUBLE PRECISION array, dimension (LDA,N)
[in]	LDA	LDA is INTEGER The leading dimension of the arrays AF, C, CC, and Q.
[in]	TAU	TAU is DOUBLE PRECISION array, dimension (min(M,N)) The scalar factors of the elementary reflectors corresponding to the LQ factorization in AF.
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (LWORK)
[in]	LWORK	LWORK is INTEGER The length of WORK. LWORK must be at least M, and should be M*NB, where NB is the blocksize for this environment.
[out]	RWORK	RWORK is DOUBLE PRECISION array, dimension (M)
[out]	RESULT	RESULT is DOUBLE PRECISION array, dimension (4) The test ratios compare two techniques for multiplying a random matrix C by an n-by-n orthogonal matrix Q. RESULT(1) = norm( QC - QC ) / ( N * norm(C) * EPS ) RESULT(2) = norm( CQ - CQ ) / ( N * norm(C) * EPS ) RESULT(3) = norm( Q'C - Q'C )/ ( N * norm(C) * EPS ) RESULT(4) = norm( CQ' - CQ' )/ ( N * norm(C) * EPS )

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 136 of file dlqt03.f.

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subroutine dpbt01	(	character	UPLO,
		integer	N,
		integer	KD,
		double precision, dimension( lda, * )	A,
		integer	LDA,
		double precision, dimension( ldafac, * )	AFAC,
		integer	LDAFAC,
		double precision, dimension( * )	RWORK,
		double precision	RESID
	)

DPBT01

Purpose:

 DPBT01 reconstructs a symmetric positive definite band matrix A from
 its L*L' or U'*U factorization and computes the residual
    norm( L*L' - A ) / ( N * norm(A) * EPS ) or
    norm( U'*U - A ) / ( N * norm(A) * EPS ),
 where EPS is the machine epsilon, L' is the conjugate transpose of
 L, and U' is the conjugate transpose of U.

Parameters:

[in]	UPLO	UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the symmetric matrix A is stored: = 'U': Upper triangular = 'L': Lower triangular
[in]	N	N is INTEGER The number of rows and columns of the matrix A. N >= 0.
[in]	KD	KD is INTEGER The number of super-diagonals of the matrix A if UPLO = 'U', or the number of sub-diagonals if UPLO = 'L'. KD >= 0.
[in]	A	A is DOUBLE PRECISION array, dimension (LDA,N) The original symmetric band matrix A. If UPLO = 'U', the upper triangular part of A is stored as a band matrix; if UPLO = 'L', the lower triangular part of A is stored. The columns of the appropriate triangle are stored in the columns of A and the diagonals of the triangle are stored in the rows of A. See DPBTRF for further details.
[in]	LDA	LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,KD+1).
[in]	AFAC	AFAC is DOUBLE PRECISION array, dimension (LDAFAC,N) The factored form of the matrix A. AFAC contains the factor L or U from the LL' 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(LL' - A) / ( N norm(A) * EPS ) If UPLO = 'U', norm(U'U - A) / ( N norm(A) * EPS )

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 119 of file dpbt01.f.

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subroutine dpbt02	(	character	UPLO,
		integer	N,
		integer	KD,
		integer	NRHS,
		double precision, dimension( lda, * )	A,
		integer	LDA,
		double precision, dimension( ldx, * )	X,
		integer	LDX,
		double precision, dimension( ldb, * )	B,
		integer	LDB,
		double precision, dimension( * )	RWORK,
		double precision	RESID
	)

DPBT02

Purpose:

 DPBT02 computes the residual for a solution of a symmetric banded
 system of equations  A*x = b:
    RESID = norm( B - A*X ) / ( norm(A) * norm(X) * EPS)
 where EPS is the machine precision.

Parameters:

[in]	UPLO	UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the symmetric matrix A is stored: = 'U': Upper triangular = 'L': Lower triangular
[in]	N	N is INTEGER The number of rows and columns of the matrix A. N >= 0.
[in]	KD	KD is INTEGER The number of super-diagonals of the matrix A if UPLO = 'U', or the number of sub-diagonals if UPLO = 'L'. KD >= 0.
[in]	NRHS	NRHS is INTEGER The number of right hand sides. NRHS >= 0.
[in]	A	A is DOUBLE PRECISION array, dimension (LDA,N) The original symmetric band matrix A. If UPLO = 'U', the upper triangular part of A is stored as a band matrix; if UPLO = 'L', the lower triangular part of A is stored. The columns of the appropriate triangle are stored in the columns of A and the diagonals of the triangle are stored in the rows of A. See DPBTRF for further details.
[in]	LDA	LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,KD+1).
[in]	X	X is DOUBLE PRECISION array, dimension (LDX,NRHS) The computed solution vectors for the system of linear equations.
[in]	LDX	LDX is INTEGER The leading dimension of the array X. LDX >= max(1,N).
[in,out]	B	B is DOUBLE PRECISION array, dimension (LDB,NRHS) On entry, the right hand side vectors for the system of linear equations. On exit, B is overwritten with the difference B - A*X.
[in]	LDB	LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).
[out]	RWORK	RWORK is DOUBLE PRECISION array, dimension (N)
[out]	RESID	RESID is DOUBLE PRECISION The maximum over the number of right hand sides of norm(B - AX) / ( norm(A) norm(X) * EPS ).

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 136 of file dpbt02.f.

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subroutine dpbt05	(	character	UPLO,
		integer	N,
		integer	KD,
		integer	NRHS,
		double precision, dimension( ldab, * )	AB,
		integer	LDAB,
		double precision, dimension( ldb, * )	B,
		integer	LDB,
		double precision, dimension( ldx, * )	X,
		integer	LDX,
		double precision, dimension( ldxact, * )	XACT,
		integer	LDXACT,
		double precision, dimension( * )	FERR,
		double precision, dimension( * )	BERR,
		double precision, dimension( * )	RESLTS
	)

DPBT05

Purpose:

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

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

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

 RESLTS(2) = residual from the iterative refinement routine
           = the maximum of BERR / ( NZ*EPS + (*) ), where
             (*) = NZ*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
             and NZ = max. number of nonzeros in any row of A, plus 1

Parameters:

[in]	UPLO	UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the symmetric matrix A is stored. = 'U': Upper triangular = 'L': Lower triangular
[in]	N	N is INTEGER The number of rows of the matrices X, B, and XACT, and the order of the matrix A. N >= 0.
[in]	KD	KD is INTEGER The number of super-diagonals of the matrix A if UPLO = 'U', or the number of sub-diagonals if UPLO = 'L'. KD >= 0.
[in]	NRHS	NRHS is INTEGER The number of columns of the matrices X, B, and XACT. NRHS >= 0.
[in]	AB	AB is DOUBLE PRECISION array, dimension (LDAB,N) The upper or lower triangle of the symmetric band matrix A, stored in the first KD+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows: if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
[in]	LDAB	LDAB is INTEGER The leading dimension of the array AB. LDAB >= KD+1.
[in]	B	B is DOUBLE PRECISION array, dimension (LDB,NRHS) The right hand side vectors for the system of linear equations.
[in]	LDB	LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).
[in]	X	X is DOUBLE PRECISION array, dimension (LDX,NRHS) The computed solution vectors. Each vector is stored as a column of the matrix X.
[in]	LDX	LDX is INTEGER The leading dimension of the array X. LDX >= max(1,N).
[in]	XACT	XACT is DOUBLE PRECISION array, dimension (LDX,NRHS) The exact solution vectors. Each vector is stored as a column of the matrix XACT.
[in]	LDXACT	LDXACT is INTEGER The leading dimension of the array XACT. LDXACT >= max(1,N).
[in]	FERR	FERR is DOUBLE PRECISION array, dimension (NRHS) The estimated forward error bounds for each solution vector X. If XTRUE is the true solution, FERR bounds the magnitude of the largest entry in (X - XTRUE) divided by the magnitude of the largest entry in X.
[in]	BERR	BERR is DOUBLE PRECISION array, dimension (NRHS) The componentwise relative backward error of each solution vector (i.e., the smallest relative change in any entry of A or B that makes X an exact solution).
[out]	RESLTS	RESLTS is DOUBLE PRECISION array, dimension (2) The maximum over the NRHS solution vectors of the ratios: RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR ) RESLTS(2) = BERR / ( NZEPS + () )

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 171 of file dpbt05.f.

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subroutine dpot01	(	character	UPLO,
		integer	N,
		double precision, dimension( lda, * )	A,
		integer	LDA,
		double precision, dimension( ldafac, * )	AFAC,
		integer	LDAFAC,
		double precision, dimension( * )	RWORK,
		double precision	RESID
	)

DPOT01

Purpose:

 DPOT01 reconstructs a symmetric positive definite matrix  A  from
 its L*L' or U'*U factorization and computes the residual
    norm( L*L' - A ) / ( N * norm(A) * EPS ) or
    norm( U'*U - A ) / ( N * norm(A) * EPS ),
 where EPS is the machine epsilon.

Parameters:

[in]	UPLO	UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the symmetric matrix A is stored: = 'U': Upper triangular = 'L': Lower triangular
[in]	N	N is INTEGER The number of rows and columns of the matrix A. N >= 0.
[in]	A	A is DOUBLE PRECISION array, dimension (LDA,N) The original symmetric matrix A.
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N)
[in,out]	AFAC	AFAC is DOUBLE PRECISION array, dimension (LDAFAC,N) On entry, the factor L or U from the LL' or U'U factorization of A. Overwritten with the reconstructed matrix, and then with the difference LL' - 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(LL' - A) / ( N norm(A) * EPS ) If UPLO = 'U', norm(U'U - A) / ( N norm(A) * EPS )

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 105 of file dpot01.f.

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subroutine dpot02	(	character	UPLO,
		integer	N,
		integer	NRHS,
		double precision, dimension( lda, * )	A,
		integer	LDA,
		double precision, dimension( ldx, * )	X,
		integer	LDX,
		double precision, dimension( ldb, * )	B,
		integer	LDB,
		double precision, dimension( * )	RWORK,
		double precision	RESID
	)

DPOT02

Purpose:

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

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

 where EPS is the machine epsilon.

Parameters:

[in]	UPLO	UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the symmetric matrix A is stored: = 'U': Upper triangular = 'L': Lower triangular
[in]	N	N is INTEGER The number of rows and columns of the matrix A. N >= 0.
[in]	NRHS	NRHS is INTEGER The number of columns of B, the matrix of right hand sides. NRHS >= 0.
[in]	A	A is DOUBLE PRECISION array, dimension (LDA,N) The original symmetric matrix A.
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N)
[in]	X	X is DOUBLE PRECISION array, dimension (LDX,NRHS) The computed solution vectors for the system of linear equations.
[in]	LDX	LDX is INTEGER The leading dimension of the array X. LDX >= max(1,N).
[in,out]	B	B is DOUBLE PRECISION array, dimension (LDB,NRHS) On entry, the right hand side vectors for the system of linear equations. On exit, B is overwritten with the difference B - A*X.
[in]	LDB	LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).
[out]	RWORK	RWORK is DOUBLE PRECISION array, dimension (N)
[out]	RESID	RESID is DOUBLE PRECISION The maximum over the number of right hand sides of norm(B - AX) / ( norm(A) norm(X) * EPS ).

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 127 of file dpot02.f.

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subroutine dpot03	(	character	UPLO,
		integer	N,
		double precision, dimension( lda, * )	A,
		integer	LDA,
		double precision, dimension( ldainv, * )	AINV,
		integer	LDAINV,
		double precision, dimension( ldwork, * )	WORK,
		integer	LDWORK,
		double precision, dimension( * )	RWORK,
		double precision	RCOND,
		double precision	RESID
	)

DPOT03

Purpose:

 DPOT03 computes the residual for a symmetric matrix times its
 inverse:
    norm( I - A*AINV ) / ( N * norm(A) * norm(AINV) * EPS ),
 where EPS is the machine epsilon.

Parameters:

[in]	UPLO	UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the symmetric matrix A is stored: = 'U': Upper triangular = 'L': Lower triangular
[in]	N	N is INTEGER The number of rows and columns of the matrix A. N >= 0.
[in]	A	A is DOUBLE PRECISION array, dimension (LDA,N) The original symmetric matrix A.
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N)
[in,out]	AINV	AINV is DOUBLE PRECISION array, dimension (LDAINV,N) On entry, the inverse of the matrix A, stored as a symmetric matrix in the same format as A. In this version, AINV is expanded into a full matrix and multiplied by A, so the opposing triangle of AINV will be changed; i.e., if the upper triangular part of AINV is stored, the lower triangular part will be used as work space.
[in]	LDAINV	LDAINV is INTEGER The leading dimension of the array AINV. LDAINV >= max(1,N).
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (LDWORK,N)
[in]	LDWORK	LDWORK is INTEGER The leading dimension of the array WORK. LDWORK >= max(1,N).
[out]	RWORK	RWORK is DOUBLE PRECISION array, dimension (N)
[out]	RCOND	RCOND is DOUBLE PRECISION The reciprocal of the condition number of A, computed as ( 1/norm(A) ) / norm(AINV).
[out]	RESID	RESID is DOUBLE PRECISION norm(I - AAINV) / ( N norm(A) * norm(AINV) * EPS )

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 125 of file dpot03.f.

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subroutine dpot05	(	character	UPLO,
		integer	N,
		integer	NRHS,
		double precision, dimension( lda, * )	A,
		integer	LDA,
		double precision, dimension( ldb, * )	B,
		integer	LDB,
		double precision, dimension( ldx, * )	X,
		integer	LDX,
		double precision, dimension( ldxact, * )	XACT,
		integer	LDXACT,
		double precision, dimension( * )	FERR,
		double precision, dimension( * )	BERR,
		double precision, dimension( * )	RESLTS
	)

DPOT05

Purpose:

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

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

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

 RESLTS(2) = residual from the iterative refinement routine
           = the maximum of BERR / ( (n+1)*EPS + (*) ), where
             (*) = (n+1)*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )

Parameters:

[in]	UPLO	UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the symmetric matrix A is stored. = 'U': Upper triangular = 'L': Lower triangular
[in]	N	N is INTEGER The number of rows of the matrices X, B, and XACT, and the order of the matrix A. N >= 0.
[in]	NRHS	NRHS is INTEGER The number of columns of the matrices X, B, and XACT. NRHS >= 0.
[in]	A	A is DOUBLE PRECISION array, dimension (LDA,N) The symmetric matrix A. If UPLO = 'U', the leading n by n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading n by n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced.
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).
[in]	B	B is DOUBLE PRECISION array, dimension (LDB,NRHS) The right hand side vectors for the system of linear equations.
[in]	LDB	LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).
[in]	X	X is DOUBLE PRECISION array, dimension (LDX,NRHS) The computed solution vectors. Each vector is stored as a column of the matrix X.
[in]	LDX	LDX is INTEGER The leading dimension of the array X. LDX >= max(1,N).
[in]	XACT	XACT is DOUBLE PRECISION array, dimension (LDX,NRHS) The exact solution vectors. Each vector is stored as a column of the matrix XACT.
[in]	LDXACT	LDXACT is INTEGER The leading dimension of the array XACT. LDXACT >= max(1,N).
[in]	FERR	FERR is DOUBLE PRECISION array, dimension (NRHS) The estimated forward error bounds for each solution vector X. If XTRUE is the true solution, FERR bounds the magnitude of the largest entry in (X - XTRUE) divided by the magnitude of the largest entry in X.
[in]	BERR	BERR is DOUBLE PRECISION array, dimension (NRHS) The componentwise relative backward error of each solution vector (i.e., the smallest relative change in any entry of A or B that makes X an exact solution).
[out]	RESLTS	RESLTS is DOUBLE PRECISION array, dimension (2) The maximum over the NRHS solution vectors of the ratios: RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR ) RESLTS(2) = BERR / ( (n+1)EPS + () )

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 164 of file dpot05.f.

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subroutine dpot06	(	character	UPLO,
		integer	N,
		integer	NRHS,
		double precision, dimension( lda, * )	A,
		integer	LDA,
		double precision, dimension( ldx, * )	X,
		integer	LDX,
		double precision, dimension( ldb, * )	B,
		integer	LDB,
		double precision, dimension( * )	RWORK,
		double precision	RESID
	)

DPOT06

Purpose:

 DPOT06 computes the residual for a solution of a system of linear
 equations  A*x = b :
    RESID = norm(B - A*X,inf) / ( norm(A,inf) * norm(X,inf) * EPS ),
 where EPS is the machine epsilon.

Parameters:

[in]	UPLO	UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the symmetric matrix A is stored: = 'U': Upper triangular = 'L': Lower triangular
[in]	N	N is INTEGER The number of rows and columns of the matrix A. N >= 0.
[in]	NRHS	NRHS is INTEGER The number of columns of B, the matrix of right hand sides. NRHS >= 0.
[in]	A	A is DOUBLE PRECISION array, dimension (LDA,N) The original M x N matrix A.
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).
[in]	X	X is DOUBLE PRECISION array, dimension (LDX,NRHS) The computed solution vectors for the system of linear equations.
[in]	LDX	LDX is INTEGER The leading dimension of the array X. If TRANS = 'N', LDX >= max(1,N); if TRANS = 'T' or 'C', LDX >= max(1,N).
[in,out]	B	B is DOUBLE PRECISION array, dimension (LDB,NRHS) On entry, the right hand side vectors for the system of linear equations. On exit, B is overwritten with the difference B - A*X.
[in]	LDB	LDB is INTEGER The leading dimension of the array B. IF TRANS = 'N', LDB >= max(1,M); if TRANS = 'T' or 'C', LDB >= max(1,N).
[out]	RWORK	RWORK is DOUBLE PRECISION array, dimension (N)
[out]	RESID	RESID is DOUBLE PRECISION The maximum over the number of right hand sides of norm(B - AX) / ( norm(A) norm(X) * EPS ).

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 127 of file dpot06.f.

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subroutine dppt01	(	character	UPLO,
		integer	N,
		double precision, dimension( * )	A,
		double precision, dimension( * )	AFAC,
		double precision, dimension( * )	RWORK,
		double precision	RESID
	)

DPPT01

Purpose:

 DPPT01 reconstructs a symmetric positive definite packed matrix A
 from its L*L' or U'*U factorization and computes the residual
    norm( L*L' - A ) / ( N * norm(A) * EPS ) or
    norm( U'*U - A ) / ( N * norm(A) * EPS ),
 where EPS is the machine epsilon.

Parameters:

[in]	UPLO	UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the symmetric matrix A is stored: = 'U': Upper triangular = 'L': Lower triangular
[in]	N	N is INTEGER The number of rows and columns of the matrix A. N >= 0.
[in]	A	A is DOUBLE PRECISION array, dimension (N*(N+1)/2) The original symmetric matrix A, stored as a packed triangular matrix.
[in,out]	AFAC	AFAC is DOUBLE PRECISION array, dimension (N(N+1)/2) On entry, the factor L or U from the LL' or U'U factorization of A, stored as a packed triangular matrix. Overwritten with the reconstructed matrix, and then with the difference LL' - A (or U'*U - A).
[out]	RWORK	RWORK is DOUBLE PRECISION array, dimension (N)
[out]	RESID	RESID is DOUBLE PRECISION If UPLO = 'L', norm(LL' - A) / ( N norm(A) * EPS ) If UPLO = 'U', norm(U'U - A) / ( N norm(A) * EPS )

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 94 of file dppt01.f.

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subroutine dppt02	(	character	UPLO,
		integer	N,
		integer	NRHS,
		double precision, dimension( * )	A,
		double precision, dimension( ldx, * )	X,
		integer	LDX,
		double precision, dimension( ldb, * )	B,
		integer	LDB,
		double precision, dimension( * )	RWORK,
		double precision	RESID
	)

DPPT02

Purpose:

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

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

 where EPS is the machine precision.

Parameters:

[in]	UPLO	UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the symmetric matrix A is stored: = 'U': Upper triangular = 'L': Lower triangular
[in]	N	N is INTEGER The number of rows and columns of the matrix A. N >= 0.
[in]	NRHS	NRHS is INTEGER The number of columns of B, the matrix of right hand sides. NRHS >= 0.
[in]	A	A is DOUBLE PRECISION array, dimension (N*(N+1)/2) The original symmetric matrix A, stored as a packed triangular matrix.
[in]	X	X is DOUBLE PRECISION array, dimension (LDX,NRHS) The computed solution vectors for the system of linear equations.
[in]	LDX	LDX is INTEGER The leading dimension of the array X. LDX >= max(1,N).
[in,out]	B	B is DOUBLE PRECISION array, dimension (LDB,NRHS) On entry, the right hand side vectors for the system of linear equations. On exit, B is overwritten with the difference B - A*X.
[in]	LDB	LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).
[out]	RWORK	RWORK is DOUBLE PRECISION array, dimension (N)
[out]	RESID	RESID is DOUBLE PRECISION The maximum over the number of right hand sides of norm(B - AX) / ( norm(A) norm(X) * EPS ).

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 122 of file dppt02.f.

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subroutine dppt03	(	character	UPLO,
		integer	N,
		double precision, dimension( * )	A,
		double precision, dimension( * )	AINV,
		double precision, dimension( ldwork, * )	WORK,
		integer	LDWORK,
		double precision, dimension( * )	RWORK,
		double precision	RCOND,
		double precision	RESID
	)

DPPT03

Purpose:

 DPPT03 computes the residual for a symmetric packed matrix times its
 inverse:
    norm( I - A*AINV ) / ( N * norm(A) * norm(AINV) * EPS ),
 where EPS is the machine epsilon.

Parameters:

[in]	UPLO	UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the symmetric matrix A is stored: = 'U': Upper triangular = 'L': Lower triangular
[in]	N	N is INTEGER The number of rows and columns of the matrix A. N >= 0.
[in]	A	A is DOUBLE PRECISION array, dimension (N*(N+1)/2) The original symmetric matrix A, stored as a packed triangular matrix.
[in]	AINV	AINV is DOUBLE PRECISION array, dimension (N*(N+1)/2) The (symmetric) inverse of the matrix A, stored as a packed triangular matrix.
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (LDWORK,N)
[in]	LDWORK	LDWORK is INTEGER The leading dimension of the array WORK. LDWORK >= max(1,N).
[out]	RWORK	RWORK is DOUBLE PRECISION array, dimension (N)
[out]	RCOND	RCOND is DOUBLE PRECISION The reciprocal of the condition number of A, computed as ( 1/norm(A) ) / norm(AINV).
[out]	RESID	RESID is DOUBLE PRECISION norm(I - AAINV) / ( N norm(A) * norm(AINV) * EPS )

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 110 of file dppt03.f.

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subroutine dppt05	(	character	UPLO,
		integer	N,
		integer	NRHS,
		double precision, dimension( * )	AP,
		double precision, dimension( ldb, * )	B,
		integer	LDB,
		double precision, dimension( ldx, * )	X,
		integer	LDX,
		double precision, dimension( ldxact, * )	XACT,
		integer	LDXACT,
		double precision, dimension( * )	FERR,
		double precision, dimension( * )	BERR,
		double precision, dimension( * )	RESLTS
	)

DPPT05

Purpose:

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

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

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

 RESLTS(2) = residual from the iterative refinement routine
           = the maximum of BERR / ( (n+1)*EPS + (*) ), where
             (*) = (n+1)*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )

Parameters:

[in]	UPLO	UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the symmetric matrix A is stored. = 'U': Upper triangular = 'L': Lower triangular
[in]	N	N is INTEGER The number of rows of the matrices X, B, and XACT, and the order of the matrix A. N >= 0.
[in]	NRHS	NRHS is INTEGER The number of columns of the matrices X, B, and XACT. NRHS >= 0.
[in]	AP	AP is DOUBLE PRECISION array, dimension (N(N+1)/2) The upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
[in]	B	B is DOUBLE PRECISION array, dimension (LDB,NRHS) The right hand side vectors for the system of linear equations.
[in]	LDB	LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).
[in]	X	X is DOUBLE PRECISION array, dimension (LDX,NRHS) The computed solution vectors. Each vector is stored as a column of the matrix X.
[in]	LDX	LDX is INTEGER The leading dimension of the array X. LDX >= max(1,N).
[in]	XACT	XACT is DOUBLE PRECISION array, dimension (LDX,NRHS) The exact solution vectors. Each vector is stored as a column of the matrix XACT.
[in]	LDXACT	LDXACT is INTEGER The leading dimension of the array XACT. LDXACT >= max(1,N).
[in]	FERR	FERR is DOUBLE PRECISION array, dimension (NRHS) The estimated forward error bounds for each solution vector X. If XTRUE is the true solution, FERR bounds the magnitude of the largest entry in (X - XTRUE) divided by the magnitude of the largest entry in X.
[in]	BERR	BERR is DOUBLE PRECISION array, dimension (NRHS) The componentwise relative backward error of each solution vector (i.e., the smallest relative change in any entry of A or B that makes X an exact solution).
[out]	RESLTS	RESLTS is DOUBLE PRECISION array, dimension (2) The maximum over the NRHS solution vectors of the ratios: RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR ) RESLTS(2) = BERR / ( (n+1)EPS + () )

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 156 of file dppt05.f.

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subroutine dpst01	(	character	UPLO,
		integer	N,
		double precision, dimension( lda, * )	A,
		integer	LDA,
		double precision, dimension( ldafac, * )	AFAC,
		integer	LDAFAC,
		double precision, dimension( ldperm, * )	PERM,
		integer	LDPERM,
		integer, dimension( * )	PIV,
		double precision, dimension( * )	RWORK,
		double precision	RESID,
		integer	RANK
	)

DPST01

Purpose:

 DPST01 reconstructs a symmetric positive semidefinite matrix A
 from its L or U factors and the permutation matrix P and computes
 the residual
    norm( P*L*L'*P' - A ) / ( N * norm(A) * EPS ) or
    norm( P*U'*U*P' - A ) / ( N * norm(A) * EPS ),
 where EPS is the machine epsilon.

Parameters:

[in]	UPLO	UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the symmetric matrix A is stored: = 'U': Upper triangular = 'L': Lower triangular
[in]	N	N is INTEGER The number of rows and columns of the matrix A. N >= 0.
[in]	A	A is DOUBLE PRECISION array, dimension (LDA,N) The original symmetric matrix A.
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N)
[in]	AFAC	AFAC is DOUBLE PRECISION array, dimension (LDAFAC,N) The factor L or U from the LL' 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 PLL'P' - A (or PU'UP' - 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(LL' - A) / ( N norm(A) * EPS ) If UPLO = 'U', norm(U'U - A) / ( N norm(A) * EPS )
[in]	RANK	RANK is INTEGER number of nonzero singular values of A.

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 134 of file dpst01.f.

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subroutine dptt01	(	integer	N,
		double precision, dimension( * )	D,
		double precision, dimension( * )	E,
		double precision, dimension( * )	DF,
		double precision, dimension( * )	EF,
		double precision, dimension( * )	WORK,
		double precision	RESID
	)

DPTT01

Purpose:

 DPTT01 reconstructs a tridiagonal matrix A from its L*D*L'
 factorization and computes the residual
    norm(L*D*L' - A) / ( n * norm(A) * EPS ),
 where EPS is the machine epsilon.

Parameters:

[in]	N	N is INTEGTER The order of the matrix A.
[in]	D	D is DOUBLE PRECISION array, dimension (N) The n diagonal elements of the tridiagonal matrix A.
[in]	E	E is DOUBLE PRECISION array, dimension (N-1) The (n-1) subdiagonal elements of the tridiagonal matrix A.
[in]	DF	DF is DOUBLE PRECISION array, dimension (N) The n diagonal elements of the factor L from the LDL' factorization of A.
[in]	EF	EF is DOUBLE PRECISION array, dimension (N-1) The (n-1) subdiagonal elements of the factor L from the LDL' factorization of A.
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (2*N)
[out]	RESID	RESID is DOUBLE PRECISION norm(LDL' - A) / (n * norm(A) * EPS)

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 92 of file dptt01.f.

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subroutine dptt02	(	integer	N,
		integer	NRHS,
		double precision, dimension( * )	D,
		double precision, dimension( * )	E,
		double precision, dimension( ldx, * )	X,
		integer	LDX,
		double precision, dimension( ldb, * )	B,
		integer	LDB,
		double precision	RESID
	)

DPTT02

Purpose:

 DPTT02 computes the residual for the solution to a symmetric
 tridiagonal system of equations:
    RESID = norm(B - A*X) / (norm(A) * norm(X) * EPS),
 where EPS is the machine epsilon.

Parameters:

[in]	N	N is INTEGTER The order of the matrix A.
[in]	NRHS	NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrices B and X. NRHS >= 0.
[in]	D	D is DOUBLE PRECISION array, dimension (N) The n diagonal elements of the tridiagonal matrix A.
[in]	E	E is DOUBLE PRECISION array, dimension (N-1) The (n-1) subdiagonal elements of the tridiagonal matrix A.
[in]	X	X is DOUBLE PRECISION array, dimension (LDX,NRHS) The n by nrhs matrix of solution vectors X.
[in]	LDX	LDX is INTEGER The leading dimension of the array X. LDX >= max(1,N).
[in,out]	B	B is DOUBLE PRECISION array, dimension (LDB,NRHS) On entry, the n by nrhs matrix of right hand side vectors B. On exit, B is overwritten with the difference B - A*X.
[in]	LDB	LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).
[out]	RESID	RESID is DOUBLE PRECISION norm(B - AX) / (norm(A) norm(X) * EPS)

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 105 of file dptt02.f.

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subroutine dptt05	(	integer	N,
		integer	NRHS,
		double precision, dimension( * )	D,
		double precision, dimension( * )	E,
		double precision, dimension( ldb, * )	B,
		integer	LDB,
		double precision, dimension( ldx, * )	X,
		integer	LDX,
		double precision, dimension( ldxact, * )	XACT,
		integer	LDXACT,
		double precision, dimension( * )	FERR,
		double precision, dimension( * )	BERR,
		double precision, dimension( * )	RESLTS
	)

DPTT05

Purpose:

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

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

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

 RESLTS(2) = residual from the iterative refinement routine
           = the maximum of BERR / ( NZ*EPS + (*) ), where
             (*) = NZ*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
             and NZ = max. number of nonzeros in any row of A, plus 1

Parameters:

[in]	N	N is INTEGER The number of rows of the matrices X, B, and XACT, and the order of the matrix A. N >= 0.
[in]	NRHS	NRHS is INTEGER The number of columns of the matrices X, B, and XACT. NRHS >= 0.
[in]	D	D is DOUBLE PRECISION array, dimension (N) The n diagonal elements of the tridiagonal matrix A.
[in]	E	E is DOUBLE PRECISION array, dimension (N-1) The (n-1) subdiagonal elements of the tridiagonal matrix A.
[in]	B	B is DOUBLE PRECISION array, dimension (LDB,NRHS) The right hand side vectors for the system of linear equations.
[in]	LDB	LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).
[in]	X	X is DOUBLE PRECISION array, dimension (LDX,NRHS) The computed solution vectors. Each vector is stored as a column of the matrix X.
[in]	LDX	LDX is INTEGER The leading dimension of the array X. LDX >= max(1,N).
[in]	XACT	XACT is DOUBLE PRECISION array, dimension (LDX,NRHS) The exact solution vectors. Each vector is stored as a column of the matrix XACT.
[in]	LDXACT	LDXACT is INTEGER The leading dimension of the array XACT. LDXACT >= max(1,N).
[in]	FERR	FERR is DOUBLE PRECISION array, dimension (NRHS) The estimated forward error bounds for each solution vector X. If XTRUE is the true solution, FERR bounds the magnitude of the largest entry in (X - XTRUE) divided by the magnitude of the largest entry in X.
[in]	BERR	BERR is DOUBLE PRECISION array, dimension (NRHS) The componentwise relative backward error of each solution vector (i.e., the smallest relative change in any entry of A or B that makes X an exact solution).
[out]	RESLTS	RESLTS is DOUBLE PRECISION array, dimension (2) The maximum over the NRHS solution vectors of the ratios: RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR ) RESLTS(2) = BERR / ( NZEPS + () )

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 150 of file dptt05.f.

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subroutine dqlt01	(	integer	M,
		integer	N,
		double precision, dimension( lda, * )	A,
		double precision, dimension( lda, * )	AF,
		double precision, dimension( lda, * )	Q,
		double precision, dimension( lda, * )	L,
		integer	LDA,
		double precision, dimension( * )	TAU,
		double precision, dimension( lwork )	WORK,
		integer	LWORK,
		double precision, dimension( * )	RWORK,
		double precision, dimension( * )	RESULT
	)

DQLT01

Purpose:

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

 DQLT01 compares L with Q'*A, and checks that Q is orthogonal.

Parameters:

[in]	M	M is INTEGER The number of rows of the matrix A. M >= 0.
[in]	N	N is INTEGER The number of columns of the matrix A. N >= 0.
[in]	A	A is DOUBLE PRECISION array, dimension (LDA,N) The m-by-n matrix A.
[out]	AF	AF is DOUBLE PRECISION array, dimension (LDA,N) Details of the QL factorization of A, as returned by DGEQLF. See DGEQLF for further details.
[out]	Q	Q is DOUBLE PRECISION array, dimension (LDA,M) The m-by-m orthogonal matrix Q.
[out]	L	L is DOUBLE PRECISION array, dimension (LDA,max(M,N))
[in]	LDA	LDA is INTEGER The leading dimension of the arrays A, AF, Q and R. LDA >= max(M,N).
[out]	TAU	TAU is DOUBLE PRECISION array, dimension (min(M,N)) The scalar factors of the elementary reflectors, as returned by DGEQLF.
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (LWORK)
[in]	LWORK	LWORK is INTEGER The dimension of the array WORK.
[out]	RWORK	RWORK is DOUBLE PRECISION array, dimension (M)
[out]	RESULT	RESULT is DOUBLE PRECISION array, dimension (2) The test ratios: RESULT(1) = norm( L - Q'A ) / ( M norm(A) * EPS ) RESULT(2) = norm( I - Q'Q ) / ( M EPS )

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 126 of file dqlt01.f.

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subroutine dqlt02	(	integer	M,
		integer	N,
		integer	K,
		double precision, dimension( lda, * )	A,
		double precision, dimension( lda, * )	AF,
		double precision, dimension( lda, * )	Q,
		double precision, dimension( lda, * )	L,
		integer	LDA,
		double precision, dimension( * )	TAU,
		double precision, dimension( lwork )	WORK,
		integer	LWORK,
		double precision, dimension( * )	RWORK,
		double precision, dimension( * )	RESULT
	)

DQLT02

Purpose:

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

 Given the QL factorization of an m-by-n matrix A, DQLT02 generates
 the orthogonal matrix Q defined by the factorization of the last k
 columns of A; it compares L(m-n+1:m,n-k+1:n) with
 Q(1:m,m-n+1:m)'*A(1:m,n-k+1:n), and checks that the columns of Q are
 orthonormal.

Parameters:

[in]	M	M is INTEGER The number of rows of the matrix Q to be generated. M >= 0.
[in]	N	N is INTEGER The number of columns of the matrix Q to be generated. M >= N >= 0.
[in]	K	K is INTEGER The number of elementary reflectors whose product defines the matrix Q. N >= K >= 0.
[in]	A	A is DOUBLE PRECISION array, dimension (LDA,N) The m-by-n matrix A which was factorized by DQLT01.
[in]	AF	AF is DOUBLE PRECISION array, dimension (LDA,N) Details of the QL factorization of A, as returned by DGEQLF. See DGEQLF for further details.
[out]	Q	Q is DOUBLE PRECISION array, dimension (LDA,N)
[out]	L	L is DOUBLE PRECISION array, dimension (LDA,N)
[in]	LDA	LDA is INTEGER The leading dimension of the arrays A, AF, Q and L. LDA >= M.
[in]	TAU	TAU is DOUBLE PRECISION array, dimension (N) The scalar factors of the elementary reflectors corresponding to the QL factorization in AF.
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (LWORK)
[in]	LWORK	LWORK is INTEGER The dimension of the array WORK.
[out]	RWORK	RWORK is DOUBLE PRECISION array, dimension (M)
[out]	RESULT	RESULT is DOUBLE PRECISION array, dimension (2) The test ratios: RESULT(1) = norm( L - Q'A ) / ( M norm(A) * EPS ) RESULT(2) = norm( I - Q'Q ) / ( M EPS )

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 136 of file dqlt02.f.

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subroutine dqlt03	(	integer	M,
		integer	N,
		integer	K,
		double precision, dimension( lda, * )	AF,
		double precision, dimension( lda, * )	C,
		double precision, dimension( lda, * )	CC,
		double precision, dimension( lda, * )	Q,
		integer	LDA,
		double precision, dimension( * )	TAU,
		double precision, dimension( lwork )	WORK,
		integer	LWORK,
		double precision, dimension( * )	RWORK,
		double precision, dimension( * )	RESULT
	)

DQLT03

Purpose:

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

 DQLT03 compares the results of a call to DORMQL with the results of
 forming Q explicitly by a call to DORGQL and then performing matrix
 multiplication by a call to DGEMM.

Parameters:

[in]	M	M is INTEGER The order of the orthogonal matrix Q. M >= 0.
[in]	N	N is INTEGER The number of rows or columns of the matrix C; C is m-by-n if Q is applied from the left, or n-by-m if Q is applied from the right. N >= 0.
[in]	K	K is INTEGER The number of elementary reflectors whose product defines the orthogonal matrix Q. M >= K >= 0.
[in]	AF	AF is DOUBLE PRECISION array, dimension (LDA,N) Details of the QL factorization of an m-by-n matrix, as returned by DGEQLF. See SGEQLF for further details.
[out]	C	C is DOUBLE PRECISION array, dimension (LDA,N)
[out]	CC	CC is DOUBLE PRECISION array, dimension (LDA,N)
[out]	Q	Q is DOUBLE PRECISION array, dimension (LDA,M)
[in]	LDA	LDA is INTEGER The leading dimension of the arrays AF, C, CC, and Q.
[in]	TAU	TAU is DOUBLE PRECISION array, dimension (min(M,N)) The scalar factors of the elementary reflectors corresponding to the QL factorization in AF.
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (LWORK)
[in]	LWORK	LWORK is INTEGER The length of WORK. LWORK must be at least M, and should be M*NB, where NB is the blocksize for this environment.
[out]	RWORK	RWORK is DOUBLE PRECISION array, dimension (M)
[out]	RESULT	RESULT is DOUBLE PRECISION array, dimension (4) The test ratios compare two techniques for multiplying a random matrix C by an m-by-m orthogonal matrix Q. RESULT(1) = norm( QC - QC ) / ( M * norm(C) * EPS ) RESULT(2) = norm( CQ - CQ ) / ( M * norm(C) * EPS ) RESULT(3) = norm( Q'C - Q'C )/ ( M * norm(C) * EPS ) RESULT(4) = norm( CQ' - CQ' )/ ( M * norm(C) * EPS )

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 136 of file dqlt03.f.

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DOUBLE PRECISION function dqpt01	(	integer	M,
		integer	N,
		integer	K,
		double precision, dimension( lda, * )	A,
		double precision, dimension( lda, * )	AF,
		integer	LDA,
		double precision, dimension( * )	TAU,
		integer, dimension( * )	JPVT,
		double precision, dimension( lwork )	WORK,
		integer	LWORK
	)

DQPT01

Purpose:

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

 This function returns ||A*P - Q*R||/(||norm(A)||*eps*M)

Parameters:

[in]	M	M is INTEGER The number of rows of the matrices A and AF.
[in]	N	N is INTEGER The number of columns of the matrices A and AF.
[in]	K	K is INTEGER The number of columns of AF that have been reduced to upper triangular form.
[in]	A	A is DOUBLE PRECISION array, dimension (LDA, N) The original matrix A.
[in]	AF	AF is DOUBLE PRECISION array, dimension (LDA,N) The (possibly partial) output of DGEQPF. The upper triangle of AF(1:k,1:k) is a partial triangular factor, the entries below the diagonal in the first k columns are the Householder vectors, and the rest of AF contains a partially updated matrix.
[in]	LDA	LDA is INTEGER The leading dimension of the arrays A and AF.
[in]	TAU	TAU is DOUBLE PRECISION array, dimension (K) Details of the Householder transformations as returned by DGEQPF.
[in]	JPVT	JPVT is INTEGER array, dimension (N) Pivot information as returned by DGEQPF.
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (LWORK)
[in]	LWORK	LWORK is INTEGER The length of the array WORK. LWORK >= M*N+N.

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 120 of file dqpt01.f.

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subroutine dqrt01	(	integer	M,
		integer	N,
		double precision, dimension( lda, * )	A,
		double precision, dimension( lda, * )	AF,
		double precision, dimension( lda, * )	Q,
		double precision, dimension( lda, * )	R,
		integer	LDA,
		double precision, dimension( * )	TAU,
		double precision, dimension( lwork )	WORK,
		integer	LWORK,
		double precision, dimension( * )	RWORK,
		double precision, dimension( * )	RESULT
	)

DQRT01

Purpose:

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

 DQRT01 compares R with Q'*A, and checks that Q is orthogonal.

Parameters:

[in]	M	M is INTEGER The number of rows of the matrix A. M >= 0.
[in]	N	N is INTEGER The number of columns of the matrix A. N >= 0.
[in]	A	A is DOUBLE PRECISION array, dimension (LDA,N) The m-by-n matrix A.
[out]	AF	AF is DOUBLE PRECISION array, dimension (LDA,N) Details of the QR factorization of A, as returned by DGEQRF. See DGEQRF for further details.
[out]	Q	Q is DOUBLE PRECISION array, dimension (LDA,M) The m-by-m orthogonal matrix Q.
[out]	R	R is DOUBLE PRECISION array, dimension (LDA,max(M,N))
[in]	LDA	LDA is INTEGER The leading dimension of the arrays A, AF, Q and R. LDA >= max(M,N).
[out]	TAU	TAU is DOUBLE PRECISION array, dimension (min(M,N)) The scalar factors of the elementary reflectors, as returned by DGEQRF.
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (LWORK)
[in]	LWORK	LWORK is INTEGER The dimension of the array WORK.
[out]	RWORK	RWORK is DOUBLE PRECISION array, dimension (M)
[out]	RESULT	RESULT is DOUBLE PRECISION array, dimension (2) The test ratios: RESULT(1) = norm( R - Q'A ) / ( M norm(A) * EPS ) RESULT(2) = norm( I - Q'Q ) / ( M EPS )

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 126 of file dqrt01.f.

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subroutine dqrt01p	(	integer	M,
		integer	N,
		double precision, dimension( lda, * )	A,
		double precision, dimension( lda, * )	AF,
		double precision, dimension( lda, * )	Q,
		double precision, dimension( lda, * )	R,
		integer	LDA,
		double precision, dimension( * )	TAU,
		double precision, dimension( lwork )	WORK,
		integer	LWORK,
		double precision, dimension( * )	RWORK,
		double precision, dimension( * )	RESULT
	)

DQRT01P

Purpose:

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

 DQRT01P compares R with Q'*A, and checks that Q is orthogonal.

Parameters:

[in]	M	M is INTEGER The number of rows of the matrix A. M >= 0.
[in]	N	N is INTEGER The number of columns of the matrix A. N >= 0.
[in]	A	A is DOUBLE PRECISION array, dimension (LDA,N) The m-by-n matrix A.
[out]	AF	AF is DOUBLE PRECISION array, dimension (LDA,N) Details of the QR factorization of A, as returned by DGEQRFP. See DGEQRFP for further details.
[out]	Q	Q is DOUBLE PRECISION array, dimension (LDA,M) The m-by-m orthogonal matrix Q.
[out]	R	R is DOUBLE PRECISION array, dimension (LDA,max(M,N))
[in]	LDA	LDA is INTEGER The leading dimension of the arrays A, AF, Q and R. LDA >= max(M,N).
[out]	TAU	TAU is DOUBLE PRECISION array, dimension (min(M,N)) The scalar factors of the elementary reflectors, as returned by DGEQRFP.
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (LWORK)
[in]	LWORK	LWORK is INTEGER The dimension of the array WORK.
[out]	RWORK	RWORK is DOUBLE PRECISION array, dimension (M)
[out]	RESULT	RESULT is DOUBLE PRECISION array, dimension (2) The test ratios: RESULT(1) = norm( R - Q'A ) / ( M norm(A) * EPS ) RESULT(2) = norm( I - Q'Q ) / ( M EPS )

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 126 of file dqrt01p.f.

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subroutine dqrt02	(	integer	M,
		integer	N,
		integer	K,
		double precision, dimension( lda, * )	A,
		double precision, dimension( lda, * )	AF,
		double precision, dimension( lda, * )	Q,
		double precision, dimension( lda, * )	R,
		integer	LDA,
		double precision, dimension( * )	TAU,
		double precision, dimension( lwork )	WORK,
		integer	LWORK,
		double precision, dimension( * )	RWORK,
		double precision, dimension( * )	RESULT
	)

DQRT02

Purpose:

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

 Given the QR factorization of an m-by-n matrix A, DQRT02 generates
 the orthogonal matrix Q defined by the factorization of the first k
 columns of A; it compares R(1:n,1:k) with Q(1:m,1:n)'*A(1:m,1:k),
 and checks that the columns of Q are orthonormal.

Parameters:

[in]	M	M is INTEGER The number of rows of the matrix Q to be generated. M >= 0.
[in]	N	N is INTEGER The number of columns of the matrix Q to be generated. M >= N >= 0.
[in]	K	K is INTEGER The number of elementary reflectors whose product defines the matrix Q. N >= K >= 0.
[in]	A	A is DOUBLE PRECISION array, dimension (LDA,N) The m-by-n matrix A which was factorized by DQRT01.
[in]	AF	AF is DOUBLE PRECISION array, dimension (LDA,N) Details of the QR factorization of A, as returned by DGEQRF. See DGEQRF for further details.
[out]	Q	Q is DOUBLE PRECISION array, dimension (LDA,N)
[out]	R	R is DOUBLE PRECISION array, dimension (LDA,N)
[in]	LDA	LDA is INTEGER The leading dimension of the arrays A, AF, Q and R. LDA >= M.
[in]	TAU	TAU is DOUBLE PRECISION array, dimension (N) The scalar factors of the elementary reflectors corresponding to the QR factorization in AF.
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (LWORK)
[in]	LWORK	LWORK is INTEGER The dimension of the array WORK.
[out]	RWORK	RWORK is DOUBLE PRECISION array, dimension (M)
[out]	RESULT	RESULT is DOUBLE PRECISION array, dimension (2) The test ratios: RESULT(1) = norm( R - Q'A ) / ( M norm(A) * EPS ) RESULT(2) = norm( I - Q'Q ) / ( M EPS )

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 135 of file dqrt02.f.

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subroutine dqrt03	(	integer	M,
		integer	N,
		integer	K,
		double precision, dimension( lda, * )	AF,
		double precision, dimension( lda, * )	C,
		double precision, dimension( lda, * )	CC,
		double precision, dimension( lda, * )	Q,
		integer	LDA,
		double precision, dimension( * )	TAU,
		double precision, dimension( lwork )	WORK,
		integer	LWORK,
		double precision, dimension( * )	RWORK,
		double precision, dimension( * )	RESULT
	)

DQRT03

Purpose:

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

 DQRT03 compares the results of a call to DORMQR with the results of
 forming Q explicitly by a call to DORGQR and then performing matrix
 multiplication by a call to DGEMM.

Parameters:

[in]	M	M is INTEGER The order of the orthogonal matrix Q. M >= 0.
[in]	N	N is INTEGER The number of rows or columns of the matrix C; C is m-by-n if Q is applied from the left, or n-by-m if Q is applied from the right. N >= 0.
[in]	K	K is INTEGER The number of elementary reflectors whose product defines the orthogonal matrix Q. M >= K >= 0.
[in]	AF	AF is DOUBLE PRECISION array, dimension (LDA,N) Details of the QR factorization of an m-by-n matrix, as 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( QC - QC ) / ( M * norm(C) * EPS ) RESULT(2) = norm( CQ - CQ ) / ( M * norm(C) * EPS ) RESULT(3) = norm( Q'C - Q'C )/ ( M * norm(C) * EPS ) RESULT(4) = norm( CQ' - CQ' )/ ( M * norm(C) * EPS )

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 136 of file dqrt03.f.

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subroutine dqrt04	(	integer	M,
		integer	N,
		integer	NB,
		double precision, dimension(6)	RESULT
	)

DQRT04

Purpose:

 DQRT04 tests DGEQRT and DGEMQRT.

Parameters:

[in]	M	M is INTEGER Number of rows in test matrix.
[in]	N	N is INTEGER Number of columns in test matrix.
[in]	NB	NB is INTEGER Block size of test matrix. NB <= Min(M,N).
[out]	RESULT	RESULT is DOUBLE PRECISION array, dimension (6) Results of each of the six tests below. RESULT(1) = \| A - Q R \| RESULT(2) = \| I - Q^H Q \| RESULT(3) = \| Q C - Q C \| RESULT(4) = \| Q^H C - Q^H C \| RESULT(5) = \| C Q - C Q \| RESULT(6) = \| C Q^H - C Q^H \|

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: April 2012

Definition at line 74 of file dqrt04.f.

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subroutine dqrt05	(	integer	M,
		integer	N,
		integer	L,
		integer	NB,
		double precision, dimension(6)	RESULT
	)

DQRT05

Purpose:

 DQRT05 tests DTPQRT and DTPMQRT.

Parameters:

[in]	M	M is INTEGER Number of rows in lower part of the test matrix.
[in]	N	N is INTEGER Number of columns in test matrix.
[in]	L	L is INTEGER The number of rows of the upper trapezoidal part the lower test matrix. 0 <= L <= M.
[in]	NB	NB is INTEGER Block size of test matrix. NB <= N.
[out]	RESULT	RESULT is DOUBLE PRECISION array, dimension (6) Results of each of the six tests below. RESULT(1) = \| A - Q R \| RESULT(2) = \| I - Q^H Q \| RESULT(3) = \| Q C - Q C \| RESULT(4) = \| Q^H C - Q^H C \| RESULT(5) = \| C Q - C Q \| RESULT(6) = \| C Q^H - C Q^H \|

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: April 2012

Definition at line 81 of file dqrt05.f.

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DOUBLE PRECISION function dqrt11	(	integer	M,
		integer	K,
		double precision, dimension( lda, * )	A,
		integer	LDA,
		double precision, dimension( * )	TAU,
		double precision, dimension( lwork )	WORK,
		integer	LWORK
	)

DQRT11

Purpose:

 DQRT11 computes the test ratio

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

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

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

 where tau(k) is stored in TAU(k) and v(k) is an m-vector of the form
 [ 0 ... 0 1 x(k) ]', where x(k) is a vector of length m-k stored
 in A(k+1:m,k).

Parameters:

[in]	M	M is INTEGER The number of rows of the matrix A.
[in]	K	K is INTEGER The number of columns of A whose subdiagonal entries contain information about orthogonal transformations.
[in]	A	A is DOUBLE PRECISION array, dimension (LDA,K) The (possibly partial) output of a QR reduction routine.
[in]	LDA	LDA is INTEGER The leading dimension of the array A.
[in]	TAU	TAU is DOUBLE PRECISION array, dimension (K) The scaling factors tau for the elementary transformations as computed by the QR factorization routine.
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (LWORK)
[in]	LWORK	LWORK is INTEGER The length of the array WORK. LWORK >= M*M + M.

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 99 of file dqrt11.f.

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DOUBLE PRECISION function dqrt12	(	integer	M,
		integer	N,
		double precision, dimension( lda, * )	A,
		integer	LDA,
		double precision, dimension( * )	S,
		double precision, dimension( lwork )	WORK,
		integer	LWORK
	)

DQRT12

Purpose:

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

      || s - svlues||/(||svlues||*eps*max(M,N))

Parameters:

[in]	M	M is INTEGER The number of rows of the matrix A.
[in]	N	N is INTEGER The number of columns of the matrix A.
[in]	A	A is DOUBLE PRECISION array, dimension (LDA,N) The M-by-N matrix A. Only the upper trapezoid is referenced.
[in]	LDA	LDA is INTEGER The leading dimension of the array A.
[in]	S	S is DOUBLE PRECISION array, dimension (min(M,N)) The singular values of the matrix A.
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (LWORK)
[in]	LWORK	LWORK is INTEGER The length of the array WORK. LWORK >= max(MN + 4min(M,N) + max(M,N), MN+2MIN( M, N )+4*N).

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 90 of file dqrt12.f.

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subroutine dqrt13	(	integer	SCALE,
		integer	M,
		integer	N,
		double precision, dimension( lda, * )	A,
		integer	LDA,
		double precision	NORMA,
		integer, dimension( 4 )	ISEED
	)

DQRT13

Purpose:

 DQRT13 generates a full-rank matrix that may be scaled to have large
 or small norm.

Parameters:

[in]	SCALE	SCALE is INTEGER SCALE = 1: normally scaled matrix SCALE = 2: matrix scaled up SCALE = 3: matrix scaled down
[in]	M	M is INTEGER The number of rows of the matrix A.
[in]	N	N is INTEGER The number of columns of A.
[out]	A	A is DOUBLE PRECISION array, dimension (LDA,N) The M-by-N matrix A.
[in]	LDA	LDA is INTEGER The leading dimension of the array A.
[out]	NORMA	NORMA is DOUBLE PRECISION The one-norm of A.
[in,out]	ISEED	ISEED is integer array, dimension (4) Seed for random number generator

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 92 of file dqrt13.f.

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DOUBLE PRECISION function dqrt14	(	character	TRANS,
		integer	M,
		integer	N,
		integer	NRHS,
		double precision, dimension( lda, * )	A,
		integer	LDA,
		double precision, dimension( ldx, * )	X,
		integer	LDX,
		double precision, dimension( lwork )	WORK,
		integer	LWORK
	)

DQRT14

Purpose:

 DQRT14 checks whether X is in the row space of A or A'.  It does so
 by scaling both X and A such that their norms are in the range
 [sqrt(eps), 1/sqrt(eps)], then computing a QR factorization of [A,X]
 (if TRANS = 'T') or an LQ factorization of [A',X]' (if TRANS = 'N'),
 and returning the norm of the trailing triangle, scaled by
 MAX(M,N,NRHS)*eps.

Parameters:

[in]	TRANS	TRANS is CHARACTER*1 = 'N': No transpose, check for X in the row space of A = 'T': Transpose, check for X in the row space of A'.
[in]	M	M is INTEGER The number of rows of the matrix A.
[in]	N	N is INTEGER The number of columns of the matrix A.
[in]	NRHS	NRHS is INTEGER The number of right hand sides, i.e., the number of columns of X.
[in]	A	A is DOUBLE PRECISION array, dimension (LDA,N) The M-by-N matrix A.
[in]	LDA	LDA is INTEGER The leading dimension of the array A.
[in]	X	X is DOUBLE PRECISION array, dimension (LDX,NRHS) If TRANS = 'N', the N-by-NRHS matrix X. IF TRANS = 'T', the M-by-NRHS matrix X.
[in]	LDX	LDX is INTEGER The leading dimension of the array X.
[out]	WORK	WORK is DOUBLE PRECISION array dimension (LWORK)
[in]	LWORK	LWORK is INTEGER length of workspace array required If TRANS = 'N', LWORK >= (M+NRHS)(N+2); if TRANS = 'T', LWORK >= (N+NRHS)(M+2).

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 116 of file dqrt14.f.

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subroutine dqrt15	(	integer	SCALE,
		integer	RKSEL,
		integer	M,
		integer	N,
		integer	NRHS,
		double precision, dimension( lda, * )	A,
		integer	LDA,
		double precision, dimension( ldb, * )	B,
		integer	LDB,
		double precision, dimension( * )	S,
		integer	RANK,
		double precision	NORMA,
		double precision	NORMB,
		integer, dimension( 4 )	ISEED,
		double precision, dimension( lwork )	WORK,
		integer	LWORK
	)

DQRT15

Purpose:

 DQRT15 generates a matrix with full or deficient rank and of various
 norms.

Parameters:

[in]	SCALE	SCALE is INTEGER SCALE = 1: normally scaled matrix SCALE = 2: matrix scaled up SCALE = 3: matrix scaled down
[in]	RKSEL	RKSEL is INTEGER RKSEL = 1: full rank matrix RKSEL = 2: rank-deficient matrix
[in]	M	M is INTEGER The number of rows of the matrix A.
[in]	N	N is INTEGER The number of columns of A.
[in]	NRHS	NRHS is INTEGER The number of columns of B.
[out]	A	A is DOUBLE PRECISION array, dimension (LDA,N) The M-by-N matrix A.
[in]	LDA	LDA is INTEGER The leading dimension of the array A.
[out]	B	B is DOUBLE PRECISION array, dimension (LDB, NRHS) A matrix that is in the range space of matrix A.
[in]	LDB	LDB is INTEGER The leading dimension of the array B.
[out]	S	S is DOUBLE PRECISION array, dimension MIN(M,N) Singular values of A.
[out]	RANK	RANK is INTEGER number of nonzero singular values of A.
[out]	NORMA	NORMA is DOUBLE PRECISION one-norm of A.
[out]	NORMB	NORMB is DOUBLE PRECISION one-norm of B.
[in,out]	ISEED	ISEED is integer array, dimension (4) seed for random number generator.
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (LWORK)
[in]	LWORK	LWORK is INTEGER length of work space required. LWORK >= MAX(M+MIN(M,N),NRHSMIN(M,N),2N+M)

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 148 of file dqrt15.f.

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subroutine dqrt16	(	character	TRANS,
		integer	M,
		integer	N,
		integer	NRHS,
		double precision, dimension( lda, * )	A,
		integer	LDA,
		double precision, dimension( ldx, * )	X,
		integer	LDX,
		double precision, dimension( ldb, * )	B,
		integer	LDB,
		double precision, dimension( * )	RWORK,
		double precision	RESID
	)

DQRT16

Purpose:

 DQRT16 computes the residual for a solution of a system of linear
 equations  A*x = b  or  A'*x = b:
    RESID = norm(B - A*X) / ( max(m,n) * norm(A) * norm(X) * EPS ),
 where EPS is the machine epsilon.

Parameters:

[in]	TRANS	TRANS is CHARACTER1 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 - AX) / ( max(m,n) norm(A) * norm(X) * EPS ).

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 133 of file dqrt16.f.

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DOUBLE PRECISION function dqrt17	(	character	TRANS,
		integer	IRESID,
		integer	M,
		integer	N,
		integer	NRHS,
		double precision, dimension( lda, * )	A,
		integer	LDA,
		double precision, dimension( ldx, * )	X,
		integer	LDX,
		double precision, dimension( ldb, * )	B,
		integer	LDB,
		double precision, dimension( ldb, * )	C,
		double precision, dimension( lwork )	WORK,
		integer	LWORK
	)

DQRT17

Purpose:

 DQRT17 computes the ratio

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

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

    alpha = ||B|| if IRESID = 1 (zero-residual problem)
    alpha = ||R|| if IRESID = 2 (otherwise).

Parameters:

[in]	TRANS	TRANS is CHARACTER*1 Specifies whether or not the transpose of A is used. = 'N': No transpose, op(A) = A. = 'T': Transpose, op(A) = A'.
[in]	IRESID	IRESID is INTEGER IRESID = 1 indicates zero-residual problem. IRESID = 2 indicates non-zero residual.
[in]	M	M is INTEGER The number of rows of the matrix A. If TRANS = 'N', the number of rows of the matrix B. If TRANS = 'T', the number of rows of the matrix X.
[in]	N	N is INTEGER The number of columns of the matrix A. If TRANS = 'N', the number of rows of the matrix X. If TRANS = 'T', the number of rows of the matrix B.
[in]	NRHS	NRHS is INTEGER The number of columns of the matrices X and B.
[in]	A	A is DOUBLE PRECISION array, dimension (LDA,N) The m-by-n matrix A.
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= M.
[in]	X	X is DOUBLE PRECISION array, dimension (LDX,NRHS) If TRANS = 'N', the n-by-nrhs matrix X. If TRANS = 'T', the m-by-nrhs matrix X.
[in]	LDX	LDX is INTEGER The leading dimension of the array X. If TRANS = 'N', LDX >= N. If TRANS = 'T', LDX >= M.
[in]	B	B is DOUBLE PRECISION array, dimension (LDB,NRHS) If TRANS = 'N', the m-by-nrhs matrix B. If TRANS = 'T', the n-by-nrhs matrix B.
[in]	LDB	LDB is INTEGER The leading dimension of the array B. If TRANS = 'N', LDB >= M. If TRANS = 'T', LDB >= N.
[out]	C	C is DOUBLE PRECISION array, dimension (LDB,NRHS)
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (LWORK)
[in]	LWORK	LWORK is INTEGER The length of the array WORK. LWORK >= NRHS*(M+N).

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 150 of file dqrt17.f.

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subroutine drqt01	(	integer	M,
		integer	N,
		double precision, dimension( lda, * )	A,
		double precision, dimension( lda, * )	AF,
		double precision, dimension( lda, * )	Q,
		double precision, dimension( lda, * )	R,
		integer	LDA,
		double precision, dimension( * )	TAU,
		double precision, dimension( lwork )	WORK,
		integer	LWORK,
		double precision, dimension( * )	RWORK,
		double precision, dimension( * )	RESULT
	)

DRQT01

Purpose:

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

 DRQT01 compares R with A*Q', and checks that Q is orthogonal.

Parameters:

[in]	M	M is INTEGER The number of rows of the matrix A. M >= 0.
[in]	N	N is INTEGER The number of columns of the matrix A. N >= 0.
[in]	A	A is DOUBLE PRECISION array, dimension (LDA,N) The m-by-n matrix A.
[out]	AF	AF is DOUBLE PRECISION array, dimension (LDA,N) Details of the RQ factorization of A, as returned by DGERQF. See DGERQF for further details.
[out]	Q	Q is DOUBLE PRECISION array, dimension (LDA,N) The n-by-n orthogonal matrix Q.
[out]	R	R is DOUBLE PRECISION array, dimension (LDA,max(M,N))
[in]	LDA	LDA is INTEGER The leading dimension of the arrays A, AF, Q and L. LDA >= max(M,N).
[out]	TAU	TAU is DOUBLE PRECISION array, dimension (min(M,N)) The scalar factors of the elementary reflectors, as returned by DGERQF.
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (LWORK)
[in]	LWORK	LWORK is INTEGER The dimension of the array WORK.
[out]	RWORK	RWORK is DOUBLE PRECISION array, dimension (max(M,N))
[out]	RESULT	RESULT is DOUBLE PRECISION array, dimension (2) The test ratios: RESULT(1) = norm( R - AQ' ) / ( N norm(A) * EPS ) RESULT(2) = norm( I - QQ' ) / ( N EPS )

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 126 of file drqt01.f.

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subroutine drqt02	(	integer	M,
		integer	N,
		integer	K,
		double precision, dimension( lda, * )	A,
		double precision, dimension( lda, * )	AF,
		double precision, dimension( lda, * )	Q,
		double precision, dimension( lda, * )	R,
		integer	LDA,
		double precision, dimension( * )	TAU,
		double precision, dimension( lwork )	WORK,
		integer	LWORK,
		double precision, dimension( * )	RWORK,
		double precision, dimension( * )	RESULT
	)

DRQT02

Purpose:

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

 Given the RQ factorization of an m-by-n matrix A, DRQT02 generates
 the orthogonal matrix Q defined by the factorization of the last k
 rows of A; it compares R(m-k+1:m,n-m+1:n) with
 A(m-k+1:m,1:n)*Q(n-m+1:n,1:n)', and checks that the rows of Q are
 orthonormal.

Parameters:

[in]	M	M is INTEGER The number of rows of the matrix Q to be generated. M >= 0.
[in]	N	N is INTEGER The number of columns of the matrix Q to be generated. N >= M >= 0.
[in]	K	K is INTEGER The number of elementary reflectors whose product defines the matrix Q. M >= K >= 0.
[in]	A	A is DOUBLE PRECISION array, dimension (LDA,N) The m-by-n matrix A which was factorized by DRQT01.
[in]	AF	AF is DOUBLE PRECISION array, dimension (LDA,N) Details of the RQ factorization of A, as returned by DGERQF. See DGERQF for further details.
[out]	Q	Q is DOUBLE PRECISION array, dimension (LDA,N)
[out]	R	R is DOUBLE PRECISION array, dimension (LDA,M)
[in]	LDA	LDA is INTEGER The leading dimension of the arrays A, AF, Q and L. LDA >= N.
[in]	TAU	TAU is DOUBLE PRECISION array, dimension (M) The scalar factors of the elementary reflectors corresponding to the RQ factorization in AF.
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (LWORK)
[in]	LWORK	LWORK is INTEGER The dimension of the array WORK.
[out]	RWORK	RWORK is DOUBLE PRECISION array, dimension (M)
[out]	RESULT	RESULT is DOUBLE PRECISION array, dimension (2) The test ratios: RESULT(1) = norm( R - AQ' ) / ( N norm(A) * EPS ) RESULT(2) = norm( I - QQ' ) / ( N EPS )

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 136 of file drqt02.f.

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subroutine drqt03	(	integer	M,
		integer	N,
		integer	K,
		double precision, dimension( lda, * )	AF,
		double precision, dimension( lda, * )	C,
		double precision, dimension( lda, * )	CC,
		double precision, dimension( lda, * )	Q,
		integer	LDA,
		double precision, dimension( * )	TAU,
		double precision, dimension( lwork )	WORK,
		integer	LWORK,
		double precision, dimension( * )	RWORK,
		double precision, dimension( * )	RESULT
	)

DRQT03

Purpose:

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

 DRQT03 compares the results of a call to DORMRQ with the results of
 forming Q explicitly by a call to DORGRQ and then performing matrix
 multiplication by a call to DGEMM.

Parameters:

[in]	M	M is INTEGER The number of rows or columns of the matrix C; C is n-by-m if Q is applied from the left, or m-by-n if Q is applied from the right. M >= 0.
[in]	N	N is INTEGER The order of the orthogonal matrix Q. N >= 0.
[in]	K	K is INTEGER The number of elementary reflectors whose product defines the orthogonal matrix Q. N >= K >= 0.
[in]	AF	AF is DOUBLE PRECISION array, dimension (LDA,N) Details of the RQ factorization of an m-by-n matrix, as returned by DGERQF. See SGERQF for further details.
[out]	C	C is DOUBLE PRECISION array, dimension (LDA,N)
[out]	CC	CC is DOUBLE PRECISION array, dimension (LDA,N)
[out]	Q	Q is DOUBLE PRECISION array, dimension (LDA,N)
[in]	LDA	LDA is INTEGER The leading dimension of the arrays AF, C, CC, and Q.
[in]	TAU	TAU is DOUBLE PRECISION array, dimension (min(M,N)) The scalar factors of the elementary reflectors corresponding to the RQ factorization in AF.
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (LWORK)
[in]	LWORK	LWORK is INTEGER The length of WORK. LWORK must be at least M, and should be M*NB, where NB is the blocksize for this environment.
[out]	RWORK	RWORK is DOUBLE PRECISION array, dimension (M)
[out]	RESULT	RESULT is DOUBLE PRECISION array, dimension (4) The test ratios compare two techniques for multiplying a random matrix C by an n-by-n orthogonal matrix Q. RESULT(1) = norm( QC - QC ) / ( N * norm(C) * EPS ) RESULT(2) = norm( CQ - CQ ) / ( N * norm(C) * EPS ) RESULT(3) = norm( Q'C - Q'C )/ ( N * norm(C) * EPS ) RESULT(4) = norm( CQ' - CQ' )/ ( N * norm(C) * EPS )

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 136 of file drqt03.f.

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DOUBLE PRECISION function drzt01	(	integer	M,
		integer	N,
		double precision, dimension( lda, * )	A,
		double precision, dimension( lda, * )	AF,
		integer	LDA,
		double precision, dimension( * )	TAU,
		double precision, dimension( lwork )	WORK,
		integer	LWORK
	)

DRZT01

Purpose:

 DRZT01 returns
      || A - R*Q || / ( M * eps * ||A|| )
 for an upper trapezoidal A that was factored with DTZRZF.

Parameters:

[in]	M	M is INTEGER The number of rows of the matrices A and AF.
[in]	N	N is INTEGER The number of columns of the matrices A and AF.
[in]	A	A is DOUBLE PRECISION array, dimension (LDA,N) The original upper trapezoidal M by N matrix A.
[in]	AF	AF is DOUBLE PRECISION array, dimension (LDA,N) The output of DTZRZF for input matrix A. The lower triangle is not referenced.
[in]	LDA	LDA is INTEGER The leading dimension of the arrays A and AF.
[in]	TAU	TAU is DOUBLE PRECISION array, dimension (M) Details of the Householder transformations as returned by DTZRZF.
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (LWORK)
[in]	LWORK	LWORK is INTEGER The length of the array WORK. LWORK >= mn + mnb.

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 98 of file drzt01.f.

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DOUBLE PRECISION function drzt02	(	integer	M,
		integer	N,
		double precision, dimension( lda, * )	AF,
		integer	LDA,
		double precision, dimension( * )	TAU,
		double precision, dimension( lwork )	WORK,
		integer	LWORK
	)

DRZT02

Purpose:

 DRZT02 returns
      || I - Q'*Q || / ( M * eps)
 where the matrix Q is defined by the Householder transformations
 generated by DTZRZF.

Parameters:

[in]	M	M is INTEGER The number of rows of the matrix AF.
[in]	N	N is INTEGER The number of columns of the matrix AF.
[in]	AF	AF is DOUBLE PRECISION array, dimension (LDA,N) The output of DTZRZF.
[in]	LDA	LDA is INTEGER The leading dimension of the array AF.
[in]	TAU	TAU is DOUBLE PRECISION array, dimension (M) Details of the Householder transformations as returned by DTZRZF.
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (LWORK)
[in]	LWORK	LWORK is INTEGER length of WORK array. LWORK >= NN+NNB.

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 91 of file drzt02.f.

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subroutine dspt01	(	character	UPLO,
		integer	N,
		double precision, dimension( * )	A,
		double precision, dimension( * )	AFAC,
		integer, dimension( * )	IPIV,
		double precision, dimension( ldc, * )	C,
		integer	LDC,
		double precision, dimension( * )	RWORK,
		double precision	RESID
	)

DSPT01

Purpose:

 DSPT01 reconstructs a symmetric indefinite packed matrix A from its
 block L*D*L' or U*D*U' factorization and computes the residual
      norm( C - A ) / ( N * norm(A) * EPS ),
 where C is the reconstructed matrix and EPS is the machine epsilon.

Parameters:

[in]	UPLO	UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the symmetric matrix A is stored: = 'U': Upper triangular = 'L': Lower triangular
[in]	N	N is INTEGER The number of rows and columns of the matrix A. N >= 0.
[in]	A	A is DOUBLE PRECISION array, dimension (N*(N+1)/2) The original symmetric matrix A, stored as a packed triangular matrix.
[in]	AFAC	AFAC is DOUBLE PRECISION array, dimension (N(N+1)/2) The factored form of the matrix A, stored as a packed triangular matrix. AFAC contains the block diagonal matrix D and the multipliers used to obtain the factor L or U from the block LDL' or UD*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(LDL' - A) / ( N * norm(A) * EPS ) If UPLO = 'U', norm(UDU' - A) / ( N * norm(A) * EPS )

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 111 of file dspt01.f.

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subroutine dsyt01	(	character	UPLO,
		integer	N,
		double precision, dimension( lda, * )	A,
		integer	LDA,
		double precision, dimension( ldafac, * )	AFAC,
		integer	LDAFAC,
		integer, dimension( * )	IPIV,
		double precision, dimension( ldc, * )	C,
		integer	LDC,
		double precision, dimension( * )	RWORK,
		double precision	RESID
	)

DSYT01

Purpose:

 DSYT01 reconstructs a symmetric indefinite matrix A from its
 block L*D*L' or U*D*U' factorization and computes the residual
    norm( C - A ) / ( N * norm(A) * EPS ),
 where C is the reconstructed matrix and EPS is the machine epsilon.

Parameters:

[in]	UPLO	UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the symmetric matrix A is stored: = 'U': Upper triangular = 'L': Lower triangular
[in]	N	N is INTEGER The number of rows and columns of the matrix A. N >= 0.
[in]	A	A is DOUBLE PRECISION array, dimension (LDA,N) The original symmetric matrix A.
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N)
[in]	AFAC	AFAC is DOUBLE PRECISION array, dimension (LDAFAC,N) The factored form of the matrix A. AFAC contains the block diagonal matrix D and the multipliers used to obtain the factor L or U from the block LDL' or UDU' 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(LDL' - A) / ( N * norm(A) * EPS ) If UPLO = 'U', norm(UDU' - A) / ( N * norm(A) * EPS )

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 124 of file dsyt01.f.

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subroutine dtbt02	(	character	UPLO,
		character	TRANS,
		character	DIAG,
		integer	N,
		integer	KD,
		integer	NRHS,
		double precision, dimension( ldab, * )	AB,
		integer	LDAB,
		double precision, dimension( ldx, * )	X,
		integer	LDX,
		double precision, dimension( ldb, * )	B,
		integer	LDB,
		double precision, dimension( * )	WORK,
		double precision	RESID
	)

DTBT02

Purpose:

 DTBT02 computes the residual for the computed solution to a
 triangular system of linear equations  A*x = b  or  A' *x = b when
 A is a triangular band matrix.  Here A' is the transpose of A and
 x and b are N by NRHS matrices.  The test ratio is the maximum over
 the number of right hand sides of
    norm(b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
 where op(A) denotes A or A' and EPS is the machine epsilon.

Parameters:

[in]	UPLO	UPLO is CHARACTER*1 Specifies whether the matrix A is upper or lower triangular. = 'U': Upper triangular = 'L': Lower triangular
[in]	TRANS	TRANS is CHARACTER1 Specifies the operation applied to A. = 'N': A x = b (No transpose) = 'T': A'x = b (Transpose) = 'C': A'x = b (Conjugate transpose = Transpose)
[in]	DIAG	DIAG is CHARACTER*1 Specifies whether or not the matrix A is unit triangular. = 'N': Non-unit triangular = 'U': Unit triangular
[in]	N	N is INTEGER The order of the matrix A. N >= 0.
[in]	KD	KD is INTEGER The number of superdiagonals or subdiagonals of the triangular band matrix A. KD >= 0.
[in]	NRHS	NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrices X and B. NRHS >= 0.
[in]	AB	AB is DOUBLE PRECISION array, dimension (LDAB,N) The upper or lower triangular band matrix A, stored in the first kd+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows: if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
[in]	LDAB	LDAB is INTEGER The leading dimension of the array AB. LDAB >= KD+1.
[in]	X	X is DOUBLE PRECISION array, dimension (LDX,NRHS) The computed solution vectors for the system of linear equations.
[in]	LDX	LDX is INTEGER The leading dimension of the array X. LDX >= max(1,N).
[in]	B	B is DOUBLE PRECISION array, dimension (LDB,NRHS) The right hand side vectors for the system of linear equations.
[in]	LDB	LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (N)
[out]	RESID	RESID is DOUBLE PRECISION The maximum over the number of right hand sides of norm(op(A)x - b) / ( norm(op(A)) norm(x) * EPS ).

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 154 of file dtbt02.f.

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subroutine dtbt03	(	character	UPLO,
		character	TRANS,
		character	DIAG,
		integer	N,
		integer	KD,
		integer	NRHS,
		double precision, dimension( ldab, * )	AB,
		integer	LDAB,
		double precision	SCALE,
		double precision, dimension( * )	CNORM,
		double precision	TSCAL,
		double precision, dimension( ldx, * )	X,
		integer	LDX,
		double precision, dimension( ldb, * )	B,
		integer	LDB,
		double precision, dimension( * )	WORK,
		double precision	RESID
	)

DTBT03

Purpose:

 DTBT03 computes the residual for the solution to a scaled triangular
 system of equations  A*x = s*b  or  A'*x = s*b  when A is a
 triangular band matrix. Here A' is the transpose of A, s is a scalar,
 and x and b are N by NRHS matrices.  The test ratio is the maximum
 over the number of right hand sides of
    norm(s*b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
 where op(A) denotes A or A' and EPS is the machine epsilon.

Parameters:

[in]	UPLO	UPLO is CHARACTER*1 Specifies whether the matrix A is upper or lower triangular. = 'U': Upper triangular = 'L': Lower triangular
[in]	TRANS	TRANS is CHARACTER1 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 - sb) / ( norm(op(A)) * norm(x) * EPS ).

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 174 of file dtbt03.f.

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subroutine dtbt05	(	character	UPLO,
		character	TRANS,
		character	DIAG,
		integer	N,
		integer	KD,
		integer	NRHS,
		double precision, dimension( ldab, * )	AB,
		integer	LDAB,
		double precision, dimension( ldb, * )	B,
		integer	LDB,
		double precision, dimension( ldx, * )	X,
		integer	LDX,
		double precision, dimension( ldxact, * )	XACT,
		integer	LDXACT,
		double precision, dimension( * )	FERR,
		double precision, dimension( * )	BERR,
		double precision, dimension( * )	RESLTS
	)

DTBT05

Purpose:

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

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

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

 RESLTS(2) = residual from the iterative refinement routine
           = the maximum of BERR / ( NZ*EPS + (*) ), where
             (*) = NZ*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
             and NZ = max. number of nonzeros in any row of A, plus 1

Parameters:

[in]	UPLO	UPLO is CHARACTER*1 Specifies whether the matrix A is upper or lower triangular. = 'U': Upper triangular = 'L': Lower triangular
[in]	TRANS	TRANS is CHARACTER1 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 / ( NZEPS + () )

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 189 of file dtbt05.f.

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subroutine dtbt06	(	double precision	RCOND,
		double precision	RCONDC,
		character	UPLO,
		character	DIAG,
		integer	N,
		integer	KD,
		double precision, dimension( ldab, * )	AB,
		integer	LDAB,
		double precision, dimension( * )	WORK,
		double precision	RAT
	)

DTBT06

Purpose:

 DTBT06 computes a test ratio comparing RCOND (the reciprocal
 condition number of a triangular matrix A) and RCONDC, the estimate
 computed by DTBCON.  Information about the triangular matrix A is
 used if one estimate is zero and the other is non-zero to decide if
 underflow in the estimate is justified.

Parameters:

[in]	RCOND	RCOND is DOUBLE PRECISION The estimate of the reciprocal condition number obtained by forming the explicit inverse of the matrix A and computing RCOND = 1/( norm(A) * norm(inv(A)) ).
[in]	RCONDC	RCONDC is DOUBLE PRECISION The estimate of the reciprocal condition number computed by DTBCON.
[in]	UPLO	UPLO is CHARACTER Specifies whether the matrix A is upper or lower triangular. = 'U': Upper triangular = 'L': Lower triangular
[in]	DIAG	DIAG is CHARACTER Specifies whether or not the matrix A is unit triangular. = 'N': Non-unit triangular = 'U': Unit triangular
[in]	N	N is INTEGER The order of the matrix A. N >= 0.
[in]	KD	KD is INTEGER The number of superdiagonals or subdiagonals of the triangular band matrix A. KD >= 0.
[in]	AB	AB is DOUBLE PRECISION array, dimension (LDAB,N) The upper or lower triangular band matrix A, stored in the first kd+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows: if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
[in]	LDAB	LDAB is INTEGER The leading dimension of the array AB. LDAB >= KD+1.
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (N)
[out]	RAT	RAT is DOUBLE PRECISION The test ratio. If both RCOND and RCONDC are nonzero, RAT = MAX( RCOND, RCONDC )/MIN( RCOND, RCONDC ) - 1. If RAT = 0, the two estimates are exactly the same.

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 125 of file dtbt06.f.

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subroutine dtpt01	(	character	UPLO,
		character	DIAG,
		integer	N,
		double precision, dimension( * )	AP,
		double precision, dimension( * )	AINVP,
		double precision	RCOND,
		double precision, dimension( * )	WORK,
		double precision	RESID
	)

DTPT01

Purpose:

 DTPT01 computes the residual for a triangular matrix A times its
 inverse when A is stored in packed format:
    RESID = norm(A*AINV - I) / ( N * norm(A) * norm(AINV) * EPS ),
 where EPS is the machine epsilon.

Parameters:

[in]	UPLO	UPLO is CHARACTER*1 Specifies whether the matrix A is upper or lower triangular. = 'U': Upper triangular = 'L': Lower triangular
[in]	DIAG	DIAG is CHARACTER*1 Specifies whether or not the matrix A is unit triangular. = 'N': Non-unit triangular = 'U': Unit triangular
[in]	N	N is INTEGER The order of the matrix A. N >= 0.
[in]	AP	AP is DOUBLE PRECISION array, dimension (N(N+1)/2) The original upper or lower triangular matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP((j-1)j/2 + i) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP((j-1)(n-j) + j(j+1)/2 + i-j) = A(i,j) for j<=i<=n.
[in,out]	AINVP	AINVP is DOUBLE PRECISION array, dimension (N*(N+1)/2) On entry, the (triangular) inverse of the matrix A, packed columnwise in a linear array as in AP. On exit, the contents of AINVP are destroyed.
[out]	RCOND	RCOND is DOUBLE PRECISION The reciprocal condition number of A, computed as 1/(norm(A) * norm(AINV)).
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (N)
[out]	RESID	RESID is DOUBLE PRECISION norm(AAINV - I) / ( N norm(A) * norm(AINV) * EPS )

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 109 of file dtpt01.f.

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subroutine dtpt02	(	character	UPLO,
		character	TRANS,
		character	DIAG,
		integer	N,
		integer	NRHS,
		double precision, dimension( * )	AP,
		double precision, dimension( ldx, * )	X,
		integer	LDX,
		double precision, dimension( ldb, * )	B,
		integer	LDB,
		double precision, dimension( * )	WORK,
		double precision	RESID
	)

DTPT02

Purpose:

 DTPT02 computes the residual for the computed solution to a
 triangular system of linear equations  A*x = b  or  A'*x = b  when
 the triangular matrix A is stored in packed format.  Here A' is the
 transpose of A and x and b are N by NRHS matrices.  The test ratio is
 the maximum over the number of right hand sides of
    norm(b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
 where op(A) denotes A or A' and EPS is the machine epsilon.

Parameters:

[in]	UPLO	UPLO is CHARACTER*1 Specifies whether the matrix A is upper or lower triangular. = 'U': Upper triangular = 'L': Lower triangular
[in]	TRANS	TRANS is CHARACTER1 Specifies the operation applied to A. = 'N': A x = b (No transpose) = 'T': A'x = b (Transpose) = 'C': A'x = b (Conjugate transpose = Transpose)
[in]	DIAG	DIAG is CHARACTER*1 Specifies whether or not the matrix A is unit triangular. = 'N': Non-unit triangular = 'U': Unit triangular
[in]	N	N is INTEGER The order of the matrix A. N >= 0.
[in]	NRHS	NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrices X and B. NRHS >= 0.
[in]	AP	AP is DOUBLE PRECISION array, dimension (N(N+1)/2) The upper or lower triangular matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP((j-1)j/2 + i) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP((j-1)(n-j) + j(j+1)/2 + i-j) = A(i,j) for j<=i<=n.
[in]	X	X is DOUBLE PRECISION array, dimension (LDX,NRHS) The computed solution vectors for the system of linear equations.
[in]	LDX	LDX is INTEGER The leading dimension of the array X. LDX >= max(1,N).
[in]	B	B is DOUBLE PRECISION array, dimension (LDB,NRHS) The right hand side vectors for the system of linear equations.
[in]	LDB	LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (N)
[out]	RESID	RESID is DOUBLE PRECISION The maximum over the number of right hand sides of norm(op(A)x - b) / ( norm(op(A)) norm(x) * EPS ).

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 141 of file dtpt02.f.

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subroutine dtpt03	(	character	UPLO,
		character	TRANS,
		character	DIAG,
		integer	N,
		integer	NRHS,
		double precision, dimension( * )	AP,
		double precision	SCALE,
		double precision, dimension( * )	CNORM,
		double precision	TSCAL,
		double precision, dimension( ldx, * )	X,
		integer	LDX,
		double precision, dimension( ldb, * )	B,
		integer	LDB,
		double precision, dimension( * )	WORK,
		double precision	RESID
	)

DTPT03

Purpose:

 DTPT03 computes the residual for the solution to a scaled triangular
 system of equations A*x = s*b  or  A'*x = s*b  when the triangular
 matrix A is stored in packed format.  Here A' is the transpose of A,
 s is a scalar, and x and b are N by NRHS matrices.  The test ratio is
 the maximum over the number of right hand sides of
    norm(s*b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
 where op(A) denotes A or A' and EPS is the machine epsilon.

Parameters:

[in]	UPLO	UPLO is CHARACTER*1 Specifies whether the matrix A is upper or lower triangular. = 'U': Upper triangular = 'L': Lower triangular
[in]	TRANS	TRANS is CHARACTER1 Specifies the operation applied to A. = 'N': A x = sb (No transpose) = 'T': A'x = sb (Transpose) = 'C': A'x = s*b (Conjugate transpose = Transpose)
[in]	DIAG	DIAG is CHARACTER*1 Specifies whether or not the matrix A is unit triangular. = 'N': Non-unit triangular = 'U': Unit triangular
[in]	N	N is INTEGER The order of the matrix A. N >= 0.
[in]	NRHS	NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrices X and B. NRHS >= 0.
[in]	AP	AP is DOUBLE PRECISION array, dimension (N(N+1)/2) The upper or lower triangular matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP((j-1)j/2 + i) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP((j-1)(n-j) + j(j+1)/2 + i-j) = A(i,j) for j<=i<=n.
[in]	SCALE	SCALE is DOUBLE PRECISION The scaling factor s used in solving the triangular system.
[in]	CNORM	CNORM is DOUBLE PRECISION array, dimension (N) The 1-norms of the columns of A, not counting the diagonal.
[in]	TSCAL	TSCAL is DOUBLE PRECISION The scaling factor used in computing the 1-norms in CNORM. CNORM actually contains the column norms of TSCAL*A.
[in]	X	X is DOUBLE PRECISION array, dimension (LDX,NRHS) The computed solution vectors for the system of linear equations.
[in]	LDX	LDX is INTEGER The leading dimension of the array X. LDX >= max(1,N).
[in]	B	B is DOUBLE PRECISION array, dimension (LDB,NRHS) The right hand side vectors for the system of linear equations.
[in]	LDB	LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (N)
[out]	RESID	RESID is DOUBLE PRECISION The maximum over the number of right hand sides of norm(op(A)x - sb) / ( norm(op(A)) * norm(x) * EPS ).

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 161 of file dtpt03.f.

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subroutine dtpt05	(	character	UPLO,
		character	TRANS,
		character	DIAG,
		integer	N,
		integer	NRHS,
		double precision, dimension( * )	AP,
		double precision, dimension( ldb, * )	B,
		integer	LDB,
		double precision, dimension( ldx, * )	X,
		integer	LDX,
		double precision, dimension( ldxact, * )	XACT,
		integer	LDXACT,
		double precision, dimension( * )	FERR,
		double precision, dimension( * )	BERR,
		double precision, dimension( * )	RESLTS
	)

DTPT05

Purpose:

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

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

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

 RESLTS(2) = residual from the iterative refinement routine
           = the maximum of BERR / ( (n+1)*EPS + (*) ), where
             (*) = (n+1)*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )

Parameters:

[in]	UPLO	UPLO is CHARACTER*1 Specifies whether the matrix A is upper or lower triangular. = 'U': Upper triangular = 'L': Lower triangular
[in]	TRANS	TRANS is CHARACTER1 Specifies the form of the system of equations. = 'N': A X = B (No transpose) = 'T': A'* X = B (Transpose) = 'C': A'* X = B (Conjugate transpose = Transpose)
[in]	DIAG	DIAG is CHARACTER*1 Specifies whether or not the matrix A is unit triangular. = 'N': Non-unit triangular = 'U': Unit triangular
[in]	N	N is INTEGER The number of rows of the matrices X, B, and XACT, and the order of the matrix A. N >= 0.
[in]	NRHS	NRHS is INTEGER The number of columns of the matrices X, B, and XACT. NRHS >= 0.
[in]	AP	AP is DOUBLE PRECISION array, dimension (N(N+1)/2) The upper or lower triangular matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. If DIAG = 'U', the diagonal elements of A are not referenced and are assumed to be 1.
[in]	B	B is DOUBLE PRECISION array, dimension (LDB,NRHS) The right hand side vectors for the system of linear equations.
[in]	LDB	LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).
[in]	X	X is DOUBLE PRECISION array, dimension (LDX,NRHS) The computed solution vectors. Each vector is stored as a column of the matrix X.
[in]	LDX	LDX is INTEGER The leading dimension of the array X. LDX >= max(1,N).
[in]	XACT	XACT is DOUBLE PRECISION array, dimension (LDX,NRHS) The exact solution vectors. Each vector is stored as a column of the matrix XACT.
[in]	LDXACT	LDXACT is INTEGER The leading dimension of the array XACT. LDXACT >= max(1,N).
[in]	FERR	FERR is DOUBLE PRECISION array, dimension (NRHS) The estimated forward error bounds for each solution vector X. If XTRUE is the true solution, FERR bounds the magnitude of the largest entry in (X - XTRUE) divided by the magnitude of the largest entry in X.
[in]	BERR	BERR is DOUBLE PRECISION array, dimension (NRHS) The componentwise relative backward error of each solution vector (i.e., the smallest relative change in any entry of A or B that makes X an exact solution).
[out]	RESLTS	RESLTS is DOUBLE PRECISION array, dimension (2) The maximum over the NRHS solution vectors of the ratios: RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR ) RESLTS(2) = BERR / ( (n+1)EPS + () )

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 174 of file dtpt05.f.

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subroutine dtpt06	(	double precision	RCOND,
		double precision	RCONDC,
		character	UPLO,
		character	DIAG,
		integer	N,
		double precision, dimension( * )	AP,
		double precision, dimension( * )	WORK,
		double precision	RAT
	)

DTPT06

Purpose:

 DTPT06 computes a test ratio comparing RCOND (the reciprocal
 condition number of a triangular matrix A) and RCONDC, the estimate
 computed by DTPCON.  Information about the triangular matrix A is
 used if one estimate is zero and the other is non-zero to decide if
 underflow in the estimate is justified.

Parameters:

[in]	RCOND	RCOND is DOUBLE PRECISION The estimate of the reciprocal condition number obtained by forming the explicit inverse of the matrix A and computing RCOND = 1/( norm(A) * norm(inv(A)) ).
[in]	RCONDC	RCONDC is DOUBLE PRECISION The estimate of the reciprocal condition number computed by DTPCON.
[in]	UPLO	UPLO is CHARACTER Specifies whether the matrix A is upper or lower triangular. = 'U': Upper triangular = 'L': Lower triangular
[in]	DIAG	DIAG is CHARACTER Specifies whether or not the matrix A is unit triangular. = 'N': Non-unit triangular = 'U': Unit triangular
[in]	N	N is INTEGER The order of the matrix A. N >= 0.
[in]	AP	AP is DOUBLE PRECISION array, dimension (N(N+1)/2) The upper or lower triangular matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP((j-1)j/2 + i) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP((j-1)(n-j) + j(j+1)/2 + i-j) = A(i,j) for j<=i<=n.
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (N)
[out]	RAT	RAT is DOUBLE PRECISION The test ratio. If both RCOND and RCONDC are nonzero, RAT = MAX( RCOND, RCONDC )/MIN( RCOND, RCONDC ) - 1. If RAT = 0, the two estimates are exactly the same.

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 112 of file dtpt06.f.

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subroutine dtrt01	(	character	UPLO,
		character	DIAG,
		integer	N,
		double precision, dimension( lda, * )	A,
		integer	LDA,
		double precision, dimension( ldainv, * )	AINV,
		integer	LDAINV,
		double precision	RCOND,
		double precision, dimension( * )	WORK,
		double precision	RESID
	)

DTRT01

Purpose:

 DTRT01 computes the residual for a triangular matrix A times its
 inverse:
    RESID = norm( A*AINV - I ) / ( N * norm(A) * norm(AINV) * EPS ),
 where EPS is the machine epsilon.

Parameters:

[in]	UPLO	UPLO is CHARACTER*1 Specifies whether the matrix A is upper or lower triangular. = 'U': Upper triangular = 'L': Lower triangular
[in]	DIAG	DIAG is CHARACTER*1 Specifies whether or not the matrix A is unit triangular. = 'N': Non-unit triangular = 'U': Unit triangular
[in]	N	N is INTEGER The order of the matrix A. N >= 0.
[in]	A	A is DOUBLE PRECISION array, dimension (LDA,N) The triangular matrix A. If UPLO = 'U', the leading n by n upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading n by n lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. If DIAG = 'U', the diagonal elements of A are also not referenced and are assumed to be 1.
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).
[in,out]	AINV	AINV is DOUBLE PRECISION array, dimension (LDAINV,N) On entry, the (triangular) inverse of the matrix A, in the same storage format as A. On exit, the contents of AINV are destroyed.
[in]	LDAINV	LDAINV is INTEGER The leading dimension of the array AINV. LDAINV >= max(1,N).
[out]	RCOND	RCOND is DOUBLE PRECISION The reciprocal condition number of A, computed as 1/(norm(A) * norm(AINV)).
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (N)
[out]	RESID	RESID is DOUBLE PRECISION norm(AAINV - I) / ( N norm(A) * norm(AINV) * EPS )

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 124 of file dtrt01.f.

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subroutine dtrt02	(	character	UPLO,
		character	TRANS,
		character	DIAG,
		integer	N,
		integer	NRHS,
		double precision, dimension( lda, * )	A,
		integer	LDA,
		double precision, dimension( ldx, * )	X,
		integer	LDX,
		double precision, dimension( ldb, * )	B,
		integer	LDB,
		double precision, dimension( * )	WORK,
		double precision	RESID
	)

DTRT02

Purpose:

 DTRT02 computes the residual for the computed solution to a
 triangular system of linear equations  A*x = b  or  A'*x = b.
 Here A is a triangular matrix, A' is the transpose of A, and x and b
 are N by NRHS matrices.  The test ratio is the maximum over the
 number of right hand sides of
    norm(b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
 where op(A) denotes A or A' and EPS is the machine epsilon.

Parameters:

[in]	UPLO	UPLO is CHARACTER*1 Specifies whether the matrix A is upper or lower triangular. = 'U': Upper triangular = 'L': Lower triangular
[in]	TRANS	TRANS is CHARACTER1 Specifies the operation applied to A. = 'N': A x = b (No transpose) = 'T': A'x = b (Transpose) = 'C': A'x = b (Conjugate transpose = Transpose)
[in]	DIAG	DIAG is CHARACTER*1 Specifies whether or not the matrix A is unit triangular. = 'N': Non-unit triangular = 'U': Unit triangular
[in]	N	N is INTEGER The order of the matrix A. N >= 0.
[in]	NRHS	NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrices X and B. NRHS >= 0.
[in]	A	A is DOUBLE PRECISION array, dimension (LDA,N) The triangular matrix A. If UPLO = 'U', the leading n by n upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading n by n lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. If DIAG = 'U', the diagonal elements of A are also not referenced and are assumed to be 1.
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).
[in]	X	X is DOUBLE PRECISION array, dimension (LDX,NRHS) The computed solution vectors for the system of linear equations.
[in]	LDX	LDX is INTEGER The leading dimension of the array X. LDX >= max(1,N).
[in]	B	B is DOUBLE PRECISION array, dimension (LDB,NRHS) The right hand side vectors for the system of linear equations.
[in]	LDB	LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (N)
[out]	RESID	RESID is DOUBLE PRECISION The maximum over the number of right hand sides of norm(op(A)x - b) / ( norm(op(A)) norm(x) * EPS ).

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 150 of file dtrt02.f.

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subroutine dtrt03	(	character	UPLO,
		character	TRANS,
		character	DIAG,
		integer	N,
		integer	NRHS,
		double precision, dimension( lda, * )	A,
		integer	LDA,
		double precision	SCALE,
		double precision, dimension( * )	CNORM,
		double precision	TSCAL,
		double precision, dimension( ldx, * )	X,
		integer	LDX,
		double precision, dimension( ldb, * )	B,
		integer	LDB,
		double precision, dimension( * )	WORK,
		double precision	RESID
	)

DTRT03

Purpose:

 DTRT03 computes the residual for the solution to a scaled triangular
 system of equations A*x = s*b  or  A'*x = s*b.
 Here A is a triangular matrix, A' is the transpose of A, s is a
 scalar, and x and b are N by NRHS matrices.  The test ratio is the
 maximum over the number of right hand sides of
    norm(s*b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
 where op(A) denotes A or A' and EPS is the machine epsilon.

Parameters:

[in]	UPLO	UPLO is CHARACTER*1 Specifies whether the matrix A is upper or lower triangular. = 'U': Upper triangular = 'L': Lower triangular
[in]	TRANS	TRANS is CHARACTER1 Specifies the operation applied to A. = 'N': A x = sb (No transpose) = 'T': A'x = sb (Transpose) = 'C': A'x = s*b (Conjugate transpose = Transpose)
[in]	DIAG	DIAG is CHARACTER*1 Specifies whether or not the matrix A is unit triangular. = 'N': Non-unit triangular = 'U': Unit triangular
[in]	N	N is INTEGER The order of the matrix A. N >= 0.
[in]	NRHS	NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrices X and B. NRHS >= 0.
[in]	A	A is DOUBLE PRECISION array, dimension (LDA,N) The triangular matrix A. If UPLO = 'U', the leading n by n upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading n by n lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. If DIAG = 'U', the diagonal elements of A are also not referenced and are assumed to be 1.
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).
[in]	SCALE	SCALE is DOUBLE PRECISION The scaling factor s used in solving the triangular system.
[in]	CNORM	CNORM is DOUBLE PRECISION array, dimension (N) The 1-norms of the columns of A, not counting the diagonal.
[in]	TSCAL	TSCAL is DOUBLE PRECISION The scaling factor used in computing the 1-norms in CNORM. CNORM actually contains the column norms of TSCAL*A.
[in]	X	X is DOUBLE PRECISION array, dimension (LDX,NRHS) The computed solution vectors for the system of linear equations.
[in]	LDX	LDX is INTEGER The leading dimension of the array X. LDX >= max(1,N).
[in]	B	B is DOUBLE PRECISION array, dimension (LDB,NRHS) The right hand side vectors for the system of linear equations.
[in]	LDB	LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (N)
[out]	RESID	RESID is DOUBLE PRECISION The maximum over the number of right hand sides of norm(op(A)x - sb) / ( norm(op(A)) * norm(x) * EPS ).

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 169 of file dtrt03.f.

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subroutine dtrt05	(	character	UPLO,
		character	TRANS,
		character	DIAG,
		integer	N,
		integer	NRHS,
		double precision, dimension( lda, * )	A,
		integer	LDA,
		double precision, dimension( ldb, * )	B,
		integer	LDB,
		double precision, dimension( ldx, * )	X,
		integer	LDX,
		double precision, dimension( ldxact, * )	XACT,
		integer	LDXACT,
		double precision, dimension( * )	FERR,
		double precision, dimension( * )	BERR,
		double precision, dimension( * )	RESLTS
	)

DTRT05

Purpose:

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

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

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

 RESLTS(2) = residual from the iterative refinement routine
           = the maximum of BERR / ( (n+1)*EPS + (*) ), where
             (*) = (n+1)*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )

Parameters:

[in]	UPLO	UPLO is CHARACTER*1 Specifies whether the matrix A is upper or lower triangular. = 'U': Upper triangular = 'L': Lower triangular
[in]	TRANS	TRANS is CHARACTER1 Specifies the form of the system of equations. = 'N': A X = B (No transpose) = 'T': A'* X = B (Transpose) = 'C': A'* X = B (Conjugate transpose = Transpose)
[in]	DIAG	DIAG is CHARACTER*1 Specifies whether or not the matrix A is unit triangular. = 'N': Non-unit triangular = 'U': Unit triangular
[in]	N	N is INTEGER The number of rows of the matrices X, B, and XACT, and the order of the matrix A. N >= 0.
[in]	NRHS	NRHS is INTEGER The number of columns of the matrices X, B, and XACT. NRHS >= 0.
[in]	A	A is DOUBLE PRECISION array, dimension (LDA,N) The triangular matrix A. If UPLO = 'U', the leading n by n upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading n by n lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. If DIAG = 'U', the diagonal elements of A are also not referenced and are assumed to be 1.
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).
[in]	B	B is DOUBLE PRECISION array, dimension (LDB,NRHS) The right hand side vectors for the system of linear equations.
[in]	LDB	LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).
[in]	X	X is DOUBLE PRECISION array, dimension (LDX,NRHS) The computed solution vectors. Each vector is stored as a column of the matrix X.
[in]	LDX	LDX is INTEGER The leading dimension of the array X. LDX >= max(1,N).
[in]	XACT	XACT is DOUBLE PRECISION array, dimension (LDX,NRHS) The exact solution vectors. Each vector is stored as a column of the matrix XACT.
[in]	LDXACT	LDXACT is INTEGER The leading dimension of the array XACT. LDXACT >= max(1,N).
[in]	FERR	FERR is DOUBLE PRECISION array, dimension (NRHS) The estimated forward error bounds for each solution vector X. If XTRUE is the true solution, FERR bounds the magnitude of the largest entry in (X - XTRUE) divided by the magnitude of the largest entry in X.
[in]	BERR	BERR is DOUBLE PRECISION array, dimension (NRHS) The componentwise relative backward error of each solution vector (i.e., the smallest relative change in any entry of A or B that makes X an exact solution).
[out]	RESLTS	RESLTS is DOUBLE PRECISION array, dimension (2) The maximum over the NRHS solution vectors of the ratios: RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR ) RESLTS(2) = BERR / ( (n+1)EPS + () )

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 181 of file dtrt05.f.

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subroutine dtrt06	(	double precision	RCOND,
		double precision	RCONDC,
		character	UPLO,
		character	DIAG,
		integer	N,
		double precision, dimension( lda, * )	A,
		integer	LDA,
		double precision, dimension( * )	WORK,
		double precision	RAT
	)

DTRT06

Purpose:

 DTRT06 computes a test ratio comparing RCOND (the reciprocal
 condition number of a triangular matrix A) and RCONDC, the estimate
 computed by DTRCON.  Information about the triangular matrix A is
 used if one estimate is zero and the other is non-zero to decide if
 underflow in the estimate is justified.

Parameters:

[in]	RCOND	RCOND is DOUBLE PRECISION The estimate of the reciprocal condition number obtained by forming the explicit inverse of the matrix A and computing RCOND = 1/( norm(A) * norm(inv(A)) ).
[in]	RCONDC	RCONDC is DOUBLE PRECISION The estimate of the reciprocal condition number computed by DTRCON.
[in]	UPLO	UPLO is CHARACTER Specifies whether the matrix A is upper or lower triangular. = 'U': Upper triangular = 'L': Lower triangular
[in]	DIAG	DIAG is CHARACTER Specifies whether or not the matrix A is unit triangular. = 'N': Non-unit triangular = 'U': Unit triangular
[in]	N	N is INTEGER The order of the matrix A. N >= 0.
[in]	A	A is DOUBLE PRECISION array, dimension (LDA,N) The triangular matrix A. If UPLO = 'U', the leading n by n upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading n by n lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. If DIAG = 'U', the diagonal elements of A are also not referenced and are assumed to be 1.
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (N)
[out]	RAT	RAT is DOUBLE PRECISION The test ratio. If both RCOND and RCONDC are nonzero, RAT = MAX( RCOND, RCONDC )/MIN( RCOND, RCONDC ) - 1. If RAT = 0, the two estimates are exactly the same.

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 121 of file dtrt06.f.

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DOUBLE PRECISION function dtzt01	(	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
	)

DTZT01

Purpose:

 DTZT01 returns
      || A - R*Q || / ( M * eps * ||A|| )
 for an upper trapezoidal A that was factored with DTZRQF.

Parameters:

[in]	M	M is INTEGER The number of rows of the matrices A and AF.
[in]	N	N is INTEGER The number of columns of the matrices A and AF.
[in]	A	A is DOUBLE PRECISION array, dimension (LDA,N) The original upper trapezoidal M by N matrix A.
[in]	AF	AF is DOUBLE PRECISION array, dimension (LDA,N) The output of DTZRQF 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 DTZRQF.
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (LWORK)
[in]	LWORK	LWORK is INTEGER The length of the array WORK. LWORK >= m*n + m.

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 98 of file dtzt01.f.

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DOUBLE PRECISION function dtzt02	(	integer	M,
		integer	N,
		double precision, dimension( lda, * )	AF,
		integer	LDA,
		double precision, dimension( * )	TAU,
		double precision, dimension( lwork )	WORK,
		integer	LWORK
	)

DTZT02

Purpose:

 DTZT02 returns
      || I - Q'*Q || / ( M * eps)
 where the matrix Q is defined by the Householder transformations
 generated by DTZRQF.

Parameters:

[in]	M	M is INTEGER The number of rows of the matrix AF.
[in]	N	N is INTEGER The number of columns of the matrix AF.
[in]	AF	AF is DOUBLE PRECISION array, dimension (LDA,N) The output of DTZRQF.
[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 DTZRQF.
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (LWORK)
[in]	LWORK	LWORK is INTEGER length of WORK array. Must be >= N*N+N

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 91 of file dtzt02.f.

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Functions/Subroutines

Detailed Description

Function/Subroutine Documentation