Collaboration diagram for real:

Functions/Subroutines
program	schkaa
	SCHKAA
subroutine	schkeq (THRESH, NOUT)
	SCHKEQ
subroutine	schkgb (DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NNS, NSVAL, THRESH, TSTERR, A, LA, AFAC, LAFAC, B, X, XACT, WORK, RWORK, IWORK, NOUT)
	SCHKGB
subroutine	schkge (DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
	SCHKGE
subroutine	schkgt (DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR, A, AF, B, X, XACT, WORK, RWORK, IWORK, NOUT)
	SCHKGT
subroutine	schklq (DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NXVAL, NRHS, THRESH, TSTERR, NMAX, A, AF, AQ, AL, AC, B, X, XACT, TAU, WORK, RWORK, NOUT)
	SCHKLQ
subroutine	schkpb (DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
	SCHKPB
subroutine	schkpo (DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
	SCHKPO
subroutine	schkpp (DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
	SCHKPP
subroutine	schkps (DOTYPE, NN, NVAL, NNB, NBVAL, NRANK, RANKVAL, THRESH, TSTERR, NMAX, A, AFAC, PERM, PIV, WORK, RWORK, NOUT)
	SCHKPS
subroutine	schkpt (DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR, A, D, E, B, X, XACT, WORK, RWORK, NOUT)
	SCHKPT
subroutine	schkq3 (DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NXVAL, THRESH, A, COPYA, S, TAU, WORK, IWORK, NOUT)
	SCHKQ3
subroutine	schkql (DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NXVAL, NRHS, THRESH, TSTERR, NMAX, A, AF, AQ, AL, AC, B, X, XACT, TAU, WORK, RWORK, NOUT)
	SCHKQL
subroutine	schkqp (DOTYPE, NM, MVAL, NN, NVAL, THRESH, TSTERR, A, COPYA, S, TAU, WORK, IWORK, NOUT)
	SCHKQP
subroutine	schkqr (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)
	SCHKQR
subroutine	schkqrt (THRESH, TSTERR, NM, MVAL, NN, NVAL, NNB, NBVAL, NOUT)
	SCHKQRT
subroutine	schkqrtp (THRESH, TSTERR, NM, MVAL, NN, NVAL, NNB, NBVAL, NOUT)
	SCHKQRTP
program	schkrfp
	SCHKRFP
subroutine	schkrq (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)
	SCHKRQ
subroutine	schksp (DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
	SCHKSP
subroutine	schksy (DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
	SCHKSY
subroutine	schktb (DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, AB, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
	SCHKTB
subroutine	schktp (DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, AP, AINVP, B, X, XACT, WORK, RWORK, IWORK, NOUT)
	SCHKTP
subroutine	schktr (DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, A, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
	SCHKTR
subroutine	schktz (DOTYPE, NM, MVAL, NN, NVAL, THRESH, TSTERR, A, COPYA, S, TAU, WORK, NOUT)
	SCHKTZ
subroutine	sdrvgb (DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, A, LA, AFB, LAFB, ASAV, B, BSAV, X, XACT, S, WORK, RWORK, IWORK, NOUT)
	SDRVGB
subroutine	sdrvge (DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, A, AFAC, ASAV, B, BSAV, X, XACT, S, WORK, RWORK, IWORK, NOUT)
	SDRVGE
subroutine	sdrvgt (DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, A, AF, B, X, XACT, WORK, RWORK, IWORK, NOUT)
	SDRVGT
subroutine	sdrvls (DOTYPE, NM, MVAL, NN, NVAL, NNS, NSVAL, NNB, NBVAL, NXVAL, THRESH, TSTERR, A, COPYA, B, COPYB, C, S, COPYS, WORK, IWORK, NOUT)
	SDRVLS
subroutine	sdrvpb (DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, A, AFAC, ASAV, B, BSAV, X, XACT, S, WORK, RWORK, IWORK, NOUT)
	SDRVPB
subroutine	sdrvpo (DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, A, AFAC, ASAV, B, BSAV, X, XACT, S, WORK, RWORK, IWORK, NOUT)
	SDRVPO
subroutine	sdrvpp (DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, A, AFAC, ASAV, B, BSAV, X, XACT, S, WORK, RWORK, IWORK, NOUT)
	SDRVPP
subroutine	sdrvpt (DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, A, D, E, B, X, XACT, WORK, RWORK, NOUT)
	SDRVPT
subroutine	sdrvrf1 (NOUT, NN, NVAL, THRESH, A, LDA, ARF, WORK)
	SDRVRF1
subroutine	sdrvrf2 (NOUT, NN, NVAL, A, LDA, ARF, AP, ASAV)
	SDRVRF2
subroutine	sdrvrf3 (NOUT, NN, NVAL, THRESH, A, LDA, ARF, B1, B2, S_WORK_SLANGE, S_WORK_SGEQRF, TAU)
	SDRVRF3
subroutine	sdrvrf4 (NOUT, NN, NVAL, THRESH, C1, C2, LDC, CRF, A, LDA, S_WORK_SLANGE)
	SDRVRF4
subroutine	sdrvrfp (NOUT, NN, NVAL, NNS, NSVAL, NNT, NTVAL, THRESH, A, ASAV, AFAC, AINV, B, BSAV, XACT, X, ARF, ARFINV, S_WORK_SLATMS, S_WORK_SPOT01, S_TEMP_SPOT02, S_TEMP_SPOT03, S_WORK_SLANSY, S_WORK_SPOT02, S_WORK_SPOT03)
	SDRVRFP
subroutine	sdrvsp (DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
	SDRVSP
subroutine	sdrvsy (DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
	SDRVSY
subroutine	sebchvxx (THRESH, PATH)
	SEBCHVXX
subroutine	serrge (PATH, NUNIT)
	SERRGE
subroutine	serrgt (PATH, NUNIT)
	SERRGT
subroutine	serrlq (PATH, NUNIT)
	SERRLQ
subroutine	serrls (PATH, NUNIT)
	SERRLS
subroutine	serrpo (PATH, NUNIT)
	SERRPO
subroutine	serrps (PATH, NUNIT)
	SERRPS
subroutine	serrql (PATH, NUNIT)
	SERRQL
subroutine	serrqp (PATH, NUNIT)
	SERRQP
subroutine	serrqr (PATH, NUNIT)
	SERRQR
subroutine	serrqrt (PATH, NUNIT)
	SERRQRT
subroutine	serrqrtp (PATH, NUNIT)
	SERRQRTP
subroutine	serrrfp (NUNIT)
	SERRRFP
subroutine	serrrq (PATH, NUNIT)
	SERRRQ
subroutine	serrsy (PATH, NUNIT)
	SERRSY
subroutine	serrtr (PATH, NUNIT)
	SERRTR
subroutine	serrtz (PATH, NUNIT)
	SERRTZ
subroutine	serrvx (PATH, NUNIT)
	SERRVX
subroutine	sgbt01 (M, N, KL, KU, A, LDA, AFAC, LDAFAC, IPIV, WORK, RESID)
	SGBT01
subroutine	sgbt02 (TRANS, M, N, KL, KU, NRHS, A, LDA, X, LDX, B, LDB, RESID)
	SGBT02
subroutine	sgbt05 (TRANS, N, KL, KU, NRHS, AB, LDAB, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
	SGBT05
subroutine	sgelqs (M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK, INFO)
	SGELQS
LOGICAL function	sgennd (M, N, A, LDA)
	SGENND
subroutine	sgeqls (M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK, INFO)
	SGEQLS
subroutine	sgeqrs (M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK, INFO)
	SGEQRS
subroutine	sgerqs (M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK, INFO)
	SGERQS
subroutine	sget01 (M, N, A, LDA, AFAC, LDAFAC, IPIV, RWORK, RESID)
	SGET01
subroutine	sget02 (TRANS, M, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
	SGET02
subroutine	sget03 (N, A, LDA, AINV, LDAINV, WORK, LDWORK, RWORK, RCOND, RESID)
	SGET03
subroutine	sget04 (N, NRHS, X, LDX, XACT, LDXACT, RCOND, RESID)
	SGET04
REAL function	sget06 (RCOND, RCONDC)
	SGET06
subroutine	sget07 (TRANS, N, NRHS, A, LDA, B, LDB, X, LDX, XACT, LDXACT, FERR, CHKFERR, BERR, RESLTS)
	SGET07
subroutine	sgtt01 (N, DL, D, DU, DLF, DF, DUF, DU2, IPIV, WORK, LDWORK, RWORK, RESID)
	SGTT01
subroutine	sgtt02 (TRANS, N, NRHS, DL, D, DU, X, LDX, B, LDB, RESID)
	SGTT02
subroutine	sgtt05 (TRANS, N, NRHS, DL, D, DU, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
	SGTT05
subroutine	slahilb (N, NRHS, A, LDA, X, LDX, B, LDB, WORK, INFO)
	SLAHILB
subroutine	slaord (JOB, N, X, INCX)
	SLAORD
subroutine	slaptm (N, NRHS, ALPHA, D, E, X, LDX, BETA, B, LDB)
	SLAPTM
subroutine	slarhs (PATH, XTYPE, UPLO, TRANS, M, N, KL, KU, NRHS, A, LDA, X, LDX, B, LDB, ISEED, INFO)
	SLARHS
subroutine	slatb4 (PATH, IMAT, M, N, TYPE, KL, KU, ANORM, MODE, CNDNUM, DIST)
	SLATB4
subroutine	slatb5 (PATH, IMAT, N, TYPE, KL, KU, ANORM, MODE, CNDNUM, DIST)
	SLATB5
subroutine	slattb (IMAT, UPLO, TRANS, DIAG, ISEED, N, KD, AB, LDAB, B, WORK, INFO)
	SLATTB
subroutine	slattp (IMAT, UPLO, TRANS, DIAG, ISEED, N, A, B, WORK, INFO)
	SLATTP
subroutine	slattr (IMAT, UPLO, TRANS, DIAG, ISEED, N, A, LDA, B, WORK, INFO)
	SLATTR
subroutine	slavsp (UPLO, TRANS, DIAG, N, NRHS, A, IPIV, B, LDB, INFO)
	SLAVSP
subroutine	slavsy (UPLO, TRANS, DIAG, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
	SLAVSY
subroutine	slqt01 (M, N, A, AF, Q, L, LDA, TAU, WORK, LWORK, RWORK, RESULT)
	SLQT01
subroutine	slqt02 (M, N, K, A, AF, Q, L, LDA, TAU, WORK, LWORK, RWORK, RESULT)
	SLQT02
subroutine	slqt03 (M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK, RWORK, RESULT)
	SLQT03
subroutine	spbt01 (UPLO, N, KD, A, LDA, AFAC, LDAFAC, RWORK, RESID)
	SPBT01
subroutine	spbt02 (UPLO, N, KD, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
	SPBT02
subroutine	spbt05 (UPLO, N, KD, NRHS, AB, LDAB, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
	SPBT05
subroutine	spot01 (UPLO, N, A, LDA, AFAC, LDAFAC, RWORK, RESID)
	SPOT01
subroutine	spot02 (UPLO, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
	SPOT02
subroutine	spot03 (UPLO, N, A, LDA, AINV, LDAINV, WORK, LDWORK, RWORK, RCOND, RESID)
	SPOT03
subroutine	spot05 (UPLO, N, NRHS, A, LDA, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
	SPOT05
subroutine	sppt01 (UPLO, N, A, AFAC, RWORK, RESID)
	SPPT01
subroutine	sppt02 (UPLO, N, NRHS, A, X, LDX, B, LDB, RWORK, RESID)
	SPPT02
subroutine	sppt03 (UPLO, N, A, AINV, WORK, LDWORK, RWORK, RCOND, RESID)
	SPPT03
subroutine	sppt05 (UPLO, N, NRHS, AP, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
	SPPT05
subroutine	spst01 (UPLO, N, A, LDA, AFAC, LDAFAC, PERM, LDPERM, PIV, RWORK, RESID, RANK)
	SPST01
subroutine	sptt01 (N, D, E, DF, EF, WORK, RESID)
	SPTT01
subroutine	sptt02 (N, NRHS, D, E, X, LDX, B, LDB, RESID)
	SPTT02
subroutine	sptt05 (N, NRHS, D, E, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
	SPTT05
subroutine	sqlt01 (M, N, A, AF, Q, L, LDA, TAU, WORK, LWORK, RWORK, RESULT)
	SQLT01
subroutine	sqlt02 (M, N, K, A, AF, Q, L, LDA, TAU, WORK, LWORK, RWORK, RESULT)
	SQLT02
subroutine	sqlt03 (M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK, RWORK, RESULT)
	SQLT03
REAL function	sqpt01 (M, N, K, A, AF, LDA, TAU, JPVT, WORK, LWORK)
	SQPT01
subroutine	sqrt01 (M, N, A, AF, Q, R, LDA, TAU, WORK, LWORK, RWORK, RESULT)
	SQRT01
subroutine	sqrt01p (M, N, A, AF, Q, R, LDA, TAU, WORK, LWORK, RWORK, RESULT)
	SQRT01P
subroutine	sqrt02 (M, N, K, A, AF, Q, R, LDA, TAU, WORK, LWORK, RWORK, RESULT)
	SQRT02
subroutine	sqrt03 (M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK, RWORK, RESULT)
	SQRT03
subroutine	sqrt04 (M, N, NB, RESULT)
	SQRT04
subroutine	sqrt05 (M, N, L, NB, RESULT)
	SQRT05
REAL function	sqrt11 (M, K, A, LDA, TAU, WORK, LWORK)
	SQRT11
REAL function	sqrt12 (M, N, A, LDA, S, WORK, LWORK)
	SQRT12
subroutine	sqrt13 (SCALE, M, N, A, LDA, NORMA, ISEED)
	SQRT13
REAL function	sqrt14 (TRANS, M, N, NRHS, A, LDA, X, LDX, WORK, LWORK)
	SQRT14
subroutine	sqrt15 (SCALE, RKSEL, M, N, NRHS, A, LDA, B, LDB, S, RANK, NORMA, NORMB, ISEED, WORK, LWORK)
	SQRT15
subroutine	sqrt16 (TRANS, M, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
	SQRT16
REAL function	sqrt17 (TRANS, IRESID, M, N, NRHS, A, LDA, X, LDX, B, LDB, C, WORK, LWORK)
	SQRT17
subroutine	srqt01 (M, N, A, AF, Q, R, LDA, TAU, WORK, LWORK, RWORK, RESULT)
	SRQT01
subroutine	srqt02 (M, N, K, A, AF, Q, R, LDA, TAU, WORK, LWORK, RWORK, RESULT)
	SRQT02
subroutine	srqt03 (M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK, RWORK, RESULT)
	SRQT03
REAL function	srzt01 (M, N, A, AF, LDA, TAU, WORK, LWORK)
	SRZT01
REAL function	srzt02 (M, N, AF, LDA, TAU, WORK, LWORK)
	SRZT02
subroutine	sspt01 (UPLO, N, A, AFAC, IPIV, C, LDC, RWORK, RESID)
	SSPT01
subroutine	ssyt01 (UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, LDC, RWORK, RESID)
	SSYT01
subroutine	stbt02 (UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, X, LDX, B, LDB, WORK, RESID)
	STBT02
subroutine	stbt03 (UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, SCALE, CNORM, TSCAL, X, LDX, B, LDB, WORK, RESID)
	STBT03
subroutine	stbt05 (UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
	STBT05
subroutine	stbt06 (RCOND, RCONDC, UPLO, DIAG, N, KD, AB, LDAB, WORK, RAT)
	STBT06
subroutine	stpt01 (UPLO, DIAG, N, AP, AINVP, RCOND, WORK, RESID)
	STPT01
subroutine	stpt02 (UPLO, TRANS, DIAG, N, NRHS, AP, X, LDX, B, LDB, WORK, RESID)
	STPT02
subroutine	stpt03 (UPLO, TRANS, DIAG, N, NRHS, AP, SCALE, CNORM, TSCAL, X, LDX, B, LDB, WORK, RESID)
	STPT03
subroutine	stpt05 (UPLO, TRANS, DIAG, N, NRHS, AP, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
	STPT05
subroutine	stpt06 (RCOND, RCONDC, UPLO, DIAG, N, AP, WORK, RAT)
	STPT06
subroutine	strt01 (UPLO, DIAG, N, A, LDA, AINV, LDAINV, RCOND, WORK, RESID)
	STRT01
subroutine	strt02 (UPLO, TRANS, DIAG, N, NRHS, A, LDA, X, LDX, B, LDB, WORK, RESID)
	STRT02
subroutine	strt03 (UPLO, TRANS, DIAG, N, NRHS, A, LDA, SCALE, CNORM, TSCAL, X, LDX, B, LDB, WORK, RESID)
	STRT03
subroutine	strt05 (UPLO, TRANS, DIAG, N, NRHS, A, LDA, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
	STRT05
subroutine	strt06 (RCOND, RCONDC, UPLO, DIAG, N, A, LDA, WORK, RAT)
	STRT06
REAL function	stzt01 (M, N, A, AF, LDA, TAU, WORK, LWORK)
	STZT01
REAL function	stzt02 (M, N, AF, LDA, TAU, WORK, LWORK)
	STZT02

Detailed Description

This is the group of real LAPACK TESTING LIN routines.

Function/Subroutine Documentation

program schkaa ( )

SCHKAA

Purpose:

 SCHKAA is the main test program for the REAL 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 REAL 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
 SGE   11               List types on next line if 0 < NTYPES < 11
 SGB    8               List types on next line if 0 < NTYPES <  8
 SGT   12               List types on next line if 0 < NTYPES < 12
 SPO    9               List types on next line if 0 < NTYPES <  9
 SPS    9               List types on next line if 0 < NTYPES <  9
 SPP    9               List types on next line if 0 < NTYPES <  9
 SPB    8               List types on next line if 0 < NTYPES <  8
 SPT   12               List types on next line if 0 < NTYPES < 12
 SSY   10               List types on next line if 0 < NTYPES < 10
 SSR   10               List types on next line if 0 < NTYPES < 10
 SSP   10               List types on next line if 0 < NTYPES < 10
 STR   18               List types on next line if 0 < NTYPES < 18
 STP   18               List types on next line if 0 < NTYPES < 18
 STB   17               List types on next line if 0 < NTYPES < 17
 SQR    8               List types on next line if 0 < NTYPES <  8
 SRQ    8               List types on next line if 0 < NTYPES <  8
 SLQ    8               List types on next line if 0 < NTYPES <  8
 SQL    8               List types on next line if 0 < NTYPES <  8
 SQP    6               List types on next line if 0 < NTYPES <  6
 STZ    3               List types on next line if 0 < NTYPES <  3
 SLS    6               List types on next line if 0 < NTYPES <  6
 SEQ
 SQT
 SQX

  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 schkaa.f.

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subroutine schkeq	(	real	THRESH,
		integer	NOUT
	)

SCHKEQ

Purpose:

 SCHKEQ tests SGEEQU, SGBEQU, SPOEQU, SPPEQU and SPBEQU

Parameters:

[in]	THRESH	THRESH is REAL 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 schkeq.f.

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

SCHKGB

Purpose:

 SCHKGB tests SGBTRF, -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 REAL 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 REAL 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 REAL 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 REAL array, dimension (NMAX*NSMAX) where NSMAX is the largest entry in NSVAL.
[out]	X	X is REAL array, dimension (NMAX*NSMAX)
[out]	XACT	XACT is REAL array, dimension (NMAX*NSMAX)
[out]	WORK	WORK is REAL array, dimension (NMAX*max(3,NSMAX,NMAX))
[out]	RWORK	RWORK is REAL 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 schkgb.f.

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

SCHKGE

Purpose:

 SCHKGE tests SGETRF, -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 REAL 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 REAL array, dimension (NMAX*NMAX)
[out]	AFAC	AFAC is REAL array, dimension (NMAX*NMAX)
[out]	AINV	AINV is REAL array, dimension (NMAX*NMAX)
[out]	B	B is REAL array, dimension (NMAX*NSMAX) where NSMAX is the largest entry in NSVAL.
[out]	X	X is REAL array, dimension (NMAX*NSMAX)
[out]	XACT	XACT is REAL array, dimension (NMAX*NSMAX)
[out]	WORK	WORK is REAL array, dimension (NMAX*max(3,NSMAX))
[out]	RWORK	RWORK is REAL 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:: April 2012

Definition at line 184 of file schkge.f.

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

SCHKGT

Purpose:

 SCHKGT tests SGTTRF, -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 REAL 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 REAL array, dimension (NMAX*4)
[out]	AF	AF is REAL array, dimension (NMAX*4)
[out]	B	B is REAL array, dimension (NMAX*NSMAX) where NSMAX is the largest entry in NSVAL.
[out]	X	X is REAL array, dimension (NMAX*NSMAX)
[out]	XACT	XACT is REAL array, dimension (NMAX*NSMAX)
[out]	WORK	WORK is REAL array, dimension (NMAX*max(3,NSMAX))
[out]	RWORK	RWORK is REAL 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 schkgt.f.

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

SCHKLQ

Purpose:

 SCHKLQ tests SGELQF, SORGLQ and SORMLQ.

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 REAL 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 REAL array, dimension (NMAX*NMAX)
[out]	AF	AF is REAL array, dimension (NMAX*NMAX)
[out]	AQ	AQ is REAL array, dimension (NMAX*NMAX)
[out]	AL	AL is REAL array, dimension (NMAX*NMAX)
[out]	AC	AC is REAL array, dimension (NMAX*NMAX)
[out]	B	B is REAL array, dimension (NMAX*NRHS)
[out]	X	X is REAL array, dimension (NMAX*NRHS)
[out]	XACT	XACT is REAL array, dimension (NMAX*NRHS)
[out]	TAU	TAU is REAL array, dimension (NMAX)
[out]	WORK	WORK is REAL array, dimension (NMAX*NMAX)
[out]	RWORK	RWORK is REAL 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 schklq.f.

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

SCHKPB

Purpose:

 SCHKPB tests SPBTRF, -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 REAL The threshold value for the test ratios. A result is included in the output file if RESULT >= THRESH. To have every test ratio printed, use THRESH = 0.
[in]	TSTERR	TSTERR is LOGICAL Flag that indicates whether error exits are to be tested.
[in]	NMAX	NMAX is INTEGER The maximum value permitted for N, used in dimensioning the work arrays.
[out]	A	A is REAL array, dimension (NMAX*NMAX)
[out]	AFAC	AFAC is REAL array, dimension (NMAX*NMAX)
[out]	AINV	AINV is REAL array, dimension (NMAX*NMAX)
[out]	B	B is REAL array, dimension (NMAX*NSMAX) where NSMAX is the largest entry in NSVAL.
[out]	X	X is REAL array, dimension (NMAX*NSMAX)
[out]	XACT	XACT is REAL array, dimension (NMAX*NSMAX)
[out]	WORK	WORK is REAL array, dimension (NMAX*max(3,NSMAX))
[out]	RWORK	RWORK is REAL 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 schkpb.f.

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

SCHKPO

Purpose:

 SCHKPO tests SPOTRF, -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 REAL The threshold value for the test ratios. A result is included in the output file if RESULT >= THRESH. To have every test ratio printed, use THRESH = 0.
[in]	TSTERR	TSTERR is LOGICAL Flag that indicates whether error exits are to be tested.
[in]	NMAX	NMAX is INTEGER The maximum value permitted for N, used in dimensioning the work arrays.
[out]	A	A is REAL array, dimension (NMAX*NMAX)
[out]	AFAC	AFAC is REAL array, dimension (NMAX*NMAX)
[out]	AINV	AINV is REAL array, dimension (NMAX*NMAX)
[out]	B	B is REAL array, dimension (NMAX*NSMAX) where NSMAX is the largest entry in NSVAL.
[out]	X	X is REAL array, dimension (NMAX*NSMAX)
[out]	XACT	XACT is REAL array, dimension (NMAX*NSMAX)
[out]	WORK	WORK is REAL array, dimension (NMAX*max(3,NSMAX))
[out]	RWORK	RWORK is REAL 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 schkpo.f.

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

SCHKPP

Purpose:

 SCHKPP tests SPPTRF, -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 REAL The threshold value for the test ratios. A result is included in the output file if RESULT >= THRESH. To have every test ratio printed, use THRESH = 0.
[in]	TSTERR	TSTERR is LOGICAL Flag that indicates whether error exits are to be tested.
[in]	NMAX	NMAX is INTEGER The maximum value permitted for N, used in dimensioning the work arrays.
[out]	A	A is REAL array, dimension (NMAX*(NMAX+1)/2)
[out]	AFAC	AFAC is REAL array, dimension (NMAX*(NMAX+1)/2)
[out]	AINV	AINV is REAL array, dimension (NMAX*(NMAX+1)/2)
[out]	B	B is REAL array, dimension (NMAX*NSMAX) where NSMAX is the largest entry in NSVAL.
[out]	X	X is REAL array, dimension (NMAX*NSMAX)
[out]	XACT	XACT is REAL array, dimension (NMAX*NSMAX)
[out]	WORK	WORK is REAL array, dimension (NMAX*max(3,NSMAX))
[out]	RWORK	RWORK is REAL 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 schkpp.f.

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

SCHKPS

Purpose:

 SCHKPS tests SPSTRF.

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 REAL The threshold value for the test ratios. A result is included in the output file if RESULT >= THRESH. To have every test ratio printed, use THRESH = 0.
[in]	TSTERR	TSTERR is LOGICAL Flag that indicates whether error exits are to be tested.
[in]	NMAX	NMAX is INTEGER The maximum value permitted for N, used in dimensioning the work arrays.
[out]	A	A is REAL array, dimension (NMAX*NMAX)
[out]	AFAC	AFAC is REAL array, dimension (NMAX*NMAX)
[out]	PERM	PERM is REAL array, dimension (NMAX*NMAX)
[out]	PIV	PIV is INTEGER array, dimension (NMAX)
[out]	WORK	WORK is REAL array, dimension (NMAX*3)
[out]	RWORK	RWORK is REAL 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 schkps.f.

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

SCHKPT

Purpose:

 SCHKPT tests SPTTRF, -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 REAL 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 REAL array, dimension (NMAX*2)
[out]	D	D is REAL array, dimension (NMAX*2)
[out]	E	E is REAL array, dimension (NMAX*2)
[out]	B	B is REAL array, dimension (NMAX*NSMAX) where NSMAX is the largest entry in NSVAL.
[out]	X	X is REAL array, dimension (NMAX*NSMAX)
[out]	XACT	XACT is REAL array, dimension (NMAX*NSMAX)
[out]	WORK	WORK is REAL array, dimension (NMAX*max(3,NSMAX))
[out]	RWORK	RWORK is REAL 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 schkpt.f.

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subroutine schkq3	(	logical, dimension( * )	DOTYPE,
		integer	NM,
		integer, dimension( * )	MVAL,
		integer	NN,
		integer, dimension( * )	NVAL,
		integer	NNB,
		integer, dimension( * )	NBVAL,
		integer, dimension( * )	NXVAL,
		real	THRESH,
		real, dimension( * )	A,
		real, dimension( * )	COPYA,
		real, dimension( * )	S,
		real, dimension( * )	TAU,
		real, dimension( * )	WORK,
		integer, dimension( * )	IWORK,
		integer	NOUT
	)

SCHKQ3

Purpose:

 SCHKQ3 tests SGEQP3.

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 REAL 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 REAL 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 REAL array, dimension (MMAX*NMAX)
[out]	S	S is REAL array, dimension (min(MMAX,NMAX))
[out]	TAU	TAU is REAL array, dimension (MMAX)
[out]	WORK	WORK is REAL 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 schkq3.f.

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

SCHKQL

Purpose:

 SCHKQL tests SGEQLF, SORGQL and SORMQL.

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 REAL 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 REAL array, dimension (NMAX*NMAX)
[out]	AF	AF is REAL array, dimension (NMAX*NMAX)
[out]	AQ	AQ is REAL array, dimension (NMAX*NMAX)
[out]	AL	AL is REAL array, dimension (NMAX*NMAX)
[out]	AC	AC is REAL array, dimension (NMAX*NMAX)
[out]	B	B is REAL array, dimension (NMAX*NRHS)
[out]	X	X is REAL array, dimension (NMAX*NRHS)
[out]	XACT	XACT is REAL array, dimension (NMAX*NRHS)
[out]	TAU	TAU is REAL array, dimension (NMAX)
[out]	WORK	WORK is REAL array, dimension (NMAX*NMAX)
[out]	RWORK	RWORK is REAL 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 schkql.f.

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subroutine schkqp	(	logical, dimension( * )	DOTYPE,
		integer	NM,
		integer, dimension( * )	MVAL,
		integer	NN,
		integer, dimension( * )	NVAL,
		real	THRESH,
		logical	TSTERR,
		real, dimension( * )	A,
		real, dimension( * )	COPYA,
		real, dimension( * )	S,
		real, dimension( * )	TAU,
		real, dimension( * )	WORK,
		integer, dimension( * )	IWORK,
		integer	NOUT
	)

SCHKQP

Purpose:

 SCHKQP tests SGEQPF.

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 REAL 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 REAL 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 REAL array, dimension (MMAX*NMAX)
[out]	S	S is REAL array, dimension (min(MMAX,NMAX))
[out]	TAU	TAU is REAL array, dimension (MMAX)
[out]	WORK	WORK is REAL 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 schkqp.f.

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

SCHKQR

Purpose:

 SCHKQR tests SGEQRF, SORGQR and SORMQR.

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 REAL 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 REAL array, dimension (NMAX*NMAX)
[out]	AF	AF is REAL array, dimension (NMAX*NMAX)
[out]	AQ	AQ is REAL array, dimension (NMAX*NMAX)
[out]	AR	AR is REAL array, dimension (NMAX*NMAX)
[out]	AC	AC is REAL array, dimension (NMAX*NMAX)
[out]	B	B is REAL array, dimension (NMAX*NRHS)
[out]	X	X is REAL array, dimension (NMAX*NRHS)
[out]	XACT	XACT is REAL array, dimension (NMAX*NRHS)
[out]	TAU	TAU is REAL array, dimension (NMAX)
[out]	WORK	WORK is REAL array, dimension (NMAX*NMAX)
[out]	RWORK	RWORK is REAL 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 schkqr.f.

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subroutine schkqrt	(	real	THRESH,
		logical	TSTERR,
		integer	NM,
		integer, dimension( * )	MVAL,
		integer	NN,
		integer, dimension( * )	NVAL,
		integer	NNB,
		integer, dimension( * )	NBVAL,
		integer	NOUT
	)

SCHKQRT

Purpose:

 SCHKQRT tests SGEQRT and SGEMQRT.

Parameters:

[in]	THRESH	THRESH is REAL 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 100 of file schkqrt.f.

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subroutine schkqrtp	(	real	THRESH,
		logical	TSTERR,
		integer	NM,
		integer, dimension( * )	MVAL,
		integer	NN,
		integer, dimension( * )	NVAL,
		integer	NNB,
		integer, dimension( * )	NBVAL,
		integer	NOUT
	)

SCHKQRTP

Purpose:

 SCHKQRTP tests STPQRT and STPMQRT.

Parameters:

[in]	THRESH	THRESH is REAL 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 schkqrtp.f.

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program schkrfp ( )

SCHKRFP

Purpose:

 SCHKRFP is the main test program for the REAL 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 schkrfp.f.

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

SCHKRQ

Purpose:

 SCHKRQ tests SGERQF, SORGRQ and SORMRQ.

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 REAL 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 REAL array, dimension (NMAX*NMAX)
[out]	AF	AF is REAL array, dimension (NMAX*NMAX)
[out]	AQ	AQ is REAL array, dimension (NMAX*NMAX)
[out]	AR	AR is REAL array, dimension (NMAX*NMAX)
[out]	AC	AC is REAL array, dimension (NMAX*NMAX)
[out]	B	B is REAL array, dimension (NMAX*NRHS)
[out]	X	X is REAL array, dimension (NMAX*NRHS)
[out]	XACT	XACT is REAL array, dimension (NMAX*NRHS)
[out]	TAU	TAU is REAL array, dimension (NMAX)
[out]	WORK	WORK is REAL array, dimension (NMAX*NMAX)
[out]	RWORK	RWORK is REAL 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 schkrq.f.

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

SCHKSP

Purpose:

 SCHKSP tests SSPTRF, -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 REAL The threshold value for the test ratios. A result is included in the output file if RESULT >= THRESH. To have every test ratio printed, use THRESH = 0.
[in]	TSTERR	TSTERR is LOGICAL Flag that indicates whether error exits are to be tested.
[in]	NMAX	NMAX is INTEGER The maximum value permitted for N, used in dimensioning the work arrays.
[out]	A	A is REAL array, dimension (NMAX*(NMAX+1)/2)
[out]	AFAC	AFAC is REAL array, dimension (NMAX*(NMAX+1)/2)
[out]	AINV	AINV is REAL array, dimension (NMAX*(NMAX+1)/2)
[out]	B	B is REAL array, dimension (NMAX*NSMAX) where NSMAX is the largest entry in NSVAL.
[out]	X	X is REAL array, dimension (NMAX*NSMAX)
[out]	XACT	XACT is REAL array, dimension (NMAX*NSMAX)
[out]	WORK	WORK is REAL array, dimension (NMAX*max(2,NSMAX))
[out]	RWORK	RWORK is REAL 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 schksp.f.

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

SCHKSY

Purpose:

 SCHKSY tests SSYTRF, -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 REAL The threshold value for the test ratios. A result is included in the output file if RESULT >= THRESH. To have every test ratio printed, use THRESH = 0.
[in]	TSTERR	TSTERR is LOGICAL Flag that indicates whether error exits are to be tested.
[in]	NMAX	NMAX is INTEGER The maximum value permitted for N, used in dimensioning the work arrays.
[out]	A	A is REAL array, dimension (NMAX*NMAX)
[out]	AFAC	AFAC is REAL array, dimension (NMAX*NMAX)
[out]	AINV	AINV is REAL array, dimension (NMAX*NMAX)
[out]	B	B is REAL array, dimension (NMAX*NSMAX) where NSMAX is the largest entry in NSVAL.
[out]	X	X is REAL array, dimension (NMAX*NSMAX)
[out]	XACT	XACT is REAL array, dimension (NMAX*NSMAX)
[out]	WORK	WORK is REAL array, dimension (NMAX*max(3,NSMAX))
[out]	RWORK	RWORK is REAL 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 schksy.f.

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

SCHKTB

Purpose:

 SCHKTB tests STBTRS, -RFS, and -CON, and SLATBS.

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 REAL 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 REAL array, dimension (NMAX*NMAX)
[out]	AINV	AINV is REAL array, dimension (NMAX*NMAX)
[out]	B	B is REAL array, dimension (NMAX*NSMAX) where NSMAX is the largest entry in NSVAL.
[out]	X	X is REAL array, dimension (NMAX*NSMAX)
[out]	XACT	XACT is REAL array, dimension (NMAX*NSMAX)
[out]	WORK	WORK is REAL array, dimension (NMAX*max(3,NSMAX))
[out]	RWORK	RWORK is REAL 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 schktb.f.

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

SCHKTP

Purpose:

 SCHKTP tests STPTRI, -TRS, -RFS, and -CON, and SLATPS

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 REAL 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 REAL array, dimension (NMAX*(NMAX+1)/2)
[out]	AINVP	AINVP is REAL array, dimension (NMAX*(NMAX+1)/2)
[out]	B	B is REAL array, dimension (NMAX*NSMAX) where NSMAX is the largest entry in NSVAL.
[out]	X	X is REAL array, dimension (NMAX*NSMAX)
[out]	XACT	XACT is REAL array, dimension (NMAX*NSMAX)
[out]	WORK	WORK is REAL array, dimension (NMAX*max(3,NSMAX))
[out]	IWORK	IWORK is INTEGER array, dimension (NMAX)
[out]	RWORK	RWORK is REAL 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 schktp.f.

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

SCHKTR

Purpose:

 SCHKTR tests STRTRI, -TRS, -RFS, and -CON, and SLATRS

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 REAL 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 REAL array, dimension (NMAX*NMAX)
[out]	AINV	AINV is REAL array, dimension (NMAX*NMAX)
[out]	B	B is REAL array, dimension (NMAX*NSMAX) where NSMAX is the largest entry in NSVAL.
[out]	X	X is REAL array, dimension (NMAX*NSMAX)
[out]	XACT	XACT is REAL array, dimension (NMAX*NSMAX)
[out]	WORK	WORK is REAL array, dimension (NMAX*max(3,NSMAX))
[out]	RWORK	RWORK is REAL 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 schktr.f.

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

SCHKTZ

Purpose:

 SCHKTZ tests STZRQF 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 REAL 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 REAL 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 REAL array, dimension (MMAX*NMAX)
[out]	S	S is REAL array, dimension (min(MMAX,NMAX))
[out]	TAU	TAU is REAL array, dimension (MMAX)
[out]	WORK	WORK is REAL 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 schktz.f.

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

SDRVGB

SDRVGBX

Purpose:

 SDRVGB tests the driver routines SGBSV 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 REAL 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 REAL 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 REAL 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 REAL array, dimension (LA)
[out]	B	B is REAL array, dimension (NMAX*NRHS)
[out]	BSAV	BSAV is REAL array, dimension (NMAX*NRHS)
[out]	X	X is REAL array, dimension (NMAX*NRHS)
[out]	XACT	XACT is REAL array, dimension (NMAX*NRHS)
[out]	S	S is REAL array, dimension (2*NMAX)
[out]	WORK	WORK is REAL array, dimension (NMAX*max(3,NRHS,NMAX))
[out]	RWORK	RWORK is REAL 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:

 SDRVGB tests the driver routines SGBSV, -SVX, and -SVXX.

 Note that this file is used only when the XBLAS are available,
 otherwise sdrvgb.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 REAL 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 REAL 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 REAL 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 REAL array, dimension (LA)
[out]	B	B is REAL array, dimension (NMAX*NRHS)
[out]	BSAV	BSAV is REAL array, dimension (NMAX*NRHS)
[out]	X	X is REAL array, dimension (NMAX*NRHS)
[out]	XACT	XACT is REAL array, dimension (NMAX*NRHS)
[out]	S	S is REAL array, dimension (2*NMAX)
[out]	WORK	WORK is REAL array, dimension (NMAX*max(3,NRHS,NMAX))
[out]	RWORK	RWORK is REAL 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 sdrvgb.f.

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

SDRVGE

SDRVGEX

Purpose:

 SDRVGE tests the driver routines SGESV 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 REAL The threshold value for the test ratios. A result is included in the output file if RESULT >= THRESH. To have every test ratio printed, use THRESH = 0.
[in]	TSTERR	TSTERR is LOGICAL Flag that indicates whether error exits are to be tested.
[in]	NMAX	NMAX is INTEGER The maximum value permitted for N, used in dimensioning the work arrays.
[out]	A	A is REAL array, dimension (NMAX*NMAX)
[out]	AFAC	AFAC is REAL array, dimension (NMAX*NMAX)
[out]	ASAV	ASAV is REAL array, dimension (NMAX*NMAX)
[out]	B	B is REAL array, dimension (NMAX*NRHS)
[out]	BSAV	BSAV is REAL array, dimension (NMAX*NRHS)
[out]	X	X is REAL array, dimension (NMAX*NRHS)
[out]	XACT	XACT is REAL array, dimension (NMAX*NRHS)
[out]	S	S is REAL array, dimension (2*NMAX)
[out]	WORK	WORK is REAL array, dimension (NMAX*max(3,NRHS))
[out]	RWORK	RWORK is REAL 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:

 SDRVGE tests the driver routines SGESV, -SVX, and -SVXX.

 Note that this file is used only when the XBLAS are available,
 otherwise sdrvge.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 REAL The threshold value for the test ratios. A result is included in the output file if RESULT >= THRESH. To have every test ratio printed, use THRESH = 0.
[in]	TSTERR	TSTERR is LOGICAL Flag that indicates whether error exits are to be tested.
[in]	NMAX	NMAX is INTEGER The maximum value permitted for N, used in dimensioning the work arrays.
[out]	A	A is REAL array, dimension (NMAX*NMAX)
[out]	AFAC	AFAC is REAL array, dimension (NMAX*NMAX)
[out]	ASAV	ASAV is REAL array, dimension (NMAX*NMAX)
[out]	B	B is REAL array, dimension (NMAX*NRHS)
[out]	BSAV	BSAV is REAL array, dimension (NMAX*NRHS)
[out]	X	X is REAL array, dimension (NMAX*NRHS)
[out]	XACT	XACT is REAL array, dimension (NMAX*NRHS)
[out]	S	S is REAL array, dimension (2*NMAX)
[out]	WORK	WORK is REAL array, dimension (NMAX*max(3,NRHS))
[out]	RWORK	RWORK is REAL 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 sdrvge.f.

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

SDRVGT

Purpose:

 SDRVGT tests SGTSV 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 REAL 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 REAL array, dimension (NMAX*4)
[out]	AF	AF is REAL array, dimension (NMAX*4)
[out]	B	B is REAL array, dimension (NMAX*NRHS)
[out]	X	X is REAL array, dimension (NMAX*NRHS)
[out]	XACT	XACT is REAL array, dimension (NMAX*NRHS)
[out]	WORK	WORK is REAL array, dimension (NMAX*max(3,NRHS))
[out]	RWORK	RWORK is REAL 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 sdrvgt.f.

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subroutine sdrvls	(	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,
		real	THRESH,
		logical	TSTERR,
		real, dimension( * )	A,
		real, dimension( * )	COPYA,
		real, dimension( * )	B,
		real, dimension( * )	COPYB,
		real, dimension( * )	C,
		real, dimension( * )	S,
		real, dimension( * )	COPYS,
		real, dimension( * )	WORK,
		integer, dimension( * )	IWORK,
		integer	NOUT
	)

SDRVLS

Purpose:

 SDRVLS tests the least squares driver routines SGELS, SGELSS, SGELSX,
 SGELSY and SGELSD.

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 REAL 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 REAL 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 REAL array, dimension (MMAX*NMAX)
[out]	B	B is REAL 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 REAL array, dimension (MMAX*NSMAX)
[out]	C	C is REAL array, dimension (MMAX*NSMAX)
[out]	S	S is REAL array, dimension (min(MMAX,NMAX))
[out]	COPYS	COPYS is REAL array, dimension (min(MMAX,NMAX))
[out]	WORK	WORK is REAL 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 sdrvls.f.

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

SDRVPB

Purpose:

 SDRVPB tests the driver routines SPBSV 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 REAL The threshold value for the test ratios. A result is included in the output file if RESULT >= THRESH. To have every test ratio printed, use THRESH = 0.
[in]	TSTERR	TSTERR is LOGICAL Flag that indicates whether error exits are to be tested.
[in]	NMAX	NMAX is INTEGER The maximum value permitted for N, used in dimensioning the work arrays.
[out]	A	A is REAL array, dimension (NMAX*NMAX)
[out]	AFAC	AFAC is REAL array, dimension (NMAX*NMAX)
[out]	ASAV	ASAV is REAL array, dimension (NMAX*NMAX)
[out]	B	B is REAL array, dimension (NMAX*NRHS)
[out]	BSAV	BSAV is REAL array, dimension (NMAX*NRHS)
[out]	X	X is REAL array, dimension (NMAX*NRHS)
[out]	XACT	XACT is REAL array, dimension (NMAX*NRHS)
[out]	S	S is REAL array, dimension (NMAX)
[out]	WORK	WORK is REAL array, dimension (NMAX*max(3,NRHS))
[out]	RWORK	RWORK is REAL 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 sdrvpb.f.

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

SDRVPO

SDRVPOX

Purpose:

 SDRVPO tests the driver routines SPOSV 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 REAL The threshold value for the test ratios. A result is included in the output file if RESULT >= THRESH. To have every test ratio printed, use THRESH = 0.
[in]	TSTERR	TSTERR is LOGICAL Flag that indicates whether error exits are to be tested.
[in]	NMAX	NMAX is INTEGER The maximum value permitted for N, used in dimensioning the work arrays.
[out]	A	A is REAL array, dimension (NMAX*NMAX)
[out]	AFAC	AFAC is REAL array, dimension (NMAX*NMAX)
[out]	ASAV	ASAV is REAL array, dimension (NMAX*NMAX)
[out]	B	B is REAL array, dimension (NMAX*NRHS)
[out]	BSAV	BSAV is REAL array, dimension (NMAX*NRHS)
[out]	X	X is REAL array, dimension (NMAX*NRHS)
[out]	XACT	XACT is REAL array, dimension (NMAX*NRHS)
[out]	S	S is REAL array, dimension (NMAX)
[out]	WORK	WORK is REAL array, dimension (NMAX*max(3,NRHS))
[out]	RWORK	RWORK is REAL 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:

 SDRVPO tests the driver routines SPOSV, -SVX, and -SVXX.

 Note that this file is used only when the XBLAS are available,
 otherwise sdrvpo.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 REAL The threshold value for the test ratios. A result is included in the output file if RESULT >= THRESH. To have every test ratio printed, use THRESH = 0.
[in]	TSTERR	TSTERR is LOGICAL Flag that indicates whether error exits are to be tested.
[in]	NMAX	NMAX is INTEGER The maximum value permitted for N, used in dimensioning the work arrays.
[out]	A	A is REAL array, dimension (NMAX*NMAX)
[out]	AFAC	AFAC is REAL array, dimension (NMAX*NMAX)
[out]	ASAV	ASAV is REAL array, dimension (NMAX*NMAX)
[out]	B	B is REAL array, dimension (NMAX*NRHS)
[out]	BSAV	BSAV is REAL array, dimension (NMAX*NRHS)
[out]	X	X is REAL array, dimension (NMAX*NRHS)
[out]	XACT	XACT is REAL array, dimension (NMAX*NRHS)
[out]	S	S is REAL array, dimension (NMAX)
[out]	WORK	WORK is REAL array, dimension (NMAX*max(3,NRHS))
[out]	RWORK	RWORK is REAL 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 sdrvpo.f.

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

SDRVPP

Purpose:

 SDRVPP tests the driver routines SPPSV 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 REAL The threshold value for the test ratios. A result is included in the output file if RESULT >= THRESH. To have every test ratio printed, use THRESH = 0.
[in]	TSTERR	TSTERR is LOGICAL Flag that indicates whether error exits are to be tested.
[in]	NMAX	NMAX is INTEGER The maximum value permitted for N, used in dimensioning the work arrays.
[out]	A	A is REAL array, dimension (NMAX*(NMAX+1)/2)
[out]	AFAC	AFAC is REAL array, dimension (NMAX*(NMAX+1)/2)
[out]	ASAV	ASAV is REAL array, dimension (NMAX*(NMAX+1)/2)
[out]	B	B is REAL array, dimension (NMAX*NRHS)
[out]	BSAV	BSAV is REAL array, dimension (NMAX*NRHS)
[out]	X	X is REAL array, dimension (NMAX*NRHS)
[out]	XACT	XACT is REAL array, dimension (NMAX*NRHS)
[out]	S	S is REAL array, dimension (NMAX)
[out]	WORK	WORK is REAL array, dimension (NMAX*max(3,NRHS))
[out]	RWORK	RWORK is REAL 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 sdrvpp.f.

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

SDRVPT

Purpose:

 SDRVPT tests SPTSV 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 REAL 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 REAL array, dimension (NMAX*2)
[out]	D	D is REAL array, dimension (NMAX*2)
[out]	E	E is REAL array, dimension (NMAX*2)
[out]	B	B is REAL array, dimension (NMAX*NRHS)
[out]	X	X is REAL array, dimension (NMAX*NRHS)
[out]	XACT	XACT is REAL array, dimension (NMAX*NRHS)
[out]	WORK	WORK is REAL array, dimension (NMAX*max(3,NRHS))
[out]	RWORK	RWORK is REAL 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 sdrvpt.f.

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subroutine sdrvrf1	(	integer	NOUT,
		integer	NN,
		integer, dimension( nn )	NVAL,
		real	THRESH,
		real, dimension( lda, * )	A,
		integer	LDA,
		real, dimension( * )	ARF,
		real, dimension( * )	WORK
	)

SDRVRF1

Purpose:

 SDRVRF1 tests the LAPACK RFP routines:
     SLANSF

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 REAL 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 REAL array, dimension (LDA,NMAX)
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= max(1,NMAX).
[out]	ARF	ARF is REAL array, dimension ((NMAX*(NMAX+1))/2).
[out]	WORK	WORK is REAL 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 sdrvrf1.f.

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subroutine sdrvrf2	(	integer	NOUT,
		integer	NN,
		integer, dimension( nn )	NVAL,
		real, dimension( lda, * )	A,
		integer	LDA,
		real, dimension( * )	ARF,
		real, dimension(*)	AP,
		real, dimension( lda, * )	ASAV
	)

SDRVRF2

Purpose:

 SDRVRF2 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 REAL array, dimension (LDA,NMAX)
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= max(1,NMAX).
[out]	ARF	ARF is REAL array, dimension ((NMAX*(NMAX+1))/2).
[out]	AP	AP is REAL array, dimension ((NMAX*(NMAX+1))/2).
[out]	ASAV	ASAV is REAL 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 sdrvrf2.f.

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subroutine sdrvrf3	(	integer	NOUT,
		integer	NN,
		integer, dimension( nn )	NVAL,
		real	THRESH,
		real, dimension( lda, * )	A,
		integer	LDA,
		real, dimension( * )	ARF,
		real, dimension( lda, * )	B1,
		real, dimension( lda, * )	B2,
		real, dimension( * )	S_WORK_SLANGE,
		real, dimension( * )	S_WORK_SGEQRF,
		real, dimension( * )	TAU
	)

SDRVRF3

Purpose:

 SDRVRF3 tests the LAPACK RFP routines:
     STFSM

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 REAL 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 REAL array, dimension (LDA,NMAX)
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= max(1,NMAX).
[out]	ARF	ARF is REAL array, dimension ((NMAX*(NMAX+1))/2).
[out]	B1	B1 is REAL array, dimension (LDA,NMAX)
[out]	B2	B2 is REAL array, dimension (LDA,NMAX)
[out]	S_WORK_SLANGE	S_WORK_SLANGE is REAL array, dimension (NMAX)
[out]	S_WORK_SGEQRF	S_WORK_SGEQRF is REAL array, dimension (NMAX)
[out]	TAU	TAU is REAL 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 sdrvrf3.f.

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subroutine sdrvrf4	(	integer	NOUT,
		integer	NN,
		integer, dimension( nn )	NVAL,
		real	THRESH,
		real, dimension( ldc, * )	C1,
		real, dimension( ldc, *)	C2,
		integer	LDC,
		real, dimension( * )	CRF,
		real, dimension( lda, * )	A,
		integer	LDA,
		real, dimension( * )	S_WORK_SLANGE
	)

SDRVRF4

Purpose:

 SDRVRF4 tests the LAPACK RFP routines:
     SSFRK

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 REAL 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 REAL array, dimension (LDC,NMAX)
[out]	C2	C2 is REAL array, dimension (LDC,NMAX)
[in]	LDC	LDC is INTEGER The leading dimension of the array A. LDA >= max(1,NMAX).
[out]	CRF	CRF is REAL array, dimension ((NMAX*(NMAX+1))/2).
[out]	A	A is REAL array, dimension (LDA,NMAX)
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= max(1,NMAX).
[out]	S_WORK_SLANGE	S_WORK_SLANGE is REAL 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 sdrvrf4.f.

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subroutine sdrvrfp	(	integer	NOUT,
		integer	NN,
		integer, dimension( nn )	NVAL,
		integer	NNS,
		integer, dimension( nns )	NSVAL,
		integer	NNT,
		integer, dimension( nnt )	NTVAL,
		real	THRESH,
		real, dimension( * )	A,
		real, dimension( * )	ASAV,
		real, dimension( * )	AFAC,
		real, dimension( * )	AINV,
		real, dimension( * )	B,
		real, dimension( * )	BSAV,
		real, dimension( * )	XACT,
		real, dimension( * )	X,
		real, dimension( * )	ARF,
		real, dimension( * )	ARFINV,
		real, dimension( * )	S_WORK_SLATMS,
		real, dimension( * )	S_WORK_SPOT01,
		real, dimension( * )	S_TEMP_SPOT02,
		real, dimension( * )	S_TEMP_SPOT03,
		real, dimension( * )	S_WORK_SLANSY,
		real, dimension( * )	S_WORK_SPOT02,
		real, dimension( * )	S_WORK_SPOT03
	)

SDRVRFP

Purpose:

 SDRVRFP tests the LAPACK RFP routines:
     SPFTRF, SPFTRS, and SPFTRI.

 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 STRTTF and
 STFTTR.

 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 SPFTRF, 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 SPFTRF 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 REAL 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 REAL array, dimension (NMAX*NMAX)
[out]	ASAV	ASAV is REAL array, dimension (NMAX*NMAX)
[out]	AFAC	AFAC is REAL array, dimension (NMAX*NMAX)
[out]	AINV	AINV is REAL array, dimension (NMAX*NMAX)
[out]	B	B is REAL array, dimension (NMAX*MAXRHS)
[out]	BSAV	BSAV is REAL array, dimension (NMAX*MAXRHS)
[out]	XACT	XACT is REAL array, dimension (NMAX*MAXRHS)
[out]	X	X is REAL array, dimension (NMAX*MAXRHS)
[out]	ARF	ARF is REAL array, dimension ((NMAX*(NMAX+1))/2)
[out]	ARFINV	ARFINV is REAL array, dimension ((NMAX*(NMAX+1))/2)
[out]	S_WORK_SLATMS	S_WORK_SLATMS is REAL array, dimension ( 3*NMAX )
[out]	S_WORK_SPOT01	S_WORK_SPOT01 is REAL array, dimension ( NMAX )
[out]	S_TEMP_SPOT02	S_TEMP_SPOT02 is REAL array, dimension ( NMAX*MAXRHS )
[out]	S_TEMP_SPOT03	S_TEMP_SPOT03 is REAL array, dimension ( NMAX*NMAX )
[out]	S_WORK_SLATMS	S_WORK_SLATMS is REAL array, dimension ( NMAX )
[out]	S_WORK_SLANSY	S_WORK_SLANSY is REAL array, dimension ( NMAX )
[out]	S_WORK_SPOT02	S_WORK_SPOT02 is REAL array, dimension ( NMAX )
[out]	S_WORK_SPOT03	S_WORK_SPOT03 is REAL 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 sdrvrfp.f.

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

SDRVSP

Purpose:

 SDRVSP tests the driver routines SSPSV 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 REAL The threshold value for the test ratios. A result is included in the output file if RESULT >= THRESH. To have every test ratio printed, use THRESH = 0.
[in]	TSTERR	TSTERR is LOGICAL Flag that indicates whether error exits are to be tested.
[in]	NMAX	NMAX is INTEGER The maximum value permitted for N, used in dimensioning the work arrays.
[out]	A	A is REAL array, dimension (NMAX*(NMAX+1)/2)
[out]	AFAC	AFAC is REAL array, dimension (NMAX*(NMAX+1)/2)
[out]	AINV	AINV is REAL array, dimension (NMAX*(NMAX+1)/2)
[out]	B	B is REAL array, dimension (NMAX*NRHS)
[out]	X	X is REAL array, dimension (NMAX*NRHS)
[out]	XACT	XACT is REAL array, dimension (NMAX*NRHS)
[out]	WORK	WORK is REAL array, dimension (NMAX*max(2,NRHS))
[out]	RWORK	RWORK is REAL array, dimension (NMAX+2*NRHS)
[out]	IWORK	IWORK is INTEGER array, dimension (2*NMAX)
[in]	NOUT	NOUT is INTEGER The unit number for output.

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

Date:: November 2011

Definition at line 155 of file sdrvsp.f.

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

SDRVSY

SDRVSYX

Purpose:

 SDRVSY tests the driver routines SSYSV 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 REAL The threshold value for the test ratios. A result is included in the output file if RESULT >= THRESH. To have every test ratio printed, use THRESH = 0.
[in]	TSTERR	TSTERR is LOGICAL Flag that indicates whether error exits are to be tested.
[in]	NMAX	NMAX is INTEGER The maximum value permitted for N, used in dimensioning the work arrays.
[out]	A	A is REAL array, dimension (NMAX*NMAX)
[out]	AFAC	AFAC is REAL array, dimension (NMAX*NMAX)
[out]	AINV	AINV is REAL array, dimension (NMAX*NMAX)
[out]	B	B is REAL array, dimension (NMAX*NRHS)
[out]	X	X is REAL array, dimension (NMAX*NRHS)
[out]	XACT	XACT is REAL array, dimension (NMAX*NRHS)
[out]	WORK	WORK is REAL array, dimension (NMAX*max(2,NRHS))
[out]	RWORK	RWORK is REAL array, dimension (NMAX+2*NRHS)
[out]	IWORK	IWORK is INTEGER array, dimension (2*NMAX)
[in]	NOUT	NOUT is INTEGER The unit number for output.

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

Date:: November 2011

Purpose:

 SDRVSY tests the driver routines SSYSV, -SVX, and -SVXX

 Note that this file is used only when the XBLAS are available,
 otherwise sdrvsy.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 REAL The threshold value for the test ratios. A result is included in the output file if RESULT >= THRESH. To have every test ratio printed, use THRESH = 0.
[in]	TSTERR	TSTERR is LOGICAL Flag that indicates whether error exits are to be tested.
[in]	NMAX	NMAX is INTEGER The maximum value permitted for N, used in dimensioning the work arrays.
[out]	A	A is REAL array, dimension (NMAX*NMAX)
[out]	AFAC	AFAC is REAL array, dimension (NMAX*NMAX)
[out]	AINV	AINV is REAL array, dimension (NMAX*NMAX)
[out]	B	B is REAL array, dimension (NMAX*NRHS)
[out]	X	X is REAL array, dimension (NMAX*NRHS)
[out]	XACT	XACT is REAL array, dimension (NMAX*NRHS)
[out]	WORK	WORK is REAL array, dimension (NMAX*max(2,NRHS))
[out]	RWORK	RWORK is REAL array, dimension (NMAX+2*NRHS)
[out]	IWORK	IWORK is INTEGER array, dimension (2*NMAX)
[in]	NOUT	NOUT is INTEGER The unit number for output.

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

Date:: November 2011

Definition at line 152 of file sdrvsy.f.

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subroutine sebchvxx	(	real	THRESH,
		character*3	PATH
	)

SEBCHVXX

Purpose:

  SEBCHVXX will run S**SVXX on a series of Hilbert matrices and then
  compare the error bounds returned by SGESVXX 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, SGESVXX 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 SGESVXX.  Let RCONDc be the RCOND returned by SGESVXX
          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 )).

       7. 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 sebchvxx.f.

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subroutine serrge	(	character*3	PATH,
		integer	NUNIT
	)

SERRGE

SERRGEX

Purpose:

 SERRGE tests the error exits for the REAL 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:

 SERRGE tests the error exits for the REAL routines
 for general matrices.

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

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subroutine serrgt	(	character*3	PATH,
		integer	NUNIT
	)

SERRGT

Purpose:

 SERRGT tests the error exits for the REAL 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 serrgt.f.

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subroutine serrlq	(	character*3	PATH,
		integer	NUNIT
	)

SERRLQ

Purpose:

 SERRLQ tests the error exits for the REAL 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 serrlq.f.

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subroutine serrls	(	character*3	PATH,
		integer	NUNIT
	)

SERRLS

Purpose:

 SERRLS tests the error exits for the REAL least squares
 driver routines (SGELS, 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 serrls.f.

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subroutine serrpo	(	character*3	PATH,
		integer	NUNIT
	)

SERRPO

SERRPOX

Purpose:

 SERRPO tests the error exits for the REAL 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:

 SERRPO tests the error exits for the REAL routines
 for symmetric positive definite matrices.

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

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subroutine serrps	(	character*3	PATH,
		integer	NUNIT
	)

SERRPS

Purpose:

 SERRPS tests the error exits for the REAL routines
 for SPSTRF..

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 serrps.f.

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subroutine serrql	(	character*3	PATH,
		integer	NUNIT
	)

SERRQL

Purpose:

 SERRQL tests the error exits for the REAL 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 serrql.f.

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subroutine serrqp	(	character*3	PATH,
		integer	NUNIT
	)

SERRQP

Purpose:

 SERRQP tests the error exits for SGEQPF and SGEQP3.

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 serrqp.f.

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subroutine serrqr	(	character*3	PATH,
		integer	NUNIT
	)

SERRQR

Purpose:

 SERRQR tests the error exits for the REAL 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 serrqr.f.

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subroutine serrqrt	(	character*3	PATH,
		integer	NUNIT
	)

SERRQRT

Purpose:

 SERRQRT tests the error exits for the REAL 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 serrqrt.f.

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subroutine serrqrtp	(	character*3	PATH,
		integer	NUNIT
	)

SERRQRTP

Purpose:

 SERRQRTP 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 serrqrtp.f.

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subroutine serrrfp ( integer NUNIT )

SERRRFP

Purpose:

 SERRRFP tests the error exits for the REAL driver routines
 for solving linear systems of equations.

 SDRVRFP tests the REAL LAPACK RFP routines:
     STFSM, STFTRI, SSFRK, STFTTP, STFTTR, SPFTRF, SPFTRS, STPTTF,
     STPTTR, STRTTF, and STRTTP

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 serrrfp.f.

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subroutine serrrq	(	character*3	PATH,
		integer	NUNIT
	)

SERRRQ

Purpose:

 SERRRQ tests the error exits for the REAL 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 serrrq.f.

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subroutine serrsy	(	character*3	PATH,
		integer	NUNIT
	)

SERRSY

SERRSYX

Purpose:

 SERRSY tests the error exits for the REAL 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:

 SERRSY tests the error exits for the REAL routines
 for symmetric indefinite matrices.

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

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subroutine serrtr	(	character*3	PATH,
		integer	NUNIT
	)

SERRTR

Purpose:

 SERRTR tests the error exits for the REAL 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 serrtr.f.

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subroutine serrtz	(	character*3	PATH,
		integer	NUNIT
	)

SERRTZ

Purpose:

 SERRTZ tests the error exits for STZRQF 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 serrtz.f.

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subroutine serrvx	(	character*3	PATH,
		integer	NUNIT
	)

SERRVX

SERRVXX

Purpose:

 SERRVX tests the error exits for the REAL 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:

 SERRVX tests the error exits for the REAL 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 serrvx.f.

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subroutine sgbt01	(	integer	M,
		integer	N,
		integer	KL,
		integer	KU,
		real, dimension( lda, * )	A,
		integer	LDA,
		real, dimension( ldafac, * )	AFAC,
		integer	LDAFAC,
		integer, dimension( * )	IPIV,
		real, dimension( * )	WORK,
		real	RESID
	)

SGBT01

Purpose:

 SGBT01 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 REAL 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 REAL 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 SGBTRF. 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 SGBTRF 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 SGBTRF.
[out]	WORK	WORK is REAL array, dimension (2*KL+KU+1)
[out]	RESID	RESID is REAL 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 sgbt01.f.

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subroutine sgbt02	(	character	TRANS,
		integer	M,
		integer	N,
		integer	KL,
		integer	KU,
		integer	NRHS,
		real, dimension( lda, * )	A,
		integer	LDA,
		real, dimension( ldx, * )	X,
		integer	LDX,
		real, dimension( ldb, * )	B,
		integer	LDB,
		real	RESID
	)

SGBT02

Purpose:

 SGBT02 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 REAL 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 REAL 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 REAL 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 REAL 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 sgbt02.f.

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subroutine sgbt05	(	character	TRANS,
		integer	N,
		integer	KL,
		integer	KU,
		integer	NRHS,
		real, dimension( ldab, * )	AB,
		integer	LDAB,
		real, dimension( ldb, * )	B,
		integer	LDB,
		real, dimension( ldx, * )	X,
		integer	LDX,
		real, dimension( ldxact, * )	XACT,
		integer	LDXACT,
		real, dimension( * )	FERR,
		real, dimension( * )	BERR,
		real, dimension( * )	RESLTS
	)

SGBT05

Purpose:

 SGBT05 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 REAL 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 REAL 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 REAL 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 REAL 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 REAL 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 REAL 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 REAL 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 sgbt05.f.

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

SGELQS

Purpose:

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

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 REAL array, dimension (LDA,N) Details of the LQ factorization of the original matrix A as returned by SGELQF.
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= M.
[in]	TAU	TAU is REAL array, dimension (M) Details of the orthogonal matrix Q.
[in,out]	B	B is REAL 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 REAL 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 sgelqs.f.

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LOGICAL function sgennd	(	integer	M,
		integer	N,
		real, dimension( lda, * )	A,
		integer	LDA
	)

SGENND

Purpose:

    SGENND 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 REAL 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 sgennd.f.

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

SGEQLS

Purpose:

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

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 REAL array, dimension (LDA,N) Details of the QL factorization of the original matrix A as returned by SGEQLF.
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= M.
[in]	TAU	TAU is REAL array, dimension (N) Details of the orthogonal matrix Q.
[in,out]	B	B is REAL 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 REAL 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 sgeqls.f.

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

SGEQRS

Purpose:

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

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 REAL array, dimension (LDA,N) Details of the QR factorization of the original matrix A as returned by SGEQRF.
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= M.
[in]	TAU	TAU is REAL array, dimension (N) Details of the orthogonal matrix Q.
[in,out]	B	B is REAL 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 REAL 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 sgeqrs.f.

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

SGERQS

Purpose:

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

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 REAL array, dimension (LDA,N) Details of the RQ factorization of the original matrix A as returned by SGERQF.
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= M.
[in]	TAU	TAU is REAL array, dimension (M) Details of the orthogonal matrix Q.
[in,out]	B	B is REAL 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 REAL 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 sgerqs.f.

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subroutine sget01	(	integer	M,
		integer	N,
		real, dimension( lda, * )	A,
		integer	LDA,
		real, dimension( ldafac, * )	AFAC,
		integer	LDAFAC,
		integer, dimension( * )	IPIV,
		real, dimension( * )	RWORK,
		real	RESID
	)

SGET01

Purpose:

 SGET01 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 REAL 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 REAL 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 SGETRF. 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 SGETRF.
[out]	RWORK	RWORK is REAL array, dimension (M)
[out]	RESID	RESID is REAL 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 sget01.f.

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subroutine sget02	(	character	TRANS,
		integer	M,
		integer	N,
		integer	NRHS,
		real, dimension( lda, * )	A,
		integer	LDA,
		real, dimension( ldx, * )	X,
		integer	LDX,
		real, dimension( ldb, * )	B,
		integer	LDB,
		real, dimension( * )	RWORK,
		real	RESID
	)

SGET02

Purpose:

 SGET02 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 REAL 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 REAL 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 REAL 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 REAL array, dimension (M)
[out]	RESID	RESID is REAL 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 sget02.f.

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subroutine sget03	(	integer	N,
		real, dimension( lda, * )	A,
		integer	LDA,
		real, dimension( ldainv, * )	AINV,
		integer	LDAINV,
		real, dimension( ldwork, * )	WORK,
		integer	LDWORK,
		real, dimension( * )	RWORK,
		real	RCOND,
		real	RESID
	)

SGET03

Purpose:

 SGET03 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 REAL 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 REAL 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 REAL array, dimension (LDWORK,N)
[in]	LDWORK	LDWORK is INTEGER The leading dimension of the array WORK. LDWORK >= max(1,N).
[out]	RWORK	RWORK is REAL array, dimension (N)
[out]	RCOND	RCOND is REAL The reciprocal of the condition number of A, computed as ( 1/norm(A) ) / norm(AINV).
[out]	RESID	RESID is REAL 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 sget03.f.

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subroutine sget04	(	integer	N,
		integer	NRHS,
		real, dimension( ldx, * )	X,
		integer	LDX,
		real, dimension( ldxact, * )	XACT,
		integer	LDXACT,
		real	RCOND,
		real	RESID
	)

SGET04

Purpose:

 SGET04 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 REAL 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 REAL 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 REAL The reciprocal of the condition number of the coefficient matrix in the system of equations.
[out]	RESID	RESID is REAL 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 sget04.f.

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REAL function sget06	(	real	RCOND,
		real	RCONDC
	)

SGET06

Purpose:

 SGET06 computes a test ratio to compare two values for RCOND.

Parameters:

[in]	RCOND	RCOND is REAL The estimate of the reciprocal of the condition number of A, as computed by SGECON.
[in]	RCONDC	RCONDC is REAL 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 sget06.f.

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subroutine sget07	(	character	TRANS,
		integer	N,
		integer	NRHS,
		real, dimension( lda, * )	A,
		integer	LDA,
		real, dimension( ldb, * )	B,
		integer	LDB,
		real, dimension( ldx, * )	X,
		integer	LDX,
		real, dimension( ldxact, * )	XACT,
		integer	LDXACT,
		real, dimension( * )	FERR,
		logical	CHKFERR,
		real, dimension( * )	BERR,
		real, dimension( * )	RESLTS
	)

SGET07

Purpose:

 SGET07 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 REAL 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 REAL 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 REAL 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 REAL 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 REAL 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 REAL 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 REAL 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 sget07.f.

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subroutine sgtt01	(	integer	N,
		real, dimension( * )	DL,
		real, dimension( * )	D,
		real, dimension( * )	DU,
		real, dimension( * )	DLF,
		real, dimension( * )	DF,
		real, dimension( * )	DUF,
		real, dimension( * )	DU2,
		integer, dimension( * )	IPIV,
		real, dimension( ldwork, * )	WORK,
		integer	LDWORK,
		real, dimension( * )	RWORK,
		real	RESID
	)

SGTT01

Purpose:

 SGTT01 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 REAL array, dimension (N-1) The (n-1) sub-diagonal elements of A.
[in]	D	D is REAL array, dimension (N) The diagonal elements of A.
[in]	DU	DU is REAL array, dimension (N-1) The (n-1) super-diagonal elements of A.
[in]	DLF	DLF is REAL array, dimension (N-1) The (n-1) multipliers that define the matrix L from the LU factorization of A.
[in]	DF	DF is REAL array, dimension (N) The n diagonal elements of the upper triangular matrix U from the LU factorization of A.
[in]	DUF	DUF is REAL array, dimension (N-1) The (n-1) elements of the first super-diagonal of U.
[in]	DU2	DU2 is REAL 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 REAL array, dimension (LDWORK,N)
[in]	LDWORK	LDWORK is INTEGER The leading dimension of the array WORK. LDWORK >= max(1,N).
[out]	RWORK	RWORK is REAL array, dimension (N)
[out]	RESID	RESID is REAL 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 sgtt01.f.

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subroutine sgtt02	(	character	TRANS,
		integer	N,
		integer	NRHS,
		real, dimension( * )	DL,
		real, dimension( * )	D,
		real, dimension( * )	DU,
		real, dimension( ldx, * )	X,
		integer	LDX,
		real, dimension( ldb, * )	B,
		integer	LDB,
		real	RESID
	)

SGTT02

Purpose:

 SGTT02 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 REAL array, dimension (N-1) The (n-1) sub-diagonal elements of A.
[in]	D	D is REAL array, dimension (N) The diagonal elements of A.
[in]	DU	DU is REAL array, dimension (N-1) The (n-1) super-diagonal elements of A.
[in]	X	X is REAL 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 REAL 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 REAL 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 sgtt02.f.

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subroutine sgtt05	(	character	TRANS,
		integer	N,
		integer	NRHS,
		real, dimension( * )	DL,
		real, dimension( * )	D,
		real, dimension( * )	DU,
		real, dimension( ldb, * )	B,
		integer	LDB,
		real, dimension( ldx, * )	X,
		integer	LDX,
		real, dimension( ldxact, * )	XACT,
		integer	LDXACT,
		real, dimension( * )	FERR,
		real, dimension( * )	BERR,
		real, dimension( * )	RESLTS
	)

SGTT05

Purpose:

 SGTT05 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 REAL array, dimension (N-1) The (n-1) sub-diagonal elements of A.
[in]	D	D is REAL array, dimension (N) The diagonal elements of A.
[in]	DU	DU is REAL array, dimension (N-1) The (n-1) super-diagonal elements of A.
[in]	B	B is REAL 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 REAL 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 REAL 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 REAL 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 REAL 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 REAL 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 sgtt05.f.

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

SLAHILB

Purpose:

 SLAHILB 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 REAL 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 REAL 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 REAL 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 REAL 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 slahilb.f.

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subroutine slaord	(	character	JOB,
		integer	N,
		real, dimension( * )	X,
		integer	INCX
	)

SLAORD

Purpose:

 SLAORD 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 REAL 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 slaord.f.

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subroutine slaptm	(	integer	N,
		integer	NRHS,
		real	ALPHA,
		real, dimension( * )	D,
		real, dimension( * )	E,
		real, dimension( ldx, * )	X,
		integer	LDX,
		real	BETA,
		real, dimension( ldb, * )	B,
		integer	LDB
	)

SLAPTM

Purpose:

 SLAPTM 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 REAL The scalar alpha. ALPHA must be 1. or -1.; otherwise, it is assumed to be 0.
[in]	D	D is REAL array, dimension (N) The n diagonal elements of the tridiagonal matrix A.
[in]	E	E is REAL array, dimension (N-1) The (n-1) subdiagonal or superdiagonal elements of A.
[in]	X	X is REAL 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 REAL The scalar beta. BETA must be 0., 1., or -1.; otherwise, it is assumed to be 1.
[in,out]	B	B is REAL 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 slaptm.f.

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

SLARHS

Purpose:

 SLARHS 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 REAL 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) REAL 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 REAL 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 SLATMS). 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 slarhs.f.

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subroutine slatb4	(	character*3	PATH,
		integer	IMAT,
		integer	M,
		integer	N,
		character	TYPE,
		integer	KL,
		integer	KU,
		real	ANORM,
		integer	MODE,
		real	CNDNUM,
		character	DIST
	)

SLATB4

Purpose:

 SLATB4 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 REAL 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 REAL 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 slatb4.f.

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subroutine slatb5	(	character*3	PATH,
		integer	IMAT,
		integer	N,
		character	TYPE,
		integer	KL,
		integer	KU,
		real	ANORM,
		integer	MODE,
		real	CNDNUM,
		character	DIST
	)

SLATB5

Purpose:

 SLATB5 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 REAL 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 REAL 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 slatb5.f.

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

SLATTB

Purpose:

 SLATTB 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 SLATMS). 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 REAL 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 REAL array, dimension (N)
[out]	WORK	WORK is REAL 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 slattb.f.

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subroutine slattp	(	integer	IMAT,
		character	UPLO,
		character	TRANS,
		character	DIAG,
		integer, dimension( 4 )	ISEED,
		integer	N,
		real, dimension( * )	A,
		real, dimension( * )	B,
		real, dimension( * )	WORK,
		integer	INFO
	)

SLATTP

Purpose:

 SLATTP 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 SLATMS). Modified on exit.
[in]	N	N is INTEGER The order of the matrix to be generated.
[out]	A	A is REAL 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 REAL array, dimension (N) The right hand side vector, if IMAT > 10.
[out]	WORK	WORK is REAL 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 slattp.f.

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

SLATTR

Purpose:

 SLATTR 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 SLATMS). Modified on exit.
[in]	N	N is INTEGER The order of the matrix to be generated.
[out]	A	A is REAL 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 REAL array, dimension (N) The right hand side vector, if IMAT > 10.
[out]	WORK	WORK is REAL 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 slattr.f.

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subroutine slavsp	(	character	UPLO,
		character	TRANS,
		character	DIAG,
		integer	N,
		integer	NRHS,
		real, dimension( * )	A,
		integer, dimension( * )	IPIV,
		real, dimension( ldb, * )	B,
		integer	LDB,
		integer	INFO
	)

SLAVSP

Purpose:

 SLAVSP  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 SSPTRF.

 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 REAL 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 SSPTRF.
[in]	IPIV	IPIV is INTEGER array, dimension (N) The pivot indices from SSPTRF.
[in,out]	B	B is REAL 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 slavsp.f.

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

SLAVSY

Purpose:

 SLAVSY  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 SSYTRF.

 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 REAL array, dimension (LDA,N) The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by SSYTRF.
[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 SSYTRF. 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 REAL 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 slavsy.f.

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subroutine slqt01	(	integer	M,
		integer	N,
		real, dimension( lda, * )	A,
		real, dimension( lda, * )	AF,
		real, dimension( lda, * )	Q,
		real, dimension( lda, * )	L,
		integer	LDA,
		real, dimension( * )	TAU,
		real, dimension( lwork )	WORK,
		integer	LWORK,
		real, dimension( * )	RWORK,
		real, dimension( * )	RESULT
	)

SLQT01

Purpose:

 SLQT01 tests SGELQF, which computes the LQ factorization of an m-by-n
 matrix A, and partially tests SORGLQ which forms the n-by-n
 orthogonal matrix Q.

 SLQT01 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 REAL array, dimension (LDA,N) The m-by-n matrix A.
[out]	AF	AF is REAL array, dimension (LDA,N) Details of the LQ factorization of A, as returned by SGELQF. See SGELQF for further details.
[out]	Q	Q is REAL array, dimension (LDA,N) The n-by-n orthogonal matrix Q.
[out]	L	L is REAL 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 REAL array, dimension (min(M,N)) The scalar factors of the elementary reflectors, as returned by SGELQF.
[out]	WORK	WORK is REAL array, dimension (LWORK)
[in]	LWORK	LWORK is INTEGER The dimension of the array WORK.
[out]	RWORK	RWORK is REAL array, dimension (max(M,N))
[out]	RESULT	RESULT is REAL 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 slqt01.f.

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subroutine slqt02	(	integer	M,
		integer	N,
		integer	K,
		real, dimension( lda, * )	A,
		real, dimension( lda, * )	AF,
		real, dimension( lda, * )	Q,
		real, dimension( lda, * )	L,
		integer	LDA,
		real, dimension( * )	TAU,
		real, dimension( lwork )	WORK,
		integer	LWORK,
		real, dimension( * )	RWORK,
		real, dimension( * )	RESULT
	)

SLQT02

Purpose:

 SLQT02 tests SORGLQ, 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, SLQT02 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 REAL array, dimension (LDA,N) The m-by-n matrix A which was factorized by SLQT01.
[in]	AF	AF is REAL array, dimension (LDA,N) Details of the LQ factorization of A, as returned by SGELQF. See SGELQF for further details.
[out]	Q	Q is REAL array, dimension (LDA,N)
[out]	L	L is REAL 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 REAL array, dimension (M) The scalar factors of the elementary reflectors corresponding to the LQ factorization in AF.
[out]	WORK	WORK is REAL array, dimension (LWORK)
[in]	LWORK	LWORK is INTEGER The dimension of the array WORK.
[out]	RWORK	RWORK is REAL array, dimension (M)
[out]	RESULT	RESULT is REAL 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 slqt02.f.

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subroutine slqt03	(	integer	M,
		integer	N,
		integer	K,
		real, dimension( lda, * )	AF,
		real, dimension( lda, * )	C,
		real, dimension( lda, * )	CC,
		real, dimension( lda, * )	Q,
		integer	LDA,
		real, dimension( * )	TAU,
		real, dimension( lwork )	WORK,
		integer	LWORK,
		real, dimension( * )	RWORK,
		real, dimension( * )	RESULT
	)

SLQT03

Purpose:

 SLQT03 tests SORMLQ, which computes Q*C, Q'*C, C*Q or C*Q'.

 SLQT03 compares the results of a call to SORMLQ with the results of
 forming Q explicitly by a call to SORGLQ and then performing matrix
 multiplication by a call to SGEMM.

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 REAL array, dimension (LDA,N) Details of the LQ factorization of an m-by-n matrix, as returned by SGELQF. See SGELQF for further details.
[out]	C	C is REAL array, dimension (LDA,N)
[out]	CC	CC is REAL array, dimension (LDA,N)
[out]	Q	Q is REAL array, dimension (LDA,N)
[in]	LDA	LDA is INTEGER The leading dimension of the arrays AF, C, CC, and Q.
[in]	TAU	TAU is REAL array, dimension (min(M,N)) The scalar factors of the elementary reflectors corresponding to the LQ factorization in AF.
[out]	WORK	WORK is REAL 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 REAL array, dimension (M)
[out]	RESULT	RESULT is REAL 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 slqt03.f.

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subroutine spbt01	(	character	UPLO,
		integer	N,
		integer	KD,
		real, dimension( lda, * )	A,
		integer	LDA,
		real, dimension( ldafac, * )	AFAC,
		integer	LDAFAC,
		real, dimension( * )	RWORK,
		real	RESID
	)

SPBT01

Purpose:

 SPBT01 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 REAL 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 SPBTRF for further details.
[in]	LDA	LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,KD+1).
[in]	AFAC	AFAC is REAL 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 SPBTRF.
[in]	LDAFAC	LDAFAC is INTEGER The leading dimension of the array AFAC. LDAFAC >= max(1,KD+1).
[out]	RWORK	RWORK is REAL array, dimension (N)
[out]	RESID	RESID is REAL 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 spbt01.f.

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subroutine spbt02	(	character	UPLO,
		integer	N,
		integer	KD,
		integer	NRHS,
		real, dimension( lda, * )	A,
		integer	LDA,
		real, dimension( ldx, * )	X,
		integer	LDX,
		real, dimension( ldb, * )	B,
		integer	LDB,
		real, dimension( * )	RWORK,
		real	RESID
	)

SPBT02

Purpose:

 SPBT02 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 REAL 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 SPBTRF for further details.
[in]	LDA	LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,KD+1).
[in]	X	X is REAL 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 REAL 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 REAL array, dimension (N)
[out]	RESID	RESID is REAL 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 spbt02.f.

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subroutine spbt05	(	character	UPLO,
		integer	N,
		integer	KD,
		integer	NRHS,
		real, dimension( ldab, * )	AB,
		integer	LDAB,
		real, dimension( ldb, * )	B,
		integer	LDB,
		real, dimension( ldx, * )	X,
		integer	LDX,
		real, dimension( ldxact, * )	XACT,
		integer	LDXACT,
		real, dimension( * )	FERR,
		real, dimension( * )	BERR,
		real, dimension( * )	RESLTS
	)

SPBT05

Purpose:

 SPBT05 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 REAL 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 REAL 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 REAL 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 REAL 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 REAL 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 REAL 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 REAL 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 spbt05.f.

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subroutine spot01	(	character	UPLO,
		integer	N,
		real, dimension( lda, * )	A,
		integer	LDA,
		real, dimension( ldafac, * )	AFAC,
		integer	LDAFAC,
		real, dimension( * )	RWORK,
		real	RESID
	)

SPOT01

Purpose:

 SPOT01 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 REAL 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 REAL 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 REAL array, dimension (N)
[out]	RESID	RESID is REAL 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 spot01.f.

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subroutine spot02	(	character	UPLO,
		integer	N,
		integer	NRHS,
		real, dimension( lda, * )	A,
		integer	LDA,
		real, dimension( ldx, * )	X,
		integer	LDX,
		real, dimension( ldb, * )	B,
		integer	LDB,
		real, dimension( * )	RWORK,
		real	RESID
	)

SPOT02

Purpose:

 SPOT02 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 REAL 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 REAL 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 REAL 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 REAL array, dimension (N)
[out]	RESID	RESID is REAL 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 spot02.f.

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subroutine spot03	(	character	UPLO,
		integer	N,
		real, dimension( lda, * )	A,
		integer	LDA,
		real, dimension( ldainv, * )	AINV,
		integer	LDAINV,
		real, dimension( ldwork, * )	WORK,
		integer	LDWORK,
		real, dimension( * )	RWORK,
		real	RCOND,
		real	RESID
	)

SPOT03

Purpose:

 SPOT03 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 REAL 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 REAL 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 REAL array, dimension (LDWORK,N)
[in]	LDWORK	LDWORK is INTEGER The leading dimension of the array WORK. LDWORK >= max(1,N).
[out]	RWORK	RWORK is REAL array, dimension (N)
[out]	RCOND	RCOND is REAL The reciprocal of the condition number of A, computed as ( 1/norm(A) ) / norm(AINV).
[out]	RESID	RESID is REAL 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 spot03.f.

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subroutine spot05	(	character	UPLO,
		integer	N,
		integer	NRHS,
		real, dimension( lda, * )	A,
		integer	LDA,
		real, dimension( ldb, * )	B,
		integer	LDB,
		real, dimension( ldx, * )	X,
		integer	LDX,
		real, dimension( ldxact, * )	XACT,
		integer	LDXACT,
		real, dimension( * )	FERR,
		real, dimension( * )	BERR,
		real, dimension( * )	RESLTS
	)

SPOT05

Purpose:

 SPOT05 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 REAL 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 REAL 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 REAL 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 REAL 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 REAL 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 REAL 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 REAL 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 spot05.f.

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subroutine sppt01	(	character	UPLO,
		integer	N,
		real, dimension( * )	A,
		real, dimension( * )	AFAC,
		real, dimension( * )	RWORK,
		real	RESID
	)

SPPT01

Purpose:

 SPPT01 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 REAL array, dimension (N*(N+1)/2) The original symmetric matrix A, stored as a packed triangular matrix.
[in,out]	AFAC	AFAC is REAL 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 REAL array, dimension (N)
[out]	RESID	RESID is REAL 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 sppt01.f.

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subroutine sppt02	(	character	UPLO,
		integer	N,
		integer	NRHS,
		real, dimension( * )	A,
		real, dimension( ldx, * )	X,
		integer	LDX,
		real, dimension( ldb, * )	B,
		integer	LDB,
		real, dimension( * )	RWORK,
		real	RESID
	)

SPPT02

Purpose:

 SPPT02 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 REAL array, dimension (N*(N+1)/2) The original symmetric matrix A, stored as a packed triangular matrix.
[in]	X	X is REAL 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 REAL 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 REAL array, dimension (N)
[out]	RESID	RESID is REAL 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 sppt02.f.

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subroutine sppt03	(	character	UPLO,
		integer	N,
		real, dimension( * )	A,
		real, dimension( * )	AINV,
		real, dimension( ldwork, * )	WORK,
		integer	LDWORK,
		real, dimension( * )	RWORK,
		real	RCOND,
		real	RESID
	)

SPPT03

Purpose:

 SPPT03 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 REAL array, dimension (N*(N+1)/2) The original symmetric matrix A, stored as a packed triangular matrix.
[in]	AINV	AINV is REAL array, dimension (N*(N+1)/2) The (symmetric) inverse of the matrix A, stored as a packed triangular matrix.
[out]	WORK	WORK is REAL array, dimension (LDWORK,N)
[in]	LDWORK	LDWORK is INTEGER The leading dimension of the array WORK. LDWORK >= max(1,N).
[out]	RWORK	RWORK is REAL array, dimension (N)
[out]	RCOND	RCOND is REAL The reciprocal of the condition number of A, computed as ( 1/norm(A) ) / norm(AINV).
[out]	RESID	RESID is REAL 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 sppt03.f.

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subroutine sppt05	(	character	UPLO,
		integer	N,
		integer	NRHS,
		real, dimension( * )	AP,
		real, dimension( ldb, * )	B,
		integer	LDB,
		real, dimension( ldx, * )	X,
		integer	LDX,
		real, dimension( ldxact, * )	XACT,
		integer	LDXACT,
		real, dimension( * )	FERR,
		real, dimension( * )	BERR,
		real, dimension( * )	RESLTS
	)

SPPT05

Purpose:

 SPPT05 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 REAL 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 REAL 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 REAL 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 REAL 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 REAL 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 REAL 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 REAL 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 sppt05.f.

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subroutine spst01	(	character	UPLO,
		integer	N,
		real, dimension( lda, * )	A,
		integer	LDA,
		real, dimension( ldafac, * )	AFAC,
		integer	LDAFAC,
		real, dimension( ldperm, * )	PERM,
		integer	LDPERM,
		integer, dimension( * )	PIV,
		real, dimension( * )	RWORK,
		real	RESID,
		integer	RANK
	)

SPST01

Purpose:

 SPST01 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 REAL 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 REAL 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 REAL 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 REAL array, dimension (N)
[out]	RESID	RESID is REAL 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 spst01.f.

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subroutine sptt01	(	integer	N,
		real, dimension( * )	D,
		real, dimension( * )	E,
		real, dimension( * )	DF,
		real, dimension( * )	EF,
		real, dimension( * )	WORK,
		real	RESID
	)

SPTT01

Purpose:

 SPTT01 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 REAL array, dimension (N) The n diagonal elements of the tridiagonal matrix A.
[in]	E	E is REAL array, dimension (N-1) The (n-1) subdiagonal elements of the tridiagonal matrix A.
[in]	DF	DF is REAL array, dimension (N) The n diagonal elements of the factor L from the LDL' factorization of A.
[in]	EF	EF is REAL array, dimension (N-1) The (n-1) subdiagonal elements of the factor L from the LDL' factorization of A.
[out]	WORK	WORK is REAL array, dimension (2*N)
[out]	RESID	RESID is REAL 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 sptt01.f.

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subroutine sptt02	(	integer	N,
		integer	NRHS,
		real, dimension( * )	D,
		real, dimension( * )	E,
		real, dimension( ldx, * )	X,
		integer	LDX,
		real, dimension( ldb, * )	B,
		integer	LDB,
		real	RESID
	)

SPTT02

Purpose:

 SPTT02 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 REAL array, dimension (N) The n diagonal elements of the tridiagonal matrix A.
[in]	E	E is REAL array, dimension (N-1) The (n-1) subdiagonal elements of the tridiagonal matrix A.
[in]	X	X is REAL 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 REAL 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 REAL 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 sptt02.f.

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subroutine sptt05	(	integer	N,
		integer	NRHS,
		real, dimension( * )	D,
		real, dimension( * )	E,
		real, dimension( ldb, * )	B,
		integer	LDB,
		real, dimension( ldx, * )	X,
		integer	LDX,
		real, dimension( ldxact, * )	XACT,
		integer	LDXACT,
		real, dimension( * )	FERR,
		real, dimension( * )	BERR,
		real, dimension( * )	RESLTS
	)

SPTT05

Purpose:

 SPTT05 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 REAL array, dimension (N) The n diagonal elements of the tridiagonal matrix A.
[in]	E	E is REAL array, dimension (N-1) The (n-1) subdiagonal elements of the tridiagonal matrix A.
[in]	B	B is REAL 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 REAL 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 REAL 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 REAL 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 REAL 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 REAL 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 sptt05.f.

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subroutine sqlt01	(	integer	M,
		integer	N,
		real, dimension( lda, * )	A,
		real, dimension( lda, * )	AF,
		real, dimension( lda, * )	Q,
		real, dimension( lda, * )	L,
		integer	LDA,
		real, dimension( * )	TAU,
		real, dimension( lwork )	WORK,
		integer	LWORK,
		real, dimension( * )	RWORK,
		real, dimension( * )	RESULT
	)

SQLT01

Purpose:

 SQLT01 tests SGEQLF, which computes the QL factorization of an m-by-n
 matrix A, and partially tests SORGQL which forms the m-by-m
 orthogonal matrix Q.

 SQLT01 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 REAL array, dimension (LDA,N) The m-by-n matrix A.
[out]	AF	AF is REAL array, dimension (LDA,N) Details of the QL factorization of A, as returned by SGEQLF. See SGEQLF for further details.
[out]	Q	Q is REAL array, dimension (LDA,M) The m-by-m orthogonal matrix Q.
[out]	L	L is REAL 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 REAL array, dimension (min(M,N)) The scalar factors of the elementary reflectors, as returned by SGEQLF.
[out]	WORK	WORK is REAL array, dimension (LWORK)
[in]	LWORK	LWORK is INTEGER The dimension of the array WORK.
[out]	RWORK	RWORK is REAL array, dimension (M)
[out]	RESULT	RESULT is REAL 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 sqlt01.f.

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subroutine sqlt02	(	integer	M,
		integer	N,
		integer	K,
		real, dimension( lda, * )	A,
		real, dimension( lda, * )	AF,
		real, dimension( lda, * )	Q,
		real, dimension( lda, * )	L,
		integer	LDA,
		real, dimension( * )	TAU,
		real, dimension( lwork )	WORK,
		integer	LWORK,
		real, dimension( * )	RWORK,
		real, dimension( * )	RESULT
	)

SQLT02

Purpose:

 SQLT02 tests SORGQL, 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, SQLT02 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 REAL array, dimension (LDA,N) The m-by-n matrix A which was factorized by SQLT01.
[in]	AF	AF is REAL array, dimension (LDA,N) Details of the QL factorization of A, as returned by SGEQLF. See SGEQLF for further details.
[out]	Q	Q is REAL array, dimension (LDA,N)
[out]	L	L is REAL 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 REAL array, dimension (N) The scalar factors of the elementary reflectors corresponding to the QL factorization in AF.
[out]	WORK	WORK is REAL array, dimension (LWORK)
[in]	LWORK	LWORK is INTEGER The dimension of the array WORK.
[out]	RWORK	RWORK is REAL array, dimension (M)
[out]	RESULT	RESULT is REAL 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 sqlt02.f.

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subroutine sqlt03	(	integer	M,
		integer	N,
		integer	K,
		real, dimension( lda, * )	AF,
		real, dimension( lda, * )	C,
		real, dimension( lda, * )	CC,
		real, dimension( lda, * )	Q,
		integer	LDA,
		real, dimension( * )	TAU,
		real, dimension( lwork )	WORK,
		integer	LWORK,
		real, dimension( * )	RWORK,
		real, dimension( * )	RESULT
	)

SQLT03

Purpose:

 SQLT03 tests SORMQL, which computes Q*C, Q'*C, C*Q or C*Q'.

 SQLT03 compares the results of a call to SORMQL with the results of
 forming Q explicitly by a call to SORGQL and then performing matrix
 multiplication by a call to SGEMM.

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 REAL array, dimension (LDA,N) Details of the QL factorization of an m-by-n matrix, as returned by SGEQLF. See SGEQLF for further details.
[out]	C	C is REAL array, dimension (LDA,N)
[out]	CC	CC is REAL array, dimension (LDA,N)
[out]	Q	Q is REAL array, dimension (LDA,M)
[in]	LDA	LDA is INTEGER The leading dimension of the arrays AF, C, CC, and Q.
[in]	TAU	TAU is REAL array, dimension (min(M,N)) The scalar factors of the elementary reflectors corresponding to the QL factorization in AF.
[out]	WORK	WORK is REAL 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 REAL array, dimension (M)
[out]	RESULT	RESULT is REAL 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 sqlt03.f.

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REAL function sqpt01	(	integer	M,
		integer	N,
		integer	K,
		real, dimension( lda, * )	A,
		real, dimension( lda, * )	AF,
		integer	LDA,
		real, dimension( * )	TAU,
		integer, dimension( * )	JPVT,
		real, dimension( lwork )	WORK,
		integer	LWORK
	)

SQPT01

Purpose:

 SQPT01 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 REAL array, dimension (LDA, N) The original matrix A.
[in]	AF	AF is REAL array, dimension (LDA,N) The (possibly partial) output of SGEQPF. 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 REAL array, dimension (K) Details of the Householder transformations as returned by SGEQPF.
[in]	JPVT	JPVT is INTEGER array, dimension (N) Pivot information as returned by SGEQPF.
[out]	WORK	WORK is REAL 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 sqpt01.f.

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subroutine sqrt01	(	integer	M,
		integer	N,
		real, dimension( lda, * )	A,
		real, dimension( lda, * )	AF,
		real, dimension( lda, * )	Q,
		real, dimension( lda, * )	R,
		integer	LDA,
		real, dimension( * )	TAU,
		real, dimension( lwork )	WORK,
		integer	LWORK,
		real, dimension( * )	RWORK,
		real, dimension( * )	RESULT
	)

SQRT01

Purpose:

 SQRT01 tests SGEQRF, which computes the QR factorization of an m-by-n
 matrix A, and partially tests SORGQR which forms the m-by-m
 orthogonal matrix Q.

 SQRT01 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 REAL array, dimension (LDA,N) The m-by-n matrix A.
[out]	AF	AF is REAL array, dimension (LDA,N) Details of the QR factorization of A, as returned by SGEQRF. See SGEQRF for further details.
[out]	Q	Q is REAL array, dimension (LDA,M) The m-by-m orthogonal matrix Q.
[out]	R	R is REAL 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 REAL array, dimension (min(M,N)) The scalar factors of the elementary reflectors, as returned by SGEQRF.
[out]	WORK	WORK is REAL array, dimension (LWORK)
[in]	LWORK	LWORK is INTEGER The dimension of the array WORK.
[out]	RWORK	RWORK is REAL array, dimension (M)
[out]	RESULT	RESULT is REAL 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 sqrt01.f.

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subroutine sqrt01p	(	integer	M,
		integer	N,
		real, dimension( lda, * )	A,
		real, dimension( lda, * )	AF,
		real, dimension( lda, * )	Q,
		real, dimension( lda, * )	R,
		integer	LDA,
		real, dimension( * )	TAU,
		real, dimension( lwork )	WORK,
		integer	LWORK,
		real, dimension( * )	RWORK,
		real, dimension( * )	RESULT
	)

SQRT01P

Purpose:

 SQRT01P tests SGEQRFP, which computes the QR factorization of an m-by-n
 matrix A, and partially tests SORGQR which forms the m-by-m
 orthogonal matrix Q.

 SQRT01P 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 REAL array, dimension (LDA,N) The m-by-n matrix A.
[out]	AF	AF is REAL array, dimension (LDA,N) Details of the QR factorization of A, as returned by SGEQRFP. See SGEQRFP for further details.
[out]	Q	Q is REAL array, dimension (LDA,M) The m-by-m orthogonal matrix Q.
[out]	R	R is REAL 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 REAL array, dimension (min(M,N)) The scalar factors of the elementary reflectors, as returned by SGEQRFP.
[out]	WORK	WORK is REAL array, dimension (LWORK)
[in]	LWORK	LWORK is INTEGER The dimension of the array WORK.
[out]	RWORK	RWORK is REAL array, dimension (M)
[out]	RESULT	RESULT is REAL 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 sqrt01p.f.

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subroutine sqrt02	(	integer	M,
		integer	N,
		integer	K,
		real, dimension( lda, * )	A,
		real, dimension( lda, * )	AF,
		real, dimension( lda, * )	Q,
		real, dimension( lda, * )	R,
		integer	LDA,
		real, dimension( * )	TAU,
		real, dimension( lwork )	WORK,
		integer	LWORK,
		real, dimension( * )	RWORK,
		real, dimension( * )	RESULT
	)

SQRT02

Purpose:

 SQRT02 tests SORGQR, 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, SQRT02 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 REAL array, dimension (LDA,N) The m-by-n matrix A which was factorized by SQRT01.
[in]	AF	AF is REAL array, dimension (LDA,N) Details of the QR factorization of A, as returned by SGEQRF. See SGEQRF for further details.
[out]	Q	Q is REAL array, dimension (LDA,N)
[out]	R	R is REAL 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 REAL array, dimension (N) The scalar factors of the elementary reflectors corresponding to the QR factorization in AF.
[out]	WORK	WORK is REAL array, dimension (LWORK)
[in]	LWORK	LWORK is INTEGER The dimension of the array WORK.
[out]	RWORK	RWORK is REAL array, dimension (M)
[out]	RESULT	RESULT is REAL 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 sqrt02.f.

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subroutine sqrt03	(	integer	M,
		integer	N,
		integer	K,
		real, dimension( lda, * )	AF,
		real, dimension( lda, * )	C,
		real, dimension( lda, * )	CC,
		real, dimension( lda, * )	Q,
		integer	LDA,
		real, dimension( * )	TAU,
		real, dimension( lwork )	WORK,
		integer	LWORK,
		real, dimension( * )	RWORK,
		real, dimension( * )	RESULT
	)

SQRT03

Purpose:

 SQRT03 tests SORMQR, which computes Q*C, Q'*C, C*Q or C*Q'.

 SQRT03 compares the results of a call to SORMQR with the results of
 forming Q explicitly by a call to SORGQR and then performing matrix
 multiplication by a call to SGEMM.

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 REAL array, dimension (LDA,N) Details of the QR factorization of an m-by-n matrix, as returnedby SGEQRF. See SGEQRF for further details.
[out]	C	C is REAL array, dimension (LDA,N)
[out]	CC	CC is REAL array, dimension (LDA,N)
[out]	Q	Q is REAL array, dimension (LDA,M)
[in]	LDA	LDA is INTEGER The leading dimension of the arrays AF, C, CC, and Q.
[in]	TAU	TAU is REAL array, dimension (min(M,N)) The scalar factors of the elementary reflectors corresponding to the QR factorization in AF.
[out]	WORK	WORK is REAL 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 REAL array, dimension (M)
[out]	RESULT	RESULT is REAL 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 sqrt03.f.

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subroutine sqrt04	(	integer	M,
		integer	N,
		integer	NB,
		real, dimension(6)	RESULT
	)

SQRT04

Purpose:

 SQRT04 tests SGEQRT and SGEMQRT.

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 REAL 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 sqrt04.f.

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subroutine sqrt05	(	integer	M,
		integer	N,
		integer	L,
		integer	NB,
		real, dimension(6)	RESULT
	)

SQRT05

Purpose:

 SQRT05 tests STPQRT and STPMQRT.

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 REAL 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 sqrt05.f.

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REAL function sqrt11	(	integer	M,
		integer	K,
		real, dimension( lda, * )	A,
		integer	LDA,
		real, dimension( * )	TAU,
		real, dimension( lwork )	WORK,
		integer	LWORK
	)

SQRT11

Purpose:

 SQRT11 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 REAL 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 REAL array, dimension (K) The scaling factors tau for the elementary transformations as computed by the QR factorization routine.
[out]	WORK	WORK is REAL 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 sqrt11.f.

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REAL function sqrt12	(	integer	M,
		integer	N,
		real, dimension( lda, * )	A,
		integer	LDA,
		real, dimension( * )	S,
		real, dimension( lwork )	WORK,
		integer	LWORK
	)

SQRT12

Purpose:

 SQRT12 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 REAL 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 REAL array, dimension (min(M,N)) The singular values of the matrix A.
[out]	WORK	WORK is REAL 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 sqrt12.f.

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subroutine sqrt13	(	integer	SCALE,
		integer	M,
		integer	N,
		real, dimension( lda, * )	A,
		integer	LDA,
		real	NORMA,
		integer, dimension( 4 )	ISEED
	)

SQRT13

Purpose:

 SQRT13 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 REAL 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 REAL 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 sqrt13.f.

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REAL function sqrt14	(	character	TRANS,
		integer	M,
		integer	N,
		integer	NRHS,
		real, dimension( lda, * )	A,
		integer	LDA,
		real, dimension( ldx, * )	X,
		integer	LDX,
		real, dimension( lwork )	WORK,
		integer	LWORK
	)

SQRT14

Purpose:

 SQRT14 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 REAL 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 REAL 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 REAL 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 sqrt14.f.

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subroutine sqrt15	(	integer	SCALE,
		integer	RKSEL,
		integer	M,
		integer	N,
		integer	NRHS,
		real, dimension( lda, * )	A,
		integer	LDA,
		real, dimension( ldb, * )	B,
		integer	LDB,
		real, dimension( * )	S,
		integer	RANK,
		real	NORMA,
		real	NORMB,
		integer, dimension( 4 )	ISEED,
		real, dimension( lwork )	WORK,
		integer	LWORK
	)

SQRT15

Purpose:

 SQRT15 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 REAL 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 REAL 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 REAL 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 REAL one-norm of A.
[out]	NORMB	NORMB is REAL one-norm of B.
[in,out]	ISEED	ISEED is integer array, dimension (4) seed for random number generator.
[out]	WORK	WORK is REAL 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 sqrt15.f.

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subroutine sqrt16	(	character	TRANS,
		integer	M,
		integer	N,
		integer	NRHS,
		real, dimension( lda, * )	A,
		integer	LDA,
		real, dimension( ldx, * )	X,
		integer	LDX,
		real, dimension( ldb, * )	B,
		integer	LDB,
		real, dimension( * )	RWORK,
		real	RESID
	)

SQRT16

Purpose:

 SQRT16 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 REAL 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 REAL 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 REAL 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 REAL array, dimension (M)
[out]	RESID	RESID is REAL 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 sqrt16.f.

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REAL function sqrt17	(	character	TRANS,
		integer	IRESID,
		integer	M,
		integer	N,
		integer	NRHS,
		real, dimension( lda, * )	A,
		integer	LDA,
		real, dimension( ldx, * )	X,
		integer	LDX,
		real, dimension( ldb, * )	B,
		integer	LDB,
		real, dimension( ldb, * )	C,
		real, dimension( lwork )	WORK,
		integer	LWORK
	)

SQRT17

Purpose:

 SQRT17 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 REAL 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 REAL 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 REAL 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 REAL array, dimension (LDB,NRHS)
[out]	WORK	WORK is REAL 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 sqrt17.f.

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subroutine srqt01	(	integer	M,
		integer	N,
		real, dimension( lda, * )	A,
		real, dimension( lda, * )	AF,
		real, dimension( lda, * )	Q,
		real, dimension( lda, * )	R,
		integer	LDA,
		real, dimension( * )	TAU,
		real, dimension( lwork )	WORK,
		integer	LWORK,
		real, dimension( * )	RWORK,
		real, dimension( * )	RESULT
	)

SRQT01

Purpose:

 SRQT01 tests SGERQF, which computes the RQ factorization of an m-by-n
 matrix A, and partially tests SORGRQ which forms the n-by-n
 orthogonal matrix Q.

 SRQT01 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 REAL array, dimension (LDA,N) The m-by-n matrix A.
[out]	AF	AF is REAL array, dimension (LDA,N) Details of the RQ factorization of A, as returned by SGERQF. See SGERQF for further details.
[out]	Q	Q is REAL array, dimension (LDA,N) The n-by-n orthogonal matrix Q.
[out]	R	R is REAL 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 REAL array, dimension (min(M,N)) The scalar factors of the elementary reflectors, as returned by SGERQF.
[out]	WORK	WORK is REAL array, dimension (LWORK)
[in]	LWORK	LWORK is INTEGER The dimension of the array WORK.
[out]	RWORK	RWORK is REAL array, dimension (max(M,N))
[out]	RESULT	RESULT is REAL 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 srqt01.f.

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subroutine srqt02	(	integer	M,
		integer	N,
		integer	K,
		real, dimension( lda, * )	A,
		real, dimension( lda, * )	AF,
		real, dimension( lda, * )	Q,
		real, dimension( lda, * )	R,
		integer	LDA,
		real, dimension( * )	TAU,
		real, dimension( lwork )	WORK,
		integer	LWORK,
		real, dimension( * )	RWORK,
		real, dimension( * )	RESULT
	)

SRQT02

Purpose:

 SRQT02 tests SORGRQ, 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, SRQT02 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 REAL array, dimension (LDA,N) The m-by-n matrix A which was factorized by SRQT01.
[in]	AF	AF is REAL array, dimension (LDA,N) Details of the RQ factorization of A, as returned by SGERQF. See SGERQF for further details.
[out]	Q	Q is REAL array, dimension (LDA,N)
[out]	R	R is REAL 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 REAL array, dimension (M) The scalar factors of the elementary reflectors corresponding to the RQ factorization in AF.
[out]	WORK	WORK is REAL array, dimension (LWORK)
[in]	LWORK	LWORK is INTEGER The dimension of the array WORK.
[out]	RWORK	RWORK is REAL array, dimension (M)
[out]	RESULT	RESULT is REAL 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 srqt02.f.

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subroutine srqt03	(	integer	M,
		integer	N,
		integer	K,
		real, dimension( lda, * )	AF,
		real, dimension( lda, * )	C,
		real, dimension( lda, * )	CC,
		real, dimension( lda, * )	Q,
		integer	LDA,
		real, dimension( * )	TAU,
		real, dimension( lwork )	WORK,
		integer	LWORK,
		real, dimension( * )	RWORK,
		real, dimension( * )	RESULT
	)

SRQT03

Purpose:

 SRQT03 tests SORMRQ, which computes Q*C, Q'*C, C*Q or C*Q'.

 SRQT03 compares the results of a call to SORMRQ with the results of
 forming Q explicitly by a call to SORGRQ and then performing matrix
 multiplication by a call to SGEMM.

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 REAL array, dimension (LDA,N) Details of the RQ factorization of an m-by-n matrix, as returned by SGERQF. See SGERQF for further details.
[out]	C	C is REAL array, dimension (LDA,N)
[out]	CC	CC is REAL array, dimension (LDA,N)
[out]	Q	Q is REAL array, dimension (LDA,N)
[in]	LDA	LDA is INTEGER The leading dimension of the arrays AF, C, CC, and Q.
[in]	TAU	TAU is REAL array, dimension (min(M,N)) The scalar factors of the elementary reflectors corresponding to the RQ factorization in AF.
[out]	WORK	WORK is REAL 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 REAL array, dimension (M)
[out]	RESULT	RESULT is REAL 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 srqt03.f.

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REAL function srzt01	(	integer	M,
		integer	N,
		real, dimension( lda, * )	A,
		real, dimension( lda, * )	AF,
		integer	LDA,
		real, dimension( * )	TAU,
		real, dimension( lwork )	WORK,
		integer	LWORK
	)

SRZT01

Purpose:

 SRZT01 returns
      || A - R*Q || / ( M * eps * ||A|| )
 for an upper trapezoidal A that was factored with STZRZF.

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 REAL array, dimension (LDA,N) The original upper trapezoidal M by N matrix A.
[in]	AF	AF is REAL array, dimension (LDA,N) The output of STZRZF 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 REAL array, dimension (M) Details of the Householder transformations as returned by STZRZF.
[out]	WORK	WORK is REAL 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 srzt01.f.

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REAL function srzt02	(	integer	M,
		integer	N,
		real, dimension( lda, * )	AF,
		integer	LDA,
		real, dimension( * )	TAU,
		real, dimension( lwork )	WORK,
		integer	LWORK
	)

SRZT02

Purpose:

 SRZT02 returns
      || I - Q'*Q || / ( M * eps)
 where the matrix Q is defined by the Householder transformations
 generated by STZRZF.

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 REAL array, dimension (LDA,N) The output of STZRZF.
[in]	LDA	LDA is INTEGER The leading dimension of the array AF.
[in]	TAU	TAU is REAL array, dimension (M) Details of the Householder transformations as returned by STZRZF.
[out]	WORK	WORK is REAL 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 srzt02.f.

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subroutine sspt01	(	character	UPLO,
		integer	N,
		real, dimension( * )	A,
		real, dimension( * )	AFAC,
		integer, dimension( * )	IPIV,
		real, dimension( ldc, * )	C,
		integer	LDC,
		real, dimension( * )	RWORK,
		real	RESID
	)

SSPT01

Purpose:

 SSPT01 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 REAL array, dimension (N*(N+1)/2) The original symmetric matrix A, stored as a packed triangular matrix.
[in]	AFAC	AFAC is REAL 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 SSPTRF.
[in]	IPIV	IPIV is INTEGER array, dimension (N) The pivot indices from SSPTRF.
[out]	C	C is REAL array, dimension (LDC,N)
[in]	LDC	LDC is INTEGER The leading dimension of the array C. LDC >= max(1,N).
[out]	RWORK	RWORK is REAL array, dimension (N)
[out]	RESID	RESID is REAL 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 sspt01.f.

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subroutine ssyt01	(	character	UPLO,
		integer	N,
		real, dimension( lda, * )	A,
		integer	LDA,
		real, dimension( ldafac, * )	AFAC,
		integer	LDAFAC,
		integer, dimension( * )	IPIV,
		real, dimension( ldc, * )	C,
		integer	LDC,
		real, dimension( * )	RWORK,
		real	RESID
	)

SSYT01

Purpose:

 SSYT01 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 REAL 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 REAL 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 SSYTRF.
[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 SSYTRF.
[out]	C	C is REAL array, dimension (LDC,N)
[in]	LDC	LDC is INTEGER The leading dimension of the array C. LDC >= max(1,N).
[out]	RWORK	RWORK is REAL array, dimension (N)
[out]	RESID	RESID is REAL 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:: April 2012

Definition at line 124 of file ssyt01.f.

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subroutine stbt02	(	character	UPLO,
		character	TRANS,
		character	DIAG,
		integer	N,
		integer	KD,
		integer	NRHS,
		real, dimension( ldab, * )	AB,
		integer	LDAB,
		real, dimension( ldx, * )	X,
		integer	LDX,
		real, dimension( ldb, * )	B,
		integer	LDB,
		real, dimension( * )	WORK,
		real	RESID
	)

STBT02

Purpose:

 STBT02 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 REAL 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 REAL 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 REAL 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 REAL array, dimension (N)
[out]	RESID	RESID is REAL 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 stbt02.f.

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subroutine stbt03	(	character	UPLO,
		character	TRANS,
		character	DIAG,
		integer	N,
		integer	KD,
		integer	NRHS,
		real, dimension( ldab, * )	AB,
		integer	LDAB,
		real	SCALE,
		real, dimension( * )	CNORM,
		real	TSCAL,
		real, dimension( ldx, * )	X,
		integer	LDX,
		real, dimension( ldb, * )	B,
		integer	LDB,
		real, dimension( * )	WORK,
		real	RESID
	)

STBT03

Purpose:

 STBT03 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 REAL 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 REAL The scaling factor s used in solving the triangular system.
[in]	CNORM	CNORM is REAL array, dimension (N) The 1-norms of the columns of A, not counting the diagonal.
[in]	TSCAL	TSCAL is REAL The scaling factor used in computing the 1-norms in CNORM. CNORM actually contains the column norms of TSCAL*A.
[in]	X	X is REAL 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 REAL 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 REAL array, dimension (N)
[out]	RESID	RESID is REAL 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 stbt03.f.

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subroutine stbt05	(	character	UPLO,
		character	TRANS,
		character	DIAG,
		integer	N,
		integer	KD,
		integer	NRHS,
		real, dimension( ldab, * )	AB,
		integer	LDAB,
		real, dimension( ldb, * )	B,
		integer	LDB,
		real, dimension( ldx, * )	X,
		integer	LDX,
		real, dimension( ldxact, * )	XACT,
		integer	LDXACT,
		real, dimension( * )	FERR,
		real, dimension( * )	BERR,
		real, dimension( * )	RESLTS
	)

STBT05

Purpose:

 STBT05 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 REAL 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 REAL 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 REAL 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 REAL 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 REAL 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 REAL 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 REAL 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 stbt05.f.

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subroutine stbt06	(	real	RCOND,
		real	RCONDC,
		character	UPLO,
		character	DIAG,
		integer	N,
		integer	KD,
		real, dimension( ldab, * )	AB,
		integer	LDAB,
		real, dimension( * )	WORK,
		real	RAT
	)

STBT06

Purpose:

 STBT06 computes a test ratio comparing RCOND (the reciprocal
 condition number of a triangular matrix A) and RCONDC, the estimate
 computed by STBCON.  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 REAL 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 REAL The estimate of the reciprocal condition number computed by STBCON.
[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 REAL 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 REAL array, dimension (N)
[out]	RAT	RAT is REAL 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 stbt06.f.

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subroutine stpt01	(	character	UPLO,
		character	DIAG,
		integer	N,
		real, dimension( * )	AP,
		real, dimension( * )	AINVP,
		real	RCOND,
		real, dimension( * )	WORK,
		real	RESID
	)

STPT01

Purpose:

 STPT01 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 REAL 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 REAL 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 REAL The reciprocal condition number of A, computed as 1/(norm(A) * norm(AINV)).
[out]	WORK	WORK is REAL array, dimension (N)
[out]	RESID	RESID is REAL 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 stpt01.f.

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subroutine stpt02	(	character	UPLO,
		character	TRANS,
		character	DIAG,
		integer	N,
		integer	NRHS,
		real, dimension( * )	AP,
		real, dimension( ldx, * )	X,
		integer	LDX,
		real, dimension( ldb, * )	B,
		integer	LDB,
		real, dimension( * )	WORK,
		real	RESID
	)

STPT02

Purpose:

 STPT02 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 REAL 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 REAL 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 REAL 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 REAL array, dimension (N)
[out]	RESID	RESID is REAL 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 stpt02.f.

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subroutine stpt03	(	character	UPLO,
		character	TRANS,
		character	DIAG,
		integer	N,
		integer	NRHS,
		real, dimension( * )	AP,
		real	SCALE,
		real, dimension( * )	CNORM,
		real	TSCAL,
		real, dimension( ldx, * )	X,
		integer	LDX,
		real, dimension( ldb, * )	B,
		integer	LDB,
		real, dimension( * )	WORK,
		real	RESID
	)

STPT03

Purpose:

 STPT03 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 REAL 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 REAL The scaling factor s used in solving the triangular system.
[in]	CNORM	CNORM is REAL array, dimension (N) The 1-norms of the columns of A, not counting the diagonal.
[in]	TSCAL	TSCAL is REAL The scaling factor used in computing the 1-norms in CNORM. CNORM actually contains the column norms of TSCAL*A.
[in]	X	X is REAL 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 REAL 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 REAL array, dimension (N)
[out]	RESID	RESID is REAL 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 stpt03.f.

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subroutine stpt05	(	character	UPLO,
		character	TRANS,
		character	DIAG,
		integer	N,
		integer	NRHS,
		real, dimension( * )	AP,
		real, dimension( ldb, * )	B,
		integer	LDB,
		real, dimension( ldx, * )	X,
		integer	LDX,
		real, dimension( ldxact, * )	XACT,
		integer	LDXACT,
		real, dimension( * )	FERR,
		real, dimension( * )	BERR,
		real, dimension( * )	RESLTS
	)

STPT05

Purpose:

 STPT05 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 REAL 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 REAL 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 REAL 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 REAL 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 REAL 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 REAL 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 REAL 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 stpt05.f.

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subroutine stpt06	(	real	RCOND,
		real	RCONDC,
		character	UPLO,
		character	DIAG,
		integer	N,
		real, dimension( * )	AP,
		real, dimension( * )	WORK,
		real	RAT
	)

STPT06

Purpose:

 STPT06 computes a test ratio comparing RCOND (the reciprocal
 condition number of a triangular matrix A) and RCONDC, the estimate
 computed by STPCON.  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 REAL 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 REAL The estimate of the reciprocal condition number computed by STPCON.
[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 REAL 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 REAL array, dimension (N)
[out]	RAT	RAT is REAL 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 stpt06.f.

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subroutine strt01	(	character	UPLO,
		character	DIAG,
		integer	N,
		real, dimension( lda, * )	A,
		integer	LDA,
		real, dimension( ldainv, * )	AINV,
		integer	LDAINV,
		real	RCOND,
		real, dimension( * )	WORK,
		real	RESID
	)

STRT01

Purpose:

 STRT01 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 REAL 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 REAL 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 REAL The reciprocal condition number of A, computed as 1/(norm(A) * norm(AINV)).
[out]	WORK	WORK is REAL array, dimension (N)
[out]	RESID	RESID is REAL 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 strt01.f.

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subroutine strt02	(	character	UPLO,
		character	TRANS,
		character	DIAG,
		integer	N,
		integer	NRHS,
		real, dimension( lda, * )	A,
		integer	LDA,
		real, dimension( ldx, * )	X,
		integer	LDX,
		real, dimension( ldb, * )	B,
		integer	LDB,
		real, dimension( * )	WORK,
		real	RESID
	)

STRT02

Purpose:

 STRT02 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 REAL 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 REAL 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 REAL 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 REAL array, dimension (N)
[out]	RESID	RESID is REAL 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 strt02.f.

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subroutine strt03	(	character	UPLO,
		character	TRANS,
		character	DIAG,
		integer	N,
		integer	NRHS,
		real, dimension( lda, * )	A,
		integer	LDA,
		real	SCALE,
		real, dimension( * )	CNORM,
		real	TSCAL,
		real, dimension( ldx, * )	X,
		integer	LDX,
		real, dimension( ldb, * )	B,
		integer	LDB,
		real, dimension( * )	WORK,
		real	RESID
	)

STRT03

Purpose:

 STRT03 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 REAL 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 REAL The scaling factor s used in solving the triangular system.
[in]	CNORM	CNORM is REAL array, dimension (N) The 1-norms of the columns of A, not counting the diagonal.
[in]	TSCAL	TSCAL is REAL The scaling factor used in computing the 1-norms in CNORM. CNORM actually contains the column norms of TSCAL*A.
[in]	X	X is REAL 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 REAL 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 REAL array, dimension (N)
[out]	RESID	RESID is REAL 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 strt03.f.

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subroutine strt05	(	character	UPLO,
		character	TRANS,
		character	DIAG,
		integer	N,
		integer	NRHS,
		real, dimension( lda, * )	A,
		integer	LDA,
		real, dimension( ldb, * )	B,
		integer	LDB,
		real, dimension( ldx, * )	X,
		integer	LDX,
		real, dimension( ldxact, * )	XACT,
		integer	LDXACT,
		real, dimension( * )	FERR,
		real, dimension( * )	BERR,
		real, dimension( * )	RESLTS
	)

STRT05

Purpose:

 STRT05 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 REAL 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 REAL 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 REAL 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 REAL 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 REAL 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 REAL 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 REAL 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 strt05.f.

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subroutine strt06	(	real	RCOND,
		real	RCONDC,
		character	UPLO,
		character	DIAG,
		integer	N,
		real, dimension( lda, * )	A,
		integer	LDA,
		real, dimension( * )	WORK,
		real	RAT
	)

STRT06

Purpose:

 STRT06 computes a test ratio comparing RCOND (the reciprocal
 condition number of a triangular matrix A) and RCONDC, the estimate
 computed by STRCON.  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 REAL 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 REAL The estimate of the reciprocal condition number computed by STRCON.
[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 REAL 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 REAL array, dimension (N)
[out]	RAT	RAT is REAL 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 strt06.f.

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REAL function stzt01	(	integer	M,
		integer	N,
		real, dimension( lda, * )	A,
		real, dimension( lda, * )	AF,
		integer	LDA,
		real, dimension( * )	TAU,
		real, dimension( lwork )	WORK,
		integer	LWORK
	)

STZT01

Purpose:

 STZT01 returns
      || A - R*Q || / ( M * eps * ||A|| )
 for an upper trapezoidal A that was factored with STZRQF.

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 REAL array, dimension (LDA,N) The original upper trapezoidal M by N matrix A.
[in]	AF	AF is REAL array, dimension (LDA,N) The output of STZRQF 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 REAL array, dimension (M) Details of the Householder transformations as returned by STZRQF.
[out]	WORK	WORK is REAL 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 stzt01.f.

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REAL function stzt02	(	integer	M,
		integer	N,
		real, dimension( lda, * )	AF,
		integer	LDA,
		real, dimension( * )	TAU,
		real, dimension( lwork )	WORK,
		integer	LWORK
	)

STZT02

Purpose:

 STZT02 returns
      || I - Q'*Q || / ( M * eps)
 where the matrix Q is defined by the Householder transformations
 generated by STZRQF.

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 REAL array, dimension (LDA,N) The output of STZRQF.
[in]	LDA	LDA is INTEGER The leading dimension of the array AF.
[in]	TAU	TAU is REAL array, dimension (M) Details of the Householder transformations as returned by STZRQF.
[out]	WORK	WORK is REAL 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 stzt02.f.

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Functions/Subroutines

Detailed Description

Function/Subroutine Documentation