Collaboration diagram for complex:

Functions/Subroutines
program	cchkaa
	CCHKAA
subroutine	cchkeq (THRESH, NOUT)
	CCHKEQ
subroutine	cchkgb (DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NNS, NSVAL, THRESH, TSTERR, A, LA, AFAC, LAFAC, B, X, XACT, WORK, RWORK, IWORK, NOUT)
	CCHKGB
subroutine	cchkge (DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
	CCHKGE
subroutine	cchkgt (DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR, A, AF, B, X, XACT, WORK, RWORK, IWORK, NOUT)
	CCHKGT
subroutine	cchkhe (DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
	CCHKHE
subroutine	cchkhp (DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
	CCHKHP
subroutine	cchklq (DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NXVAL, NRHS, THRESH, TSTERR, NMAX, A, AF, AQ, AL, AC, B, X, XACT, TAU, WORK, RWORK, NOUT)
	CCHKLQ
subroutine	cchkpb (DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, NOUT)
	CCHKPB
subroutine	cchkpo (DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, NOUT)
	CCHKPO
subroutine	cchkpp (DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, NOUT)
	CCHKPP
subroutine	cchkps (DOTYPE, NN, NVAL, NNB, NBVAL, NRANK, RANKVAL, THRESH, TSTERR, NMAX, A, AFAC, PERM, PIV, WORK, RWORK, NOUT)
	CCHKPS
subroutine	cchkpt (DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR, A, D, E, B, X, XACT, WORK, RWORK, NOUT)
	CCHKPT
subroutine	cchkq3 (DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NXVAL, THRESH, A, COPYA, S, TAU, WORK, RWORK, IWORK, NOUT)
	CCHKQ3
subroutine	cchkql (DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NXVAL, NRHS, THRESH, TSTERR, NMAX, A, AF, AQ, AL, AC, B, X, XACT, TAU, WORK, RWORK, NOUT)
	CCHKQL
subroutine	cchkqp (DOTYPE, NM, MVAL, NN, NVAL, THRESH, TSTERR, A, COPYA, S, TAU, WORK, RWORK, IWORK, NOUT)
	CCHKQP
subroutine	cchkqr (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)
	CCHKQR
subroutine	cchkqrt (THRESH, TSTERR, NM, MVAL, NN, NVAL, NNB, NBVAL, NOUT)
	CCHKQRT
subroutine	cchkqrtp (THRESH, TSTERR, NM, MVAL, NN, NVAL, NNB, NBVAL, NOUT)
	CCHKQRTP
program	cchkrfp
	CCHKRFP
subroutine	cchkrq (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)
	CCHKRQ
subroutine	cchksp (DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
	CCHKSP
subroutine	cchksy (DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
	CCHKSY
subroutine	cchktb (DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, AB, AINV, B, X, XACT, WORK, RWORK, NOUT)
	CCHKTB
subroutine	cchktp (DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, AP, AINVP, B, X, XACT, WORK, RWORK, NOUT)
	CCHKTP
subroutine	cchktr (DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, A, AINV, B, X, XACT, WORK, RWORK, NOUT)
	CCHKTR
subroutine	cchktz (DOTYPE, NM, MVAL, NN, NVAL, THRESH, TSTERR, A, COPYA, S, TAU, WORK, RWORK, NOUT)
	CCHKTZ
subroutine	cdrvgb (DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, A, LA, AFB, LAFB, ASAV, B, BSAV, X, XACT, S, WORK, RWORK, IWORK, NOUT)
	CDRVGB
subroutine	cdrvge (DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, A, AFAC, ASAV, B, BSAV, X, XACT, S, WORK, RWORK, IWORK, NOUT)
	CDRVGE
subroutine	cdrvgt (DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, A, AF, B, X, XACT, WORK, RWORK, IWORK, NOUT)
	CDRVGT
subroutine	cdrvhe (DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
	CDRVHE
subroutine	cdrvhp (DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
	CDRVHP
subroutine	cdrvls (DOTYPE, NM, MVAL, NN, NVAL, NNS, NSVAL, NNB, NBVAL, NXVAL, THRESH, TSTERR, A, COPYA, B, COPYB, C, S, COPYS, WORK, RWORK, IWORK, NOUT)
	CDRVLS
subroutine	cdrvpb (DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, A, AFAC, ASAV, B, BSAV, X, XACT, S, WORK, RWORK, NOUT)
	CDRVPB
subroutine	cdrvpo (DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, A, AFAC, ASAV, B, BSAV, X, XACT, S, WORK, RWORK, NOUT)
	CDRVPO
subroutine	cdrvpp (DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, A, AFAC, ASAV, B, BSAV, X, XACT, S, WORK, RWORK, NOUT)
	CDRVPP
subroutine	cdrvpt (DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, A, D, E, B, X, XACT, WORK, RWORK, NOUT)
	CDRVPT
subroutine	cdrvrf1 (NOUT, NN, NVAL, THRESH, A, LDA, ARF, WORK)
	CDRVRF1
subroutine	cdrvrf2 (NOUT, NN, NVAL, A, LDA, ARF, AP, ASAV)
	CDRVRF2
subroutine	cdrvrf3 (NOUT, NN, NVAL, THRESH, A, LDA, ARF, B1, B2, S_WORK_CLANGE, C_WORK_CGEQRF, TAU)
	CDRVRF3
subroutine	cdrvrf4 (NOUT, NN, NVAL, THRESH, C1, C2, LDC, CRF, A, LDA, S_WORK_CLANGE)
	CDRVRF4
subroutine	cdrvrfp (NOUT, NN, NVAL, NNS, NSVAL, NNT, NTVAL, THRESH, A, ASAV, AFAC, AINV, B, BSAV, XACT, X, ARF, ARFINV, C_WORK_CLATMS, C_WORK_CPOT02, C_WORK_CPOT03, S_WORK_CLATMS, S_WORK_CLANHE, S_WORK_CPOT01, S_WORK_CPOT02, S_WORK_CPOT03)
	CDRVRFP
subroutine	cdrvsp (DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
	CDRVSP
subroutine	cdrvsy (DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
	CDRVSY
subroutine	cebchvxx (THRESH, PATH)
	CEBCHVXX
subroutine	cerrge (PATH, NUNIT)
	CERRGE
subroutine	cerrgt (PATH, NUNIT)
	CERRGT
subroutine	cerrhe (PATH, NUNIT)
	CERRHE
subroutine	cerrlq (PATH, NUNIT)
	CERRLQ
subroutine	cerrls (PATH, NUNIT)
	CERRLS
subroutine	cerrpo (PATH, NUNIT)
	CERRPO
subroutine	cerrps (PATH, NUNIT)
	CERRPS
subroutine	cerrql (PATH, NUNIT)
	CERRQL
subroutine	cerrqp (PATH, NUNIT)
	CERRQP
subroutine	cerrqr (PATH, NUNIT)
	CERRQR
subroutine	cerrqrt (PATH, NUNIT)
	CERRQRT
subroutine	cerrqrtp (PATH, NUNIT)
	CERRQRTP
subroutine	cerrrfp (NUNIT)
	CERRRFP
subroutine	cerrrq (PATH, NUNIT)
	CERRRQ
subroutine	cerrsy (PATH, NUNIT)
	CERRSY
subroutine	cerrtr (PATH, NUNIT)
	CERRTR
subroutine	cerrtz (PATH, NUNIT)
	CERRTZ
subroutine	cerrvx (PATH, NUNIT)
	CERRVX
subroutine	cgbt01 (M, N, KL, KU, A, LDA, AFAC, LDAFAC, IPIV, WORK, RESID)
	CGBT01
subroutine	cgbt02 (TRANS, M, N, KL, KU, NRHS, A, LDA, X, LDX, B, LDB, RESID)
	CGBT02
subroutine	cgbt05 (TRANS, N, KL, KU, NRHS, AB, LDAB, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
	CGBT05
subroutine	cgelqs (M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK, INFO)
	CGELQS
LOGICAL function	cgennd (M, N, A, LDA)
	CGENND
subroutine	cgeqls (M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK, INFO)
	CGEQLS
subroutine	cgeqrs (M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK, INFO)
	CGEQRS
subroutine	cgerqs (M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK, INFO)
	CGERQS
subroutine	cget01 (M, N, A, LDA, AFAC, LDAFAC, IPIV, RWORK, RESID)
	CGET01
subroutine	cget02 (TRANS, M, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
	CGET02
subroutine	cget03 (N, A, LDA, AINV, LDAINV, WORK, LDWORK, RWORK, RCOND, RESID)
	CGET03
subroutine	cget04 (N, NRHS, X, LDX, XACT, LDXACT, RCOND, RESID)
	CGET04
subroutine	cget07 (TRANS, N, NRHS, A, LDA, B, LDB, X, LDX, XACT, LDXACT, FERR, CHKFERR, BERR, RESLTS)
	CGET07
subroutine	cgtt01 (N, DL, D, DU, DLF, DF, DUF, DU2, IPIV, WORK, LDWORK, RWORK, RESID)
	CGTT01
subroutine	cgtt02 (TRANS, N, NRHS, DL, D, DU, X, LDX, B, LDB, RESID)
	CGTT02
subroutine	cgtt05 (TRANS, N, NRHS, DL, D, DU, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
	CGTT05
subroutine	chet01 (UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, LDC, RWORK, RESID)
	CHET01
subroutine	chkxer (SRNAMT, INFOT, NOUT, LERR, OK)
	CHKXER
subroutine	chpt01 (UPLO, N, A, AFAC, IPIV, C, LDC, RWORK, RESID)
	CHPT01
subroutine	clahilb (N, NRHS, A, LDA, X, LDX, B, LDB, WORK, INFO, PATH)
	CLAHILB
subroutine	claipd (N, A, INDA, VINDA)
	CLAIPD
subroutine	claptm (UPLO, N, NRHS, ALPHA, D, E, X, LDX, BETA, B, LDB)
	CLAPTM
subroutine	clarhs (PATH, XTYPE, UPLO, TRANS, M, N, KL, KU, NRHS, A, LDA, X, LDX, B, LDB, ISEED, INFO)
	CLARHS
subroutine	clatb4 (PATH, IMAT, M, N, TYPE, KL, KU, ANORM, MODE, CNDNUM, DIST)
	CLATB4
subroutine	clatb5 (PATH, IMAT, N, TYPE, KL, KU, ANORM, MODE, CNDNUM, DIST)
	CLATB5
subroutine	clatsp (UPLO, N, X, ISEED)
	CLATSP
subroutine	clatsy (UPLO, N, X, LDX, ISEED)
	CLATSY
subroutine	clattb (IMAT, UPLO, TRANS, DIAG, ISEED, N, KD, AB, LDAB, B, WORK, RWORK, INFO)
	CLATTB
subroutine	clattp (IMAT, UPLO, TRANS, DIAG, ISEED, N, AP, B, WORK, RWORK, INFO)
	CLATTP
subroutine	clattr (IMAT, UPLO, TRANS, DIAG, ISEED, N, A, LDA, B, WORK, RWORK, INFO)
	CLATTR
subroutine	clavhe (UPLO, TRANS, DIAG, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
	CLAVHE
subroutine	clavhp (UPLO, TRANS, DIAG, N, NRHS, A, IPIV, B, LDB, INFO)
	CLAVHP
subroutine	clavsp (UPLO, TRANS, DIAG, N, NRHS, A, IPIV, B, LDB, INFO)
	CLAVSP
subroutine	clavsy (UPLO, TRANS, DIAG, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
	CLAVSY
subroutine	clqt01 (M, N, A, AF, Q, L, LDA, TAU, WORK, LWORK, RWORK, RESULT)
	CLQT01
subroutine	clqt02 (M, N, K, A, AF, Q, L, LDA, TAU, WORK, LWORK, RWORK, RESULT)
	CLQT02
subroutine	clqt03 (M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK, RWORK, RESULT)
	CLQT03
subroutine	cpbt01 (UPLO, N, KD, A, LDA, AFAC, LDAFAC, RWORK, RESID)
	CPBT01
subroutine	cpbt02 (UPLO, N, KD, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
	CPBT02
subroutine	cpbt05 (UPLO, N, KD, NRHS, AB, LDAB, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
	CPBT05
subroutine	cpot01 (UPLO, N, A, LDA, AFAC, LDAFAC, RWORK, RESID)
	CPOT01
subroutine	cpot02 (UPLO, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
	CPOT02
subroutine	cpot03 (UPLO, N, A, LDA, AINV, LDAINV, WORK, LDWORK, RWORK, RCOND, RESID)
	CPOT03
subroutine	cpot05 (UPLO, N, NRHS, A, LDA, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
	CPOT05
subroutine	cppt01 (UPLO, N, A, AFAC, RWORK, RESID)
	CPPT01
subroutine	cppt02 (UPLO, N, NRHS, A, X, LDX, B, LDB, RWORK, RESID)
	CPPT02
subroutine	cppt03 (UPLO, N, A, AINV, WORK, LDWORK, RWORK, RCOND, RESID)
	CPPT03
subroutine	cppt05 (UPLO, N, NRHS, AP, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
	CPPT05
subroutine	cpst01 (UPLO, N, A, LDA, AFAC, LDAFAC, PERM, LDPERM, PIV, RWORK, RESID, RANK)
	CPST01
subroutine	cptt01 (N, D, E, DF, EF, WORK, RESID)
	CPTT01
subroutine	cptt02 (UPLO, N, NRHS, D, E, X, LDX, B, LDB, RESID)
	CPTT02
subroutine	cptt05 (N, NRHS, D, E, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
	CPTT05
subroutine	cqlt01 (M, N, A, AF, Q, L, LDA, TAU, WORK, LWORK, RWORK, RESULT)
	CQLT01
subroutine	cqlt02 (M, N, K, A, AF, Q, L, LDA, TAU, WORK, LWORK, RWORK, RESULT)
	CQLT02
subroutine	cqlt03 (M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK, RWORK, RESULT)
	CQLT03
REAL function	cqpt01 (M, N, K, A, AF, LDA, TAU, JPVT, WORK, LWORK)
	CQPT01
subroutine	cqrt01 (M, N, A, AF, Q, R, LDA, TAU, WORK, LWORK, RWORK, RESULT)
	CQRT01
subroutine	cqrt01p (M, N, A, AF, Q, R, LDA, TAU, WORK, LWORK, RWORK, RESULT)
	CQRT01P
subroutine	cqrt02 (M, N, K, A, AF, Q, R, LDA, TAU, WORK, LWORK, RWORK, RESULT)
	CQRT02
subroutine	cqrt03 (M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK, RWORK, RESULT)
	CQRT03
subroutine	cqrt04 (M, N, NB, RESULT)
	CQRT04
subroutine	cqrt05 (M, N, L, NB, RESULT)
	CQRT05
REAL function	cqrt11 (M, K, A, LDA, TAU, WORK, LWORK)
	CQRT11
REAL function	cqrt12 (M, N, A, LDA, S, WORK, LWORK, RWORK)
	CQRT12
subroutine	cqrt13 (SCALE, M, N, A, LDA, NORMA, ISEED)
	CQRT13
REAL function	cqrt14 (TRANS, M, N, NRHS, A, LDA, X, LDX, WORK, LWORK)
	CQRT14
subroutine	cqrt15 (SCALE, RKSEL, M, N, NRHS, A, LDA, B, LDB, S, RANK, NORMA, NORMB, ISEED, WORK, LWORK)
	CQRT15
subroutine	cqrt16 (TRANS, M, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
	CQRT16
REAL function	cqrt17 (TRANS, IRESID, M, N, NRHS, A, LDA, X, LDX, B, LDB, C, WORK, LWORK)
	CQRT17
subroutine	crqt01 (M, N, A, AF, Q, R, LDA, TAU, WORK, LWORK, RWORK, RESULT)
	CRQT01
subroutine	crqt02 (M, N, K, A, AF, Q, R, LDA, TAU, WORK, LWORK, RWORK, RESULT)
	CRQT02
subroutine	crqt03 (M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK, RWORK, RESULT)
	CRQT03
REAL function	crzt01 (M, N, A, AF, LDA, TAU, WORK, LWORK)
	CRZT01
REAL function	crzt02 (M, N, AF, LDA, TAU, WORK, LWORK)
	CRZT02
subroutine	csbmv (UPLO, N, K, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
	CSBMV
subroutine	cspt01 (UPLO, N, A, AFAC, IPIV, C, LDC, RWORK, RESID)
	CSPT01
subroutine	cspt02 (UPLO, N, NRHS, A, X, LDX, B, LDB, RWORK, RESID)
	CSPT02
subroutine	cspt03 (UPLO, N, A, AINV, WORK, LDW, RWORK, RCOND, RESID)
	CSPT03
subroutine	csyt01 (UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, LDC, RWORK, RESID)
	CSYT01
subroutine	csyt02 (UPLO, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
	CSYT02
subroutine	csyt03 (UPLO, N, A, LDA, AINV, LDAINV, WORK, LDWORK, RWORK, RCOND, RESID)
	CSYT03
subroutine	ctbt02 (UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, X, LDX, B, LDB, WORK, RWORK, RESID)
	CTBT02
subroutine	ctbt03 (UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, SCALE, CNORM, TSCAL, X, LDX, B, LDB, WORK, RESID)
	CTBT03
subroutine	ctbt05 (UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
	CTBT05
subroutine	ctbt06 (RCOND, RCONDC, UPLO, DIAG, N, KD, AB, LDAB, RWORK, RAT)
	CTBT06
subroutine	ctpt01 (UPLO, DIAG, N, AP, AINVP, RCOND, RWORK, RESID)
	CTPT01
subroutine	ctpt02 (UPLO, TRANS, DIAG, N, NRHS, AP, X, LDX, B, LDB, WORK, RWORK, RESID)
	CTPT02
subroutine	ctpt03 (UPLO, TRANS, DIAG, N, NRHS, AP, SCALE, CNORM, TSCAL, X, LDX, B, LDB, WORK, RESID)
	CTPT03
subroutine	ctpt05 (UPLO, TRANS, DIAG, N, NRHS, AP, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
	CTPT05
subroutine	ctpt06 (RCOND, RCONDC, UPLO, DIAG, N, AP, RWORK, RAT)
	CTPT06
subroutine	ctrt01 (UPLO, DIAG, N, A, LDA, AINV, LDAINV, RCOND, RWORK, RESID)
	CTRT01
subroutine	ctrt02 (UPLO, TRANS, DIAG, N, NRHS, A, LDA, X, LDX, B, LDB, WORK, RWORK, RESID)
	CTRT02
subroutine	ctrt03 (UPLO, TRANS, DIAG, N, NRHS, A, LDA, SCALE, CNORM, TSCAL, X, LDX, B, LDB, WORK, RESID)
	CTRT03
subroutine	ctrt05 (UPLO, TRANS, DIAG, N, NRHS, A, LDA, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
	CTRT05
subroutine	ctrt06 (RCOND, RCONDC, UPLO, DIAG, N, A, LDA, RWORK, RAT)
	CTRT06
REAL function	ctzt01 (M, N, A, AF, LDA, TAU, WORK, LWORK)
	CTZT01
REAL function	ctzt02 (M, N, AF, LDA, TAU, WORK, LWORK)
	CTZT02

Detailed Description

This is the group of complex LAPACK TESTING LIN routines.

Function/Subroutine Documentation

program cchkaa ( )

CCHKAA

Purpose:

 CCHKAA is the main test program for the COMPLEX 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 42 lines:
 Data file for testing COMPLEX LAPACK linear equation 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)
 30.0                   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
 CGE   11               List types on next line if 0 < NTYPES < 11
 CGB    8               List types on next line if 0 < NTYPES <  8
 CGT   12               List types on next line if 0 < NTYPES < 12
 CPO    9               List types on next line if 0 < NTYPES <  9
 CPO    9               List types on next line if 0 < NTYPES <  9
 CPP    9               List types on next line if 0 < NTYPES <  9
 CPB    8               List types on next line if 0 < NTYPES <  8
 CPT   12               List types on next line if 0 < NTYPES < 12
 CHE   10               List types on next line if 0 < NTYPES < 10
 CHP   10               List types on next line if 0 < NTYPES < 10
 CSY   11               List types on next line if 0 < NTYPES < 11
 CSR   11               List types on next line if 0 < NTYPES < 11
 CSP   11               List types on next line if 0 < NTYPES < 11
 CTR   18               List types on next line if 0 < NTYPES < 18
 CTP   18               List types on next line if 0 < NTYPES < 18
 CTB   17               List types on next line if 0 < NTYPES < 17
 CQR    8               List types on next line if 0 < NTYPES <  8
 CRQ    8               List types on next line if 0 < NTYPES <  8
 CLQ    8               List types on next line if 0 < NTYPES <  8
 CQL    8               List types on next line if 0 < NTYPES <  8
 CQP    6               List types on next line if 0 < NTYPES <  6
 CTZ    3               List types on next line if 0 < NTYPES <  3
 CLS    6               List types on next line if 0 < NTYPES <  6
 CEQ
 CQT
 CQX

  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:: September 2012

Definition at line 109 of file cchkaa.f.

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subroutine cchkeq	(	real	THRESH,
		integer	NOUT
	)

CCHKEQ

Purpose:

 CCHKEQ tests CGEEQU, CGBEQU, CPOEQU, CPPEQU and CPBEQU

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 cchkeq.f.

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subroutine cchkgb	(	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,
		complex, dimension( * )	A,
		integer	LA,
		complex, dimension( * )	AFAC,
		integer	LAFAC,
		complex, dimension( * )	B,
		complex, dimension( * )	X,
		complex, dimension( * )	XACT,
		complex, dimension( * )	WORK,
		real, dimension( * )	RWORK,
		integer, dimension( * )	IWORK,
		integer	NOUT
	)

CCHKGB

Purpose:

 CCHKGB tests CGBTRF, -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 COMPLEX 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 COMPLEX 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 COMPLEX array, dimension (NMAX*NSMAX)
[out]	X	X is COMPLEX array, dimension (NMAX*NSMAX)
[out]	XACT	XACT is COMPLEX array, dimension (NMAX*NSMAX)
[out]	WORK	WORK is COMPLEX 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 (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 cchkgb.f.

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subroutine cchkge	(	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,
		complex, dimension( * )	A,
		complex, dimension( * )	AFAC,
		complex, dimension( * )	AINV,
		complex, dimension( * )	B,
		complex, dimension( * )	X,
		complex, dimension( * )	XACT,
		complex, dimension( * )	WORK,
		real, dimension( * )	RWORK,
		integer, dimension( * )	IWORK,
		integer	NOUT
	)

CCHKGE

Purpose:

 CCHKGE tests CGETRF, -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 COMPLEX array, dimension (NMAX*NMAX)
[out]	AFAC	AFAC is COMPLEX array, dimension (NMAX*NMAX)
[out]	AINV	AINV is COMPLEX array, dimension (NMAX*NMAX)
[out]	B	B is COMPLEX array, dimension (NMAX*NSMAX) where NSMAX is the largest entry in NSVAL.
[out]	X	X is COMPLEX array, dimension (NMAX*NSMAX)
[out]	XACT	XACT is COMPLEX array, dimension (NMAX*NSMAX)
[out]	WORK	WORK is COMPLEX array, dimension (NMAX*max(3,NSMAX))
[out]	RWORK	RWORK is REAL array, dimension (max(2NMAX,2NSMAX+NWORK))
[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 185 of file cchkge.f.

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

CCHKGT

Purpose:

 CCHKGT tests CGTTRF, -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 COMPLEX array, dimension (NMAX*4)
[out]	AF	AF is COMPLEX array, dimension (NMAX*4)
[out]	B	B is COMPLEX array, dimension (NMAX*NSMAX) where NSMAX is the largest entry in NSVAL.
[out]	X	X is COMPLEX array, dimension (NMAX*NSMAX)
[out]	XACT	XACT is COMPLEX array, dimension (NMAX*NSMAX)
[out]	WORK	WORK is COMPLEX 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 147 of file cchkgt.f.

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

CCHKHE

Purpose:

 CCHKHE tests CHETRF, -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 COMPLEX array, dimension (NMAX*NMAX)
[out]	AFAC	AFAC is COMPLEX array, dimension (NMAX*NMAX)
[out]	AINV	AINV is COMPLEX array, dimension (NMAX*NMAX)
[out]	B	B is COMPLEX array, dimension (NMAX*NSMAX) where NSMAX is the largest entry in NSVAL.
[out]	X	X is COMPLEX array, dimension (NMAX*NSMAX)
[out]	XACT	XACT is COMPLEX array, dimension (NMAX*NSMAX)
[out]	WORK	WORK is COMPLEX 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 172 of file cchkhe.f.

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

CCHKHP

Purpose:

 CCHKHP tests CHPTRF, -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 COMPLEX array, dimension (NMAX*(NMAX+1)/2)
[out]	AFAC	AFAC is COMPLEX array, dimension (NMAX*(NMAX+1)/2)
[out]	AINV	AINV is COMPLEX array, dimension (NMAX*(NMAX+1)/2)
[out]	B	B is COMPLEX array, dimension (NMAX*NSMAX) where NSMAX is the largest entry in NSVAL.
[out]	X	X is COMPLEX array, dimension (NMAX*NSMAX)
[out]	XACT	XACT is COMPLEX array, dimension (NMAX*NSMAX)
[out]	WORK	WORK is COMPLEX array, dimension (NMAX*max(2,NSMAX))
[out]	RWORK	RWORK is REAL array, dimension (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 163 of file cchkhp.f.

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subroutine cchklq	(	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,
		complex, dimension( * )	A,
		complex, dimension( * )	AF,
		complex, dimension( * )	AQ,
		complex, dimension( * )	AL,
		complex, dimension( * )	AC,
		complex, dimension( * )	B,
		complex, dimension( * )	X,
		complex, dimension( * )	XACT,
		complex, dimension( * )	TAU,
		complex, dimension( * )	WORK,
		real, dimension( * )	RWORK,
		integer	NOUT
	)

CCHKLQ

Purpose:

 CCHKLQ tests CGELQF, CUNGLQ and CUNMLQ.

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

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

CCHKPB

Purpose:

 CCHKPB tests CPBTRF, -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))
[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 167 of file cchkpb.f.

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

CCHKPO

Purpose:

 CCHKPO tests CPOTRF, -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 COMPLEX array, dimension (NMAX*NMAX)
[out]	AFAC	AFAC is COMPLEX array, dimension (NMAX*NMAX)
[out]	AINV	AINV is COMPLEX array, dimension (NMAX*NMAX)
[out]	B	B is COMPLEX array, dimension (NMAX*NSMAX) where NSMAX is the largest entry in NSVAL.
[out]	X	X is COMPLEX array, dimension (NMAX*NSMAX)
[out]	XACT	XACT is COMPLEX array, dimension (NMAX*NSMAX)
[out]	WORK	WORK is COMPLEX array, dimension (NMAX*max(3,NSMAX))
[out]	RWORK	RWORK is REAL array, dimension (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 167 of file cchkpo.f.

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

CCHKPP

Purpose:

 CCHKPP tests CPPTRF, -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 COMPLEX array, dimension (NMAX*(NMAX+1)/2)
[out]	AFAC	AFAC is COMPLEX array, dimension (NMAX*(NMAX+1)/2)
[out]	AINV	AINV is COMPLEX array, dimension (NMAX*(NMAX+1)/2)
[out]	B	B is COMPLEX array, dimension (NMAX*NSMAX) where NSMAX is the largest entry in NSVAL.
[out]	X	X is COMPLEX array, dimension (NMAX*NSMAX)
[out]	XACT	XACT is COMPLEX array, dimension (NMAX*NSMAX)
[out]	WORK	WORK is COMPLEX 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 158 of file cchkpp.f.

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

CCHKPS

Purpose:

 CCHKPS tests CPSTRF.

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 COMPLEX array, dimension (NMAX*NMAX)
[out]	AFAC	AFAC is COMPLEX array, dimension (NMAX*NMAX)
[out]	PERM	PERM is COMPLEX array, dimension (NMAX*NMAX)
[out]	PIV	PIV is INTEGER array, dimension (NMAX)
[out]	WORK	WORK is COMPLEX 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 cchkps.f.

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

CCHKPT

Purpose:

 CCHKPT tests CPTTRF, -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 COMPLEX array, dimension (NMAX*2)
[out]	D	D is REAL array, dimension (NMAX*2)
[out]	E	E is COMPLEX array, dimension (NMAX*2)
[out]	B	B is COMPLEX array, dimension (NMAX*NSMAX) where NSMAX is the largest entry in NSVAL.
[out]	X	X is COMPLEX array, dimension (NMAX*NSMAX)
[out]	XACT	XACT is COMPLEX array, dimension (NMAX*NSMAX)
[out]	WORK	WORK is COMPLEX 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 147 of file cchkpt.f.

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subroutine cchkq3	(	logical, dimension( * )	DOTYPE,
		integer	NM,
		integer, dimension( * )	MVAL,
		integer	NN,
		integer, dimension( * )	NVAL,
		integer	NNB,
		integer, dimension( * )	NBVAL,
		integer, dimension( * )	NXVAL,
		real	THRESH,
		complex, dimension( * )	A,
		complex, dimension( * )	COPYA,
		real, dimension( * )	S,
		complex, dimension( * )	TAU,
		complex, dimension( * )	WORK,
		real, dimension( * )	RWORK,
		integer, dimension( * )	IWORK,
		integer	NOUT
	)

CCHKQ3

Purpose:

 CCHKQ3 tests CGEQP3.

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 COMPLEX 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 COMPLEX array, dimension (MMAX*NMAX)
[out]	S	S is REAL array, dimension (min(MMAX,NMAX))
[out]	TAU	TAU is COMPLEX array, dimension (MMAX)
[out]	WORK	WORK is COMPLEX array, dimension (max(Mmax(M,N) + 4min(M,N) + max(M,N)))
[out]	RWORK	RWORK is REAL array, dimension (4*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

Definition at line 157 of file cchkq3.f.

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subroutine cchkql	(	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,
		complex, dimension( * )	A,
		complex, dimension( * )	AF,
		complex, dimension( * )	AQ,
		complex, dimension( * )	AL,
		complex, dimension( * )	AC,
		complex, dimension( * )	B,
		complex, dimension( * )	X,
		complex, dimension( * )	XACT,
		complex, dimension( * )	TAU,
		complex, dimension( * )	WORK,
		real, dimension( * )	RWORK,
		integer	NOUT
	)

CCHKQL

Purpose:

 CCHKQL tests CGEQLF, CUNGQL and CUNMQL.

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

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

CCHKQP

Purpose:

 CCHKQP tests CGEQPF.

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 COMPLEX 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 COMPLEX array, dimension (MMAX*NMAX)
[out]	S	S is REAL array, dimension (min(MMAX,NMAX))
[out]	TAU	TAU is COMPLEX array, dimension (MMAX)
[out]	WORK	WORK is COMPLEX array, dimension (max(Mmax(M,N) + 4min(M,N) + max(M,N)))
[out]	RWORK	RWORK is REAL array, dimension (4*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 143 of file cchkqp.f.

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subroutine cchkqr	(	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,
		complex, dimension( * )	A,
		complex, dimension( * )	AF,
		complex, dimension( * )	AQ,
		complex, dimension( * )	AR,
		complex, dimension( * )	AC,
		complex, dimension( * )	B,
		complex, dimension( * )	X,
		complex, dimension( * )	XACT,
		complex, dimension( * )	TAU,
		complex, dimension( * )	WORK,
		real, dimension( * )	RWORK,
		integer, dimension( * )	IWORK,
		integer	NOUT
	)

CCHKQR

Purpose:

 CCHKQR tests CGEQRF, CUNGQR and CUNMQR.

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

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

CCHKQRT

Purpose:

 CCHKQRT tests CGEQRT and CGEMQRT.

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 cchkqrt.f.

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

CCHKQRTP

Purpose:

 CCHKQRTP tests CTPQRT and CTPMQRT.

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 cchkqrtp.f.

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program cchkrfp ( )

CCHKRFP

Purpose:

 CCHKRFP is the main test program for the COMPLEX 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 cchkrfp.f.

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subroutine cchkrq	(	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,
		complex, dimension( * )	A,
		complex, dimension( * )	AF,
		complex, dimension( * )	AQ,
		complex, dimension( * )	AR,
		complex, dimension( * )	AC,
		complex, dimension( * )	B,
		complex, dimension( * )	X,
		complex, dimension( * )	XACT,
		complex, dimension( * )	TAU,
		complex, dimension( * )	WORK,
		real, dimension( * )	RWORK,
		integer, dimension( * )	IWORK,
		integer	NOUT
	)

CCHKRQ

Purpose:

 CCHKRQ tests CGERQF, CUNGRQ and CUNMRQ.

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

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

CCHKSP

Purpose:

 CCHKSP tests CSPTRF, -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 COMPLEX array, dimension (NMAX*(NMAX+1)/2)
[out]	AFAC	AFAC is COMPLEX array, dimension (NMAX*(NMAX+1)/2)
[out]	AINV	AINV is COMPLEX array, dimension (NMAX*(NMAX+1)/2)
[out]	B	B is COMPLEX array, dimension (NMAX*NSMAX) where NSMAX is the largest entry in NSVAL.
[out]	X	X is COMPLEX array, dimension (NMAX*NSMAX)
[out]	XACT	XACT is COMPLEX array, dimension (NMAX*NSMAX)
[out]	WORK	WORK is COMPLEX array, dimension (NMAX*max(2,NSMAX))
[out]	RWORK	RWORK is REAL array, dimension (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 163 of file cchksp.f.

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

CCHKSY

Purpose:

 CCHKSY tests CSYTRF, -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 COMPLEX array, dimension (NMAX*NMAX)
[out]	AFAC	AFAC is COMPLEX array, dimension (NMAX*NMAX)
[out]	AINV	AINV is COMPLEX array, dimension (NMAX*NMAX)
[out]	B	B is COMPLEX array, dimension (NMAX*NSMAX) where NSMAX is the largest entry in NSVAL.
[out]	X	X is COMPLEX array, dimension (NMAX*NSMAX)
[out]	XACT	XACT is COMPLEX array, dimension (NMAX*NSMAX)
[out]	WORK	WORK is COMPLEX array, dimension (NMAX*max(2,NSMAX))
[out]	RWORK	RWORK is REAL array, dimension (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:: April 2012

Definition at line 172 of file cchksy.f.

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

CCHKTB

Purpose:

 CCHKTB tests CTBTRS, -RFS, and -CON, and CLATBS.

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 COMPLEX array, dimension (NMAX*NMAX)
[out]	AINV	AINV is COMPLEX array, dimension (NMAX*NMAX)
[out]	B	B is COMPLEX array, dimension (NMAX*NSMAX) where NSMAX is the largest entry in NSVAL.
[out]	X	X is COMPLEX array, dimension (NMAX*NSMAX)
[out]	XACT	XACT is COMPLEX array, dimension (NMAX*NSMAX)
[out]	WORK	WORK is COMPLEX 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 149 of file cchktb.f.

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

CCHKTP

Purpose:

 CCHKTP tests CTPTRI, -TRS, -RFS, and -CON, and CLATPS

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 COMPLEX array, dimension (NMAX*(NMAX+1)/2)
[out]	AINVP	AINVP is COMPLEX array, dimension (NMAX*(NMAX+1)/2)
[out]	B	B is COMPLEX array, dimension (NMAX*NSMAX) where NSMAX is the largest entry in NSVAL.
[out]	X	X is COMPLEX array, dimension (NMAX*NSMAX)
[out]	XACT	XACT is COMPLEX array, dimension (NMAX*NSMAX)
[out]	WORK	WORK is COMPLEX 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 150 of file cchktp.f.

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

CCHKTR

Purpose:

 CCHKTR tests CTRTRI, -TRS, -RFS, and -CON, and CLATRS

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 COMPLEX array, dimension (NMAX*NMAX)
[out]	AINV	AINV is COMPLEX array, dimension (NMAX*NMAX)
[out]	B	B is COMPLEX array, dimension (NMAX*NSMAX) where NSMAX is the largest entry in NSVAL.
[out]	X	X is COMPLEX array, dimension (NMAX*NSMAX)
[out]	XACT	XACT is COMPLEX array, dimension (NMAX*NSMAX)
[out]	WORK	WORK is COMPLEX 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 162 of file cchktr.f.

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

CCHKTZ

Purpose:

 CCHKTZ tests CTZRQF and CTZRZF.

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 COMPLEX 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 COMPLEX array, dimension (MMAX*NMAX)
[out]	S	S is REAL array, dimension (min(MMAX,NMAX))
[out]	TAU	TAU is COMPLEX array, dimension (MMAX)
[out]	WORK	WORK is COMPLEX array, dimension (MMAXNMAX + 4NMAX + MMAX)
[out]	RWORK	RWORK is REAL 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 137 of file cchktz.f.

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

CDRVGB

CDRVGBX

Purpose:

 CDRVGB tests the driver routines CGBSV 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 COMPLEX 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 COMPLEX 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 COMPLEX array, dimension (LA)
[out]	B	B is COMPLEX array, dimension (NMAX*NRHS)
[out]	BSAV	BSAV is COMPLEX array, dimension (NMAX*NRHS)
[out]	X	X is COMPLEX array, dimension (NMAX*NRHS)
[out]	XACT	XACT is COMPLEX array, dimension (NMAX*NRHS)
[out]	S	S is REAL array, dimension (2*NMAX)
[out]	WORK	WORK is COMPLEX 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 (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:

 CDRVGB tests the driver routines CGBSV, -SVX, and -SVXX.

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

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

CDRVGE

CDRVGEX

Purpose:

 CDRVGE tests the driver routines CGESV 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 COMPLEX array, dimension (NMAX*NMAX)
[out]	AFAC	AFAC is COMPLEX array, dimension (NMAX*NMAX)
[out]	ASAV	ASAV is COMPLEX array, dimension (NMAX*NMAX)
[out]	B	B is COMPLEX array, dimension (NMAX*NRHS)
[out]	BSAV	BSAV is COMPLEX array, dimension (NMAX*NRHS)
[out]	X	X is COMPLEX array, dimension (NMAX*NRHS)
[out]	XACT	XACT is COMPLEX array, dimension (NMAX*NRHS)
[out]	S	S is REAL array, dimension (2*NMAX)
[out]	WORK	WORK is COMPLEX array, dimension (NMAX*max(3,NRHS))
[out]	RWORK	RWORK is REAL array, dimension (2*NRHS+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

Purpose:

 CDRVGE tests the driver routines CGESV, -SVX, and -SVXX.

 Note that this file is used only when the XBLAS are available,
 otherwise cdrvge.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 COMPLEX array, dimension (NMAX*NMAX)
[out]	AFAC	AFAC is COMPLEX array, dimension (NMAX*NMAX)
[out]	ASAV	ASAV is COMPLEX array, dimension (NMAX*NMAX)
[out]	B	B is COMPLEX array, dimension (NMAX*NRHS)
[out]	BSAV	BSAV is COMPLEX array, dimension (NMAX*NRHS)
[out]	X	X is COMPLEX array, dimension (NMAX*NRHS)
[out]	XACT	XACT is COMPLEX array, dimension (NMAX*NRHS)
[out]	S	S is REAL array, dimension (2*NMAX)
[out]	WORK	WORK is COMPLEX array, dimension (NMAX*max(3,NRHS))
[out]	RWORK	RWORK is REAL array, dimension (2*NRHS+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:: April 2012

Definition at line 163 of file cdrvge.f.

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

CDRVGT

Purpose:

 CDRVGT tests CGTSV 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 COMPLEX array, dimension (NMAX*4)
[out]	AF	AF is COMPLEX array, dimension (NMAX*4)
[out]	B	B is COMPLEX array, dimension (NMAX*NRHS)
[out]	X	X is COMPLEX array, dimension (NMAX*NRHS)
[out]	XACT	XACT is COMPLEX array, dimension (NMAX*NRHS)
[out]	WORK	WORK is COMPLEX array, dimension (NMAX*max(3,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 139 of file cdrvgt.f.

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

CDRVHE

CDRVHEX

Purpose:

 CDRVHE tests the driver routines CHESV 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 COMPLEX array, dimension (NMAX*NMAX)
[out]	AFAC	AFAC is COMPLEX array, dimension (NMAX*NMAX)
[out]	AINV	AINV is COMPLEX array, dimension (NMAX*NMAX)
[out]	B	B is COMPLEX array, dimension (NMAX*NRHS)
[out]	X	X is COMPLEX array, dimension (NMAX*NRHS)
[out]	XACT	XACT is COMPLEX array, dimension (NMAX*NRHS)
[out]	WORK	WORK is COMPLEX array, dimension (NMAX*max(2,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:

 CDRVHE tests the driver routines CHESV, -SVX, and -SVXX.

 Note that this file is used only when the XBLAS are available,
 otherwise cdrvhe.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 COMPLEX array, dimension (NMAX*NMAX)
[out]	AFAC	AFAC is COMPLEX array, dimension (NMAX*NMAX)
[out]	AINV	AINV is COMPLEX array, dimension (NMAX*NMAX)
[out]	B	B is COMPLEX array, dimension (NMAX*NRHS)
[out]	X	X is COMPLEX array, dimension (NMAX*NRHS)
[out]	XACT	XACT is COMPLEX array, dimension (NMAX*NRHS)
[out]	WORK	WORK is COMPLEX array, dimension (NMAX*max(2,NRHS))
[out]	RWORK	RWORK is REAL array, dimension (2NMAX+2NRHS)
[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:: April 2012

Definition at line 153 of file cdrvhe.f.

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

CDRVHP

Purpose:

 CDRVHP tests the driver routines CHPSV 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 COMPLEX array, dimension (NMAX*(NMAX+1)/2)
[out]	AFAC	AFAC is COMPLEX array, dimension (NMAX*(NMAX+1)/2)
[out]	AINV	AINV is COMPLEX array, dimension (NMAX*(NMAX+1)/2)
[out]	B	B is COMPLEX array, dimension (NMAX*NRHS)
[out]	X	X is COMPLEX array, dimension (NMAX*NRHS)
[out]	XACT	XACT is COMPLEX array, dimension (NMAX*NRHS)
[out]	WORK	WORK is COMPLEX array, dimension (NMAX*max(2,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 156 of file cdrvhp.f.

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subroutine cdrvls	(	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,
		complex, dimension( * )	A,
		complex, dimension( * )	COPYA,
		complex, dimension( * )	B,
		complex, dimension( * )	COPYB,
		complex, dimension( * )	C,
		real, dimension( * )	S,
		real, dimension( * )	COPYS,
		complex, dimension( * )	WORK,
		real, dimension( * )	RWORK,
		integer, dimension( * )	IWORK,
		integer	NOUT
	)

CDRVLS

Purpose:

 CDRVLS tests the least squares driver routines CGELS, CGELSX, CGELSS,
 CGELSY and CGELSD.

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 unitary 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 unitary 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]	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]	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 COMPLEX 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 COMPLEX array, dimension (MMAX*NMAX)
[out]	B	B is COMPLEX 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 COMPLEX array, dimension (MMAX*NSMAX)
[out]	C	C is COMPLEX 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 COMPLEX array, dimension (MMAXNMAX + 4NMAX + MMAX).
[out]	RWORK	RWORK is REAL array, dimension (5*NMAX-1)
[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 209 of file cdrvls.f.

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

CDRVPB

Purpose:

 CDRVPB tests the driver routines CPBSV 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 COMPLEX array, dimension (NMAX*NMAX)
[out]	AFAC	AFAC is COMPLEX array, dimension (NMAX*NMAX)
[out]	ASAV	ASAV is COMPLEX array, dimension (NMAX*NMAX)
[out]	B	B is COMPLEX array, dimension (NMAX*NRHS)
[out]	BSAV	BSAV is COMPLEX array, dimension (NMAX*NRHS)
[out]	X	X is COMPLEX array, dimension (NMAX*NRHS)
[out]	XACT	XACT is COMPLEX array, dimension (NMAX*NRHS)
[out]	S	S is REAL array, dimension (NMAX)
[out]	WORK	WORK is COMPLEX array, dimension (NMAX*max(3,NRHS))
[out]	RWORK	RWORK is REAL array, dimension (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 158 of file cdrvpb.f.

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

CDRVPO

CDRVPOX

Purpose:

 CDRVPO tests the driver routines CPOSV 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 COMPLEX array, dimension (NMAX*NMAX)
[out]	AFAC	AFAC is COMPLEX array, dimension (NMAX*NMAX)
[out]	ASAV	ASAV is COMPLEX array, dimension (NMAX*NMAX)
[out]	B	B is COMPLEX array, dimension (NMAX*NRHS)
[out]	BSAV	BSAV is COMPLEX array, dimension (NMAX*NRHS)
[out]	X	X is COMPLEX array, dimension (NMAX*NRHS)
[out]	XACT	XACT is COMPLEX array, dimension (NMAX*NRHS)
[out]	S	S is REAL array, dimension (NMAX)
[out]	WORK	WORK is COMPLEX array, dimension (NMAX*max(3,NRHS))
[out]	RWORK	RWORK is REAL array, dimension (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

Purpose:

 CDRVPO tests the driver routines CPOSV, -SVX, and -SVXX.

 Note that this file is used only when the XBLAS are available,
 otherwise cdrvpo.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 COMPLEX array, dimension (NMAX*NMAX)
[out]	AFAC	AFAC is COMPLEX array, dimension (NMAX*NMAX)
[out]	ASAV	ASAV is COMPLEX array, dimension (NMAX*NMAX)
[out]	B	B is COMPLEX array, dimension (NMAX*NRHS)
[out]	BSAV	BSAV is COMPLEX array, dimension (NMAX*NRHS)
[out]	X	X is COMPLEX array, dimension (NMAX*NRHS)
[out]	XACT	XACT is COMPLEX array, dimension (NMAX*NRHS)
[out]	S	S is REAL array, dimension (NMAX)
[out]	WORK	WORK is COMPLEX array, dimension (NMAX*max(3,NRHS))
[out]	RWORK	RWORK is REAL array, dimension (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 158 of file cdrvpo.f.

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

CDRVPP

Purpose:

 CDRVPP tests the driver routines CPPSV 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 COMPLEX array, dimension (NMAX*(NMAX+1)/2)
[out]	AFAC	AFAC is COMPLEX array, dimension (NMAX*(NMAX+1)/2)
[out]	ASAV	ASAV is COMPLEX array, dimension (NMAX*(NMAX+1)/2)
[out]	B	B is COMPLEX array, dimension (NMAX*NRHS)
[out]	BSAV	BSAV is COMPLEX array, dimension (NMAX*NRHS)
[out]	X	X is COMPLEX array, dimension (NMAX*NRHS)
[out]	XACT	XACT is COMPLEX array, dimension (NMAX*NRHS)
[out]	S	S is REAL array, dimension (NMAX)
[out]	WORK	WORK is COMPLEX array, dimension (NMAX*max(3,NRHS))
[out]	RWORK	RWORK is REAL array, dimension (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 158 of file cdrvpp.f.

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

CDRVPT

Purpose:

 CDRVPT tests CPTSV 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 COMPLEX array, dimension (NMAX*2)
[out]	D	D is REAL array, dimension (NMAX*2)
[out]	E	E is COMPLEX array, dimension (NMAX*2)
[out]	B	B is COMPLEX array, dimension (NMAX*NRHS)
[out]	X	X is COMPLEX array, dimension (NMAX*NRHS)
[out]	XACT	XACT is COMPLEX array, dimension (NMAX*NRHS)
[out]	WORK	WORK is COMPLEX array, dimension (NMAX*max(3,NRHS))
[out]	RWORK	RWORK is REAL array, dimension (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 cdrvpt.f.

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subroutine cdrvrf1	(	integer	NOUT,
		integer	NN,
		integer, dimension( nn )	NVAL,
		real	THRESH,
		complex, dimension( lda, * )	A,
		integer	LDA,
		complex, dimension( * )	ARF,
		real, dimension( * )	WORK
	)

CDRVRF1

Purpose:

 CDRVRF1 tests the LAPACK RFP routines:
     CLANHF.F

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

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

Date:: November 2011

Definition at line 96 of file cdrvrf1.f.

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subroutine cdrvrf2	(	integer	NOUT,
		integer	NN,
		integer, dimension( nn )	NVAL,
		complex, dimension( lda, * )	A,
		integer	LDA,
		complex, dimension( * )	ARF,
		complex, dimension(*)	AP,
		complex, dimension( lda, * )	ASAV
	)

CDRVRF2

Purpose:

 CDRVRF2 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 COMPLEX array, dimension (LDA,NMAX)
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= max(1,NMAX).
[out]	ARF	ARF is COMPLEX array, dimension ((NMAX*(NMAX+1))/2).
[out]	AP	AP is COMPLEX array, dimension ((NMAX*(NMAX+1))/2).
[out]	ASAV	ASAV is COMPLEX6 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 cdrvrf2.f.

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subroutine cdrvrf3	(	integer	NOUT,
		integer	NN,
		integer, dimension( nn )	NVAL,
		real	THRESH,
		complex, dimension( lda, * )	A,
		integer	LDA,
		complex, dimension( * )	ARF,
		complex, dimension( lda, * )	B1,
		complex, dimension( lda, * )	B2,
		real, dimension( * )	S_WORK_CLANGE,
		complex, dimension( * )	C_WORK_CGEQRF,
		complex, dimension( * )	TAU
	)

CDRVRF3

Purpose:

 CDRVRF3 tests the LAPACK RFP routines:
     CTFSM

Parameters:

[in]	NOUT	NOUT is INTEGER The unit number for output.
[in]	NN	NN is INTEGER The number of values of N contained in the vector NVAL.
[in]	NVAL	NVAL is INTEGER array, dimension (NN) The values of the matrix dimension N.
[in]	THRESH	THRESH is DOUBLE PRECISION The threshold value for the test ratios. A result is included in the output file if RESULT >= THRESH. To have every test ratio printed, use THRESH = 0.
[out]	A	A is COMPLEX*16 array, dimension (LDA,NMAX)
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= max(1,NMAX).
[out]	ARF	ARF is COMPLEX array, dimension ((NMAX*(NMAX+1))/2).
[out]	B1	B1 is COMPLEX array, dimension (LDA,NMAX)
[out]	B2	B2 is COMPLEX array, dimension (LDA,NMAX)
[out]	S_WORK_CLANGE	S_WORK_CLANGE is REAL array, dimension (NMAX)
[out]	C_WORK_CGEQRF	C_WORK_CGEQRF is COMPLEX array, dimension (NMAX)
[out]	TAU	TAU is COMPLEX array, dimension (NMAX)

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

Date:: November 2011

Definition at line 119 of file cdrvrf3.f.

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subroutine cdrvrf4	(	integer	NOUT,
		integer	NN,
		integer, dimension( nn )	NVAL,
		real	THRESH,
		complex, dimension( ldc, * )	C1,
		complex, dimension( ldc, *)	C2,
		integer	LDC,
		complex, dimension( * )	CRF,
		complex, dimension( lda, * )	A,
		integer	LDA,
		real, dimension( * )	S_WORK_CLANGE
	)

CDRVRF4

Purpose:

 CDRVRF4 tests the LAPACK RFP routines:
     CHFRK

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 COMPLEX array, dimension (LDC,NMAX)
[out]	C2	C2 is COMPLEX array, dimension (LDC,NMAX)
[in]	LDC	LDC is INTEGER The leading dimension of the array A. LDA >= max(1,NMAX).
[out]	CRF	CRF is COMPLEX array, dimension ((NMAX*(NMAX+1))/2).
[out]	A	A is COMPLEX array, dimension (LDA,NMAX)
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= max(1,NMAX).
[out]	S_WORK_CLANGE	S_WORK_CLANGE 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 114 of file cdrvrf4.f.

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subroutine cdrvrfp	(	integer	NOUT,
		integer	NN,
		integer, dimension( nn )	NVAL,
		integer	NNS,
		integer, dimension( nns )	NSVAL,
		integer	NNT,
		integer, dimension( nnt )	NTVAL,
		real	THRESH,
		complex, dimension( * )	A,
		complex, dimension( * )	ASAV,
		complex, dimension( * )	AFAC,
		complex, dimension( * )	AINV,
		complex, dimension( * )	B,
		complex, dimension( * )	BSAV,
		complex, dimension( * )	XACT,
		complex, dimension( * )	X,
		complex, dimension( * )	ARF,
		complex, dimension( * )	ARFINV,
		complex, dimension( * )	C_WORK_CLATMS,
		complex, dimension( * )	C_WORK_CPOT02,
		complex, dimension( * )	C_WORK_CPOT03,
		real, dimension( * )	S_WORK_CLATMS,
		real, dimension( * )	S_WORK_CLANHE,
		real, dimension( * )	S_WORK_CPOT01,
		real, dimension( * )	S_WORK_CPOT02,
		real, dimension( * )	S_WORK_CPOT03
	)

CDRVRFP

Purpose:

 CDRVRFP tests the LAPACK RFP routines:
     CPFTRF, CPFTRS, and CPFTRI.

 This testing routine follow the same tests as CDRVPO (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 CTRTTF and
 CTFTTR.

 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 CPFTRF, 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 CPFTRF 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 COMPLEX array, dimension (NMAX*NMAX)
[out]	ASAV	ASAV is COMPLEX array, dimension (NMAX*NMAX)
[out]	AFAC	AFAC is COMPLEX array, dimension (NMAX*NMAX)
[out]	AINV	AINV is COMPLEX array, dimension (NMAX*NMAX)
[out]	B	B is COMPLEX array, dimension (NMAX*MAXRHS)
[out]	BSAV	BSAV is COMPLEX array, dimension (NMAX*MAXRHS)
[out]	XACT	XACT is COMPLEX array, dimension (NMAX*MAXRHS)
[out]	X	X is COMPLEX array, dimension (NMAX*MAXRHS)
[out]	ARF	ARF is COMPLEX array, dimension ((NMAX*(NMAX+1))/2)
[out]	ARFINV	ARFINV is COMPLEX array, dimension ((NMAX*(NMAX+1))/2)
[out]	C_WORK_CLATMS	C_WORK_CLATMS is COMPLEX array, dimension ( 3*NMAX )
[out]	C_WORK_CPOT02	C_WORK_CPOT02 is COMPLEX array, dimension ( NMAX*MAXRHS )
[out]	C_WORK_CPOT03	C_WORK_CPOT03 is COMPLEX array, dimension ( NMAX*NMAX )
[out]	S_WORK_CLATMS	S_WORK_CLATMS is REAL array, dimension ( NMAX )
[out]	S_WORK_CLANHE	S_WORK_CLANHE is REAL array, dimension ( NMAX )
[out]	S_WORK_CPOT01	S_WORK_CPOT01 is REAL array, dimension ( NMAX )
[out]	S_WORK_CPOT02	S_WORK_CPOT02 is REAL array, dimension ( NMAX )
[out]	S_WORK_CPOT03	S_WORK_CPOT03 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 240 of file cdrvrfp.f.

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

CDRVSP

Purpose:

 CDRVSP tests the driver routines CSPSV 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 COMPLEX array, dimension (NMAX*(NMAX+1)/2)
[out]	AFAC	AFAC is COMPLEX array, dimension (NMAX*(NMAX+1)/2)
[out]	AINV	AINV is COMPLEX array, dimension (NMAX*(NMAX+1)/2)
[out]	B	B is COMPLEX array, dimension (NMAX*NRHS)
[out]	X	X is COMPLEX array, dimension (NMAX*NRHS)
[out]	XACT	XACT is COMPLEX array, dimension (NMAX*NRHS)
[out]	WORK	WORK is COMPLEX array, dimension (NMAX*max(2,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 156 of file cdrvsp.f.

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

CDRVSY

CDRVSYX

Purpose:

 CDRVSY tests the driver routines CSYSV 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 COMPLEX array, dimension (NMAX*NMAX)
[out]	AFAC	AFAC is COMPLEX array, dimension (NMAX*NMAX)
[out]	AINV	AINV is COMPLEX array, dimension (NMAX*NMAX)
[out]	B	B is COMPLEX array, dimension (NMAX*NRHS)
[out]	X	X is COMPLEX array, dimension (NMAX*NRHS)
[out]	XACT	XACT is COMPLEX array, dimension (NMAX*NRHS)
[out]	WORK	WORK is COMPLEX array, dimension (NMAX*max(2,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:

 CDRVSY tests the driver routines CSYSV, -SVX, and -SVXX.

 Note that this file is used only when the XBLAS are available,
 otherwise cdrvsy.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 COMPLEX array, dimension (NMAX*NMAX)
[out]	AFAC	AFAC is COMPLEX array, dimension (NMAX*NMAX)
[out]	AINV	AINV is COMPLEX array, dimension (NMAX*NMAX)
[out]	B	B is COMPLEX array, dimension (NMAX*NRHS)
[out]	X	X is COMPLEX array, dimension (NMAX*NRHS)
[out]	XACT	XACT is COMPLEX array, dimension (NMAX*NRHS)
[out]	WORK	WORK is COMPLEX array, dimension (NMAX*max(2,NRHS))
[out]	RWORK	RWORK is REAL array, dimension (2NMAX+2NRHS)
[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:: April 2012

Definition at line 153 of file cdrvsy.f.

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subroutine cebchvxx	(	real	THRESH,
		character*3	PATH
	)

CEBCHVXX

Purpose:

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

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

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

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

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

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

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

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

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

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

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

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

Date:: November 2011

Definition at line 97 of file cebchvxx.f.

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subroutine cerrge	(	character*3	PATH,
		integer	NUNIT
	)

CERRGE

CERRGEX

Purpose:

 CERRGE tests the error exits for the COMPLEX 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:

 CERRGE tests the error exits for the COMPLEX routines
 for general matrices.

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

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subroutine cerrgt	(	character*3	PATH,
		integer	NUNIT
	)

CERRGT

Purpose:

 CERRGT tests the error exits for the COMPLEX 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 cerrgt.f.

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subroutine cerrhe	(	character*3	PATH,
		integer	NUNIT
	)

CERRHE

CERRHEX

Purpose:

 CERRHE tests the error exits for the COMPLEX routines
 for Hermitian indefinite matrices.

Parameters:

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

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

Date:: November 2011

Purpose:

 CERRHE tests the error exits for the COMPLEX routines
 for Hermitian indefinite matrices.

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

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subroutine cerrlq	(	character*3	PATH,
		integer	NUNIT
	)

CERRLQ

Purpose:

 CERRLQ tests the error exits for the COMPLEX 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 cerrlq.f.

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subroutine cerrls	(	character*3	PATH,
		integer	NUNIT
	)

CERRLS

Purpose:

 CERRLS tests the error exits for the COMPLEX least squares
 driver routines (CGELS, CGELSS, CGELSX, CGELSY, CGELSD).

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 cerrls.f.

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subroutine cerrpo	(	character*3	PATH,
		integer	NUNIT
	)

CERRPO

CERRPOX

Purpose:

 CERRPO tests the error exits for the COMPLEX routines
 for Hermitian 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:

 CERRPO tests the error exits for the COMPLEX routines
 for Hermitian positive definite matrices.

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

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subroutine cerrps	(	character*3	PATH,
		integer	NUNIT
	)

CERRPS

Purpose:

 CERRPS tests the error exits for the COMPLEX routines
 for CPSTRF..

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 cerrps.f.

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subroutine cerrql	(	character*3	PATH,
		integer	NUNIT
	)

CERRQL

Purpose:

 CERRQL tests the error exits for the COMPLEX 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 cerrql.f.

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subroutine cerrqp	(	character*3	PATH,
		integer	NUNIT
	)

CERRQP

Purpose:

 CERRQP tests the error exits for CGEQPF and CGEQP3.

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 cerrqp.f.

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subroutine cerrqr	(	character*3	PATH,
		integer	NUNIT
	)

CERRQR

Purpose:

 CERRQR tests the error exits for the COMPLEX 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 cerrqr.f.

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subroutine cerrqrt	(	character*3	PATH,
		integer	NUNIT
	)

CERRQRT

Purpose:

 CERRQRT tests the error exits for the COMPLEX 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 cerrqrt.f.

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subroutine cerrqrtp	(	character*3	PATH,
		integer	NUNIT
	)

CERRQRTP

Purpose:

 CERRQRTP 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 cerrqrtp.f.

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subroutine cerrrfp ( integer NUNIT )

CERRRFP

Purpose:

 CERRRFP tests the error exits for the COMPLEX driver routines
 for solving linear systems of equations.

 CDRVRFP tests the COMPLEX LAPACK RFP routines:
     CTFSM, CTFTRI, CHFRK, CTFTTP, CTFTTR, CPFTRF, CPFTRS, CTPTTF,
     CTPTTR, CTRTTF, and CTRTTP

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 cerrrfp.f.

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subroutine cerrrq	(	character*3	PATH,
		integer	NUNIT
	)

CERRRQ

Purpose:

 CERRRQ tests the error exits for the COMPLEX 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 cerrrq.f.

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subroutine cerrsy	(	character*3	PATH,
		integer	NUNIT
	)

CERRSY

CERRSYX

Purpose:

 CERRSY tests the error exits for the COMPLEX 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:

 CERRSY tests the error exits for the COMPLEX routines
 for symmetric indefinite matrices.

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

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subroutine cerrtr	(	character*3	PATH,
		integer	NUNIT
	)

CERRTR

Purpose:

 CERRTR tests the error exits for the COMPLEX 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 55 of file cerrtr.f.

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subroutine cerrtz	(	character*3	PATH,
		integer	NUNIT
	)

CERRTZ

Purpose:

 CERRTZ tests the error exits for CTZRQF and CTZRZF.

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 cerrtz.f.

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subroutine cerrvx	(	character*3	PATH,
		integer	NUNIT
	)

CERRVX

CERRVXX

Purpose:

 CERRVX tests the error exits for the COMPLEX 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:

 CERRVX tests the error exits for the COMPLEX 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 cerrvx.f.

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subroutine cgbt01	(	integer	M,
		integer	N,
		integer	KL,
		integer	KU,
		complex, dimension( lda, * )	A,
		integer	LDA,
		complex, dimension( ldafac, * )	AFAC,
		integer	LDAFAC,
		integer, dimension( * )	IPIV,
		complex, dimension( * )	WORK,
		real	RESID
	)

CGBT01

Purpose:

 CGBT01 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 COMPLEX 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 COMPLEX 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 CGBTRF. 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 CGBTRF 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 CGBTRF.
[out]	WORK	WORK is COMPLEX 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 cgbt01.f.

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subroutine cgbt02	(	character	TRANS,
		integer	M,
		integer	N,
		integer	KL,
		integer	KU,
		integer	NRHS,
		complex, dimension( lda, * )	A,
		integer	LDA,
		complex, dimension( ldx, * )	X,
		integer	LDX,
		complex, dimension( ldb, * )	B,
		integer	LDB,
		real	RESID
	)

CGBT02

Purpose:

 CGBT02 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 COMPLEX 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 COMPLEX 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 COMPLEX 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 cgbt02.f.

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subroutine cgbt05	(	character	TRANS,
		integer	N,
		integer	KL,
		integer	KU,
		integer	NRHS,
		complex, dimension( ldab, * )	AB,
		integer	LDAB,
		complex, dimension( ldb, * )	B,
		integer	LDB,
		complex, dimension( ldx, * )	X,
		integer	LDX,
		complex, dimension( ldxact, * )	XACT,
		integer	LDXACT,
		real, dimension( * )	FERR,
		real, dimension( * )	BERR,
		real, dimension( * )	RESLTS
	)

CGBT05

Purpose:

 CGBT05 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 COMPLEX 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 COMPLEX 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 COMPLEX 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 COMPLEX 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 cgbt05.f.

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

CGELQS

Purpose:

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

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

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LOGICAL function cgennd	(	integer	M,
		integer	N,
		complex, dimension( lda, * )	A,
		integer	LDA
	)

CGENND

Purpose:

    CGENND tests that its argument has a real, 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 COMPLEX 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 cgennd.f.

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

CGEQLS

Purpose:

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

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

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

CGEQRS

Purpose:

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

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

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

CGERQS

Purpose:

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

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

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subroutine cget01	(	integer	M,
		integer	N,
		complex, dimension( lda, * )	A,
		integer	LDA,
		complex, dimension( ldafac, * )	AFAC,
		integer	LDAFAC,
		integer, dimension( * )	IPIV,
		real, dimension( * )	RWORK,
		real	RESID
	)

CGET01

Purpose:

 CGET01 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 COMPLEX 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 COMPLEX 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 CGETRF. 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 CGETRF.
[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 108 of file cget01.f.

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subroutine cget02	(	character	TRANS,
		integer	M,
		integer	N,
		integer	NRHS,
		complex, dimension( lda, * )	A,
		integer	LDA,
		complex, dimension( ldx, * )	X,
		integer	LDX,
		complex, dimension( ldb, * )	B,
		integer	LDB,
		real, dimension( * )	RWORK,
		real	RESID
	)

CGET02

Purpose:

 CGET02 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^Tx = b, where A^T is the transpose of A = 'C': A^Hx = b, where A^H is the conjugate 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 COMPLEX 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 COMPLEX 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 COMPLEX 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 cget02.f.

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subroutine cget03	(	integer	N,
		complex, dimension( lda, * )	A,
		integer	LDA,
		complex, dimension( ldainv, * )	AINV,
		integer	LDAINV,
		complex, dimension( ldwork, * )	WORK,
		integer	LDWORK,
		real, dimension( * )	RWORK,
		real	RCOND,
		real	RESID
	)

CGET03

Purpose:

 CGET03 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 COMPLEX 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 COMPLEX 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 COMPLEX 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 110 of file cget03.f.

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subroutine cget04	(	integer	N,
		integer	NRHS,
		complex, dimension( ldx, * )	X,
		integer	LDX,
		complex, dimension( ldxact, * )	XACT,
		integer	LDXACT,
		real	RCOND,
		real	RESID
	)

CGET04

Purpose:

 CGET04 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 COMPLEX 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 COMPLEX 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 cget04.f.

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subroutine cget07	(	character	TRANS,
		integer	N,
		integer	NRHS,
		complex, dimension( lda, * )	A,
		integer	LDA,
		complex, dimension( ldb, * )	B,
		integer	LDB,
		complex, dimension( ldx, * )	X,
		integer	LDX,
		complex, dimension( ldxact, * )	XACT,
		integer	LDXACT,
		real, dimension( * )	FERR,
		logical	CHKFERR,
		real, dimension( * )	BERR,
		real, dimension( * )	RESLTS
	)

CGET07

Purpose:

 CGET07 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 COMPLEX 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 COMPLEX 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 COMPLEX 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 COMPLEX 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 166 of file cget07.f.

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subroutine cgtt01	(	integer	N,
		complex, dimension( * )	DL,
		complex, dimension( * )	D,
		complex, dimension( * )	DU,
		complex, dimension( * )	DLF,
		complex, dimension( * )	DF,
		complex, dimension( * )	DUF,
		complex, dimension( * )	DU2,
		integer, dimension( * )	IPIV,
		complex, dimension( ldwork, * )	WORK,
		integer	LDWORK,
		real, dimension( * )	RWORK,
		real	RESID
	)

CGTT01

Purpose:

 CGTT01 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 COMPLEX array, dimension (N-1) The (n-1) sub-diagonal elements of A.
[in]	D	D is COMPLEX array, dimension (N) The diagonal elements of A.
[in]	DU	DU is COMPLEX array, dimension (N-1) The (n-1) super-diagonal elements of A.
[in]	DLF	DLF is COMPLEX array, dimension (N-1) The (n-1) multipliers that define the matrix L from the LU factorization of A.
[in]	DF	DF is COMPLEX array, dimension (N) The n diagonal elements of the upper triangular matrix U from the LU factorization of A.
[in]	DUF	DUF is COMPLEX array, dimension (N-1) The (n-1) elements of the first super-diagonal of U.
[in]	DU2	DU2 is COMPLEX 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 COMPLEX 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 cgtt01.f.

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subroutine cgtt02	(	character	TRANS,
		integer	N,
		integer	NRHS,
		complex, dimension( * )	DL,
		complex, dimension( * )	D,
		complex, dimension( * )	DU,
		complex, dimension( ldx, * )	X,
		integer	LDX,
		complex, dimension( ldb, * )	B,
		integer	LDB,
		real	RESID
	)

CGTT02

Purpose:

 CGTT02 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*T X (Transpose) = 'C': B - A*H X (Conjugate 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 COMPLEX array, dimension (N-1) The (n-1) sub-diagonal elements of A.
[in]	D	D is COMPLEX array, dimension (N) The diagonal elements of A.
[in]	DU	DU is COMPLEX array, dimension (N-1) The (n-1) super-diagonal elements of A.
[in]	X	X is COMPLEX 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 COMPLEX 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 cgtt02.f.

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subroutine cgtt05	(	character	TRANS,
		integer	N,
		integer	NRHS,
		complex, dimension( * )	DL,
		complex, dimension( * )	D,
		complex, dimension( * )	DU,
		complex, dimension( ldb, * )	B,
		integer	LDB,
		complex, dimension( ldx, * )	X,
		integer	LDX,
		complex, dimension( ldxact, * )	XACT,
		integer	LDXACT,
		real, dimension( * )	FERR,
		real, dimension( * )	BERR,
		real, dimension( * )	RESLTS
	)

CGTT05

Purpose:

 CGTT05 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 COMPLEX array, dimension (N-1) The (n-1) sub-diagonal elements of A.
[in]	D	D is COMPLEX array, dimension (N) The diagonal elements of A.
[in]	DU	DU is COMPLEX array, dimension (N-1) The (n-1) super-diagonal elements of A.
[in]	B	B is COMPLEX 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 COMPLEX 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 COMPLEX 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 cgtt05.f.

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subroutine chet01	(	character	UPLO,
		integer	N,
		complex, dimension( lda, * )	A,
		integer	LDA,
		complex, dimension( ldafac, * )	AFAC,
		integer	LDAFAC,
		integer, dimension( * )	IPIV,
		complex, dimension( ldc, * )	C,
		integer	LDC,
		real, dimension( * )	RWORK,
		real	RESID
	)

CHET01

Purpose:

 CHET01 reconstructs a Hermitian 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, 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 Hermitian 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 COMPLEX array, dimension (LDA,N) The original Hermitian matrix A.
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N)
[in]	AFAC	AFAC is COMPLEX 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 CHETRF.
[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 CHETRF.
[out]	C	C is COMPLEX 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 126 of file chet01.f.

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subroutine chkxer	(	character()	SRNAMT,
		integer	INFOT,
		integer	NOUT,
		logical	LERR,
		logical	OK
	)

CHKXER

Purpose:

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

Date:: November 2011

Definition at line 60 of file chkxer.f.

subroutine chpt01	(	character	UPLO,
		integer	N,
		complex, dimension( * )	A,
		complex, dimension( * )	AFAC,
		integer, dimension( * )	IPIV,
		complex, dimension( ldc, * )	C,
		integer	LDC,
		real, dimension( * )	RWORK,
		real	RESID
	)

CHPT01

Purpose:

 CHPT01 reconstructs a Hermitian 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, 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 Hermitian 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 COMPLEX array, dimension (N*(N+1)/2) The original Hermitian matrix A, stored as a packed triangular matrix.
[in]	AFAC	AFAC is COMPLEX 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 CHPTRF.
[in]	IPIV	IPIV is INTEGER array, dimension (N) The pivot indices from CHPTRF.
[out]	C	C is COMPLEX 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 114 of file chpt01.f.

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subroutine clahilb	(	integer	N,
		integer	NRHS,
		complex, dimension(lda,n)	A,
		integer	LDA,
		complex, dimension(ldx, nrhs)	X,
		integer	LDX,
		complex, dimension(ldb, nrhs)	B,
		integer	LDB,
		real, dimension(n)	WORK,
		integer	INFO,
		character*3	PATH
	)

CLAHILB

Purpose:

 CLAHILB 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 COMPLEX 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 COMPLEX 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
[in]	PATH	PATH is CHARACTER*3 The LAPACK path name.

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

Date:: November 2011

Definition at line 134 of file clahilb.f.

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subroutine claipd	(	integer	N,
		complex, dimension( * )	A,
		integer	INDA,
		integer	VINDA
	)

CLAIPD

Purpose:

 CLAIPD sets the imaginary part of the diagonal elements of a complex
 matrix A to a large value.  This is used to test LAPACK routines for
 complex Hermitian matrices, which are not supposed to access or use
 the imaginary parts of the diagonals.

Parameters:

[in]	N	N is INTEGER The number of diagonal elements of A.
[in,out]	A	A is COMPLEX array, dimension (1+(N-1)INDA+(N-2)VINDA) On entry, the complex (Hermitian) matrix A. On exit, the imaginary parts of the diagonal elements are set to BIGNUM = EPS / SAFMIN, where EPS is the machine epsilon and SAFMIN is the safe minimum.
[in]	INDA	INDA is INTEGER The increment between A(1) and the next diagonal element of A. Typical values are = LDA+1: square matrices with leading dimension LDA = 2: packed upper triangular matrix, starting at A(1,1) = N: packed lower triangular matrix, starting at A(1,1)
[in]	VINDA	VINDA is INTEGER The change in the diagonal increment between columns of A. Typical values are = 0: no change, the row and column increments in A are fixed = 1: packed upper triangular matrix = -1: packed lower triangular matrix

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

Date:: November 2011

Definition at line 84 of file claipd.f.

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

CLAPTM

Purpose:

 CLAPTM multiplies an N by NRHS matrix X by a Hermitian 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]	UPLO	UPLO is CHARACTER Specifies whether the superdiagonal or the subdiagonal of the tridiagonal matrix A is stored. = 'U': Upper, E is the superdiagonal of A. = 'L': Lower, E is the subdiagonal of A.
[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 COMPLEX array, dimension (N-1) The (n-1) subdiagonal or superdiagonal elements of A.
[in]	X	X is COMPLEX 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 COMPLEX 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 129 of file claptm.f.

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

CLARHS

Purpose:

 CLARHS 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, A**T (transpose of A), or A**H (conjugate
 transpose of A).

Parameters:

[in]	PATH	PATH is CHARACTER*3 The type of the complex matrix A. PATH may be given in any combination of upper and lower case. Valid paths include xGE: General m x n matrix xGB: General banded matrix xPO: Hermitian positive definite, 2-D storage xPP: Hermitian positive definite packed xPB: Hermitian positive definite banded xHE: Hermitian indefinite, 2-D storage xHP: Hermitian indefinite packed xHB: Hermitian indefinite 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 Used only if A is symmetric or triangular; specifies whether the upper or lower triangular part of the matrix A is stored. = 'U': Upper triangular = 'L': Lower triangular
[in]	TRANS	TRANS is CHARACTER1 Used only if A is nonsymmetric; specifies the operation applied to the matrix A. = 'N': B := A X = 'T': B := A*T X = 'C': B := A*H X
[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 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 COMPLEX 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) COMPLEX 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 COMPLEX 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 CLATMS). Modified on exit.
[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 209 of file clarhs.f.

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subroutine clatb4	(	character*3	PATH,
		integer	IMAT,
		integer	M,
		integer	N,
		character	TYPE,
		integer	KL,
		integer	KU,
		real	ANORM,
		integer	MODE,
		real	CNDNUM,
		character	DIST
	)

CLATB4

Purpose:

 CLATB4 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 clatb4.f.

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subroutine clatb5	(	character*3	PATH,
		integer	IMAT,
		integer	N,
		character	TYPE,
		integer	KL,
		integer	KU,
		real	ANORM,
		integer	MODE,
		real	CNDNUM,
		character	DIST
	)

CLATB5

Purpose:

 CLATB5 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 clatb5.f.

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subroutine clatsp	(	character	UPLO,
		integer	N,
		complex, dimension( * )	X,
		integer, dimension( * )	ISEED
	)

CLATSP

Purpose:

 CLATSP generates a special test matrix for the complex symmetric
 (indefinite) factorization for packed matrices.  The pivot blocks of
 the generated matrix will be in the following order:
    2x2 pivot block, non diagonalizable
    1x1 pivot block
    2x2 pivot block, diagonalizable
    (cycle repeats)
 A row interchange is required for each non-diagonalizable 2x2 block.

Parameters:

[in]	UPLO	UPLO is CHARACTER Specifies whether the generated matrix is to be upper or lower triangular. = 'U': Upper triangular = 'L': Lower triangular
[in]	N	N is INTEGER The dimension of the matrix to be generated.
[out]	X	X is COMPLEX array, dimension (N*(N+1)/2) The generated matrix in packed storage format. The matrix consists of 3x3 and 2x2 diagonal blocks which result in the pivot sequence given above. The matrix outside these diagonal blocks is zero.
[in,out]	ISEED	ISEED is INTEGER array, dimension (4) On entry, the seed for the random number generator. The last of the four integers must be odd. (modified on exit)

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

Date:: November 2011

Definition at line 85 of file clatsp.f.

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subroutine clatsy	(	character	UPLO,
		integer	N,
		complex, dimension( ldx, * )	X,
		integer	LDX,
		integer, dimension( * )	ISEED
	)

CLATSY

Purpose:

 CLATSY generates a special test matrix for the complex symmetric
 (indefinite) factorization.  The pivot blocks of the generated matrix
 will be in the following order:
    2x2 pivot block, non diagonalizable
    1x1 pivot block
    2x2 pivot block, diagonalizable
    (cycle repeats)
 A row interchange is required for each non-diagonalizable 2x2 block.

Parameters:

[in]	UPLO	UPLO is CHARACTER Specifies whether the generated matrix is to be upper or lower triangular. = 'U': Upper triangular = 'L': Lower triangular
[in]	N	N is INTEGER The dimension of the matrix to be generated.
[out]	X	X is COMPLEX array, dimension (LDX,N) The generated matrix, consisting of 3x3 and 2x2 diagonal blocks which result in the pivot sequence given above. The matrix outside of these diagonal blocks is zero.
[in]	LDX	LDX is INTEGER The leading dimension of the array X.
[in,out]	ISEED	ISEED is INTEGER array, dimension (4) On entry, the seed for the random number generator. The last of the four integers must be odd. (modified on exit)

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

Date:: November 2011

Definition at line 90 of file clatsy.f.

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

CLATTB

Purpose:

 CLATTB 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 CLATMS). 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 COMPLEX 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 COMPLEX array, dimension (N)
[out]	WORK	WORK is COMPLEX array, dimension (2*N)
[out]	RWORK	RWORK is REAL array, dimension (N)
[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 141 of file clattb.f.

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subroutine clattp	(	integer	IMAT,
		character	UPLO,
		character	TRANS,
		character	DIAG,
		integer, dimension( 4 )	ISEED,
		integer	N,
		complex, dimension( * )	AP,
		complex, dimension( * )	B,
		complex, dimension( * )	WORK,
		real, dimension( * )	RWORK,
		integer	INFO
	)

CLATTP

Purpose:

 CLATTP 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
[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 CLATMS). Modified on exit.
[in]	N	N is INTEGER The order of the matrix to be generated.
[out]	AP	AP is COMPLEX 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 COMPLEX array, dimension (N) The right hand side vector, if IMAT > 10.
[out]	WORK	WORK is COMPLEX array, dimension (2*N)
[out]	RWORK	RWORK is REAL array, dimension (N)
[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 131 of file clattp.f.

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

CLATTR

Purpose:

 CLATTR 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
[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 CLATMS). Modified on exit.
[in]	N	N is INTEGER The order of the matrix to be generated.
[out]	A	A is COMPLEX array, dimension (LDA,N) The triangular matrix A. If UPLO = 'U', the leading N x 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 x N lower triangular part of the array A contains the lower triangular matrix 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).
[out]	B	B is COMPLEX array, dimension (N) The right hand side vector, if IMAT > 10.
[out]	WORK	WORK is COMPLEX array, dimension (2*N)
[out]	RWORK	RWORK is REAL array, dimension (N)
[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 138 of file clattr.f.

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

CLAVHE

Purpose:

    CLAVHE  performs one of the matrix-vector operations
       x := A*x  or  x := A^H*x,
    where x is an N element vector and  A is one of the factors
    from the symmetric factorization computed by CHETRF.
    CHETRF produces a factorization of the form
         U * D * U^H     or     L * D * L^H,
    where U (or L) is a product of permutation and unit upper (lower)
    triangular matrices, U^H (or L^H) is the conjugate transpose of
    U (or L), and D is Hermitian and block diagonal with 1 x 1 and
    2 x 2 diagonal blocks.  The multipliers for the transformations
    and the upper or lower triangular parts of the diagonal blocks
    are stored in the leading upper or lower triangle of the 2-D
    array A.

    If TRANS = 'N' or 'n', CLAVHE multiplies either by U or U * D
    (or L or L * D).
    If TRANS = 'C' or 'c', CLAVHE multiplies either by U^H or D * U^H
    (or L^H or D * L^H ).

  UPLO   - CHARACTER*1
           On entry, UPLO specifies whether the triangular matrix
           stored in A is upper or lower triangular.
              UPLO = 'U' or 'u'   The matrix is upper triangular.
              UPLO = 'L' or 'l'   The matrix is lower triangular.
           Unchanged on exit.

  TRANS  - CHARACTER*1
           On entry, TRANS specifies the operation to be performed as
           follows:
              TRANS = 'N' or 'n'   x := A*x.
              TRANS = 'C' or 'c'   x := A^H*x.
           Unchanged on exit.

  DIAG   - CHARACTER*1
           On entry, DIAG specifies whether the diagonal blocks are
           assumed to be unit matrices:
              DIAG = 'U' or 'u'   Diagonal blocks are unit matrices.
              DIAG = 'N' or 'n'   Diagonal blocks are non-unit.
           Unchanged on exit.

  N      - INTEGER
           On entry, N specifies the order of the matrix A.
           N must be at least zero.
           Unchanged on exit.

  NRHS   - INTEGER
           On entry, NRHS specifies the number of right hand sides,
           i.e., the number of vectors x to be multiplied by A.
           NRHS must be at least zero.
           Unchanged on exit.

  A      - COMPLEX array, dimension( LDA, N )
           On entry, A contains a block diagonal matrix and the
           multipliers of the transformations used to obtain it,
           stored as a 2-D triangular matrix.
           Unchanged on exit.

  LDA    - INTEGER
           On entry, LDA specifies the first dimension of A as declared
           in the calling ( sub ) program. LDA must be at least
           max( 1, N ).
           Unchanged on exit.

  IPIV   - INTEGER array, dimension( N )
           On entry, IPIV contains the vector of pivot indices as
           determined by CSYTRF or CHETRF.
           If IPIV( K ) = K, no interchange was done.
           If IPIV( K ) <> K but IPIV( K ) > 0, then row K was inter-
           changed with row IPIV( K ) and a 1 x 1 pivot block was used.
           If IPIV( K ) < 0 and UPLO = 'U', then row K-1 was exchanged
           with row | IPIV( K ) | and a 2 x 2 pivot block was used.
           If IPIV( K ) < 0 and UPLO = 'L', then row K+1 was exchanged
           with row | IPIV( K ) | and a 2 x 2 pivot block was used.

  B      - COMPLEX array, dimension( LDB, NRHS )
           On entry, B contains NRHS vectors of length N.
           On exit, B is overwritten with the product A * B.

  LDB    - INTEGER
           On entry, LDB contains the leading dimension of B as
           declared in the calling program.  LDB must be at least
           max( 1, N ).
           Unchanged on exit.

  INFO   - INTEGER
           INFO is the error flag.
           On exit, a value of 0 indicates a successful exit.
           A negative value, say -K, indicates that the K-th argument
           has an illegal value.

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

Date:: November 2011

Definition at line 138 of file clavhe.f.

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

CLAVHP

Purpose:

    CLAVHP  performs one of the matrix-vector operations
       x := A*x  or  x := A^H*x,
    where x is an N element vector and  A is one of the factors
    from the symmetric factorization computed by CHPTRF.
    CHPTRF produces a factorization of the form
         U * D * U^H     or     L * D * L^H,
    where U (or L) is a product of permutation and unit upper (lower)
    triangular matrices, U^H (or L^H) is the conjugate transpose of
    U (or L), and D is Hermitian and block diagonal with 1 x 1 and
    2 x 2 diagonal blocks.  The multipliers for the transformations
    and the upper or lower triangular parts of the diagonal blocks
    are stored columnwise in packed format in the linear array A.

    If TRANS = 'N' or 'n', CLAVHP multiplies either by U or U * D
    (or L or L * D).
    If TRANS = 'C' or 'c', CLAVHP multiplies either by U^H or D * U^H
    (or L^H or D * L^H ).

  UPLO   - CHARACTER*1
           On entry, UPLO specifies whether the triangular matrix
           stored in A is upper or lower triangular.
              UPLO = 'U' or 'u'   The matrix is upper triangular.
              UPLO = 'L' or 'l'   The matrix is lower triangular.
           Unchanged on exit.

  TRANS  - CHARACTER*1
           On entry, TRANS specifies the operation to be performed as
           follows:
              TRANS = 'N' or 'n'   x := A*x.
              TRANS = 'C' or 'c'   x := A^H*x.
           Unchanged on exit.

  DIAG   - CHARACTER*1
           On entry, DIAG specifies whether the diagonal blocks are
           assumed to be unit matrices, as follows:
              DIAG = 'U' or 'u'   Diagonal blocks are unit matrices.
              DIAG = 'N' or 'n'   Diagonal blocks are non-unit.
           Unchanged on exit.

  N      - INTEGER
           On entry, N specifies the order of the matrix A.
           N must be at least zero.
           Unchanged on exit.

  NRHS   - INTEGER
           On entry, NRHS specifies the number of right hand sides,
           i.e., the number of vectors x to be multiplied by A.
           NRHS must be at least zero.
           Unchanged on exit.

  A      - COMPLEX array, dimension( N*(N+1)/2 )
           On entry, A contains a block diagonal matrix and the
           multipliers of the transformations used to obtain it,
           stored as a packed triangular matrix.
           Unchanged on exit.

  IPIV   - INTEGER array, dimension( N )
           On entry, IPIV contains the vector of pivot indices as
           determined by CSPTRF or CHPTRF.
           If IPIV( K ) = K, no interchange was done.
           If IPIV( K ) <> K but IPIV( K ) > 0, then row K was inter-
           changed with row IPIV( K ) and a 1 x 1 pivot block was used.
           If IPIV( K ) < 0 and UPLO = 'U', then row K-1 was exchanged
           with row | IPIV( K ) | and a 2 x 2 pivot block was used.
           If IPIV( K ) < 0 and UPLO = 'L', then row K+1 was exchanged
           with row | IPIV( K ) | and a 2 x 2 pivot block was used.

  B      - COMPLEX array, dimension( LDB, NRHS )
           On entry, B contains NRHS vectors of length N.
           On exit, B is overwritten with the product A * B.

  LDB    - INTEGER
           On entry, LDB contains the leading dimension of B as
           declared in the calling program.  LDB must be at least
           max( 1, N ).
           Unchanged on exit.

  INFO   - INTEGER
           INFO is the error flag.
           On exit, a value of 0 indicates a successful exit.
           A negative value, say -K, indicates that the K-th argument
           has an illegal value.

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

Date:: November 2011

Definition at line 131 of file clavhp.f.

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

CLAVSP

Purpose:

    CLAVSP  performs one of the matrix-vector operations
       x := A*x  or  x := A^T*x,
    where x is an N element vector and  A is one of the factors
    from the symmetric factorization computed by CSPTRF.
    CSPTRF produces a factorization of the form
         U * D * U^T     or     L * D * L^T,
    where U (or L) is a product of permutation and unit upper (lower)
    triangular matrices, U^T (or L^T) is the transpose of
    U (or L), and D is symmetric and block diagonal with 1 x 1 and
    2 x 2 diagonal blocks.  The multipliers for the transformations
    and the upper or lower triangular parts of the diagonal blocks
    are stored columnwise in packed format in the linear array A.

    If TRANS = 'N' or 'n', CLAVSP multiplies either by U or U * D
    (or L or L * D).
    If TRANS = 'C' or 'c', CLAVSP multiplies either by U^T or D * U^T
    (or L^T or D * L^T ).

  UPLO   - CHARACTER*1
           On entry, UPLO specifies whether the triangular matrix
           stored in A is upper or lower triangular.
              UPLO = 'U' or 'u'   The matrix is upper triangular.
              UPLO = 'L' or 'l'   The matrix is lower triangular.
           Unchanged on exit.

  TRANS  - CHARACTER*1
           On entry, TRANS specifies the operation to be performed as
           follows:
              TRANS = 'N' or 'n'   x := A*x.
              TRANS = 'T' or 't'   x := A^T*x.
           Unchanged on exit.

  DIAG   - CHARACTER*1
           On entry, DIAG specifies whether the diagonal blocks are
           assumed to be unit matrices, as follows:
              DIAG = 'U' or 'u'   Diagonal blocks are unit matrices.
              DIAG = 'N' or 'n'   Diagonal blocks are non-unit.
           Unchanged on exit.

  N      - INTEGER
           On entry, N specifies the order of the matrix A.
           N must be at least zero.
           Unchanged on exit.

  NRHS   - INTEGER
           On entry, NRHS specifies the number of right hand sides,
           i.e., the number of vectors x to be multiplied by A.
           NRHS must be at least zero.
           Unchanged on exit.

  A      - COMPLEX array, dimension( N*(N+1)/2 )
           On entry, A contains a block diagonal matrix and the
           multipliers of the transformations used to obtain it,
           stored as a packed triangular matrix.
           Unchanged on exit.

  IPIV   - INTEGER array, dimension( N )
           On entry, IPIV contains the vector of pivot indices as
           determined by CSPTRF.
           If IPIV( K ) = K, no interchange was done.
           If IPIV( K ) <> K but IPIV( K ) > 0, then row K was inter-
           changed with row IPIV( K ) and a 1 x 1 pivot block was used.
           If IPIV( K ) < 0 and UPLO = 'U', then row K-1 was exchanged
           with row | IPIV( K ) | and a 2 x 2 pivot block was used.
           If IPIV( K ) < 0 and UPLO = 'L', then row K+1 was exchanged
           with row | IPIV( K ) | and a 2 x 2 pivot block was used.

  B      - COMPLEX array, dimension( LDB, NRHS )
           On entry, B contains NRHS vectors of length N.
           On exit, B is overwritten with the product A * B.

  LDB    - INTEGER
           On entry, LDB contains the leading dimension of B as
           declared in the calling program.  LDB must be at least
           max( 1, N ).
           Unchanged on exit.

  INFO   - INTEGER
           INFO is the error flag.
           On exit, a value of 0 indicates a successful exit.
           A negative value, say -K, indicates that the K-th argument
           has an illegal value.

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

Date:: November 2011

Definition at line 131 of file clavsp.f.

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

CLAVSY

Purpose:

 CLAVSY  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 CSYTRF.

 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')

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
[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 COMPLEX array, dimension (LDA,N) The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by CSYTRF.
[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 CSYTRF or CHETRF. 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 COMPLEX 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 152 of file clavsy.f.

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subroutine clqt01	(	integer	M,
		integer	N,
		complex, dimension( lda, * )	A,
		complex, dimension( lda, * )	AF,
		complex, dimension( lda, * )	Q,
		complex, dimension( lda, * )	L,
		integer	LDA,
		complex, dimension( * )	TAU,
		complex, dimension( lwork )	WORK,
		integer	LWORK,
		real, dimension( * )	RWORK,
		real, dimension( * )	RESULT
	)

CLQT01

Purpose:

 CLQT01 tests CGELQF, which computes the LQ factorization of an m-by-n
 matrix A, and partially tests CUNGLQ which forms the n-by-n
 orthogonal matrix Q.

 CLQT01 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 COMPLEX array, dimension (LDA,N) The m-by-n matrix A.
[out]	AF	AF is COMPLEX array, dimension (LDA,N) Details of the LQ factorization of A, as returned by CGELQF. See CGELQF for further details.
[out]	Q	Q is COMPLEX array, dimension (LDA,N) The n-by-n orthogonal matrix Q.
[out]	L	L is COMPLEX 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 COMPLEX array, dimension (min(M,N)) The scalar factors of the elementary reflectors, as returned by CGELQF.
[out]	WORK	WORK is COMPLEX 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 clqt01.f.

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subroutine clqt02	(	integer	M,
		integer	N,
		integer	K,
		complex, dimension( lda, * )	A,
		complex, dimension( lda, * )	AF,
		complex, dimension( lda, * )	Q,
		complex, dimension( lda, * )	L,
		integer	LDA,
		complex, dimension( * )	TAU,
		complex, dimension( lwork )	WORK,
		integer	LWORK,
		real, dimension( * )	RWORK,
		real, dimension( * )	RESULT
	)

CLQT02

Purpose:

 CLQT02 tests CUNGLQ, 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, CLQT02 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 COMPLEX array, dimension (LDA,N) The m-by-n matrix A which was factorized by CLQT01.
[in]	AF	AF is COMPLEX array, dimension (LDA,N) Details of the LQ factorization of A, as returned by CGELQF. See CGELQF for further details.
[out]	Q	Q is COMPLEX array, dimension (LDA,N)
[out]	L	L is COMPLEX 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 COMPLEX array, dimension (M) The scalar factors of the elementary reflectors corresponding to the LQ factorization in AF.
[out]	WORK	WORK is COMPLEX 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 clqt02.f.

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subroutine clqt03	(	integer	M,
		integer	N,
		integer	K,
		complex, dimension( lda, * )	AF,
		complex, dimension( lda, * )	C,
		complex, dimension( lda, * )	CC,
		complex, dimension( lda, * )	Q,
		integer	LDA,
		complex, dimension( * )	TAU,
		complex, dimension( lwork )	WORK,
		integer	LWORK,
		real, dimension( * )	RWORK,
		real, dimension( * )	RESULT
	)

CLQT03

Purpose:

 CLQT03 tests CUNMLQ, which computes Q*C, Q'*C, C*Q or C*Q'.

 CLQT03 compares the results of a call to CUNMLQ with the results of
 forming Q explicitly by a call to CUNGLQ and then performing matrix
 multiplication by a call to CGEMM.

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 COMPLEX array, dimension (LDA,N) Details of the LQ factorization of an m-by-n matrix, as returned by CGELQF. See CGELQF for further details.
[out]	C	C is COMPLEX array, dimension (LDA,N)
[out]	CC	CC is COMPLEX array, dimension (LDA,N)
[out]	Q	Q is COMPLEX array, dimension (LDA,N)
[in]	LDA	LDA is INTEGER The leading dimension of the arrays AF, C, CC, and Q.
[in]	TAU	TAU is COMPLEX array, dimension (min(M,N)) The scalar factors of the elementary reflectors corresponding to the LQ factorization in AF.
[out]	WORK	WORK is COMPLEX 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 clqt03.f.

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subroutine cpbt01	(	character	UPLO,
		integer	N,
		integer	KD,
		complex, dimension( lda, * )	A,
		integer	LDA,
		complex, dimension( ldafac, * )	AFAC,
		integer	LDAFAC,
		real, dimension( * )	RWORK,
		real	RESID
	)

CPBT01

Purpose:

 CPBT01 reconstructs a Hermitian 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 Hermitian 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 COMPLEX array, dimension (LDA,N) The original Hermitian 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 CPBTRF for further details.
[in]	LDA	LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,KD+1).
[in]	AFAC	AFAC is COMPLEX 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 CPBTRF.
[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 120 of file cpbt01.f.

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subroutine cpbt02	(	character	UPLO,
		integer	N,
		integer	KD,
		integer	NRHS,
		complex, dimension( lda, * )	A,
		integer	LDA,
		complex, dimension( ldx, * )	X,
		integer	LDX,
		complex, dimension( ldb, * )	B,
		integer	LDB,
		real, dimension( * )	RWORK,
		real	RESID
	)

CPBT02

Purpose:

 CPBT02 computes the residual for a solution of a Hermitian 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 Hermitian 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 COMPLEX array, dimension (LDA,N) The original Hermitian 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 CPBTRF for further details.
[in]	LDA	LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,KD+1).
[in]	X	X is COMPLEX 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 COMPLEX 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 cpbt02.f.

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subroutine cpbt05	(	character	UPLO,
		integer	N,
		integer	KD,
		integer	NRHS,
		complex, dimension( ldab, * )	AB,
		integer	LDAB,
		complex, dimension( ldb, * )	B,
		integer	LDB,
		complex, dimension( ldx, * )	X,
		integer	LDX,
		complex, dimension( ldxact, * )	XACT,
		integer	LDXACT,
		real, dimension( * )	FERR,
		real, dimension( * )	BERR,
		real, dimension( * )	RESLTS
	)

CPBT05

Purpose:

 CPBT05 tests the error bounds from iterative refinement for the
 computed solution to a system of equations A*X = B, where A is a
 Hermitian 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 Hermitian 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 COMPLEX array, dimension (LDAB,N) The upper or lower triangle of the Hermitian 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 COMPLEX 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 COMPLEX 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 COMPLEX 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 cpbt05.f.

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subroutine cpot01	(	character	UPLO,
		integer	N,
		complex, dimension( lda, * )	A,
		integer	LDA,
		complex, dimension( ldafac, * )	AFAC,
		integer	LDAFAC,
		real, dimension( * )	RWORK,
		real	RESID
	)

CPOT01

Purpose:

 CPOT01 reconstructs a Hermitian 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, 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 Hermitian 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 COMPLEX array, dimension (LDA,N) The original Hermitian matrix A.
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N)
[in,out]	AFAC	AFAC is COMPLEX 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 107 of file cpot01.f.

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subroutine cpot02	(	character	UPLO,
		integer	N,
		integer	NRHS,
		complex, dimension( lda, * )	A,
		integer	LDA,
		complex, dimension( ldx, * )	X,
		integer	LDX,
		complex, dimension( ldb, * )	B,
		integer	LDB,
		real, dimension( * )	RWORK,
		real	RESID
	)

CPOT02

Purpose:

 CPOT02 computes the residual for the solution of a Hermitian 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 Hermitian 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 COMPLEX array, dimension (LDA,N) The original Hermitian matrix A.
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N)
[in]	X	X is COMPLEX 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 COMPLEX 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 cpot02.f.

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subroutine cpot03	(	character	UPLO,
		integer	N,
		complex, dimension( lda, * )	A,
		integer	LDA,
		complex, dimension( ldainv, * )	AINV,
		integer	LDAINV,
		complex, dimension( ldwork, * )	WORK,
		integer	LDWORK,
		real, dimension( * )	RWORK,
		real	RCOND,
		real	RESID
	)

CPOT03

Purpose:

 CPOT03 computes the residual for a Hermitian 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 Hermitian 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 COMPLEX array, dimension (LDA,N) The original Hermitian matrix A.
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N)
[in,out]	AINV	AINV is COMPLEX array, dimension (LDAINV,N) On entry, the inverse of the matrix A, stored as a Hermitian 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 COMPLEX 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 126 of file cpot03.f.

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subroutine cpot05	(	character	UPLO,
		integer	N,
		integer	NRHS,
		complex, dimension( lda, * )	A,
		integer	LDA,
		complex, dimension( ldb, * )	B,
		integer	LDB,
		complex, dimension( ldx, * )	X,
		integer	LDX,
		complex, dimension( ldxact, * )	XACT,
		integer	LDXACT,
		real, dimension( * )	FERR,
		real, dimension( * )	BERR,
		real, dimension( * )	RESLTS
	)

CPOT05

Purpose:

 CPOT05 tests the error bounds from iterative refinement for the
 computed solution to a system of equations A*X = B, where A is a
 Hermitian 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 Hermitian 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 COMPLEX array, dimension (LDA,N) The Hermitian 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 COMPLEX 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 COMPLEX 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 COMPLEX 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 165 of file cpot05.f.

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subroutine cppt01	(	character	UPLO,
		integer	N,
		complex, dimension( * )	A,
		complex, dimension( * )	AFAC,
		real, dimension( * )	RWORK,
		real	RESID
	)

CPPT01

Purpose:

 CPPT01 reconstructs a Hermitian 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, 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 Hermitian 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 COMPLEX array, dimension (N*(N+1)/2) The original Hermitian matrix A, stored as a packed triangular matrix.
[in,out]	AFAC	AFAC is COMPLEX 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 96 of file cppt01.f.

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subroutine cppt02	(	character	UPLO,
		integer	N,
		integer	NRHS,
		complex, dimension( * )	A,
		complex, dimension( ldx, * )	X,
		integer	LDX,
		complex, dimension( ldb, * )	B,
		integer	LDB,
		real, dimension( * )	RWORK,
		real	RESID
	)

CPPT02

Purpose:

 CPPT02 computes the residual in the solution of a Hermitian 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 Hermitian 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 COMPLEX array, dimension (N*(N+1)/2) The original Hermitian matrix A, stored as a packed triangular matrix.
[in]	X	X is COMPLEX 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 COMPLEX 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 123 of file cppt02.f.

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subroutine cppt03	(	character	UPLO,
		integer	N,
		complex, dimension( * )	A,
		complex, dimension( * )	AINV,
		complex, dimension( ldwork, * )	WORK,
		integer	LDWORK,
		real, dimension( * )	RWORK,
		real	RCOND,
		real	RESID
	)

CPPT03

Purpose:

 CPPT03 computes the residual for a Hermitian 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 Hermitian 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 COMPLEX array, dimension (N*(N+1)/2) The original Hermitian matrix A, stored as a packed triangular matrix.
[in]	AINV	AINV is COMPLEX array, dimension (N*(N+1)/2) The (Hermitian) inverse of the matrix A, stored as a packed triangular matrix.
[out]	WORK	WORK is COMPLEX 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 cppt03.f.

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subroutine cppt05	(	character	UPLO,
		integer	N,
		integer	NRHS,
		complex, dimension( * )	AP,
		complex, dimension( ldb, * )	B,
		integer	LDB,
		complex, dimension( ldx, * )	X,
		integer	LDX,
		complex, dimension( ldxact, * )	XACT,
		integer	LDXACT,
		real, dimension( * )	FERR,
		real, dimension( * )	BERR,
		real, dimension( * )	RESLTS
	)

CPPT05

Purpose:

 CPPT05 tests the error bounds from iterative refinement for the
 computed solution to a system of equations A*X = B, where A is a
 Hermitian 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 Hermitian 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 COMPLEX array, dimension (N(N+1)/2) The upper or lower triangle of the Hermitian 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 COMPLEX 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 COMPLEX 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 COMPLEX 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 157 of file cppt05.f.

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subroutine cpst01	(	character	UPLO,
		integer	N,
		complex, dimension( lda, * )	A,
		integer	LDA,
		complex, dimension( ldafac, * )	AFAC,
		integer	LDAFAC,
		complex, dimension( ldperm, * )	PERM,
		integer	LDPERM,
		integer, dimension( * )	PIV,
		real, dimension( * )	RWORK,
		real	RESID,
		integer	RANK
	)

CPST01

Purpose:

 CPST01 reconstructs an Hermitian 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, 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 Hermitian 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 COMPLEX array, dimension (LDA,N) The original Hermitian matrix A.
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N)
[in]	AFAC	AFAC is COMPLEX 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 COMPLEX 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 136 of file cpst01.f.

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subroutine cptt01	(	integer	N,
		real, dimension( * )	D,
		complex, dimension( * )	E,
		real, dimension( * )	DF,
		complex, dimension( * )	EF,
		complex, dimension( * )	WORK,
		real	RESID
	)

CPTT01

Purpose:

 CPTT01 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 COMPLEX 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 COMPLEX array, dimension (N-1) The (n-1) subdiagonal elements of the factor L from the LDL' factorization of A.
[out]	WORK	WORK is COMPLEX 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 93 of file cptt01.f.

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subroutine cptt02	(	character	UPLO,
		integer	N,
		integer	NRHS,
		real, dimension( * )	D,
		complex, dimension( * )	E,
		complex, dimension( ldx, * )	X,
		integer	LDX,
		complex, dimension( ldb, * )	B,
		integer	LDB,
		real	RESID
	)

CPTT02

Purpose:

 CPTT02 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]	UPLO	UPLO is CHARACTER*1 Specifies whether the superdiagonal or the subdiagonal of the tridiagonal matrix A is stored. = 'U': E is the superdiagonal of A = 'L': E is the subdiagonal of A
[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 COMPLEX array, dimension (N-1) The (n-1) subdiagonal elements of the tridiagonal matrix A.
[in]	X	X is COMPLEX 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 COMPLEX 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 116 of file cptt02.f.

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subroutine cptt05	(	integer	N,
		integer	NRHS,
		real, dimension( * )	D,
		complex, dimension( * )	E,
		complex, dimension( ldb, * )	B,
		integer	LDB,
		complex, dimension( ldx, * )	X,
		integer	LDX,
		complex, dimension( ldxact, * )	XACT,
		integer	LDXACT,
		real, dimension( * )	FERR,
		real, dimension( * )	BERR,
		real, dimension( * )	RESLTS
	)

CPTT05

Purpose:

 CPTT05 tests the error bounds from iterative refinement for the
 computed solution to a system of equations A*X = B, where A is a
 Hermitian 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 COMPLEX array, dimension (N-1) The (n-1) subdiagonal elements of the tridiagonal matrix A.
[in]	B	B is COMPLEX 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 COMPLEX 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 COMPLEX 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 cptt05.f.

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subroutine cqlt01	(	integer	M,
		integer	N,
		complex, dimension( lda, * )	A,
		complex, dimension( lda, * )	AF,
		complex, dimension( lda, * )	Q,
		complex, dimension( lda, * )	L,
		integer	LDA,
		complex, dimension( * )	TAU,
		complex, dimension( lwork )	WORK,
		integer	LWORK,
		real, dimension( * )	RWORK,
		real, dimension( * )	RESULT
	)

CQLT01

Purpose:

 CQLT01 tests CGEQLF, which computes the QL factorization of an m-by-n
 matrix A, and partially tests CUNGQL which forms the m-by-m
 orthogonal matrix Q.

 CQLT01 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 COMPLEX array, dimension (LDA,N) The m-by-n matrix A.
[out]	AF	AF is COMPLEX array, dimension (LDA,N) Details of the QL factorization of A, as returned by CGEQLF. See CGEQLF for further details.
[out]	Q	Q is COMPLEX array, dimension (LDA,M) The m-by-m orthogonal matrix Q.
[out]	L	L is COMPLEX 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 COMPLEX array, dimension (min(M,N)) The scalar factors of the elementary reflectors, as returned by CGEQLF.
[out]	WORK	WORK is COMPLEX 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 cqlt01.f.

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subroutine cqlt02	(	integer	M,
		integer	N,
		integer	K,
		complex, dimension( lda, * )	A,
		complex, dimension( lda, * )	AF,
		complex, dimension( lda, * )	Q,
		complex, dimension( lda, * )	L,
		integer	LDA,
		complex, dimension( * )	TAU,
		complex, dimension( lwork )	WORK,
		integer	LWORK,
		real, dimension( * )	RWORK,
		real, dimension( * )	RESULT
	)

CQLT02

Purpose:

 CQLT02 tests CUNGQL, 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, CQLT02 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 COMPLEX array, dimension (LDA,N) The m-by-n matrix A which was factorized by CQLT01.
[in]	AF	AF is COMPLEX array, dimension (LDA,N) Details of the QL factorization of A, as returned by CGEQLF. See CGEQLF for further details.
[out]	Q	Q is COMPLEX array, dimension (LDA,N)
[out]	L	L is COMPLEX 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 COMPLEX array, dimension (N) The scalar factors of the elementary reflectors corresponding to the QL factorization in AF.
[out]	WORK	WORK is COMPLEX 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 cqlt02.f.

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subroutine cqlt03	(	integer	M,
		integer	N,
		integer	K,
		complex, dimension( lda, * )	AF,
		complex, dimension( lda, * )	C,
		complex, dimension( lda, * )	CC,
		complex, dimension( lda, * )	Q,
		integer	LDA,
		complex, dimension( * )	TAU,
		complex, dimension( lwork )	WORK,
		integer	LWORK,
		real, dimension( * )	RWORK,
		real, dimension( * )	RESULT
	)

CQLT03

Purpose:

 CQLT03 tests CUNMQL, which computes Q*C, Q'*C, C*Q or C*Q'.

 CQLT03 compares the results of a call to CUNMQL with the results of
 forming Q explicitly by a call to CUNGQL and then performing matrix
 multiplication by a call to CGEMM.

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 COMPLEX array, dimension (LDA,N) Details of the QL factorization of an m-by-n matrix, as returned by CGEQLF. See CGEQLF for further details.
[out]	C	C is COMPLEX array, dimension (LDA,N)
[out]	CC	CC is COMPLEX array, dimension (LDA,N)
[out]	Q	Q is COMPLEX array, dimension (LDA,M)
[in]	LDA	LDA is INTEGER The leading dimension of the arrays AF, C, CC, and Q.
[in]	TAU	TAU is COMPLEX array, dimension (min(M,N)) The scalar factors of the elementary reflectors corresponding to the QL factorization in AF.
[out]	WORK	WORK is COMPLEX 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 cqlt03.f.

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REAL function cqpt01	(	integer	M,
		integer	N,
		integer	K,
		complex, dimension( lda, * )	A,
		complex, dimension( lda, * )	AF,
		integer	LDA,
		complex, dimension( * )	TAU,
		integer, dimension( * )	JPVT,
		complex, dimension( lwork )	WORK,
		integer	LWORK
	)

CQPT01

Purpose:

 CQPT01 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 COMPLEX array, dimension (LDA, N) The original matrix A.
[in]	AF	AF is COMPLEX array, dimension (LDA,N) The (possibly partial) output of CGEQPF. 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 COMPLEX array, dimension (K) Details of the Householder transformations as returned by CGEQPF.
[in]	JPVT	JPVT is INTEGER array, dimension (N) Pivot information as returned by CGEQPF.
[out]	WORK	WORK is COMPLEX 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 cqpt01.f.

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subroutine cqrt01	(	integer	M,
		integer	N,
		complex, dimension( lda, * )	A,
		complex, dimension( lda, * )	AF,
		complex, dimension( lda, * )	Q,
		complex, dimension( lda, * )	R,
		integer	LDA,
		complex, dimension( * )	TAU,
		complex, dimension( lwork )	WORK,
		integer	LWORK,
		real, dimension( * )	RWORK,
		real, dimension( * )	RESULT
	)

CQRT01

Purpose:

 CQRT01 tests CGEQRF, which computes the QR factorization of an m-by-n
 matrix A, and partially tests CUNGQR which forms the m-by-m
 orthogonal matrix Q.

 CQRT01 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 COMPLEX array, dimension (LDA,N) The m-by-n matrix A.
[out]	AF	AF is COMPLEX array, dimension (LDA,N) Details of the QR factorization of A, as returned by CGEQRF. See CGEQRF for further details.
[out]	Q	Q is COMPLEX array, dimension (LDA,M) The m-by-m orthogonal matrix Q.
[out]	R	R is COMPLEX 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 COMPLEX array, dimension (min(M,N)) The scalar factors of the elementary reflectors, as returned by CGEQRF.
[out]	WORK	WORK is COMPLEX 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 cqrt01.f.

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subroutine cqrt01p	(	integer	M,
		integer	N,
		complex, dimension( lda, * )	A,
		complex, dimension( lda, * )	AF,
		complex, dimension( lda, * )	Q,
		complex, dimension( lda, * )	R,
		integer	LDA,
		complex, dimension( * )	TAU,
		complex, dimension( lwork )	WORK,
		integer	LWORK,
		real, dimension( * )	RWORK,
		real, dimension( * )	RESULT
	)

CQRT01P

Purpose:

 CQRT01P tests CGEQRFP, which computes the QR factorization of an m-by-n
 matrix A, and partially tests CUNGQR which forms the m-by-m
 orthogonal matrix Q.

 CQRT01P 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 COMPLEX array, dimension (LDA,N) The m-by-n matrix A.
[out]	AF	AF is COMPLEX array, dimension (LDA,N) Details of the QR factorization of A, as returned by CGEQRFP. See CGEQRFP for further details.
[out]	Q	Q is COMPLEX array, dimension (LDA,M) The m-by-m orthogonal matrix Q.
[out]	R	R is COMPLEX 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 COMPLEX array, dimension (min(M,N)) The scalar factors of the elementary reflectors, as returned by CGEQRFP.
[out]	WORK	WORK is COMPLEX 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 cqrt01p.f.

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subroutine cqrt02	(	integer	M,
		integer	N,
		integer	K,
		complex, dimension( lda, * )	A,
		complex, dimension( lda, * )	AF,
		complex, dimension( lda, * )	Q,
		complex, dimension( lda, * )	R,
		integer	LDA,
		complex, dimension( * )	TAU,
		complex, dimension( lwork )	WORK,
		integer	LWORK,
		real, dimension( * )	RWORK,
		real, dimension( * )	RESULT
	)

CQRT02

Purpose:

 CQRT02 tests CUNGQR, 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, CQRT02 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 COMPLEX array, dimension (LDA,N) The m-by-n matrix A which was factorized by CQRT01.
[in]	AF	AF is COMPLEX array, dimension (LDA,N) Details of the QR factorization of A, as returned by CGEQRF. See CGEQRF for further details.
[out]	Q	Q is COMPLEX array, dimension (LDA,N)
[out]	R	R is COMPLEX 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 COMPLEX array, dimension (N) The scalar factors of the elementary reflectors corresponding to the QR factorization in AF.
[out]	WORK	WORK is COMPLEX 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 cqrt02.f.

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subroutine cqrt03	(	integer	M,
		integer	N,
		integer	K,
		complex, dimension( lda, * )	AF,
		complex, dimension( lda, * )	C,
		complex, dimension( lda, * )	CC,
		complex, dimension( lda, * )	Q,
		integer	LDA,
		complex, dimension( * )	TAU,
		complex, dimension( lwork )	WORK,
		integer	LWORK,
		real, dimension( * )	RWORK,
		real, dimension( * )	RESULT
	)

CQRT03

Purpose:

 CQRT03 tests CUNMQR, which computes Q*C, Q'*C, C*Q or C*Q'.

 CQRT03 compares the results of a call to CUNMQR with the results of
 forming Q explicitly by a call to CUNGQR and then performing matrix
 multiplication by a call to CGEMM.

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 COMPLEX array, dimension (LDA,N) Details of the QR factorization of an m-by-n matrix, as returnedby CGEQRF. See CGEQRF for further details.
[out]	C	C is COMPLEX array, dimension (LDA,N)
[out]	CC	CC is COMPLEX array, dimension (LDA,N)
[out]	Q	Q is COMPLEX array, dimension (LDA,M)
[in]	LDA	LDA is INTEGER The leading dimension of the arrays AF, C, CC, and Q.
[in]	TAU	TAU is COMPLEX array, dimension (min(M,N)) The scalar factors of the elementary reflectors corresponding to the QR factorization in AF.
[out]	WORK	WORK is COMPLEX 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 cqrt03.f.

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subroutine cqrt04	(	integer	M,
		integer	N,
		integer	NB,
		real, dimension(6)	RESULT
	)

CQRT04

Purpose:

 CQRT04 tests CGEQRT and CGEMQRT.

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 cqrt04.f.

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subroutine cqrt05	(	integer	M,
		integer	N,
		integer	L,
		integer	NB,
		real, dimension(6)	RESULT
	)

CQRT05

Purpose:

 CQRT05 tests CTPQRT and CTPMQRT.

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 cqrt05.f.

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REAL function cqrt11	(	integer	M,
		integer	K,
		complex, dimension( lda, * )	A,
		integer	LDA,
		complex, dimension( * )	TAU,
		complex, dimension( lwork )	WORK,
		integer	LWORK
	)

CQRT11

Purpose:

 CQRT11 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 COMPLEX 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 COMPLEX array, dimension (K) The scaling factors tau for the elementary transformations as computed by the QR factorization routine.
[out]	WORK	WORK is COMPLEX 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 cqrt11.f.

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REAL function cqrt12	(	integer	M,
		integer	N,
		complex, dimension( lda, * )	A,
		integer	LDA,
		real, dimension( * )	S,
		complex, dimension( lwork )	WORK,
		integer	LWORK,
		real, dimension( * )	RWORK
	)

CQRT12

Purpose:

 CQRT12 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 COMPLEX 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 COMPLEX array, dimension (LWORK)
[in]	LWORK	LWORK is INTEGER The length of the array WORK. LWORK >= MN + 2min(M,N) + max(M,N).
[out]	RWORK	RWORK is REAL array, dimension (4*min(M,N))

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

Date:: November 2011

Definition at line 97 of file cqrt12.f.

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subroutine cqrt13	(	integer	SCALE,
		integer	M,
		integer	N,
		complex, dimension( lda, * )	A,
		integer	LDA,
		real	NORMA,
		integer, dimension( 4 )	ISEED
	)

CQRT13

Purpose:

 CQRT13 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 COMPLEX 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 cqrt13.f.

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REAL function cqrt14	(	character	TRANS,
		integer	M,
		integer	N,
		integer	NRHS,
		complex, dimension( lda, * )	A,
		integer	LDA,
		complex, dimension( ldx, * )	X,
		integer	LDX,
		complex, dimension( lwork )	WORK,
		integer	LWORK
	)

CQRT14

Purpose:

 CQRT14 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 = 'C') 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 = 'C': Conjugate transpose, check for X in 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 COMPLEX 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 COMPLEX array, dimension (LDX,NRHS) If TRANS = 'N', the N-by-NRHS matrix X. IF TRANS = 'C', the M-by-NRHS matrix X.
[in]	LDX	LDX is INTEGER The leading dimension of the array X.
[out]	WORK	WORK is COMPLEX array dimension (LWORK)
[in]	LWORK	LWORK is INTEGER length of workspace array required If TRANS = 'N', LWORK >= (M+NRHS)(N+2); if TRANS = 'C', 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 cqrt14.f.

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subroutine cqrt15	(	integer	SCALE,
		integer	RKSEL,
		integer	M,
		integer	N,
		integer	NRHS,
		complex, dimension( lda, * )	A,
		integer	LDA,
		complex, dimension( ldb, * )	B,
		integer	LDB,
		real, dimension( * )	S,
		integer	RANK,
		real	NORMA,
		real	NORMB,
		integer, dimension( 4 )	ISEED,
		complex, dimension( lwork )	WORK,
		integer	LWORK
	)

CQRT15

Purpose:

 CQRT15 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 COMPLEX 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 COMPLEX 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 norm of A.
[out]	NORMB	NORMB is REAL one-norm norm of B.
[in,out]	ISEED	ISEED is integer array, dimension (4) seed for random number generator.
[out]	WORK	WORK is COMPLEX 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 149 of file cqrt15.f.

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subroutine cqrt16	(	character	TRANS,
		integer	M,
		integer	N,
		integer	NRHS,
		complex, dimension( lda, * )	A,
		integer	LDA,
		complex, dimension( ldx, * )	X,
		integer	LDX,
		complex, dimension( ldb, * )	B,
		integer	LDB,
		real, dimension( * )	RWORK,
		real	RESID
	)

CQRT16

Purpose:

 CQRT16 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^Tx = b, where A^T is the transpose of A = 'C': A^Hx = b, where A^H is the conjugate 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 COMPLEX 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 COMPLEX 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 COMPLEX 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 cqrt16.f.

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REAL function cqrt17	(	character	TRANS,
		integer	IRESID,
		integer	M,
		integer	N,
		integer	NRHS,
		complex, dimension( lda, * )	A,
		integer	LDA,
		complex, dimension( ldx, * )	X,
		integer	LDX,
		complex, dimension( ldb, * )	B,
		integer	LDB,
		complex, dimension( ldb, * )	C,
		complex, dimension( lwork )	WORK,
		integer	LWORK
	)

CQRT17

Purpose:

 CQRT17 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. = 'C': Conjugate 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 = 'C', 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 = 'C', 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 COMPLEX 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 COMPLEX array, dimension (LDX,NRHS) If TRANS = 'N', the n-by-nrhs matrix X. If TRANS = 'C', 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 = 'C', LDX >= M.
[in]	B	B is COMPLEX array, dimension (LDB,NRHS) If TRANS = 'N', the m-by-nrhs matrix B. If TRANS = 'C', 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 = 'C', LDB >= N.
[out]	C	C is COMPLEX array, dimension (LDB,NRHS)
[out]	WORK	WORK is COMPLEX 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 cqrt17.f.

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subroutine crqt01	(	integer	M,
		integer	N,
		complex, dimension( lda, * )	A,
		complex, dimension( lda, * )	AF,
		complex, dimension( lda, * )	Q,
		complex, dimension( lda, * )	R,
		integer	LDA,
		complex, dimension( * )	TAU,
		complex, dimension( lwork )	WORK,
		integer	LWORK,
		real, dimension( * )	RWORK,
		real, dimension( * )	RESULT
	)

CRQT01

Purpose:

 CRQT01 tests CGERQF, which computes the RQ factorization of an m-by-n
 matrix A, and partially tests CUNGRQ which forms the n-by-n
 orthogonal matrix Q.

 CRQT01 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 COMPLEX array, dimension (LDA,N) The m-by-n matrix A.
[out]	AF	AF is COMPLEX array, dimension (LDA,N) Details of the RQ factorization of A, as returned by CGERQF. See CGERQF for further details.
[out]	Q	Q is COMPLEX array, dimension (LDA,N) The n-by-n orthogonal matrix Q.
[out]	R	R is COMPLEX 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 COMPLEX array, dimension (min(M,N)) The scalar factors of the elementary reflectors, as returned by CGERQF.
[out]	WORK	WORK is COMPLEX 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 crqt01.f.

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subroutine crqt02	(	integer	M,
		integer	N,
		integer	K,
		complex, dimension( lda, * )	A,
		complex, dimension( lda, * )	AF,
		complex, dimension( lda, * )	Q,
		complex, dimension( lda, * )	R,
		integer	LDA,
		complex, dimension( * )	TAU,
		complex, dimension( lwork )	WORK,
		integer	LWORK,
		real, dimension( * )	RWORK,
		real, dimension( * )	RESULT
	)

CRQT02

Purpose:

 CRQT02 tests CUNGRQ, 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, CRQT02 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 COMPLEX array, dimension (LDA,N) The m-by-n matrix A which was factorized by CRQT01.
[in]	AF	AF is COMPLEX array, dimension (LDA,N) Details of the RQ factorization of A, as returned by CGERQF. See CGERQF for further details.
[out]	Q	Q is COMPLEX array, dimension (LDA,N)
[out]	R	R is COMPLEX 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 COMPLEX array, dimension (M) The scalar factors of the elementary reflectors corresponding to the RQ factorization in AF.
[out]	WORK	WORK is COMPLEX 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 crqt02.f.

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subroutine crqt03	(	integer	M,
		integer	N,
		integer	K,
		complex, dimension( lda, * )	AF,
		complex, dimension( lda, * )	C,
		complex, dimension( lda, * )	CC,
		complex, dimension( lda, * )	Q,
		integer	LDA,
		complex, dimension( * )	TAU,
		complex, dimension( lwork )	WORK,
		integer	LWORK,
		real, dimension( * )	RWORK,
		real, dimension( * )	RESULT
	)

CRQT03

Purpose:

 CRQT03 tests CUNMRQ, which computes Q*C, Q'*C, C*Q or C*Q'.

 CRQT03 compares the results of a call to CUNMRQ with the results of
 forming Q explicitly by a call to CUNGRQ and then performing matrix
 multiplication by a call to CGEMM.

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 COMPLEX array, dimension (LDA,N) Details of the RQ factorization of an m-by-n matrix, as returned by CGERQF. See CGERQF for further details.
[out]	C	C is COMPLEX array, dimension (LDA,N)
[out]	CC	CC is COMPLEX array, dimension (LDA,N)
[out]	Q	Q is COMPLEX array, dimension (LDA,N)
[in]	LDA	LDA is INTEGER The leading dimension of the arrays AF, C, CC, and Q.
[in]	TAU	TAU is COMPLEX array, dimension (min(M,N)) The scalar factors of the elementary reflectors corresponding to the RQ factorization in AF.
[out]	WORK	WORK is COMPLEX 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 crqt03.f.

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REAL function crzt01	(	integer	M,
		integer	N,
		complex, dimension( lda, * )	A,
		complex, dimension( lda, * )	AF,
		integer	LDA,
		complex, dimension( * )	TAU,
		complex, dimension( lwork )	WORK,
		integer	LWORK
	)

CRZT01

Purpose:

 CRZT01 returns
      || A - R*Q || / ( M * eps * ||A|| )
 for an upper trapezoidal A that was factored with CTZRZF.

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 COMPLEX array, dimension (LDA,N) The original upper trapezoidal M by N matrix A.
[in]	AF	AF is COMPLEX array, dimension (LDA,N) The output of CTZRZF 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 COMPLEX array, dimension (M) Details of the Householder transformations as returned by CTZRZF.
[out]	WORK	WORK is COMPLEX 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 crzt01.f.

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REAL function crzt02	(	integer	M,
		integer	N,
		complex, dimension( lda, * )	AF,
		integer	LDA,
		complex, dimension( * )	TAU,
		complex, dimension( lwork )	WORK,
		integer	LWORK
	)

CRZT02

Purpose:

 CRZT02 returns
      || I - Q'*Q || / ( M * eps)
 where the matrix Q is defined by the Householder transformations
 generated by CTZRZF.

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 COMPLEX array, dimension (LDA,N) The output of CTZRZF.
[in]	LDA	LDA is INTEGER The leading dimension of the array AF.
[in]	TAU	TAU is COMPLEX array, dimension (M) Details of the Householder transformations as returned by CTZRZF.
[out]	WORK	WORK is COMPLEX array, dimension (LWORK)
[in]	LWORK	LWORK is INTEGER Length of WORK array. LWORK >= 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 crzt02.f.

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subroutine csbmv	(	character	UPLO,
		integer	N,
		integer	K,
		complex	ALPHA,
		complex, dimension( lda, * )	A,
		integer	LDA,
		complex, dimension( * )	X,
		integer	INCX,
		complex	BETA,
		complex, dimension( * )	Y,
		integer	INCY
	)

CSBMV

Purpose:

 CSBMV  performs the matrix-vector  operation

    y := alpha*A*x + beta*y,

 where alpha and beta are scalars, x and y are n element vectors and
 A is an n by n symmetric band matrix, with k super-diagonals.

  UPLO   - CHARACTER*1
           On entry, UPLO specifies whether the upper or lower
           triangular part of the band matrix A is being supplied as
           follows:

              UPLO = 'U' or 'u'   The upper triangular part of A is
                                  being supplied.

              UPLO = 'L' or 'l'   The lower triangular part of A is
                                  being supplied.

           Unchanged on exit.

  N      - INTEGER
           On entry, N specifies the order of the matrix A.
           N must be at least zero.
           Unchanged on exit.

  K      - INTEGER
           On entry, K specifies the number of super-diagonals of the
           matrix A. K must satisfy  0 .le. K.
           Unchanged on exit.

  ALPHA  - COMPLEX
           On entry, ALPHA specifies the scalar alpha.
           Unchanged on exit.

  A      - COMPLEX array, dimension( LDA, N )
           Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
           by n part of the array A must contain the upper triangular
           band part of the symmetric matrix, supplied column by
           column, with the leading diagonal of the matrix in row
           ( k + 1 ) of the array, the first super-diagonal starting at
           position 2 in row k, and so on. The top left k by k triangle
           of the array A is not referenced.
           The following program segment will transfer the upper
           triangular part of a symmetric band matrix from conventional
           full matrix storage to band storage:

                 DO 20, J = 1, N
                    M = K + 1 - J
                    DO 10, I = MAX( 1, J - K ), J
                       A( M + I, J ) = matrix( I, J )
              10    CONTINUE
              20 CONTINUE

           Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
           by n part of the array A must contain the lower triangular
           band part of the symmetric matrix, supplied column by
           column, with the leading diagonal of the matrix in row 1 of
           the array, the first sub-diagonal starting at position 1 in
           row 2, and so on. The bottom right k by k triangle of the
           array A is not referenced.
           The following program segment will transfer the lower
           triangular part of a symmetric band matrix from conventional
           full matrix storage to band storage:

                 DO 20, J = 1, N
                    M = 1 - J
                    DO 10, I = J, MIN( N, J + K )
                       A( M + I, J ) = matrix( I, J )
              10    CONTINUE
              20 CONTINUE

           Unchanged on exit.

  LDA    - INTEGER
           On entry, LDA specifies the first dimension of A as declared
           in the calling (sub) program. LDA must be at least
           ( k + 1 ).
           Unchanged on exit.

  X      - COMPLEX array, dimension at least
           ( 1 + ( N - 1 )*abs( INCX ) ).
           Before entry, the incremented array X must contain the
           vector x.
           Unchanged on exit.

  INCX   - INTEGER
           On entry, INCX specifies the increment for the elements of
           X. INCX must not be zero.
           Unchanged on exit.

  BETA   - COMPLEX
           On entry, BETA specifies the scalar beta.
           Unchanged on exit.

  Y      - COMPLEX array, dimension at least
           ( 1 + ( N - 1 )*abs( INCY ) ).
           Before entry, the incremented array Y must contain the
           vector y. On exit, Y is overwritten by the updated vector y.

  INCY   - INTEGER
           On entry, INCY specifies the increment for the elements of
           Y. INCY must not be zero.
           Unchanged on exit.

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

Date:: November 2011

Definition at line 152 of file csbmv.f.

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subroutine cspt01	(	character	UPLO,
		integer	N,
		complex, dimension( * )	A,
		complex, dimension( * )	AFAC,
		integer, dimension( * )	IPIV,
		complex, dimension( ldc, * )	C,
		integer	LDC,
		real, dimension( * )	RWORK,
		real	RESID
	)

CSPT01

Purpose:

 CSPT01 reconstructs a symmetric indefinite packed matrix A from its
 diagonal pivoting factorization A = U*D*U' or A = L*D*L' 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 Hermitian matrix A is stored: = 'U': Upper triangular = 'L': Lower triangular
[in]	N	N is INTEGER The order of the matrix A. N >= 0.
[in]	A	A is COMPLEX array, dimension (N*(N+1)/2) The original symmetric matrix A, stored as a packed triangular matrix.
[in]	AFAC	AFAC is COMPLEX 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 LDL' or UD*U' factorization as computed by CSPTRF.
[in]	IPIV	IPIV is INTEGER array, dimension (N) The pivot indices from CSPTRF.
[out]	C	C is COMPLEX 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 113 of file cspt01.f.

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subroutine cspt02	(	character	UPLO,
		integer	N,
		integer	NRHS,
		complex, dimension( * )	A,
		complex, dimension( ldx, * )	X,
		integer	LDX,
		complex, dimension( ldb, * )	B,
		integer	LDB,
		real, dimension( * )	RWORK,
		real	RESID
	)

CSPT02

Purpose:

 CSPT02 computes the residual in the solution of a complex 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 complex 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 COMPLEX array, dimension (N*(N+1)/2) The original complex symmetric matrix A, stored as a packed triangular matrix.
[in]	X	X is COMPLEX 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 COMPLEX 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 123 of file cspt02.f.

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subroutine cspt03	(	character	UPLO,
		integer	N,
		complex, dimension( * )	A,
		complex, dimension( * )	AINV,
		complex, dimension( ldw, * )	WORK,
		integer	LDW,
		real, dimension( * )	RWORK,
		real	RCOND,
		real	RESID
	)

CSPT03

Purpose:

 CSPT03 computes the residual for a complex 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 complex 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 COMPLEX array, dimension (N*(N+1)/2) The original complex symmetric matrix A, stored as a packed triangular matrix.
[in]	AINV	AINV is COMPLEX array, dimension (N*(N+1)/2) The (symmetric) inverse of the matrix A, stored as a packed triangular matrix.
[out]	WORK	WORK is COMPLEX array, dimension (LDW,N)
[in]	LDW	LDW is INTEGER The leading dimension of the array WORK. LDW >= 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 cspt03.f.

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subroutine csyt01	(	character	UPLO,
		integer	N,
		complex, dimension( lda, * )	A,
		integer	LDA,
		complex, dimension( ldafac, * )	AFAC,
		integer	LDAFAC,
		integer, dimension( * )	IPIV,
		complex, dimension( ldc, * )	C,
		integer	LDC,
		real, dimension( * )	RWORK,
		real	RESID
	)

CSYT01

Purpose:

 CSYT01 reconstructs a complex 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, EPS is the machine epsilon,
 L' is the transpose of L, and U' is the transpose of U.

Parameters:

[in]	UPLO	UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the complex 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 COMPLEX array, dimension (LDA,N) The original complex symmetric matrix A.
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N)
[in]	AFAC	AFAC is COMPLEX 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 CSYTRF.
[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 CSYTRF.
[out]	C	C is COMPLEX 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 125 of file csyt01.f.

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subroutine csyt02	(	character	UPLO,
		integer	N,
		integer	NRHS,
		complex, dimension( lda, * )	A,
		integer	LDA,
		complex, dimension( ldx, * )	X,
		integer	LDX,
		complex, dimension( ldb, * )	B,
		integer	LDB,
		real, dimension( * )	RWORK,
		real	RESID
	)

CSYT02

Purpose:

 CSYT02 computes the residual for a solution to a complex 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 COMPLEX array, dimension (LDA,N) The original complex symmetric matrix A.
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N)
[in]	X	X is COMPLEX 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 COMPLEX 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 csyt02.f.

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subroutine csyt03	(	character	UPLO,
		integer	N,
		complex, dimension( lda, * )	A,
		integer	LDA,
		complex, dimension( ldainv, * )	AINV,
		integer	LDAINV,
		complex, dimension( ldwork, * )	WORK,
		integer	LDWORK,
		real, dimension( * )	RWORK,
		real	RCOND,
		real	RESID
	)

CSYT03

Purpose:

 CSYT03 computes the residual for a complex 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 complex 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 COMPLEX array, dimension (LDA,N) The original complex symmetric matrix A.
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N)
[in,out]	AINV	AINV is COMPLEX 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 COMPLEX 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 RCOND = 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 126 of file csyt03.f.

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subroutine ctbt02	(	character	UPLO,
		character	TRANS,
		character	DIAG,
		integer	N,
		integer	KD,
		integer	NRHS,
		complex, dimension( ldab, * )	AB,
		integer	LDAB,
		complex, dimension( ldx, * )	X,
		integer	LDX,
		complex, dimension( ldb, * )	B,
		integer	LDB,
		complex, dimension( * )	WORK,
		real, dimension( * )	RWORK,
		real	RESID
	)

CTBT02

Purpose:

 CTBT02 computes the residual for the computed solution to a
 triangular system of linear equations  A*x = b,  A**T *x = b,  or
 A**H *x = b  when A is a triangular band matrix.  Here A**T denotes
 the transpose of A, A**H denotes the conjugate 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, A**T, or A**H, 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*T x = b (Transpose) = 'C': A*H x = b (Conjugate 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 COMPLEX array, dimension (LDA,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 >= max(1,KD+1).
[in]	X	X is COMPLEX 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 COMPLEX 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 COMPLEX array, dimension (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(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 161 of file ctbt02.f.

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subroutine ctbt03	(	character	UPLO,
		character	TRANS,
		character	DIAG,
		integer	N,
		integer	KD,
		integer	NRHS,
		complex, dimension( ldab, * )	AB,
		integer	LDAB,
		real	SCALE,
		real, dimension( * )	CNORM,
		real	TSCAL,
		complex, dimension( ldx, * )	X,
		integer	LDX,
		complex, dimension( ldb, * )	B,
		integer	LDB,
		complex, dimension( * )	WORK,
		real	RESID
	)

CTBT03

Purpose:

 CTBT03 computes the residual for the solution to a scaled triangular
 system of equations  A*x = s*b,  A**T *x = s*b,  or  A**H *x = s*b
 when A is a triangular band matrix.  Here A**T  denotes the transpose
 of A, A**H denotes the conjugate 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, A**T, or A**H, 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': AT x = sb (Transpose) = 'C': AH x = s*b (Conjugate 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 COMPLEX 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 COMPLEX 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 COMPLEX 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 COMPLEX 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 176 of file ctbt03.f.

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subroutine ctbt05	(	character	UPLO,
		character	TRANS,
		character	DIAG,
		integer	N,
		integer	KD,
		integer	NRHS,
		complex, dimension( ldab, * )	AB,
		integer	LDAB,
		complex, dimension( ldb, * )	B,
		integer	LDB,
		complex, dimension( ldx, * )	X,
		integer	LDX,
		complex, dimension( ldxact, * )	XACT,
		integer	LDXACT,
		real, dimension( * )	FERR,
		real, dimension( * )	BERR,
		real, dimension( * )	RESLTS
	)

CTBT05

Purpose:

 CTBT05 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 COMPLEX 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 COMPLEX 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 COMPLEX 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 COMPLEX 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 ctbt05.f.

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subroutine ctbt06	(	real	RCOND,
		real	RCONDC,
		character	UPLO,
		character	DIAG,
		integer	N,
		integer	KD,
		complex, dimension( ldab, * )	AB,
		integer	LDAB,
		real, dimension( * )	RWORK,
		real	RAT
	)

CTBT06

Purpose:

 CTBT06 computes a test ratio comparing RCOND (the reciprocal
 condition number of a triangular matrix A) and RCONDC, the estimate
 computed by CTBCON.  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 CTBCON.
[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 COMPLEX 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]	RWORK	RWORK 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 126 of file ctbt06.f.

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subroutine ctpt01	(	character	UPLO,
		character	DIAG,
		integer	N,
		complex, dimension( * )	AP,
		complex, dimension( * )	AINVP,
		real	RCOND,
		real, dimension( * )	RWORK,
		real	RESID
	)

CTPT01

Purpose:

 CTPT01 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 COMPLEX 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]	AINVP	AINVP is COMPLEX 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]	RWORK	RWORK 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 110 of file ctpt01.f.

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subroutine ctpt02	(	character	UPLO,
		character	TRANS,
		character	DIAG,
		integer	N,
		integer	NRHS,
		complex, dimension( * )	AP,
		complex, dimension( ldx, * )	X,
		integer	LDX,
		complex, dimension( ldb, * )	B,
		integer	LDB,
		complex, dimension( * )	WORK,
		real, dimension( * )	RWORK,
		real	RESID
	)

CTPT02

Purpose:

 CTPT02 computes the residual for the computed solution to a
 triangular system of linear equations  A*x = b,  A**T *x = b,  or
 A**H *x = b, when the triangular matrix A is stored in packed format.
 Here A**T denotes the transpose of A, A**H denotes the conjugate
 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
 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, A**T, or A**H, 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*T x = b (Transpose) = 'C': A*H x = b (Conjugate 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 COMPLEX 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 COMPLEX 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 COMPLEX 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 COMPLEX array, dimension (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(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 149 of file ctpt02.f.

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subroutine ctpt03	(	character	UPLO,
		character	TRANS,
		character	DIAG,
		integer	N,
		integer	NRHS,
		complex, dimension( * )	AP,
		real	SCALE,
		real, dimension( * )	CNORM,
		real	TSCAL,
		complex, dimension( ldx, * )	X,
		integer	LDX,
		complex, dimension( ldb, * )	B,
		integer	LDB,
		complex, dimension( * )	WORK,
		real	RESID
	)

CTPT03

Purpose:

 CTPT03 computes the residual for the solution to a scaled triangular
 system of equations A*x = s*b,  A**T *x = s*b,  or  A**H *x = s*b,
 when the triangular matrix A is stored in packed format.  Here A**T
 denotes the transpose of A, A**H denotes the conjugate 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, A**T, or A**H, 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': AT x = sb (Transpose) = 'C': AH x = s*b (Conjugate 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 COMPLEX 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 COMPLEX 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 COMPLEX 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 COMPLEX 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 162 of file ctpt03.f.

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subroutine ctpt05	(	character	UPLO,
		character	TRANS,
		character	DIAG,
		integer	N,
		integer	NRHS,
		complex, dimension( * )	AP,
		complex, dimension( ldb, * )	B,
		integer	LDB,
		complex, dimension( ldx, * )	X,
		integer	LDX,
		complex, dimension( ldxact, * )	XACT,
		integer	LDXACT,
		real, dimension( * )	FERR,
		real, dimension( * )	BERR,
		real, dimension( * )	RESLTS
	)

CTPT05

Purpose:

 CTPT05 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 COMPLEX 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 COMPLEX 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 COMPLEX 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 COMPLEX 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 175 of file ctpt05.f.

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subroutine ctpt06	(	real	RCOND,
		real	RCONDC,
		character	UPLO,
		character	DIAG,
		integer	N,
		complex, dimension( * )	AP,
		real, dimension( * )	RWORK,
		real	RAT
	)

CTPT06

Purpose:

 CTPT06 computes a test ratio comparing RCOND (the reciprocal
 condition number of the triangular matrix A) and RCONDC, the estimate
 computed by CTPCON.  Information about the triangular matrix 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 CTPCON.
[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 COMPLEX 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]	RWORK	RWORK 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 113 of file ctpt06.f.

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subroutine ctrt01	(	character	UPLO,
		character	DIAG,
		integer	N,
		complex, dimension( lda, * )	A,
		integer	LDA,
		complex, dimension( ldainv, * )	AINV,
		integer	LDAINV,
		real	RCOND,
		real, dimension( * )	RWORK,
		real	RESID
	)

CTRT01

Purpose:

 CTRT01 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 COMPLEX 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]	AINV	AINV is COMPLEX 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]	RWORK	RWORK 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 125 of file ctrt01.f.

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subroutine ctrt02	(	character	UPLO,
		character	TRANS,
		character	DIAG,
		integer	N,
		integer	NRHS,
		complex, dimension( lda, * )	A,
		integer	LDA,
		complex, dimension( ldx, * )	X,
		integer	LDX,
		complex, dimension( ldb, * )	B,
		integer	LDB,
		complex, dimension( * )	WORK,
		real, dimension( * )	RWORK,
		real	RESID
	)

CTRT02

Purpose:

 CTRT02 computes the residual for the computed solution to a
 triangular system of linear equations  A*x = b,  A**T *x = b,
 or A**H *x = b.  Here A is a triangular matrix, A**T is the transpose
 of A, A**H is the conjugate 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, A**T, or A**H, 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*T x = b (Transpose) = 'C': A*H x = b (Conjugate 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 COMPLEX 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 COMPLEX 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 COMPLEX 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 COMPLEX array, dimension (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(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 157 of file ctrt02.f.

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subroutine ctrt03	(	character	UPLO,
		character	TRANS,
		character	DIAG,
		integer	N,
		integer	NRHS,
		complex, dimension( lda, * )	A,
		integer	LDA,
		real	SCALE,
		real, dimension( * )	CNORM,
		real	TSCAL,
		complex, dimension( ldx, * )	X,
		integer	LDX,
		complex, dimension( ldb, * )	B,
		integer	LDB,
		complex, dimension( * )	WORK,
		real	RESID
	)

CTRT03

Purpose:

 CTRT03 computes the residual for the solution to a scaled triangular
 system of equations A*x = s*b,  A**T *x = s*b,  or  A**H *x = s*b.
 Here A is a triangular matrix, A**T denotes the transpose of A, A**H
 denotes the conjugate 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, A**T, or A**H, 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': AT x = sb (Transpose) = 'C': AH x = s*b (Conjugate 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 COMPLEX 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 COMPLEX 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 COMPLEX 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 COMPLEX 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 171 of file ctrt03.f.

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subroutine ctrt05	(	character	UPLO,
		character	TRANS,
		character	DIAG,
		integer	N,
		integer	NRHS,
		complex, dimension( lda, * )	A,
		integer	LDA,
		complex, dimension( ldb, * )	B,
		integer	LDB,
		complex, dimension( ldx, * )	X,
		integer	LDX,
		complex, dimension( ldxact, * )	XACT,
		integer	LDXACT,
		real, dimension( * )	FERR,
		real, dimension( * )	BERR,
		real, dimension( * )	RESLTS
	)

CTRT05

Purpose:

 CTRT05 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 COMPLEX 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 COMPLEX 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 COMPLEX 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 COMPLEX 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 182 of file ctrt05.f.

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subroutine ctrt06	(	real	RCOND,
		real	RCONDC,
		character	UPLO,
		character	DIAG,
		integer	N,
		complex, dimension( lda, * )	A,
		integer	LDA,
		real, dimension( * )	RWORK,
		real	RAT
	)

CTRT06

Purpose:

 CTRT06 computes a test ratio comparing RCOND (the reciprocal
 condition number of a triangular matrix A) and RCONDC, the estimate
 computed by CTRCON.  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 CTRCON.
[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 COMPLEX 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]	RWORK	RWORK 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 122 of file ctrt06.f.

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REAL function ctzt01	(	integer	M,
		integer	N,
		complex, dimension( lda, * )	A,
		complex, dimension( lda, * )	AF,
		integer	LDA,
		complex, dimension( * )	TAU,
		complex, dimension( lwork )	WORK,
		integer	LWORK
	)

CTZT01

Purpose:

 CTZT01 returns
      || A - R*Q || / ( M * eps * ||A|| )
 for an upper trapezoidal A that was factored with CTZRQF.

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 COMPLEX array, dimension (LDA,N) The original upper trapezoidal M by N matrix A.
[in]	AF	AF is COMPLEX array, dimension (LDA,N) The output of CTZRQF 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 COMPLEX array, dimension (M) Details of the Householder transformations as returned by CTZRQF.
[out]	WORK	WORK is COMPLEX 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 ctzt01.f.

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REAL function ctzt02	(	integer	M,
		integer	N,
		complex, dimension( lda, * )	AF,
		integer	LDA,
		complex, dimension( * )	TAU,
		complex, dimension( lwork )	WORK,
		integer	LWORK
	)

CTZT02

Purpose:

 CTZT02 returns
      || I - Q'*Q || / ( M * eps)
 where the matrix Q is defined by the Householder transformations
 generated by CTZRQF.

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 COMPLEX array, dimension (LDA,N) The output of CTZRQF.
[in]	LDA	LDA is INTEGER The leading dimension of the array AF.
[in]	TAU	TAU is COMPLEX array, dimension (M) Details of the Householder transformations as returned by CTZRQF.
[out]	WORK	WORK is COMPLEX 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 ctzt02.f.

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Functions/Subroutines

Detailed Description

Function/Subroutine Documentation