LAPACK  3.4.2
LAPACK: Linear Algebra PACKage
 All Files Functions Groups
complex
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 >= (2*KLMAX+KUMAX+1)*NMAX
          where KLMAX is the largest entry in the local array KLVAL,
                KUMAX is the largest entry in the local array KUVAL and
                NMAX is the largest entry in the input array NVAL.
[out]B
          B is 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(2*NMAX,2*NSMAX+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(M*max(M,N) + 4*min(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(M*max(M,N) + 4*min(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
                      (MMAX*NMAX + 4*NMAX + 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 >= (2*NMAX-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 >= (3*NMAX-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 >= (2*NMAX-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 >= (3*NMAX-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 (2*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:
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 = U*D*V 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 = U*D*V 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
                      (MMAX*NMAX + 4*NMAX + 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 (2*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:
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 L*U 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 2*KL+KU+1.  See CGBTRF for further details.
[in]LDAFAC
          LDAFAC is INTEGER
          The leading dimension of the array AFAC.
          LDAFAC >= max(1,2*KL*KU+1).
[in]IPIV
          IPIV is INTEGER array, dimension (min(M,N))
          The pivot indices from CGBTRF.
[out]WORK
          WORK is COMPLEX array, dimension (2*KL+KU+1)
[out]RESID
          RESID is REAL
          norm(L*U - A) / ( N * norm(A) * EPS )
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011

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 CHARACTER*1
          Specifies the form of the system of equations:
          = 'N':  A *x = b
          = 'T':  A'*x = b, where A' is the transpose of A
          = 'C':  A'*x = b, where A' is the transpose of A
[in]M
          M is INTEGER
          The number of rows of the matrix A.  M >= 0.
[in]N
          N is INTEGER
          The number of columns of the matrix A.  N >= 0.
[in]KL
          KL is INTEGER
          The number of subdiagonals within the band of A.  KL >= 0.
[in]KU
          KU is INTEGER
          The number of superdiagonals within the band of A.  KU >= 0.
[in]NRHS
          NRHS is INTEGER
          The number of columns of B.  NRHS >= 0.
[in]A
          A is 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 - 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 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 CHARACTER*1
          Specifies the form of the system of equations.
          = 'N':  A * X = B     (No transpose)
          = 'T':  A**T * X = B  (Transpose)
          = 'C':  A**H * X = B  (Conjugate transpose = Transpose)
[in]N
          N is INTEGER
          The number of rows of the matrices X, B, and XACT, and the
          order of the matrix A.  N >= 0.
[in]KL
          KL is INTEGER
          The number of subdiagonals within the band of A.  KL >= 0.
[in]KU
          KU is INTEGER
          The number of superdiagonals within the band of A.  KU >= 0.
[in]NRHS
          NRHS is INTEGER
          The number of columns of the matrices X, B, and XACT.
          NRHS >= 0.
[in]AB
          AB is 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 / ( NZ*EPS + (*) )
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 L*U factorization as computed by CGETRF.
          Overwritten with the reconstructed matrix, and then with the
          difference L*U - A.
[in]LDAFAC
          LDAFAC is INTEGER
          The leading dimension of the array AFAC.  LDAFAC >= max(1,M).
[in]IPIV
          IPIV is INTEGER array, dimension (N)
          The pivot indices from CGETRF.
[out]RWORK
          RWORK is REAL array, dimension (M)
[out]RESID
          RESID is REAL
          norm(L*U - A) / ( N * norm(A) * EPS )
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011

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 CHARACTER*1
          Specifies the form of the system of equations:
          = 'N':  A *x = b
          = 'T':  A^T*x = b, where A^T is the transpose of A
          = 'C':  A^H*x = 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 - 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 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 - AINV*A) / ( N * norm(A) * norm(AINV) * EPS )
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011

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 CHARACTER*1
          Specifies the form of the system of equations.
          = 'N':  A * X = B     (No transpose)
          = 'T':  A**T * X = B  (Transpose)
          = 'C':  A**H * X = B  (Conjugate transpose = Transpose)
[in]N
          N is INTEGER
          The number of rows of the matrices X and XACT.  N >= 0.
[in]NRHS
          NRHS is INTEGER
          The number of columns of the matrices X and XACT.  NRHS >= 0.
[in]A
          A is 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(L*U - 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 CHARACTER*1
          Specifies the form of the system of equations.
          = 'N':  A * X = B     (No transpose)
          = 'T':  A**T * X = B  (Transpose)
          = 'C':  A**H * X = B  (Conjugate transpose = Transpose)
[in]N
          N is INTEGER
          The number of rows of the matrices X and XACT.  N >= 0.
[in]NRHS
          NRHS is INTEGER
          The number of columns of the matrices X and XACT.  NRHS >= 0.
[in]DL
          DL is 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 / ( NZ*EPS + (*) )
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 L*D*L' or U*D*U' 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(L*D*L' - A) / ( N * norm(A) * EPS )
          If UPLO = 'U', norm(U*D*U' - A) / ( N * norm(A) * EPS )
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011

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 L*D*L' or U*D*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(L*D*L' - A) / ( N * norm(A) * EPS )
          If UPLO = 'U', norm(U*D*U' - A) / ( N * norm(A) * EPS )
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011

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, ..., 2*N-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 CHARACTER*1
          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 CHARACTER*1
          Specifies the operation to be performed:
          = 'N':  x := A*x
          = 'T':  x := A'*x
[in]DIAG
          DIAG is CHARACTER*1
          Specifies whether or not the diagonal blocks are unit
          matrices.  If the diagonal blocks are assumed to be unit,
          then A = U or A = L, otherwise A = U*D or A = L*D.
          = 'U':  Diagonal blocks are assumed to be unit matrices.
          = 'N':  Diagonal blocks are assumed to be non-unit matrices.
[in]N
          N is INTEGER
          The number of rows and columns of the matrix A.  N >= 0.
[in]NRHS
          NRHS is INTEGER
          The number of right hand sides, i.e., the number of vectors
          x to be multiplied by A.  NRHS >= 0.
[in]A
          A is 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 - A*Q' ) / ( N * norm(A) * EPS )
          RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011

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 - A*Q' ) / ( N * norm(A) * EPS )
          RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011

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( Q*C - Q*C )  / ( N * norm(C) * EPS )
          RESULT(2) = norm( C*Q - C*Q )  / ( N * norm(C) * EPS )
          RESULT(3) = norm( Q'*C - Q'*C )/ ( N * norm(C) * EPS )
          RESULT(4) = norm( C*Q' - C*Q' )/ ( N * norm(C) * EPS )
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011

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 L*L' 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(L*L' - A) / ( N * norm(A) * EPS )
          If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS )
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011

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 - 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 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 / ( NZ*EPS + (*) )
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 L*L' or U'*U
          factorization of A.
          Overwritten with the reconstructed matrix, and then with the
          difference L*L' - A (or U'*U - A).
[in]LDAFAC
          LDAFAC is INTEGER
          The leading dimension of the array AFAC.  LDAFAC >= max(1,N).
[out]RWORK
          RWORK is REAL array, dimension (N)
[out]RESID
          RESID is REAL
          If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS )
          If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS )
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011

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 - 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 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 - A*AINV) / ( N * norm(A) * norm(AINV) * EPS )
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011

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 L*L' or U'*U
          factorization of A, stored as a packed triangular matrix.
          Overwritten with the reconstructed matrix, and then with the
          difference L*L' - A (or U'*U - A).
[out]RWORK
          RWORK is REAL array, dimension (N)
[out]RESID
          RESID is REAL
          If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS )
          If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS )
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011

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 - 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 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 - A*AINV) / ( N * norm(A) * norm(AINV) * EPS )
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011

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 L*L' or U'*U
          factorization of A.
[in]LDAFAC
          LDAFAC is INTEGER
          The leading dimension of the array AFAC.  LDAFAC >= max(1,N).
[out]PERM
          PERM is COMPLEX array, dimension (LDPERM,N)
          Overwritten with the reconstructed matrix, and then with the
          difference P*L*L'*P' - A (or P*U'*U*P' - A)
[in]LDPERM
          LDPERM is INTEGER
          The leading dimension of the array PERM.
          LDAPERM >= max(1,N).
[in]PIV
          PIV is INTEGER array, dimension (N)
          PIV is such that the nonzero entries are
          P( PIV( K ), K ) = 1.
[out]RWORK
          RWORK is REAL array, dimension (N)
[out]RESID
          RESID is REAL
          If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS )
          If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS )
[in]RANK
          RANK is INTEGER
          number of nonzero singular values of A.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011

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 L*D*L'
          factorization of A.
[in]EF
          EF is COMPLEX array, dimension (N-1)
          The (n-1) subdiagonal elements of the factor L from the
          L*D*L' factorization of A.
[out]WORK
          WORK is COMPLEX array, dimension (2*N)
[out]RESID
          RESID is REAL
          norm(L*D*L' - A) / (n * norm(A) * EPS)
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011

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 - 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 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 / ( NZ*EPS + (*) )
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( Q*C - Q*C )  / ( M * norm(C) * EPS )
          RESULT(2) = norm( C*Q - C*Q )  / ( M * norm(C) * EPS )
          RESULT(3) = norm( Q'*C - Q'*C )/ ( M * norm(C) * EPS )
          RESULT(4) = norm( C*Q' - C*Q' )/ ( M * norm(C) * EPS )
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011

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( Q*C - Q*C )  / ( M * norm(C) * EPS )
          RESULT(2) = norm( C*Q - C*Q )  / ( M * norm(C) * EPS )
          RESULT(3) = norm( Q'*C - Q'*C )/ ( M * norm(C) * EPS )
          RESULT(4) = norm( C*Q' - C*Q' )/ ( M * norm(C) * EPS )
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011

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 >= M*N + 2*min(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),NRHS*MIN(M,N),2*N+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 CHARACTER*1
          Specifies the form of the system of equations:
          = 'N':  A *x = b
          = 'T':  A^T*x = b, where A^T is the transpose of A
          = 'C':  A^H*x = 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 - A*X) / ( max(m,n) * norm(A) * norm(X) * EPS ).
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011

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 - A*Q' ) / ( N * norm(A) * EPS )
          RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011

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 - A*Q' ) / ( N * norm(A) * EPS )
          RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011

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( Q*C - Q*C )  / ( N * norm(C) * EPS )
          RESULT(2) = norm( C*Q - C*Q )  / ( N * norm(C) * EPS )
          RESULT(3) = norm( Q'*C - Q'*C )/ ( N * norm(C) * EPS )
          RESULT(4) = norm( C*Q' - C*Q' )/ ( N * norm(C) * EPS )
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011

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
          L*D*L' or U*D*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(L*D*L' - A) / ( N * norm(A) * EPS )
          If UPLO = 'U', norm(U*D*U' - A) / ( N * norm(A) * EPS )
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011

Definition at line 113 of file cspt01.f.

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subroutine cspt02 ( character  UPLO,
integer  N,
integer  NRHS