|
1
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 |
REAL FUNCTION CQRT17( TRANS, IRESID, M, N, NRHS, A,
$ LDA, X, LDX, B, LDB, C, WORK, LWORK ) * * -- LAPACK test routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. CHARACTER TRANS INTEGER IRESID, LDA, LDB, LDX, LWORK, M, N, NRHS * .. * .. Array Arguments .. COMPLEX A( LDA, * ), B( LDB, * ), C( LDB, * ), $ WORK( LWORK ), X( LDX, * ) * .. * * 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). * * Arguments * ========= * * TRANS (input) CHARACTER*1 * Specifies whether or not the transpose of A is used. * = 'N': No transpose, op(A) = A. * = 'C': Conjugate transpose, op(A) = A'. * * IRESID (input) INTEGER * IRESID = 1 indicates zero-residual problem. * IRESID = 2 indicates non-zero residual. * * M (input) 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. * * N (input) 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. * * NRHS (input) INTEGER * The number of columns of the matrices X and B. * * A (input) COMPLEX array, dimension (LDA,N) * The m-by-n matrix A. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= M. * * X (input) COMPLEX array, dimension (LDX,NRHS) * If TRANS = 'N', the n-by-nrhs matrix X. * If TRANS = 'C', the m-by-nrhs matrix X. * * LDX (input) INTEGER * The leading dimension of the array X. * If TRANS = 'N', LDX >= N. * If TRANS = 'C', LDX >= M. * * B (input) COMPLEX array, dimension (LDB,NRHS) * If TRANS = 'N', the m-by-nrhs matrix B. * If TRANS = 'C', the n-by-nrhs matrix B. * * LDB (input) INTEGER * The leading dimension of the array B. * If TRANS = 'N', LDB >= M. * If TRANS = 'C', LDB >= N. * * C (workspace) COMPLEX array, dimension (LDB,NRHS) * * WORK (workspace) COMPLEX array, dimension (LWORK) * * LWORK (input) INTEGER * The length of the array WORK. LWORK >= NRHS*(M+N). * * ===================================================================== * * .. Parameters .. REAL ZERO, ONE PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0 ) * .. * .. Local Scalars .. INTEGER INFO, ISCL, NCOLS, NROWS REAL BIGNUM, ERR, NORMA, NORMB, NORMRS, NORMX, $ SMLNUM * .. * .. Local Arrays .. REAL RWORK( 1 ) * .. * .. External Functions .. LOGICAL LSAME REAL CLANGE, SLAMCH EXTERNAL LSAME, CLANGE, SLAMCH * .. * .. External Subroutines .. EXTERNAL CGEMM, CLACPY, CLASCL, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC CMPLX, MAX, REAL * .. * .. Executable Statements .. * CQRT17 = ZERO * IF( LSAME( TRANS, 'N' ) ) THEN NROWS = M NCOLS = N ELSE IF( LSAME( TRANS, 'C' ) ) THEN NROWS = N NCOLS = M ELSE CALL XERBLA( 'CQRT17', 1 ) RETURN END IF * IF( LWORK.LT.NCOLS*NRHS ) THEN CALL XERBLA( 'CQRT17', 13 ) RETURN END IF * IF( M.LE.0 .OR. N.LE.0 .OR. NRHS.LE.0 ) $ RETURN * NORMA = CLANGE( 'One-norm', M, N, A, LDA, RWORK ) SMLNUM = SLAMCH( 'Safe minimum' ) / SLAMCH( 'Precision' ) BIGNUM = ONE / SMLNUM ISCL = 0 * * compute residual and scale it * CALL CLACPY( 'All', NROWS, NRHS, B, LDB, C, LDB ) CALL CGEMM( TRANS, 'No transpose', NROWS, NRHS, NCOLS, $ CMPLX( -ONE ), A, LDA, X, LDX, CMPLX( ONE ), C, LDB ) NORMRS = CLANGE( 'Max', NROWS, NRHS, C, LDB, RWORK ) IF( NORMRS.GT.SMLNUM ) THEN ISCL = 1 CALL CLASCL( 'General', 0, 0, NORMRS, ONE, NROWS, NRHS, C, LDB, $ INFO ) END IF * * compute R'*A * CALL CGEMM( 'Conjugate transpose', TRANS, NRHS, NCOLS, NROWS, $ CMPLX( ONE ), C, LDB, A, LDA, CMPLX( ZERO ), WORK, $ NRHS ) * * compute and properly scale error * ERR = CLANGE( 'One-norm', NRHS, NCOLS, WORK, NRHS, RWORK ) IF( NORMA.NE.ZERO ) $ ERR = ERR / NORMA * IF( ISCL.EQ.1 ) $ ERR = ERR*NORMRS * IF( IRESID.EQ.1 ) THEN NORMB = CLANGE( 'One-norm', NROWS, NRHS, B, LDB, RWORK ) IF( NORMB.NE.ZERO ) $ ERR = ERR / NORMB ELSE NORMX = CLANGE( 'One-norm', NCOLS, NRHS, X, LDX, RWORK ) IF( NORMX.NE.ZERO ) $ ERR = ERR / NORMX END IF * CQRT17 = ERR / ( SLAMCH( 'Epsilon' )*REAL( MAX( M, N, NRHS ) ) ) RETURN * * End of CQRT17 * END |