|
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 |
SUBROUTINE ZPOT06( UPLO, N, NRHS, A, LDA, X, LDX, B, LDB,
$ RWORK, RESID ) * * -- LAPACK test routine (version 3.1.2) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * May 2007 * * .. Scalar Arguments .. CHARACTER UPLO INTEGER LDA, LDB, LDX, N, NRHS DOUBLE PRECISION RESID * .. * .. Array Arguments .. DOUBLE PRECISION RWORK( * ) COMPLEX*16 A( LDA, * ), B( LDB, * ), X( LDX, * ) * .. * * Purpose * ======= * * ZPOT06 computes the residual for a solution of a system of linear * equations A*x = b : * RESID = norm(B - A*X,inf) / ( norm(A,inf) * norm(X,inf) * EPS ), * where EPS is the machine epsilon. * * Arguments * ========= * * UPLO (input) CHARACTER*1 * Specifies whether the upper or lower triangular part of the * symmetric matrix A is stored: * = 'U': Upper triangular * = 'L': Lower triangular * * N (input) INTEGER * The number of rows and columns of the matrix A. N >= 0. * * NRHS (input) INTEGER * The number of columns of B, the matrix of right hand sides. * NRHS >= 0. * * A (input) COMPLEX*16 array, dimension (LDA,N) * The original M x N matrix A. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= max(1,N). * * X (input) COMPLEX*16 array, dimension (LDX,NRHS) * The computed solution vectors for the system of linear * equations. * * LDX (input) INTEGER * The leading dimension of the array X. If TRANS = 'N', * LDX >= max(1,N); if TRANS = 'T' or 'C', LDX >= max(1,N). * * B (input/output) COMPLEX*16 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. * * LDB (input) INTEGER * The leading dimension of the array B. IF TRANS = 'N', * LDB >= max(1,M); if TRANS = 'T' or 'C', LDB >= max(1,N). * * RWORK (workspace) DOUBLE PRECISION array, dimension (N) * * RESID (output) DOUBLE PRECISION * The maximum over the number of right hand sides of * norm(B - A*X) / ( norm(A) * norm(X) * EPS ). * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE, NEGONE PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) PARAMETER ( NEGONE = -1.0D+0 ) COMPLEX*16 CONE, NEGCONE PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ) ) PARAMETER ( NEGCONE = ( -1.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. INTEGER IFAIL, J DOUBLE PRECISION ANORM, BNORM, EPS, XNORM COMPLEX*16 ZDUM * .. * .. External Functions .. LOGICAL LSAME INTEGER IZAMAX DOUBLE PRECISION DLAMCH, ZLANSY EXTERNAL LSAME, IZAMAX, DLAMCH, ZLANSY * .. * .. External Subroutines .. EXTERNAL ZHEMM * .. * .. Intrinsic Functions .. INTRINSIC ABS, DBLE, DIMAG, MAX * .. * .. Statement Functions .. DOUBLE PRECISION CABS1 * .. * .. Statement Function definitions .. CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) ) * .. * .. * .. Executable Statements .. * * Quick exit if N = 0 or NRHS = 0 * IF( N.LE.0 .OR. NRHS.EQ.0 ) THEN RESID = ZERO RETURN END IF * * Exit with RESID = 1/EPS if ANORM = 0. * EPS = DLAMCH( 'Epsilon' ) ANORM = ZLANSY( 'I', UPLO, N, A, LDA, RWORK ) IF( ANORM.LE.ZERO ) THEN RESID = ONE / EPS RETURN END IF * * Compute B - A*X and store in B. IFAIL=0 * CALL ZHEMM( 'Left', UPLO, N, NRHS, NEGCONE, A, LDA, X, $ LDX, CONE, B, LDB ) * * Compute the maximum over the number of right hand sides of * norm(B - A*X) / ( norm(A) * norm(X) * EPS ) . * RESID = ZERO DO 10 J = 1, NRHS BNORM = CABS1(B(IZAMAX( N, B( 1, J ), 1 ),J)) XNORM = CABS1(X(IZAMAX( N, X( 1, J ), 1 ),J)) IF( XNORM.LE.ZERO ) THEN RESID = ONE / EPS ELSE RESID = MAX( RESID, ( ( BNORM / ANORM ) / XNORM ) / EPS ) END IF 10 CONTINUE * RETURN * * End of ZPOT06 * END |