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 |
SUBROUTINE ZSYT03( UPLO, N, A, LDA, AINV, LDAINV, WORK, LDWORK,
$ RWORK, RCOND, RESID ) * * -- LAPACK test routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. CHARACTER UPLO INTEGER LDA, LDAINV, LDWORK, N DOUBLE PRECISION RCOND, RESID * .. * .. Array Arguments .. DOUBLE PRECISION RWORK( * ) COMPLEX*16 A( LDA, * ), AINV( LDAINV, * ), $ WORK( LDWORK, * ) * .. * * Purpose * ======= * * ZSYT03 computes the residual for a complex symmetric matrix times * its inverse: * norm( I - A*AINV ) / ( N * norm(A) * norm(AINV) * EPS ) * where EPS is the machine epsilon. * * Arguments * ========== * * UPLO (input) CHARACTER*1 * Specifies whether the upper or lower triangular part of the * complex 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. * * A (input) COMPLEX*16 array, dimension (LDA,N) * The original complex symmetric matrix A. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= max(1,N) * * AINV (input/output) COMPLEX*16 array, dimension (LDAINV,N) * On entry, the inverse of the matrix A, stored as a symmetric * matrix in the same format as A. * In this version, AINV is expanded into a full matrix and * multiplied by A, so the opposing triangle of AINV will be * changed; i.e., if the upper triangular part of AINV is * stored, the lower triangular part will be used as work space. * * LDAINV (input) INTEGER * The leading dimension of the array AINV. LDAINV >= max(1,N). * * WORK (workspace) COMPLEX*16 array, dimension (LDWORK,N) * * LDWORK (input) INTEGER * The leading dimension of the array WORK. LDWORK >= max(1,N). * * RWORK (workspace) DOUBLE PRECISION array, dimension (N) * * RCOND (output) DOUBLE PRECISION * The reciprocal of the condition number of A, computed as * RCOND = 1/ (norm(A) * norm(AINV)). * * RESID (output) DOUBLE PRECISION * norm(I - A*AINV) / ( N * norm(A) * norm(AINV) * EPS ) * * ===================================================================== * * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) COMPLEX*16 CZERO, CONE PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ), $ CONE = ( 1.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. INTEGER I, J DOUBLE PRECISION AINVNM, ANORM, EPS * .. * .. External Functions .. LOGICAL LSAME DOUBLE PRECISION DLAMCH, ZLANGE, ZLANSY EXTERNAL LSAME, DLAMCH, ZLANGE, ZLANSY * .. * .. External Subroutines .. EXTERNAL ZSYMM * .. * .. Intrinsic Functions .. INTRINSIC DBLE * .. * .. Executable Statements .. * * Quick exit if N = 0 * IF( N.LE.0 ) THEN RCOND = ONE RESID = ZERO RETURN END IF * * Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0. * EPS = DLAMCH( 'Epsilon' ) ANORM = ZLANSY( '1', UPLO, N, A, LDA, RWORK ) AINVNM = ZLANSY( '1', UPLO, N, AINV, LDAINV, RWORK ) IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN RCOND = ZERO RESID = ONE / EPS RETURN END IF RCOND = ( ONE / ANORM ) / AINVNM * * Expand AINV into a full matrix and call ZSYMM to multiply * AINV on the left by A (store the result in WORK). * IF( LSAME( UPLO, 'U' ) ) THEN DO 20 J = 1, N DO 10 I = 1, J - 1 AINV( J, I ) = AINV( I, J ) 10 CONTINUE 20 CONTINUE ELSE DO 40 J = 1, N DO 30 I = J + 1, N AINV( J, I ) = AINV( I, J ) 30 CONTINUE 40 CONTINUE END IF CALL ZSYMM( 'Left', UPLO, N, N, -CONE, A, LDA, AINV, LDAINV, $ CZERO, WORK, LDWORK ) * * Add the identity matrix to WORK . * DO 50 I = 1, N WORK( I, I ) = WORK( I, I ) + CONE 50 CONTINUE * * Compute norm(I - A*AINV) / (N * norm(A) * norm(AINV) * EPS) * RESID = ZLANGE( '1', N, N, WORK, LDWORK, RWORK ) * RESID = ( ( RESID*RCOND ) / EPS ) / DBLE( N ) * RETURN * * End of ZSYT03 * END |