|
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 |
SUBROUTINE SSGT01( ITYPE, UPLO, N, M, A, LDA, B, LDB, Z, LDZ, D,
$ WORK, RESULT ) * * -- LAPACK test routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * modified August 1997, a new parameter M is added to the calling * sequence. * * .. Scalar Arguments .. CHARACTER UPLO INTEGER ITYPE, LDA, LDB, LDZ, M, N * .. * .. Array Arguments .. REAL A( LDA, * ), B( LDB, * ), D( * ), RESULT( * ), $ WORK( * ), Z( LDZ, * ) * .. * * Purpose * ======= * * SSGT01 checks a decomposition of the form * * A Z = B Z D or * A B Z = Z D or * B A Z = Z D * * where A is a symmetric matrix, B is * symmetric positive definite, Z is orthogonal, and D is diagonal. * * One of the following test ratios is computed: * * ITYPE = 1: RESULT(1) = | A Z - B Z D | / ( |A| |Z| n ulp ) * * ITYPE = 2: RESULT(1) = | A B Z - Z D | / ( |A| |Z| n ulp ) * * ITYPE = 3: RESULT(1) = | B A Z - Z D | / ( |A| |Z| n ulp ) * * Arguments * ========= * * ITYPE (input) INTEGER * The form of the symmetric generalized eigenproblem. * = 1: A*z = (lambda)*B*z * = 2: A*B*z = (lambda)*z * = 3: B*A*z = (lambda)*z * * UPLO (input) CHARACTER*1 * Specifies whether the upper or lower triangular part of the * symmetric matrices A and B is stored. * = 'U': Upper triangular * = 'L': Lower triangular * * N (input) INTEGER * The order of the matrix A. N >= 0. * * M (input) INTEGER * The number of eigenvalues found. 0 <= M <= N. * * A (input) REAL array, dimension (LDA, N) * The original symmetric matrix A. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= max(1,N). * * B (input) REAL array, dimension (LDB, N) * The original symmetric positive definite matrix B. * * LDB (input) INTEGER * The leading dimension of the array B. LDB >= max(1,N). * * Z (input) REAL array, dimension (LDZ, M) * The computed eigenvectors of the generalized eigenproblem. * * LDZ (input) INTEGER * The leading dimension of the array Z. LDZ >= max(1,N). * * D (input) REAL array, dimension (M) * The computed eigenvalues of the generalized eigenproblem. * * WORK (workspace) REAL array, dimension (N*N) * * RESULT (output) REAL array, dimension (1) * The test ratio as described above. * * ===================================================================== * * .. Parameters .. REAL ZERO, ONE PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0 ) * .. * .. Local Scalars .. INTEGER I REAL ANORM, ULP * .. * .. External Functions .. REAL SLAMCH, SLANGE, SLANSY EXTERNAL SLAMCH, SLANGE, SLANSY * .. * .. External Subroutines .. EXTERNAL SSCAL, SSYMM * .. * .. Executable Statements .. * RESULT( 1 ) = ZERO IF( N.LE.0 ) $ RETURN * ULP = SLAMCH( 'Epsilon' ) * * Compute product of 1-norms of A and Z. * ANORM = SLANSY( '1', UPLO, N, A, LDA, WORK )* $ SLANGE( '1', N, M, Z, LDZ, WORK ) IF( ANORM.EQ.ZERO ) $ ANORM = ONE * IF( ITYPE.EQ.1 ) THEN * * Norm of AZ - BZD * CALL SSYMM( 'Left', UPLO, N, M, ONE, A, LDA, Z, LDZ, ZERO, $ WORK, N ) DO 10 I = 1, M CALL SSCAL( N, D( I ), Z( 1, I ), 1 ) 10 CONTINUE CALL SSYMM( 'Left', UPLO, N, M, ONE, B, LDB, Z, LDZ, -ONE, $ WORK, N ) * RESULT( 1 ) = ( SLANGE( '1', N, M, WORK, N, WORK ) / ANORM ) / $ ( N*ULP ) * ELSE IF( ITYPE.EQ.2 ) THEN * * Norm of ABZ - ZD * CALL SSYMM( 'Left', UPLO, N, M, ONE, B, LDB, Z, LDZ, ZERO, $ WORK, N ) DO 20 I = 1, M CALL SSCAL( N, D( I ), Z( 1, I ), 1 ) 20 CONTINUE CALL SSYMM( 'Left', UPLO, N, M, ONE, A, LDA, WORK, N, -ONE, Z, $ LDZ ) * RESULT( 1 ) = ( SLANGE( '1', N, M, Z, LDZ, WORK ) / ANORM ) / $ ( N*ULP ) * ELSE IF( ITYPE.EQ.3 ) THEN * * Norm of BAZ - ZD * CALL SSYMM( 'Left', UPLO, N, M, ONE, A, LDA, Z, LDZ, ZERO, $ WORK, N ) DO 30 I = 1, M CALL SSCAL( N, D( I ), Z( 1, I ), 1 ) 30 CONTINUE CALL SSYMM( 'Left', UPLO, N, M, ONE, B, LDB, WORK, N, -ONE, Z, $ LDZ ) * RESULT( 1 ) = ( SLANGE( '1', N, M, Z, LDZ, WORK ) / ANORM ) / $ ( N*ULP ) END IF * RETURN * * End of SSGT01 * END |