|
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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 |
SUBROUTINE CHEGS2( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
* * -- LAPACK routine (version 3.3.1) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * -- April 2011 -- * * .. Scalar Arguments .. CHARACTER UPLO INTEGER INFO, ITYPE, LDA, LDB, N * .. * .. Array Arguments .. COMPLEX A( LDA, * ), B( LDB, * ) * .. * * Purpose * ======= * * CHEGS2 reduces a complex Hermitian-definite generalized * eigenproblem to standard form. * * If ITYPE = 1, the problem is A*x = lambda*B*x, * and A is overwritten by inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H) * * If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or * B*A*x = lambda*x, and A is overwritten by U*A*U**H or L**H *A*L. * * B must have been previously factorized as U**H *U or L*L**H by ZPOTRF. * * Arguments * ========= * * ITYPE (input) INTEGER * = 1: compute inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H); * = 2 or 3: compute U*A*U**H or L**H *A*L. * * UPLO (input) CHARACTER*1 * Specifies whether the upper or lower triangular part of the * Hermitian matrix A is stored, and how B has been factorized. * = 'U': Upper triangular * = 'L': Lower triangular * * N (input) INTEGER * The order of the matrices A and B. N >= 0. * * A (input/output) COMPLEX array, dimension (LDA,N) * On entry, 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. * * On exit, if INFO = 0, the transformed matrix, stored in the * same format as A. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= max(1,N). * * B (input) COMPLEX array, dimension (LDB,N) * The triangular factor from the Cholesky factorization of B, * as returned by CPOTRF. * * LDB (input) INTEGER * The leading dimension of the array B. LDB >= max(1,N). * * INFO (output) INTEGER * = 0: successful exit. * < 0: if INFO = -i, the i-th argument had an illegal value. * * ===================================================================== * * .. Parameters .. REAL ONE, HALF PARAMETER ( ONE = 1.0E+0, HALF = 0.5E+0 ) COMPLEX CONE PARAMETER ( CONE = ( 1.0E+0, 0.0E+0 ) ) * .. * .. Local Scalars .. LOGICAL UPPER INTEGER K REAL AKK, BKK COMPLEX CT * .. * .. External Subroutines .. EXTERNAL CAXPY, CHER2, CLACGV, CSSCAL, CTRMV, CTRSV, $ XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 UPPER = LSAME( UPLO, 'U' ) IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN INFO = -1 ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN INFO = -2 ELSE IF( N.LT.0 ) THEN INFO = -3 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN INFO = -5 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN INFO = -7 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'CHEGS2', -INFO ) RETURN END IF * IF( ITYPE.EQ.1 ) THEN IF( UPPER ) THEN * * Compute inv(U**H)*A*inv(U) * DO 10 K = 1, N * * Update the upper triangle of A(k:n,k:n) * AKK = A( K, K ) BKK = B( K, K ) AKK = AKK / BKK**2 A( K, K ) = AKK IF( K.LT.N ) THEN CALL CSSCAL( N-K, ONE / BKK, A( K, K+1 ), LDA ) CT = -HALF*AKK CALL CLACGV( N-K, A( K, K+1 ), LDA ) CALL CLACGV( N-K, B( K, K+1 ), LDB ) CALL CAXPY( N-K, CT, B( K, K+1 ), LDB, A( K, K+1 ), $ LDA ) CALL CHER2( UPLO, N-K, -CONE, A( K, K+1 ), LDA, $ B( K, K+1 ), LDB, A( K+1, K+1 ), LDA ) CALL CAXPY( N-K, CT, B( K, K+1 ), LDB, A( K, K+1 ), $ LDA ) CALL CLACGV( N-K, B( K, K+1 ), LDB ) CALL CTRSV( UPLO, 'Conjugate transpose', 'Non-unit', $ N-K, B( K+1, K+1 ), LDB, A( K, K+1 ), $ LDA ) CALL CLACGV( N-K, A( K, K+1 ), LDA ) END IF 10 CONTINUE ELSE * * Compute inv(L)*A*inv(L**H) * DO 20 K = 1, N * * Update the lower triangle of A(k:n,k:n) * AKK = A( K, K ) BKK = B( K, K ) AKK = AKK / BKK**2 A( K, K ) = AKK IF( K.LT.N ) THEN CALL CSSCAL( N-K, ONE / BKK, A( K+1, K ), 1 ) CT = -HALF*AKK CALL CAXPY( N-K, CT, B( K+1, K ), 1, A( K+1, K ), 1 ) CALL CHER2( UPLO, N-K, -CONE, A( K+1, K ), 1, $ B( K+1, K ), 1, A( K+1, K+1 ), LDA ) CALL CAXPY( N-K, CT, B( K+1, K ), 1, A( K+1, K ), 1 ) CALL CTRSV( UPLO, 'No transpose', 'Non-unit', N-K, $ B( K+1, K+1 ), LDB, A( K+1, K ), 1 ) END IF 20 CONTINUE END IF ELSE IF( UPPER ) THEN * * Compute U*A*U**H * DO 30 K = 1, N * * Update the upper triangle of A(1:k,1:k) * AKK = A( K, K ) BKK = B( K, K ) CALL CTRMV( UPLO, 'No transpose', 'Non-unit', K-1, B, $ LDB, A( 1, K ), 1 ) CT = HALF*AKK CALL CAXPY( K-1, CT, B( 1, K ), 1, A( 1, K ), 1 ) CALL CHER2( UPLO, K-1, CONE, A( 1, K ), 1, B( 1, K ), 1, $ A, LDA ) CALL CAXPY( K-1, CT, B( 1, K ), 1, A( 1, K ), 1 ) CALL CSSCAL( K-1, BKK, A( 1, K ), 1 ) A( K, K ) = AKK*BKK**2 30 CONTINUE ELSE * * Compute L**H *A*L * DO 40 K = 1, N * * Update the lower triangle of A(1:k,1:k) * AKK = A( K, K ) BKK = B( K, K ) CALL CLACGV( K-1, A( K, 1 ), LDA ) CALL CTRMV( UPLO, 'Conjugate transpose', 'Non-unit', K-1, $ B, LDB, A( K, 1 ), LDA ) CT = HALF*AKK CALL CLACGV( K-1, B( K, 1 ), LDB ) CALL CAXPY( K-1, CT, B( K, 1 ), LDB, A( K, 1 ), LDA ) CALL CHER2( UPLO, K-1, CONE, A( K, 1 ), LDA, B( K, 1 ), $ LDB, A, LDA ) CALL CAXPY( K-1, CT, B( K, 1 ), LDB, A( K, 1 ), LDA ) CALL CLACGV( K-1, B( K, 1 ), LDB ) CALL CSSCAL( K-1, BKK, A( K, 1 ), LDA ) CALL CLACGV( K-1, A( K, 1 ), LDA ) A( K, K ) = AKK*BKK**2 40 CONTINUE END IF END IF RETURN * * End of CHEGS2 * END |