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Mise à jour de lapack vers la version 3.3.0.
1: SUBROUTINE DSYGS2( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) 2: * 3: * -- LAPACK routine (version 3.2) -- 4: * -- LAPACK is a software package provided by Univ. of Tennessee, -- 5: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 6: * November 2006 7: * 8: * .. Scalar Arguments .. 9: CHARACTER UPLO 10: INTEGER INFO, ITYPE, LDA, LDB, N 11: * .. 12: * .. Array Arguments .. 13: DOUBLE PRECISION A( LDA, * ), B( LDB, * ) 14: * .. 15: * 16: * Purpose 17: * ======= 18: * 19: * DSYGS2 reduces a real symmetric-definite generalized eigenproblem 20: * to standard form. 21: * 22: * If ITYPE = 1, the problem is A*x = lambda*B*x, 23: * and A is overwritten by inv(U')*A*inv(U) or inv(L)*A*inv(L') 24: * 25: * If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or 26: * B*A*x = lambda*x, and A is overwritten by U*A*U` or L'*A*L. 27: * 28: * B must have been previously factorized as U'*U or L*L' by DPOTRF. 29: * 30: * Arguments 31: * ========= 32: * 33: * ITYPE (input) INTEGER 34: * = 1: compute inv(U')*A*inv(U) or inv(L)*A*inv(L'); 35: * = 2 or 3: compute U*A*U' or L'*A*L. 36: * 37: * UPLO (input) CHARACTER*1 38: * Specifies whether the upper or lower triangular part of the 39: * symmetric matrix A is stored, and how B has been factorized. 40: * = 'U': Upper triangular 41: * = 'L': Lower triangular 42: * 43: * N (input) INTEGER 44: * The order of the matrices A and B. N >= 0. 45: * 46: * A (input/output) DOUBLE PRECISION array, dimension (LDA,N) 47: * On entry, the symmetric matrix A. If UPLO = 'U', the leading 48: * n by n upper triangular part of A contains the upper 49: * triangular part of the matrix A, and the strictly lower 50: * triangular part of A is not referenced. If UPLO = 'L', the 51: * leading n by n lower triangular part of A contains the lower 52: * triangular part of the matrix A, and the strictly upper 53: * triangular part of A is not referenced. 54: * 55: * On exit, if INFO = 0, the transformed matrix, stored in the 56: * same format as A. 57: * 58: * LDA (input) INTEGER 59: * The leading dimension of the array A. LDA >= max(1,N). 60: * 61: * B (input) DOUBLE PRECISION array, dimension (LDB,N) 62: * The triangular factor from the Cholesky factorization of B, 63: * as returned by DPOTRF. 64: * 65: * LDB (input) INTEGER 66: * The leading dimension of the array B. LDB >= max(1,N). 67: * 68: * INFO (output) INTEGER 69: * = 0: successful exit. 70: * < 0: if INFO = -i, the i-th argument had an illegal value. 71: * 72: * ===================================================================== 73: * 74: * .. Parameters .. 75: DOUBLE PRECISION ONE, HALF 76: PARAMETER ( ONE = 1.0D0, HALF = 0.5D0 ) 77: * .. 78: * .. Local Scalars .. 79: LOGICAL UPPER 80: INTEGER K 81: DOUBLE PRECISION AKK, BKK, CT 82: * .. 83: * .. External Subroutines .. 84: EXTERNAL DAXPY, DSCAL, DSYR2, DTRMV, DTRSV, XERBLA 85: * .. 86: * .. Intrinsic Functions .. 87: INTRINSIC MAX 88: * .. 89: * .. External Functions .. 90: LOGICAL LSAME 91: EXTERNAL LSAME 92: * .. 93: * .. Executable Statements .. 94: * 95: * Test the input parameters. 96: * 97: INFO = 0 98: UPPER = LSAME( UPLO, 'U' ) 99: IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN 100: INFO = -1 101: ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN 102: INFO = -2 103: ELSE IF( N.LT.0 ) THEN 104: INFO = -3 105: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN 106: INFO = -5 107: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN 108: INFO = -7 109: END IF 110: IF( INFO.NE.0 ) THEN 111: CALL XERBLA( 'DSYGS2', -INFO ) 112: RETURN 113: END IF 114: * 115: IF( ITYPE.EQ.1 ) THEN 116: IF( UPPER ) THEN 117: * 118: * Compute inv(U')*A*inv(U) 119: * 120: DO 10 K = 1, N 121: * 122: * Update the upper triangle of A(k:n,k:n) 123: * 124: AKK = A( K, K ) 125: BKK = B( K, K ) 126: AKK = AKK / BKK**2 127: A( K, K ) = AKK 128: IF( K.LT.N ) THEN 129: CALL DSCAL( N-K, ONE / BKK, A( K, K+1 ), LDA ) 130: CT = -HALF*AKK 131: CALL DAXPY( N-K, CT, B( K, K+1 ), LDB, A( K, K+1 ), 132: $ LDA ) 133: CALL DSYR2( UPLO, N-K, -ONE, A( K, K+1 ), LDA, 134: $ B( K, K+1 ), LDB, A( K+1, K+1 ), LDA ) 135: CALL DAXPY( N-K, CT, B( K, K+1 ), LDB, A( K, K+1 ), 136: $ LDA ) 137: CALL DTRSV( UPLO, 'Transpose', 'Non-unit', N-K, 138: $ B( K+1, K+1 ), LDB, A( K, K+1 ), LDA ) 139: END IF 140: 10 CONTINUE 141: ELSE 142: * 143: * Compute inv(L)*A*inv(L') 144: * 145: DO 20 K = 1, N 146: * 147: * Update the lower triangle of A(k:n,k:n) 148: * 149: AKK = A( K, K ) 150: BKK = B( K, K ) 151: AKK = AKK / BKK**2 152: A( K, K ) = AKK 153: IF( K.LT.N ) THEN 154: CALL DSCAL( N-K, ONE / BKK, A( K+1, K ), 1 ) 155: CT = -HALF*AKK 156: CALL DAXPY( N-K, CT, B( K+1, K ), 1, A( K+1, K ), 1 ) 157: CALL DSYR2( UPLO, N-K, -ONE, A( K+1, K ), 1, 158: $ B( K+1, K ), 1, A( K+1, K+1 ), LDA ) 159: CALL DAXPY( N-K, CT, B( K+1, K ), 1, A( K+1, K ), 1 ) 160: CALL DTRSV( UPLO, 'No transpose', 'Non-unit', N-K, 161: $ B( K+1, K+1 ), LDB, A( K+1, K ), 1 ) 162: END IF 163: 20 CONTINUE 164: END IF 165: ELSE 166: IF( UPPER ) THEN 167: * 168: * Compute U*A*U' 169: * 170: DO 30 K = 1, N 171: * 172: * Update the upper triangle of A(1:k,1:k) 173: * 174: AKK = A( K, K ) 175: BKK = B( K, K ) 176: CALL DTRMV( UPLO, 'No transpose', 'Non-unit', K-1, B, 177: $ LDB, A( 1, K ), 1 ) 178: CT = HALF*AKK 179: CALL DAXPY( K-1, CT, B( 1, K ), 1, A( 1, K ), 1 ) 180: CALL DSYR2( UPLO, K-1, ONE, A( 1, K ), 1, B( 1, K ), 1, 181: $ A, LDA ) 182: CALL DAXPY( K-1, CT, B( 1, K ), 1, A( 1, K ), 1 ) 183: CALL DSCAL( K-1, BKK, A( 1, K ), 1 ) 184: A( K, K ) = AKK*BKK**2 185: 30 CONTINUE 186: ELSE 187: * 188: * Compute L'*A*L 189: * 190: DO 40 K = 1, N 191: * 192: * Update the lower triangle of A(1:k,1:k) 193: * 194: AKK = A( K, K ) 195: BKK = B( K, K ) 196: CALL DTRMV( UPLO, 'Transpose', 'Non-unit', K-1, B, LDB, 197: $ A( K, 1 ), LDA ) 198: CT = HALF*AKK 199: CALL DAXPY( K-1, CT, B( K, 1 ), LDB, A( K, 1 ), LDA ) 200: CALL DSYR2( UPLO, K-1, ONE, A( K, 1 ), LDA, B( K, 1 ), 201: $ LDB, A, LDA ) 202: CALL DAXPY( K-1, CT, B( K, 1 ), LDB, A( K, 1 ), LDA ) 203: CALL DSCAL( K-1, BKK, A( K, 1 ), LDA ) 204: A( K, K ) = AKK*BKK**2 205: 40 CONTINUE 206: END IF 207: END IF 208: RETURN 209: * 210: * End of DSYGS2 211: * 212: END