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Mise à jour de lapack vers la version 3.3.0.
1: SUBROUTINE DSYGST( 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: * DSYGST 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**T)*A*inv(U) or inv(L)*A*inv(L**T) 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**T or L**T*A*L. 27: * 28: * B must have been previously factorized as U**T*U or L*L**T by DPOTRF. 29: * 30: * Arguments 31: * ========= 32: * 33: * ITYPE (input) INTEGER 34: * = 1: compute inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T); 35: * = 2 or 3: compute U*A*U**T or L**T*A*L. 36: * 37: * UPLO (input) CHARACTER*1 38: * = 'U': Upper triangle of A is stored and B is factored as 39: * U**T*U; 40: * = 'L': Lower triangle of A is stored and B is factored as 41: * L*L**T. 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, KB, NB 81: * .. 82: * .. External Subroutines .. 83: EXTERNAL DSYGS2, DSYMM, DSYR2K, DTRMM, DTRSM, XERBLA 84: * .. 85: * .. Intrinsic Functions .. 86: INTRINSIC MAX, MIN 87: * .. 88: * .. External Functions .. 89: LOGICAL LSAME 90: INTEGER ILAENV 91: EXTERNAL LSAME, ILAENV 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( 'DSYGST', -INFO ) 112: RETURN 113: END IF 114: * 115: * Quick return if possible 116: * 117: IF( N.EQ.0 ) 118: $ RETURN 119: * 120: * Determine the block size for this environment. 121: * 122: NB = ILAENV( 1, 'DSYGST', UPLO, N, -1, -1, -1 ) 123: * 124: IF( NB.LE.1 .OR. NB.GE.N ) THEN 125: * 126: * Use unblocked code 127: * 128: CALL DSYGS2( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) 129: ELSE 130: * 131: * Use blocked code 132: * 133: IF( ITYPE.EQ.1 ) THEN 134: IF( UPPER ) THEN 135: * 136: * Compute inv(U')*A*inv(U) 137: * 138: DO 10 K = 1, N, NB 139: KB = MIN( N-K+1, NB ) 140: * 141: * Update the upper triangle of A(k:n,k:n) 142: * 143: CALL DSYGS2( ITYPE, UPLO, KB, A( K, K ), LDA, 144: $ B( K, K ), LDB, INFO ) 145: IF( K+KB.LE.N ) THEN 146: CALL DTRSM( 'Left', UPLO, 'Transpose', 'Non-unit', 147: $ KB, N-K-KB+1, ONE, B( K, K ), LDB, 148: $ A( K, K+KB ), LDA ) 149: CALL DSYMM( 'Left', UPLO, KB, N-K-KB+1, -HALF, 150: $ A( K, K ), LDA, B( K, K+KB ), LDB, ONE, 151: $ A( K, K+KB ), LDA ) 152: CALL DSYR2K( UPLO, 'Transpose', N-K-KB+1, KB, -ONE, 153: $ A( K, K+KB ), LDA, B( K, K+KB ), LDB, 154: $ ONE, A( K+KB, K+KB ), LDA ) 155: CALL DSYMM( 'Left', UPLO, KB, N-K-KB+1, -HALF, 156: $ A( K, K ), LDA, B( K, K+KB ), LDB, ONE, 157: $ A( K, K+KB ), LDA ) 158: CALL DTRSM( 'Right', UPLO, 'No transpose', 159: $ 'Non-unit', KB, N-K-KB+1, ONE, 160: $ B( K+KB, K+KB ), LDB, A( K, K+KB ), 161: $ LDA ) 162: END IF 163: 10 CONTINUE 164: ELSE 165: * 166: * Compute inv(L)*A*inv(L') 167: * 168: DO 20 K = 1, N, NB 169: KB = MIN( N-K+1, NB ) 170: * 171: * Update the lower triangle of A(k:n,k:n) 172: * 173: CALL DSYGS2( ITYPE, UPLO, KB, A( K, K ), LDA, 174: $ B( K, K ), LDB, INFO ) 175: IF( K+KB.LE.N ) THEN 176: CALL DTRSM( 'Right', UPLO, 'Transpose', 'Non-unit', 177: $ N-K-KB+1, KB, ONE, B( K, K ), LDB, 178: $ A( K+KB, K ), LDA ) 179: CALL DSYMM( 'Right', UPLO, N-K-KB+1, KB, -HALF, 180: $ A( K, K ), LDA, B( K+KB, K ), LDB, ONE, 181: $ A( K+KB, K ), LDA ) 182: CALL DSYR2K( UPLO, 'No transpose', N-K-KB+1, KB, 183: $ -ONE, A( K+KB, K ), LDA, B( K+KB, K ), 184: $ LDB, ONE, A( K+KB, K+KB ), LDA ) 185: CALL DSYMM( 'Right', UPLO, N-K-KB+1, KB, -HALF, 186: $ A( K, K ), LDA, B( K+KB, K ), LDB, ONE, 187: $ A( K+KB, K ), LDA ) 188: CALL DTRSM( 'Left', UPLO, 'No transpose', 189: $ 'Non-unit', N-K-KB+1, KB, ONE, 190: $ B( K+KB, K+KB ), LDB, A( K+KB, K ), 191: $ LDA ) 192: END IF 193: 20 CONTINUE 194: END IF 195: ELSE 196: IF( UPPER ) THEN 197: * 198: * Compute U*A*U' 199: * 200: DO 30 K = 1, N, NB 201: KB = MIN( N-K+1, NB ) 202: * 203: * Update the upper triangle of A(1:k+kb-1,1:k+kb-1) 204: * 205: CALL DTRMM( 'Left', UPLO, 'No transpose', 'Non-unit', 206: $ K-1, KB, ONE, B, LDB, A( 1, K ), LDA ) 207: CALL DSYMM( 'Right', UPLO, K-1, KB, HALF, A( K, K ), 208: $ LDA, B( 1, K ), LDB, ONE, A( 1, K ), LDA ) 209: CALL DSYR2K( UPLO, 'No transpose', K-1, KB, ONE, 210: $ A( 1, K ), LDA, B( 1, K ), LDB, ONE, A, 211: $ LDA ) 212: CALL DSYMM( 'Right', UPLO, K-1, KB, HALF, A( K, K ), 213: $ LDA, B( 1, K ), LDB, ONE, A( 1, K ), LDA ) 214: CALL DTRMM( 'Right', UPLO, 'Transpose', 'Non-unit', 215: $ K-1, KB, ONE, B( K, K ), LDB, A( 1, K ), 216: $ LDA ) 217: CALL DSYGS2( ITYPE, UPLO, KB, A( K, K ), LDA, 218: $ B( K, K ), LDB, INFO ) 219: 30 CONTINUE 220: ELSE 221: * 222: * Compute L'*A*L 223: * 224: DO 40 K = 1, N, NB 225: KB = MIN( N-K+1, NB ) 226: * 227: * Update the lower triangle of A(1:k+kb-1,1:k+kb-1) 228: * 229: CALL DTRMM( 'Right', UPLO, 'No transpose', 'Non-unit', 230: $ KB, K-1, ONE, B, LDB, A( K, 1 ), LDA ) 231: CALL DSYMM( 'Left', UPLO, KB, K-1, HALF, A( K, K ), 232: $ LDA, B( K, 1 ), LDB, ONE, A( K, 1 ), LDA ) 233: CALL DSYR2K( UPLO, 'Transpose', K-1, KB, ONE, 234: $ A( K, 1 ), LDA, B( K, 1 ), LDB, ONE, A, 235: $ LDA ) 236: CALL DSYMM( 'Left', UPLO, KB, K-1, HALF, A( K, K ), 237: $ LDA, B( K, 1 ), LDB, ONE, A( K, 1 ), LDA ) 238: CALL DTRMM( 'Left', UPLO, 'Transpose', 'Non-unit', KB, 239: $ K-1, ONE, B( K, K ), LDB, A( K, 1 ), LDA ) 240: CALL DSYGS2( ITYPE, UPLO, KB, A( K, K ), LDA, 241: $ B( K, K ), LDB, INFO ) 242: 40 CONTINUE 243: END IF 244: END IF 245: END IF 246: RETURN 247: * 248: * End of DSYGST 249: * 250: END