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Mise à jour de lapack vers la version 3.3.0.
1: SUBROUTINE DSYGVD( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK, 2: $ LWORK, IWORK, LIWORK, INFO ) 3: * 4: * -- LAPACK driver routine (version 3.2) -- 5: * -- LAPACK is a software package provided by Univ. of Tennessee, -- 6: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 7: * November 2006 8: * 9: * .. Scalar Arguments .. 10: CHARACTER JOBZ, UPLO 11: INTEGER INFO, ITYPE, LDA, LDB, LIWORK, LWORK, N 12: * .. 13: * .. Array Arguments .. 14: INTEGER IWORK( * ) 15: DOUBLE PRECISION A( LDA, * ), B( LDB, * ), W( * ), WORK( * ) 16: * .. 17: * 18: * Purpose 19: * ======= 20: * 21: * DSYGVD computes all the eigenvalues, and optionally, the eigenvectors 22: * of a real generalized symmetric-definite eigenproblem, of the form 23: * A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and 24: * B are assumed to be symmetric and B is also positive definite. 25: * If eigenvectors are desired, it uses a divide and conquer algorithm. 26: * 27: * The divide and conquer algorithm makes very mild assumptions about 28: * floating point arithmetic. It will work on machines with a guard 29: * digit in add/subtract, or on those binary machines without guard 30: * digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or 31: * Cray-2. It could conceivably fail on hexadecimal or decimal machines 32: * without guard digits, but we know of none. 33: * 34: * Arguments 35: * ========= 36: * 37: * ITYPE (input) INTEGER 38: * Specifies the problem type to be solved: 39: * = 1: A*x = (lambda)*B*x 40: * = 2: A*B*x = (lambda)*x 41: * = 3: B*A*x = (lambda)*x 42: * 43: * JOBZ (input) CHARACTER*1 44: * = 'N': Compute eigenvalues only; 45: * = 'V': Compute eigenvalues and eigenvectors. 46: * 47: * UPLO (input) CHARACTER*1 48: * = 'U': Upper triangles of A and B are stored; 49: * = 'L': Lower triangles of A and B are stored. 50: * 51: * N (input) INTEGER 52: * The order of the matrices A and B. N >= 0. 53: * 54: * A (input/output) DOUBLE PRECISION array, dimension (LDA, N) 55: * On entry, the symmetric matrix A. If UPLO = 'U', the 56: * leading N-by-N upper triangular part of A contains the 57: * upper triangular part of the matrix A. If UPLO = 'L', 58: * the leading N-by-N lower triangular part of A contains 59: * the lower triangular part of the matrix A. 60: * 61: * On exit, if JOBZ = 'V', then if INFO = 0, A contains the 62: * matrix Z of eigenvectors. The eigenvectors are normalized 63: * as follows: 64: * if ITYPE = 1 or 2, Z**T*B*Z = I; 65: * if ITYPE = 3, Z**T*inv(B)*Z = I. 66: * If JOBZ = 'N', then on exit the upper triangle (if UPLO='U') 67: * or the lower triangle (if UPLO='L') of A, including the 68: * diagonal, is destroyed. 69: * 70: * LDA (input) INTEGER 71: * The leading dimension of the array A. LDA >= max(1,N). 72: * 73: * B (input/output) DOUBLE PRECISION array, dimension (LDB, N) 74: * On entry, the symmetric matrix B. If UPLO = 'U', the 75: * leading N-by-N upper triangular part of B contains the 76: * upper triangular part of the matrix B. If UPLO = 'L', 77: * the leading N-by-N lower triangular part of B contains 78: * the lower triangular part of the matrix B. 79: * 80: * On exit, if INFO <= N, the part of B containing the matrix is 81: * overwritten by the triangular factor U or L from the Cholesky 82: * factorization B = U**T*U or B = L*L**T. 83: * 84: * LDB (input) INTEGER 85: * The leading dimension of the array B. LDB >= max(1,N). 86: * 87: * W (output) DOUBLE PRECISION array, dimension (N) 88: * If INFO = 0, the eigenvalues in ascending order. 89: * 90: * WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) 91: * On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 92: * 93: * LWORK (input) INTEGER 94: * The dimension of the array WORK. 95: * If N <= 1, LWORK >= 1. 96: * If JOBZ = 'N' and N > 1, LWORK >= 2*N+1. 97: * If JOBZ = 'V' and N > 1, LWORK >= 1 + 6*N + 2*N**2. 98: * 99: * If LWORK = -1, then a workspace query is assumed; the routine 100: * only calculates the optimal sizes of the WORK and IWORK 101: * arrays, returns these values as the first entries of the WORK 102: * and IWORK arrays, and no error message related to LWORK or 103: * LIWORK is issued by XERBLA. 104: * 105: * IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK)) 106: * On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. 107: * 108: * LIWORK (input) INTEGER 109: * The dimension of the array IWORK. 110: * If N <= 1, LIWORK >= 1. 111: * If JOBZ = 'N' and N > 1, LIWORK >= 1. 112: * If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N. 113: * 114: * If LIWORK = -1, then a workspace query is assumed; the 115: * routine only calculates the optimal sizes of the WORK and 116: * IWORK arrays, returns these values as the first entries of 117: * the WORK and IWORK arrays, and no error message related to 118: * LWORK or LIWORK is issued by XERBLA. 119: * 120: * INFO (output) INTEGER 121: * = 0: successful exit 122: * < 0: if INFO = -i, the i-th argument had an illegal value 123: * > 0: DPOTRF or DSYEVD returned an error code: 124: * <= N: if INFO = i and JOBZ = 'N', then the algorithm 125: * failed to converge; i off-diagonal elements of an 126: * intermediate tridiagonal form did not converge to 127: * zero; 128: * if INFO = i and JOBZ = 'V', then the algorithm 129: * failed to compute an eigenvalue while working on 130: * the submatrix lying in rows and columns INFO/(N+1) 131: * through mod(INFO,N+1); 132: * > N: if INFO = N + i, for 1 <= i <= N, then the leading 133: * minor of order i of B is not positive definite. 134: * The factorization of B could not be completed and 135: * no eigenvalues or eigenvectors were computed. 136: * 137: * Further Details 138: * =============== 139: * 140: * Based on contributions by 141: * Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA 142: * 143: * Modified so that no backsubstitution is performed if DSYEVD fails to 144: * converge (NEIG in old code could be greater than N causing out of 145: * bounds reference to A - reported by Ralf Meyer). Also corrected the 146: * description of INFO and the test on ITYPE. Sven, 16 Feb 05. 147: * ===================================================================== 148: * 149: * .. Parameters .. 150: DOUBLE PRECISION ONE 151: PARAMETER ( ONE = 1.0D+0 ) 152: * .. 153: * .. Local Scalars .. 154: LOGICAL LQUERY, UPPER, WANTZ 155: CHARACTER TRANS 156: INTEGER LIOPT, LIWMIN, LOPT, LWMIN 157: * .. 158: * .. External Functions .. 159: LOGICAL LSAME 160: EXTERNAL LSAME 161: * .. 162: * .. External Subroutines .. 163: EXTERNAL DPOTRF, DSYEVD, DSYGST, DTRMM, DTRSM, XERBLA 164: * .. 165: * .. Intrinsic Functions .. 166: INTRINSIC DBLE, MAX 167: * .. 168: * .. Executable Statements .. 169: * 170: * Test the input parameters. 171: * 172: WANTZ = LSAME( JOBZ, 'V' ) 173: UPPER = LSAME( UPLO, 'U' ) 174: LQUERY = ( LWORK.EQ.-1 .OR. LIWORK.EQ.-1 ) 175: * 176: INFO = 0 177: IF( N.LE.1 ) THEN 178: LIWMIN = 1 179: LWMIN = 1 180: ELSE IF( WANTZ ) THEN 181: LIWMIN = 3 + 5*N 182: LWMIN = 1 + 6*N + 2*N**2 183: ELSE 184: LIWMIN = 1 185: LWMIN = 2*N + 1 186: END IF 187: LOPT = LWMIN 188: LIOPT = LIWMIN 189: IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN 190: INFO = -1 191: ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN 192: INFO = -2 193: ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN 194: INFO = -3 195: ELSE IF( N.LT.0 ) THEN 196: INFO = -4 197: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN 198: INFO = -6 199: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN 200: INFO = -8 201: END IF 202: * 203: IF( INFO.EQ.0 ) THEN 204: WORK( 1 ) = LOPT 205: IWORK( 1 ) = LIOPT 206: * 207: IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN 208: INFO = -11 209: ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN 210: INFO = -13 211: END IF 212: END IF 213: * 214: IF( INFO.NE.0 ) THEN 215: CALL XERBLA( 'DSYGVD', -INFO ) 216: RETURN 217: ELSE IF( LQUERY ) THEN 218: RETURN 219: END IF 220: * 221: * Quick return if possible 222: * 223: IF( N.EQ.0 ) 224: $ RETURN 225: * 226: * Form a Cholesky factorization of B. 227: * 228: CALL DPOTRF( UPLO, N, B, LDB, INFO ) 229: IF( INFO.NE.0 ) THEN 230: INFO = N + INFO 231: RETURN 232: END IF 233: * 234: * Transform problem to standard eigenvalue problem and solve. 235: * 236: CALL DSYGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) 237: CALL DSYEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, IWORK, LIWORK, 238: $ INFO ) 239: LOPT = MAX( DBLE( LOPT ), DBLE( WORK( 1 ) ) ) 240: LIOPT = MAX( DBLE( LIOPT ), DBLE( IWORK( 1 ) ) ) 241: * 242: IF( WANTZ .AND. INFO.EQ.0 ) THEN 243: * 244: * Backtransform eigenvectors to the original problem. 245: * 246: IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN 247: * 248: * For A*x=(lambda)*B*x and A*B*x=(lambda)*x; 249: * backtransform eigenvectors: x = inv(L)'*y or inv(U)*y 250: * 251: IF( UPPER ) THEN 252: TRANS = 'N' 253: ELSE 254: TRANS = 'T' 255: END IF 256: * 257: CALL DTRSM( 'Left', UPLO, TRANS, 'Non-unit', N, N, ONE, 258: $ B, LDB, A, LDA ) 259: * 260: ELSE IF( ITYPE.EQ.3 ) THEN 261: * 262: * For B*A*x=(lambda)*x; 263: * backtransform eigenvectors: x = L*y or U'*y 264: * 265: IF( UPPER ) THEN 266: TRANS = 'T' 267: ELSE 268: TRANS = 'N' 269: END IF 270: * 271: CALL DTRMM( 'Left', UPLO, TRANS, 'Non-unit', N, N, ONE, 272: $ B, LDB, A, LDA ) 273: END IF 274: END IF 275: * 276: WORK( 1 ) = LOPT 277: IWORK( 1 ) = LIOPT 278: * 279: RETURN 280: * 281: * End of DSYGVD 282: * 283: END