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Mise à jour de lapack vers la version 3.3.0.
1: SUBROUTINE ZHEGVD( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK, 2: $ LWORK, RWORK, LRWORK, 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, LRWORK, LWORK, N 12: * .. 13: * .. Array Arguments .. 14: INTEGER IWORK( * ) 15: DOUBLE PRECISION RWORK( * ), W( * ) 16: COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * ) 17: * .. 18: * 19: * Purpose 20: * ======= 21: * 22: * ZHEGVD computes all the eigenvalues, and optionally, the eigenvectors 23: * of a complex generalized Hermitian-definite eigenproblem, of the form 24: * A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and 25: * B are assumed to be Hermitian and B is also positive definite. 26: * If eigenvectors are desired, it uses a divide and conquer algorithm. 27: * 28: * The divide and conquer algorithm makes very mild assumptions about 29: * floating point arithmetic. It will work on machines with a guard 30: * digit in add/subtract, or on those binary machines without guard 31: * digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or 32: * Cray-2. It could conceivably fail on hexadecimal or decimal machines 33: * without guard digits, but we know of none. 34: * 35: * Arguments 36: * ========= 37: * 38: * ITYPE (input) INTEGER 39: * Specifies the problem type to be solved: 40: * = 1: A*x = (lambda)*B*x 41: * = 2: A*B*x = (lambda)*x 42: * = 3: B*A*x = (lambda)*x 43: * 44: * JOBZ (input) CHARACTER*1 45: * = 'N': Compute eigenvalues only; 46: * = 'V': Compute eigenvalues and eigenvectors. 47: * 48: * UPLO (input) CHARACTER*1 49: * = 'U': Upper triangles of A and B are stored; 50: * = 'L': Lower triangles of A and B are stored. 51: * 52: * N (input) INTEGER 53: * The order of the matrices A and B. N >= 0. 54: * 55: * A (input/output) COMPLEX*16 array, dimension (LDA, N) 56: * On entry, the Hermitian matrix A. If UPLO = 'U', the 57: * leading N-by-N upper triangular part of A contains the 58: * upper triangular part of the matrix A. If UPLO = 'L', 59: * the leading N-by-N lower triangular part of A contains 60: * the lower triangular part of the matrix A. 61: * 62: * On exit, if JOBZ = 'V', then if INFO = 0, A contains the 63: * matrix Z of eigenvectors. The eigenvectors are normalized 64: * as follows: 65: * if ITYPE = 1 or 2, Z**H*B*Z = I; 66: * if ITYPE = 3, Z**H*inv(B)*Z = I. 67: * If JOBZ = 'N', then on exit the upper triangle (if UPLO='U') 68: * or the lower triangle (if UPLO='L') of A, including the 69: * diagonal, is destroyed. 70: * 71: * LDA (input) INTEGER 72: * The leading dimension of the array A. LDA >= max(1,N). 73: * 74: * B (input/output) COMPLEX*16 array, dimension (LDB, N) 75: * On entry, the Hermitian matrix B. If UPLO = 'U', the 76: * leading N-by-N upper triangular part of B contains the 77: * upper triangular part of the matrix B. If UPLO = 'L', 78: * the leading N-by-N lower triangular part of B contains 79: * the lower triangular part of the matrix B. 80: * 81: * On exit, if INFO <= N, the part of B containing the matrix is 82: * overwritten by the triangular factor U or L from the Cholesky 83: * factorization B = U**H*U or B = L*L**H. 84: * 85: * LDB (input) INTEGER 86: * The leading dimension of the array B. LDB >= max(1,N). 87: * 88: * W (output) DOUBLE PRECISION array, dimension (N) 89: * If INFO = 0, the eigenvalues in ascending order. 90: * 91: * WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK)) 92: * On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 93: * 94: * LWORK (input) INTEGER 95: * The length of the array WORK. 96: * If N <= 1, LWORK >= 1. 97: * If JOBZ = 'N' and N > 1, LWORK >= N + 1. 98: * If JOBZ = 'V' and N > 1, LWORK >= 2*N + N**2. 99: * 100: * If LWORK = -1, then a workspace query is assumed; the routine 101: * only calculates the optimal sizes of the WORK, RWORK and 102: * IWORK arrays, returns these values as the first entries of 103: * the WORK, RWORK and IWORK arrays, and no error message 104: * related to LWORK or LRWORK or LIWORK is issued by XERBLA. 105: * 106: * RWORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LRWORK)) 107: * On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK. 108: * 109: * LRWORK (input) INTEGER 110: * The dimension of the array RWORK. 111: * If N <= 1, LRWORK >= 1. 112: * If JOBZ = 'N' and N > 1, LRWORK >= N. 113: * If JOBZ = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2. 114: * 115: * If LRWORK = -1, then a workspace query is assumed; the 116: * routine only calculates the optimal sizes of the WORK, RWORK 117: * and IWORK arrays, returns these values as the first entries 118: * of the WORK, RWORK and IWORK arrays, and no error message 119: * related to LWORK or LRWORK or LIWORK is issued by XERBLA. 120: * 121: * IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK)) 122: * On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. 123: * 124: * LIWORK (input) INTEGER 125: * The dimension of the array IWORK. 126: * If N <= 1, LIWORK >= 1. 127: * If JOBZ = 'N' and N > 1, LIWORK >= 1. 128: * If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N. 129: * 130: * If LIWORK = -1, then a workspace query is assumed; the 131: * routine only calculates the optimal sizes of the WORK, RWORK 132: * and IWORK arrays, returns these values as the first entries 133: * of the WORK, RWORK and IWORK arrays, and no error message 134: * related to LWORK or LRWORK or LIWORK is issued by XERBLA. 135: * 136: * INFO (output) INTEGER 137: * = 0: successful exit 138: * < 0: if INFO = -i, the i-th argument had an illegal value 139: * > 0: ZPOTRF or ZHEEVD returned an error code: 140: * <= N: if INFO = i and JOBZ = 'N', then the algorithm 141: * failed to converge; i off-diagonal elements of an 142: * intermediate tridiagonal form did not converge to 143: * zero; 144: * if INFO = i and JOBZ = 'V', then the algorithm 145: * failed to compute an eigenvalue while working on 146: * the submatrix lying in rows and columns INFO/(N+1) 147: * through mod(INFO,N+1); 148: * > N: if INFO = N + i, for 1 <= i <= N, then the leading 149: * minor of order i of B is not positive definite. 150: * The factorization of B could not be completed and 151: * no eigenvalues or eigenvectors were computed. 152: * 153: * Further Details 154: * =============== 155: * 156: * Based on contributions by 157: * Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA 158: * 159: * Modified so that no backsubstitution is performed if ZHEEVD fails to 160: * converge (NEIG in old code could be greater than N causing out of 161: * bounds reference to A - reported by Ralf Meyer). Also corrected the 162: * description of INFO and the test on ITYPE. Sven, 16 Feb 05. 163: * ===================================================================== 164: * 165: * .. Parameters .. 166: COMPLEX*16 CONE 167: PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ) ) 168: * .. 169: * .. Local Scalars .. 170: LOGICAL LQUERY, UPPER, WANTZ 171: CHARACTER TRANS 172: INTEGER LIOPT, LIWMIN, LOPT, LROPT, LRWMIN, LWMIN 173: * .. 174: * .. External Functions .. 175: LOGICAL LSAME 176: EXTERNAL LSAME 177: * .. 178: * .. External Subroutines .. 179: EXTERNAL XERBLA, ZHEEVD, ZHEGST, ZPOTRF, ZTRMM, ZTRSM 180: * .. 181: * .. Intrinsic Functions .. 182: INTRINSIC DBLE, MAX 183: * .. 184: * .. Executable Statements .. 185: * 186: * Test the input parameters. 187: * 188: WANTZ = LSAME( JOBZ, 'V' ) 189: UPPER = LSAME( UPLO, 'U' ) 190: LQUERY = ( LWORK.EQ.-1 .OR. LRWORK.EQ.-1 .OR. LIWORK.EQ.-1 ) 191: * 192: INFO = 0 193: IF( N.LE.1 ) THEN 194: LWMIN = 1 195: LRWMIN = 1 196: LIWMIN = 1 197: ELSE IF( WANTZ ) THEN 198: LWMIN = 2*N + N*N 199: LRWMIN = 1 + 5*N + 2*N*N 200: LIWMIN = 3 + 5*N 201: ELSE 202: LWMIN = N + 1 203: LRWMIN = N 204: LIWMIN = 1 205: END IF 206: LOPT = LWMIN 207: LROPT = LRWMIN 208: LIOPT = LIWMIN 209: IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN 210: INFO = -1 211: ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN 212: INFO = -2 213: ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN 214: INFO = -3 215: ELSE IF( N.LT.0 ) THEN 216: INFO = -4 217: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN 218: INFO = -6 219: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN 220: INFO = -8 221: END IF 222: * 223: IF( INFO.EQ.0 ) THEN 224: WORK( 1 ) = LOPT 225: RWORK( 1 ) = LROPT 226: IWORK( 1 ) = LIOPT 227: * 228: IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN 229: INFO = -11 230: ELSE IF( LRWORK.LT.LRWMIN .AND. .NOT.LQUERY ) THEN 231: INFO = -13 232: ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN 233: INFO = -15 234: END IF 235: END IF 236: * 237: IF( INFO.NE.0 ) THEN 238: CALL XERBLA( 'ZHEGVD', -INFO ) 239: RETURN 240: ELSE IF( LQUERY ) THEN 241: RETURN 242: END IF 243: * 244: * Quick return if possible 245: * 246: IF( N.EQ.0 ) 247: $ RETURN 248: * 249: * Form a Cholesky factorization of B. 250: * 251: CALL ZPOTRF( UPLO, N, B, LDB, INFO ) 252: IF( INFO.NE.0 ) THEN 253: INFO = N + INFO 254: RETURN 255: END IF 256: * 257: * Transform problem to standard eigenvalue problem and solve. 258: * 259: CALL ZHEGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) 260: CALL ZHEEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK, LRWORK, 261: $ IWORK, LIWORK, INFO ) 262: LOPT = MAX( DBLE( LOPT ), DBLE( WORK( 1 ) ) ) 263: LROPT = MAX( DBLE( LROPT ), DBLE( RWORK( 1 ) ) ) 264: LIOPT = MAX( DBLE( LIOPT ), DBLE( IWORK( 1 ) ) ) 265: * 266: IF( WANTZ .AND. INFO.EQ.0 ) THEN 267: * 268: * Backtransform eigenvectors to the original problem. 269: * 270: IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN 271: * 272: * For A*x=(lambda)*B*x and A*B*x=(lambda)*x; 273: * backtransform eigenvectors: x = inv(L)'*y or inv(U)*y 274: * 275: IF( UPPER ) THEN 276: TRANS = 'N' 277: ELSE 278: TRANS = 'C' 279: END IF 280: * 281: CALL ZTRSM( 'Left', UPLO, TRANS, 'Non-unit', N, N, CONE, 282: $ B, LDB, A, LDA ) 283: * 284: ELSE IF( ITYPE.EQ.3 ) THEN 285: * 286: * For B*A*x=(lambda)*x; 287: * backtransform eigenvectors: x = L*y or U'*y 288: * 289: IF( UPPER ) THEN 290: TRANS = 'C' 291: ELSE 292: TRANS = 'N' 293: END IF 294: * 295: CALL ZTRMM( 'Left', UPLO, TRANS, 'Non-unit', N, N, CONE, 296: $ B, LDB, A, LDA ) 297: END IF 298: END IF 299: * 300: WORK( 1 ) = LOPT 301: RWORK( 1 ) = LROPT 302: IWORK( 1 ) = LIOPT 303: * 304: RETURN 305: * 306: * End of ZHEGVD 307: * 308: END