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Mise à jour de lapack vers la version 3.3.0.
1: SUBROUTINE ZHPGVD( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, 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, LDZ, LIWORK, LRWORK, LWORK, N 12: * .. 13: * .. Array Arguments .. 14: INTEGER IWORK( * ) 15: DOUBLE PRECISION RWORK( * ), W( * ) 16: COMPLEX*16 AP( * ), BP( * ), WORK( * ), Z( LDZ, * ) 17: * .. 18: * 19: * Purpose 20: * ======= 21: * 22: * ZHPGVD 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, stored in packed format, and B is also 26: * positive definite. 27: * If eigenvectors are desired, it uses a divide and conquer algorithm. 28: * 29: * The divide and conquer algorithm makes very mild assumptions about 30: * floating point arithmetic. It will work on machines with a guard 31: * digit in add/subtract, or on those binary machines without guard 32: * digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or 33: * Cray-2. It could conceivably fail on hexadecimal or decimal machines 34: * without guard digits, but we know of none. 35: * 36: * Arguments 37: * ========= 38: * 39: * ITYPE (input) INTEGER 40: * Specifies the problem type to be solved: 41: * = 1: A*x = (lambda)*B*x 42: * = 2: A*B*x = (lambda)*x 43: * = 3: B*A*x = (lambda)*x 44: * 45: * JOBZ (input) CHARACTER*1 46: * = 'N': Compute eigenvalues only; 47: * = 'V': Compute eigenvalues and eigenvectors. 48: * 49: * UPLO (input) CHARACTER*1 50: * = 'U': Upper triangles of A and B are stored; 51: * = 'L': Lower triangles of A and B are stored. 52: * 53: * N (input) INTEGER 54: * The order of the matrices A and B. N >= 0. 55: * 56: * AP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2) 57: * On entry, the upper or lower triangle of the Hermitian matrix 58: * A, packed columnwise in a linear array. The j-th column of A 59: * is stored in the array AP as follows: 60: * if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; 61: * if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. 62: * 63: * On exit, the contents of AP are destroyed. 64: * 65: * BP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2) 66: * On entry, the upper or lower triangle of the Hermitian matrix 67: * B, packed columnwise in a linear array. The j-th column of B 68: * is stored in the array BP as follows: 69: * if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j; 70: * if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n. 71: * 72: * On exit, the triangular factor U or L from the Cholesky 73: * factorization B = U**H*U or B = L*L**H, in the same storage 74: * format as B. 75: * 76: * W (output) DOUBLE PRECISION array, dimension (N) 77: * If INFO = 0, the eigenvalues in ascending order. 78: * 79: * Z (output) COMPLEX*16 array, dimension (LDZ, N) 80: * If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of 81: * eigenvectors. The eigenvectors are normalized as follows: 82: * if ITYPE = 1 or 2, Z**H*B*Z = I; 83: * if ITYPE = 3, Z**H*inv(B)*Z = I. 84: * If JOBZ = 'N', then Z is not referenced. 85: * 86: * LDZ (input) INTEGER 87: * The leading dimension of the array Z. LDZ >= 1, and if 88: * JOBZ = 'V', LDZ >= max(1,N). 89: * 90: * WORK (workspace) COMPLEX*16 array, dimension (MAX(1,LWORK)) 91: * On exit, if INFO = 0, WORK(1) returns the required LWORK. 92: * 93: * LWORK (input) INTEGER 94: * The dimension of array WORK. 95: * If N <= 1, LWORK >= 1. 96: * If JOBZ = 'N' and N > 1, LWORK >= N. 97: * If JOBZ = 'V' and N > 1, LWORK >= 2*N. 98: * 99: * If LWORK = -1, then a workspace query is assumed; the routine 100: * only calculates the required sizes of the WORK, RWORK and 101: * IWORK arrays, returns these values as the first entries of 102: * the WORK, RWORK and IWORK arrays, and no error message 103: * related to LWORK or LRWORK or LIWORK is issued by XERBLA. 104: * 105: * RWORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LRWORK)) 106: * On exit, if INFO = 0, RWORK(1) returns the required LRWORK. 107: * 108: * LRWORK (input) INTEGER 109: * The dimension of array RWORK. 110: * If N <= 1, LRWORK >= 1. 111: * If JOBZ = 'N' and N > 1, LRWORK >= N. 112: * If JOBZ = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2. 113: * 114: * If LRWORK = -1, then a workspace query is assumed; the 115: * routine only calculates the required sizes of the WORK, RWORK 116: * and IWORK arrays, returns these values as the first entries 117: * of the WORK, RWORK and IWORK arrays, and no error message 118: * related to LWORK or LRWORK or LIWORK is issued by XERBLA. 119: * 120: * IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK)) 121: * On exit, if INFO = 0, IWORK(1) returns the required LIWORK. 122: * 123: * LIWORK (input) INTEGER 124: * The dimension of array IWORK. 125: * If JOBZ = 'N' or N <= 1, LIWORK >= 1. 126: * If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N. 127: * 128: * If LIWORK = -1, then a workspace query is assumed; the 129: * routine only calculates the required sizes of the WORK, RWORK 130: * and IWORK arrays, returns these values as the first entries 131: * of the WORK, RWORK and IWORK arrays, and no error message 132: * related to LWORK or LRWORK or LIWORK is issued by XERBLA. 133: * 134: * INFO (output) INTEGER 135: * = 0: successful exit 136: * < 0: if INFO = -i, the i-th argument had an illegal value 137: * > 0: ZPPTRF or ZHPEVD returned an error code: 138: * <= N: if INFO = i, ZHPEVD failed to converge; 139: * i off-diagonal elements of an intermediate 140: * tridiagonal form did not convergeto zero; 141: * > N: if INFO = N + i, for 1 <= i <= n, then the leading 142: * minor of order i of B is not positive definite. 143: * The factorization of B could not be completed and 144: * no eigenvalues or eigenvectors were computed. 145: * 146: * Further Details 147: * =============== 148: * 149: * Based on contributions by 150: * Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA 151: * 152: * ===================================================================== 153: * 154: * .. Local Scalars .. 155: LOGICAL LQUERY, UPPER, WANTZ 156: CHARACTER TRANS 157: INTEGER J, LIWMIN, LRWMIN, LWMIN, NEIG 158: * .. 159: * .. External Functions .. 160: LOGICAL LSAME 161: EXTERNAL LSAME 162: * .. 163: * .. External Subroutines .. 164: EXTERNAL XERBLA, ZHPEVD, ZHPGST, ZPPTRF, ZTPMV, ZTPSV 165: * .. 166: * .. Intrinsic Functions .. 167: INTRINSIC DBLE, MAX 168: * .. 169: * .. Executable Statements .. 170: * 171: * Test the input parameters. 172: * 173: WANTZ = LSAME( JOBZ, 'V' ) 174: UPPER = LSAME( UPLO, 'U' ) 175: LQUERY = ( LWORK.EQ.-1 .OR. LRWORK.EQ.-1 .OR. LIWORK.EQ.-1 ) 176: * 177: INFO = 0 178: IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN 179: INFO = -1 180: ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN 181: INFO = -2 182: ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN 183: INFO = -3 184: ELSE IF( N.LT.0 ) THEN 185: INFO = -4 186: ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN 187: INFO = -9 188: END IF 189: * 190: IF( INFO.EQ.0 ) THEN 191: IF( N.LE.1 ) THEN 192: LWMIN = 1 193: LIWMIN = 1 194: LRWMIN = 1 195: ELSE 196: IF( WANTZ ) THEN 197: LWMIN = 2*N 198: LRWMIN = 1 + 5*N + 2*N**2 199: LIWMIN = 3 + 5*N 200: ELSE 201: LWMIN = N 202: LRWMIN = N 203: LIWMIN = 1 204: END IF 205: END IF 206: * 207: WORK( 1 ) = LWMIN 208: RWORK( 1 ) = LRWMIN 209: IWORK( 1 ) = LIWMIN 210: IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN 211: INFO = -11 212: ELSE IF( LRWORK.LT.LRWMIN .AND. .NOT.LQUERY ) THEN 213: INFO = -13 214: ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN 215: INFO = -15 216: END IF 217: END IF 218: * 219: IF( INFO.NE.0 ) THEN 220: CALL XERBLA( 'ZHPGVD', -INFO ) 221: RETURN 222: ELSE IF( LQUERY ) THEN 223: RETURN 224: END IF 225: * 226: * Quick return if possible 227: * 228: IF( N.EQ.0 ) 229: $ RETURN 230: * 231: * Form a Cholesky factorization of B. 232: * 233: CALL ZPPTRF( UPLO, N, BP, INFO ) 234: IF( INFO.NE.0 ) THEN 235: INFO = N + INFO 236: RETURN 237: END IF 238: * 239: * Transform problem to standard eigenvalue problem and solve. 240: * 241: CALL ZHPGST( ITYPE, UPLO, N, AP, BP, INFO ) 242: CALL ZHPEVD( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK, RWORK, 243: $ LRWORK, IWORK, LIWORK, INFO ) 244: LWMIN = MAX( DBLE( LWMIN ), DBLE( WORK( 1 ) ) ) 245: LRWMIN = MAX( DBLE( LRWMIN ), DBLE( RWORK( 1 ) ) ) 246: LIWMIN = MAX( DBLE( LIWMIN ), DBLE( IWORK( 1 ) ) ) 247: * 248: IF( WANTZ ) THEN 249: * 250: * Backtransform eigenvectors to the original problem. 251: * 252: NEIG = N 253: IF( INFO.GT.0 ) 254: $ NEIG = INFO - 1 255: IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN 256: * 257: * For A*x=(lambda)*B*x and A*B*x=(lambda)*x; 258: * backtransform eigenvectors: x = inv(L)'*y or inv(U)*y 259: * 260: IF( UPPER ) THEN 261: TRANS = 'N' 262: ELSE 263: TRANS = 'C' 264: END IF 265: * 266: DO 10 J = 1, NEIG 267: CALL ZTPSV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ), 268: $ 1 ) 269: 10 CONTINUE 270: * 271: ELSE IF( ITYPE.EQ.3 ) THEN 272: * 273: * For B*A*x=(lambda)*x; 274: * backtransform eigenvectors: x = L*y or U'*y 275: * 276: IF( UPPER ) THEN 277: TRANS = 'C' 278: ELSE 279: TRANS = 'N' 280: END IF 281: * 282: DO 20 J = 1, NEIG 283: CALL ZTPMV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ), 284: $ 1 ) 285: 20 CONTINUE 286: END IF 287: END IF 288: * 289: WORK( 1 ) = LWMIN 290: RWORK( 1 ) = LRWMIN 291: IWORK( 1 ) = LIWMIN 292: RETURN 293: * 294: * End of ZHPGVD 295: * 296: END