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Mise à jour de lapack vers la version 3.3.0.
1: SUBROUTINE ZHBGVD( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, 2: $ Z, LDZ, WORK, LWORK, RWORK, LRWORK, IWORK, 3: $ LIWORK, INFO ) 4: * 5: * -- LAPACK driver routine (version 3.2) -- 6: * -- LAPACK is a software package provided by Univ. of Tennessee, -- 7: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 8: * November 2006 9: * 10: * .. Scalar Arguments .. 11: CHARACTER JOBZ, UPLO 12: INTEGER INFO, KA, KB, LDAB, LDBB, LDZ, LIWORK, LRWORK, 13: $ LWORK, N 14: * .. 15: * .. Array Arguments .. 16: INTEGER IWORK( * ) 17: DOUBLE PRECISION RWORK( * ), W( * ) 18: COMPLEX*16 AB( LDAB, * ), BB( LDBB, * ), WORK( * ), 19: $ Z( LDZ, * ) 20: * .. 21: * 22: * Purpose 23: * ======= 24: * 25: * ZHBGVD computes all the eigenvalues, and optionally, the eigenvectors 26: * of a complex generalized Hermitian-definite banded eigenproblem, of 27: * the form A*x=(lambda)*B*x. Here A and B are assumed to be Hermitian 28: * and banded, and B is also positive definite. If eigenvectors are 29: * desired, it uses a divide and conquer algorithm. 30: * 31: * The divide and conquer algorithm makes very mild assumptions about 32: * floating point arithmetic. It will work on machines with a guard 33: * digit in add/subtract, or on those binary machines without guard 34: * digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or 35: * Cray-2. It could conceivably fail on hexadecimal or decimal machines 36: * without guard digits, but we know of none. 37: * 38: * Arguments 39: * ========= 40: * 41: * JOBZ (input) CHARACTER*1 42: * = 'N': Compute eigenvalues only; 43: * = 'V': Compute eigenvalues and eigenvectors. 44: * 45: * UPLO (input) CHARACTER*1 46: * = 'U': Upper triangles of A and B are stored; 47: * = 'L': Lower triangles of A and B are stored. 48: * 49: * N (input) INTEGER 50: * The order of the matrices A and B. N >= 0. 51: * 52: * KA (input) INTEGER 53: * The number of superdiagonals of the matrix A if UPLO = 'U', 54: * or the number of subdiagonals if UPLO = 'L'. KA >= 0. 55: * 56: * KB (input) INTEGER 57: * The number of superdiagonals of the matrix B if UPLO = 'U', 58: * or the number of subdiagonals if UPLO = 'L'. KB >= 0. 59: * 60: * AB (input/output) COMPLEX*16 array, dimension (LDAB, N) 61: * On entry, the upper or lower triangle of the Hermitian band 62: * matrix A, stored in the first ka+1 rows of the array. The 63: * j-th column of A is stored in the j-th column of the array AB 64: * as follows: 65: * if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j; 66: * if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka). 67: * 68: * On exit, the contents of AB are destroyed. 69: * 70: * LDAB (input) INTEGER 71: * The leading dimension of the array AB. LDAB >= KA+1. 72: * 73: * BB (input/output) COMPLEX*16 array, dimension (LDBB, N) 74: * On entry, the upper or lower triangle of the Hermitian band 75: * matrix B, stored in the first kb+1 rows of the array. The 76: * j-th column of B is stored in the j-th column of the array BB 77: * as follows: 78: * if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j; 79: * if UPLO = 'L', BB(1+i-j,j) = B(i,j) for j<=i<=min(n,j+kb). 80: * 81: * On exit, the factor S from the split Cholesky factorization 82: * B = S**H*S, as returned by ZPBSTF. 83: * 84: * LDBB (input) INTEGER 85: * The leading dimension of the array BB. LDBB >= KB+1. 86: * 87: * W (output) DOUBLE PRECISION array, dimension (N) 88: * If INFO = 0, the eigenvalues in ascending order. 89: * 90: * Z (output) COMPLEX*16 array, dimension (LDZ, N) 91: * If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of 92: * eigenvectors, with the i-th column of Z holding the 93: * eigenvector associated with W(i). The eigenvectors are 94: * normalized so that Z**H*B*Z = I. 95: * If JOBZ = 'N', then Z is not referenced. 96: * 97: * LDZ (input) INTEGER 98: * The leading dimension of the array Z. LDZ >= 1, and if 99: * JOBZ = 'V', LDZ >= N. 100: * 101: * WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK)) 102: * On exit, if INFO=0, WORK(1) returns the optimal LWORK. 103: * 104: * LWORK (input) INTEGER 105: * The dimension of the array WORK. 106: * If N <= 1, LWORK >= 1. 107: * If JOBZ = 'N' and N > 1, LWORK >= N. 108: * If JOBZ = 'V' and N > 1, LWORK >= 2*N**2. 109: * 110: * If LWORK = -1, then a workspace query is assumed; the routine 111: * only calculates the optimal sizes of the WORK, RWORK and 112: * IWORK arrays, returns these values as the first entries of 113: * the WORK, RWORK and IWORK arrays, and no error message 114: * related to LWORK or LRWORK or LIWORK is issued by XERBLA. 115: * 116: * RWORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LRWORK)) 117: * On exit, if INFO=0, RWORK(1) returns the optimal LRWORK. 118: * 119: * LRWORK (input) INTEGER 120: * The dimension of array RWORK. 121: * If N <= 1, LRWORK >= 1. 122: * If JOBZ = 'N' and N > 1, LRWORK >= N. 123: * If JOBZ = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2. 124: * 125: * If LRWORK = -1, then a workspace query is assumed; the 126: * routine only calculates the optimal sizes of the WORK, RWORK 127: * and IWORK arrays, returns these values as the first entries 128: * of the WORK, RWORK and IWORK arrays, and no error message 129: * related to LWORK or LRWORK or LIWORK is issued by XERBLA. 130: * 131: * IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK)) 132: * On exit, if INFO=0, IWORK(1) returns the optimal LIWORK. 133: * 134: * LIWORK (input) INTEGER 135: * The dimension of array IWORK. 136: * If JOBZ = 'N' or N <= 1, LIWORK >= 1. 137: * If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N. 138: * 139: * If LIWORK = -1, then a workspace query is assumed; the 140: * routine only calculates the optimal sizes of the WORK, RWORK 141: * and IWORK arrays, returns these values as the first entries 142: * of the WORK, RWORK and IWORK arrays, and no error message 143: * related to LWORK or LRWORK or LIWORK is issued by XERBLA. 144: * 145: * INFO (output) INTEGER 146: * = 0: successful exit 147: * < 0: if INFO = -i, the i-th argument had an illegal value 148: * > 0: if INFO = i, and i is: 149: * <= N: the algorithm failed to converge: 150: * i off-diagonal elements of an intermediate 151: * tridiagonal form did not converge to zero; 152: * > N: if INFO = N + i, for 1 <= i <= N, then ZPBSTF 153: * returned INFO = i: B is not positive definite. 154: * The factorization of B could not be completed and 155: * no eigenvalues or eigenvectors were computed. 156: * 157: * Further Details 158: * =============== 159: * 160: * Based on contributions by 161: * Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA 162: * 163: * ===================================================================== 164: * 165: * .. Parameters .. 166: COMPLEX*16 CONE, CZERO 167: PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ), 168: $ CZERO = ( 0.0D+0, 0.0D+0 ) ) 169: * .. 170: * .. Local Scalars .. 171: LOGICAL LQUERY, UPPER, WANTZ 172: CHARACTER VECT 173: INTEGER IINFO, INDE, INDWK2, INDWRK, LIWMIN, LLRWK, 174: $ LLWK2, LRWMIN, LWMIN 175: * .. 176: * .. External Functions .. 177: LOGICAL LSAME 178: EXTERNAL LSAME 179: * .. 180: * .. External Subroutines .. 181: EXTERNAL DSTERF, XERBLA, ZGEMM, ZHBGST, ZHBTRD, ZLACPY, 182: $ ZPBSTF, ZSTEDC 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**2 199: LRWMIN = 1 + 5*N + 2*N**2 200: LIWMIN = 3 + 5*N 201: ELSE 202: LWMIN = N 203: LRWMIN = N 204: LIWMIN = 1 205: END IF 206: IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN 207: INFO = -1 208: ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN 209: INFO = -2 210: ELSE IF( N.LT.0 ) THEN 211: INFO = -3 212: ELSE IF( KA.LT.0 ) THEN 213: INFO = -4 214: ELSE IF( KB.LT.0 .OR. KB.GT.KA ) THEN 215: INFO = -5 216: ELSE IF( LDAB.LT.KA+1 ) THEN 217: INFO = -7 218: ELSE IF( LDBB.LT.KB+1 ) THEN 219: INFO = -9 220: ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN 221: INFO = -12 222: END IF 223: * 224: IF( INFO.EQ.0 ) THEN 225: WORK( 1 ) = LWMIN 226: RWORK( 1 ) = LRWMIN 227: IWORK( 1 ) = LIWMIN 228: * 229: IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN 230: INFO = -14 231: ELSE IF( LRWORK.LT.LRWMIN .AND. .NOT.LQUERY ) THEN 232: INFO = -16 233: ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN 234: INFO = -18 235: END IF 236: END IF 237: * 238: IF( INFO.NE.0 ) THEN 239: CALL XERBLA( 'ZHBGVD', -INFO ) 240: RETURN 241: ELSE IF( LQUERY ) THEN 242: RETURN 243: END IF 244: * 245: * Quick return if possible 246: * 247: IF( N.EQ.0 ) 248: $ RETURN 249: * 250: * Form a split Cholesky factorization of B. 251: * 252: CALL ZPBSTF( UPLO, N, KB, BB, LDBB, INFO ) 253: IF( INFO.NE.0 ) THEN 254: INFO = N + INFO 255: RETURN 256: END IF 257: * 258: * Transform problem to standard eigenvalue problem. 259: * 260: INDE = 1 261: INDWRK = INDE + N 262: INDWK2 = 1 + N*N 263: LLWK2 = LWORK - INDWK2 + 2 264: LLRWK = LRWORK - INDWRK + 2 265: CALL ZHBGST( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, Z, LDZ, 266: $ WORK, RWORK( INDWRK ), IINFO ) 267: * 268: * Reduce Hermitian band matrix to tridiagonal form. 269: * 270: IF( WANTZ ) THEN 271: VECT = 'U' 272: ELSE 273: VECT = 'N' 274: END IF 275: CALL ZHBTRD( VECT, UPLO, N, KA, AB, LDAB, W, RWORK( INDE ), Z, 276: $ LDZ, WORK, IINFO ) 277: * 278: * For eigenvalues only, call DSTERF. For eigenvectors, call ZSTEDC. 279: * 280: IF( .NOT.WANTZ ) THEN 281: CALL DSTERF( N, W, RWORK( INDE ), INFO ) 282: ELSE 283: CALL ZSTEDC( 'I', N, W, RWORK( INDE ), WORK, N, WORK( INDWK2 ), 284: $ LLWK2, RWORK( INDWRK ), LLRWK, IWORK, LIWORK, 285: $ INFO ) 286: CALL ZGEMM( 'N', 'N', N, N, N, CONE, Z, LDZ, WORK, N, CZERO, 287: $ WORK( INDWK2 ), N ) 288: CALL ZLACPY( 'A', N, N, WORK( INDWK2 ), N, Z, LDZ ) 289: END IF 290: * 291: WORK( 1 ) = LWMIN 292: RWORK( 1 ) = LRWMIN 293: IWORK( 1 ) = LIWMIN 294: RETURN 295: * 296: * End of ZHBGVD 297: * 298: END