|
1
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 |
SUBROUTINE CHBGVD( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W,
$ Z, LDZ, WORK, LWORK, RWORK, LRWORK, IWORK, $ LIWORK, INFO ) * * -- LAPACK driver routine (version 3.3.1) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * -- April 2011 -- * @generated c * * .. Scalar Arguments .. CHARACTER JOBZ, UPLO INTEGER INFO, KA, KB, LDAB, LDBB, LDZ, LIWORK, LRWORK, $ LWORK, N * .. * .. Array Arguments .. INTEGER IWORK( * ) REAL RWORK( * ), W( * ) COMPLEX AB( LDAB, * ), BB( LDBB, * ), WORK( * ), $ Z( LDZ, * ) * .. * * Purpose * ======= * * CHBGVD computes all the eigenvalues, and optionally, the eigenvectors * of a complex generalized Hermitian-definite banded eigenproblem, of * the form A*x=(lambda)*B*x. Here A and B are assumed to be Hermitian * and banded, and B is also positive definite. If eigenvectors are * desired, it uses a divide and conquer algorithm. * * The divide and conquer algorithm makes very mild assumptions about * floating point arithmetic. It will work on machines with a guard * digit in add/subtract, or on those binary machines without guard * digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or * Cray-2. It could conceivably fail on hexadecimal or decimal machines * without guard digits, but we know of none. * * Arguments * ========= * * JOBZ (input) CHARACTER*1 * = 'N': Compute eigenvalues only; * = 'V': Compute eigenvalues and eigenvectors. * * UPLO (input) CHARACTER*1 * = 'U': Upper triangles of A and B are stored; * = 'L': Lower triangles of A and B are stored. * * N (input) INTEGER * The order of the matrices A and B. N >= 0. * * KA (input) INTEGER * The number of superdiagonals of the matrix A if UPLO = 'U', * or the number of subdiagonals if UPLO = 'L'. KA >= 0. * * KB (input) INTEGER * The number of superdiagonals of the matrix B if UPLO = 'U', * or the number of subdiagonals if UPLO = 'L'. KB >= 0. * * AB (input/output) COMPLEX array, dimension (LDAB, N) * On entry, the upper or lower triangle of the Hermitian band * matrix A, stored in the first ka+1 rows of the array. The * j-th column of A is stored in the j-th column of the array AB * as follows: * if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j; * if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka). * * On exit, the contents of AB are destroyed. * * LDAB (input) INTEGER * The leading dimension of the array AB. LDAB >= KA+1. * * BB (input/output) COMPLEX array, dimension (LDBB, N) * On entry, the upper or lower triangle of the Hermitian band * matrix B, stored in the first kb+1 rows of the array. The * j-th column of B is stored in the j-th column of the array BB * as follows: * if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j; * if UPLO = 'L', BB(1+i-j,j) = B(i,j) for j<=i<=min(n,j+kb). * * On exit, the factor S from the split Cholesky factorization * B = S**H*S, as returned by CPBSTF. * * LDBB (input) INTEGER * The leading dimension of the array BB. LDBB >= KB+1. * * W (output) REAL array, dimension (N) * If INFO = 0, the eigenvalues in ascending order. * * Z (output) COMPLEX array, dimension (LDZ, N) * If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of * eigenvectors, with the i-th column of Z holding the * eigenvector associated with W(i). The eigenvectors are * normalized so that Z**H*B*Z = I. * If JOBZ = 'N', then Z is not referenced. * * LDZ (input) INTEGER * The leading dimension of the array Z. LDZ >= 1, and if * JOBZ = 'V', LDZ >= N. * * WORK (workspace/output) COMPLEX array, dimension (MAX(1,LWORK)) * On exit, if INFO=0, WORK(1) returns the optimal LWORK. * * LWORK (input) INTEGER * The dimension of the array WORK. * If N <= 1, LWORK >= 1. * If JOBZ = 'N' and N > 1, LWORK >= N. * If JOBZ = 'V' and N > 1, LWORK >= 2*N**2. * * If LWORK = -1, then a workspace query is assumed; the routine * only calculates the optimal sizes of the WORK, RWORK and * IWORK arrays, returns these values as the first entries of * the WORK, RWORK and IWORK arrays, and no error message * related to LWORK or LRWORK or LIWORK is issued by XERBLA. * * RWORK (workspace/output) REAL array, dimension (MAX(1,LRWORK)) * On exit, if INFO=0, RWORK(1) returns the optimal LRWORK. * * LRWORK (input) INTEGER * The dimension of array RWORK. * If N <= 1, LRWORK >= 1. * If JOBZ = 'N' and N > 1, LRWORK >= N. * If JOBZ = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2. * * If LRWORK = -1, then a workspace query is assumed; the * routine only calculates the optimal sizes of the WORK, RWORK * and IWORK arrays, returns these values as the first entries * of the WORK, RWORK and IWORK arrays, and no error message * related to LWORK or LRWORK or LIWORK is issued by XERBLA. * * IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK)) * On exit, if INFO=0, IWORK(1) returns the optimal LIWORK. * * LIWORK (input) INTEGER * The dimension of array IWORK. * If JOBZ = 'N' or N <= 1, LIWORK >= 1. * If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N. * * If LIWORK = -1, then a workspace query is assumed; the * routine only calculates the optimal sizes of the WORK, RWORK * and IWORK arrays, returns these values as the first entries * of the WORK, RWORK and IWORK arrays, and no error message * related to LWORK or LRWORK or LIWORK is issued by XERBLA. * * INFO (output) INTEGER * = 0: successful exit * < 0: if INFO = -i, the i-th argument had an illegal value * > 0: if INFO = i, and i is: * <= N: the algorithm failed to converge: * i off-diagonal elements of an intermediate * tridiagonal form did not converge to zero; * > N: if INFO = N + i, for 1 <= i <= N, then CPBSTF * returned INFO = i: B is not positive definite. * The factorization of B could not be completed and * no eigenvalues or eigenvectors were computed. * * Further Details * =============== * * Based on contributions by * Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA * * ===================================================================== * * .. Parameters .. COMPLEX CONE, CZERO PARAMETER ( CONE = ( 1.0E+0, 0.0E+0 ), $ CZERO = ( 0.0E+0, 0.0E+0 ) ) * .. * .. Local Scalars .. LOGICAL LQUERY, UPPER, WANTZ CHARACTER VECT INTEGER IINFO, INDE, INDWK2, INDWRK, LIWMIN, LLRWK, $ LLWK2, LRWMIN, LWMIN * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL SSTERF, XERBLA, CGEMM, CHBGST, CHBTRD, CLACPY, $ CPBSTF, CSTEDC * .. * .. Executable Statements .. * * Test the input parameters. * WANTZ = LSAME( JOBZ, 'V' ) UPPER = LSAME( UPLO, 'U' ) LQUERY = ( LWORK.EQ.-1 .OR. LRWORK.EQ.-1 .OR. LIWORK.EQ.-1 ) * INFO = 0 IF( N.LE.1 ) THEN LWMIN = 1+N LRWMIN = 1+N LIWMIN = 1 ELSE IF( WANTZ ) THEN LWMIN = 2*N**2 LRWMIN = 1 + 5*N + 2*N**2 LIWMIN = 3 + 5*N ELSE LWMIN = N LRWMIN = N LIWMIN = 1 END IF IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN INFO = -1 ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN INFO = -2 ELSE IF( N.LT.0 ) THEN INFO = -3 ELSE IF( KA.LT.0 ) THEN INFO = -4 ELSE IF( KB.LT.0 .OR. KB.GT.KA ) THEN INFO = -5 ELSE IF( LDAB.LT.KA+1 ) THEN INFO = -7 ELSE IF( LDBB.LT.KB+1 ) THEN INFO = -9 ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN INFO = -12 END IF * IF( INFO.EQ.0 ) THEN WORK( 1 ) = LWMIN RWORK( 1 ) = LRWMIN IWORK( 1 ) = LIWMIN * IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN INFO = -14 ELSE IF( LRWORK.LT.LRWMIN .AND. .NOT.LQUERY ) THEN INFO = -16 ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN INFO = -18 END IF END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'CHBGVD', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) $ RETURN * * Form a split Cholesky factorization of B. * CALL CPBSTF( UPLO, N, KB, BB, LDBB, INFO ) IF( INFO.NE.0 ) THEN INFO = N + INFO RETURN END IF * * Transform problem to standard eigenvalue problem. * INDE = 1 INDWRK = INDE + N INDWK2 = 1 + N*N LLWK2 = LWORK - INDWK2 + 2 LLRWK = LRWORK - INDWRK + 2 CALL CHBGST( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, Z, LDZ, $ WORK, RWORK( INDWRK ), IINFO ) * * Reduce Hermitian band matrix to tridiagonal form. * IF( WANTZ ) THEN VECT = 'U' ELSE VECT = 'N' END IF CALL CHBTRD( VECT, UPLO, N, KA, AB, LDAB, W, RWORK( INDE ), Z, $ LDZ, WORK, IINFO ) * * For eigenvalues only, call SSTERF. For eigenvectors, call CSTEDC. * IF( .NOT.WANTZ ) THEN CALL SSTERF( N, W, RWORK( INDE ), INFO ) ELSE CALL CSTEDC( 'I', N, W, RWORK( INDE ), WORK, N, WORK( INDWK2 ), $ LLWK2, RWORK( INDWRK ), LLRWK, IWORK, LIWORK, $ INFO ) CALL CGEMM( 'N', 'N', N, N, N, CONE, Z, LDZ, WORK, N, CZERO, $ WORK( INDWK2 ), N ) CALL CLACPY( 'A', N, N, WORK( INDWK2 ), N, Z, LDZ ) END IF * WORK( 1 ) = LWMIN RWORK( 1 ) = LRWMIN IWORK( 1 ) = LIWMIN RETURN * * End of CHBGVD * END |