Annotation of rpl/lapack/lapack/zhegvd.f, revision 1.9
1.9 ! bertrand 1: *> \brief \b ZHEGST
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download ZHEGVD + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhegvd.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhegvd.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhegvd.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE ZHEGVD( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK,
! 22: * LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO )
! 23: *
! 24: * .. Scalar Arguments ..
! 25: * CHARACTER JOBZ, UPLO
! 26: * INTEGER INFO, ITYPE, LDA, LDB, LIWORK, LRWORK, LWORK, N
! 27: * ..
! 28: * .. Array Arguments ..
! 29: * INTEGER IWORK( * )
! 30: * DOUBLE PRECISION RWORK( * ), W( * )
! 31: * COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
! 32: * ..
! 33: *
! 34: *
! 35: *> \par Purpose:
! 36: * =============
! 37: *>
! 38: *> \verbatim
! 39: *>
! 40: *> ZHEGVD computes all the eigenvalues, and optionally, the eigenvectors
! 41: *> of a complex generalized Hermitian-definite eigenproblem, of the form
! 42: *> A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and
! 43: *> B are assumed to be Hermitian and B is also positive definite.
! 44: *> If eigenvectors are desired, it uses a divide and conquer algorithm.
! 45: *>
! 46: *> The divide and conquer algorithm makes very mild assumptions about
! 47: *> floating point arithmetic. It will work on machines with a guard
! 48: *> digit in add/subtract, or on those binary machines without guard
! 49: *> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
! 50: *> Cray-2. It could conceivably fail on hexadecimal or decimal machines
! 51: *> without guard digits, but we know of none.
! 52: *> \endverbatim
! 53: *
! 54: * Arguments:
! 55: * ==========
! 56: *
! 57: *> \param[in] ITYPE
! 58: *> \verbatim
! 59: *> ITYPE is INTEGER
! 60: *> Specifies the problem type to be solved:
! 61: *> = 1: A*x = (lambda)*B*x
! 62: *> = 2: A*B*x = (lambda)*x
! 63: *> = 3: B*A*x = (lambda)*x
! 64: *> \endverbatim
! 65: *>
! 66: *> \param[in] JOBZ
! 67: *> \verbatim
! 68: *> JOBZ is CHARACTER*1
! 69: *> = 'N': Compute eigenvalues only;
! 70: *> = 'V': Compute eigenvalues and eigenvectors.
! 71: *> \endverbatim
! 72: *>
! 73: *> \param[in] UPLO
! 74: *> \verbatim
! 75: *> UPLO is CHARACTER*1
! 76: *> = 'U': Upper triangles of A and B are stored;
! 77: *> = 'L': Lower triangles of A and B are stored.
! 78: *> \endverbatim
! 79: *>
! 80: *> \param[in] N
! 81: *> \verbatim
! 82: *> N is INTEGER
! 83: *> The order of the matrices A and B. N >= 0.
! 84: *> \endverbatim
! 85: *>
! 86: *> \param[in,out] A
! 87: *> \verbatim
! 88: *> A is COMPLEX*16 array, dimension (LDA, N)
! 89: *> On entry, the Hermitian matrix A. If UPLO = 'U', the
! 90: *> leading N-by-N upper triangular part of A contains the
! 91: *> upper triangular part of the matrix A. If UPLO = 'L',
! 92: *> the leading N-by-N lower triangular part of A contains
! 93: *> the lower triangular part of the matrix A.
! 94: *>
! 95: *> On exit, if JOBZ = 'V', then if INFO = 0, A contains the
! 96: *> matrix Z of eigenvectors. The eigenvectors are normalized
! 97: *> as follows:
! 98: *> if ITYPE = 1 or 2, Z**H*B*Z = I;
! 99: *> if ITYPE = 3, Z**H*inv(B)*Z = I.
! 100: *> If JOBZ = 'N', then on exit the upper triangle (if UPLO='U')
! 101: *> or the lower triangle (if UPLO='L') of A, including the
! 102: *> diagonal, is destroyed.
! 103: *> \endverbatim
! 104: *>
! 105: *> \param[in] LDA
! 106: *> \verbatim
! 107: *> LDA is INTEGER
! 108: *> The leading dimension of the array A. LDA >= max(1,N).
! 109: *> \endverbatim
! 110: *>
! 111: *> \param[in,out] B
! 112: *> \verbatim
! 113: *> B is COMPLEX*16 array, dimension (LDB, N)
! 114: *> On entry, the Hermitian matrix B. If UPLO = 'U', the
! 115: *> leading N-by-N upper triangular part of B contains the
! 116: *> upper triangular part of the matrix B. If UPLO = 'L',
! 117: *> the leading N-by-N lower triangular part of B contains
! 118: *> the lower triangular part of the matrix B.
! 119: *>
! 120: *> On exit, if INFO <= N, the part of B containing the matrix is
! 121: *> overwritten by the triangular factor U or L from the Cholesky
! 122: *> factorization B = U**H*U or B = L*L**H.
! 123: *> \endverbatim
! 124: *>
! 125: *> \param[in] LDB
! 126: *> \verbatim
! 127: *> LDB is INTEGER
! 128: *> The leading dimension of the array B. LDB >= max(1,N).
! 129: *> \endverbatim
! 130: *>
! 131: *> \param[out] W
! 132: *> \verbatim
! 133: *> W is DOUBLE PRECISION array, dimension (N)
! 134: *> If INFO = 0, the eigenvalues in ascending order.
! 135: *> \endverbatim
! 136: *>
! 137: *> \param[out] WORK
! 138: *> \verbatim
! 139: *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
! 140: *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
! 141: *> \endverbatim
! 142: *>
! 143: *> \param[in] LWORK
! 144: *> \verbatim
! 145: *> LWORK is INTEGER
! 146: *> The length of the array WORK.
! 147: *> If N <= 1, LWORK >= 1.
! 148: *> If JOBZ = 'N' and N > 1, LWORK >= N + 1.
! 149: *> If JOBZ = 'V' and N > 1, LWORK >= 2*N + N**2.
! 150: *>
! 151: *> If LWORK = -1, then a workspace query is assumed; the routine
! 152: *> only calculates the optimal sizes of the WORK, RWORK and
! 153: *> IWORK arrays, returns these values as the first entries of
! 154: *> the WORK, RWORK and IWORK arrays, and no error message
! 155: *> related to LWORK or LRWORK or LIWORK is issued by XERBLA.
! 156: *> \endverbatim
! 157: *>
! 158: *> \param[out] RWORK
! 159: *> \verbatim
! 160: *> RWORK is DOUBLE PRECISION array, dimension (MAX(1,LRWORK))
! 161: *> On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.
! 162: *> \endverbatim
! 163: *>
! 164: *> \param[in] LRWORK
! 165: *> \verbatim
! 166: *> LRWORK is INTEGER
! 167: *> The dimension of the array RWORK.
! 168: *> If N <= 1, LRWORK >= 1.
! 169: *> If JOBZ = 'N' and N > 1, LRWORK >= N.
! 170: *> If JOBZ = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2.
! 171: *>
! 172: *> If LRWORK = -1, then a workspace query is assumed; the
! 173: *> routine only calculates the optimal sizes of the WORK, RWORK
! 174: *> and IWORK arrays, returns these values as the first entries
! 175: *> of the WORK, RWORK and IWORK arrays, and no error message
! 176: *> related to LWORK or LRWORK or LIWORK is issued by XERBLA.
! 177: *> \endverbatim
! 178: *>
! 179: *> \param[out] IWORK
! 180: *> \verbatim
! 181: *> IWORK is INTEGER array, dimension (MAX(1,LIWORK))
! 182: *> On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
! 183: *> \endverbatim
! 184: *>
! 185: *> \param[in] LIWORK
! 186: *> \verbatim
! 187: *> LIWORK is INTEGER
! 188: *> The dimension of the array IWORK.
! 189: *> If N <= 1, LIWORK >= 1.
! 190: *> If JOBZ = 'N' and N > 1, LIWORK >= 1.
! 191: *> If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N.
! 192: *>
! 193: *> If LIWORK = -1, then a workspace query is assumed; the
! 194: *> routine only calculates the optimal sizes of the WORK, RWORK
! 195: *> and IWORK arrays, returns these values as the first entries
! 196: *> of the WORK, RWORK and IWORK arrays, and no error message
! 197: *> related to LWORK or LRWORK or LIWORK is issued by XERBLA.
! 198: *> \endverbatim
! 199: *>
! 200: *> \param[out] INFO
! 201: *> \verbatim
! 202: *> INFO is INTEGER
! 203: *> = 0: successful exit
! 204: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 205: *> > 0: ZPOTRF or ZHEEVD returned an error code:
! 206: *> <= N: if INFO = i and JOBZ = 'N', then the algorithm
! 207: *> failed to converge; i off-diagonal elements of an
! 208: *> intermediate tridiagonal form did not converge to
! 209: *> zero;
! 210: *> if INFO = i and JOBZ = 'V', then the algorithm
! 211: *> failed to compute an eigenvalue while working on
! 212: *> the submatrix lying in rows and columns INFO/(N+1)
! 213: *> through mod(INFO,N+1);
! 214: *> > N: if INFO = N + i, for 1 <= i <= N, then the leading
! 215: *> minor of order i of B is not positive definite.
! 216: *> The factorization of B could not be completed and
! 217: *> no eigenvalues or eigenvectors were computed.
! 218: *> \endverbatim
! 219: *
! 220: * Authors:
! 221: * ========
! 222: *
! 223: *> \author Univ. of Tennessee
! 224: *> \author Univ. of California Berkeley
! 225: *> \author Univ. of Colorado Denver
! 226: *> \author NAG Ltd.
! 227: *
! 228: *> \date November 2011
! 229: *
! 230: *> \ingroup complex16HEeigen
! 231: *
! 232: *> \par Further Details:
! 233: * =====================
! 234: *>
! 235: *> \verbatim
! 236: *>
! 237: *> Modified so that no backsubstitution is performed if ZHEEVD fails to
! 238: *> converge (NEIG in old code could be greater than N causing out of
! 239: *> bounds reference to A - reported by Ralf Meyer). Also corrected the
! 240: *> description of INFO and the test on ITYPE. Sven, 16 Feb 05.
! 241: *> \endverbatim
! 242: *
! 243: *> \par Contributors:
! 244: * ==================
! 245: *>
! 246: *> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
! 247: *>
! 248: * =====================================================================
1.1 bertrand 249: SUBROUTINE ZHEGVD( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK,
250: $ LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO )
251: *
1.9 ! bertrand 252: * -- LAPACK driver routine (version 3.4.0) --
1.1 bertrand 253: * -- LAPACK is a software package provided by Univ. of Tennessee, --
254: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.9 ! bertrand 255: * November 2011
1.1 bertrand 256: *
257: * .. Scalar Arguments ..
258: CHARACTER JOBZ, UPLO
259: INTEGER INFO, ITYPE, LDA, LDB, LIWORK, LRWORK, LWORK, N
260: * ..
261: * .. Array Arguments ..
262: INTEGER IWORK( * )
263: DOUBLE PRECISION RWORK( * ), W( * )
264: COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
265: * ..
266: *
267: * =====================================================================
268: *
269: * .. Parameters ..
270: COMPLEX*16 CONE
271: PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ) )
272: * ..
273: * .. Local Scalars ..
274: LOGICAL LQUERY, UPPER, WANTZ
275: CHARACTER TRANS
276: INTEGER LIOPT, LIWMIN, LOPT, LROPT, LRWMIN, LWMIN
277: * ..
278: * .. External Functions ..
279: LOGICAL LSAME
280: EXTERNAL LSAME
281: * ..
282: * .. External Subroutines ..
283: EXTERNAL XERBLA, ZHEEVD, ZHEGST, ZPOTRF, ZTRMM, ZTRSM
284: * ..
285: * .. Intrinsic Functions ..
286: INTRINSIC DBLE, MAX
287: * ..
288: * .. Executable Statements ..
289: *
290: * Test the input parameters.
291: *
292: WANTZ = LSAME( JOBZ, 'V' )
293: UPPER = LSAME( UPLO, 'U' )
294: LQUERY = ( LWORK.EQ.-1 .OR. LRWORK.EQ.-1 .OR. LIWORK.EQ.-1 )
295: *
296: INFO = 0
297: IF( N.LE.1 ) THEN
298: LWMIN = 1
299: LRWMIN = 1
300: LIWMIN = 1
301: ELSE IF( WANTZ ) THEN
302: LWMIN = 2*N + N*N
303: LRWMIN = 1 + 5*N + 2*N*N
304: LIWMIN = 3 + 5*N
305: ELSE
306: LWMIN = N + 1
307: LRWMIN = N
308: LIWMIN = 1
309: END IF
310: LOPT = LWMIN
311: LROPT = LRWMIN
312: LIOPT = LIWMIN
313: IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
314: INFO = -1
315: ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
316: INFO = -2
317: ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
318: INFO = -3
319: ELSE IF( N.LT.0 ) THEN
320: INFO = -4
321: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
322: INFO = -6
323: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
324: INFO = -8
325: END IF
326: *
327: IF( INFO.EQ.0 ) THEN
328: WORK( 1 ) = LOPT
329: RWORK( 1 ) = LROPT
330: IWORK( 1 ) = LIOPT
331: *
332: IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
333: INFO = -11
334: ELSE IF( LRWORK.LT.LRWMIN .AND. .NOT.LQUERY ) THEN
335: INFO = -13
336: ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
337: INFO = -15
338: END IF
339: END IF
340: *
341: IF( INFO.NE.0 ) THEN
342: CALL XERBLA( 'ZHEGVD', -INFO )
343: RETURN
344: ELSE IF( LQUERY ) THEN
345: RETURN
346: END IF
347: *
348: * Quick return if possible
349: *
350: IF( N.EQ.0 )
351: $ RETURN
352: *
353: * Form a Cholesky factorization of B.
354: *
355: CALL ZPOTRF( UPLO, N, B, LDB, INFO )
356: IF( INFO.NE.0 ) THEN
357: INFO = N + INFO
358: RETURN
359: END IF
360: *
361: * Transform problem to standard eigenvalue problem and solve.
362: *
363: CALL ZHEGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
364: CALL ZHEEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK, LRWORK,
365: $ IWORK, LIWORK, INFO )
366: LOPT = MAX( DBLE( LOPT ), DBLE( WORK( 1 ) ) )
367: LROPT = MAX( DBLE( LROPT ), DBLE( RWORK( 1 ) ) )
368: LIOPT = MAX( DBLE( LIOPT ), DBLE( IWORK( 1 ) ) )
369: *
370: IF( WANTZ .AND. INFO.EQ.0 ) THEN
371: *
372: * Backtransform eigenvectors to the original problem.
373: *
374: IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
375: *
376: * For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
1.8 bertrand 377: * backtransform eigenvectors: x = inv(L)**H *y or inv(U)*y
1.1 bertrand 378: *
379: IF( UPPER ) THEN
380: TRANS = 'N'
381: ELSE
382: TRANS = 'C'
383: END IF
384: *
385: CALL ZTRSM( 'Left', UPLO, TRANS, 'Non-unit', N, N, CONE,
386: $ B, LDB, A, LDA )
387: *
388: ELSE IF( ITYPE.EQ.3 ) THEN
389: *
390: * For B*A*x=(lambda)*x;
1.8 bertrand 391: * backtransform eigenvectors: x = L*y or U**H *y
1.1 bertrand 392: *
393: IF( UPPER ) THEN
394: TRANS = 'C'
395: ELSE
396: TRANS = 'N'
397: END IF
398: *
399: CALL ZTRMM( 'Left', UPLO, TRANS, 'Non-unit', N, N, CONE,
400: $ B, LDB, A, LDA )
401: END IF
402: END IF
403: *
404: WORK( 1 ) = LOPT
405: RWORK( 1 ) = LROPT
406: IWORK( 1 ) = LIOPT
407: *
408: RETURN
409: *
410: * End of ZHEGVD
411: *
412: END
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