Annotation of rpl/lapack/lapack/dsyevd.f, revision 1.8
1.8 ! bertrand 1: *> \brief <b> DSYEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices</b>
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download DSYEVD + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsyevd.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsyevd.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsyevd.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE DSYEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, IWORK,
! 22: * LIWORK, INFO )
! 23: *
! 24: * .. Scalar Arguments ..
! 25: * CHARACTER JOBZ, UPLO
! 26: * INTEGER INFO, LDA, LIWORK, LWORK, N
! 27: * ..
! 28: * .. Array Arguments ..
! 29: * INTEGER IWORK( * )
! 30: * DOUBLE PRECISION A( LDA, * ), W( * ), WORK( * )
! 31: * ..
! 32: *
! 33: *
! 34: *> \par Purpose:
! 35: * =============
! 36: *>
! 37: *> \verbatim
! 38: *>
! 39: *> DSYEVD computes all eigenvalues and, optionally, eigenvectors of a
! 40: *> real symmetric matrix A. If eigenvectors are desired, it uses a
! 41: *> divide and conquer algorithm.
! 42: *>
! 43: *> The divide and conquer algorithm makes very mild assumptions about
! 44: *> floating point arithmetic. It will work on machines with a guard
! 45: *> digit in add/subtract, or on those binary machines without guard
! 46: *> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
! 47: *> Cray-2. It could conceivably fail on hexadecimal or decimal machines
! 48: *> without guard digits, but we know of none.
! 49: *>
! 50: *> Because of large use of BLAS of level 3, DSYEVD needs N**2 more
! 51: *> workspace than DSYEVX.
! 52: *> \endverbatim
! 53: *
! 54: * Arguments:
! 55: * ==========
! 56: *
! 57: *> \param[in] JOBZ
! 58: *> \verbatim
! 59: *> JOBZ is CHARACTER*1
! 60: *> = 'N': Compute eigenvalues only;
! 61: *> = 'V': Compute eigenvalues and eigenvectors.
! 62: *> \endverbatim
! 63: *>
! 64: *> \param[in] UPLO
! 65: *> \verbatim
! 66: *> UPLO is CHARACTER*1
! 67: *> = 'U': Upper triangle of A is stored;
! 68: *> = 'L': Lower triangle of A is stored.
! 69: *> \endverbatim
! 70: *>
! 71: *> \param[in] N
! 72: *> \verbatim
! 73: *> N is INTEGER
! 74: *> The order of the matrix A. N >= 0.
! 75: *> \endverbatim
! 76: *>
! 77: *> \param[in,out] A
! 78: *> \verbatim
! 79: *> A is DOUBLE PRECISION array, dimension (LDA, N)
! 80: *> On entry, the symmetric matrix A. If UPLO = 'U', the
! 81: *> leading N-by-N upper triangular part of A contains the
! 82: *> upper triangular part of the matrix A. If UPLO = 'L',
! 83: *> the leading N-by-N lower triangular part of A contains
! 84: *> the lower triangular part of the matrix A.
! 85: *> On exit, if JOBZ = 'V', then if INFO = 0, A contains the
! 86: *> orthonormal eigenvectors of the matrix A.
! 87: *> If JOBZ = 'N', then on exit the lower triangle (if UPLO='L')
! 88: *> or the upper triangle (if UPLO='U') of A, including the
! 89: *> diagonal, is destroyed.
! 90: *> \endverbatim
! 91: *>
! 92: *> \param[in] LDA
! 93: *> \verbatim
! 94: *> LDA is INTEGER
! 95: *> The leading dimension of the array A. LDA >= max(1,N).
! 96: *> \endverbatim
! 97: *>
! 98: *> \param[out] W
! 99: *> \verbatim
! 100: *> W is DOUBLE PRECISION array, dimension (N)
! 101: *> If INFO = 0, the eigenvalues in ascending order.
! 102: *> \endverbatim
! 103: *>
! 104: *> \param[out] WORK
! 105: *> \verbatim
! 106: *> WORK is DOUBLE PRECISION array,
! 107: *> dimension (LWORK)
! 108: *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
! 109: *> \endverbatim
! 110: *>
! 111: *> \param[in] LWORK
! 112: *> \verbatim
! 113: *> LWORK is INTEGER
! 114: *> The dimension of the array WORK.
! 115: *> If N <= 1, LWORK must be at least 1.
! 116: *> If JOBZ = 'N' and N > 1, LWORK must be at least 2*N+1.
! 117: *> If JOBZ = 'V' and N > 1, LWORK must be at least
! 118: *> 1 + 6*N + 2*N**2.
! 119: *>
! 120: *> If LWORK = -1, then a workspace query is assumed; the routine
! 121: *> only calculates the optimal sizes of the WORK and IWORK
! 122: *> arrays, returns these values as the first entries of the WORK
! 123: *> and IWORK arrays, and no error message related to LWORK or
! 124: *> LIWORK is issued by XERBLA.
! 125: *> \endverbatim
! 126: *>
! 127: *> \param[out] IWORK
! 128: *> \verbatim
! 129: *> IWORK is INTEGER array, dimension (MAX(1,LIWORK))
! 130: *> On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
! 131: *> \endverbatim
! 132: *>
! 133: *> \param[in] LIWORK
! 134: *> \verbatim
! 135: *> LIWORK is INTEGER
! 136: *> The dimension of the array IWORK.
! 137: *> If N <= 1, LIWORK must be at least 1.
! 138: *> If JOBZ = 'N' and N > 1, LIWORK must be at least 1.
! 139: *> If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N.
! 140: *>
! 141: *> If LIWORK = -1, then a workspace query is assumed; the
! 142: *> routine only calculates the optimal sizes of the WORK and
! 143: *> IWORK arrays, returns these values as the first entries of
! 144: *> the WORK and IWORK arrays, and no error message related to
! 145: *> LWORK or LIWORK is issued by XERBLA.
! 146: *> \endverbatim
! 147: *>
! 148: *> \param[out] INFO
! 149: *> \verbatim
! 150: *> INFO is INTEGER
! 151: *> = 0: successful exit
! 152: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 153: *> > 0: if INFO = i and JOBZ = 'N', then the algorithm failed
! 154: *> to converge; i off-diagonal elements of an intermediate
! 155: *> tridiagonal form did not converge to zero;
! 156: *> if INFO = i and JOBZ = 'V', then the algorithm failed
! 157: *> to compute an eigenvalue while working on the submatrix
! 158: *> lying in rows and columns INFO/(N+1) through
! 159: *> mod(INFO,N+1).
! 160: *> \endverbatim
! 161: *
! 162: * Authors:
! 163: * ========
! 164: *
! 165: *> \author Univ. of Tennessee
! 166: *> \author Univ. of California Berkeley
! 167: *> \author Univ. of Colorado Denver
! 168: *> \author NAG Ltd.
! 169: *
! 170: *> \date November 2011
! 171: *
! 172: *> \ingroup doubleSYeigen
! 173: *
! 174: *> \par Contributors:
! 175: * ==================
! 176: *>
! 177: *> Jeff Rutter, Computer Science Division, University of California
! 178: *> at Berkeley, USA \n
! 179: *> Modified by Francoise Tisseur, University of Tennessee \n
! 180: *> Modified description of INFO. Sven, 16 Feb 05. \n
! 181:
! 182:
! 183: *>
! 184: * =====================================================================
1.1 bertrand 185: SUBROUTINE DSYEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, IWORK,
186: $ LIWORK, INFO )
187: *
1.8 ! bertrand 188: * -- LAPACK driver routine (version 3.4.0) --
1.1 bertrand 189: * -- LAPACK is a software package provided by Univ. of Tennessee, --
190: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.8 ! bertrand 191: * November 2011
1.1 bertrand 192: *
193: * .. Scalar Arguments ..
194: CHARACTER JOBZ, UPLO
195: INTEGER INFO, LDA, LIWORK, LWORK, N
196: * ..
197: * .. Array Arguments ..
198: INTEGER IWORK( * )
199: DOUBLE PRECISION A( LDA, * ), W( * ), WORK( * )
200: * ..
201: *
202: * =====================================================================
203: *
204: * .. Parameters ..
205: DOUBLE PRECISION ZERO, ONE
206: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
207: * ..
208: * .. Local Scalars ..
209: *
210: LOGICAL LOWER, LQUERY, WANTZ
211: INTEGER IINFO, INDE, INDTAU, INDWK2, INDWRK, ISCALE,
212: $ LIOPT, LIWMIN, LLWORK, LLWRK2, LOPT, LWMIN
213: DOUBLE PRECISION ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
214: $ SMLNUM
215: * ..
216: * .. External Functions ..
217: LOGICAL LSAME
218: INTEGER ILAENV
219: DOUBLE PRECISION DLAMCH, DLANSY
220: EXTERNAL LSAME, DLAMCH, DLANSY, ILAENV
221: * ..
222: * .. External Subroutines ..
223: EXTERNAL DLACPY, DLASCL, DORMTR, DSCAL, DSTEDC, DSTERF,
224: $ DSYTRD, XERBLA
225: * ..
226: * .. Intrinsic Functions ..
227: INTRINSIC MAX, SQRT
228: * ..
229: * .. Executable Statements ..
230: *
231: * Test the input parameters.
232: *
233: WANTZ = LSAME( JOBZ, 'V' )
234: LOWER = LSAME( UPLO, 'L' )
235: LQUERY = ( LWORK.EQ.-1 .OR. LIWORK.EQ.-1 )
236: *
237: INFO = 0
238: IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
239: INFO = -1
240: ELSE IF( .NOT.( LOWER .OR. LSAME( UPLO, 'U' ) ) ) THEN
241: INFO = -2
242: ELSE IF( N.LT.0 ) THEN
243: INFO = -3
244: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
245: INFO = -5
246: END IF
247: *
248: IF( INFO.EQ.0 ) THEN
249: IF( N.LE.1 ) THEN
250: LIWMIN = 1
251: LWMIN = 1
252: LOPT = LWMIN
253: LIOPT = LIWMIN
254: ELSE
255: IF( WANTZ ) THEN
256: LIWMIN = 3 + 5*N
257: LWMIN = 1 + 6*N + 2*N**2
258: ELSE
259: LIWMIN = 1
260: LWMIN = 2*N + 1
261: END IF
262: LOPT = MAX( LWMIN, 2*N +
263: $ ILAENV( 1, 'DSYTRD', UPLO, N, -1, -1, -1 ) )
264: LIOPT = LIWMIN
265: END IF
266: WORK( 1 ) = LOPT
267: IWORK( 1 ) = LIOPT
268: *
269: IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
270: INFO = -8
271: ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
272: INFO = -10
273: END IF
274: END IF
275: *
276: IF( INFO.NE.0 ) THEN
277: CALL XERBLA( 'DSYEVD', -INFO )
278: RETURN
279: ELSE IF( LQUERY ) THEN
280: RETURN
281: END IF
282: *
283: * Quick return if possible
284: *
285: IF( N.EQ.0 )
286: $ RETURN
287: *
288: IF( N.EQ.1 ) THEN
289: W( 1 ) = A( 1, 1 )
290: IF( WANTZ )
291: $ A( 1, 1 ) = ONE
292: RETURN
293: END IF
294: *
295: * Get machine constants.
296: *
297: SAFMIN = DLAMCH( 'Safe minimum' )
298: EPS = DLAMCH( 'Precision' )
299: SMLNUM = SAFMIN / EPS
300: BIGNUM = ONE / SMLNUM
301: RMIN = SQRT( SMLNUM )
302: RMAX = SQRT( BIGNUM )
303: *
304: * Scale matrix to allowable range, if necessary.
305: *
306: ANRM = DLANSY( 'M', UPLO, N, A, LDA, WORK )
307: ISCALE = 0
308: IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN
309: ISCALE = 1
310: SIGMA = RMIN / ANRM
311: ELSE IF( ANRM.GT.RMAX ) THEN
312: ISCALE = 1
313: SIGMA = RMAX / ANRM
314: END IF
315: IF( ISCALE.EQ.1 )
316: $ CALL DLASCL( UPLO, 0, 0, ONE, SIGMA, N, N, A, LDA, INFO )
317: *
318: * Call DSYTRD to reduce symmetric matrix to tridiagonal form.
319: *
320: INDE = 1
321: INDTAU = INDE + N
322: INDWRK = INDTAU + N
323: LLWORK = LWORK - INDWRK + 1
324: INDWK2 = INDWRK + N*N
325: LLWRK2 = LWORK - INDWK2 + 1
326: *
327: CALL DSYTRD( UPLO, N, A, LDA, W, WORK( INDE ), WORK( INDTAU ),
328: $ WORK( INDWRK ), LLWORK, IINFO )
329: LOPT = 2*N + WORK( INDWRK )
330: *
331: * For eigenvalues only, call DSTERF. For eigenvectors, first call
332: * DSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the
333: * tridiagonal matrix, then call DORMTR to multiply it by the
334: * Householder transformations stored in A.
335: *
336: IF( .NOT.WANTZ ) THEN
337: CALL DSTERF( N, W, WORK( INDE ), INFO )
338: ELSE
339: CALL DSTEDC( 'I', N, W, WORK( INDE ), WORK( INDWRK ), N,
340: $ WORK( INDWK2 ), LLWRK2, IWORK, LIWORK, INFO )
341: CALL DORMTR( 'L', UPLO, 'N', N, N, A, LDA, WORK( INDTAU ),
342: $ WORK( INDWRK ), N, WORK( INDWK2 ), LLWRK2, IINFO )
343: CALL DLACPY( 'A', N, N, WORK( INDWRK ), N, A, LDA )
344: LOPT = MAX( LOPT, 1+6*N+2*N**2 )
345: END IF
346: *
347: * If matrix was scaled, then rescale eigenvalues appropriately.
348: *
349: IF( ISCALE.EQ.1 )
350: $ CALL DSCAL( N, ONE / SIGMA, W, 1 )
351: *
352: WORK( 1 ) = LOPT
353: IWORK( 1 ) = LIOPT
354: *
355: RETURN
356: *
357: * End of DSYEVD
358: *
359: END
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