#include "ESMF_LapackBlas.inc" !> \brief <b> DSYEVR computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices</b> ! ! =========== DOCUMENTATION =========== ! ! Online html documentation available at ! http://www.netlib.org/lapack/explore-html/ ! !> \htmlonly !> Download DSYEVR + dependencies !> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsyevr.f"> !> [TGZ]</a> !> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsyevr.f"> !> [ZIP]</a> !> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsyevr.f"> !> [TXT]</a> !> \endhtmlonly ! ! Definition: ! =========== ! ! SUBROUTINE DSYEVR( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU, ! ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK, ! IWORK, LIWORK, INFO ) ! ! .. Scalar Arguments .. ! CHARACTER JOBZ, RANGE, UPLO ! INTEGER IL, INFO, IU, LDA, LDZ, LIWORK, LWORK, M, N ! DOUBLE PRECISION ABSTOL, VL, VU ! .. ! .. Array Arguments .. ! INTEGER ISUPPZ( * ), IWORK( * ) ! DOUBLE PRECISION A( LDA, * ), W( * ), WORK( * ), Z( LDZ, * ) ! .. ! ! !> \par Purpose: ! ============= !> !> \verbatim !> !> DSYEVR computes selected eigenvalues and, optionally, eigenvectors !> of a real symmetric matrix A. Eigenvalues and eigenvectors can be !> selected by specifying either a range of values or a range of !> indices for the desired eigenvalues. !> !> DSYEVR first reduces the matrix A to tridiagonal form T with a call !> to DSYTRD. Then, whenever possible, DSYEVR calls DSTEMR to compute !> the eigenspectrum using Relatively Robust Representations. DSTEMR !> computes eigenvalues by the dqds algorithm, while orthogonal !> eigenvectors are computed from various "good" L D L^T representations !> (also known as Relatively Robust Representations). Gram-Schmidt !> orthogonalization is avoided as far as possible. More specifically, !> the various steps of the algorithm are as follows. !> !> For each unreduced block (submatrix) of T, !> (a) Compute T - sigma I = L D L^T, so that L and D !> define all the wanted eigenvalues to high relative accuracy. !> This means that small relative changes in the entries of D and L !> cause only small relative changes in the eigenvalues and !> eigenvectors. The standard (unfactored) representation of the !> tridiagonal matrix T does not have this property in general. !> (b) Compute the eigenvalues to suitable accuracy. !> If the eigenvectors are desired, the algorithm attains full !> accuracy of the computed eigenvalues only right before !> the corresponding vectors have to be computed, see steps c) and d). !> (c) For each cluster of close eigenvalues, select a new !> shift close to the cluster, find a new factorization, and refine !> the shifted eigenvalues to suitable accuracy. !> (d) For each eigenvalue with a large enough relative separation compute !> the corresponding eigenvector by forming a rank revealing twisted !> factorization. Go back to (c) for any clusters that remain. !> !> The desired accuracy of the output can be specified by the input !> parameter ABSTOL. !> !> For more details, see DSTEMR's documentation and: !> - Inderjit S. Dhillon and Beresford N. Parlett: "Multiple representations !> to compute orthogonal eigenvectors of symmetric tridiagonal matrices," !> Linear Algebra and its Applications, 387(1), pp. 1-28, August 2004. !> - Inderjit Dhillon and Beresford Parlett: "Orthogonal Eigenvectors and !> Relative Gaps," SIAM Journal on Matrix Analysis and Applications, Vol. 25, !> 2004. Also LAPACK Working Note 154. !> - Inderjit Dhillon: "A new O(n^2) algorithm for the symmetric !> tridiagonal eigenvalue/eigenvector problem", !> Computer Science Division Technical Report No. UCB/CSD-97-971, !> UC Berkeley, May 1997. !> !> !> Note 1 : DSYEVR calls DSTEMR when the full spectrum is requested !> on machines which conform to the ieee-754 floating point standard. !> DSYEVR calls DSTEBZ and DSTEIN on non-ieee machines and !> when partial spectrum requests are made. !> !> Normal execution of DSTEMR may create NaNs and infinities and !> hence may abort due to a floating point exception in environments !> which do not handle NaNs and infinities in the ieee standard default !> manner. !> \endverbatim ! ! Arguments: ! ========== ! !> \param[in] JOBZ !> \verbatim !> JOBZ is CHARACTER*1 !> = 'N': Compute eigenvalues only; !> = 'V': Compute eigenvalues and eigenvectors. !> \endverbatim !> !> \param[in] RANGE !> \verbatim !> RANGE is CHARACTER*1 !> = 'A': all eigenvalues will be found. !> = 'V': all eigenvalues in the half-open interval (VL,VU] !> will be found. !> = 'I': the IL-th through IU-th eigenvalues will be found. !> For RANGE = 'V' or 'I' and IU - IL < N - 1, DSTEBZ and !> DSTEIN are called !> \endverbatim !> !> \param[in] UPLO !> \verbatim !> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A is stored; !> = 'L': Lower triangle of A is stored. !> \endverbatim !> !> \param[in] N !> \verbatim !> N is INTEGER !> The order of the matrix A. N >= 0. !> \endverbatim !> !> \param[in,out] A !> \verbatim !> A is DOUBLE PRECISION array, dimension (LDA, N) !> On entry, the symmetric matrix A. If UPLO = 'U', the !> leading N-by-N upper triangular part of A contains the !> upper triangular part of the matrix A. If UPLO = 'L', !> the leading N-by-N lower triangular part of A contains !> the lower triangular part of the matrix A. !> On exit, the lower triangle (if UPLO='L') or the upper !> triangle (if UPLO='U') of A, including the diagonal, is !> destroyed. !> \endverbatim !> !> \param[in] LDA !> \verbatim !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !> \endverbatim !> !> \param[in] VL !> \verbatim !> VL is DOUBLE PRECISION !> If RANGE='V', the lower bound of the interval to !> be searched for eigenvalues. VL < VU. !> Not referenced if RANGE = 'A' or 'I'. !> \endverbatim !> !> \param[in] VU !> \verbatim !> VU is DOUBLE PRECISION !> If RANGE='V', the upper bound of the interval to !> be searched for eigenvalues. VL < VU. !> Not referenced if RANGE = 'A' or 'I'. !> \endverbatim !> !> \param[in] IL !> \verbatim !> IL is INTEGER !> If RANGE='I', the index of the !> smallest eigenvalue to be returned. !> 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. !> Not referenced if RANGE = 'A' or 'V'. !> \endverbatim !> !> \param[in] IU !> \verbatim !> IU is INTEGER !> If RANGE='I', the index of the !> largest eigenvalue to be returned. !> 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. !> Not referenced if RANGE = 'A' or 'V'. !> \endverbatim !> !> \param[in] ABSTOL !> \verbatim !> ABSTOL is DOUBLE PRECISION !> The absolute error tolerance for the eigenvalues. !> An approximate eigenvalue is accepted as converged !> when it is determined to lie in an interval [a,b] !> of width less than or equal to !> !> ABSTOL + EPS * max( |a|,|b| ) , !> !> where EPS is the machine precision. If ABSTOL is less than !> or equal to zero, then EPS*|T| will be used in its place, !> where |T| is the 1-norm of the tridiagonal matrix obtained !> by reducing A to tridiagonal form. !> !> See "Computing Small Singular Values of Bidiagonal Matrices !> with Guaranteed High Relative Accuracy," by Demmel and !> Kahan, LAPACK Working Note #3. !> !> If high relative accuracy is important, set ABSTOL to !> DLAMCH( 'Safe minimum' ). Doing so will guarantee that !> eigenvalues are computed to high relative accuracy when !> possible in future releases. The current code does not !> make any guarantees about high relative accuracy, but !> future releases will. See J. Barlow and J. Demmel, !> "Computing Accurate Eigensystems of Scaled Diagonally !> Dominant Matrices", LAPACK Working Note #7, for a discussion !> of which matrices define their eigenvalues to high relative !> accuracy. !> \endverbatim !> !> \param[out] M !> \verbatim !> M is INTEGER !> The total number of eigenvalues found. 0 <= M <= N. !> If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1. !> \endverbatim !> !> \param[out] W !> \verbatim !> W is DOUBLE PRECISION array, dimension (N) !> The first M elements contain the selected eigenvalues in !> ascending order. !> \endverbatim !> !> \param[out] Z !> \verbatim !> Z is DOUBLE PRECISION array, dimension (LDZ, max(1,M)) !> If JOBZ = 'V', then if INFO = 0, the first M columns of Z !> contain the orthonormal eigenvectors of the matrix A !> corresponding to the selected eigenvalues, with the i-th !> column of Z holding the eigenvector associated with W(i). !> If JOBZ = 'N', then Z is not referenced. !> Note: the user must ensure that at least max(1,M) columns are !> supplied in the array Z; if RANGE = 'V', the exact value of M !> is not known in advance and an upper bound must be used. !> Supplying N columns is always safe. !> \endverbatim !> !> \param[in] LDZ !> \verbatim !> LDZ is INTEGER !> The leading dimension of the array Z. LDZ >= 1, and if !> JOBZ = 'V', LDZ >= max(1,N). !> \endverbatim !> !> \param[out] ISUPPZ !> \verbatim !> ISUPPZ is INTEGER array, dimension ( 2*max(1,M) ) !> The support of the eigenvectors in Z, i.e., the indices !> indicating the nonzero elements in Z. The i-th eigenvector !> is nonzero only in elements ISUPPZ( 2*i-1 ) through !> ISUPPZ( 2*i ). This is an output of DSTEMR (tridiagonal !> matrix). The support of the eigenvectors of A is typically !> 1:N because of the orthogonal transformations applied by DORMTR. !> Implemented only for RANGE = 'A' or 'I' and IU - IL = N - 1 !> \endverbatim !> !> \param[out] WORK !> \verbatim !> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. !> \endverbatim !> !> \param[in] LWORK !> \verbatim !> LWORK is INTEGER !> The dimension of the array WORK. LWORK >= max(1,26*N). !> For optimal efficiency, LWORK >= (NB+6)*N, !> where NB is the max of the blocksize for DSYTRD and DORMTR !> returned by ILAENV. !> !> If LWORK = -1, then a workspace query is assumed; the routine !> only calculates the optimal size of the WORK array, returns !> this value as the first entry of the WORK array, and no error !> message related to LWORK is issued by XERBLA. !> \endverbatim !> !> \param[out] IWORK !> \verbatim !> IWORK is INTEGER array, dimension (MAX(1,LIWORK)) !> On exit, if INFO = 0, IWORK(1) returns the optimal LWORK. !> \endverbatim !> !> \param[in] LIWORK !> \verbatim !> LIWORK is INTEGER !> The dimension of the array IWORK. LIWORK >= max(1,10*N). !> !> If LIWORK = -1, then a workspace query is assumed; the !> routine only calculates the optimal size of the IWORK array, !> returns this value as the first entry of the IWORK array, and !> no error message related to LIWORK is issued by XERBLA. !> \endverbatim !> !> \param[out] INFO !> \verbatim !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> > 0: Internal error !> \endverbatim ! ! Authors: ! ======== ! !> \author Univ. of Tennessee !> \author Univ. of California Berkeley !> \author Univ. of Colorado Denver !> \author NAG Ltd. ! !> \date June 2016 ! !> \ingroup doubleSYeigen ! !> \par Contributors: ! ================== !> !> Inderjit Dhillon, IBM Almaden, USA \n !> Osni Marques, LBNL/NERSC, USA \n !> Ken Stanley, Computer Science Division, University of !> California at Berkeley, USA \n !> Jason Riedy, Computer Science Division, University of !> California at Berkeley, USA \n !> ! ===================================================================== SUBROUTINE DSYEVR( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU, & ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK, & IWORK, LIWORK, INFO ) ! ! -- LAPACK driver routine (version 3.7.1) -- ! -- LAPACK is a software package provided by Univ. of Tennessee, -- ! -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- ! June 2016 ! ! .. Scalar Arguments .. CHARACTER JOBZ, RANGE, UPLO INTEGER IL, INFO, IU, LDA, LDZ, LIWORK, LWORK, M, N DOUBLE PRECISION ABSTOL, VL, VU ! .. ! .. Array Arguments .. INTEGER ISUPPZ( * ), IWORK( * ) DOUBLE PRECISION A( LDA, * ), W( * ), WORK( * ), Z( LDZ, * ) ! .. ! ! ===================================================================== ! ! .. Parameters .. DOUBLE PRECISION ZERO, ONE, TWO PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0, TWO = 2.0D+0 ) ! .. ! .. Local Scalars .. LOGICAL ALLEIG, INDEIG, LOWER, LQUERY, VALEIG, WANTZ, & TRYRAC CHARACTER ORDER INTEGER I, IEEEOK, IINFO, IMAX, INDD, INDDD, INDE, & INDEE, INDIBL, INDIFL, INDISP, INDIWO, INDTAU, & INDWK, INDWKN, ISCALE, J, JJ, LIWMIN, & LLWORK, LLWRKN, LWKOPT, LWMIN, NB, NSPLIT DOUBLE PRECISION ABSTLL, ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, & SIGMA, SMLNUM, TMP1, VLL, VUU ! .. ! .. External Functions .. LOGICAL LSAME INTEGER ILAENV DOUBLE PRECISION DLAMCH, DLANSY EXTERNAL LSAME, ILAENV, DLAMCH, DLANSY ! .. ! .. External Subroutines .. EXTERNAL DCOPY, DORMTR, DSCAL, DSTEBZ, DSTEMR, DSTEIN, & DSTERF, DSWAP, DSYTRD, XERBLA ! .. ! .. Intrinsic Functions .. INTRINSIC MAX, MIN, SQRT ! .. ! .. Executable Statements .. ! ! Test the input parameters. ! IEEEOK = ILAENV( 10, 'DSYEVR', 'N', 1, 2, 3, 4 ) ! LOWER = LSAME( UPLO, 'L' ) WANTZ = LSAME( JOBZ, 'V' ) ALLEIG = LSAME( RANGE, 'A' ) VALEIG = LSAME( RANGE, 'V' ) INDEIG = LSAME( RANGE, 'I' ) ! LQUERY = ( ( LWORK.EQ.-1 ) .OR. ( LIWORK.EQ.-1 ) ) ! LWMIN = MAX( 1, 26*N ) LIWMIN = MAX( 1, 10*N ) ! INFO = 0 IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN INFO = -1 ELSE IF( .NOT.( ALLEIG .OR. VALEIG .OR. INDEIG ) ) THEN INFO = -2 ELSE IF( .NOT.( LOWER .OR. LSAME( UPLO, 'U' ) ) ) THEN INFO = -3 ELSE IF( N.LT.0 ) THEN INFO = -4 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN INFO = -6 ELSE IF( VALEIG ) THEN IF( N.GT.0 .AND. VU.LE.VL ) & INFO = -8 ELSE IF( INDEIG ) THEN IF( IL.LT.1 .OR. IL.GT.MAX( 1, N ) ) THEN INFO = -9 ELSE IF( IU.LT.MIN( N, IL ) .OR. IU.GT.N ) THEN INFO = -10 END IF END IF END IF IF( INFO.EQ.0 ) THEN IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN INFO = -15 ELSE IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN INFO = -18 ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN INFO = -20 END IF END IF ! IF( INFO.EQ.0 ) THEN NB = ILAENV( 1, 'DSYTRD', UPLO, N, -1, -1, -1 ) NB = MAX( NB, ILAENV( 1, 'DORMTR', UPLO, N, -1, -1, -1 ) ) LWKOPT = MAX( ( NB+1 )*N, LWMIN ) WORK( 1 ) = LWKOPT IWORK( 1 ) = LIWMIN END IF ! IF( INFO.NE.0 ) THEN CALL XERBLA( 'DSYEVR', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF ! ! Quick return if possible ! M = 0 IF( N.EQ.0 ) THEN WORK( 1 ) = 1 RETURN END IF ! IF( N.EQ.1 ) THEN WORK( 1 ) = 7 IF( ALLEIG .OR. INDEIG ) THEN M = 1 W( 1 ) = A( 1, 1 ) ELSE IF( VL.LT.A( 1, 1 ) .AND. VU.GE.A( 1, 1 ) ) THEN M = 1 W( 1 ) = A( 1, 1 ) END IF END IF IF( WANTZ ) THEN Z( 1, 1 ) = ONE ISUPPZ( 1 ) = 1 ISUPPZ( 2 ) = 1 END IF RETURN END IF ! ! Get machine constants. ! SAFMIN = DLAMCH( 'Safe minimum' ) EPS = DLAMCH( 'Precision' ) SMLNUM = SAFMIN / EPS BIGNUM = ONE / SMLNUM RMIN = SQRT( SMLNUM ) RMAX = MIN( SQRT( BIGNUM ), ONE / SQRT( SQRT( SAFMIN ) ) ) ! ! Scale matrix to allowable range, if necessary. ! ISCALE = 0 ABSTLL = ABSTOL IF (VALEIG) THEN VLL = VL VUU = VU END IF ANRM = DLANSY( 'M', UPLO, N, A, LDA, WORK ) IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN ISCALE = 1 SIGMA = RMIN / ANRM ELSE IF( ANRM.GT.RMAX ) THEN ISCALE = 1 SIGMA = RMAX / ANRM END IF IF( ISCALE.EQ.1 ) THEN IF( LOWER ) THEN DO 10 J = 1, N CALL DSCAL( N-J+1, SIGMA, A( J, J ), 1 ) 10 CONTINUE ELSE DO 20 J = 1, N CALL DSCAL( J, SIGMA, A( 1, J ), 1 ) 20 CONTINUE END IF IF( ABSTOL.GT.0 ) & ABSTLL = ABSTOL*SIGMA IF( VALEIG ) THEN VLL = VL*SIGMA VUU = VU*SIGMA END IF END IF ! Initialize indices into workspaces. Note: The IWORK indices are ! used only if DSTERF or DSTEMR fail. ! WORK(INDTAU:INDTAU+N-1) stores the scalar factors of the ! elementary reflectors used in DSYTRD. INDTAU = 1 ! WORK(INDD:INDD+N-1) stores the tridiagonal's diagonal entries. INDD = INDTAU + N ! WORK(INDE:INDE+N-1) stores the off-diagonal entries of the ! tridiagonal matrix from DSYTRD. INDE = INDD + N ! WORK(INDDD:INDDD+N-1) is a copy of the diagonal entries over ! -written by DSTEMR (the DSTERF path copies the diagonal to W). INDDD = INDE + N ! WORK(INDEE:INDEE+N-1) is a copy of the off-diagonal entries over ! -written while computing the eigenvalues in DSTERF and DSTEMR. INDEE = INDDD + N ! INDWK is the starting offset of the left-over workspace, and ! LLWORK is the remaining workspace size. INDWK = INDEE + N LLWORK = LWORK - INDWK + 1 ! IWORK(INDIBL:INDIBL+M-1) corresponds to IBLOCK in DSTEBZ and ! stores the block indices of each of the M<=N eigenvalues. INDIBL = 1 ! IWORK(INDISP:INDISP+NSPLIT-1) corresponds to ISPLIT in DSTEBZ and ! stores the starting and finishing indices of each block. INDISP = INDIBL + N ! IWORK(INDIFL:INDIFL+N-1) stores the indices of eigenvectors ! that corresponding to eigenvectors that fail to converge in ! DSTEIN. This information is discarded; if any fail, the driver ! returns INFO > 0. INDIFL = INDISP + N ! INDIWO is the offset of the remaining integer workspace. INDIWO = INDIFL + N ! ! Call DSYTRD to reduce symmetric matrix to tridiagonal form. ! CALL DSYTRD( UPLO, N, A, LDA, WORK( INDD ), WORK( INDE ), & WORK( INDTAU ), WORK( INDWK ), LLWORK, IINFO ) ! ! If all eigenvalues are desired ! then call DSTERF or DSTEMR and DORMTR. ! IF( ( ALLEIG .OR. ( INDEIG .AND. IL.EQ.1 .AND. IU.EQ.N ) ) .AND. & IEEEOK.EQ.1 ) THEN IF( .NOT.WANTZ ) THEN CALL DCOPY( N, WORK( INDD ), 1, W, 1 ) CALL DCOPY( N-1, WORK( INDE ), 1, WORK( INDEE ), 1 ) CALL DSTERF( N, W, WORK( INDEE ), INFO ) ELSE CALL DCOPY( N-1, WORK( INDE ), 1, WORK( INDEE ), 1 ) CALL DCOPY( N, WORK( INDD ), 1, WORK( INDDD ), 1 ) ! IF (ABSTOL .LE. TWO*N*EPS) THEN TRYRAC = .TRUE. ELSE TRYRAC = .FALSE. END IF CALL DSTEMR( JOBZ, 'A', N, WORK( INDDD ), WORK( INDEE ), & VL, VU, IL, IU, M, W, Z, LDZ, N, ISUPPZ, & TRYRAC, WORK( INDWK ), LWORK, IWORK, LIWORK, & INFO ) ! ! ! ! Apply orthogonal matrix used in reduction to tridiagonal ! form to eigenvectors returned by DSTEMR. ! IF( WANTZ .AND. INFO.EQ.0 ) THEN INDWKN = INDE LLWRKN = LWORK - INDWKN + 1 CALL DORMTR( 'L', UPLO, 'N', N, M, A, LDA, & WORK( INDTAU ), Z, LDZ, WORK( INDWKN ), & LLWRKN, IINFO ) END IF END IF ! ! IF( INFO.EQ.0 ) THEN ! Everything worked. Skip DSTEBZ/DSTEIN. IWORK(:) are ! undefined. M = N GO TO 30 END IF INFO = 0 END IF ! ! Otherwise, call DSTEBZ and, if eigenvectors are desired, DSTEIN. ! Also call DSTEBZ and DSTEIN if DSTEMR fails. ! IF( WANTZ ) THEN ORDER = 'B' ELSE ORDER = 'E' END IF CALL DSTEBZ( RANGE, ORDER, N, VLL, VUU, IL, IU, ABSTLL, & WORK( INDD ), WORK( INDE ), M, NSPLIT, W, & IWORK( INDIBL ), IWORK( INDISP ), WORK( INDWK ), & IWORK( INDIWO ), INFO ) ! IF( WANTZ ) THEN CALL DSTEIN( N, WORK( INDD ), WORK( INDE ), M, W, & IWORK( INDIBL ), IWORK( INDISP ), Z, LDZ, & WORK( INDWK ), IWORK( INDIWO ), IWORK( INDIFL ), & INFO ) ! ! Apply orthogonal matrix used in reduction to tridiagonal ! form to eigenvectors returned by DSTEIN. ! INDWKN = INDE LLWRKN = LWORK - INDWKN + 1 CALL DORMTR( 'L', UPLO, 'N', N, M, A, LDA, WORK( INDTAU ), Z, & LDZ, WORK( INDWKN ), LLWRKN, IINFO ) END IF ! ! If matrix was scaled, then rescale eigenvalues appropriately. ! ! Jump here if DSTEMR/DSTEIN succeeded. 30 CONTINUE IF( ISCALE.EQ.1 ) THEN IF( INFO.EQ.0 ) THEN IMAX = M ELSE IMAX = INFO - 1 END IF CALL DSCAL( IMAX, ONE / SIGMA, W, 1 ) END IF ! ! If eigenvalues are not in order, then sort them, along with ! eigenvectors. Note: We do not sort the IFAIL portion of IWORK. ! It may not be initialized (if DSTEMR/DSTEIN succeeded), and we do ! not return this detailed information to the user. ! IF( WANTZ ) THEN DO 50 J = 1, M - 1 I = 0 TMP1 = W( J ) DO 40 JJ = J + 1, M IF( W( JJ ).LT.TMP1 ) THEN I = JJ TMP1 = W( JJ ) END IF 40 CONTINUE ! IF( I.NE.0 ) THEN W( I ) = W( J ) W( J ) = TMP1 CALL DSWAP( N, Z( 1, I ), 1, Z( 1, J ), 1 ) END IF 50 CONTINUE END IF ! ! Set WORK(1) to optimal workspace size. ! WORK( 1 ) = LWKOPT IWORK( 1 ) = LIWMIN ! RETURN ! ! End of DSYEVR ! END