*> \brief CHEEVR_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices * * @generated from zheevr_2stage.f, fortran z -> c, Sat Nov 5 23:18:11 2016 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download CHEEVR_2STAGE + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE CHEEVR_2STAGE( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, * IL, IU, ABSTOL, M, W, Z, LDZ, ISUPPZ, * WORK, LWORK, RWORK, LRWORK, IWORK, * LIWORK, INFO ) * * IMPLICIT NONE * * .. Scalar Arguments .. * CHARACTER JOBZ, RANGE, UPLO * INTEGER IL, INFO, IU, LDA, LDZ, LIWORK, LRWORK, LWORK, * $ M, N * REAL ABSTOL, VL, VU * .. * .. Array Arguments .. * INTEGER ISUPPZ( * ), IWORK( * ) * REAL RWORK( * ), W( * ) * COMPLEX A( LDA, * ), WORK( * ), Z( LDZ, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> CHEEVR_2STAGE computes selected eigenvalues and, optionally, eigenvectors *> of a complex Hermitian matrix A using the 2stage technique for *> the reduction to tridiagonal. Eigenvalues and eigenvectors can *> be selected by specifying either a range of values or a range of *> indices for the desired eigenvalues. *> *> CHEEVR_2STAGE first reduces the matrix A to tridiagonal form T with a call *> to CHETRD. Then, whenever possible, CHEEVR_2STAGE calls CSTEMR to compute *> eigenspectrum using Relatively Robust Representations. CSTEMR *> 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 : CHEEVR_2STAGE calls CSTEMR when the full spectrum is requested *> on machines which conform to the ieee-754 floating point standard. *> CHEEVR_2STAGE calls SSTEBZ and CSTEIN on non-ieee machines and *> when partial spectrum requests are made. *> *> Normal execution of CSTEMR 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. *> Not available in this release. *> \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, SSTEBZ and *> CSTEIN 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 COMPLEX array, dimension (LDA, N) *> On entry, the Hermitian 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 REAL *> 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 REAL *> 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 REAL *> 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 *> SLAMCH( '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 REAL array, dimension (N) *> The first M elements contain the selected eigenvalues in *> ascending order. *> \endverbatim *> *> \param[out] Z *> \verbatim *> Z is COMPLEX 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. *> \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 CSTEMR (tridiagonal *> matrix). The support of the eigenvectors of A is typically *> 1:N because of the unitary transformations applied by CUNMTR. *> Implemented only for RANGE = 'A' or 'I' and IU - IL = N - 1 *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX 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. *> If JOBZ = 'N' and N > 1, LWORK must be queried. *> LWORK = MAX(1, 26*N, dimension) where *> dimension = max(stage1,stage2) + (KD+1)*N + N *> = N*KD + N*max(KD+1,FACTOPTNB) *> + max(2*KD*KD, KD*NTHREADS) *> + (KD+1)*N + N *> where KD is the blocking size of the reduction, *> FACTOPTNB is the blocking used by the QR or LQ *> algorithm, usually FACTOPTNB=128 is a good choice *> NTHREADS is the number of threads used when *> openMP compilation is enabled, otherwise =1. *> If JOBZ = 'V' and N > 1, LWORK must be queried. Not yet available *> *> 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. *> \endverbatim *> *> \param[out] RWORK *> \verbatim *> RWORK is REAL array, dimension (MAX(1,LRWORK)) *> On exit, if INFO = 0, RWORK(1) returns the optimal *> (and minimal) LRWORK. *> \endverbatim *> *> \param[in] LRWORK *> \verbatim *> LRWORK is INTEGER *> The length of the array RWORK. LRWORK >= max(1,24*N). *> *> 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. *> \endverbatim *> *> \param[out] IWORK *> \verbatim *> IWORK is INTEGER array, dimension (MAX(1,LIWORK)) *> On exit, if INFO = 0, IWORK(1) returns the optimal *> (and minimal) LIWORK. *> \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 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. *> \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 complexHEeigen * *> \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 *> *> \par Further Details: * ===================== *> *> \verbatim *> *> All details about the 2stage techniques are available in: *> *> Azzam Haidar, Hatem Ltaief, and Jack Dongarra. *> Parallel reduction to condensed forms for symmetric eigenvalue problems *> using aggregated fine-grained and memory-aware kernels. In Proceedings *> of 2011 International Conference for High Performance Computing, *> Networking, Storage and Analysis (SC '11), New York, NY, USA, *> Article 8 , 11 pages. *> http://doi.acm.org/10.1145/2063384.2063394 *> *> A. Haidar, J. Kurzak, P. Luszczek, 2013. *> An improved parallel singular value algorithm and its implementation *> for multicore hardware, In Proceedings of 2013 International Conference *> for High Performance Computing, Networking, Storage and Analysis (SC '13). *> Denver, Colorado, USA, 2013. *> Article 90, 12 pages. *> http://doi.acm.org/10.1145/2503210.2503292 *> *> A. Haidar, R. Solca, S. Tomov, T. Schulthess and J. Dongarra. *> A novel hybrid CPU-GPU generalized eigensolver for electronic structure *> calculations based on fine-grained memory aware tasks. *> International Journal of High Performance Computing Applications. *> Volume 28 Issue 2, Pages 196-209, May 2014. *> http://hpc.sagepub.com/content/28/2/196 *> *> \endverbatim * * ===================================================================== SUBROUTINE CHEEVR_2STAGE( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, $ IL, IU, ABSTOL, M, W, Z, LDZ, ISUPPZ, $ WORK, LWORK, RWORK, LRWORK, IWORK, $ LIWORK, INFO ) * IMPLICIT NONE * * -- LAPACK driver routine (version 3.8.0) -- * -- 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, LRWORK, LWORK, $ M, N REAL ABSTOL, VL, VU * .. * .. Array Arguments .. INTEGER ISUPPZ( * ), IWORK( * ) REAL RWORK( * ), W( * ) COMPLEX A( LDA, * ), WORK( * ), Z( LDZ, * ) * .. * * ===================================================================== * * .. Parameters .. REAL ZERO, ONE, TWO PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0, TWO = 2.0E+0 ) * .. * .. Local Scalars .. LOGICAL ALLEIG, INDEIG, LOWER, LQUERY, TEST, VALEIG, $ WANTZ, TRYRAC CHARACTER ORDER INTEGER I, IEEEOK, IINFO, IMAX, INDIBL, INDIFL, INDISP, $ INDIWO, INDRD, INDRDD, INDRE, INDREE, INDRWK, $ INDTAU, INDWK, INDWKN, ISCALE, ITMP1, J, JJ, $ LIWMIN, LLWORK, LLRWORK, LLWRKN, LRWMIN, $ LWMIN, NSPLIT, LHTRD, LWTRD, KD, IB, INDHOUS REAL ABSTLL, ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, $ SIGMA, SMLNUM, TMP1, VLL, VUU * .. * .. External Functions .. LOGICAL LSAME INTEGER ILAENV, ILAENV2STAGE REAL SLAMCH, CLANSY EXTERNAL LSAME, SLAMCH, CLANSY, ILAENV, ILAENV2STAGE * .. * .. External Subroutines .. EXTERNAL SCOPY, SSCAL, SSTEBZ, SSTERF, XERBLA, CSSCAL, $ CHETRD_2STAGE, CSTEMR, CSTEIN, CSWAP, CUNMTR * .. * .. Intrinsic Functions .. INTRINSIC REAL, MAX, MIN, SQRT * .. * .. Executable Statements .. * * Test the input parameters. * IEEEOK = ILAENV( 10, 'CHEEVR', '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. ( LRWORK.EQ.-1 ) .OR. $ ( LIWORK.EQ.-1 ) ) * KD = ILAENV2STAGE( 1, 'CHETRD_2STAGE', JOBZ, N, -1, -1, -1 ) IB = ILAENV2STAGE( 2, 'CHETRD_2STAGE', JOBZ, N, KD, -1, -1 ) LHTRD = ILAENV2STAGE( 3, 'CHETRD_2STAGE', JOBZ, N, KD, IB, -1 ) LWTRD = ILAENV2STAGE( 4, 'CHETRD_2STAGE', JOBZ, N, KD, IB, -1 ) LWMIN = N + LHTRD + LWTRD LRWMIN = MAX( 1, 24*N ) LIWMIN = MAX( 1, 10*N ) * INFO = 0 IF( .NOT.( 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 END IF 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 = -18 ELSE IF( LRWORK.LT.LRWMIN .AND. .NOT.LQUERY ) THEN INFO = -20 ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN INFO = -22 END IF END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'CHEEVR_2STAGE', -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 ) = 2 IF( ALLEIG .OR. INDEIG ) THEN M = 1 W( 1 ) = REAL( A( 1, 1 ) ) ELSE IF( VL.LT.REAL( A( 1, 1 ) ) .AND. VU.GE.REAL( A( 1, 1 ) ) ) $ THEN M = 1 W( 1 ) = REAL( 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 = SLAMCH( 'Safe minimum' ) EPS = SLAMCH( '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 = CLANSY( 'M', UPLO, N, A, LDA, RWORK ) 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 CSSCAL( N-J+1, SIGMA, A( J, J ), 1 ) 10 CONTINUE ELSE DO 20 J = 1, N CALL CSSCAL( 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 SSTERF or CSTEMR fail. * WORK(INDTAU:INDTAU+N-1) stores the complex scalar factors of the * elementary reflectors used in CHETRD. INDTAU = 1 * INDWK is the starting offset of the remaining complex workspace, * and LLWORK is the remaining complex workspace size. INDHOUS = INDTAU + N INDWK = INDHOUS + LHTRD LLWORK = LWORK - INDWK + 1 * RWORK(INDRD:INDRD+N-1) stores the real tridiagonal's diagonal * entries. INDRD = 1 * RWORK(INDRE:INDRE+N-1) stores the off-diagonal entries of the * tridiagonal matrix from CHETRD. INDRE = INDRD + N * RWORK(INDRDD:INDRDD+N-1) is a copy of the diagonal entries over * -written by CSTEMR (the SSTERF path copies the diagonal to W). INDRDD = INDRE + N * RWORK(INDREE:INDREE+N-1) is a copy of the off-diagonal entries over * -written while computing the eigenvalues in SSTERF and CSTEMR. INDREE = INDRDD + N * INDRWK is the starting offset of the left-over real workspace, and * LLRWORK is the remaining workspace size. INDRWK = INDREE + N LLRWORK = LRWORK - INDRWK + 1 * IWORK(INDIBL:INDIBL+M-1) corresponds to IBLOCK in SSTEBZ and * stores the block indices of each of the M<=N eigenvalues. INDIBL = 1 * IWORK(INDISP:INDISP+NSPLIT-1) corresponds to ISPLIT in SSTEBZ 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 * CSTEIN. 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 CHETRD_2STAGE to reduce Hermitian matrix to tridiagonal form. * CALL CHETRD_2STAGE( JOBZ, UPLO, N, A, LDA, RWORK( INDRD ), $ RWORK( INDRE ), WORK( INDTAU ), $ WORK( INDHOUS ), LHTRD, $ WORK( INDWK ), LLWORK, IINFO ) * * If all eigenvalues are desired * then call SSTERF or CSTEMR and CUNMTR. * TEST = .FALSE. IF( INDEIG ) THEN IF( IL.EQ.1 .AND. IU.EQ.N ) THEN TEST = .TRUE. END IF END IF IF( ( ALLEIG.OR.TEST ) .AND. ( IEEEOK.EQ.1 ) ) THEN IF( .NOT.WANTZ ) THEN CALL SCOPY( N, RWORK( INDRD ), 1, W, 1 ) CALL SCOPY( N-1, RWORK( INDRE ), 1, RWORK( INDREE ), 1 ) CALL SSTERF( N, W, RWORK( INDREE ), INFO ) ELSE CALL SCOPY( N-1, RWORK( INDRE ), 1, RWORK( INDREE ), 1 ) CALL SCOPY( N, RWORK( INDRD ), 1, RWORK( INDRDD ), 1 ) * IF (ABSTOL .LE. TWO*N*EPS) THEN TRYRAC = .TRUE. ELSE TRYRAC = .FALSE. END IF CALL CSTEMR( JOBZ, 'A', N, RWORK( INDRDD ), $ RWORK( INDREE ), VL, VU, IL, IU, M, W, $ Z, LDZ, N, ISUPPZ, TRYRAC, $ RWORK( INDRWK ), LLRWORK, $ IWORK, LIWORK, INFO ) * * Apply unitary matrix used in reduction to tridiagonal * form to eigenvectors returned by CSTEMR. * IF( WANTZ .AND. INFO.EQ.0 ) THEN INDWKN = INDWK LLWRKN = LWORK - INDWKN + 1 CALL CUNMTR( 'L', UPLO, 'N', N, M, A, LDA, $ WORK( INDTAU ), Z, LDZ, WORK( INDWKN ), $ LLWRKN, IINFO ) END IF END IF * * IF( INFO.EQ.0 ) THEN M = N GO TO 30 END IF INFO = 0 END IF * * Otherwise, call SSTEBZ and, if eigenvectors are desired, CSTEIN. * Also call SSTEBZ and CSTEIN if CSTEMR fails. * IF( WANTZ ) THEN ORDER = 'B' ELSE ORDER = 'E' END IF CALL SSTEBZ( RANGE, ORDER, N, VLL, VUU, IL, IU, ABSTLL, $ RWORK( INDRD ), RWORK( INDRE ), M, NSPLIT, W, $ IWORK( INDIBL ), IWORK( INDISP ), RWORK( INDRWK ), $ IWORK( INDIWO ), INFO ) * IF( WANTZ ) THEN CALL CSTEIN( N, RWORK( INDRD ), RWORK( INDRE ), M, W, $ IWORK( INDIBL ), IWORK( INDISP ), Z, LDZ, $ RWORK( INDRWK ), IWORK( INDIWO ), IWORK( INDIFL ), $ INFO ) * * Apply unitary matrix used in reduction to tridiagonal * form to eigenvectors returned by CSTEIN. * INDWKN = INDWK LLWRKN = LWORK - INDWKN + 1 CALL CUNMTR( '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. * 30 CONTINUE IF( ISCALE.EQ.1 ) THEN IF( INFO.EQ.0 ) THEN IMAX = M ELSE IMAX = INFO - 1 END IF CALL SSCAL( IMAX, ONE / SIGMA, W, 1 ) END IF * * If eigenvalues are not in order, then sort them, along with * eigenvectors. * 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 ITMP1 = IWORK( INDIBL+I-1 ) W( I ) = W( J ) IWORK( INDIBL+I-1 ) = IWORK( INDIBL+J-1 ) W( J ) = TMP1 IWORK( INDIBL+J-1 ) = ITMP1 CALL CSWAP( N, Z( 1, I ), 1, Z( 1, J ), 1 ) END IF 50 CONTINUE END IF * * Set WORK(1) to optimal workspace size. * WORK( 1 ) = LWMIN RWORK( 1 ) = LRWMIN IWORK( 1 ) = LIWMIN * RETURN * * End of CHEEVR_2STAGE * END