--- rpl/lapack/lapack/dsyevr.f 2010/04/21 13:45:25 1.2
+++ rpl/lapack/lapack/dsyevr.f 2012/12/14 14:22:40 1.13
@@ -1,11 +1,334 @@
+*> \brief DSYEVR computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download DSYEVR + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \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 SSTEIN 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
+*> \endverbatim
+*>
+*> \param[in] VU
+*> \verbatim
+*> VU is DOUBLE PRECISION
+*> If RANGE='V', the lower and upper bounds 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
+*> \endverbatim
+*>
+*> \param[in] IU
+*> \verbatim
+*> IU is INTEGER
+*> If RANGE='I', the indices (in ascending order) of the
+*> smallest and largest eigenvalues 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 ).
+*> 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 September 2012
+*
+*> \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 3.2) --
+* -- LAPACK driver routine (version 3.4.2) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-* November 2006
+* September 2012
*
* .. Scalar Arguments ..
CHARACTER JOBZ, RANGE, UPLO
@@ -17,214 +340,6 @@
DOUBLE PRECISION A( LDA, * ), W( * ), WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
-*
-* 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 SSTEIN 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.
-*
-* Arguments
-* =========
-*
-* JOBZ (input) CHARACTER*1
-* = 'N': Compute eigenvalues only;
-* = 'V': Compute eigenvalues and eigenvectors.
-*
-* RANGE (input) 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
-*
-* UPLO (input) CHARACTER*1
-* = 'U': Upper triangle of A is stored;
-* = 'L': Lower triangle of A is stored.
-*
-* N (input) INTEGER
-* The order of the matrix A. N >= 0.
-*
-* A (input/output) 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.
-*
-* LDA (input) INTEGER
-* The leading dimension of the array A. LDA >= max(1,N).
-*
-* VL (input) DOUBLE PRECISION
-* VU (input) DOUBLE PRECISION
-* If RANGE='V', the lower and upper bounds of the interval to
-* be searched for eigenvalues. VL < VU.
-* Not referenced if RANGE = 'A' or 'I'.
-*
-* IL (input) INTEGER
-* IU (input) INTEGER
-* If RANGE='I', the indices (in ascending order) of the
-* smallest and largest eigenvalues 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'.
-*
-* ABSTOL (input) 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.
-*
-* M (output) INTEGER
-* The total number of eigenvalues found. 0 <= M <= N.
-* If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
-*
-* W (output) DOUBLE PRECISION array, dimension (N)
-* The first M elements contain the selected eigenvalues in
-* ascending order.
-*
-* Z (output) 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.
-*
-* LDZ (input) INTEGER
-* The leading dimension of the array Z. LDZ >= 1, and if
-* JOBZ = 'V', LDZ >= max(1,N).
-*
-* ISUPPZ (output) 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 ).
-********** Implemented only for RANGE = 'A' or 'I' and IU - IL = N - 1
-*
-* WORK (workspace/output) DOUBLE PRECISION 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. 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.
-*
-* IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
-* On exit, if INFO = 0, IWORK(1) returns the optimal LWORK.
-*
-* LIWORK (input) 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.
-*
-* INFO (output) INTEGER
-* = 0: successful exit
-* < 0: if INFO = -i, the i-th argument had an illegal value
-* > 0: Internal error
-*
-* Further Details
-* ===============
-*
-* Based on contributions by
-* Inderjit Dhillon, IBM Almaden, USA
-* Osni Marques, LBNL/NERSC, USA
-* Ken Stanley, Computer Science Division, University of
-* California at Berkeley, USA
-* Jason Riedy, Computer Science Division, University of
-* California at Berkeley, USA
-*
* =====================================================================
*
* .. Parameters ..
@@ -339,8 +454,11 @@
W( 1 ) = A( 1, 1 )
END IF
END IF
- IF( WANTZ )
- $ Z( 1, 1 ) = ONE
+ IF( WANTZ ) THEN
+ Z( 1, 1 ) = ONE
+ ISUPPZ( 1 ) = 1
+ ISUPPZ( 2 ) = 1
+ END IF
RETURN
END IF
*
@@ -357,8 +475,10 @@
*
ISCALE = 0
ABSTLL = ABSTOL
- VLL = VL
- VUU = VU
+ 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
@@ -419,7 +539,7 @@
* returns INFO > 0.
INDIFL = INDISP + N
* INDIWO is the offset of the remaining integer workspace.
- INDIWO = INDISP + N
+ INDIWO = INDIFL + N
*
* Call DSYTRD to reduce symmetric matrix to tridiagonal form.