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authorjulie <julielangou@users.noreply.github.com>2011-10-06 06:53:11 +0000
committerjulie <julielangou@users.noreply.github.com>2011-10-06 06:53:11 +0000
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+*> \brief \b SSTEBZ
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+* Definition
+* ==========
+*
+* SUBROUTINE SSTEDC( COMPZ, N, D, E, Z, LDZ, WORK, LWORK, IWORK,
+* LIWORK, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER COMPZ
+* INTEGER INFO, LDZ, LIWORK, LWORK, N
+* ..
+* .. Array Arguments ..
+* INTEGER IWORK( * )
+* REAL D( * ), E( * ), WORK( * ), Z( LDZ, * )
+* ..
+*
+* Purpose
+* =======
+*
+*>\details \b Purpose:
+*>\verbatim
+*>
+*> SSTEDC computes all eigenvalues and, optionally, eigenvectors of a
+*> symmetric tridiagonal matrix using the divide and conquer method.
+*> The eigenvectors of a full or band real symmetric matrix can also be
+*> found if SSYTRD or SSPTRD or SSBTRD has been used to reduce this
+*> matrix to tridiagonal form.
+*>
+*> This code makes very mild assumptions about floating point
+*> arithmetic. It will work on machines with a guard digit in
+*> add/subtract, or on those binary machines without guard digits
+*> which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2.
+*> It could conceivably fail on hexadecimal or decimal machines
+*> without guard digits, but we know of none. See SLAED3 for details.
+*>
+*>\endverbatim
+*
+* Arguments
+* =========
+*
+*> \param[in] COMPZ
+*> \verbatim
+*> COMPZ is CHARACTER*1
+*> = 'N': Compute eigenvalues only.
+*> = 'I': Compute eigenvectors of tridiagonal matrix also.
+*> = 'V': Compute eigenvectors of original dense symmetric
+*> matrix also. On entry, Z contains the orthogonal
+*> matrix used to reduce the original matrix to
+*> tridiagonal form.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The dimension of the symmetric tridiagonal matrix. N >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] D
+*> \verbatim
+*> D is REAL array, dimension (N)
+*> On entry, the diagonal elements of the tridiagonal matrix.
+*> On exit, if INFO = 0, the eigenvalues in ascending order.
+*> \endverbatim
+*>
+*> \param[in,out] E
+*> \verbatim
+*> E is REAL array, dimension (N-1)
+*> On entry, the subdiagonal elements of the tridiagonal matrix.
+*> On exit, E has been destroyed.
+*> \endverbatim
+*>
+*> \param[in,out] Z
+*> \verbatim
+*> Z is REAL array, dimension (LDZ,N)
+*> On entry, if COMPZ = 'V', then Z contains the orthogonal
+*> matrix used in the reduction to tridiagonal form.
+*> On exit, if INFO = 0, then if COMPZ = 'V', Z contains the
+*> orthonormal eigenvectors of the original symmetric matrix,
+*> and if COMPZ = 'I', Z contains the orthonormal eigenvectors
+*> of the symmetric tridiagonal matrix.
+*> If COMPZ = 'N', then Z is not referenced.
+*> \endverbatim
+*>
+*> \param[in] LDZ
+*> \verbatim
+*> LDZ is INTEGER
+*> The leading dimension of the array Z. LDZ >= 1.
+*> If eigenvectors are desired, then LDZ >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*> WORK is REAL 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 COMPZ = 'N' or N <= 1 then LWORK must be at least 1.
+*> If COMPZ = 'V' and N > 1 then LWORK must be at least
+*> ( 1 + 3*N + 2*N*lg N + 4*N**2 ),
+*> where lg( N ) = smallest integer k such
+*> that 2**k >= N.
+*> If COMPZ = 'I' and N > 1 then LWORK must be at least
+*> ( 1 + 4*N + N**2 ).
+*> Note that for COMPZ = 'I' or 'V', then if N is less than or
+*> equal to the minimum divide size, usually 25, then LWORK need
+*> only be max(1,2*(N-1)).
+*> \endverbatim
+*> \verbatim
+*> 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 LIWORK.
+*> \endverbatim
+*>
+*> \param[in] LIWORK
+*> \verbatim
+*> LIWORK is INTEGER
+*> The dimension of the array IWORK.
+*> If COMPZ = 'N' or N <= 1 then LIWORK must be at least 1.
+*> If COMPZ = 'V' and N > 1 then LIWORK must be at least
+*> ( 6 + 6*N + 5*N*lg N ).
+*> If COMPZ = 'I' and N > 1 then LIWORK must be at least
+*> ( 3 + 5*N ).
+*> Note that for COMPZ = 'I' or 'V', then if N is less than or
+*> equal to the minimum divide size, usually 25, then LIWORK
+*> need only be 1.
+*> \endverbatim
+*> \verbatim
+*> 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: The algorithm failed to compute an eigenvalue while
+*> working on the submatrix lying in rows and columns
+*> INFO/(N+1) through mod(INFO,N+1).
+*> \endverbatim
+*>
+*
+* Authors
+* =======
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2011
+*
+*> \ingroup auxOTHERcomputational
+*
+*
+* Further Details
+* ===============
+*>\details \b Further \b Details
+*> \verbatim
+*>
+*> Based on contributions by
+*> Jeff Rutter, Computer Science Division, University of California
+*> at Berkeley, USA
+*> Modified by Francoise Tisseur, University of Tennessee.
+*>
+*> \endverbatim
+*>
+* =====================================================================
SUBROUTINE SSTEDC( COMPZ, N, D, E, Z, LDZ, WORK, LWORK, IWORK,
$ LIWORK, INFO )
*
-* -- LAPACK driver routine (version 3.2) --
+* -- LAPACK computational routine (version 3.2) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-* November 2006
+* November 2011
*
* .. Scalar Arguments ..
CHARACTER COMPZ
@@ -15,112 +202,6 @@
REAL D( * ), E( * ), WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
-*
-* SSTEDC computes all eigenvalues and, optionally, eigenvectors of a
-* symmetric tridiagonal matrix using the divide and conquer method.
-* The eigenvectors of a full or band real symmetric matrix can also be
-* found if SSYTRD or SSPTRD or SSBTRD has been used to reduce this
-* matrix to tridiagonal form.
-*
-* This code makes very mild assumptions about floating point
-* arithmetic. It will work on machines with a guard digit in
-* add/subtract, or on those binary machines without guard digits
-* which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2.
-* It could conceivably fail on hexadecimal or decimal machines
-* without guard digits, but we know of none. See SLAED3 for details.
-*
-* Arguments
-* =========
-*
-* COMPZ (input) CHARACTER*1
-* = 'N': Compute eigenvalues only.
-* = 'I': Compute eigenvectors of tridiagonal matrix also.
-* = 'V': Compute eigenvectors of original dense symmetric
-* matrix also. On entry, Z contains the orthogonal
-* matrix used to reduce the original matrix to
-* tridiagonal form.
-*
-* N (input) INTEGER
-* The dimension of the symmetric tridiagonal matrix. N >= 0.
-*
-* D (input/output) REAL array, dimension (N)
-* On entry, the diagonal elements of the tridiagonal matrix.
-* On exit, if INFO = 0, the eigenvalues in ascending order.
-*
-* E (input/output) REAL array, dimension (N-1)
-* On entry, the subdiagonal elements of the tridiagonal matrix.
-* On exit, E has been destroyed.
-*
-* Z (input/output) REAL array, dimension (LDZ,N)
-* On entry, if COMPZ = 'V', then Z contains the orthogonal
-* matrix used in the reduction to tridiagonal form.
-* On exit, if INFO = 0, then if COMPZ = 'V', Z contains the
-* orthonormal eigenvectors of the original symmetric matrix,
-* and if COMPZ = 'I', Z contains the orthonormal eigenvectors
-* of the symmetric tridiagonal matrix.
-* If COMPZ = 'N', then Z is not referenced.
-*
-* LDZ (input) INTEGER
-* The leading dimension of the array Z. LDZ >= 1.
-* If eigenvectors are desired, then LDZ >= max(1,N).
-*
-* WORK (workspace/output) REAL 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.
-* If COMPZ = 'N' or N <= 1 then LWORK must be at least 1.
-* If COMPZ = 'V' and N > 1 then LWORK must be at least
-* ( 1 + 3*N + 2*N*lg N + 4*N**2 ),
-* where lg( N ) = smallest integer k such
-* that 2**k >= N.
-* If COMPZ = 'I' and N > 1 then LWORK must be at least
-* ( 1 + 4*N + N**2 ).
-* Note that for COMPZ = 'I' or 'V', then if N is less than or
-* equal to the minimum divide size, usually 25, then LWORK need
-* only be max(1,2*(N-1)).
-*
-* 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 LIWORK.
-*
-* LIWORK (input) INTEGER
-* The dimension of the array IWORK.
-* If COMPZ = 'N' or N <= 1 then LIWORK must be at least 1.
-* If COMPZ = 'V' and N > 1 then LIWORK must be at least
-* ( 6 + 6*N + 5*N*lg N ).
-* If COMPZ = 'I' and N > 1 then LIWORK must be at least
-* ( 3 + 5*N ).
-* Note that for COMPZ = 'I' or 'V', then if N is less than or
-* equal to the minimum divide size, usually 25, then LIWORK
-* need only be 1.
-*
-* 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: The algorithm failed to compute an eigenvalue while
-* working on the submatrix lying in rows and columns
-* INFO/(N+1) through mod(INFO,N+1).
-*
-* Further Details
-* ===============
-*
-* Based on contributions by
-* Jeff Rutter, Computer Science Division, University of California
-* at Berkeley, USA
-* Modified by Francoise Tisseur, University of Tennessee.
-*
* =====================================================================
*
* .. Parameters ..