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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> SSTEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices</b>
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+* Definition
+* ==========
+*
+* SUBROUTINE SSTEVX( JOBZ, RANGE, N, D, E, VL, VU, IL, IU, ABSTOL,
+* M, W, Z, LDZ, WORK, IWORK, IFAIL, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER JOBZ, RANGE
+* INTEGER IL, INFO, IU, LDZ, M, N
+* REAL ABSTOL, VL, VU
+* ..
+* .. Array Arguments ..
+* INTEGER IFAIL( * ), IWORK( * )
+* REAL D( * ), E( * ), W( * ), WORK( * ), Z( LDZ, * )
+* ..
+*
+* Purpose
+* =======
+*
+*>\details \b Purpose:
+*>\verbatim
+*>
+*> SSTEVX computes selected eigenvalues and, optionally, eigenvectors
+*> of a real symmetric tridiagonal matrix A. Eigenvalues and
+*> eigenvectors can be selected by specifying either a range of values
+*> or a range of indices for the desired eigenvalues.
+*>
+*>\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.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The order of the matrix. N >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] D
+*> \verbatim
+*> D is REAL array, dimension (N)
+*> On entry, the n diagonal elements of the tridiagonal matrix
+*> A.
+*> On exit, D may be multiplied by a constant factor chosen
+*> to avoid over/underflow in computing the eigenvalues.
+*> \endverbatim
+*>
+*> \param[in,out] E
+*> \verbatim
+*> E is REAL array, dimension (max(1,N-1))
+*> On entry, the (n-1) subdiagonal elements of the tridiagonal
+*> matrix A in elements 1 to N-1 of E.
+*> On exit, E may be multiplied by a constant factor chosen
+*> to avoid over/underflow in computing the eigenvalues.
+*> \endverbatim
+*>
+*> \param[in] VL
+*> \verbatim
+*> VL is REAL
+*> \endverbatim
+*>
+*> \param[in] VU
+*> \verbatim
+*> VU is REAL
+*> 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 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
+*> \endverbatim
+*> \verbatim
+*> ABSTOL + EPS * max( |a|,|b| ) ,
+*> \endverbatim
+*> \verbatim
+*> 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.
+*> \endverbatim
+*> \verbatim
+*> Eigenvalues will be computed most accurately when ABSTOL is
+*> set to twice the underflow threshold 2*SLAMCH('S'), not zero.
+*> If this routine returns with INFO>0, indicating that some
+*> eigenvectors did not converge, try setting ABSTOL to
+*> 2*SLAMCH('S').
+*> \endverbatim
+*> \verbatim
+*> See "Computing Small Singular Values of Bidiagonal Matrices
+*> with Guaranteed High Relative Accuracy," by Demmel and
+*> Kahan, LAPACK Working Note #3.
+*> \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 REAL 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 an eigenvector fails to converge (INFO > 0), then that
+*> column of Z contains the latest approximation to the
+*> eigenvector, and the index of the eigenvector is returned
+*> in IFAIL. 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] WORK
+*> \verbatim
+*> WORK is REAL array, dimension (5*N)
+*> \endverbatim
+*>
+*> \param[out] IWORK
+*> \verbatim
+*> IWORK is INTEGER array, dimension (5*N)
+*> \endverbatim
+*>
+*> \param[out] IFAIL
+*> \verbatim
+*> IFAIL is INTEGER array, dimension (N)
+*> If JOBZ = 'V', then if INFO = 0, the first M elements of
+*> IFAIL are zero. If INFO > 0, then IFAIL contains the
+*> indices of the eigenvectors that failed to converge.
+*> If JOBZ = 'N', then IFAIL is not referenced.
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*> INFO is INTEGER
+*> = 0: successful exit
+*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> > 0: if INFO = i, then i eigenvectors failed to converge.
+*> Their indices are stored in array IFAIL.
+*> \endverbatim
+*>
+*
+* Authors
+* =======
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2011
+*
+*> \ingroup realOTHEReigen
+*
+* =====================================================================
SUBROUTINE SSTEVX( JOBZ, RANGE, N, D, E, VL, VU, IL, IU, ABSTOL,
$ M, W, Z, LDZ, WORK, IWORK, IFAIL, INFO )
*
-* -- LAPACK driver routine (version 3.2) --
+* -- LAPACK eigen 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 JOBZ, RANGE
@@ -16,121 +231,6 @@
REAL D( * ), E( * ), W( * ), WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
-*
-* SSTEVX computes selected eigenvalues and, optionally, eigenvectors
-* of a real symmetric tridiagonal matrix A. Eigenvalues and
-* eigenvectors can be selected by specifying either a range of values
-* or a range of indices for the desired eigenvalues.
-*
-* 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.
-*
-* N (input) INTEGER
-* The order of the matrix. N >= 0.
-*
-* D (input/output) REAL array, dimension (N)
-* On entry, the n diagonal elements of the tridiagonal matrix
-* A.
-* On exit, D may be multiplied by a constant factor chosen
-* to avoid over/underflow in computing the eigenvalues.
-*
-* E (input/output) REAL array, dimension (max(1,N-1))
-* On entry, the (n-1) subdiagonal elements of the tridiagonal
-* matrix A in elements 1 to N-1 of E.
-* On exit, E may be multiplied by a constant factor chosen
-* to avoid over/underflow in computing the eigenvalues.
-*
-* VL (input) REAL
-*
-* VU (input) REAL
-* 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) 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.
-*
-* Eigenvalues will be computed most accurately when ABSTOL is
-* set to twice the underflow threshold 2*SLAMCH('S'), not zero.
-* If this routine returns with INFO>0, indicating that some
-* eigenvectors did not converge, try setting ABSTOL to
-* 2*SLAMCH('S').
-*
-* See "Computing Small Singular Values of Bidiagonal Matrices
-* with Guaranteed High Relative Accuracy," by Demmel and
-* Kahan, LAPACK Working Note #3.
-*
-* 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) REAL array, dimension (N)
-* The first M elements contain the selected eigenvalues in
-* ascending order.
-*
-* Z (output) REAL 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 an eigenvector fails to converge (INFO > 0), then that
-* column of Z contains the latest approximation to the
-* eigenvector, and the index of the eigenvector is returned
-* in IFAIL. 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.
-*
-* LDZ (input) INTEGER
-* The leading dimension of the array Z. LDZ >= 1, and if
-* JOBZ = 'V', LDZ >= max(1,N).
-*
-* WORK (workspace) REAL array, dimension (5*N)
-*
-* IWORK (workspace) INTEGER array, dimension (5*N)
-*
-* IFAIL (output) INTEGER array, dimension (N)
-* If JOBZ = 'V', then if INFO = 0, the first M elements of
-* IFAIL are zero. If INFO > 0, then IFAIL contains the
-* indices of the eigenvectors that failed to converge.
-* If JOBZ = 'N', then IFAIL is not referenced.
-*
-* INFO (output) INTEGER
-* = 0: successful exit
-* < 0: if INFO = -i, the i-th argument had an illegal value
-* > 0: if INFO = i, then i eigenvectors failed to converge.
-* Their indices are stored in array IFAIL.
-*
* =====================================================================
*
* .. Parameters ..