--- rpl/lapack/lapack/dsbevx.f 2010/12/21 13:53:37 1.7
+++ rpl/lapack/lapack/dsbevx.f 2016/08/27 15:34:37 1.14
@@ -1,11 +1,274 @@
+*> \brief DSBEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download DSBEVX + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE DSBEVX( JOBZ, RANGE, UPLO, N, KD, AB, LDAB, Q, LDQ, VL,
+* VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, IWORK,
+* IFAIL, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER JOBZ, RANGE, UPLO
+* INTEGER IL, INFO, IU, KD, LDAB, LDQ, LDZ, M, N
+* DOUBLE PRECISION ABSTOL, VL, VU
+* ..
+* .. Array Arguments ..
+* INTEGER IFAIL( * ), IWORK( * )
+* DOUBLE PRECISION AB( LDAB, * ), Q( LDQ, * ), W( * ), WORK( * ),
+* $ Z( LDZ, * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> DSBEVX computes selected eigenvalues and, optionally, eigenvectors
+*> of a real symmetric band 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] 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] KD
+*> \verbatim
+*> KD is INTEGER
+*> The number of superdiagonals of the matrix A if UPLO = 'U',
+*> or the number of subdiagonals if UPLO = 'L'. KD >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] AB
+*> \verbatim
+*> AB is DOUBLE PRECISION array, dimension (LDAB, N)
+*> On entry, the upper or lower triangle of the symmetric band
+*> matrix A, stored in the first KD+1 rows of the array. The
+*> j-th column of A is stored in the j-th column of the array AB
+*> as follows:
+*> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
+*> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
+*>
+*> On exit, AB is overwritten by values generated during the
+*> reduction to tridiagonal form. If UPLO = 'U', the first
+*> superdiagonal and the diagonal of the tridiagonal matrix T
+*> are returned in rows KD and KD+1 of AB, and if UPLO = 'L',
+*> the diagonal and first subdiagonal of T are returned in the
+*> first two rows of AB.
+*> \endverbatim
+*>
+*> \param[in] LDAB
+*> \verbatim
+*> LDAB is INTEGER
+*> The leading dimension of the array AB. LDAB >= KD + 1.
+*> \endverbatim
+*>
+*> \param[out] Q
+*> \verbatim
+*> Q is DOUBLE PRECISION array, dimension (LDQ, N)
+*> If JOBZ = 'V', the N-by-N orthogonal matrix used in the
+*> reduction to tridiagonal form.
+*> If JOBZ = 'N', the array Q is not referenced.
+*> \endverbatim
+*>
+*> \param[in] LDQ
+*> \verbatim
+*> LDQ is INTEGER
+*> The leading dimension of the array Q. If JOBZ = 'V', then
+*> LDQ >= 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 AB to tridiagonal form.
+*>
+*> Eigenvalues will be computed most accurately when ABSTOL is
+*> set to twice the underflow threshold 2*DLAMCH('S'), not zero.
+*> If this routine returns with INFO>0, indicating that some
+*> eigenvectors did not converge, try setting ABSTOL to
+*> 2*DLAMCH('S').
+*>
+*> 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 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 an eigenvector fails to converge, 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 DOUBLE PRECISION array, dimension (7*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 June 2016
+*
+*> \ingroup doubleOTHEReigen
+*
+* =====================================================================
SUBROUTINE DSBEVX( JOBZ, RANGE, UPLO, N, KD, AB, LDAB, Q, LDQ, VL,
$ VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, IWORK,
$ IFAIL, INFO )
*
-* -- LAPACK driver routine (version 3.2) --
+* -- LAPACK driver routine (version 3.6.1) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-* November 2006
+* June 2016
*
* .. Scalar Arguments ..
CHARACTER JOBZ, RANGE, UPLO
@@ -18,142 +281,6 @@
$ Z( LDZ, * )
* ..
*
-* Purpose
-* =======
-*
-* DSBEVX computes selected eigenvalues and, optionally, eigenvectors
-* of a real symmetric band 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.
-*
-* 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.
-*
-* KD (input) INTEGER
-* The number of superdiagonals of the matrix A if UPLO = 'U',
-* or the number of subdiagonals if UPLO = 'L'. KD >= 0.
-*
-* AB (input/output) DOUBLE PRECISION array, dimension (LDAB, N)
-* On entry, the upper or lower triangle of the symmetric band
-* matrix A, stored in the first KD+1 rows of the array. The
-* j-th column of A is stored in the j-th column of the array AB
-* as follows:
-* if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
-* if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
-*
-* On exit, AB is overwritten by values generated during the
-* reduction to tridiagonal form. If UPLO = 'U', the first
-* superdiagonal and the diagonal of the tridiagonal matrix T
-* are returned in rows KD and KD+1 of AB, and if UPLO = 'L',
-* the diagonal and first subdiagonal of T are returned in the
-* first two rows of AB.
-*
-* LDAB (input) INTEGER
-* The leading dimension of the array AB. LDAB >= KD + 1.
-*
-* Q (output) DOUBLE PRECISION array, dimension (LDQ, N)
-* If JOBZ = 'V', the N-by-N orthogonal matrix used in the
-* reduction to tridiagonal form.
-* If JOBZ = 'N', the array Q is not referenced.
-*
-* LDQ (input) INTEGER
-* The leading dimension of the array Q. If JOBZ = 'V', then
-* LDQ >= 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 AB to tridiagonal form.
-*
-* Eigenvalues will be computed most accurately when ABSTOL is
-* set to twice the underflow threshold 2*DLAMCH('S'), not zero.
-* If this routine returns with INFO>0, indicating that some
-* eigenvectors did not converge, try setting ABSTOL to
-* 2*DLAMCH('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) 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 an eigenvector fails to converge, 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) DOUBLE PRECISION array, dimension (7*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 ..