--- rpl/lapack/lapack/zhbgvd.f 2011/07/22 07:38:15 1.8
+++ rpl/lapack/lapack/zhbgvd.f 2011/11/21 20:43:11 1.9
@@ -1,12 +1,261 @@
+*> \brief \b ZHBGST
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download ZHBGVD + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE ZHBGVD( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W,
+* Z, LDZ, WORK, LWORK, RWORK, LRWORK, IWORK,
+* LIWORK, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER JOBZ, UPLO
+* INTEGER INFO, KA, KB, LDAB, LDBB, LDZ, LIWORK, LRWORK,
+* $ LWORK, N
+* ..
+* .. Array Arguments ..
+* INTEGER IWORK( * )
+* DOUBLE PRECISION RWORK( * ), W( * )
+* COMPLEX*16 AB( LDAB, * ), BB( LDBB, * ), WORK( * ),
+* $ Z( LDZ, * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> ZHBGVD computes all the eigenvalues, and optionally, the eigenvectors
+*> of a complex generalized Hermitian-definite banded eigenproblem, of
+*> the form A*x=(lambda)*B*x. Here A and B are assumed to be Hermitian
+*> and banded, and B is also positive definite. If eigenvectors are
+*> desired, it uses a divide and conquer algorithm.
+*>
+*> The divide and conquer algorithm 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.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] JOBZ
+*> \verbatim
+*> JOBZ is CHARACTER*1
+*> = 'N': Compute eigenvalues only;
+*> = 'V': Compute eigenvalues and eigenvectors.
+*> \endverbatim
+*>
+*> \param[in] UPLO
+*> \verbatim
+*> UPLO is CHARACTER*1
+*> = 'U': Upper triangles of A and B are stored;
+*> = 'L': Lower triangles of A and B are stored.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The order of the matrices A and B. N >= 0.
+*> \endverbatim
+*>
+*> \param[in] KA
+*> \verbatim
+*> KA is INTEGER
+*> The number of superdiagonals of the matrix A if UPLO = 'U',
+*> or the number of subdiagonals if UPLO = 'L'. KA >= 0.
+*> \endverbatim
+*>
+*> \param[in] KB
+*> \verbatim
+*> KB is INTEGER
+*> The number of superdiagonals of the matrix B if UPLO = 'U',
+*> or the number of subdiagonals if UPLO = 'L'. KB >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] AB
+*> \verbatim
+*> AB is COMPLEX*16 array, dimension (LDAB, N)
+*> On entry, the upper or lower triangle of the Hermitian band
+*> matrix A, stored in the first ka+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(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j;
+*> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka).
+*>
+*> On exit, the contents of AB are destroyed.
+*> \endverbatim
+*>
+*> \param[in] LDAB
+*> \verbatim
+*> LDAB is INTEGER
+*> The leading dimension of the array AB. LDAB >= KA+1.
+*> \endverbatim
+*>
+*> \param[in,out] BB
+*> \verbatim
+*> BB is COMPLEX*16 array, dimension (LDBB, N)
+*> On entry, the upper or lower triangle of the Hermitian band
+*> matrix B, stored in the first kb+1 rows of the array. The
+*> j-th column of B is stored in the j-th column of the array BB
+*> as follows:
+*> if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j;
+*> if UPLO = 'L', BB(1+i-j,j) = B(i,j) for j<=i<=min(n,j+kb).
+*>
+*> On exit, the factor S from the split Cholesky factorization
+*> B = S**H*S, as returned by ZPBSTF.
+*> \endverbatim
+*>
+*> \param[in] LDBB
+*> \verbatim
+*> LDBB is INTEGER
+*> The leading dimension of the array BB. LDBB >= KB+1.
+*> \endverbatim
+*>
+*> \param[out] W
+*> \verbatim
+*> W is DOUBLE PRECISION array, dimension (N)
+*> If INFO = 0, the eigenvalues in ascending order.
+*> \endverbatim
+*>
+*> \param[out] Z
+*> \verbatim
+*> Z is COMPLEX*16 array, dimension (LDZ, N)
+*> If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
+*> eigenvectors, with the i-th column of Z holding the
+*> eigenvector associated with W(i). The eigenvectors are
+*> normalized so that Z**H*B*Z = I.
+*> If JOBZ = 'N', then Z is not referenced.
+*> \endverbatim
+*>
+*> \param[in] LDZ
+*> \verbatim
+*> LDZ is INTEGER
+*> The leading dimension of the array Z. LDZ >= 1, and if
+*> JOBZ = 'V', LDZ >= N.
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*> WORK is COMPLEX*16 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 N <= 1, LWORK >= 1.
+*> If JOBZ = 'N' and N > 1, LWORK >= N.
+*> If JOBZ = 'V' and N > 1, LWORK >= 2*N**2.
+*>
+*> 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 DOUBLE PRECISION array, dimension (MAX(1,LRWORK))
+*> On exit, if INFO=0, RWORK(1) returns the optimal LRWORK.
+*> \endverbatim
+*>
+*> \param[in] LRWORK
+*> \verbatim
+*> LRWORK is INTEGER
+*> The dimension of array RWORK.
+*> If N <= 1, LRWORK >= 1.
+*> If JOBZ = 'N' and N > 1, LRWORK >= N.
+*> If JOBZ = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2.
+*>
+*> 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 LIWORK.
+*> \endverbatim
+*>
+*> \param[in] LIWORK
+*> \verbatim
+*> LIWORK is INTEGER
+*> The dimension of array IWORK.
+*> If JOBZ = 'N' or N <= 1, LIWORK >= 1.
+*> If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*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: if INFO = i, and i is:
+*> <= N: the algorithm failed to converge:
+*> i off-diagonal elements of an intermediate
+*> tridiagonal form did not converge to zero;
+*> > N: if INFO = N + i, for 1 <= i <= N, then ZPBSTF
+*> returned INFO = i: B is not positive definite.
+*> The factorization of B could not be completed and
+*> no eigenvalues or eigenvectors were computed.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2011
+*
+*> \ingroup complex16OTHEReigen
+*
+*> \par Contributors:
+* ==================
+*>
+*> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
+*
+* =====================================================================
SUBROUTINE ZHBGVD( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W,
$ Z, LDZ, WORK, LWORK, RWORK, LRWORK, IWORK,
$ LIWORK, INFO )
*
-* -- LAPACK driver routine (version 3.3.1) --
+* -- LAPACK driver routine (version 3.4.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-* -- April 2011 --
-* @precisions normal z -> c
+* November 2011
*
* .. Scalar Arguments ..
CHARACTER JOBZ, UPLO
@@ -20,147 +269,6 @@
$ Z( LDZ, * )
* ..
*
-* Purpose
-* =======
-*
-* ZHBGVD computes all the eigenvalues, and optionally, the eigenvectors
-* of a complex generalized Hermitian-definite banded eigenproblem, of
-* the form A*x=(lambda)*B*x. Here A and B are assumed to be Hermitian
-* and banded, and B is also positive definite. If eigenvectors are
-* desired, it uses a divide and conquer algorithm.
-*
-* The divide and conquer algorithm 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.
-*
-* Arguments
-* =========
-*
-* JOBZ (input) CHARACTER*1
-* = 'N': Compute eigenvalues only;
-* = 'V': Compute eigenvalues and eigenvectors.
-*
-* UPLO (input) CHARACTER*1
-* = 'U': Upper triangles of A and B are stored;
-* = 'L': Lower triangles of A and B are stored.
-*
-* N (input) INTEGER
-* The order of the matrices A and B. N >= 0.
-*
-* KA (input) INTEGER
-* The number of superdiagonals of the matrix A if UPLO = 'U',
-* or the number of subdiagonals if UPLO = 'L'. KA >= 0.
-*
-* KB (input) INTEGER
-* The number of superdiagonals of the matrix B if UPLO = 'U',
-* or the number of subdiagonals if UPLO = 'L'. KB >= 0.
-*
-* AB (input/output) COMPLEX*16 array, dimension (LDAB, N)
-* On entry, the upper or lower triangle of the Hermitian band
-* matrix A, stored in the first ka+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(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j;
-* if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka).
-*
-* On exit, the contents of AB are destroyed.
-*
-* LDAB (input) INTEGER
-* The leading dimension of the array AB. LDAB >= KA+1.
-*
-* BB (input/output) COMPLEX*16 array, dimension (LDBB, N)
-* On entry, the upper or lower triangle of the Hermitian band
-* matrix B, stored in the first kb+1 rows of the array. The
-* j-th column of B is stored in the j-th column of the array BB
-* as follows:
-* if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j;
-* if UPLO = 'L', BB(1+i-j,j) = B(i,j) for j<=i<=min(n,j+kb).
-*
-* On exit, the factor S from the split Cholesky factorization
-* B = S**H*S, as returned by ZPBSTF.
-*
-* LDBB (input) INTEGER
-* The leading dimension of the array BB. LDBB >= KB+1.
-*
-* W (output) DOUBLE PRECISION array, dimension (N)
-* If INFO = 0, the eigenvalues in ascending order.
-*
-* Z (output) COMPLEX*16 array, dimension (LDZ, N)
-* If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
-* eigenvectors, with the i-th column of Z holding the
-* eigenvector associated with W(i). The eigenvectors are
-* normalized so that Z**H*B*Z = I.
-* If JOBZ = 'N', then Z is not referenced.
-*
-* LDZ (input) INTEGER
-* The leading dimension of the array Z. LDZ >= 1, and if
-* JOBZ = 'V', LDZ >= N.
-*
-* WORK (workspace/output) COMPLEX*16 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 N <= 1, LWORK >= 1.
-* If JOBZ = 'N' and N > 1, LWORK >= N.
-* If JOBZ = 'V' and N > 1, LWORK >= 2*N**2.
-*
-* 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.
-*
-* RWORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LRWORK))
-* On exit, if INFO=0, RWORK(1) returns the optimal LRWORK.
-*
-* LRWORK (input) INTEGER
-* The dimension of array RWORK.
-* If N <= 1, LRWORK >= 1.
-* If JOBZ = 'N' and N > 1, LRWORK >= N.
-* If JOBZ = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2.
-*
-* 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.
-*
-* 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 array IWORK.
-* If JOBZ = 'N' or N <= 1, LIWORK >= 1.
-* If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*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.
-*
-* INFO (output) INTEGER
-* = 0: successful exit
-* < 0: if INFO = -i, the i-th argument had an illegal value
-* > 0: if INFO = i, and i is:
-* <= N: the algorithm failed to converge:
-* i off-diagonal elements of an intermediate
-* tridiagonal form did not converge to zero;
-* > N: if INFO = N + i, for 1 <= i <= N, then ZPBSTF
-* returned INFO = i: B is not positive definite.
-* The factorization of B could not be completed and
-* no eigenvalues or eigenvectors were computed.
-*
-* Further Details
-* ===============
-*
-* Based on contributions by
-* Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
-*
* =====================================================================
*
* .. Parameters ..