diff options
author | julie <julielangou@users.noreply.github.com> | 2011-10-06 06:53:11 +0000 |
---|---|---|
committer | julie <julielangou@users.noreply.github.com> | 2011-10-06 06:53:11 +0000 |
commit | e1d39294aee16fa6db9ba079b14442358217db71 (patch) | |
tree | 30e5aa04c1f6596991fda5334f63dfb9b8027849 /SRC/zhbevd.f | |
parent | 5fe0466a14e395641f4f8a300ecc9dcb8058081b (diff) | |
download | lapack-e1d39294aee16fa6db9ba079b14442358217db71.tar.gz lapack-e1d39294aee16fa6db9ba079b14442358217db71.tar.bz2 lapack-e1d39294aee16fa6db9ba079b14442358217db71.zip |
Integrating Doxygen in comments
Diffstat (limited to 'SRC/zhbevd.f')
-rw-r--r-- | SRC/zhbevd.f | 330 |
1 files changed, 212 insertions, 118 deletions
diff --git a/SRC/zhbevd.f b/SRC/zhbevd.f index d41fb4eb..3d7f92b9 100644 --- a/SRC/zhbevd.f +++ b/SRC/zhbevd.f @@ -1,10 +1,220 @@ +*> \brief <b> ZHBEVD 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 ZHBEVD( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK, +* LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO ) +* +* .. Scalar Arguments .. +* CHARACTER JOBZ, UPLO +* INTEGER INFO, KD, LDAB, LDZ, LIWORK, LRWORK, LWORK, N +* .. +* .. Array Arguments .. +* INTEGER IWORK( * ) +* DOUBLE PRECISION RWORK( * ), W( * ) +* COMPLEX*16 AB( LDAB, * ), WORK( * ), Z( LDZ, * ) +* .. +* +* Purpose +* ======= +* +*>\details \b Purpose: +*>\verbatim +*> +*> ZHBEVD computes all the eigenvalues and, optionally, eigenvectors of +*> a complex Hermitian band matrix A. 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 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 COMPLEX*16 array, dimension (LDAB, N) +*> On entry, the upper or lower triangle of the Hermitian 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). +*> \endverbatim +*> \verbatim +*> 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] 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 orthonormal +*> eigenvectors of the matrix A, with the i-th column of Z +*> holding the eigenvector associated with W(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 >= max(1,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 must be at least 1. +*> If JOBZ = 'N' and N > 1, LWORK must be at least N. +*> If JOBZ = 'V' and N > 1, LWORK must be at least 2*N**2. +*> \endverbatim +*> \verbatim +*> 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 (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 must be at least 1. +*> If JOBZ = 'N' and N > 1, LRWORK must be at least N. +*> If JOBZ = 'V' and N > 1, LRWORK must be at least +*> 1 + 5*N + 2*N**2. +*> \endverbatim +*> \verbatim +*> 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 must be at least 1. +*> If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N . +*> \endverbatim +*> \verbatim +*> 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, the algorithm failed to converge; i +*> off-diagonal elements of an intermediate tridiagonal +*> form did not converge to zero. +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complex16OTHEReigen +* +* ===================================================================== SUBROUTINE ZHBEVD( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK, $ LWORK, RWORK, LRWORK, IWORK, LIWORK, 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, UPLO @@ -16,122 +226,6 @@ COMPLEX*16 AB( LDAB, * ), WORK( * ), Z( LDZ, * ) * .. * -* Purpose -* ======= -* -* ZHBEVD computes all the eigenvalues and, optionally, eigenvectors of -* a complex Hermitian band matrix A. 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 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) COMPLEX*16 array, dimension (LDAB, N) -* On entry, the upper or lower triangle of the Hermitian 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. -* -* 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 orthonormal -* eigenvectors of the matrix A, with the i-th column of Z -* holding the eigenvector associated with W(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 >= max(1,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 must be at least 1. -* If JOBZ = 'N' and N > 1, LWORK must be at least N. -* If JOBZ = 'V' and N > 1, LWORK must be at least 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 (LRWORK) -* On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK. -* -* LRWORK (input) INTEGER -* The dimension of array RWORK. -* If N <= 1, LRWORK must be at least 1. -* If JOBZ = 'N' and N > 1, LRWORK must be at least N. -* If JOBZ = 'V' and N > 1, LRWORK must be at least -* 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 must be at least 1. -* If JOBZ = 'V' and N > 1, LIWORK must be at least 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, the algorithm failed to converge; i -* off-diagonal elements of an intermediate tridiagonal -* form did not converge to zero. -* * ===================================================================== * * .. Parameters .. |