--- rpl/lapack/lapack/zheevx.f 2011/07/22 07:38:15 1.8 +++ rpl/lapack/lapack/zheevx.f 2011/11/21 20:43:11 1.9 @@ -1,12 +1,261 @@ +*> \brief ZHEEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download ZHEEVX + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE ZHEEVX( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU, +* ABSTOL, M, W, Z, LDZ, WORK, LWORK, RWORK, +* IWORK, IFAIL, INFO ) +* +* .. Scalar Arguments .. +* CHARACTER JOBZ, RANGE, UPLO +* INTEGER IL, INFO, IU, LDA, LDZ, LWORK, M, N +* DOUBLE PRECISION ABSTOL, VL, VU +* .. +* .. Array Arguments .. +* INTEGER IFAIL( * ), IWORK( * ) +* DOUBLE PRECISION RWORK( * ), W( * ) +* COMPLEX*16 A( LDA, * ), WORK( * ), Z( LDZ, * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> ZHEEVX computes selected eigenvalues and, optionally, eigenvectors +*> of a complex Hermitian 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,out] A +*> \verbatim +*> A is COMPLEX*16 array, dimension (LDA, N) +*> On entry, the Hermitian matrix A. If UPLO = 'U', the +*> leading N-by-N upper triangular part of A contains the +*> upper triangular part of the matrix A. If UPLO = 'L', +*> the leading N-by-N lower triangular part of A contains +*> the lower triangular part of the matrix A. +*> On exit, the lower triangle (if UPLO='L') or the upper +*> triangle (if UPLO='U') of A, including the diagonal, is +*> destroyed. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= max(1,N). +*> \endverbatim +*> +*> \param[in] VL +*> \verbatim +*> VL is DOUBLE PRECISION +*> \endverbatim +*> +*> \param[in] VU +*> \verbatim +*> VU is 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'. +*> \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 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 A 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) +*> On normal exit, the first M elements contain the selected +*> eigenvalues in ascending order. +*> \endverbatim +*> +*> \param[out] Z +*> \verbatim +*> Z is COMPLEX*16 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 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 length of the array WORK. LWORK >= 1, when N <= 1; +*> otherwise 2*N. +*> For optimal efficiency, LWORK >= (NB+1)*N, +*> where NB is the max of the blocksize for ZHETRD and for +*> ZUNMTR as returned by ILAENV. +*> +*> 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] RWORK +*> \verbatim +*> RWORK 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 November 2011 +* +*> \ingroup complex16HEeigen +* +* ===================================================================== SUBROUTINE ZHEEVX( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU, $ ABSTOL, M, W, Z, LDZ, WORK, LWORK, RWORK, $ IWORK, IFAIL, 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, RANGE, UPLO @@ -19,139 +268,6 @@ COMPLEX*16 A( LDA, * ), WORK( * ), Z( LDZ, * ) * .. * -* Purpose -* ======= -* -* ZHEEVX computes selected eigenvalues and, optionally, eigenvectors -* of a complex Hermitian 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. -* -* A (input/output) COMPLEX*16 array, dimension (LDA, N) -* On entry, the Hermitian matrix A. If UPLO = 'U', the -* leading N-by-N upper triangular part of A contains the -* upper triangular part of the matrix A. If UPLO = 'L', -* the leading N-by-N lower triangular part of A contains -* the lower triangular part of the matrix A. -* On exit, the lower triangle (if UPLO='L') or the upper -* triangle (if UPLO='U') of A, including the diagonal, is -* destroyed. -* -* LDA (input) INTEGER -* The leading dimension of the array A. LDA >= 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 A 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) -* On normal exit, the first M elements contain the selected -* eigenvalues in ascending order. -* -* Z (output) COMPLEX*16 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/output) COMPLEX*16 array, dimension (MAX(1,LWORK)) -* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. -* -* LWORK (input) INTEGER -* The length of the array WORK. LWORK >= 1, when N <= 1; -* otherwise 2*N. -* For optimal efficiency, LWORK >= (NB+1)*N, -* where NB is the max of the blocksize for ZHETRD and for -* ZUNMTR as returned by ILAENV. -* -* 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. -* -* RWORK (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 ..