--- rpl/lapack/lapack/zhpgvd.f 2011/07/22 07:38:16 1.8 +++ rpl/lapack/lapack/zhpgvd.f 2011/11/21 20:43:12 1.9 @@ -1,10 +1,240 @@ +*> \brief \b ZHPGST +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download ZHPGVD + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE ZHPGVD( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK, +* LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO ) +* +* .. Scalar Arguments .. +* CHARACTER JOBZ, UPLO +* INTEGER INFO, ITYPE, LDZ, LIWORK, LRWORK, LWORK, N +* .. +* .. Array Arguments .. +* INTEGER IWORK( * ) +* DOUBLE PRECISION RWORK( * ), W( * ) +* COMPLEX*16 AP( * ), BP( * ), WORK( * ), Z( LDZ, * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> ZHPGVD computes all the eigenvalues and, optionally, the eigenvectors +*> of a complex generalized Hermitian-definite eigenproblem, of the form +*> A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and +*> B are assumed to be Hermitian, stored in packed format, 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] ITYPE +*> \verbatim +*> ITYPE is INTEGER +*> Specifies the problem type to be solved: +*> = 1: A*x = (lambda)*B*x +*> = 2: A*B*x = (lambda)*x +*> = 3: B*A*x = (lambda)*x +*> \endverbatim +*> +*> \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,out] AP +*> \verbatim +*> AP is COMPLEX*16 array, dimension (N*(N+1)/2) +*> On entry, the upper or lower triangle of the Hermitian matrix +*> A, packed columnwise in a linear array. The j-th column of A +*> is stored in the array AP as follows: +*> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; +*> if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. +*> +*> On exit, the contents of AP are destroyed. +*> \endverbatim +*> +*> \param[in,out] BP +*> \verbatim +*> BP is COMPLEX*16 array, dimension (N*(N+1)/2) +*> On entry, the upper or lower triangle of the Hermitian matrix +*> B, packed columnwise in a linear array. The j-th column of B +*> is stored in the array BP as follows: +*> if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j; +*> if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n. +*> +*> On exit, the triangular factor U or L from the Cholesky +*> factorization B = U**H*U or B = L*L**H, in the same storage +*> format as B. +*> \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. The eigenvectors are normalized as follows: +*> if ITYPE = 1 or 2, Z**H*B*Z = I; +*> if ITYPE = 3, Z**H*inv(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 >= 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 required 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. +*> +*> If LWORK = -1, then a workspace query is assumed; the routine +*> only calculates the required 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 required 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 required 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 required 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 required 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: ZPPTRF or ZHPEVD returned an error code: +*> <= N: if INFO = i, ZHPEVD failed to converge; +*> i off-diagonal elements of an intermediate +*> tridiagonal form did not convergeto zero; +*> > N: if INFO = N + i, for 1 <= i <= n, then the leading +*> minor of order i of 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 ZHPGVD( ITYPE, JOBZ, UPLO, N, AP, BP, 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 -- +* November 2011 * * .. Scalar Arguments .. CHARACTER JOBZ, UPLO @@ -16,139 +246,6 @@ COMPLEX*16 AP( * ), BP( * ), WORK( * ), Z( LDZ, * ) * .. * -* Purpose -* ======= -* -* ZHPGVD computes all the eigenvalues and, optionally, the eigenvectors -* of a complex generalized Hermitian-definite eigenproblem, of the form -* A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and -* B are assumed to be Hermitian, stored in packed format, 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 -* ========= -* -* ITYPE (input) INTEGER -* Specifies the problem type to be solved: -* = 1: A*x = (lambda)*B*x -* = 2: A*B*x = (lambda)*x -* = 3: B*A*x = (lambda)*x -* -* 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. -* -* AP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2) -* On entry, the upper or lower triangle of the Hermitian matrix -* A, packed columnwise in a linear array. The j-th column of A -* is stored in the array AP as follows: -* if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; -* if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. -* -* On exit, the contents of AP are destroyed. -* -* BP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2) -* On entry, the upper or lower triangle of the Hermitian matrix -* B, packed columnwise in a linear array. The j-th column of B -* is stored in the array BP as follows: -* if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j; -* if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n. -* -* On exit, the triangular factor U or L from the Cholesky -* factorization B = U**H*U or B = L*L**H, in the same storage -* format as B. -* -* 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. The eigenvectors are normalized as follows: -* if ITYPE = 1 or 2, Z**H*B*Z = I; -* if ITYPE = 3, Z**H*inv(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 >= max(1,N). -* -* WORK (workspace) COMPLEX*16 array, dimension (MAX(1,LWORK)) -* On exit, if INFO = 0, WORK(1) returns the required 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. -* -* If LWORK = -1, then a workspace query is assumed; the routine -* only calculates the required 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) DOUBLE PRECISION array, dimension (MAX(1,LRWORK)) -* On exit, if INFO = 0, RWORK(1) returns the required 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 required 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 required 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 required 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: ZPPTRF or ZHPEVD returned an error code: -* <= N: if INFO = i, ZHPEVD failed to converge; -* i off-diagonal elements of an intermediate -* tridiagonal form did not convergeto zero; -* > N: if INFO = N + i, for 1 <= i <= n, then the leading -* minor of order i of 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 -* * ===================================================================== * * .. Local Scalars ..