version 1.5, 2010/08/07 13:22:27
|
version 1.19, 2023/08/07 08:39:08
|
Line 1
|
Line 1
|
|
*> \brief \b DSYGVD |
|
* |
|
* =========== DOCUMENTATION =========== |
|
* |
|
* Online html documentation available at |
|
* http://www.netlib.org/lapack/explore-html/ |
|
* |
|
*> \htmlonly |
|
*> Download DSYGVD + dependencies |
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsygvd.f"> |
|
*> [TGZ]</a> |
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsygvd.f"> |
|
*> [ZIP]</a> |
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsygvd.f"> |
|
*> [TXT]</a> |
|
*> \endhtmlonly |
|
* |
|
* Definition: |
|
* =========== |
|
* |
|
* SUBROUTINE DSYGVD( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK, |
|
* LWORK, IWORK, LIWORK, INFO ) |
|
* |
|
* .. Scalar Arguments .. |
|
* CHARACTER JOBZ, UPLO |
|
* INTEGER INFO, ITYPE, LDA, LDB, LIWORK, LWORK, N |
|
* .. |
|
* .. Array Arguments .. |
|
* INTEGER IWORK( * ) |
|
* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), W( * ), WORK( * ) |
|
* .. |
|
* |
|
* |
|
*> \par Purpose: |
|
* ============= |
|
*> |
|
*> \verbatim |
|
*> |
|
*> DSYGVD computes all the eigenvalues, and optionally, the eigenvectors |
|
*> of a real generalized symmetric-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 symmetric 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] A |
|
*> \verbatim |
|
*> A is DOUBLE PRECISION array, dimension (LDA, N) |
|
*> On entry, the symmetric 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, if JOBZ = 'V', then if INFO = 0, A contains the |
|
*> matrix Z of eigenvectors. The eigenvectors are normalized |
|
*> as follows: |
|
*> if ITYPE = 1 or 2, Z**T*B*Z = I; |
|
*> if ITYPE = 3, Z**T*inv(B)*Z = I. |
|
*> If JOBZ = 'N', then on exit the upper triangle (if UPLO='U') |
|
*> or the lower triangle (if UPLO='L') 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,out] B |
|
*> \verbatim |
|
*> B is DOUBLE PRECISION array, dimension (LDB, N) |
|
*> On entry, the symmetric matrix B. If UPLO = 'U', the |
|
*> leading N-by-N upper triangular part of B contains the |
|
*> upper triangular part of the matrix B. If UPLO = 'L', |
|
*> the leading N-by-N lower triangular part of B contains |
|
*> the lower triangular part of the matrix B. |
|
*> |
|
*> On exit, if INFO <= N, the part of B containing the matrix is |
|
*> overwritten by the triangular factor U or L from the Cholesky |
|
*> factorization B = U**T*U or B = L*L**T. |
|
*> \endverbatim |
|
*> |
|
*> \param[in] LDB |
|
*> \verbatim |
|
*> LDB is INTEGER |
|
*> The leading dimension of the array B. LDB >= max(1,N). |
|
*> \endverbatim |
|
*> |
|
*> \param[out] W |
|
*> \verbatim |
|
*> W is DOUBLE PRECISION array, dimension (N) |
|
*> If INFO = 0, the eigenvalues in ascending order. |
|
*> \endverbatim |
|
*> |
|
*> \param[out] WORK |
|
*> \verbatim |
|
*> WORK is DOUBLE PRECISION 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 >= 2*N+1. |
|
*> If JOBZ = 'V' and N > 1, LWORK >= 1 + 6*N + 2*N**2. |
|
*> |
|
*> If LWORK = -1, then a workspace query is assumed; the routine |
|
*> only calculates the optimal sizes of the WORK and IWORK |
|
*> arrays, returns these values as the first entries of the WORK |
|
*> and IWORK arrays, and no error message related to LWORK 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 the array IWORK. |
|
*> If N <= 1, LIWORK >= 1. |
|
*> If JOBZ = 'N' and 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 and |
|
*> IWORK arrays, returns these values as the first entries of |
|
*> the WORK and IWORK arrays, and no error message related to |
|
*> LWORK 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: DPOTRF or DSYEVD returned an error code: |
|
*> <= N: if INFO = i and JOBZ = 'N', then the algorithm |
|
*> failed to converge; i off-diagonal elements of an |
|
*> intermediate tridiagonal form did not converge to |
|
*> zero; |
|
*> if INFO = i and JOBZ = 'V', then the algorithm |
|
*> failed to compute an eigenvalue while working on |
|
*> the submatrix lying in rows and columns INFO/(N+1) |
|
*> through mod(INFO,N+1); |
|
*> > 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. |
|
* |
|
*> \ingroup doubleSYeigen |
|
* |
|
*> \par Further Details: |
|
* ===================== |
|
*> |
|
*> \verbatim |
|
*> |
|
*> Modified so that no backsubstitution is performed if DSYEVD fails to |
|
*> converge (NEIG in old code could be greater than N causing out of |
|
*> bounds reference to A - reported by Ralf Meyer). Also corrected the |
|
*> description of INFO and the test on ITYPE. Sven, 16 Feb 05. |
|
*> \endverbatim |
|
* |
|
*> \par Contributors: |
|
* ================== |
|
*> |
|
*> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA |
|
*> |
|
* ===================================================================== |
SUBROUTINE DSYGVD( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK, |
SUBROUTINE DSYGVD( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK, |
$ LWORK, IWORK, LIWORK, INFO ) |
$ LWORK, IWORK, LIWORK, INFO ) |
* |
* |
* -- LAPACK driver routine (version 3.2) -- |
* -- LAPACK driver routine -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* November 2006 |
|
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
CHARACTER JOBZ, UPLO |
CHARACTER JOBZ, UPLO |
Line 15
|
Line 238
|
DOUBLE PRECISION A( LDA, * ), B( LDB, * ), W( * ), WORK( * ) |
DOUBLE PRECISION A( LDA, * ), B( LDB, * ), W( * ), WORK( * ) |
* .. |
* .. |
* |
* |
* Purpose |
|
* ======= |
|
* |
|
* DSYGVD computes all the eigenvalues, and optionally, the eigenvectors |
|
* of a real generalized symmetric-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 symmetric 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. |
|
* |
|
* A (input/output) DOUBLE PRECISION array, dimension (LDA, N) |
|
* On entry, the symmetric 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, if JOBZ = 'V', then if INFO = 0, A contains the |
|
* matrix Z of eigenvectors. The eigenvectors are normalized |
|
* as follows: |
|
* if ITYPE = 1 or 2, Z**T*B*Z = I; |
|
* if ITYPE = 3, Z**T*inv(B)*Z = I. |
|
* If JOBZ = 'N', then on exit the upper triangle (if UPLO='U') |
|
* or the lower triangle (if UPLO='L') of A, including the |
|
* diagonal, is destroyed. |
|
* |
|
* LDA (input) INTEGER |
|
* The leading dimension of the array A. LDA >= max(1,N). |
|
* |
|
* B (input/output) DOUBLE PRECISION array, dimension (LDB, N) |
|
* On entry, the symmetric matrix B. If UPLO = 'U', the |
|
* leading N-by-N upper triangular part of B contains the |
|
* upper triangular part of the matrix B. If UPLO = 'L', |
|
* the leading N-by-N lower triangular part of B contains |
|
* the lower triangular part of the matrix B. |
|
* |
|
* On exit, if INFO <= N, the part of B containing the matrix is |
|
* overwritten by the triangular factor U or L from the Cholesky |
|
* factorization B = U**T*U or B = L*L**T. |
|
* |
|
* LDB (input) INTEGER |
|
* The leading dimension of the array B. LDB >= max(1,N). |
|
* |
|
* W (output) DOUBLE PRECISION array, dimension (N) |
|
* If INFO = 0, the eigenvalues in ascending order. |
|
* |
|
* WORK (workspace/output) DOUBLE PRECISION 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 >= 2*N+1. |
|
* If JOBZ = 'V' and N > 1, LWORK >= 1 + 6*N + 2*N**2. |
|
* |
|
* If LWORK = -1, then a workspace query is assumed; the routine |
|
* only calculates the optimal sizes of the WORK and IWORK |
|
* arrays, returns these values as the first entries of the WORK |
|
* and IWORK arrays, and no error message related to LWORK 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 the array IWORK. |
|
* If N <= 1, LIWORK >= 1. |
|
* If JOBZ = 'N' and 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 and |
|
* IWORK arrays, returns these values as the first entries of |
|
* the WORK and IWORK arrays, and no error message related to |
|
* LWORK 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: DPOTRF or DSYEVD returned an error code: |
|
* <= N: if INFO = i and JOBZ = 'N', then the algorithm |
|
* failed to converge; i off-diagonal elements of an |
|
* intermediate tridiagonal form did not converge to |
|
* zero; |
|
* if INFO = i and JOBZ = 'V', then the algorithm |
|
* failed to compute an eigenvalue while working on |
|
* the submatrix lying in rows and columns INFO/(N+1) |
|
* through mod(INFO,N+1); |
|
* > 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 |
|
* |
|
* Modified so that no backsubstitution is performed if DSYEVD fails to |
|
* converge (NEIG in old code could be greater than N causing out of |
|
* bounds reference to A - reported by Ralf Meyer). Also corrected the |
|
* description of INFO and the test on ITYPE. Sven, 16 Feb 05. |
|
* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |
Line 236
|
Line 330
|
CALL DSYGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) |
CALL DSYGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) |
CALL DSYEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, IWORK, LIWORK, |
CALL DSYEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, IWORK, LIWORK, |
$ INFO ) |
$ INFO ) |
LOPT = MAX( DBLE( LOPT ), DBLE( WORK( 1 ) ) ) |
LOPT = INT( MAX( DBLE( LOPT ), DBLE( WORK( 1 ) ) ) ) |
LIOPT = MAX( DBLE( LIOPT ), DBLE( IWORK( 1 ) ) ) |
LIOPT = INT( MAX( DBLE( LIOPT ), DBLE( IWORK( 1 ) ) ) ) |
* |
* |
IF( WANTZ .AND. INFO.EQ.0 ) THEN |
IF( WANTZ .AND. INFO.EQ.0 ) THEN |
* |
* |
Line 246
|
Line 340
|
IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN |
IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN |
* |
* |
* For A*x=(lambda)*B*x and A*B*x=(lambda)*x; |
* For A*x=(lambda)*B*x and A*B*x=(lambda)*x; |
* backtransform eigenvectors: x = inv(L)'*y or inv(U)*y |
* backtransform eigenvectors: x = inv(L)**T*y or inv(U)*y |
* |
* |
IF( UPPER ) THEN |
IF( UPPER ) THEN |
TRANS = 'N' |
TRANS = 'N' |
Line 260
|
Line 354
|
ELSE IF( ITYPE.EQ.3 ) THEN |
ELSE IF( ITYPE.EQ.3 ) THEN |
* |
* |
* For B*A*x=(lambda)*x; |
* For B*A*x=(lambda)*x; |
* backtransform eigenvectors: x = L*y or U'*y |
* backtransform eigenvectors: x = L*y or U**T*y |
* |
* |
IF( UPPER ) THEN |
IF( UPPER ) THEN |
TRANS = 'T' |
TRANS = 'T' |