version 1.6, 2010/08/13 21:03:57
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version 1.12, 2012/12/14 14:22:39
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*> \brief \b DSPGST |
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* |
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* =========== DOCUMENTATION =========== |
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* |
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* Online html documentation available at |
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* http://www.netlib.org/lapack/explore-html/ |
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* |
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*> \htmlonly |
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*> Download DSPGV + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dspgv.f"> |
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*> [TGZ]</a> |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dspgv.f"> |
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*> [ZIP]</a> |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dspgv.f"> |
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*> [TXT]</a> |
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*> \endhtmlonly |
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* |
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* Definition: |
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* =========== |
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* |
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* SUBROUTINE DSPGV( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK, |
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* INFO ) |
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* |
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* .. Scalar Arguments .. |
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* CHARACTER JOBZ, UPLO |
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* INTEGER INFO, ITYPE, LDZ, N |
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* .. |
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* .. Array Arguments .. |
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* DOUBLE PRECISION AP( * ), BP( * ), W( * ), WORK( * ), |
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* $ Z( LDZ, * ) |
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* .. |
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* |
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* |
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*> \par Purpose: |
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* ============= |
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*> |
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*> \verbatim |
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*> |
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*> DSPGV computes all the eigenvalues and, optionally, the eigenvectors |
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*> of a real generalized symmetric-definite eigenproblem, of the form |
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*> A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. |
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*> Here A and B are assumed to be symmetric, stored in packed format, |
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*> and B is also positive definite. |
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*> \endverbatim |
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* |
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* Arguments: |
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* ========== |
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* |
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*> \param[in] ITYPE |
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*> \verbatim |
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*> ITYPE is INTEGER |
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*> Specifies the problem type to be solved: |
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*> = 1: A*x = (lambda)*B*x |
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*> = 2: A*B*x = (lambda)*x |
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*> = 3: B*A*x = (lambda)*x |
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*> \endverbatim |
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*> |
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*> \param[in] JOBZ |
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*> \verbatim |
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*> JOBZ is CHARACTER*1 |
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*> = 'N': Compute eigenvalues only; |
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*> = 'V': Compute eigenvalues and eigenvectors. |
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*> \endverbatim |
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*> |
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*> \param[in] UPLO |
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*> \verbatim |
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*> UPLO is CHARACTER*1 |
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*> = 'U': Upper triangles of A and B are stored; |
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*> = 'L': Lower triangles of A and B are stored. |
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*> \endverbatim |
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*> |
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*> \param[in] N |
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*> \verbatim |
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*> N is INTEGER |
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*> The order of the matrices A and B. N >= 0. |
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*> \endverbatim |
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*> |
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*> \param[in,out] AP |
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*> \verbatim |
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*> AP is DOUBLE PRECISION array, dimension |
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*> (N*(N+1)/2) |
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*> On entry, the upper or lower triangle of the symmetric matrix |
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*> A, packed columnwise in a linear array. The j-th column of A |
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*> is stored in the array AP as follows: |
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*> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; |
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*> if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. |
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*> |
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*> On exit, the contents of AP are destroyed. |
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*> \endverbatim |
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*> |
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*> \param[in,out] BP |
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*> \verbatim |
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*> BP is DOUBLE PRECISION array, dimension (N*(N+1)/2) |
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*> On entry, the upper or lower triangle of the symmetric matrix |
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*> B, packed columnwise in a linear array. The j-th column of B |
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*> is stored in the array BP as follows: |
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*> if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j; |
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*> if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n. |
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*> |
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*> On exit, the triangular factor U or L from the Cholesky |
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*> factorization B = U**T*U or B = L*L**T, in the same storage |
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*> format as B. |
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*> \endverbatim |
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*> |
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*> \param[out] W |
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*> \verbatim |
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*> W is DOUBLE PRECISION array, dimension (N) |
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*> If INFO = 0, the eigenvalues in ascending order. |
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*> \endverbatim |
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*> |
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*> \param[out] Z |
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*> \verbatim |
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*> Z is DOUBLE PRECISION array, dimension (LDZ, N) |
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*> If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of |
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*> eigenvectors. The eigenvectors are normalized as follows: |
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*> if ITYPE = 1 or 2, Z**T*B*Z = I; |
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*> if ITYPE = 3, Z**T*inv(B)*Z = I. |
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*> If JOBZ = 'N', then Z is not referenced. |
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*> \endverbatim |
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*> |
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*> \param[in] LDZ |
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*> \verbatim |
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*> LDZ is INTEGER |
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*> The leading dimension of the array Z. LDZ >= 1, and if |
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*> JOBZ = 'V', LDZ >= max(1,N). |
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*> \endverbatim |
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*> |
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*> \param[out] WORK |
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*> \verbatim |
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*> WORK is DOUBLE PRECISION array, dimension (3*N) |
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*> \endverbatim |
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*> |
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*> \param[out] INFO |
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*> \verbatim |
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*> INFO is INTEGER |
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*> = 0: successful exit |
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*> < 0: if INFO = -i, the i-th argument had an illegal value |
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*> > 0: DPPTRF or DSPEV returned an error code: |
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*> <= N: if INFO = i, DSPEV failed to converge; |
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*> i off-diagonal elements of an intermediate |
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*> tridiagonal form did not converge to zero. |
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*> > N: if INFO = n + i, for 1 <= i <= n, then the leading |
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*> minor of order i of B is not positive definite. |
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*> The factorization of B could not be completed and |
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*> no eigenvalues or eigenvectors were computed. |
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*> \endverbatim |
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* |
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* Authors: |
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* ======== |
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* |
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*> \author Univ. of Tennessee |
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*> \author Univ. of California Berkeley |
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*> \author Univ. of Colorado Denver |
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*> \author NAG Ltd. |
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* |
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*> \date November 2011 |
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* |
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*> \ingroup doubleOTHEReigen |
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* |
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* ===================================================================== |
SUBROUTINE DSPGV( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK, |
SUBROUTINE DSPGV( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK, |
$ INFO ) |
$ INFO ) |
* |
* |
* -- LAPACK driver routine (version 3.2) -- |
* -- LAPACK driver routine (version 3.4.0) -- |
* -- 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 |
* November 2011 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
CHARACTER JOBZ, UPLO |
CHARACTER JOBZ, UPLO |
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$ Z( LDZ, * ) |
$ Z( LDZ, * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* DSPGV computes all the eigenvalues and, optionally, the eigenvectors |
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* of a real generalized symmetric-definite eigenproblem, of the form |
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* A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. |
|
* Here A and B are assumed to be symmetric, stored in packed format, |
|
* and B is also positive definite. |
|
* |
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* Arguments |
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* ========= |
|
* |
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* ITYPE (input) INTEGER |
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* Specifies the problem type to be solved: |
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* = 1: A*x = (lambda)*B*x |
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* = 2: A*B*x = (lambda)*x |
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* = 3: B*A*x = (lambda)*x |
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* |
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* JOBZ (input) CHARACTER*1 |
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* = 'N': Compute eigenvalues only; |
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* = 'V': Compute eigenvalues and eigenvectors. |
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* |
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* UPLO (input) CHARACTER*1 |
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* = 'U': Upper triangles of A and B are stored; |
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* = 'L': Lower triangles of A and B are stored. |
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* |
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* N (input) INTEGER |
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* The order of the matrices A and B. N >= 0. |
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* |
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* AP (input/output) DOUBLE PRECISION array, dimension |
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* (N*(N+1)/2) |
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* On entry, the upper or lower triangle of the symmetric matrix |
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* A, packed columnwise in a linear array. The j-th column of A |
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* is stored in the array AP as follows: |
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* if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; |
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* if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. |
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* |
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* On exit, the contents of AP are destroyed. |
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* |
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* BP (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2) |
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* On entry, the upper or lower triangle of the symmetric matrix |
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* B, packed columnwise in a linear array. The j-th column of B |
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* is stored in the array BP as follows: |
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* if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j; |
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* if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n. |
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* |
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* On exit, the triangular factor U or L from the Cholesky |
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* factorization B = U**T*U or B = L*L**T, in the same storage |
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* format as B. |
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* |
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* W (output) DOUBLE PRECISION array, dimension (N) |
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* If INFO = 0, the eigenvalues in ascending order. |
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* |
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* Z (output) DOUBLE PRECISION array, dimension (LDZ, N) |
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* If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of |
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* eigenvectors. The eigenvectors are normalized as follows: |
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* if ITYPE = 1 or 2, Z**T*B*Z = I; |
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* if ITYPE = 3, Z**T*inv(B)*Z = I. |
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* If JOBZ = 'N', then Z is not referenced. |
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* |
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* LDZ (input) INTEGER |
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* The leading dimension of the array Z. LDZ >= 1, and if |
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* JOBZ = 'V', LDZ >= max(1,N). |
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* |
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* WORK (workspace) DOUBLE PRECISION array, dimension (3*N) |
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* |
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* INFO (output) INTEGER |
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* = 0: successful exit |
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* < 0: if INFO = -i, the i-th argument had an illegal value |
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* > 0: DPPTRF or DSPEV returned an error code: |
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* <= N: if INFO = i, DSPEV failed to converge; |
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* i off-diagonal elements of an intermediate |
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* tridiagonal form did not converge to zero. |
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* > N: if INFO = n + i, for 1 <= i <= n, then the leading |
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* minor of order i of B is not positive definite. |
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* The factorization of B could not be completed and |
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* no eigenvalues or eigenvectors were computed. |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Local Scalars .. |
* .. Local Scalars .. |
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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' |
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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' |