356 lines
11 KiB
Fortran
356 lines
11 KiB
Fortran
*> \brief \b SSPGVD
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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 SSPGVD + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sspgvd.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/sspgvd.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/sspgvd.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 SSPGVD( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
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* LWORK, IWORK, LIWORK, 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, LIWORK, LWORK, N
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* ..
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* .. Array Arguments ..
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* INTEGER IWORK( * )
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* REAL 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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*> SSPGVD 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
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*> B are assumed to be symmetric, stored in packed format, and B is also
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*> positive definite.
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*> If eigenvectors are desired, it uses a divide and conquer algorithm.
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*>
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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 REAL 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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*> 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 REAL 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 REAL 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 REAL 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 REAL array, dimension (MAX(1,LWORK))
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*> On exit, if INFO = 0, WORK(1) returns the required LWORK.
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*> \endverbatim
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*>
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*> \param[in] LWORK
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*> \verbatim
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*> LWORK is INTEGER
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*> The dimension of the array WORK.
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*> If N <= 1, LWORK >= 1.
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*> If JOBZ = 'N' and N > 1, LWORK >= 2*N.
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*> If JOBZ = 'V' and N > 1, LWORK >= 1 + 6*N + 2*N**2.
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*>
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*> If LWORK = -1, then a workspace query is assumed; the routine
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*> only calculates the required sizes of the WORK and IWORK
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*> arrays, returns these values as the first entries of the WORK
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*> and IWORK arrays, and no error message related to LWORK or
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*> LIWORK is issued by XERBLA.
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*> \endverbatim
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*>
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*> \param[out] IWORK
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*> \verbatim
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*> IWORK is INTEGER array, dimension (MAX(1,LIWORK))
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*> On exit, if INFO = 0, IWORK(1) returns the required LIWORK.
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*> \endverbatim
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*>
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*> \param[in] LIWORK
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*> \verbatim
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*> LIWORK is INTEGER
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*> The dimension of the array IWORK.
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*> If JOBZ = 'N' or N <= 1, LIWORK >= 1.
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*> If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N.
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*>
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*> If LIWORK = -1, then a workspace query is assumed; the
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*> routine only calculates the required sizes of the WORK and
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*> IWORK arrays, returns these values as the first entries of
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*> the WORK and IWORK arrays, and no error message related to
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*> LWORK or LIWORK is issued by XERBLA.
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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: SPPTRF or SSPEVD returned an error code:
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*> <= N: if INFO = i, SSPEVD 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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*> principal minor of order i of B is not positive.
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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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*> \ingroup realOTHEReigen
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*
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*> \par Contributors:
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* ==================
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*>
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*> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
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*
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* =====================================================================
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SUBROUTINE SSPGVD( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
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$ LWORK, IWORK, LIWORK, INFO )
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*
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* -- LAPACK driver routine --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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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, LIWORK, LWORK, N
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* ..
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* .. Array Arguments ..
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INTEGER IWORK( * )
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REAL 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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*
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* .. Local Scalars ..
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LOGICAL LQUERY, UPPER, WANTZ
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CHARACTER TRANS
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INTEGER J, LIWMIN, LWMIN, NEIG
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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EXTERNAL LSAME
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* ..
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* .. External Subroutines ..
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EXTERNAL SPPTRF, SSPEVD, SSPGST, STPMV, STPSV, XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX, REAL
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* ..
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* .. Executable Statements ..
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*
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* Test the input parameters.
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*
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WANTZ = LSAME( JOBZ, 'V' )
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UPPER = LSAME( UPLO, 'U' )
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LQUERY = ( LWORK.EQ.-1 .OR. LIWORK.EQ.-1 )
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*
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INFO = 0
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IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
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INFO = -1
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ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
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INFO = -2
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ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
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INFO = -3
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ELSE IF( N.LT.0 ) THEN
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INFO = -4
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ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
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INFO = -9
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END IF
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*
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IF( INFO.EQ.0 ) THEN
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IF( N.LE.1 ) THEN
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LIWMIN = 1
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LWMIN = 1
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ELSE
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IF( WANTZ ) THEN
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LIWMIN = 3 + 5*N
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LWMIN = 1 + 6*N + 2*N**2
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ELSE
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LIWMIN = 1
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LWMIN = 2*N
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END IF
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END IF
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WORK( 1 ) = LWMIN
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IWORK( 1 ) = LIWMIN
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IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
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INFO = -11
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ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
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INFO = -13
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END IF
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END IF
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*
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'SSPGVD', -INFO )
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RETURN
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ELSE IF( LQUERY ) THEN
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RETURN
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END IF
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*
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* Quick return if possible
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*
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IF( N.EQ.0 )
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$ RETURN
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*
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* Form a Cholesky factorization of BP.
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*
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CALL SPPTRF( UPLO, N, BP, INFO )
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IF( INFO.NE.0 ) THEN
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INFO = N + INFO
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RETURN
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END IF
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*
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* Transform problem to standard eigenvalue problem and solve.
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*
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CALL SSPGST( ITYPE, UPLO, N, AP, BP, INFO )
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CALL SSPEVD( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK, IWORK,
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$ LIWORK, INFO )
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LWMIN = INT( MAX( REAL( LWMIN ), REAL( WORK( 1 ) ) ) )
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LIWMIN = INT( MAX( REAL( LIWMIN ), REAL( IWORK( 1 ) ) ) )
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*
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IF( WANTZ ) THEN
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*
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* Backtransform eigenvectors to the original problem.
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*
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NEIG = N
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IF( INFO.GT.0 )
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$ NEIG = INFO - 1
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IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
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*
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* For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
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* backtransform eigenvectors: x = inv(L)**T *y or inv(U)*y
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*
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IF( UPPER ) THEN
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TRANS = 'N'
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ELSE
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TRANS = 'T'
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END IF
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*
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DO 10 J = 1, NEIG
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CALL STPSV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ),
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$ 1 )
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10 CONTINUE
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*
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ELSE IF( ITYPE.EQ.3 ) THEN
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*
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* For B*A*x=(lambda)*x;
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* backtransform eigenvectors: x = L*y or U**T *y
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*
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IF( UPPER ) THEN
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TRANS = 'T'
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ELSE
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TRANS = 'N'
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END IF
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*
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DO 20 J = 1, NEIG
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CALL STPMV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ),
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$ 1 )
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20 CONTINUE
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END IF
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END IF
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*
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WORK( 1 ) = LWMIN
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IWORK( 1 ) = LIWMIN
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*
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RETURN
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*
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* End of SSPGVD
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*
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END
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