version 1.2, 2010/04/21 13:45:24
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version 1.17, 2017/06/17 10:54:02
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*> \brief \b DSPGVD |
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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 DSPGVD + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dspgvd.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/dspgvd.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/dspgvd.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 DSPGVD( 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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* 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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*> DSPGVD 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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*> The divide and conquer algorithm makes very mild assumptions about |
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*> floating point arithmetic. It will work on machines with a guard |
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*> digit in add/subtract, or on those binary machines without guard |
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*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or |
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*> Cray-2. It could conceivably fail on hexadecimal or decimal machines |
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*> without guard digits, but we know of none. |
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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 (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 (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: DPPTRF or DSPEVD returned an error code: |
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*> <= N: if INFO = i, DSPEVD 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 December 2016 |
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* |
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*> \ingroup doubleOTHEReigen |
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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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* ===================================================================== |
SUBROUTINE DSPGVD( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK, |
SUBROUTINE DSPGVD( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK, |
$ LWORK, IWORK, LIWORK, INFO ) |
$ LWORK, IWORK, LIWORK, INFO ) |
* |
* |
* -- LAPACK driver routine (version 3.2) -- |
* -- LAPACK driver routine (version 3.7.0) -- |
* -- 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 |
* December 2016 |
* |
* |
* .. 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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* DSPGVD 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, stored in packed format, and B is also |
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* 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. |
|
* |
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* Arguments |
|
* ========= |
|
* |
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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 (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/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) |
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* On exit, if INFO = 0, WORK(1) returns the required LWORK. |
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* |
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* LWORK (input) 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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* |
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* IWORK (workspace/output) 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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* |
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* LIWORK (input) 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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* |
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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 DSPEVD returned an error code: |
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* <= N: if INFO = i, DSPEVD 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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* Further Details |
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* =============== |
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* |
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* Based on contributions by |
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* Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
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DOUBLE PRECISION TWO |
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PARAMETER ( TWO = 2.0D+0 ) |
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* .. |
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* .. Local Scalars .. |
* .. Local Scalars .. |
LOGICAL LQUERY, UPPER, WANTZ |
LOGICAL LQUERY, UPPER, WANTZ |
CHARACTER TRANS |
CHARACTER TRANS |
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END IF |
END IF |
WORK( 1 ) = LWMIN |
WORK( 1 ) = LWMIN |
IWORK( 1 ) = LIWMIN |
IWORK( 1 ) = LIWMIN |
* |
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IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN |
IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN |
INFO = -11 |
INFO = -11 |
ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN |
ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN |
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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' |