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557 lines
16 KiB
557 lines
16 KiB
2 years ago
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*> \brief \b SSYCONVF
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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 SSYCONVF + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ssyconvf.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/ssyconvf.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/ssyconvf.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 SSYCONVF( UPLO, WAY, N, A, LDA, E, IPIV, INFO )
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*
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* .. Scalar Arguments ..
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* CHARACTER UPLO, WAY
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* INTEGER INFO, LDA, N
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* ..
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* .. Array Arguments ..
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* INTEGER IPIV( * )
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* REAL A( LDA, * ), E( * )
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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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*> If parameter WAY = 'C':
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*> SSYCONVF converts the factorization output format used in
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*> SSYTRF provided on entry in parameter A into the factorization
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*> output format used in SSYTRF_RK (or SSYTRF_BK) that is stored
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*> on exit in parameters A and E. It also converts in place details of
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*> the interchanges stored in IPIV from the format used in SSYTRF into
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*> the format used in SSYTRF_RK (or SSYTRF_BK).
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*>
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*> If parameter WAY = 'R':
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*> SSYCONVF performs the conversion in reverse direction, i.e.
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*> converts the factorization output format used in SSYTRF_RK
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*> (or SSYTRF_BK) provided on entry in parameters A and E into
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*> the factorization output format used in SSYTRF that is stored
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*> on exit in parameter A. It also converts in place details of
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*> the interchanges stored in IPIV from the format used in SSYTRF_RK
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*> (or SSYTRF_BK) into the format used in SSYTRF.
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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] UPLO
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*> \verbatim
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*> UPLO is CHARACTER*1
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*> Specifies whether the details of the factorization are
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*> stored as an upper or lower triangular matrix A.
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*> = 'U': Upper triangular
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*> = 'L': Lower triangular
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*> \endverbatim
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*>
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*> \param[in] WAY
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*> \verbatim
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*> WAY is CHARACTER*1
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*> = 'C': Convert
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*> = 'R': Revert
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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 matrix A. N >= 0.
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*> \endverbatim
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*>
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*> \param[in,out] A
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*> \verbatim
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*> A is REAL array, dimension (LDA,N)
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*>
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*> 1) If WAY ='C':
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*>
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*> On entry, contains factorization details in format used in
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*> SSYTRF:
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*> a) all elements of the symmetric block diagonal
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*> matrix D on the diagonal of A and on superdiagonal
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*> (or subdiagonal) of A, and
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*> b) If UPLO = 'U': multipliers used to obtain factor U
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*> in the superdiagonal part of A.
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*> If UPLO = 'L': multipliers used to obtain factor L
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*> in the superdiagonal part of A.
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*>
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*> On exit, contains factorization details in format used in
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*> SSYTRF_RK or SSYTRF_BK:
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*> a) ONLY diagonal elements of the symmetric block diagonal
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*> matrix D on the diagonal of A, i.e. D(k,k) = A(k,k);
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*> (superdiagonal (or subdiagonal) elements of D
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*> are stored on exit in array E), and
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*> b) If UPLO = 'U': factor U in the superdiagonal part of A.
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*> If UPLO = 'L': factor L in the subdiagonal part of A.
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*>
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*> 2) If WAY = 'R':
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*>
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*> On entry, contains factorization details in format used in
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*> SSYTRF_RK or SSYTRF_BK:
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*> a) ONLY diagonal elements of the symmetric block diagonal
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*> matrix D on the diagonal of A, i.e. D(k,k) = A(k,k);
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*> (superdiagonal (or subdiagonal) elements of D
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*> are stored on exit in array E), and
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*> b) If UPLO = 'U': factor U in the superdiagonal part of A.
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*> If UPLO = 'L': factor L in the subdiagonal part of A.
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*>
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*> On exit, contains factorization details in format used in
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*> SSYTRF:
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*> a) all elements of the symmetric block diagonal
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*> matrix D on the diagonal of A and on superdiagonal
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*> (or subdiagonal) of A, and
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*> b) If UPLO = 'U': multipliers used to obtain factor U
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*> in the superdiagonal part of A.
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*> If UPLO = 'L': multipliers used to obtain factor L
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*> in the superdiagonal part of A.
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*> \endverbatim
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*>
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*> \param[in] LDA
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*> \verbatim
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*> LDA is INTEGER
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*> The leading dimension of the array A. LDA >= max(1,N).
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*> \endverbatim
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*>
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*> \param[in,out] E
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*> \verbatim
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*> E is REAL array, dimension (N)
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*>
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*> 1) If WAY ='C':
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*>
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*> On entry, just a workspace.
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*>
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*> On exit, contains the superdiagonal (or subdiagonal)
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*> elements of the symmetric block diagonal matrix D
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*> with 1-by-1 or 2-by-2 diagonal blocks, where
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*> If UPLO = 'U': E(i) = D(i-1,i), i=2:N, E(1) is set to 0;
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*> If UPLO = 'L': E(i) = D(i+1,i), i=1:N-1, E(N) is set to 0.
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*>
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*> 2) If WAY = 'R':
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*>
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*> On entry, contains the superdiagonal (or subdiagonal)
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*> elements of the symmetric block diagonal matrix D
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*> with 1-by-1 or 2-by-2 diagonal blocks, where
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*> If UPLO = 'U': E(i) = D(i-1,i),i=2:N, E(1) not referenced;
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*> If UPLO = 'L': E(i) = D(i+1,i),i=1:N-1, E(N) not referenced.
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*>
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*> On exit, is not changed
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*> \endverbatim
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*.
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*> \param[in,out] IPIV
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*> \verbatim
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*> IPIV is INTEGER array, dimension (N)
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*>
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*> 1) If WAY ='C':
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*> On entry, details of the interchanges and the block
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*> structure of D in the format used in SSYTRF.
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*> On exit, details of the interchanges and the block
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*> structure of D in the format used in SSYTRF_RK
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*> ( or SSYTRF_BK).
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*>
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*> 1) If WAY ='R':
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*> On entry, details of the interchanges and the block
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*> structure of D in the format used in SSYTRF_RK
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*> ( or SSYTRF_BK).
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*> On exit, details of the interchanges and the block
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*> structure of D in the format used in SSYTRF.
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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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*> \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 singleSYcomputational
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*
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*> \par Contributors:
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* ==================
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*>
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*> \verbatim
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*>
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*> November 2017, Igor Kozachenko,
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*> Computer Science Division,
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*> University of California, Berkeley
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*>
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*> \endverbatim
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* =====================================================================
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SUBROUTINE SSYCONVF( UPLO, WAY, N, A, LDA, E, IPIV, INFO )
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*
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* -- LAPACK computational 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 UPLO, WAY
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INTEGER INFO, LDA, N
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* ..
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* .. Array Arguments ..
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INTEGER IPIV( * )
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REAL A( LDA, * ), E( * )
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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REAL ZERO
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PARAMETER ( ZERO = 0.0E+0 )
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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 SSWAP, XERBLA
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* .. Local Scalars ..
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LOGICAL UPPER, CONVERT
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INTEGER I, IP
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* ..
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* .. Executable Statements ..
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*
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INFO = 0
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UPPER = LSAME( UPLO, 'U' )
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CONVERT = LSAME( WAY, 'C' )
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IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
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INFO = -1
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ELSE IF( .NOT.CONVERT .AND. .NOT.LSAME( WAY, 'R' ) ) THEN
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INFO = -2
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ELSE IF( N.LT.0 ) THEN
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INFO = -3
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ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
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INFO = -5
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'SSYCONVF', -INFO )
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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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IF( UPPER ) THEN
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*
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* Begin A is UPPER
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*
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IF ( CONVERT ) THEN
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*
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* Convert A (A is upper)
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*
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*
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* Convert VALUE
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*
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* Assign superdiagonal entries of D to array E and zero out
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* corresponding entries in input storage A
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*
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I = N
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E( 1 ) = ZERO
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DO WHILE ( I.GT.1 )
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IF( IPIV( I ).LT.0 ) THEN
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E( I ) = A( I-1, I )
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E( I-1 ) = ZERO
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A( I-1, I ) = ZERO
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I = I - 1
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ELSE
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E( I ) = ZERO
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END IF
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I = I - 1
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END DO
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*
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* Convert PERMUTATIONS and IPIV
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*
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* Apply permutations to submatrices of upper part of A
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* in factorization order where i decreases from N to 1
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*
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I = N
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DO WHILE ( I.GE.1 )
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IF( IPIV( I ).GT.0 ) THEN
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*
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* 1-by-1 pivot interchange
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*
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* Swap rows i and IPIV(i) in A(1:i,N-i:N)
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*
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IP = IPIV( I )
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IF( I.LT.N ) THEN
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IF( IP.NE.I ) THEN
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CALL SSWAP( N-I, A( I, I+1 ), LDA,
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$ A( IP, I+1 ), LDA )
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END IF
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END IF
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*
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ELSE
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*
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* 2-by-2 pivot interchange
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*
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* Swap rows i-1 and IPIV(i) in A(1:i,N-i:N)
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*
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IP = -IPIV( I )
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IF( I.LT.N ) THEN
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IF( IP.NE.(I-1) ) THEN
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CALL SSWAP( N-I, A( I-1, I+1 ), LDA,
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$ A( IP, I+1 ), LDA )
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END IF
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END IF
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*
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* Convert IPIV
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* There is no interchange of rows i and and IPIV(i),
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* so this should be reflected in IPIV format for
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* *SYTRF_RK ( or *SYTRF_BK)
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*
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IPIV( I ) = I
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*
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I = I - 1
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*
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END IF
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I = I - 1
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END DO
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*
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ELSE
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*
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* Revert A (A is upper)
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*
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*
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* Revert PERMUTATIONS and IPIV
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*
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* Apply permutations to submatrices of upper part of A
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* in reverse factorization order where i increases from 1 to N
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*
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I = 1
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DO WHILE ( I.LE.N )
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IF( IPIV( I ).GT.0 ) THEN
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*
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* 1-by-1 pivot interchange
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*
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* Swap rows i and IPIV(i) in A(1:i,N-i:N)
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*
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IP = IPIV( I )
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IF( I.LT.N ) THEN
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IF( IP.NE.I ) THEN
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CALL SSWAP( N-I, A( IP, I+1 ), LDA,
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$ A( I, I+1 ), LDA )
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END IF
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END IF
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*
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ELSE
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*
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* 2-by-2 pivot interchange
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*
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* Swap rows i-1 and IPIV(i) in A(1:i,N-i:N)
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*
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I = I + 1
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||
|
|
IP = -IPIV( I )
|
||
|
|
IF( I.LT.N ) THEN
|
||
|
|
IF( IP.NE.(I-1) ) THEN
|
||
|
|
CALL SSWAP( N-I, A( IP, I+1 ), LDA,
|
||
|
|
$ A( I-1, I+1 ), LDA )
|
||
|
|
END IF
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Convert IPIV
|
||
|
|
* There is one interchange of rows i-1 and IPIV(i-1),
|
||
|
|
* so this should be recorded in two consecutive entries
|
||
|
|
* in IPIV format for *SYTRF
|
||
|
|
*
|
||
|
|
IPIV( I ) = IPIV( I-1 )
|
||
|
|
*
|
||
|
|
END IF
|
||
|
|
I = I + 1
|
||
|
|
END DO
|
||
|
|
*
|
||
|
|
* Revert VALUE
|
||
|
|
* Assign superdiagonal entries of D from array E to
|
||
|
|
* superdiagonal entries of A.
|
||
|
|
*
|
||
|
|
I = N
|
||
|
|
DO WHILE ( I.GT.1 )
|
||
|
|
IF( IPIV( I ).LT.0 ) THEN
|
||
|
|
A( I-1, I ) = E( I )
|
||
|
|
I = I - 1
|
||
|
|
END IF
|
||
|
|
I = I - 1
|
||
|
|
END DO
|
||
|
|
*
|
||
|
|
* End A is UPPER
|
||
|
|
*
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
ELSE
|
||
|
|
*
|
||
|
|
* Begin A is LOWER
|
||
|
|
*
|
||
|
|
IF ( CONVERT ) THEN
|
||
|
|
*
|
||
|
|
* Convert A (A is lower)
|
||
|
|
*
|
||
|
|
*
|
||
|
|
* Convert VALUE
|
||
|
|
* Assign subdiagonal entries of D to array E and zero out
|
||
|
|
* corresponding entries in input storage A
|
||
|
|
*
|
||
|
|
I = 1
|
||
|
|
E( N ) = ZERO
|
||
|
|
DO WHILE ( I.LE.N )
|
||
|
|
IF( I.LT.N .AND. IPIV(I).LT.0 ) THEN
|
||
|
|
E( I ) = A( I+1, I )
|
||
|
|
E( I+1 ) = ZERO
|
||
|
|
A( I+1, I ) = ZERO
|
||
|
|
I = I + 1
|
||
|
|
ELSE
|
||
|
|
E( I ) = ZERO
|
||
|
|
END IF
|
||
|
|
I = I + 1
|
||
|
|
END DO
|
||
|
|
*
|
||
|
|
* Convert PERMUTATIONS and IPIV
|
||
|
|
*
|
||
|
|
* Apply permutations to submatrices of lower part of A
|
||
|
|
* in factorization order where k increases from 1 to N
|
||
|
|
*
|
||
|
|
I = 1
|
||
|
|
DO WHILE ( I.LE.N )
|
||
|
|
IF( IPIV( I ).GT.0 ) THEN
|
||
|
|
*
|
||
|
|
* 1-by-1 pivot interchange
|
||
|
|
*
|
||
|
|
* Swap rows i and IPIV(i) in A(i:N,1:i-1)
|
||
|
|
*
|
||
|
|
IP = IPIV( I )
|
||
|
|
IF ( I.GT.1 ) THEN
|
||
|
|
IF( IP.NE.I ) THEN
|
||
|
|
CALL SSWAP( I-1, A( I, 1 ), LDA,
|
||
|
|
$ A( IP, 1 ), LDA )
|
||
|
|
END IF
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
ELSE
|
||
|
|
*
|
||
|
|
* 2-by-2 pivot interchange
|
||
|
|
*
|
||
|
|
* Swap rows i+1 and IPIV(i) in A(i:N,1:i-1)
|
||
|
|
*
|
||
|
|
IP = -IPIV( I )
|
||
|
|
IF ( I.GT.1 ) THEN
|
||
|
|
IF( IP.NE.(I+1) ) THEN
|
||
|
|
CALL SSWAP( I-1, A( I+1, 1 ), LDA,
|
||
|
|
$ A( IP, 1 ), LDA )
|
||
|
|
END IF
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Convert IPIV
|
||
|
|
* There is no interchange of rows i and and IPIV(i),
|
||
|
|
* so this should be reflected in IPIV format for
|
||
|
|
* *SYTRF_RK ( or *SYTRF_BK)
|
||
|
|
*
|
||
|
|
IPIV( I ) = I
|
||
|
|
*
|
||
|
|
I = I + 1
|
||
|
|
*
|
||
|
|
END IF
|
||
|
|
I = I + 1
|
||
|
|
END DO
|
||
|
|
*
|
||
|
|
ELSE
|
||
|
|
*
|
||
|
|
* Revert A (A is lower)
|
||
|
|
*
|
||
|
|
*
|
||
|
|
* Revert PERMUTATIONS and IPIV
|
||
|
|
*
|
||
|
|
* Apply permutations to submatrices of lower part of A
|
||
|
|
* in reverse factorization order where i decreases from N to 1
|
||
|
|
*
|
||
|
|
I = N
|
||
|
|
DO WHILE ( I.GE.1 )
|
||
|
|
IF( IPIV( I ).GT.0 ) THEN
|
||
|
|
*
|
||
|
|
* 1-by-1 pivot interchange
|
||
|
|
*
|
||
|
|
* Swap rows i and IPIV(i) in A(i:N,1:i-1)
|
||
|
|
*
|
||
|
|
IP = IPIV( I )
|
||
|
|
IF ( I.GT.1 ) THEN
|
||
|
|
IF( IP.NE.I ) THEN
|
||
|
|
CALL SSWAP( I-1, A( IP, 1 ), LDA,
|
||
|
|
$ A( I, 1 ), LDA )
|
||
|
|
END IF
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
ELSE
|
||
|
|
*
|
||
|
|
* 2-by-2 pivot interchange
|
||
|
|
*
|
||
|
|
* Swap rows i+1 and IPIV(i) in A(i:N,1:i-1)
|
||
|
|
*
|
||
|
|
I = I - 1
|
||
|
|
IP = -IPIV( I )
|
||
|
|
IF ( I.GT.1 ) THEN
|
||
|
|
IF( IP.NE.(I+1) ) THEN
|
||
|
|
CALL SSWAP( I-1, A( IP, 1 ), LDA,
|
||
|
|
$ A( I+1, 1 ), LDA )
|
||
|
|
END IF
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Convert IPIV
|
||
|
|
* There is one interchange of rows i+1 and IPIV(i+1),
|
||
|
|
* so this should be recorded in consecutive entries
|
||
|
|
* in IPIV format for *SYTRF
|
||
|
|
*
|
||
|
|
IPIV( I ) = IPIV( I+1 )
|
||
|
|
*
|
||
|
|
END IF
|
||
|
|
I = I - 1
|
||
|
|
END DO
|
||
|
|
*
|
||
|
|
* Revert VALUE
|
||
|
|
* Assign subdiagonal entries of D from array E to
|
||
|
|
* subdiagonal entries of A.
|
||
|
|
*
|
||
|
|
I = 1
|
||
|
|
DO WHILE ( I.LE.N-1 )
|
||
|
|
IF( IPIV( I ).LT.0 ) THEN
|
||
|
|
A( I + 1, I ) = E( I )
|
||
|
|
I = I + 1
|
||
|
|
END IF
|
||
|
|
I = I + 1
|
||
|
|
END DO
|
||
|
|
*
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* End A is LOWER
|
||
|
|
*
|
||
|
|
END IF
|
||
|
|
|
||
|
|
RETURN
|
||
|
|
*
|
||
|
|
* End of SSYCONVF
|
||
|
|
*
|
||
|
|
END
|