246 lines
7.5 KiB
Fortran
246 lines
7.5 KiB
Fortran
*> \brief \b ZSYTRI_3
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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 ZSYTRI_3 + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zsytri_3.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/zsytri_3.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/zsytri_3.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 ZSYTRI_3( UPLO, N, A, LDA, E, IPIV, WORK, LWORK,
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* INFO )
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*
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* .. Scalar Arguments ..
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* CHARACTER UPLO
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* INTEGER INFO, LDA, LWORK, N
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* ..
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* .. Array Arguments ..
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* INTEGER IPIV( * )
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* COMPLEX*16 A( LDA, * ), E( * ), WORK( * )
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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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*> ZSYTRI_3 computes the inverse of a complex symmetric indefinite
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*> matrix A using the factorization computed by ZSYTRF_RK or ZSYTRF_BK:
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*>
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*> A = P*U*D*(U**T)*(P**T) or A = P*L*D*(L**T)*(P**T),
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*>
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*> where U (or L) is unit upper (or lower) triangular matrix,
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*> U**T (or L**T) is the transpose of U (or L), P is a permutation
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*> matrix, P**T is the transpose of P, and D is symmetric and block
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*> diagonal with 1-by-1 and 2-by-2 diagonal blocks.
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*>
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*> ZSYTRI_3 sets the leading dimension of the workspace before calling
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*> ZSYTRI_3X that actually computes the inverse. This is the blocked
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*> version of the algorithm, calling Level 3 BLAS.
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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.
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*> = 'U': Upper triangle of A is stored;
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*> = 'L': Lower triangle of A is 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 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 COMPLEX*16 array, dimension (LDA,N)
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*> On entry, diagonal of the block diagonal matrix D and
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*> factors U or L as computed by ZSYTRF_RK and ZSYTRF_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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*> should be provided on entry 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, if INFO = 0, the symmetric inverse of the original
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*> matrix.
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*> If UPLO = 'U': the upper triangular part of the inverse
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*> is formed and the part of A below the diagonal is not
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*> referenced;
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*> If UPLO = 'L': the lower triangular part of the inverse
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*> is formed and the part of A above the diagonal is not
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*> referenced.
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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] E
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*> \verbatim
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*> E is COMPLEX*16 array, dimension (N)
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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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*> NOTE: For 1-by-1 diagonal block D(k), where
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*> 1 <= k <= N, the element E(k) is not referenced in both
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*> UPLO = 'U' or UPLO = 'L' cases.
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*> \endverbatim
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*>
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*> \param[in] IPIV
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*> \verbatim
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*> IPIV is INTEGER array, dimension (N)
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*> Details of the interchanges and the block structure of D
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*> as determined by ZSYTRF_RK or ZSYTRF_BK.
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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 COMPLEX*16 array, dimension (N+NB+1)*(NB+3).
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*> On exit, if INFO = 0, WORK(1) returns the optimal 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 length of WORK. LWORK >= (N+NB+1)*(NB+3).
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*>
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*> If LDWORK = -1, then a workspace query is assumed;
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*> the routine only calculates the optimal size of the optimal
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*> size of the WORK array, returns this value as the first
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*> entry of the WORK array, and no error message related to
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*> LWORK 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: if INFO = i, D(i,i) = 0; the matrix is singular and its
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*> inverse could not be 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 complex16SYcomputational
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*
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*> \par Contributors:
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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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* =====================================================================
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SUBROUTINE ZSYTRI_3( UPLO, N, A, LDA, E, IPIV, WORK, LWORK,
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$ 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
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INTEGER INFO, LDA, LWORK, N
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* ..
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* .. Array Arguments ..
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INTEGER IPIV( * )
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COMPLEX*16 A( LDA, * ), E( * ), WORK( * )
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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 UPPER, LQUERY
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INTEGER LWKOPT, NB
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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INTEGER ILAENV
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EXTERNAL LSAME, ILAENV
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* ..
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* .. External Subroutines ..
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EXTERNAL ZSYTRI_3X, XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX
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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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INFO = 0
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UPPER = LSAME( UPLO, 'U' )
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LQUERY = ( LWORK.EQ.-1 )
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*
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* Determine the block size
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*
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NB = MAX( 1, ILAENV( 1, 'ZSYTRI_3', UPLO, N, -1, -1, -1 ) )
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LWKOPT = ( N+NB+1 ) * ( NB+3 )
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*
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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( N.LT.0 ) THEN
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INFO = -2
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ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
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INFO = -4
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ELSE IF ( LWORK .LT. LWKOPT .AND. .NOT.LQUERY ) THEN
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INFO = -8
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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( 'ZSYTRI_3', -INFO )
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RETURN
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ELSE IF( LQUERY ) THEN
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WORK( 1 ) = LWKOPT
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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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CALL ZSYTRI_3X( UPLO, N, A, LDA, E, IPIV, WORK, NB, INFO )
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*
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WORK( 1 ) = LWKOPT
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*
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RETURN
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*
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* End of ZSYTRI_3
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*
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END
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