You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
246 lines
7.4 KiB
246 lines
7.4 KiB
2 years ago
|
*> \brief \b CSYTRI_3
|
||
|
|
*
|
||
|
|
* =========== DOCUMENTATION ===========
|
||
|
|
*
|
||
|
|
* Online html documentation available at
|
||
|
|
* http://www.netlib.org/lapack/explore-html/
|
||
|
|
*
|
||
|
|
*> \htmlonly
|
||
|
|
*> Download CSYTRI_3 + dependencies
|
||
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/csytri_3.f">
|
||
|
|
*> [TGZ]</a>
|
||
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/csytri_3.f">
|
||
|
|
*> [ZIP]</a>
|
||
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/csytri_3.f">
|
||
|
|
*> [TXT]</a>
|
||
|
|
*> \endhtmlonly
|
||
|
|
*
|
||
|
|
* Definition:
|
||
|
|
* ===========
|
||
|
|
*
|
||
|
|
* SUBROUTINE CSYTRI_3( UPLO, N, A, LDA, E, IPIV, WORK, LWORK,
|
||
|
|
* INFO )
|
||
|
|
*
|
||
|
|
* .. Scalar Arguments ..
|
||
|
|
* CHARACTER UPLO
|
||
|
|
* INTEGER INFO, LDA, LWORK, N
|
||
|
|
* ..
|
||
|
|
* .. Array Arguments ..
|
||
|
|
* INTEGER IPIV( * )
|
||
|
|
* COMPLEX A( LDA, * ), E( * ), WORK( * )
|
||
|
|
* ..
|
||
|
|
*
|
||
|
|
*
|
||
|
|
*> \par Purpose:
|
||
|
|
* =============
|
||
|
|
*>
|
||
|
|
*> \verbatim
|
||
|
|
*> CSYTRI_3 computes the inverse of a complex symmetric indefinite
|
||
|
|
*> matrix A using the factorization computed by CSYTRF_RK or CSYTRF_BK:
|
||
|
|
*>
|
||
|
|
*> A = P*U*D*(U**T)*(P**T) or A = P*L*D*(L**T)*(P**T),
|
||
|
|
*>
|
||
|
|
*> where U (or L) is unit upper (or lower) triangular matrix,
|
||
|
|
*> U**T (or L**T) is the transpose of U (or L), P is a permutation
|
||
|
|
*> matrix, P**T is the transpose of P, and D is symmetric and block
|
||
|
|
*> diagonal with 1-by-1 and 2-by-2 diagonal blocks.
|
||
|
|
*>
|
||
|
|
*> CSYTRI_3 sets the leading dimension of the workspace before calling
|
||
|
|
*> CSYTRI_3X that actually computes the inverse. This is the blocked
|
||
|
|
*> version of the algorithm, calling Level 3 BLAS.
|
||
|
|
*> \endverbatim
|
||
|
|
*
|
||
|
|
* Arguments:
|
||
|
|
* ==========
|
||
|
|
*
|
||
|
|
*> \param[in] UPLO
|
||
|
|
*> \verbatim
|
||
|
|
*> UPLO is CHARACTER*1
|
||
|
|
*> Specifies whether the details of the factorization are
|
||
|
|
*> stored as an upper or lower triangular matrix.
|
||
|
|
*> = 'U': Upper triangle of A is stored;
|
||
|
|
*> = 'L': Lower triangle of A is stored.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] N
|
||
|
|
*> \verbatim
|
||
|
|
*> N is INTEGER
|
||
|
|
*> The order of the matrix A. N >= 0.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in,out] A
|
||
|
|
*> \verbatim
|
||
|
|
*> A is COMPLEX array, dimension (LDA,N)
|
||
|
|
*> On entry, diagonal of the block diagonal matrix D and
|
||
|
|
*> factors U or L as computed by CSYTRF_RK and CSYTRF_BK:
|
||
|
|
*> a) ONLY diagonal elements of the symmetric block diagonal
|
||
|
|
*> matrix D on the diagonal of A, i.e. D(k,k) = A(k,k);
|
||
|
|
*> (superdiagonal (or subdiagonal) elements of D
|
||
|
|
*> should be provided on entry in array E), and
|
||
|
|
*> b) If UPLO = 'U': factor U in the superdiagonal part of A.
|
||
|
|
*> If UPLO = 'L': factor L in the subdiagonal part of A.
|
||
|
|
*>
|
||
|
|
*> On exit, if INFO = 0, the symmetric inverse of the original
|
||
|
|
*> matrix.
|
||
|
|
*> If UPLO = 'U': the upper triangular part of the inverse
|
||
|
|
*> is formed and the part of A below the diagonal is not
|
||
|
|
*> referenced;
|
||
|
|
*> If UPLO = 'L': the lower triangular part of the inverse
|
||
|
|
*> is formed and the part of A above the diagonal is not
|
||
|
|
*> referenced.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] LDA
|
||
|
|
*> \verbatim
|
||
|
|
*> LDA is INTEGER
|
||
|
|
*> The leading dimension of the array A. LDA >= max(1,N).
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] E
|
||
|
|
*> \verbatim
|
||
|
|
*> E is COMPLEX array, dimension (N)
|
||
|
|
*> On entry, contains the superdiagonal (or subdiagonal)
|
||
|
|
*> elements of the symmetric block diagonal matrix D
|
||
|
|
*> with 1-by-1 or 2-by-2 diagonal blocks, where
|
||
|
|
*> If UPLO = 'U': E(i) = D(i-1,i),i=2:N, E(1) not referenced;
|
||
|
|
*> If UPLO = 'L': E(i) = D(i+1,i),i=1:N-1, E(N) not referenced.
|
||
|
|
*>
|
||
|
|
*> NOTE: For 1-by-1 diagonal block D(k), where
|
||
|
|
*> 1 <= k <= N, the element E(k) is not referenced in both
|
||
|
|
*> UPLO = 'U' or UPLO = 'L' cases.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] IPIV
|
||
|
|
*> \verbatim
|
||
|
|
*> IPIV is INTEGER array, dimension (N)
|
||
|
|
*> Details of the interchanges and the block structure of D
|
||
|
|
*> as determined by CSYTRF_RK or CSYTRF_BK.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[out] WORK
|
||
|
|
*> \verbatim
|
||
|
|
*> WORK is COMPLEX array, dimension (N+NB+1)*(NB+3).
|
||
|
|
*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] LWORK
|
||
|
|
*> \verbatim
|
||
|
|
*> LWORK is INTEGER
|
||
|
|
*> The length of WORK. LWORK >= (N+NB+1)*(NB+3).
|
||
|
|
*>
|
||
|
|
*> If LDWORK = -1, then a workspace query is assumed;
|
||
|
|
*> the routine only calculates the optimal size of the optimal
|
||
|
|
*> size of the WORK array, returns this value as the first
|
||
|
|
*> entry of the WORK array, and no error message related to
|
||
|
|
*> LWORK is issued by XERBLA.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[out] INFO
|
||
|
|
*> \verbatim
|
||
|
|
*> INFO is INTEGER
|
||
|
|
*> = 0: successful exit
|
||
|
|
*> < 0: if INFO = -i, the i-th argument had an illegal value
|
||
|
|
*> > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
|
||
|
|
*> inverse could not be computed.
|
||
|
|
*> \endverbatim
|
||
|
|
*
|
||
|
|
* Authors:
|
||
|
|
* ========
|
||
|
|
*
|
||
|
|
*> \author Univ. of Tennessee
|
||
|
|
*> \author Univ. of California Berkeley
|
||
|
|
*> \author Univ. of Colorado Denver
|
||
|
|
*> \author NAG Ltd.
|
||
|
|
*
|
||
|
|
*> \ingroup complexSYcomputational
|
||
|
|
*
|
||
|
|
*> \par Contributors:
|
||
|
|
* ==================
|
||
|
|
*> \verbatim
|
||
|
|
*>
|
||
|
|
*> November 2017, Igor Kozachenko,
|
||
|
|
*> Computer Science Division,
|
||
|
|
*> University of California, Berkeley
|
||
|
|
*>
|
||
|
|
*> \endverbatim
|
||
|
|
*
|
||
|
|
* =====================================================================
|
||
|
|
SUBROUTINE CSYTRI_3( UPLO, N, A, LDA, E, IPIV, WORK, LWORK,
|
||
|
|
$ INFO )
|
||
|
|
*
|
||
|
|
* -- LAPACK computational routine --
|
||
|
|
* -- LAPACK is a software package provided by Univ. of Tennessee, --
|
||
|
|
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||
|
|
*
|
||
|
|
* .. Scalar Arguments ..
|
||
|
|
CHARACTER UPLO
|
||
|
|
INTEGER INFO, LDA, LWORK, N
|
||
|
|
* ..
|
||
|
|
* .. Array Arguments ..
|
||
|
|
INTEGER IPIV( * )
|
||
|
|
COMPLEX A( LDA, * ), E( * ), WORK( * )
|
||
|
|
* ..
|
||
|
|
*
|
||
|
|
* =====================================================================
|
||
|
|
*
|
||
|
|
* .. Local Scalars ..
|
||
|
|
LOGICAL UPPER, LQUERY
|
||
|
|
INTEGER LWKOPT, NB
|
||
|
|
* ..
|
||
|
|
* .. External Functions ..
|
||
|
|
LOGICAL LSAME
|
||
|
|
INTEGER ILAENV
|
||
|
|
EXTERNAL LSAME, ILAENV
|
||
|
|
* ..
|
||
|
|
* .. External Subroutines ..
|
||
|
|
EXTERNAL CSYTRI_3X, XERBLA
|
||
|
|
* ..
|
||
|
|
* .. Intrinsic Functions ..
|
||
|
|
INTRINSIC MAX
|
||
|
|
* ..
|
||
|
|
* .. Executable Statements ..
|
||
|
|
*
|
||
|
|
* Test the input parameters.
|
||
|
|
*
|
||
|
|
INFO = 0
|
||
|
|
UPPER = LSAME( UPLO, 'U' )
|
||
|
|
LQUERY = ( LWORK.EQ.-1 )
|
||
|
|
*
|
||
|
|
* Determine the block size
|
||
|
|
*
|
||
|
|
NB = MAX( 1, ILAENV( 1, 'CSYTRI_3', UPLO, N, -1, -1, -1 ) )
|
||
|
|
LWKOPT = ( N+NB+1 ) * ( NB+3 )
|
||
|
|
*
|
||
|
|
IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
|
||
|
|
INFO = -1
|
||
|
|
ELSE IF( N.LT.0 ) THEN
|
||
|
|
INFO = -2
|
||
|
|
ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
|
||
|
|
INFO = -4
|
||
|
|
ELSE IF ( LWORK .LT. LWKOPT .AND. .NOT.LQUERY ) THEN
|
||
|
|
INFO = -8
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
IF( INFO.NE.0 ) THEN
|
||
|
|
CALL XERBLA( 'CSYTRI_3', -INFO )
|
||
|
|
RETURN
|
||
|
|
ELSE IF( LQUERY ) THEN
|
||
|
|
WORK( 1 ) = LWKOPT
|
||
|
|
RETURN
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Quick return if possible
|
||
|
|
*
|
||
|
|
IF( N.EQ.0 )
|
||
|
|
$ RETURN
|
||
|
|
*
|
||
|
|
CALL CSYTRI_3X( UPLO, N, A, LDA, E, IPIV, WORK, NB, INFO )
|
||
|
|
*
|
||
|
|
WORK( 1 ) = LWKOPT
|
||
|
|
*
|
||
|
|
RETURN
|
||
|
|
*
|
||
|
|
* End of CSYTRI_3
|
||
|
|
*
|
||
|
|
END
|