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|
*> \brief \b CSYTRI_ROOK
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download CSYTRI_ROOK + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/csytri_rook.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/csytri_rook.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/csytri_rook.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE CSYTRI_ROOK( UPLO, N, A, LDA, IPIV, WORK, INFO )
*
* .. Scalar Arguments ..
* CHARACTER UPLO
* INTEGER INFO, LDA, N
* ..
* .. Array Arguments ..
* INTEGER IPIV( * )
* COMPLEX A( LDA, * ), WORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> CSYTRI_ROOK computes the inverse of a complex symmetric
*> matrix A using the factorization A = U*D*U**T or A = L*D*L**T
*> computed by CSYTRF_ROOK.
*> \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 triangular, form is A = U*D*U**T;
*> = 'L': Lower triangular, form is A = L*D*L**T.
*> \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, the block diagonal matrix D and the multipliers
*> used to obtain the factor U or L as computed by CSYTRF_ROOK.
*>
*> 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] IPIV
*> \verbatim
*> IPIV is INTEGER array, dimension (N)
*> Details of the interchanges and the block structure of D
*> as determined by CSYTRF_ROOK.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is COMPLEX array, dimension (N)
*> \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.
*
*> \date December 2016
*
*> \ingroup complexSYcomputational
*
*> \par Contributors:
* ==================
*>
*> \verbatim
*>
*> December 2016, Igor Kozachenko,
*> Computer Science Division,
*> University of California, Berkeley
*>
*> September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
*> School of Mathematics,
*> University of Manchester
*>
*> \endverbatim
*
* =====================================================================
SUBROUTINE CSYTRI_ROOK( UPLO, N, A, LDA, IPIV, WORK, INFO )
*
* -- LAPACK computational routine (version 3.7.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* December 2016
*
* .. Scalar Arguments ..
CHARACTER UPLO
INTEGER INFO, LDA, N
* ..
* .. Array Arguments ..
INTEGER IPIV( * )
COMPLEX A( LDA, * ), WORK( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
COMPLEX CONE, CZERO
PARAMETER ( CONE = ( 1.0E+0, 0.0E+0 ),
$ CZERO = ( 0.0E+0, 0.0E+0 ) )
* ..
* .. Local Scalars ..
LOGICAL UPPER
INTEGER K, KP, KSTEP
COMPLEX AK, AKKP1, AKP1, D, T, TEMP
* ..
* .. External Functions ..
LOGICAL LSAME
COMPLEX CDOTU
EXTERNAL LSAME, CDOTU
* ..
* .. External Subroutines ..
EXTERNAL CCOPY, CSWAP, CSYMV, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
INFO = 0
UPPER = LSAME( UPLO, 'U' )
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
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'CSYTRI_ROOK', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 )
$ RETURN
*
* Check that the diagonal matrix D is nonsingular.
*
IF( UPPER ) THEN
*
* Upper triangular storage: examine D from bottom to top
*
DO 10 INFO = N, 1, -1
IF( IPIV( INFO ).GT.0 .AND. A( INFO, INFO ).EQ.CZERO )
$ RETURN
10 CONTINUE
ELSE
*
* Lower triangular storage: examine D from top to bottom.
*
DO 20 INFO = 1, N
IF( IPIV( INFO ).GT.0 .AND. A( INFO, INFO ).EQ.CZERO )
$ RETURN
20 CONTINUE
END IF
INFO = 0
*
IF( UPPER ) THEN
*
* Compute inv(A) from the factorization A = U*D*U**T.
*
* K is the main loop index, increasing from 1 to N in steps of
* 1 or 2, depending on the size of the diagonal blocks.
*
K = 1
30 CONTINUE
*
* If K > N, exit from loop.
*
IF( K.GT.N )
$ GO TO 40
*
IF( IPIV( K ).GT.0 ) THEN
*
* 1 x 1 diagonal block
*
* Invert the diagonal block.
*
A( K, K ) = CONE / A( K, K )
*
* Compute column K of the inverse.
*
IF( K.GT.1 ) THEN
CALL CCOPY( K-1, A( 1, K ), 1, WORK, 1 )
CALL CSYMV( UPLO, K-1, -CONE, A, LDA, WORK, 1, CZERO,
$ A( 1, K ), 1 )
A( K, K ) = A( K, K ) - CDOTU( K-1, WORK, 1, A( 1, K ),
$ 1 )
END IF
KSTEP = 1
ELSE
*
* 2 x 2 diagonal block
*
* Invert the diagonal block.
*
T = A( K, K+1 )
AK = A( K, K ) / T
AKP1 = A( K+1, K+1 ) / T
AKKP1 = A( K, K+1 ) / T
D = T*( AK*AKP1-CONE )
A( K, K ) = AKP1 / D
A( K+1, K+1 ) = AK / D
A( K, K+1 ) = -AKKP1 / D
*
* Compute columns K and K+1 of the inverse.
*
IF( K.GT.1 ) THEN
CALL CCOPY( K-1, A( 1, K ), 1, WORK, 1 )
CALL CSYMV( UPLO, K-1, -CONE, A, LDA, WORK, 1, CZERO,
$ A( 1, K ), 1 )
A( K, K ) = A( K, K ) - CDOTU( K-1, WORK, 1, A( 1, K ),
$ 1 )
A( K, K+1 ) = A( K, K+1 ) -
$ CDOTU( K-1, A( 1, K ), 1, A( 1, K+1 ), 1 )
CALL CCOPY( K-1, A( 1, K+1 ), 1, WORK, 1 )
CALL CSYMV( UPLO, K-1, -CONE, A, LDA, WORK, 1, CZERO,
$ A( 1, K+1 ), 1 )
A( K+1, K+1 ) = A( K+1, K+1 ) -
$ CDOTU( K-1, WORK, 1, A( 1, K+1 ), 1 )
END IF
KSTEP = 2
END IF
*
IF( KSTEP.EQ.1 ) THEN
*
* Interchange rows and columns K and IPIV(K) in the leading
* submatrix A(1:k+1,1:k+1)
*
KP = IPIV( K )
IF( KP.NE.K ) THEN
IF( KP.GT.1 )
$ CALL CSWAP( KP-1, A( 1, K ), 1, A( 1, KP ), 1 )
CALL CSWAP( K-KP-1, A( KP+1, K ), 1, A( KP, KP+1 ), LDA )
TEMP = A( K, K )
A( K, K ) = A( KP, KP )
A( KP, KP ) = TEMP
END IF
ELSE
*
* Interchange rows and columns K and K+1 with -IPIV(K) and
* -IPIV(K+1)in the leading submatrix A(1:k+1,1:k+1)
*
KP = -IPIV( K )
IF( KP.NE.K ) THEN
IF( KP.GT.1 )
$ CALL CSWAP( KP-1, A( 1, K ), 1, A( 1, KP ), 1 )
CALL CSWAP( K-KP-1, A( KP+1, K ), 1, A( KP, KP+1 ), LDA )
*
TEMP = A( K, K )
A( K, K ) = A( KP, KP )
A( KP, KP ) = TEMP
TEMP = A( K, K+1 )
A( K, K+1 ) = A( KP, K+1 )
A( KP, K+1 ) = TEMP
END IF
*
K = K + 1
KP = -IPIV( K )
IF( KP.NE.K ) THEN
IF( KP.GT.1 )
$ CALL CSWAP( KP-1, A( 1, K ), 1, A( 1, KP ), 1 )
CALL CSWAP( K-KP-1, A( KP+1, K ), 1, A( KP, KP+1 ), LDA )
TEMP = A( K, K )
A( K, K ) = A( KP, KP )
A( KP, KP ) = TEMP
END IF
END IF
*
K = K + 1
GO TO 30
40 CONTINUE
*
ELSE
*
* Compute inv(A) from the factorization A = L*D*L**T.
*
* K is the main loop index, increasing from 1 to N in steps of
* 1 or 2, depending on the size of the diagonal blocks.
*
K = N
50 CONTINUE
*
* If K < 1, exit from loop.
*
IF( K.LT.1 )
$ GO TO 60
*
IF( IPIV( K ).GT.0 ) THEN
*
* 1 x 1 diagonal block
*
* Invert the diagonal block.
*
A( K, K ) = CONE / A( K, K )
*
* Compute column K of the inverse.
*
IF( K.LT.N ) THEN
CALL CCOPY( N-K, A( K+1, K ), 1, WORK, 1 )
CALL CSYMV( UPLO, N-K,-CONE, A( K+1, K+1 ), LDA, WORK, 1,
$ CZERO, A( K+1, K ), 1 )
A( K, K ) = A( K, K ) - CDOTU( N-K, WORK, 1, A( K+1, K ),
$ 1 )
END IF
KSTEP = 1
ELSE
*
* 2 x 2 diagonal block
*
* Invert the diagonal block.
*
T = A( K, K-1 )
AK = A( K-1, K-1 ) / T
AKP1 = A( K, K ) / T
AKKP1 = A( K, K-1 ) / T
D = T*( AK*AKP1-CONE )
A( K-1, K-1 ) = AKP1 / D
A( K, K ) = AK / D
A( K, K-1 ) = -AKKP1 / D
*
* Compute columns K-1 and K of the inverse.
*
IF( K.LT.N ) THEN
CALL CCOPY( N-K, A( K+1, K ), 1, WORK, 1 )
CALL CSYMV( UPLO, N-K,-CONE, A( K+1, K+1 ), LDA, WORK, 1,
$ CZERO, A( K+1, K ), 1 )
A( K, K ) = A( K, K ) - CDOTU( N-K, WORK, 1, A( K+1, K ),
$ 1 )
A( K, K-1 ) = A( K, K-1 ) -
$ CDOTU( N-K, A( K+1, K ), 1, A( K+1, K-1 ),
$ 1 )
CALL CCOPY( N-K, A( K+1, K-1 ), 1, WORK, 1 )
CALL CSYMV( UPLO, N-K,-CONE, A( K+1, K+1 ), LDA, WORK, 1,
$ CZERO, A( K+1, K-1 ), 1 )
A( K-1, K-1 ) = A( K-1, K-1 ) -
$ CDOTU( N-K, WORK, 1, A( K+1, K-1 ), 1 )
END IF
KSTEP = 2
END IF
*
IF( KSTEP.EQ.1 ) THEN
*
* Interchange rows and columns K and IPIV(K) in the trailing
* submatrix A(k-1:n,k-1:n)
*
KP = IPIV( K )
IF( KP.NE.K ) THEN
IF( KP.LT.N )
$ CALL CSWAP( N-KP, A( KP+1, K ), 1, A( KP+1, KP ), 1 )
CALL CSWAP( KP-K-1, A( K+1, K ), 1, A( KP, K+1 ), LDA )
TEMP = A( K, K )
A( K, K ) = A( KP, KP )
A( KP, KP ) = TEMP
END IF
ELSE
*
* Interchange rows and columns K and K-1 with -IPIV(K) and
* -IPIV(K-1) in the trailing submatrix A(k-1:n,k-1:n)
*
KP = -IPIV( K )
IF( KP.NE.K ) THEN
IF( KP.LT.N )
$ CALL CSWAP( N-KP, A( KP+1, K ), 1, A( KP+1, KP ), 1 )
CALL CSWAP( KP-K-1, A( K+1, K ), 1, A( KP, K+1 ), LDA )
*
TEMP = A( K, K )
A( K, K ) = A( KP, KP )
A( KP, KP ) = TEMP
TEMP = A( K, K-1 )
A( K, K-1 ) = A( KP, K-1 )
A( KP, K-1 ) = TEMP
END IF
*
K = K - 1
KP = -IPIV( K )
IF( KP.NE.K ) THEN
IF( KP.LT.N )
$ CALL CSWAP( N-KP, A( KP+1, K ), 1, A( KP+1, KP ), 1 )
CALL CSWAP( KP-K-1, A( K+1, K ), 1, A( KP, K+1 ), LDA )
TEMP = A( K, K )
A( K, K ) = A( KP, KP )
A( KP, KP ) = TEMP
END IF
END IF
*
K = K - 1
GO TO 50
60 CONTINUE
END IF
*
RETURN
*
* End of CSYTRI_ROOK
*
END
|
