*> \brief \b CHETRI
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
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*
* Definition:
* ===========
*
* SUBROUTINE CHETRI( 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
*>
*> CHETRI computes the inverse of a complex Hermitian indefinite matrix
*> A using the factorization A = U*D*U**H or A = L*D*L**H computed by
*> CHETRF.
*> \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**H;
*> = 'L': Lower triangular, form is A = L*D*L**H.
*> \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 CHETRF.
*>
*> On exit, if INFO = 0, the (Hermitian) 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 CHETRF.
*> \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 complexHEcomputational
*
* =====================================================================
SUBROUTINE CHETRI( 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 ..
REAL ONE
COMPLEX CONE, ZERO
PARAMETER ( ONE = 1.0E+0, CONE = ( 1.0E+0, 0.0E+0 ),
$ ZERO = ( 0.0E+0, 0.0E+0 ) )
* ..
* .. Local Scalars ..
LOGICAL UPPER
INTEGER J, K, KP, KSTEP
REAL AK, AKP1, D, T
COMPLEX AKKP1, TEMP
* ..
* .. External Functions ..
LOGICAL LSAME
COMPLEX CDOTC
EXTERNAL LSAME, CDOTC
* ..
* .. External Subroutines ..
EXTERNAL CCOPY, CHEMV, CSWAP, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, CONJG, MAX, REAL
* ..
* .. 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( 'CHETRI', -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.ZERO )
$ 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.ZERO )
$ RETURN
20 CONTINUE
END IF
INFO = 0
*
IF( UPPER ) THEN
*
* Compute inv(A) from the factorization A = U*D*U**H.
*
* 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 50
*
IF( IPIV( K ).GT.0 ) THEN
*
* 1 x 1 diagonal block
*
* Invert the diagonal block.
*
A( K, K ) = ONE / REAL( 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 CHEMV( UPLO, K-1, -CONE, A, LDA, WORK, 1, ZERO,
$ A( 1, K ), 1 )
A( K, K ) = A( K, K ) - REAL( CDOTC( K-1, WORK, 1, A( 1,
$ K ), 1 ) )
END IF
KSTEP = 1
ELSE
*
* 2 x 2 diagonal block
*
* Invert the diagonal block.
*
T = ABS( A( K, K+1 ) )
AK = REAL( A( K, K ) ) / T
AKP1 = REAL( A( K+1, K+1 ) ) / T
AKKP1 = A( K, K+1 ) / T
D = T*( AK*AKP1-ONE )
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 CHEMV( UPLO, K-1, -CONE, A, LDA, WORK, 1, ZERO,
$ A( 1, K ), 1 )
A( K, K ) = A( K, K ) - REAL( CDOTC( K-1, WORK, 1, A( 1,
$ K ), 1 ) )
A( K, K+1 ) = A( K, K+1 ) -
$ CDOTC( K-1, A( 1, K ), 1, A( 1, K+1 ), 1 )
CALL CCOPY( K-1, A( 1, K+1 ), 1, WORK, 1 )
CALL CHEMV( UPLO, K-1, -CONE, A, LDA, WORK, 1, ZERO,
$ A( 1, K+1 ), 1 )
A( K+1, K+1 ) = A( K+1, K+1 ) -
$ REAL( CDOTC( K-1, WORK, 1, A( 1, K+1 ),
$ 1 ) )
END IF
KSTEP = 2
END IF
*
KP = ABS( IPIV( K ) )
IF( KP.NE.K ) THEN
*
* Interchange rows and columns K and KP in the leading
* submatrix A(1:k+1,1:k+1)
*
CALL CSWAP( KP-1, A( 1, K ), 1, A( 1, KP ), 1 )
DO 40 J = KP + 1, K - 1
TEMP = CONJG( A( J, K ) )
A( J, K ) = CONJG( A( KP, J ) )
A( KP, J ) = TEMP
40 CONTINUE
A( KP, K ) = CONJG( A( KP, K ) )
TEMP = A( K, K )
A( K, K ) = A( KP, KP )
A( KP, KP ) = TEMP
IF( KSTEP.EQ.2 ) THEN
TEMP = A( K, K+1 )
A( K, K+1 ) = A( KP, K+1 )
A( KP, K+1 ) = TEMP
END IF
END IF
*
K = K + KSTEP
GO TO 30
50 CONTINUE
*
ELSE
*
* Compute inv(A) from the factorization A = L*D*L**H.
*
* 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
60 CONTINUE
*
* If K < 1, exit from loop.
*
IF( K.LT.1 )
$ GO TO 80
*
IF( IPIV( K ).GT.0 ) THEN
*
* 1 x 1 diagonal block
*
* Invert the diagonal block.
*
A( K, K ) = ONE / REAL( 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 CHEMV( UPLO, N-K, -CONE, A( K+1, K+1 ), LDA, WORK,
$ 1, ZERO, A( K+1, K ), 1 )
A( K, K ) = A( K, K ) - REAL( CDOTC( N-K, WORK, 1,
$ A( K+1, K ), 1 ) )
END IF
KSTEP = 1
ELSE
*
* 2 x 2 diagonal block
*
* Invert the diagonal block.
*
T = ABS( A( K, K-1 ) )
AK = REAL( A( K-1, K-1 ) ) / T
AKP1 = REAL( A( K, K ) ) / T
AKKP1 = A( K, K-1 ) / T
D = T*( AK*AKP1-ONE )
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 CHEMV( UPLO, N-K, -CONE, A( K+1, K+1 ), LDA, WORK,
$ 1, ZERO, A( K+1, K ), 1 )
A( K, K ) = A( K, K ) - REAL( CDOTC( N-K, WORK, 1,
$ A( K+1, K ), 1 ) )
A( K, K-1 ) = A( K, K-1 ) -
$ CDOTC( 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 CHEMV( UPLO, N-K, -CONE, A( K+1, K+1 ), LDA, WORK,
$ 1, ZERO, A( K+1, K-1 ), 1 )
A( K-1, K-1 ) = A( K-1, K-1 ) -
$ REAL( CDOTC( N-K, WORK, 1, A( K+1, K-1 ),
$ 1 ) )
END IF
KSTEP = 2
END IF
*
KP = ABS( IPIV( K ) )
IF( KP.NE.K ) THEN
*
* Interchange rows and columns K and KP in the trailing
* submatrix A(k-1:n,k-1:n)
*
IF( KP.LT.N )
$ CALL CSWAP( N-KP, A( KP+1, K ), 1, A( KP+1, KP ), 1 )
DO 70 J = K + 1, KP - 1
TEMP = CONJG( A( J, K ) )
A( J, K ) = CONJG( A( KP, J ) )
A( KP, J ) = TEMP
70 CONTINUE
A( KP, K ) = CONJG( A( KP, K ) )
TEMP = A( K, K )
A( K, K ) = A( KP, KP )
A( KP, KP ) = TEMP
IF( KSTEP.EQ.2 ) THEN
TEMP = A( K, K-1 )
A( K, K-1 ) = A( KP, K-1 )
A( KP, K-1 ) = TEMP
END IF
END IF
*
K = K - KSTEP
GO TO 60
80 CONTINUE
END IF
*
RETURN
*
* End of CHETRI
*
END