*> \brief \b CSYTRI * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download CSYTRI + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE CSYTRI( 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 computes the inverse of a complex symmetric indefinite matrix *> A using the factorization A = U*D*U**T or A = L*D*L**T computed by *> CSYTRF. *> \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. *> *> 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. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX array, dimension (2*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. * *> \ingroup complexSYcomputational * * ===================================================================== SUBROUTINE CSYTRI( UPLO, N, A, LDA, IPIV, WORK, 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, N * .. * .. Array Arguments .. INTEGER IPIV( * ) COMPLEX A( LDA, * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. COMPLEX ONE, ZERO PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ), \$ ZERO = ( 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 ABS, 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', -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**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 ) = ONE / 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, -ONE, A, LDA, WORK, 1, ZERO, \$ 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-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 CSYMV( UPLO, K-1, -ONE, A, LDA, WORK, 1, ZERO, \$ 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, -ONE, A, LDA, WORK, 1, ZERO, \$ 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 * 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 ) 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 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 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 ) = ONE / 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, -ONE, A( K+1, K+1 ), LDA, WORK, 1, \$ ZERO, 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-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 CSYMV( UPLO, N-K, -ONE, A( K+1, K+1 ), LDA, WORK, 1, \$ ZERO, 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, -ONE, 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 ) - \$ CDOTU( 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 ) 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 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 50 60 CONTINUE END IF * RETURN * * End of CSYTRI * END