*> \brief \b DSYTRI2 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DSYTRI2 + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DSYTRI2( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO ) * * .. Scalar Arguments .. * CHARACTER UPLO * INTEGER INFO, LDA, LWORK, N * .. * .. Array Arguments .. * INTEGER IPIV( * ) * DOUBLE PRECISION A( LDA, * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DSYTRI2 computes the inverse of a DOUBLE PRECISION symmetric indefinite matrix *> A using the factorization A = U*D*U**T or A = L*D*L**T computed by *> DSYTRF. DSYTRI2 sets the LEADING DIMENSION of the workspace *> before calling DSYTRI2X that actually computes the inverse. *> \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 DOUBLE PRECISION 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 DSYTRF. *> *> 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 DSYTRF. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is DOUBLE PRECISION array, dimension (N+NB+1)*(NB+3) *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The dimension of the array WORK. *> WORK is size >= (N+NB+1)*(NB+3) *> If LWORK = -1, then a workspace query is assumed; the routine *> calculates: *> - 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. * *> \date November 2017 * *> \ingroup doubleSYcomputational * * ===================================================================== SUBROUTINE DSYTRI2( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO ) * * -- LAPACK computational routine (version 3.8.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2017 * * .. Scalar Arguments .. CHARACTER UPLO INTEGER INFO, LDA, LWORK, N * .. * .. Array Arguments .. INTEGER IPIV( * ) DOUBLE PRECISION A( LDA, * ), WORK( * ) * .. * * ===================================================================== * * .. Local Scalars .. LOGICAL UPPER, LQUERY INTEGER MINSIZE, NBMAX * .. * .. External Functions .. LOGICAL LSAME INTEGER ILAENV EXTERNAL LSAME, ILAENV * .. * .. External Subroutines .. EXTERNAL DSYTRI, DSYTRI2X, XERBLA * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 UPPER = LSAME( UPLO, 'U' ) LQUERY = ( LWORK.EQ.-1 ) * Get blocksize NBMAX = ILAENV( 1, 'DSYTRI2', UPLO, N, -1, -1, -1 ) IF ( NBMAX .GE. N ) THEN MINSIZE = N ELSE MINSIZE = (N+NBMAX+1)*(NBMAX+3) END IF * 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. MINSIZE .AND. .NOT.LQUERY ) THEN INFO = -7 END IF * * Quick return if possible * * IF( INFO.NE.0 ) THEN CALL XERBLA( 'DSYTRI2', -INFO ) RETURN ELSE IF( LQUERY ) THEN WORK(1)=MINSIZE RETURN END IF IF( N.EQ.0 ) $ RETURN IF( NBMAX .GE. N ) THEN CALL DSYTRI( UPLO, N, A, LDA, IPIV, WORK, INFO ) ELSE CALL DSYTRI2X( UPLO, N, A, LDA, IPIV, WORK, NBMAX, INFO ) END IF RETURN * * End of DSYTRI2 * END