#include "ESMF_LapackBlas.inc" !> \brief \b DGETRI ! ! =========== DOCUMENTATION =========== ! ! Online html documentation available at ! http://www.netlib.org/lapack/explore-html/ ! !> \htmlonly !> Download DGETRI + dependencies !> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgetri.f"> !> [TGZ]</a> !> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgetri.f"> !> [ZIP]</a> !> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgetri.f"> !> [TXT]</a> !> \endhtmlonly ! ! Definition: ! =========== ! ! SUBROUTINE DGETRI( N, A, LDA, IPIV, WORK, LWORK, INFO ) ! ! .. Scalar Arguments .. ! INTEGER INFO, LDA, LWORK, N ! .. ! .. Array Arguments .. ! INTEGER IPIV( * ) ! DOUBLE PRECISION A( LDA, * ), WORK( * ) ! .. ! ! !> \par Purpose: ! ============= !> !> \verbatim !> !> DGETRI computes the inverse of a matrix using the LU factorization !> computed by DGETRF. !> !> This method inverts U and then computes inv(A) by solving the system !> inv(A)*L = inv(U) for inv(A). !> \endverbatim ! ! Arguments: ! ========== ! !> \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 factors L and U from the factorization !> A = P*L*U as computed by DGETRF. !> On exit, if INFO = 0, the inverse of the original matrix A. !> \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) !> The pivot indices from DGETRF; for 1<=i<=N, row i of the !> matrix was interchanged with row IPIV(i). !> \endverbatim !> !> \param[out] WORK !> \verbatim !> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) !> On exit, if INFO=0, then WORK(1) returns the optimal LWORK. !> \endverbatim !> !> \param[in] LWORK !> \verbatim !> LWORK is INTEGER !> The dimension of the array WORK. LWORK >= max(1,N). !> For optimal performance LWORK >= N*NB, where NB is !> the optimal blocksize returned by ILAENV. !> !> If LWORK = -1, then a workspace query is assumed; the routine !> only 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, U(i,i) is exactly zero; 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 doubleGEcomputational ! ! ===================================================================== SUBROUTINE DGETRI( N, A, LDA, IPIV, WORK, LWORK, 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 .. INTEGER INFO, LDA, LWORK, N ! .. ! .. Array Arguments .. INTEGER IPIV( * ) DOUBLE PRECISION A( LDA, * ), WORK( * ) ! .. ! ! ===================================================================== ! ! .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) ! .. ! .. Local Scalars .. LOGICAL LQUERY INTEGER I, IWS, J, JB, JJ, JP, LDWORK, LWKOPT, NB, & NBMIN, NN ! .. ! .. External Functions .. INTEGER ILAENV EXTERNAL ILAENV ! .. ! .. External Subroutines .. EXTERNAL DGEMM, DGEMV, DSWAP, DTRSM, DTRTRI, XERBLA ! .. ! .. Intrinsic Functions .. INTRINSIC MAX, MIN ! .. ! .. Executable Statements .. ! ! Test the input parameters. ! INFO = 0 NB = ILAENV( 1, 'DGETRI', ' ', N, -1, -1, -1 ) LWKOPT = N*NB WORK( 1 ) = LWKOPT LQUERY = ( LWORK.EQ.-1 ) IF( N.LT.0 ) THEN INFO = -1 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN INFO = -3 ELSE IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN INFO = -6 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'DGETRI', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF ! ! Quick return if possible ! IF( N.EQ.0 ) & RETURN ! ! Form inv(U). If INFO > 0 from DTRTRI, then U is singular, ! and the inverse is not computed. ! CALL DTRTRI( 'Upper', 'Non-unit', N, A, LDA, INFO ) IF( INFO.GT.0 ) & RETURN ! NBMIN = 2 LDWORK = N IF( NB.GT.1 .AND. NB.LT.N ) THEN IWS = MAX( LDWORK*NB, 1 ) IF( LWORK.LT.IWS ) THEN NB = LWORK / LDWORK NBMIN = MAX( 2, ILAENV( 2, 'DGETRI', ' ', N, -1, -1, -1 ) ) END IF ELSE IWS = N END IF ! ! Solve the equation inv(A)*L = inv(U) for inv(A). ! IF( NB.LT.NBMIN .OR. NB.GE.N ) THEN ! ! Use unblocked code. ! DO 20 J = N, 1, -1 ! ! Copy current column of L to WORK and replace with zeros. ! DO 10 I = J + 1, N WORK( I ) = A( I, J ) A( I, J ) = ZERO 10 CONTINUE ! ! Compute current column of inv(A). ! IF( J.LT.N ) & CALL DGEMV( 'No transpose', N, N-J, -ONE, A( 1, J+1 ), & LDA, WORK( J+1 ), 1, ONE, A( 1, J ), 1 ) 20 CONTINUE ELSE ! ! Use blocked code. ! NN = ( ( N-1 ) / NB )*NB + 1 DO 50 J = NN, 1, -NB JB = MIN( NB, N-J+1 ) ! ! Copy current block column of L to WORK and replace with ! zeros. ! DO 40 JJ = J, J + JB - 1 DO 30 I = JJ + 1, N WORK( I+( JJ-J )*LDWORK ) = A( I, JJ ) A( I, JJ ) = ZERO 30 CONTINUE 40 CONTINUE ! ! Compute current block column of inv(A). ! IF( J+JB.LE.N ) & CALL DGEMM( 'No transpose', 'No transpose', N, JB, & N-J-JB+1, -ONE, A( 1, J+JB ), LDA, & WORK( J+JB ), LDWORK, ONE, A( 1, J ), LDA ) CALL DTRSM( 'Right', 'Lower', 'No transpose', 'Unit', N, JB, & ONE, WORK( J ), LDWORK, A( 1, J ), LDA ) 50 CONTINUE END IF ! ! Apply column interchanges. ! DO 60 J = N - 1, 1, -1 JP = IPIV( J ) IF( JP.NE.J ) & CALL DSWAP( N, A( 1, J ), 1, A( 1, JP ), 1 ) 60 CONTINUE ! WORK( 1 ) = IWS RETURN ! ! End of DGETRI ! END