262 lines
7.2 KiB
Fortran
262 lines
7.2 KiB
Fortran
*> \brief \b SGETRI
|
|
*
|
|
* =========== DOCUMENTATION ===========
|
|
*
|
|
* Online html documentation available at
|
|
* http://www.netlib.org/lapack/explore-html/
|
|
*
|
|
*> \htmlonly
|
|
*> Download SGETRI + dependencies
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sgetri.f">
|
|
*> [TGZ]</a>
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sgetri.f">
|
|
*> [ZIP]</a>
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sgetri.f">
|
|
*> [TXT]</a>
|
|
*> \endhtmlonly
|
|
*
|
|
* Definition:
|
|
* ===========
|
|
*
|
|
* SUBROUTINE SGETRI( N, A, LDA, IPIV, WORK, LWORK, INFO )
|
|
*
|
|
* .. Scalar Arguments ..
|
|
* INTEGER INFO, LDA, LWORK, N
|
|
* ..
|
|
* .. Array Arguments ..
|
|
* INTEGER IPIV( * )
|
|
* REAL A( LDA, * ), WORK( * )
|
|
* ..
|
|
*
|
|
*
|
|
*> \par Purpose:
|
|
* =============
|
|
*>
|
|
*> \verbatim
|
|
*>
|
|
*> SGETRI computes the inverse of a matrix using the LU factorization
|
|
*> computed by SGETRF.
|
|
*>
|
|
*> 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 REAL array, dimension (LDA,N)
|
|
*> On entry, the factors L and U from the factorization
|
|
*> A = P*L*U as computed by SGETRF.
|
|
*> 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 SGETRF; for 1<=i<=N, row i of the
|
|
*> matrix was interchanged with row IPIV(i).
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[out] WORK
|
|
*> \verbatim
|
|
*> WORK is REAL 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 November 2011
|
|
*
|
|
*> \ingroup realGEcomputational
|
|
*
|
|
* =====================================================================
|
|
SUBROUTINE SGETRI( N, A, LDA, IPIV, WORK, LWORK, INFO )
|
|
*
|
|
* -- LAPACK computational routine (version 3.4.0) --
|
|
* -- LAPACK is a software package provided by Univ. of Tennessee, --
|
|
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
|
* November 2011
|
|
*
|
|
* .. Scalar Arguments ..
|
|
INTEGER INFO, LDA, LWORK, N
|
|
* ..
|
|
* .. Array Arguments ..
|
|
INTEGER IPIV( * )
|
|
REAL A( LDA, * ), WORK( * )
|
|
* ..
|
|
*
|
|
* =====================================================================
|
|
*
|
|
* .. Parameters ..
|
|
REAL ZERO, ONE
|
|
PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+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 SGEMM, SGEMV, SSWAP, STRSM, STRTRI, XERBLA
|
|
* ..
|
|
* .. Intrinsic Functions ..
|
|
INTRINSIC MAX, MIN
|
|
* ..
|
|
* .. Executable Statements ..
|
|
*
|
|
* Test the input parameters.
|
|
*
|
|
INFO = 0
|
|
NB = ILAENV( 1, 'SGETRI', ' ', 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( 'SGETRI', -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 STRTRI, then U is singular,
|
|
* and the inverse is not computed.
|
|
*
|
|
CALL STRTRI( '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, 'SGETRI', ' ', 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 SGEMV( '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 SGEMM( '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 STRSM( '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 SSWAP( N, A( 1, J ), 1, A( 1, JP ), 1 )
|
|
60 CONTINUE
|
|
*
|
|
WORK( 1 ) = IWS
|
|
RETURN
|
|
*
|
|
* End of SGETRI
|
|
*
|
|
END
|