193 lines
5.6 KiB
Fortran
193 lines
5.6 KiB
Fortran
SUBROUTINE DGETRI( N, A, LDA, IPIV, WORK, LWORK, INFO )
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*
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* -- LAPACK routine (version 3.0) --
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* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
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* Courant Institute, Argonne National Lab, and Rice University
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* June 30, 1999
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*
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* .. Scalar Arguments ..
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INTEGER INFO, LDA, LWORK, N
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* ..
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* .. Array Arguments ..
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INTEGER IPIV( * )
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DOUBLE PRECISION A( LDA, * ), WORK( * )
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* ..
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*
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* Purpose
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* =======
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*
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* DGETRI computes the inverse of a matrix using the LU factorization
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* computed by DGETRF.
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*
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* This method inverts U and then computes inv(A) by solving the system
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* inv(A)*L = inv(U) for inv(A).
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*
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* Arguments
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* =========
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*
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* N (input) INTEGER
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* The order of the matrix A. N >= 0.
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*
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* A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
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* On entry, the factors L and U from the factorization
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* A = P*L*U as computed by DGETRF.
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* On exit, if INFO = 0, the inverse of the original matrix A.
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*
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* LDA (input) INTEGER
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* The leading dimension of the array A. LDA >= max(1,N).
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*
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* IPIV (input) INTEGER array, dimension (N)
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* The pivot indices from DGETRF; for 1<=i<=N, row i of the
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* matrix was interchanged with row IPIV(i).
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*
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* WORK (workspace/output) DOUBLE PRECISION array, dimension (LWORK)
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* On exit, if INFO=0, then WORK(1) returns the optimal LWORK.
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*
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* LWORK (input) INTEGER
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* The dimension of the array WORK. LWORK >= max(1,N).
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* For optimal performance LWORK >= N*NB, where NB is
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* the optimal blocksize returned by ILAENV.
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*
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* If LWORK = -1, then a workspace query is assumed; the routine
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* only calculates the optimal size of the WORK array, returns
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* this value as the first entry of the WORK array, and no error
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* message related to LWORK is issued by XERBLA.
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*
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* INFO (output) INTEGER
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* = 0: successful exit
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* < 0: if INFO = -i, the i-th argument had an illegal value
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* > 0: if INFO = i, U(i,i) is exactly zero; the matrix is
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* singular and its inverse could not be computed.
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*
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* =====================================================================
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*
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* .. Parameters ..
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DOUBLE PRECISION ZERO, ONE
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PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
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* ..
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* .. Local Scalars ..
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LOGICAL LQUERY
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INTEGER I, IWS, J, JB, JJ, JP, LDWORK, LWKOPT, NB,
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$ NBMIN, NN
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* ..
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* .. External Functions ..
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INTEGER ILAENV
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EXTERNAL ILAENV
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* ..
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* .. External Subroutines ..
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EXTERNAL DGEMM, DGEMV, DSWAP, DTRSM, DTRTRI, XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX, MIN
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* ..
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* .. Executable Statements ..
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*
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* Test the input parameters.
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*
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INFO = 0
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NB = ILAENV( 1, 'DGETRI', ' ', N, -1, -1, -1 )
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LWKOPT = N*NB
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WORK( 1 ) = LWKOPT
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LQUERY = ( LWORK.EQ.-1 )
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IF( N.LT.0 ) THEN
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INFO = -1
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ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
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INFO = -3
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ELSE IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN
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INFO = -6
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'DGETRI', -INFO )
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RETURN
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ELSE IF( LQUERY ) THEN
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RETURN
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END IF
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*
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* Quick return if possible
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*
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IF( N.EQ.0 )
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$ RETURN
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*
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* Form inv(U). If INFO > 0 from DTRTRI, then U is singular,
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* and the inverse is not computed.
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*
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CALL DTRTRI( 'Upper', 'Non-unit', N, A, LDA, INFO )
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IF( INFO.GT.0 )
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$ RETURN
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*
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NBMIN = 2
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LDWORK = N
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IF( NB.GT.1 .AND. NB.LT.N ) THEN
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IWS = MAX( LDWORK*NB, 1 )
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IF( LWORK.LT.IWS ) THEN
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NB = LWORK / LDWORK
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NBMIN = MAX( 2, ILAENV( 2, 'DGETRI', ' ', N, -1, -1, -1 ) )
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END IF
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ELSE
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IWS = N
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END IF
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*
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* Solve the equation inv(A)*L = inv(U) for inv(A).
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*
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IF( NB.LT.NBMIN .OR. NB.GE.N ) THEN
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*
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* Use unblocked code.
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*
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DO 20 J = N, 1, -1
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*
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* Copy current column of L to WORK and replace with zeros.
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*
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DO 10 I = J + 1, N
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WORK( I ) = A( I, J )
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A( I, J ) = ZERO
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10 CONTINUE
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*
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* Compute current column of inv(A).
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*
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IF( J.LT.N )
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$ CALL DGEMV( 'No transpose', N, N-J, -ONE, A( 1, J+1 ),
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$ LDA, WORK( J+1 ), 1, ONE, A( 1, J ), 1 )
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20 CONTINUE
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ELSE
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*
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* Use blocked code.
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*
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NN = ( ( N-1 ) / NB )*NB + 1
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DO 50 J = NN, 1, -NB
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JB = MIN( NB, N-J+1 )
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*
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* Copy current block column of L to WORK and replace with
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* zeros.
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*
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DO 40 JJ = J, J + JB - 1
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DO 30 I = JJ + 1, N
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WORK( I+( JJ-J )*LDWORK ) = A( I, JJ )
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A( I, JJ ) = ZERO
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30 CONTINUE
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40 CONTINUE
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*
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* Compute current block column of inv(A).
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*
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IF( J+JB.LE.N )
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$ CALL DGEMM( 'No transpose', 'No transpose', N, JB,
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$ N-J-JB+1, -ONE, A( 1, J+JB ), LDA,
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$ WORK( J+JB ), LDWORK, ONE, A( 1, J ), LDA )
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CALL DTRSM( 'Right', 'Lower', 'No transpose', 'Unit', N, JB,
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$ ONE, WORK( J ), LDWORK, A( 1, J ), LDA )
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50 CONTINUE
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END IF
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*
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* Apply column interchanges.
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*
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DO 60 J = N - 1, 1, -1
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JP = IPIV( J )
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IF( JP.NE.J )
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$ CALL DSWAP( N, A( 1, J ), 1, A( 1, JP ), 1 )
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60 CONTINUE
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*
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WORK( 1 ) = IWS
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RETURN
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*
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* End of DGETRI
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*
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END
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