194 lines
5.6 KiB
Fortran
194 lines
5.6 KiB
Fortran
SUBROUTINE ZGETRI( N, A, LDA, IPIV, WORK, LWORK, INFO )
|
|
*
|
|
* -- LAPACK routine (version 3.0) --
|
|
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
|
|
* Courant Institute, Argonne National Lab, and Rice University
|
|
* June 30, 1999
|
|
*
|
|
* .. Scalar Arguments ..
|
|
INTEGER INFO, LDA, LWORK, N
|
|
* ..
|
|
* .. Array Arguments ..
|
|
INTEGER IPIV( * )
|
|
COMPLEX*16 A( LDA, * ), WORK( * )
|
|
* ..
|
|
*
|
|
* Purpose
|
|
* =======
|
|
*
|
|
* ZGETRI computes the inverse of a matrix using the LU factorization
|
|
* computed by ZGETRF.
|
|
*
|
|
* This method inverts U and then computes inv(A) by solving the system
|
|
* inv(A)*L = inv(U) for inv(A).
|
|
*
|
|
* Arguments
|
|
* =========
|
|
*
|
|
* N (input) INTEGER
|
|
* The order of the matrix A. N >= 0.
|
|
*
|
|
* A (input/output) COMPLEX*16 array, dimension (LDA,N)
|
|
* On entry, the factors L and U from the factorization
|
|
* A = P*L*U as computed by ZGETRF.
|
|
* On exit, if INFO = 0, the inverse of the original matrix A.
|
|
*
|
|
* LDA (input) INTEGER
|
|
* The leading dimension of the array A. LDA >= max(1,N).
|
|
*
|
|
* IPIV (input) INTEGER array, dimension (N)
|
|
* The pivot indices from ZGETRF; for 1<=i<=N, row i of the
|
|
* matrix was interchanged with row IPIV(i).
|
|
*
|
|
* WORK (workspace/output) COMPLEX*16 array, dimension (LWORK)
|
|
* On exit, if INFO=0, then WORK(1) returns the optimal LWORK.
|
|
*
|
|
* LWORK (input) 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.
|
|
*
|
|
* INFO (output) 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.
|
|
*
|
|
* =====================================================================
|
|
*
|
|
* .. Parameters ..
|
|
COMPLEX*16 ZERO, ONE
|
|
PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ),
|
|
$ ONE = ( 1.0D+0, 0.0D+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 XERBLA, ZGEMM, ZGEMV, ZSWAP, ZTRSM, ZTRTRI
|
|
* ..
|
|
* .. Intrinsic Functions ..
|
|
INTRINSIC MAX, MIN
|
|
* ..
|
|
* .. Executable Statements ..
|
|
*
|
|
* Test the input parameters.
|
|
*
|
|
INFO = 0
|
|
NB = ILAENV( 1, 'ZGETRI', ' ', 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( 'ZGETRI', -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 ZTRTRI, then U is singular,
|
|
* and the inverse is not computed.
|
|
*
|
|
CALL ZTRTRI( '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, 'ZGETRI', ' ', 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 ZGEMV( '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 ZGEMM( '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 ZTRSM( '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 ZSWAP( N, A( 1, J ), 1, A( 1, JP ), 1 )
|
|
60 CONTINUE
|
|
*
|
|
WORK( 1 ) = IWS
|
|
RETURN
|
|
*
|
|
* End of ZGETRI
|
|
*
|
|
END
|