157 lines
4.5 KiB
Fortran
157 lines
4.5 KiB
Fortran
SUBROUTINE ZGETRFF( M, N, A, LDA, IPIV, 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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* September 30, 1994
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*
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* .. Scalar Arguments ..
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INTEGER INFO, LDA, M, N
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* ..
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* .. Array Arguments ..
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INTEGER IPIV( * )
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COMPLEX*16 A( LDA, * )
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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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* ZGETRF computes an LU factorization of a general M-by-N matrix A
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* using partial pivoting with row interchanges.
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*
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* The factorization has the form
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* A = P * L * U
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* where P is a permutation matrix, L is lower triangular with unit
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* diagonal elements (lower trapezoidal if m > n), and U is upper
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* triangular (upper trapezoidal if m < n).
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*
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* This is the right-looking Level 3 BLAS version of the algorithm.
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*
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* Arguments
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* =========
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*
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* M (input) INTEGER
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* The number of rows of the matrix A. M >= 0.
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*
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* N (input) INTEGER
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* The number of columns of the matrix A. N >= 0.
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*
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* A (input/output) COMPLEX*16 array, dimension (LDA,N)
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* On entry, the M-by-N matrix to be factored.
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* On exit, the factors L and U from the factorization
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* A = P*L*U; the unit diagonal elements of L are not stored.
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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,M).
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*
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* IPIV (output) INTEGER array, dimension (min(M,N))
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* The pivot indices; for 1 <= i <= min(M,N), row i of the
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* matrix was interchanged with row IPIV(i).
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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 factorization
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* has been completed, but the factor U is exactly
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* singular, and division by zero will occur if it is used
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* to solve a system of equations.
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*
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* =====================================================================
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*
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* .. Parameters ..
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COMPLEX*16 ONE
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PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) )
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* ..
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* .. Local Scalars ..
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INTEGER I, IINFO, J, JB, NB
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* ..
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* .. External Subroutines ..
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EXTERNAL XERBLA, ZGEMM, ZGETF2, ZLASWP, ZTRSM
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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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IF( M.LT.0 ) THEN
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INFO = -1
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ELSE IF( N.LT.0 ) THEN
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INFO = -2
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ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
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INFO = -4
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'ZGETRF', -INFO )
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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( M.EQ.0 .OR. N.EQ.0 )
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$ RETURN
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*
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* Determine the block size for this environment.
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*
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NB = 64
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IF( NB.LE.1 .OR. NB.GE.MIN( M, N ) ) THEN
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*
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* Use unblocked code.
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*
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CALL ZGETF2( M, N, A, LDA, IPIV, INFO )
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ELSE
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*
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* Use blocked code.
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*
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DO 20 J = 1, MIN( M, N ), NB
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JB = MIN( MIN( M, N )-J+1, NB )
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*
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* Factor diagonal and subdiagonal blocks and test for exact
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* singularity.
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*
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CALL ZGETF2( M-J+1, JB, A( J, J ), LDA, IPIV( J ), IINFO )
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*
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* Adjust INFO and the pivot indices.
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*
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IF( INFO.EQ.0 .AND. IINFO.GT.0 )
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$ INFO = IINFO + J - 1
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DO 10 I = J, MIN( M, J+JB-1 )
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IPIV( I ) = J - 1 + IPIV( I )
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10 CONTINUE
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*
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* Apply interchanges to columns 1:J-1.
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*
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CALL ZLASWP( J-1, A, LDA, J, J+JB-1, IPIV, 1 )
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*
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IF( J+JB.LE.N ) THEN
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*
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* Apply interchanges to columns J+JB:N.
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*
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CALL ZLASWP( N-J-JB+1, A( 1, J+JB ), LDA, J, J+JB-1,
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$ IPIV, 1 )
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*
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* Compute block row of U.
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*
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CALL ZTRSM( 'Left', 'Lower', 'No transpose', 'Unit', JB,
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$ N-J-JB+1, ONE, A( J, J ), LDA, A( J, J+JB ),
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$ LDA )
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IF( J+JB.LE.M ) THEN
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*
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* Update trailing submatrix.
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*
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CALL ZGEMM( 'No transpose', 'No transpose', M-J-JB+1,
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$ N-J-JB+1, JB, -ONE, A( J+JB, J ), LDA,
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$ A( J, J+JB ), LDA, ONE, A( J+JB, J+JB ),
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$ LDA )
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END IF
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END IF
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20 CONTINUE
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END IF
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RETURN
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*
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* End of ZGETRF
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*
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END
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