146 lines
4.2 KiB
FortranFixed
146 lines
4.2 KiB
FortranFixed
SUBROUTINE ZGETC2( N, A, LDA, IPIV, JPIV, INFO )
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*
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* -- LAPACK auxiliary routine (version 3.1) --
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* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
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* November 2006
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*
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* .. Scalar Arguments ..
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INTEGER INFO, LDA, N
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* ..
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* .. Array Arguments ..
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INTEGER IPIV( * ), JPIV( * )
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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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* ZGETC2 computes an LU factorization, using complete pivoting, of the
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* n-by-n matrix A. The factorization has the form A = P * L * U * Q,
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* where P and Q are permutation matrices, L is lower triangular with
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* unit diagonal elements and U is upper triangular.
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*
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* This is a level 1 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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* 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) COMPLEX*16 array, dimension (LDA, N)
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* On entry, the n-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*Q; the unit diagonal elements of L are not stored.
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* If U(k, k) appears to be less than SMIN, U(k, k) is given the
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* value of SMIN, giving a nonsingular perturbed system.
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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 (output) INTEGER array, dimension (N).
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* The pivot indices; for 1 <= i <= N, row i of the
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* matrix has been interchanged with row IPIV(i).
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*
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* JPIV (output) INTEGER array, dimension (N).
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* The pivot indices; for 1 <= j <= N, column j of the
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* matrix has been interchanged with column JPIV(j).
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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 = k, U(k, k) is likely to produce overflow if
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* one tries to solve for x in Ax = b. So U is perturbed
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* to avoid the overflow.
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*
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* Further Details
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* ===============
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*
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* Based on contributions by
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* Bo Kagstrom and Peter Poromaa, Department of Computing Science,
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* Umea University, S-901 87 Umea, Sweden.
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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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INTEGER I, IP, IPV, J, JP, JPV
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DOUBLE PRECISION BIGNUM, EPS, SMIN, SMLNUM, XMAX
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* ..
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* .. External Subroutines ..
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EXTERNAL ZGERU, ZSWAP
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* ..
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* .. External Functions ..
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DOUBLE PRECISION DLAMCH
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EXTERNAL DLAMCH
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, DCMPLX, MAX
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* ..
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* .. Executable Statements ..
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*
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* Set constants to control overflow
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*
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INFO = 0
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EPS = DLAMCH( 'P' )
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SMLNUM = DLAMCH( 'S' ) / EPS
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BIGNUM = ONE / SMLNUM
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CALL DLABAD( SMLNUM, BIGNUM )
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*
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* Factorize A using complete pivoting.
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* Set pivots less than SMIN to SMIN
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*
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DO 40 I = 1, N - 1
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*
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* Find max element in matrix A
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*
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XMAX = ZERO
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DO 20 IP = I, N
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DO 10 JP = I, N
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IF( ABS( A( IP, JP ) ).GE.XMAX ) THEN
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XMAX = ABS( A( IP, JP ) )
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IPV = IP
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JPV = JP
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END IF
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10 CONTINUE
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20 CONTINUE
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IF( I.EQ.1 )
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$ SMIN = MAX( EPS*XMAX, SMLNUM )
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*
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* Swap rows
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*
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IF( IPV.NE.I )
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$ CALL ZSWAP( N, A( IPV, 1 ), LDA, A( I, 1 ), LDA )
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IPIV( I ) = IPV
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*
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* Swap columns
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*
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IF( JPV.NE.I )
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$ CALL ZSWAP( N, A( 1, JPV ), 1, A( 1, I ), 1 )
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JPIV( I ) = JPV
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*
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* Check for singularity
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*
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IF( ABS( A( I, I ) ).LT.SMIN ) THEN
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INFO = I
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A( I, I ) = DCMPLX( SMIN, ZERO )
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END IF
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DO 30 J = I + 1, N
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A( J, I ) = A( J, I ) / A( I, I )
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30 CONTINUE
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CALL ZGERU( N-I, N-I, -DCMPLX( ONE ), A( I+1, I ), 1,
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$ A( I, I+1 ), LDA, A( I+1, I+1 ), LDA )
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40 CONTINUE
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*
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IF( ABS( A( N, N ) ).LT.SMIN ) THEN
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INFO = N
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A( N, N ) = DCMPLX( SMIN, ZERO )
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END IF
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RETURN
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*
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* End of ZGETC2
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*
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END
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