julie
be91086043
Those are just cosmetic changes to update version number and various other minor change.
148 lines
4.2 KiB
FortranFixed
148 lines
4.2 KiB
FortranFixed
SUBROUTINE DGETC2( N, A, LDA, IPIV, JPIV, INFO )
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*
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* -- LAPACK auxiliary routine (version 3.2) --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver 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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DOUBLE PRECISION 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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* DGETC2 computes an LU factorization with 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 the Level 2 BLAS 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) DOUBLE PRECISION array, dimension (LDA, N)
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* On entry, the n-by-n matrix A 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, i.e., 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 owerflow if
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* we try to solve for x in Ax = b. So U is perturbed to
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* 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 DGER, DSWAP
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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, 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 DSWAP( 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 DSWAP( 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 ) = SMIN
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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 DGER( N-I, N-I, -ONE, A( I+1, I ), 1, A( I, I+1 ), LDA,
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$ 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 ) = SMIN
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END IF
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*
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RETURN
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*
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* End of DGETC2
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*
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END
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