julie
be91086043
Those are just cosmetic changes to update version number and various other minor change.
147 lines
4.2 KiB
FortranFixed
147 lines
4.2 KiB
FortranFixed
SUBROUTINE CGETC2( N, A, LDA, IPIV, JPIV, INFO )
|
|
*
|
|
* -- LAPACK auxiliary routine (version 3.2) --
|
|
* -- LAPACK is a software package provided by Univ. of Tennessee, --
|
|
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
|
* November 2006
|
|
*
|
|
* .. Scalar Arguments ..
|
|
INTEGER INFO, LDA, N
|
|
* ..
|
|
* .. Array Arguments ..
|
|
INTEGER IPIV( * ), JPIV( * )
|
|
COMPLEX A( LDA, * )
|
|
* ..
|
|
*
|
|
* Purpose
|
|
* =======
|
|
*
|
|
* CGETC2 computes an LU factorization, using complete pivoting, of the
|
|
* n-by-n matrix A. The factorization has the form A = P * L * U * Q,
|
|
* where P and Q are permutation matrices, L is lower triangular with
|
|
* unit diagonal elements and U is upper triangular.
|
|
*
|
|
* This is a level 1 BLAS version of the algorithm.
|
|
*
|
|
* Arguments
|
|
* =========
|
|
*
|
|
* N (input) INTEGER
|
|
* The order of the matrix A. N >= 0.
|
|
*
|
|
* A (input/output) COMPLEX array, dimension (LDA, N)
|
|
* On entry, the n-by-n matrix to be factored.
|
|
* On exit, the factors L and U from the factorization
|
|
* A = P*L*U*Q; the unit diagonal elements of L are not stored.
|
|
* If U(k, k) appears to be less than SMIN, U(k, k) is given the
|
|
* value of SMIN, giving a nonsingular perturbed system.
|
|
*
|
|
* LDA (input) INTEGER
|
|
* The leading dimension of the array A. LDA >= max(1, N).
|
|
*
|
|
* IPIV (output) INTEGER array, dimension (N).
|
|
* The pivot indices; for 1 <= i <= N, row i of the
|
|
* matrix has been interchanged with row IPIV(i).
|
|
*
|
|
* JPIV (output) INTEGER array, dimension (N).
|
|
* The pivot indices; for 1 <= j <= N, column j of the
|
|
* matrix has been interchanged with column JPIV(j).
|
|
*
|
|
* INFO (output) INTEGER
|
|
* = 0: successful exit
|
|
* > 0: if INFO = k, U(k, k) is likely to produce overflow if
|
|
* one tries to solve for x in Ax = b. So U is perturbed
|
|
* to avoid the overflow.
|
|
*
|
|
* Further Details
|
|
* ===============
|
|
*
|
|
* Based on contributions by
|
|
* Bo Kagstrom and Peter Poromaa, Department of Computing Science,
|
|
* Umea University, S-901 87 Umea, Sweden.
|
|
*
|
|
* =====================================================================
|
|
*
|
|
* .. Parameters ..
|
|
REAL ZERO, ONE
|
|
PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
|
|
* ..
|
|
* .. Local Scalars ..
|
|
INTEGER I, IP, IPV, J, JP, JPV
|
|
REAL BIGNUM, EPS, SMIN, SMLNUM, XMAX
|
|
* ..
|
|
* .. External Subroutines ..
|
|
EXTERNAL CGERU, CSWAP, SLABAD
|
|
* ..
|
|
* .. External Functions ..
|
|
REAL SLAMCH
|
|
EXTERNAL SLAMCH
|
|
* ..
|
|
* .. Intrinsic Functions ..
|
|
INTRINSIC ABS, CMPLX, MAX
|
|
* ..
|
|
* .. Executable Statements ..
|
|
*
|
|
* Set constants to control overflow
|
|
*
|
|
INFO = 0
|
|
EPS = SLAMCH( 'P' )
|
|
SMLNUM = SLAMCH( 'S' ) / EPS
|
|
BIGNUM = ONE / SMLNUM
|
|
CALL SLABAD( SMLNUM, BIGNUM )
|
|
*
|
|
* Factorize A using complete pivoting.
|
|
* Set pivots less than SMIN to SMIN
|
|
*
|
|
DO 40 I = 1, N - 1
|
|
*
|
|
* Find max element in matrix A
|
|
*
|
|
XMAX = ZERO
|
|
DO 20 IP = I, N
|
|
DO 10 JP = I, N
|
|
IF( ABS( A( IP, JP ) ).GE.XMAX ) THEN
|
|
XMAX = ABS( A( IP, JP ) )
|
|
IPV = IP
|
|
JPV = JP
|
|
END IF
|
|
10 CONTINUE
|
|
20 CONTINUE
|
|
IF( I.EQ.1 )
|
|
$ SMIN = MAX( EPS*XMAX, SMLNUM )
|
|
*
|
|
* Swap rows
|
|
*
|
|
IF( IPV.NE.I )
|
|
$ CALL CSWAP( N, A( IPV, 1 ), LDA, A( I, 1 ), LDA )
|
|
IPIV( I ) = IPV
|
|
*
|
|
* Swap columns
|
|
*
|
|
IF( JPV.NE.I )
|
|
$ CALL CSWAP( N, A( 1, JPV ), 1, A( 1, I ), 1 )
|
|
JPIV( I ) = JPV
|
|
*
|
|
* Check for singularity
|
|
*
|
|
IF( ABS( A( I, I ) ).LT.SMIN ) THEN
|
|
INFO = I
|
|
A( I, I ) = CMPLX( SMIN, ZERO )
|
|
END IF
|
|
DO 30 J = I + 1, N
|
|
A( J, I ) = A( J, I ) / A( I, I )
|
|
30 CONTINUE
|
|
CALL CGERU( N-I, N-I, -CMPLX( ONE ), A( I+1, I ), 1,
|
|
$ A( I, I+1 ), LDA, A( I+1, I+1 ), LDA )
|
|
40 CONTINUE
|
|
*
|
|
IF( ABS( A( N, N ) ).LT.SMIN ) THEN
|
|
INFO = N
|
|
A( N, N ) = CMPLX( SMIN, ZERO )
|
|
END IF
|
|
RETURN
|
|
*
|
|
* End of CGETC2
|
|
*
|
|
END
|