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 SGETC2( 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( * )
|
|
REAL A( LDA, * )
|
|
* ..
|
|
*
|
|
* Purpose
|
|
* =======
|
|
*
|
|
* SGETC2 computes an LU factorization with 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 the Level 2 BLAS algorithm.
|
|
*
|
|
* Arguments
|
|
* =========
|
|
*
|
|
* N (input) INTEGER
|
|
* The order of the matrix A. N >= 0.
|
|
*
|
|
* A (input/output) REAL array, dimension (LDA, N)
|
|
* On entry, the n-by-n matrix A 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, i.e., 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 owerflow if
|
|
* we try 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 SGER, SLABAD, SSWAP
|
|
* ..
|
|
* .. External Functions ..
|
|
REAL SLAMCH
|
|
EXTERNAL SLAMCH
|
|
* ..
|
|
* .. Intrinsic Functions ..
|
|
INTRINSIC ABS, 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 SSWAP( N, A( IPV, 1 ), LDA, A( I, 1 ), LDA )
|
|
IPIV( I ) = IPV
|
|
*
|
|
* Swap columns
|
|
*
|
|
IF( JPV.NE.I )
|
|
$ CALL SSWAP( 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 ) = SMIN
|
|
END IF
|
|
DO 30 J = I + 1, N
|
|
A( J, I ) = A( J, I ) / A( I, I )
|
|
30 CONTINUE
|
|
CALL SGER( N-I, N-I, -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 ) = SMIN
|
|
END IF
|
|
*
|
|
RETURN
|
|
*
|
|
* End of SGETC2
|
|
*
|
|
END
|