sgetc2.f

          SUBROUTINE SGETC2( N, A, LDA, IPIV, JPIV, INFO )
    *
    *  -- LAPACK auxiliary routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley 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