subroutine sgetc2	(	integer	N,
		real, dimension( lda, * )	A,
		integer	LDA,
		integer, dimension( * )	IPIV,
		integer, dimension( * )	JPIV,
		integer	INFO
	)

SGETC2 computes the LU factorization with complete pivoting of the general n-by-n matrix.

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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.

Parameters

[in]	N	N is INTEGER The order of the matrix A. N >= 0.
[in,out]	A	A is 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.
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).
[out]	IPIV	IPIV is INTEGER array, dimension(N). The pivot indices; for 1 <= i <= N, row i of the matrix has been interchanged with row IPIV(i).
[out]	JPIV	JPIV is INTEGER array, dimension(N). The pivot indices; for 1 <= j <= N, column j of the matrix has been interchanged with column JPIV(j).
[out]	INFO	INFO is 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.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date

June 2016

Contributors:

Bo Kagstrom and Peter Poromaa, Department of Computing Science, Umea University, S-901 87 Umea, Sweden.

Definition at line 113 of file sgetc2.f.

*
*  -- LAPACK auxiliary routine (version 3.6.1) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     June 2016
*
*     .. Scalar Arguments ..
      INTEGER            info, lda, n
*     ..
*     .. Array Arguments ..
      INTEGER            ipiv( * ), jpiv( * )
      REAL               a( lda, * )
*     ..
*
*  =====================================================================
*
*     .. 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 ..
*
      info = 0
*
*     Quick return if possible
*
      IF( n.EQ.0 )
     $   RETURN
*
*     Set constants to control overflow
*
      eps = slamch( 'P' )
      smlnum = slamch( 'S' ) / eps
      bignum = one / smlnum
      CALL slabad( smlnum, bignum )
*
*     Handle the case N=1 by itself
*
      IF( n.EQ.1 ) THEN
         ipiv( 1 ) = 1
         jpiv( 1 ) = 1
         IF( abs( a( 1, 1 ) ).LT.smlnum ) THEN
            info = 1
            a( 1, 1 ) = smlnum
         END IF
         RETURN
      END IF
*
*     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
*
*     Set last pivots to N
*
      ipiv( n ) = n
      jpiv( n ) = n
*
      RETURN
*
*     End of SGETC2
*

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