recursive subroutine sgetrf2	(	integer	M,
		integer	N,
		real, dimension( lda, * )	A,
		integer	LDA,
		integer, dimension( * )	IPIV,
		integer	INFO
	)

SGETRF2

Purpose:

 SGETRF2 computes an LU factorization of a general M-by-N matrix A
 using partial pivoting with row interchanges.

 The factorization has the form
    A = P * L * U
 where P is a permutation matrix, L is lower triangular with unit
 diagonal elements (lower trapezoidal if m > n), and U is upper
 triangular (upper trapezoidal if m < n).

 This is the recursive version of the algorithm. It divides
 the matrix into four submatrices:
            
        [  A11 | A12  ]  where A11 is n1 by n1 and A22 is n2 by n2
    A = [ --&mdash;|--&mdash; ]  with n1 = min(m,n)/2             
                                       [ A11 ]
 The subroutine calls itself to factor [ --- ],
                                       [ A12 ]
                 [ A12 ]
 do the swaps on [ --- ], solve A12, update A22,
                 [ A22 ]

 then calls itself to factor A22 and do the swaps on A21.

Parameters

[in]	M	M is INTEGER The number of rows of the matrix A. M >= 0.
[in]	N	N is INTEGER The number of columns of the matrix A. N >= 0.
[in,out]	A	A is REAL array, dimension (LDA,N) On entry, the M-by-N matrix to be factored. On exit, the factors L and U from the factorization A = P*L*U; the unit diagonal elements of L are not stored.
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).
[out]	IPIV	IPIV is INTEGER array, dimension (min(M,N)) The pivot indices; for 1 <= i <= min(M,N), row i of the matrix was interchanged with row IPIV(i).
[out]	INFO	INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, U(i,i) is exactly zero. The factorization has been completed, but the factor U is exactly singular, and division by zero will occur if it is used to solve a system of equations.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date

June 2016

Definition at line 115 of file sgetrf2.f.

*
*  -- LAPACK computational 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, m, n
*     ..
*     .. Array Arguments ..
      INTEGER            ipiv( * )
      REAL               a( lda, * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      REAL               one, zero
      parameter                ( one = 1.0e+0, zero = 0.0e+0 )
*     ..
*     .. Local Scalars ..
      REAL               sfmin, temp
      INTEGER            i, iinfo, n1, n2
*     ..
*     .. External Functions ..
      REAL               slamch
      INTEGER            isamax
      EXTERNAL           slamch, isamax
*     ..
*     .. External Subroutines ..
      EXTERNAL           sgemm, sscal, slaswp, strsm, xerbla
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          max, min
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters
*
      info = 0
      IF( m.LT.0 ) THEN
         info = -1
      ELSE IF( n.LT.0 ) THEN
         info = -2
      ELSE IF( lda.LT.max( 1, m ) ) THEN
         info = -4
      END IF
      IF( info.NE.0 ) THEN
         CALL xerbla( 'SGETRF2', -info )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( m.EQ.0 .OR. n.EQ.0 )
     $   RETURN

      IF ( m.EQ.1 ) THEN
*
*        Use unblocked code for one row case
*        Just need to handle IPIV and INFO
*
         ipiv( 1 ) = 1
         IF ( a(1,1).EQ.zero )
     $      info = 1
*
      ELSE IF( n.EQ.1 ) THEN
*
*        Use unblocked code for one column case
*
*
*        Compute machine safe minimum
*
         sfmin = slamch('S')
*
*        Find pivot and test for singularity
*
         i = isamax( m, a( 1, 1 ), 1 )
         ipiv( 1 ) = i
         IF( a( i, 1 ).NE.zero ) THEN
*
*           Apply the interchange
*
            IF( i.NE.1 ) THEN
               temp = a( 1, 1 )
               a( 1, 1 ) = a( i, 1 )
               a( i, 1 ) = temp
            END IF
*
*           Compute elements 2:M of the column
*
            IF( abs(a( 1, 1 )) .GE. sfmin ) THEN
               CALL sscal( m-1, one / a( 1, 1 ), a( 2, 1 ), 1 )
            ELSE
               DO 10 i = 1, m-1
                  a( 1+i, 1 ) = a( 1+i, 1 ) / a( 1, 1 )
   10          CONTINUE
            END IF
*
         ELSE
            info = 1
         END IF
*
      ELSE
*
*        Use recursive code
*
         n1 = min( m, n ) / 2
         n2 = n-n1
*
*               [ A11 ]
*        Factor [ --- ]
*               [ A21 ]
*
         CALL sgetrf2( m, n1, a, lda, ipiv, iinfo )

         IF ( info.EQ.0 .AND. iinfo.GT.0 )
     $      info = iinfo
*
*                              [ A12 ]
*        Apply interchanges to [ --- ]
*                              [ A22 ]
*
         CALL slaswp( n2, a( 1, n1+1 ), lda, 1, n1, ipiv, 1 )
*
*        Solve A12
*
         CALL strsm( 'L', 'L', 'N', 'U', n1, n2, one, a, lda, 
     $               a( 1, n1+1 ), lda )
*
*        Update A22
*
         CALL sgemm( 'N', 'N', m-n1, n2, n1, -one, a( n1+1, 1 ), lda, 
     $               a( 1, n1+1 ), lda, one, a( n1+1, n1+1 ), lda )
*
*        Factor A22
*
         CALL sgetrf2( m-n1, n2, a( n1+1, n1+1 ), lda, ipiv( n1+1 ),
     $                 iinfo )
*
*        Adjust INFO and the pivot indices
*
         IF ( info.EQ.0 .AND. iinfo.GT.0 )
     $      info = iinfo + n1
         DO 20 i = n1+1, min( m, n )
            ipiv( i ) = ipiv( i ) + n1
   20    CONTINUE
*
*        Apply interchanges to A21
*
         CALL slaswp( n1, a( 1, 1 ), lda, n1+1, min( m, n), ipiv, 1 )
*
      END IF
      RETURN
*
*     End of SGETRF2
*

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