 LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 subroutine sgetf2 ( integer M, integer N, real, dimension( lda, * ) A, integer LDA, integer, dimension( * ) IPIV, integer INFO )

SGETF2 computes the LU factorization of a general m-by-n matrix using partial pivoting with row interchanges (unblocked algorithm).

Purpose:
``` SGETF2 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 right-looking Level 2 BLAS version of the algorithm.```
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 = -k, the k-th argument had an illegal value > 0: if INFO = k, U(k,k) 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.```
Date
September 2012

Definition at line 110 of file sgetf2.f.

110 *
111 * -- LAPACK computational routine (version 3.4.2) --
112 * -- LAPACK is a software package provided by Univ. of Tennessee, --
113 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
114 * September 2012
115 *
116 * .. Scalar Arguments ..
117  INTEGER info, lda, m, n
118 * ..
119 * .. Array Arguments ..
120  INTEGER ipiv( * )
121  REAL a( lda, * )
122 * ..
123 *
124 * =====================================================================
125 *
126 * .. Parameters ..
127  REAL one, zero
128  parameter ( one = 1.0e+0, zero = 0.0e+0 )
129 * ..
130 * .. Local Scalars ..
131  REAL sfmin
132  INTEGER i, j, jp
133 * ..
134 * .. External Functions ..
135  REAL slamch
136  INTEGER isamax
137  EXTERNAL slamch, isamax
138 * ..
139 * .. External Subroutines ..
140  EXTERNAL sger, sscal, sswap, xerbla
141 * ..
142 * .. Intrinsic Functions ..
143  INTRINSIC max, min
144 * ..
145 * .. Executable Statements ..
146 *
147 * Test the input parameters.
148 *
149  info = 0
150  IF( m.LT.0 ) THEN
151  info = -1
152  ELSE IF( n.LT.0 ) THEN
153  info = -2
154  ELSE IF( lda.LT.max( 1, m ) ) THEN
155  info = -4
156  END IF
157  IF( info.NE.0 ) THEN
158  CALL xerbla( 'SGETF2', -info )
159  RETURN
160  END IF
161 *
162 * Quick return if possible
163 *
164  IF( m.EQ.0 .OR. n.EQ.0 )
165  \$ RETURN
166 *
167 * Compute machine safe minimum
168 *
169  sfmin = slamch('S')
170 *
171  DO 10 j = 1, min( m, n )
172 *
173 * Find pivot and test for singularity.
174 *
175  jp = j - 1 + isamax( m-j+1, a( j, j ), 1 )
176  ipiv( j ) = jp
177  IF( a( jp, j ).NE.zero ) THEN
178 *
179 * Apply the interchange to columns 1:N.
180 *
181  IF( jp.NE.j )
182  \$ CALL sswap( n, a( j, 1 ), lda, a( jp, 1 ), lda )
183 *
184 * Compute elements J+1:M of J-th column.
185 *
186  IF( j.LT.m ) THEN
187  IF( abs(a( j, j )) .GE. sfmin ) THEN
188  CALL sscal( m-j, one / a( j, j ), a( j+1, j ), 1 )
189  ELSE
190  DO 20 i = 1, m-j
191  a( j+i, j ) = a( j+i, j ) / a( j, j )
192  20 CONTINUE
193  END IF
194  END IF
195 *
196  ELSE IF( info.EQ.0 ) THEN
197 *
198  info = j
199  END IF
200 *
201  IF( j.LT.min( m, n ) ) THEN
202 *
203 * Update trailing submatrix.
204 *
205  CALL sger( m-j, n-j, -one, a( j+1, j ), 1, a( j, j+1 ), lda,
206  \$ a( j+1, j+1 ), lda )
207  END IF
208  10 CONTINUE
209  RETURN
210 *
211 * End of SGETF2
212 *
subroutine sger(M, N, ALPHA, X, INCX, Y, INCY, A, LDA)
SGER
Definition: sger.f:132
integer function isamax(N, SX, INCX)
ISAMAX
Definition: isamax.f:53
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine sscal(N, SA, SX, INCX)
SSCAL
Definition: sscal.f:55
subroutine sswap(N, SX, INCX, SY, INCY)
SSWAP
Definition: sswap.f:53
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:69

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