LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ sgetf2()

 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.```

Definition at line 107 of file sgetf2.f.

108*
109* -- LAPACK computational routine --
110* -- LAPACK is a software package provided by Univ. of Tennessee, --
111* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
112*
113* .. Scalar Arguments ..
114 INTEGER INFO, LDA, M, N
115* ..
116* .. Array Arguments ..
117 INTEGER IPIV( * )
118 REAL A( LDA, * )
119* ..
120*
121* =====================================================================
122*
123* .. Parameters ..
124 REAL ONE, ZERO
125 parameter( one = 1.0e+0, zero = 0.0e+0 )
126* ..
127* .. Local Scalars ..
128 REAL SFMIN
129 INTEGER I, J, JP
130* ..
131* .. External Functions ..
132 REAL SLAMCH
133 INTEGER ISAMAX
134 EXTERNAL slamch, isamax
135* ..
136* .. External Subroutines ..
137 EXTERNAL sger, sscal, sswap, xerbla
138* ..
139* .. Intrinsic Functions ..
140 INTRINSIC max, min
141* ..
142* .. Executable Statements ..
143*
144* Test the input parameters.
145*
146 info = 0
147 IF( m.LT.0 ) THEN
148 info = -1
149 ELSE IF( n.LT.0 ) THEN
150 info = -2
151 ELSE IF( lda.LT.max( 1, m ) ) THEN
152 info = -4
153 END IF
154 IF( info.NE.0 ) THEN
155 CALL xerbla( 'SGETF2', -info )
156 RETURN
157 END IF
158*
159* Quick return if possible
160*
161 IF( m.EQ.0 .OR. n.EQ.0 )
162 \$ RETURN
163*
164* Compute machine safe minimum
165*
166 sfmin = slamch('S')
167*
168 DO 10 j = 1, min( m, n )
169*
170* Find pivot and test for singularity.
171*
172 jp = j - 1 + isamax( m-j+1, a( j, j ), 1 )
173 ipiv( j ) = jp
174 IF( a( jp, j ).NE.zero ) THEN
175*
176* Apply the interchange to columns 1:N.
177*
178 IF( jp.NE.j )
179 \$ CALL sswap( n, a( j, 1 ), lda, a( jp, 1 ), lda )
180*
181* Compute elements J+1:M of J-th column.
182*
183 IF( j.LT.m ) THEN
184 IF( abs(a( j, j )) .GE. sfmin ) THEN
185 CALL sscal( m-j, one / a( j, j ), a( j+1, j ), 1 )
186 ELSE
187 DO 20 i = 1, m-j
188 a( j+i, j ) = a( j+i, j ) / a( j, j )
189 20 CONTINUE
190 END IF
191 END IF
192*
193 ELSE IF( info.EQ.0 ) THEN
194*
195 info = j
196 END IF
197*
198 IF( j.LT.min( m, n ) ) THEN
199*
200* Update trailing submatrix.
201*
202 CALL sger( m-j, n-j, -one, a( j+1, j ), 1, a( j, j+1 ), lda,
203 \$ a( j+1, j+1 ), lda )
204 END IF
205 10 CONTINUE
206 RETURN
207*
208* End of SGETF2
209*
integer function isamax(N, SX, INCX)
ISAMAX
Definition: isamax.f:71
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine sswap(N, SX, INCX, SY, INCY)
SSWAP
Definition: sswap.f:82
subroutine sscal(N, SA, SX, INCX)
SSCAL
Definition: sscal.f:79
subroutine sger(M, N, ALPHA, X, INCX, Y, INCY, A, LDA)
SGER
Definition: sger.f:130
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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