LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ cgetf2()

 subroutine cgetf2 ( integer m, integer n, complex, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, integer info )

CGETF2 computes the LU factorization of a general m-by-n matrix using partial pivoting with row interchanges (unblocked algorithm).

Purpose:
CGETF2 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 COMPLEX 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 cgetf2.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 COMPLEX A( LDA, * )
119* ..
120*
121* =====================================================================
122*
123* .. Parameters ..
124 COMPLEX ONE, ZERO
125 parameter( one = ( 1.0e+0, 0.0e+0 ),
126 \$ zero = ( 0.0e+0, 0.0e+0 ) )
127* ..
128* .. Local Scalars ..
129 INTEGER J, JP
130* ..
131* .. External Functions ..
132 INTEGER ICAMAX
133 EXTERNAL icamax
134* ..
135* .. External Subroutines ..
136 EXTERNAL cgeru, crscl, cswap, xerbla
137* ..
138* .. Intrinsic Functions ..
139 INTRINSIC max, min
140* ..
141* .. Executable Statements ..
142*
143* Test the input parameters.
144*
145 info = 0
146 IF( m.LT.0 ) THEN
147 info = -1
148 ELSE IF( n.LT.0 ) THEN
149 info = -2
150 ELSE IF( lda.LT.max( 1, m ) ) THEN
151 info = -4
152 END IF
153 IF( info.NE.0 ) THEN
154 CALL xerbla( 'CGETF2', -info )
155 RETURN
156 END IF
157*
158* Quick return if possible
159*
160 IF( m.EQ.0 .OR. n.EQ.0 )
161 \$ RETURN
162*
163 DO 10 j = 1, min( m, n )
164*
165* Find pivot and test for singularity.
166*
167 jp = j - 1 + icamax( m-j+1, a( j, j ), 1 )
168 ipiv( j ) = jp
169 IF( a( jp, j ).NE.zero ) THEN
170*
171* Apply the interchange to columns 1:N.
172*
173 IF( jp.NE.j )
174 \$ CALL cswap( n, a( j, 1 ), lda, a( jp, 1 ), lda )
175*
176* Compute elements J+1:M of J-th column.
177*
178 IF( j.LT.m )
179 \$ CALL crscl( m-j, a( j, j ), a( j+1, j ), 1 )
180*
181 ELSE IF( info.EQ.0 ) THEN
182*
183 info = j
184 END IF
185*
186 IF( j.LT.min( m, n ) ) THEN
187*
188* Update trailing submatrix.
189*
190 CALL cgeru( m-j, n-j, -one, a( j+1, j ), 1, a( j, j+1 ),
191 \$ lda, a( j+1, j+1 ), lda )
192 END IF
193 10 CONTINUE
194 RETURN
195*
196* End of CGETF2
197*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine crscl(n, a, x, incx)
CRSCL multiplies a vector by the reciprocal of a real scalar.
Definition crscl.f:84
subroutine cgeru(m, n, alpha, x, incx, y, incy, a, lda)
CGERU
Definition cgeru.f:130
integer function icamax(n, cx, incx)
ICAMAX
Definition icamax.f:71
subroutine cswap(n, cx, incx, cy, incy)
CSWAP
Definition cswap.f:81
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