LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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zgetf2.f
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1*> \brief \b ZGETF2 computes the LU factorization of a general m-by-n matrix using partial pivoting with row interchanges (unblocked algorithm).
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
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13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgetf2.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE ZGETF2( M, N, A, LDA, IPIV, INFO )
22*
23* .. Scalar Arguments ..
24* INTEGER INFO, LDA, M, N
25* ..
26* .. Array Arguments ..
27* INTEGER IPIV( * )
28* COMPLEX*16 A( LDA, * )
29* ..
30*
31*
32*> \par Purpose:
33* =============
34*>
35*> \verbatim
36*>
37*> ZGETF2 computes an LU factorization of a general m-by-n matrix A
38*> using partial pivoting with row interchanges.
39*>
40*> The factorization has the form
41*> A = P * L * U
42*> where P is a permutation matrix, L is lower triangular with unit
43*> diagonal elements (lower trapezoidal if m > n), and U is upper
44*> triangular (upper trapezoidal if m < n).
45*>
46*> This is the right-looking Level 2 BLAS version of the algorithm.
47*> \endverbatim
48*
49* Arguments:
50* ==========
51*
52*> \param[in] M
53*> \verbatim
54*> M is INTEGER
55*> The number of rows of the matrix A. M >= 0.
56*> \endverbatim
57*>
58*> \param[in] N
59*> \verbatim
60*> N is INTEGER
61*> The number of columns of the matrix A. N >= 0.
62*> \endverbatim
63*>
64*> \param[in,out] A
65*> \verbatim
66*> A is COMPLEX*16 array, dimension (LDA,N)
67*> On entry, the m by n matrix to be factored.
68*> On exit, the factors L and U from the factorization
69*> A = P*L*U; the unit diagonal elements of L are not stored.
70*> \endverbatim
71*>
72*> \param[in] LDA
73*> \verbatim
74*> LDA is INTEGER
75*> The leading dimension of the array A. LDA >= max(1,M).
76*> \endverbatim
77*>
78*> \param[out] IPIV
79*> \verbatim
80*> IPIV is INTEGER array, dimension (min(M,N))
81*> The pivot indices; for 1 <= i <= min(M,N), row i of the
82*> matrix was interchanged with row IPIV(i).
83*> \endverbatim
84*>
85*> \param[out] INFO
86*> \verbatim
87*> INFO is INTEGER
88*> = 0: successful exit
89*> < 0: if INFO = -k, the k-th argument had an illegal value
90*> > 0: if INFO = k, U(k,k) is exactly zero. The factorization
91*> has been completed, but the factor U is exactly
92*> singular, and division by zero will occur if it is used
93*> to solve a system of equations.
94*> \endverbatim
95*
96* Authors:
97* ========
98*
99*> \author Univ. of Tennessee
100*> \author Univ. of California Berkeley
101*> \author Univ. of Colorado Denver
102*> \author NAG Ltd.
103*
104*> \ingroup getf2
105*
106* =====================================================================
107 SUBROUTINE zgetf2( M, N, A, LDA, IPIV, INFO )
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*16 A( LDA, * )
119* ..
120*
121* =====================================================================
122*
123* .. Parameters ..
124 COMPLEX*16 ONE, ZERO
125 parameter( one = ( 1.0d+0, 0.0d+0 ),
126 \$ zero = ( 0.0d+0, 0.0d+0 ) )
127* ..
128* .. Local Scalars ..
129 DOUBLE PRECISION SFMIN
130 INTEGER J, JP
131* ..
132* .. External Functions ..
133 DOUBLE PRECISION DLAMCH
134 INTEGER IZAMAX
135 EXTERNAL dlamch, izamax
136* ..
137* .. External Subroutines ..
138 EXTERNAL xerbla, zgeru, zrscl, zswap
139* ..
140* .. Intrinsic Functions ..
141 INTRINSIC max, min
142* ..
143* .. Executable Statements ..
144*
145* Test the input parameters.
146*
147 info = 0
148 IF( m.LT.0 ) THEN
149 info = -1
150 ELSE IF( n.LT.0 ) THEN
151 info = -2
152 ELSE IF( lda.LT.max( 1, m ) ) THEN
153 info = -4
154 END IF
155 IF( info.NE.0 ) THEN
156 CALL xerbla( 'ZGETF2', -info )
157 RETURN
158 END IF
159*
160* Quick return if possible
161*
162 IF( m.EQ.0 .OR. n.EQ.0 )
163 \$ RETURN
164*
165* Compute machine safe minimum
166*
167 sfmin = dlamch('S')
168*
169 DO 10 j = 1, min( m, n )
170*
171* Find pivot and test for singularity.
172*
173 jp = j - 1 + izamax( m-j+1, a( j, j ), 1 )
174 ipiv( j ) = jp
175 IF( a( jp, j ).NE.zero ) THEN
176*
177* Apply the interchange to columns 1:N.
178*
179 IF( jp.NE.j )
180 \$ CALL zswap( n, a( j, 1 ), lda, a( jp, 1 ), lda )
181*
182* Compute elements J+1:M of J-th column.
183*
184 IF( j.LT.m )
185 \$ CALL zrscl( m-j, a( j, j ), a( j+1, j ), 1 )
186*
187 ELSE IF( info.EQ.0 ) THEN
188*
189 info = j
190 END IF
191*
192 IF( j.LT.min( m, n ) ) THEN
193*
194* Update trailing submatrix.
195*
196 CALL zgeru( m-j, n-j, -one, a( j+1, j ), 1, a( j, j+1 ),
197 \$ lda, a( j+1, j+1 ), lda )
198 END IF
199 10 CONTINUE
200 RETURN
201*
202* End of ZGETF2
203*
204 END
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine zgeru(m, n, alpha, x, incx, y, incy, a, lda)
ZGERU
Definition zgeru.f:130
subroutine zgetf2(m, n, a, lda, ipiv, info)
ZGETF2 computes the LU factorization of a general m-by-n matrix using partial pivoting with row inter...
Definition zgetf2.f:108
subroutine zswap(n, zx, incx, zy, incy)
ZSWAP
Definition zswap.f:81
subroutine zrscl(n, a, x, incx)
ZDRSCL multiplies a vector by the reciprocal of a real scalar.
Definition zrscl.f:84