LAPACK  3.4.2 LAPACK: Linear Algebra PACKage
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 *
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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 *> \date September 2012
105 *
106 *> \ingroup complex16GEcomputational
107 *
108 * =====================================================================
109  SUBROUTINE zgetf2( M, N, A, LDA, IPIV, INFO )
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  COMPLEX*16 a( lda, * )
122 * ..
123 *
124 * =====================================================================
125 *
126 * .. Parameters ..
127  COMPLEX*16 one, zero
128  parameter( one = ( 1.0d+0, 0.0d+0 ),
129  \$ zero = ( 0.0d+0, 0.0d+0 ) )
130 * ..
131 * .. Local Scalars ..
132  DOUBLE PRECISION sfmin
133  INTEGER i, j, jp
134 * ..
135 * .. External Functions ..
136  DOUBLE PRECISION dlamch
137  INTEGER izamax
138  EXTERNAL dlamch, izamax
139 * ..
140 * .. External Subroutines ..
141  EXTERNAL xerbla, zgeru, zscal, zswap
142 * ..
143 * .. Intrinsic Functions ..
144  INTRINSIC max, min
145 * ..
146 * .. Executable Statements ..
147 *
148 * Test the input parameters.
149 *
150  info = 0
151  IF( m.LT.0 ) THEN
152  info = -1
153  ELSE IF( n.LT.0 ) THEN
154  info = -2
155  ELSE IF( lda.LT.max( 1, m ) ) THEN
156  info = -4
157  END IF
158  IF( info.NE.0 ) THEN
159  CALL xerbla( 'ZGETF2', -info )
160  return
161  END IF
162 *
163 * Quick return if possible
164 *
165  IF( m.EQ.0 .OR. n.EQ.0 )
166  \$ return
167 *
168 * Compute machine safe minimum
169 *
170  sfmin = dlamch('S')
171 *
172  DO 10 j = 1, min( m, n )
173 *
174 * Find pivot and test for singularity.
175 *
176  jp = j - 1 + izamax( m-j+1, a( j, j ), 1 )
177  ipiv( j ) = jp
178  IF( a( jp, j ).NE.zero ) THEN
179 *
180 * Apply the interchange to columns 1:N.
181 *
182  IF( jp.NE.j )
183  \$ CALL zswap( n, a( j, 1 ), lda, a( jp, 1 ), lda )
184 *
185 * Compute elements J+1:M of J-th column.
186 *
187  IF( j.LT.m ) THEN
188  IF( abs(a( j, j )) .GE. sfmin ) THEN
189  CALL zscal( m-j, one / a( j, j ), a( j+1, j ), 1 )
190  ELSE
191  DO 20 i = 1, m-j
192  a( j+i, j ) = a( j+i, j ) / a( j, j )
193  20 continue
194  END IF
195  END IF
196 *
197  ELSE IF( info.EQ.0 ) THEN
198 *
199  info = j
200  END IF
201 *
202  IF( j.LT.min( m, n ) ) THEN
203 *
204 * Update trailing submatrix.
205 *
206  CALL zgeru( m-j, n-j, -one, a( j+1, j ), 1, a( j, j+1 ),
207  \$ lda, a( j+1, j+1 ), lda )
208  END IF
209  10 continue
210  return
211 *
212 * End of ZGETF2
213 *
214  END