LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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dgetf2.f
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1*> \brief \b DGETF2 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
9*> Download DGETF2 + dependencies
10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgetf2.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgetf2.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgetf2.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE DGETF2( M, N, A, LDA, IPIV, INFO )
22*
23* .. Scalar Arguments ..
24* INTEGER INFO, LDA, M, N
25* ..
26* .. Array Arguments ..
27* INTEGER IPIV( * )
28* DOUBLE PRECISION A( LDA, * )
29* ..
30*
31*
32*> \par Purpose:
33* =============
34*>
35*> \verbatim
36*>
37*> DGETF2 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 DOUBLE PRECISION 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 doubleGEcomputational
105*
106* =====================================================================
107 SUBROUTINE dgetf2( 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 DOUBLE PRECISION A( LDA, * )
119* ..
120*
121* =====================================================================
122*
123* .. Parameters ..
124 DOUBLE PRECISION ONE, ZERO
125 parameter( one = 1.0d+0, zero = 0.0d+0 )
126* ..
127* .. Local Scalars ..
128 DOUBLE PRECISION SFMIN
129 INTEGER I, J, JP
130* ..
131* .. External Functions ..
132 DOUBLE PRECISION DLAMCH
133 INTEGER IDAMAX
134 EXTERNAL dlamch, idamax
135* ..
136* .. External Subroutines ..
137 EXTERNAL dger, dscal, dswap, 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( 'DGETF2', -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 = dlamch('S')
167*
168 DO 10 j = 1, min( m, n )
169*
170* Find pivot and test for singularity.
171*
172 jp = j - 1 + idamax( 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 dswap( 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 dscal( 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 dger( 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 DGETF2
209*
210 END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine dscal(N, DA, DX, INCX)
DSCAL
Definition: dscal.f:79
subroutine dswap(N, DX, INCX, DY, INCY)
DSWAP
Definition: dswap.f:82
subroutine dger(M, N, ALPHA, X, INCX, Y, INCY, A, LDA)
DGER
Definition: dger.f:130
subroutine dgetf2(M, N, A, LDA, IPIV, INFO)
DGETF2 computes the LU factorization of a general m-by-n matrix using partial pivoting with row inter...
Definition: dgetf2.f:108