LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 subroutine dgetrf ( integer M, integer N, double precision, dimension( lda, * ) A, integer LDA, integer, dimension( * ) IPIV, integer INFO )

DGETRF

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Purpose:
``` DGETRF 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 3 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 DOUBLE PRECISION 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 = -i, the i-th argument had an illegal value > 0: if INFO = i, U(i,i) 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.```
Date
November 2015

Definition at line 110 of file dgetrf.f.

110 *
111 * -- LAPACK computational routine (version 3.6.0) --
112 * -- LAPACK is a software package provided by Univ. of Tennessee, --
113 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
114 * November 2015
115 *
116 * .. Scalar Arguments ..
117  INTEGER info, lda, m, n
118 * ..
119 * .. Array Arguments ..
120  INTEGER ipiv( * )
121  DOUBLE PRECISION a( lda, * )
122 * ..
123 *
124 * =====================================================================
125 *
126 * .. Parameters ..
127  DOUBLE PRECISION one
128  parameter ( one = 1.0d+0 )
129 * ..
130 * .. Local Scalars ..
131  INTEGER i, iinfo, j, jb, nb
132 * ..
133 * .. External Subroutines ..
134  EXTERNAL dgemm, dgetrf2, dlaswp, dtrsm, xerbla
135 * ..
136 * .. External Functions ..
137  INTEGER ilaenv
138  EXTERNAL ilaenv
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( 'DGETRF', -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 * Determine the block size for this environment.
166 *
167  nb = ilaenv( 1, 'DGETRF', ' ', m, n, -1, -1 )
168  IF( nb.LE.1 .OR. nb.GE.min( m, n ) ) THEN
169 *
170 * Use unblocked code.
171 *
172  CALL dgetrf2( m, n, a, lda, ipiv, info )
173  ELSE
174 *
175 * Use blocked code.
176 *
177  DO 20 j = 1, min( m, n ), nb
178  jb = min( min( m, n )-j+1, nb )
179 *
180 * Factor diagonal and subdiagonal blocks and test for exact
181 * singularity.
182 *
183  CALL dgetrf2( m-j+1, jb, a( j, j ), lda, ipiv( j ), iinfo )
184 *
185 * Adjust INFO and the pivot indices.
186 *
187  IF( info.EQ.0 .AND. iinfo.GT.0 )
188  \$ info = iinfo + j - 1
189  DO 10 i = j, min( m, j+jb-1 )
190  ipiv( i ) = j - 1 + ipiv( i )
191  10 CONTINUE
192 *
193 * Apply interchanges to columns 1:J-1.
194 *
195  CALL dlaswp( j-1, a, lda, j, j+jb-1, ipiv, 1 )
196 *
197  IF( j+jb.LE.n ) THEN
198 *
199 * Apply interchanges to columns J+JB:N.
200 *
201  CALL dlaswp( n-j-jb+1, a( 1, j+jb ), lda, j, j+jb-1,
202  \$ ipiv, 1 )
203 *
204 * Compute block row of U.
205 *
206  CALL dtrsm( 'Left', 'Lower', 'No transpose', 'Unit', jb,
207  \$ n-j-jb+1, one, a( j, j ), lda, a( j, j+jb ),
208  \$ lda )
209  IF( j+jb.LE.m ) THEN
210 *
211 * Update trailing submatrix.
212 *
213  CALL dgemm( 'No transpose', 'No transpose', m-j-jb+1,
214  \$ n-j-jb+1, jb, -one, a( j+jb, j ), lda,
215  \$ a( j, j+jb ), lda, one, a( j+jb, j+jb ),
216  \$ lda )
217  END IF
218  END IF
219  20 CONTINUE
220  END IF
221  RETURN
222 *
223 * End of DGETRF
224 *
subroutine dtrsm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
DTRSM
Definition: dtrsm.f:183
subroutine dgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
DGEMM
Definition: dgemm.f:189
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
recursive subroutine dgetrf2(M, N, A, LDA, IPIV, INFO)
DGETRF2
Definition: dgetrf2.f:115
subroutine dlaswp(N, A, LDA, K1, K2, IPIV, INCX)
DLASWP performs a series of row interchanges on a general rectangular matrix.
Definition: dlaswp.f:116
integer function ilaenv(ISPEC, NAME, OPTS, N1, N2, N3, N4)
Definition: tstiee.f:83

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