 LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

◆ cgetrf()

 subroutine cgetrf ( integer M, integer N, complex, dimension( lda, * ) A, integer LDA, integer, dimension( * ) IPIV, integer INFO )

CGETRF

CGETRF VARIANT: iterative version of Sivan Toledo's recursive LU algorithm

CGETRF VARIANT: left-looking Level 3 BLAS version of the algorithm.

Purpose:
CGETRF 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 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 = -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.

Purpose:

CGETRF 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 left-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 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 = -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
December 2016

Purpose:

CGETRF 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 code implements an iterative version of Sivan Toledo's recursive
LU algorithm.  For square matrices, this iterative versions should
be within a factor of two of the optimum number of memory transfers.

The pattern is as follows, with the large blocks of U being updated
in one call to DTRSM, and the dotted lines denoting sections that
have had all pending permutations applied:

1 2 3 4 5 6 7 8
+-+-+---+-------+------
| |1|   |       |
|.+-+ 2 |       |
| | |   |       |
|.|.+-+-+   4   |
| | | |1|       |
| | |.+-+       |
| | | | |       |
|.|.|.|.+-+-+---+  8
| | | | | |1|   |
| | | | |.+-+ 2 |
| | | | | | |   |
| | | | |.|.+-+-+
| | | | | | | |1|
| | | | | | |.+-+
| | | | | | | | |
|.|.|.|.|.|.|.|.+-----
| | | | | | | | |

The 1-2-1-4-1-2-1-8-... pattern is the position of the last 1 bit in
the binary expansion of the current column.  Each Schur update is
applied as soon as the necessary portion of U is available.

 Toledo, S. 1997. Locality of Reference in LU Decomposition with
Partial Pivoting. SIAM J. Matrix Anal. Appl. 18, 4 (Oct. 1997),
1065-1081. http://dx.doi.org/10.1137/S0895479896297744
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 = -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
December 2016

Definition at line 107 of file cgetrf.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
125  parameter( one = ( 1.0e+0, 0.0e+0 ) )
126 * ..
127 * .. Local Scalars ..
128  INTEGER I, IINFO, J, JB, NB
129 * ..
130 * .. External Subroutines ..
131  EXTERNAL cgemm, cgetrf2, claswp, ctrsm, xerbla
132 * ..
133 * .. External Functions ..
134  INTEGER ILAENV
135  EXTERNAL ilaenv
136 * ..
137 * .. Intrinsic Functions ..
138  INTRINSIC max, min
139 * ..
140 * .. Executable Statements ..
141 *
142 * Test the input parameters.
143 *
144  info = 0
145  IF( m.LT.0 ) THEN
146  info = -1
147  ELSE IF( n.LT.0 ) THEN
148  info = -2
149  ELSE IF( lda.LT.max( 1, m ) ) THEN
150  info = -4
151  END IF
152  IF( info.NE.0 ) THEN
153  CALL xerbla( 'CGETRF', -info )
154  RETURN
155  END IF
156 *
157 * Quick return if possible
158 *
159  IF( m.EQ.0 .OR. n.EQ.0 )
160  \$ RETURN
161 *
162 * Determine the block size for this environment.
163 *
164  nb = ilaenv( 1, 'CGETRF', ' ', m, n, -1, -1 )
165  IF( nb.LE.1 .OR. nb.GE.min( m, n ) ) THEN
166 *
167 * Use unblocked code.
168 *
169  CALL cgetrf2( m, n, a, lda, ipiv, info )
170  ELSE
171 *
172 * Use blocked code.
173 *
174  DO 20 j = 1, min( m, n ), nb
175  jb = min( min( m, n )-j+1, nb )
176 *
177 * Factor diagonal and subdiagonal blocks and test for exact
178 * singularity.
179 *
180  CALL cgetrf2( m-j+1, jb, a( j, j ), lda, ipiv( j ), iinfo )
181 *
182 * Adjust INFO and the pivot indices.
183 *
184  IF( info.EQ.0 .AND. iinfo.GT.0 )
185  \$ info = iinfo + j - 1
186  DO 10 i = j, min( m, j+jb-1 )
187  ipiv( i ) = j - 1 + ipiv( i )
188  10 CONTINUE
189 *
190 * Apply interchanges to columns 1:J-1.
191 *
192  CALL claswp( j-1, a, lda, j, j+jb-1, ipiv, 1 )
193 *
194  IF( j+jb.LE.n ) THEN
195 *
196 * Apply interchanges to columns J+JB:N.
197 *
198  CALL claswp( n-j-jb+1, a( 1, j+jb ), lda, j, j+jb-1,
199  \$ ipiv, 1 )
200 *
201 * Compute block row of U.
202 *
203  CALL ctrsm( 'Left', 'Lower', 'No transpose', 'Unit', jb,
204  \$ n-j-jb+1, one, a( j, j ), lda, a( j, j+jb ),
205  \$ lda )
206  IF( j+jb.LE.m ) THEN
207 *
208 * Update trailing submatrix.
209 *
210  CALL cgemm( 'No transpose', 'No transpose', m-j-jb+1,
211  \$ n-j-jb+1, jb, -one, a( j+jb, j ), lda,
212  \$ a( j, j+jb ), lda, one, a( j+jb, j+jb ),
213  \$ lda )
214  END IF
215  END IF
216  20 CONTINUE
217  END IF
218  RETURN
219 *
220 * End of CGETRF
221 *
integer function ilaenv(ISPEC, NAME, OPTS, N1, N2, N3, N4)
ILAENV
Definition: ilaenv.f:162
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine cgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
CGEMM
Definition: cgemm.f:187
subroutine ctrsm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
CTRSM
Definition: ctrsm.f:180
recursive subroutine cgetrf2(M, N, A, LDA, IPIV, INFO)
CGETRF2
Definition: cgetrf2.f:113
subroutine claswp(N, A, LDA, K1, K2, IPIV, INCX)
CLASWP performs a series of row interchanges on a general rectangular matrix.
Definition: claswp.f:115
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