Computes the LU factorization of a general m-by-n matrix.
Syntax
FORTRAN 77:
call sgetrf( m, n, a, lda, ipiv, info )
call dgetrf( m, n, a, lda, ipiv, info )
call cgetrf( m, n, a, lda, ipiv, info )
call zgetrf( m, n, a, lda, ipiv, info )
FORTRAN 95:
call getrf( a [,ipiv] [,info] )
C:
lapack_int LAPACKE_<?>getrf( int matrix_order, lapack_int m, lapack_int n, <datatype>* a, lapack_int lda, lapack_int* ipiv );
Description
The routine computes the LU factorization of a general m-by-n matrix A as
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). The routine uses partial pivoting, with row interchanges.
Note
This routine supports the Progress Routine feature. See Progress Function for details.
Input Parameters
The data types are given for the Fortran interface. A <datatype> placeholder, if present, is used for the C interface data types in the C interface section above. See C Interface Conventions for the C interface principal conventions and type definitions.
m |
INTEGER. The number of rows in the matrix A (m ≥ 0). |
n |
INTEGER. The number of columns in A; n ≥ 0. |
a |
REAL for sgetrf DOUBLE PRECISION for dgetrf COMPLEX for cgetrf DOUBLE COMPLEX for zgetrf. Array, DIMENSION (lda,*). Contains the matrix A. The second dimension of a must be at least max(1, n). |
lda |
INTEGER. The leading dimension of array a. |
Output Parameters
a |
Overwritten by L and U. The unit diagonal elements of L are not stored. |
ipiv |
INTEGER. Array, DIMENSION at least max(1,min(m, n)). The pivot indices; for 1 ≤ i ≤ min(m, n), row i was interchanged with row ipiv(i). |
info |
INTEGER. If info=0, the execution is successful. If info = -i, the i-th parameter had an illegal value. If info = i, uii is 0. The factorization has been completed, but U is exactly singular. Division by 0 will occur if you use the factor U for solving a system of linear equations. |
Fortran 95 Interface Notes
Routines in Fortran 95 interface have fewer arguments in the calling sequence than their FORTRAN 77 counterparts. For general conventions applied to skip redundant or reconstructible arguments, see Fortran 95 Interface Conventions.
Specific details for the routine getrf interface are as follows:
a |
Holds the matrix A of size (m,n). |
ipiv |
Holds the vector of length min(m,n). |
Application Notes
The computed L and U are the exact factors of a perturbed matrix A + E, where
|E| ≤ c(min(m,n))ε P|L||U|
c(n) is a modest linear function of n, and ε is the machine precision.
The approximate number of floating-point operations for real flavors is
(2/3)n3 |
If m = n, |
(1/3)n2(3m-n) |
If m > n, |
(1/3)m2(3n-m) |
If m < n. |
The number of operations for complex flavors is four times greater.
After calling this routine with m = n, you can call the following: