?getrf

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 3/31/2023

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?getrf

Computes the LU factorization of a general m-by-n matrix.

Syntax

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 )

call getrf( a [,ipiv] [,info] )

Include Files

mkl.fi, lapack.f90

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

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, size `lda` by `*` . 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

Overwritten by L and U. The unit diagonal elements of L are not stored.

ipiv

INTEGER.

Array, size at least max(1,min(m, n)). Contains 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, u_ii 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.

LAPACK 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 LAPACK 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)`n`³	If `m = n`,
(1/3)`n`²(3`m`-`n`)	If `m>n`,
(1/3)`m`²(3`n`-`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:

?getrs: to solve A*X = B or A^TX = B or A^HX = B
?gecon: to estimate the condition number of A
?getri: to compute the inverse of A.

Parent topic: Matrix Factorization: LAPACK Computational Routines

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