?getrf

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 3/22/2024

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?getrf

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

Syntax

lapack_int LAPACKE_sgetrf (int matrix_layout , lapack_int m , lapack_int n , float * a , lapack_int lda , lapack_int * ipiv );

lapack_int LAPACKE_dgetrf (int matrix_layout , lapack_int m , lapack_int n , double * a , lapack_int lda , lapack_int * ipiv );

lapack_int LAPACKE_cgetrf (int matrix_layout , lapack_int m , lapack_int n , lapack_complex_float * a , lapack_int lda , lapack_int * ipiv );

lapack_int LAPACKE_zgetrf (int matrix_layout , lapack_int m , lapack_int n , lapack_complex_double * a , lapack_int lda , lapack_int * ipiv );

Include Files

mkl.h

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

matrix_layout	Specifies whether matrix storage layout is row major (LAPACK_ROW_MAJOR) or column major (LAPACK_COL_MAJOR).
m	The number of rows in the matrix `A` (`m`≥ 0).
n	The number of columns in `A`; `n`≥ 0.
a	Array, size at least max(1, ldan) for column-major layout or max(1, ldam) for row-major layout. Contains the matrix `A`.
lda	The leading dimension of array `a`, which must be at least max(1, m) for column-major layout or max(1, n) for row-major layout.

Output Parameters

a	Overwritten by `L` and `U`. The unit diagonal elements of `L` are not stored.
ipiv	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)`.

Return Values

This function returns a value info.

If info=0, the execution is successful.

If info = -i, parameter i 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.

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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Developer Reference for Intel® oneAPI Math Kernel Library for C

?getrf

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values

Application Notes

See Also