?dbtrf

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 10/15/2026

Version

Public

?dbtrf

Computes an LU factorization of a general band matrix with no pivoting (local blocked algorithm).

Syntax

void sdbtrf(MKL_INT *m, MKL_INT *n, MKL_INT *kl, MKL_INT *ku, float *ab, MKL_INT *ldab,
            MKL_INT *info);

void ddbtrf(MKL_INT *m, MKL_INT *n, MKL_INT *kl, MKL_INT *ku, double *ab, MKL_INT *ldab,
            MKL_INT *info);

void cdbtrf(MKL_INT *m, MKL_INT *n, MKL_INT *kl, MKL_INT *ku, MKL_Complex8 *ab,
            MKL_INT *ldab, MKL_INT *info);

void zdbtrf(MKL_INT *m, MKL_INT *n, MKL_INT *kl, MKL_INT *ku, MKL_Complex16 *ab,
            MKL_INT *ldab, MKL_INT *info);

Include Files

mkl_scalapack.h

Description

sdbtrf ddbtrf cdbtrf zdbtrf This routine function computes an LU factorization of a real m -by- n band matrix A without using partial pivoting or row interchanges.

This is the blocked version of the algorithm, calling BLAS Routines and Functions .

Input Parameters

m

The number of rows of the matrix A ( m ≥ 0).

n

The number of columns in A(n ≥ 0) .

kl

The number of sub-diagonals within the band of A(kl ≥ 0) .

ku

The number of super-diagonals within the band of A(ku ≥ 0) .

ab

REAL for sdbtrf DOUBLE PRECISION for ddbtrf COMPLEX for cdbtrf COMPLEX*16 for zdbtrf .

Array of size ldab * n .

The matrix A in band storage, in rows kl+1 to 2kl+ku+1 ; rows 1 to kl need not be set. The j -th column of A is stored in the array ab as follows: ab(kl+ku+1+i-j,j)ab[kl+ku+i-j+(j-1)*ldab] =A(i,j) for max(1,j-ku) ≤ i ≤ min(m,j+kl) .

ldab

The leading dimension of the array ab .

(ldab ≥ 2kl + ku +1)

Output Parameters

ab: On exit, details of the factorization: U is stored as an upper triangular band matrix with kl+ku superdiagonals in rows 1 to kl+ku+1 , and the multipliers used during the factorization are stored in rows kl+ku+2 to 2*kl+ku+1 . See the Application Notes below for further details .

info

= 0 : successful exit < 0 : if info = - i , the i -th argument had an illegal value,

Application Notes

The band storage scheme is illustrated by the following example, when m = n = 6 , kl = 2 , ku = 1 :

The function does not use array elements marked *.

NOTE:

Overview

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Developer Reference for Intel® oneAPI Math Kernel Library for C

?dbtrf

Syntax

Include Files

Description

Input Parameters

Output Parameters

Application Notes