?dbtf2

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 10/15/2026

Version

Public

?dbtf2

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

Syntax

void sdbtf2(MKL_INT *m, MKL_INT *n, MKL_INT *kl, MKL_INT *ku, float *ab, MKL_INT *ldab,
            MKL_INT *info);

void ddbtf2(MKL_INT *m, MKL_INT *n, MKL_INT *kl, MKL_INT *ku, double *ab, MKL_INT *ldab,
            MKL_INT *info);

void cdbtf2(MKL_INT *m, MKL_INT *n, MKL_INT *kl, MKL_INT *ku, MKL_Complex8 *ab,
            MKL_INT *ldab, MKL_INT *info);

void zdbtf2(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

sdbtf2 ddbtf2 cdbtf2 zdbtf2 The ?dbtf2 routine function computes an LU factorization of a general real/complex m -by- n band matrix A without using partial pivoting with row interchanges.

This is the unblocked 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 sdbtf2 DOUBLE PRECISION for ddbtf2 COMPLEX for cdbtf2 COMPLEX*16 for zdbtf2 .

Array of size ldab * n .

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,

> 0: if info = + i , the matrix element U ( i , i ) is 0. The factorization has been completed, but the factor 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 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 *; elements marked + need not be set on entry, but the function requires them to store elements of U , because of fill-in resulting from the row interchanges.

NOTE:

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Developer Reference for Intel® oneAPI Math Kernel Library for C

?dbtf2

Syntax

Include Files

Description

Input Parameters

Output Parameters

Application Notes