# ?dbtrf

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

## Syntax

call sdbtrf(m, n, kl, ku, ab, ldab, info)

call ddbtrf(m, n, kl, ku, ab, ldab, info)

call cdbtrf(m, n, kl, ku, ab, ldab, info)

call zdbtrf(m, n, kl, ku, ab, ldab, info)

## Description

This routine 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

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

n

  INTEGER. The number of columns in A`(n ≥ 0)`.

kl

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

ku

  INTEGER. 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, DIMENSION (ldab, n).

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

ldab

  INTEGER. 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

  INTEGER.

  `= 0`: successful exit

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

  `> 0`: if `info = + i, 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 routine does not use array elements marked *.

Parent topic: Auxiliary Routines