# ?dbtf2

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

## Syntax

call sdbtf2(m, n, kl, ku, ab, ldab, info)

call ddbtf2(m, n, kl, ku, ab, ldab, info)

call cdbtf2(m, n, kl, ku, ab, ldab, info)

call zdbtf2(m, n, kl, ku, ab, ldab, info)

## Description

This routine 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

  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 sdbtf2

  DOUBLE PRECISION for ddbtf2

  COMPLEX for cdbtf2

  COMPLEX*16 for zdbtf2.

  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 *; elements marked + need not be set on entry, but the routine requires them to store elements of U, because of fill-in resulting from the row interchanges.

Parent topic: Auxiliary Routines