# ?gbtf2

Computes the LU factorization of a general band matrix using the unblocked version of the algorithm.

## Syntax

call sgbtf2( m, n, kl, ku, ab, ldab, ipiv, info )

call dgbtf2( m, n, kl, ku, ab, ldab, ipiv, info )

call cgbtf2( m, n, kl, ku, ab, ldab, ipiv, info )

call zgbtf2( m, n, kl, ku, ab, ldab, ipiv, info )

• mkl.fi

## Description

The routine forms the LU factorization of a general real/complex m-by-n band matrix A with kl sub-diagonals and ku super-diagonals. The routine uses partial pivoting with row interchanges and implements the unblocked version of the algorithm, calling Level 2 BLAS. See also ?gbtrf.

## 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 sgbtf2

DOUBLE PRECISION for dgbtf2

COMPLEX for cgbtf2

DOUBLE COMPLEX for zgbtf2.

Array, DIMENSION (ldab,*).

The array ab contains the matrix A in band storage (see Matrix Arguments).

The second dimension of ab must be at least `max(1, n)`.

ldab

INTEGER. The leading dimension of the array ab.

`(ldab ≥ 2kl + ku +1)`

## Output Parameters

ab

Overwritten by details of the factorization. The diagonal and kl + ku super-diagonals of U are stored in the first 1 + kl + ku rows of ab. The multipliers used during the factorization are stored in the next kl rows.

ipiv

INTEGER.

Array, DIMENSION at least max(1,min(m,n)).

The pivot indices: row i was interchanged with row ipiv(i).

info

INTEGER. If `info =0`, the execution is successful.

If `info = -i`, the i-th parameter had an illegal value.

If `info = i`, uii 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.

Para obtener información más completa sobre las optimizaciones del compilador, consulte nuestro Aviso de optimización.