---
name: "sgbtf2"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/sgbtf2/3lapack"
---

# sgbtf2(3lapack)

computes an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges

## NAME

SGBTF2 - computes an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges

## SYNOPSIS

- SUBROUTINE SGBTF2(

  M, N, KL, KU, AB, LDAB, IPIV, INFO )

- INTEGER

  INFO, KL, KU, LDAB, M, N

- INTEGER

  IPIV( \* )

- REAL

  AB( LDAB, \* )

## PURPOSE

SGBTF2 computes an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges. This is the unblocked version of the algorithm, calling Level 2 BLAS.

## ARGUMENTS

- M (input) INTEGER

  The number of rows of the matrix A.  M \>= 0.

- N (input) INTEGER

  The number of columns of the matrix A.  N \>= 0.

- KL (input) INTEGER

  The number of subdiagonals within the band of A.  KL \>= 0.

- KU (input) INTEGER

  The number of superdiagonals within the band of A.  KU \>= 0.

- AB (input/output) REAL array, dimension (LDAB,N)

  On entry, the matrix A in band storage, in rows KL+1 to 2\*KL+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) 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 below for further details.

- LDAB (input) INTEGER

  The leading dimension of the array AB.  LDAB \>= 2\*KL+KU+1.

- IPIV (output) INTEGER array, dimension (min(M,N))

  The pivot indices; for 1 \<= i \<= min(M,N), row i of the matrix was interchanged with row IPIV(i).

- INFO (output) INTEGER

  \= 0: successful exit\
   \< 0: if INFO = -i, the i-th argument had an illegal value\
   \> 0: if INFO = +i, U(i,i) is exactly zero. The factorization has been completed, but the factor U is exactly singular, and division by zero will occur if it is used to solve a system of equations.

## FURTHER DETAILS

The band storage scheme is illustrated by the following example, when M = N = 6, KL = 2, KU = 1:\
 On entry:                       On exit:\
\
     \*    \*    \*    +    +    +       \*    \*    \*   u14  u25  u36\
     \*    \*    +    +    +    +       \*    \*   u13  u24  u35  u46\
     \*   a12  a23  a34  a45  a56      \*   u12  u23  u34  u45  u56\
    a11  a22  a33  a44  a55  a66     u11  u22  u33  u44  u55  u66\
    a21  a32  a43  a54  a65   \*      m21  m32  m43  m54  m65   \*\
    a31  a42  a53  a64   \*    \*      m31  m42  m53  m64   \*    \* Array elements marked \* are not used by the routine; elements marked + need not be set on entry, but are required by the routine to store elements of U, because of fill-in resulting from the row\
 interchanges.\