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

# sgbcon(3lapack)

estimates the reciprocal of the condition number of a real general band matrix A, in either the 1-norm or the infinity-norm,

## NAME

SGBCON - estimates the reciprocal of the condition number of a real general band matrix A, in either the 1-norm or the infinity-norm,

## SYNOPSIS

- SUBROUTINE SGBCON(

  NORM, N, KL, KU, AB, LDAB, IPIV, ANORM, RCOND, WORK, IWORK, INFO )

- CHARACTER

  NORM

- INTEGER

  INFO, KL, KU, LDAB, N

- REAL

  ANORM, RCOND

- INTEGER

  IPIV( \* ), IWORK( \* )

- REAL

  AB( LDAB, \* ), WORK( \* )

## PURPOSE

SGBCON estimates the reciprocal of the condition number of a real general band matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by SGBTRF.\
 An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as\
\
    RCOND = 1 / ( norm(A) \* norm(inv(A)) ).\

## ARGUMENTS

- NORM (input) CHARACTER\*1

  Specifies whether the 1-norm condition number or the infinity-norm condition number is required:\
   \= '1' or 'O':  1-norm;\
   \= 'I':         Infinity-norm.

- N (input) INTEGER

  The order 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) REAL array, dimension (LDAB,N)

  Details of the LU factorization of the band matrix A, as computed by SGBTRF.  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.

- LDAB (input) INTEGER

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

- IPIV (input) INTEGER array, dimension (N)

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

- ANORM (input) REAL

  If NORM = '1' or 'O', the 1-norm of the original matrix A. If NORM = 'I', the infinity-norm of the original matrix A.

- RCOND (output) REAL

  The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) \* norm(inv(A))).

- WORK (workspace) REAL array, dimension (3\*N)

  - IWORK (workspace) INTEGER array, dimension (N)

  - INFO (output) INTEGER

  \= 0:  successful exit\
   \< 0: if INFO = -i, the i-th argument had an illegal value