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

# stbcon(3lapack)

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

## NAME

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

## SYNOPSIS

- SUBROUTINE STBCON(

  NORM, UPLO, DIAG, N, KD, AB, LDAB, RCOND, WORK, IWORK, INFO )

- CHARACTER

  DIAG, NORM, UPLO

- INTEGER

  INFO, KD, LDAB, N

- REAL

  RCOND

- INTEGER

  IWORK( \* )

- REAL

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

## PURPOSE

STBCON estimates the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm. The norm of A is computed and an estimate is obtained for norm(inv(A)), then 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.

- UPLO (input) CHARACTER\*1

  \= 'U':  A is upper triangular;\
   \= 'L':  A is lower triangular.

- DIAG (input) CHARACTER\*1

  \= 'N':  A is non-unit triangular;\
   \= 'U':  A is unit triangular.

- N (input) INTEGER

  The order of the matrix A.  N \>= 0.

- KD (input) INTEGER

  The number of superdiagonals or subdiagonals of the triangular band matrix A.  KD \>= 0.

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

  The upper or lower triangular band matrix A, stored in the first kd+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows: if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)\<=i\<=j; if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j\<=i\<=min(n,j+kd). If DIAG = 'U', the diagonal elements of A are not referenced and are assumed to be 1.

- LDAB (input) INTEGER

  The leading dimension of the array AB.  LDAB \>= KD+1.

- 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