spbcon (l)  Linux Manuals
spbcon: estimates the reciprocal of the condition number (in the 1norm) of a real symmetric positive definite band matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPBTRF
Command to display spbcon
manual in Linux: $ man l spbcon
NAME
SPBCON  estimates the reciprocal of the condition number (in the 1norm) of a real symmetric positive definite band matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPBTRF
SYNOPSIS
 SUBROUTINE SPBCON(

UPLO, N, KD, AB, LDAB, ANORM, RCOND, WORK,
IWORK, INFO )

CHARACTER
UPLO

INTEGER
INFO, KD, LDAB, N

REAL
ANORM, RCOND

INTEGER
IWORK( * )

REAL
AB( LDAB, * ), WORK( * )
PURPOSE
SPBCON estimates the reciprocal of the condition number (in the
1norm) of a real symmetric positive definite band matrix using the
Cholesky factorization A = U**T*U or A = L*L**T computed by SPBTRF.
An estimate is obtained for norm(inv(A)), and the reciprocal of the
condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
ARGUMENTS
 UPLO (input) CHARACTER*1

= aqUaq: Upper triangular factor stored in AB;
= aqLaq: Lower triangular factor stored in AB.
 N (input) INTEGER

The order of the matrix A. N >= 0.
 KD (input) INTEGER

The number of superdiagonals of the matrix A if UPLO = aqUaq,
or the number of subdiagonals if UPLO = aqLaq. KD >= 0.
 AB (input) REAL array, dimension (LDAB,N)

The triangular factor U or L from the Cholesky factorization
A = U**T*U or A = L*L**T of the band matrix A, stored in the
first KD+1 rows of the array. The jth column of U or L is
stored in the jth column of the array AB as follows:
if UPLO =aqUaq, AB(kd+1+ij,j) = U(i,j) for max(1,jkd)<=i<=j;
if UPLO =aqLaq, AB(1+ij,j) = L(i,j) for j<=i<=min(n,j+kd).
 LDAB (input) INTEGER

The leading dimension of the array AB. LDAB >= KD+1.
 ANORM (input) REAL

The 1norm (or infinitynorm) of the symmetric band matrix A.
 RCOND (output) REAL

The reciprocal of the condition number of the matrix A,
computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
estimate of the 1norm of inv(A) computed in this routine.
 WORK (workspace) REAL array, dimension (3*N)

 IWORK (workspace) INTEGER array, dimension (N)

 INFO (output) INTEGER

= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value
Pages related to spbcon
 spbcon (3)
 spbequ (l)  computes row and column scalings intended to equilibrate a symmetric positive definite band matrix A and reduce its condition number (with respect to the twonorm)
 spbrfs (l)  improves the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and banded, and provides error bounds and backward error estimates for the solution
 spbstf (l)  computes a split Cholesky factorization of a real symmetric positive definite band matrix A
 spbsv (l)  computes the solution to a real system of linear equations A * X = B,
 spbsvx (l)  uses the Cholesky factorization A = U**T*U or A = L*L**T to compute the solution to a real system of linear equations A * X = B,
 spbtf2 (l)  computes the Cholesky factorization of a real symmetric positive definite band matrix A
 spbtrf (l)  computes the Cholesky factorization of a real symmetric positive definite band matrix A