dpbcon (l)  Linux Manuals
dpbcon: 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 DPBTRF
Command to display dpbcon
manual in Linux: $ man l dpbcon
NAME
DPBCON  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 DPBTRF
SYNOPSIS
 SUBROUTINE DPBCON(

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

CHARACTER
UPLO

INTEGER
INFO, KD, LDAB, N

DOUBLE
PRECISION ANORM, RCOND

INTEGER
IWORK( * )

DOUBLE
PRECISION AB( LDAB, * ), WORK( * )
PURPOSE
DPBCON 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 DPBTRF.
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) DOUBLE PRECISION 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) DOUBLE PRECISION

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

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) DOUBLE PRECISION 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 dpbcon
 dpbcon (3)
 dpbequ (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)
 dpbrfs (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
 dpbstf (l)  computes a split Cholesky factorization of a real symmetric positive definite band matrix A
 dpbsv (l)  computes the solution to a real system of linear equations A * X = B,
 dpbsvx (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,
 dpbtf2 (l)  computes the Cholesky factorization of a real symmetric positive definite band matrix A
 dpbtrf (l)  computes the Cholesky factorization of a real symmetric positive definite band matrix A