spocon (l) - Linux Manuals

spocon: estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPOTRF

NAME

SPOCON - estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPOTRF

SYNOPSIS

SUBROUTINE SPOCON(
UPLO, N, A, LDA, ANORM, RCOND, WORK, IWORK, INFO )

    
CHARACTER UPLO

    
INTEGER INFO, LDA, N

    
REAL ANORM, RCOND

    
INTEGER IWORK( * )

    
REAL A( LDA, * ), WORK( * )

PURPOSE

SPOCON estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPOTRF. 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 triangle of A is stored;
= aqLaq: Lower triangle of A is stored.
N (input) INTEGER
The order of the matrix A. N >= 0.
A (input) REAL array, dimension (LDA,N)
The triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T, as computed by SPOTRF.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
ANORM (input) REAL
The 1-norm (or infinity-norm) of the symmetric 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 1-norm 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 i-th argument had an illegal value

Pages related to spocon

  • spocon (3)
  • spoequ (l) - computes row and column scalings intended to equilibrate a symmetric positive definite matrix A and reduce its condition number (with respect to the two-norm)
  • spoequb (l) - computes row and column scalings intended to equilibrate a symmetric positive definite matrix A and reduce its condition number (with respect to the two-norm)
  • sporfs (l) - improves the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite,
  • sporfsx (l) - SPORFSX improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite, and provides error bounds and backward error estimates for the solution
  • sposv (l) - computes the solution to a real system of linear equations A * X = B,
  • sposvx (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,
  • sposvxx (l) - SPOSVXX use 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, where A is an N-by-N symmetric positive definite matrix and X and B are N-by-NRHS matrices