dsycon (l) - Linux Manuals

dsycon: estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by DSYTRF

NAME

DSYCON - estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by DSYTRF

SYNOPSIS

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

    
CHARACTER UPLO

    
INTEGER INFO, LDA, N

    
DOUBLE PRECISION ANORM, RCOND

    
INTEGER IPIV( * ), IWORK( * )

    
DOUBLE PRECISION A( LDA, * ), WORK( * )

PURPOSE

DSYCON estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by DSYTRF. 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
Specifies whether the details of the factorization are stored as an upper or lower triangular matrix. = aqUaq: Upper triangular, form is A = U*D*U**T;
= aqLaq: Lower triangular, form is A = L*D*L**T.
N (input) INTEGER
The order of the matrix A. N >= 0.
A (input) DOUBLE PRECISION array, dimension (LDA,N)
The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by DSYTRF.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
IPIV (input) INTEGER array, dimension (N)
Details of the interchanges and the block structure of D as determined by DSYTRF.
ANORM (input) DOUBLE PRECISION
The 1-norm of the original 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 1-norm of inv(A) computed in this routine.
WORK (workspace) DOUBLE PRECISION array, dimension (2*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 dsycon

  • dsycon (3)
  • dsyequb (l) - computes row and column scalings intended to equilibrate a symmetric matrix A and reduce its condition number (with respect to the two-norm)
  • dsyev (l) - computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A
  • dsyevd (l) - computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A
  • dsyevr (l) - computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A
  • dsyevx (l) - computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A
  • dsygs2 (l) - reduces a real symmetric-definite generalized eigenproblem to standard form
  • dsygst (l) - reduces a real symmetric-definite generalized eigenproblem to standard form