cppcon (l) - Linux Manuals

cppcon: estimates the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite packed matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPPTRF

NAME

CPPCON - estimates the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite packed matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPPTRF

SYNOPSIS

SUBROUTINE CPPCON(
UPLO, N, AP, ANORM, RCOND, WORK, RWORK, INFO )

    
CHARACTER UPLO

    
INTEGER INFO, N

    
REAL ANORM, RCOND

    
REAL RWORK( * )

    
COMPLEX AP( * ), WORK( * )

PURPOSE

CPPCON estimates the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite packed matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPPTRF. 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.
AP (input) COMPLEX array, dimension (N*(N+1)/2)
The triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H, packed columnwise in a linear array. The j-th column of U or L is stored in the array AP as follows: if UPLO = aqUaq, AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j; if UPLO = aqLaq, AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n.
ANORM (input) REAL
The 1-norm (or infinity-norm) of the Hermitian 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) COMPLEX array, dimension (2*N)
RWORK (workspace) REAL array, dimension (N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value

Pages related to cppcon

  • cppcon (3)
  • cppequ (l) - computes row and column scalings intended to equilibrate a Hermitian positive definite matrix A in packed storage and reduce its condition number (with respect to the two-norm)
  • cpprfs (l) - improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and packed, and provides error bounds and backward error estimates for the solution
  • cppsv (l) - computes the solution to a complex system of linear equations A * X = B,
  • cppsvx (l) - uses the Cholesky factorization A = U**H*U or A = L*L**H to compute the solution to a complex system of linear equations A * X = B,
  • cpptrf (l) - computes the Cholesky factorization of a complex Hermitian positive definite matrix A stored in packed format
  • cpptri (l) - computes the inverse of a complex Hermitian positive definite matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPPTRF
  • cpptrs (l) - solves a system of linear equations A*X = B with a Hermitian positive definite matrix A in packed storage using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPPTRF