cspcon (l) - Linux Manuals

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

NAME

CSPCON - estimates the reciprocal of the condition number (in the 1-norm) of a complex symmetric packed matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by CSPTRF

SYNOPSIS

SUBROUTINE CSPCON(
UPLO, N, AP, IPIV, ANORM, RCOND, WORK, INFO )

    
CHARACTER UPLO

    
INTEGER INFO, N

    
REAL ANORM, RCOND

    
INTEGER IPIV( * )

    
COMPLEX AP( * ), WORK( * )

PURPOSE

CSPCON estimates the reciprocal of the condition number (in the 1-norm) of a complex symmetric packed matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by CSPTRF. 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.
AP (input) COMPLEX array, dimension (N*(N+1)/2)
The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by CSPTRF, stored as a packed triangular matrix.
IPIV (input) INTEGER array, dimension (N)
Details of the interchanges and the block structure of D as determined by CSPTRF.
ANORM (input) REAL
The 1-norm of the original 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)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value

Pages related to cspcon

  • cspcon (3)
  • cspmv (l) - performs the matrix-vector operation y := alpha*A*x + beta*y,
  • cspr (l) - performs the symmetric rank 1 operation A := alpha*x*conjg( xaq ) + A,
  • csprfs (l) - improves the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite and packed, and provides error bounds and backward error estimates for the solution
  • cspsv (l) - computes the solution to a complex system of linear equations A * X = B,
  • cspsvx (l) - uses the diagonal pivoting factorization A = U*D*U**T or A = L*D*L**T to compute the solution to a complex system of linear equations A * X = B, where A is an N-by-N symmetric matrix stored in packed format and X and B are N-by-NRHS matrices
  • csptrf (l) - computes the factorization of a complex symmetric matrix A stored in packed format using the Bunch-Kaufman diagonal pivoting method
  • csptri (l) - computes the inverse of a complex symmetric indefinite matrix A in packed storage using the factorization A = U*D*U**T or A = L*D*L**T computed by CSPTRF