ztrcon (l) - Linux Manuals

ztrcon: estimates the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm

NAME

ZTRCON - estimates the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm

SYNOPSIS

SUBROUTINE ZTRCON(
NORM, UPLO, DIAG, N, A, LDA, RCOND, WORK, RWORK, INFO )

    
CHARACTER DIAG, NORM, UPLO

    
INTEGER INFO, LDA, N

    
DOUBLE PRECISION RCOND

    
DOUBLE PRECISION RWORK( * )

    
COMPLEX*16 A( LDA, * ), WORK( * )

PURPOSE

ZTRCON estimates the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm. The norm of A is computed and an estimate is obtained for norm(inv(A)), then the reciprocal of the condition number is computed as

RCOND = 1 / ( norm(A) * norm(inv(A)) ).

ARGUMENTS

NORM (input) CHARACTER*1
Specifies whether the 1-norm condition number or the infinity-norm condition number is required:
= aq1aq or aqOaq: 1-norm;
= aqIaq: Infinity-norm.
UPLO (input) CHARACTER*1

= aqUaq: A is upper triangular;
= aqLaq: A is lower triangular.
DIAG (input) CHARACTER*1

= aqNaq: A is non-unit triangular;
= aqUaq: A is unit triangular.
N (input) INTEGER
The order of the matrix A. N >= 0.
A (input) COMPLEX*16 array, dimension (LDA,N)
The triangular matrix A. If UPLO = aqUaq, the leading N-by-N upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. If UPLO = aqLaq, the leading N-by-N lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. If DIAG = aqUaq, the diagonal elements of A are also not referenced and are assumed to be 1.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
RCOND (output) DOUBLE PRECISION
The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A))).
WORK (workspace) COMPLEX*16 array, dimension (2*N)
RWORK (workspace) DOUBLE PRECISION array, dimension (N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value

Pages related to ztrcon

  • ztrcon (3)
  • ztrevc (l) - computes some or all of the right and/or left eigenvectors of a complex upper triangular matrix T
  • ztrexc (l) - reorders the Schur factorization of a complex matrix A = Q*T*Q**H, so that the diagonal element of T with row index IFST is moved to row ILST
  • ztrmm (l) - performs one of the matrix-matrix operations B := alpha*op( A )*B, or B := alpha*B*op( A ) where alpha is a scalar, B is an m by n matrix, A is a unit, or non-unit, upper or lower triangular matrix and op( A ) is one of op( A ) = A or op( A ) = Aaq or op( A ) = conjg( Aaq )
  • ztrmv (l) - performs one of the matrix-vector operations x := A*x, or x := Aaq*x, or x := conjg( Aaq )*x,
  • ztrrfs (l) - provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix
  • ztrsen (l) - reorders the Schur factorization of a complex matrix A = Q*T*Q**H, so that a selected cluster of eigenvalues appears in the leading positions on the diagonal of the upper triangular matrix T, and the leading columns of Q form an orthonormal basis of the corresponding right invariant subspace
  • ztrsm (l) - solves one of the matrix equations op( A )*X = alpha*B, or X*op( A ) = alpha*B,