CTPCON - estimate the reciprocal of the condition number
of a packed triangular matrix A, in either the 1-norm or
the infinity-norm
SYNOPSIS
SUBROUTINE CTPCON( NORM, UPLO, DIAG, N, AP, RCOND, WORK,
RWORK, INFO )
CHARACTER DIAG, NORM, UPLO
INTEGER INFO, N
REAL RCOND
REAL RWORK( * )
COMPLEX AP( * ), WORK( * )
PURPOSE
CTPCON estimates the reciprocal of the condition number of
a packed 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:
= '1' or 'O': 1-norm;
= 'I': Infinity-norm.
UPLO (input) CHARACTER*1
= 'U': A is upper triangular;
= 'L': A is lower triangular.
DIAG (input) CHARACTER*1
= 'N': A is non-unit triangular;
= 'U': A is unit triangular.
N (input) INTEGER
The order of the matrix A. N >= 0.
AP (input) COMPLEX array, dimension (N*(N+1)/2)
The upper or lower triangular matrix A, packed
columnwise in a linear array. The j-th column of
A is stored in the array AP as follows: if UPLO =
'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if
UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for
j<=i<=n. If DIAG = 'U', the diagonal elements of
A are not referenced and are assumed to be 1.
The reciprocal of the condition number of the
matrix A, computed as RCOND = 1/(norm(A) *
norm(inv(A))).
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 ille
gal value
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