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.TH CTPCON l "15 June 2000" "LAPACK version 3.0" ")"
.SH NAME
CTPCON - estimate the reciprocal of the condition number of a packed triangular matrix A, in either the 1-norm or the infinity-norm
.SH SYNOPSIS
.TP 19
SUBROUTINE CTPCON(
NORM, UPLO, DIAG, N, AP, RCOND, WORK, RWORK,
INFO )
.TP 19
.ti +4
CHARACTER
DIAG, NORM, UPLO
.TP 19
.ti +4
INTEGER
INFO, N
.TP 19
.ti +4
REAL
RCOND
.TP 19
.ti +4
REAL
RWORK( * )
.TP 19
.ti +4
COMPLEX
AP( * ), WORK( * )
.SH 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
.br
RCOND = 1 / ( norm(A) * norm(inv(A)) ).
.br
.SH ARGUMENTS
.TP 8
NORM (input) CHARACTER*1
Specifies whether the 1-norm condition number or the
infinity-norm condition number is required:
.br
= '1' or 'O': 1-norm;
.br
= 'I': Infinity-norm.
.TP 8
UPLO (input) CHARACTER*1
.br
= 'U': A is upper triangular;
.br
= 'L': A is lower triangular.
.TP 8
DIAG (input) CHARACTER*1
.br
= 'N': A is non-unit triangular;
.br
= 'U': A is unit triangular.
.TP 8
N (input) INTEGER
The order of the matrix A. N >= 0.
.TP 8
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.
.TP 8
RCOND (output) REAL
The reciprocal of the condition number of the matrix A,
computed as RCOND = 1/(norm(A) * norm(inv(A))).
.TP 8
WORK (workspace) COMPLEX array, dimension (2*N)
.TP 8
RWORK (workspace) REAL array, dimension (N)
.TP 8
INFO (output) INTEGER
= 0: successful exit
.br
< 0: if INFO = -i, the i-th argument had an illegal value
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