# ctpcon.f(3) [debian man page]

```ctpcon.f(3)							      LAPACK							       ctpcon.f(3)

NAME
ctpcon.f -

SYNOPSIS
Functions/Subroutines
subroutine ctpcon (NORM, UPLO, DIAG, N, AP, RCOND, WORK, RWORK, INFO)
CTPCON

Function/Subroutine Documentation
subroutine ctpcon (characterNORM, characterUPLO, characterDIAG, integerN, complex, dimension( * )AP, realRCOND, complex, dimension( * )WORK,
real, dimension( * )RWORK, integerINFO)
CTPCON

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)) ).

Parameters:
NORM

NORM is 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

UPLO is CHARACTER*1
= 'U':  A is upper triangular;
= 'L':  A is lower triangular.

DIAG

DIAG is CHARACTER*1
= 'N':  A is non-unit triangular;
= 'U':  A is unit triangular.

N

N is INTEGER
The order of the matrix A.  N >= 0.

AP

AP is 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.

RCOND

RCOND is REAL
The reciprocal of the condition number of the matrix A,
computed as RCOND = 1/(norm(A) * norm(inv(A))).

WORK

WORK is COMPLEX array, dimension (2*N)

RWORK

RWORK is REAL array, dimension (N)

INFO

INFO is INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value

Author:
Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:
November 2011

Definition at line 130 of file ctpcon.f.

Author
Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.1							  Sun May 26 2013						       ctpcon.f(3)```

## Check Out this Related Man Page

```CTPCON(l)								 )								 CTPCON(l)

NAME
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.

RCOND   (output) REAL
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 illegal value

LAPACK version 3.0						   15 June 2000 							 CTPCON(l)```
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