---
name: "dtpcon"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/dtpcon/3lapack"
---

# dtpcon(3lapack)

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

## NAME

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

## SYNOPSIS

- SUBROUTINE DTPCON(

  NORM, UPLO, DIAG, N, AP, RCOND, WORK, IWORK, INFO )

- CHARACTER

  DIAG, NORM, UPLO

- INTEGER

  INFO, N

- DOUBLE

  PRECISION RCOND

- INTEGER

  IWORK( \* )

- DOUBLE

  PRECISION AP( \* ), WORK( \* )

## PURPOSE

DTPCON 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) DOUBLE PRECISION 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) DOUBLE PRECISION

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

- WORK (workspace) DOUBLE PRECISION array, dimension (3\*N)

  - IWORK (workspace) INTEGER array, dimension (N)

  - INFO (output) INTEGER

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