sppcon.f −

**Functions/Subroutines**

subroutine **SPPCON** (UPLO, N, AP, ANORM, RCOND, WORK, IWORK, INFO)

SPPCON

**subroutine SPPCON (characterUPLO, integerN, real, dimension( * )AP, realANORM, realRCOND, real, dimension( * )WORK, integer, dimension( * )IWORK, integerINFO)
SPPCON**

**Purpose:**

SPPCON estimates the reciprocal of the condition number (in the

1-norm) of a real symmetric positive definite packed matrix using

the Cholesky factorization A = U**T*U or A = L*L**T computed by

SPPTRF.

An estimate is obtained for norm(inv(A)), and the reciprocal of the

condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).

**Parameters:**

*UPLO*

UPLO is CHARACTER*1

= ’U’: Upper triangle of A is stored;

= ’L’: Lower triangle of A is stored.

*N*

N is INTEGER

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

*AP*

AP is REAL array, dimension (N*(N+1)/2)

The triangular factor U or L from the Cholesky factorization

A = U**T*U or A = L*L**T, packed columnwise in a linear

array. The j-th column of U or L is stored in the array AP

as follows:

if UPLO = ’U’, AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j;

if UPLO = ’L’, AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n.

*ANORM*

ANORM is REAL

The 1-norm (or infinity-norm) of the symmetric matrix A.

*RCOND*

RCOND is REAL

The reciprocal of the condition number of the matrix A,

computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an

estimate of the 1-norm of inv(A) computed in this routine.

*WORK*

WORK is REAL array, dimension (3*N)

*IWORK*

IWORK is INTEGER 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 119 of file sppcon.f.

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