# spptrf.f - Man Page

## Synopsis

### Functions/Subroutines

subroutine **spptrf** (UPLO, **N**, AP, INFO)**SPPTRF**

## Function/Subroutine Documentation

### subroutine spptrf (character UPLO, integer N, real, dimension( * ) AP, integer INFO)

**SPPTRF**

**Purpose:**

SPPTRF computes the Cholesky factorization of a real symmetric positive definite matrix A stored in packed format. The factorization has the form A = U**T * U, if UPLO = 'U', or A = L * L**T, if UPLO = 'L', where U is an upper triangular matrix and L is lower triangular.

**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) On entry, the upper or lower triangle of the symmetric 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. See below for further details. On exit, if INFO = 0, the triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T, in the same storage format as A.

*INFO*INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, the leading minor of order i is not positive definite, and the factorization could not be completed.

**Author:**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date:**December 2016

**Further Details:**

The packed storage scheme is illustrated by the following example when N = 4, UPLO = 'U': Two-dimensional storage of the symmetric matrix A: a11 a12 a13 a14 a22 a23 a24 a33 a34 (aij = aji) a44 Packed storage of the upper triangle of A: AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]

Definition at line 121 of file spptrf.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page spptrf(3) is an alias of spptrf.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK