# spptrf.f(3) [centos man page]

```spptrf.f(3)							      LAPACK							       spptrf.f(3)

NAME
spptrf.f -

SYNOPSIS
Functions/Subroutines
subroutine spptrf (UPLO, N, AP, INFO)
SPPTRF

Function/Subroutine Documentation
subroutine spptrf (characterUPLO, integerN, real, dimension( * )AP, integerINFO)
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

NAG Ltd.

Date:
November 2011

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 120 of file spptrf.f.

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

Version 3.4.2							  Tue Sep 25 2012						       spptrf.f(3)```

## Check Out this Related Man Page

```SPPTRF(l)								 )								 SPPTRF(l)

NAME
SPPTRF - compute the Cholesky factorization of a real symmetric positive definite matrix A stored in packed format

SYNOPSIS
SUBROUTINE SPPTRF( UPLO, N, AP, INFO )

CHARACTER	  UPLO

INTEGER	  INFO, N

REAL 	  AP( * )

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.

ARGUMENTS
UPLO    (input) CHARACTER*1
= 'U':  Upper triangle of A is stored;
= 'L':  Lower triangle of A is stored.

N       (input) INTEGER
The order of the matrix A.  N >= 0.

AP      (input/output) 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    (output) 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.

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 ]

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