.TH SPPTRF 1 "November 2006" " LAPACK routine (version 3.1) " " LAPACK routine (version 3.1) "
.SH NAME
SPPTRF - the Cholesky factorization of a real symmetric positive definite matrix A stored in packed format
.SH SYNOPSIS
.TP 19
SUBROUTINE SPPTRF(
UPLO, N, AP, INFO )
.TP 19
.ti +4
CHARACTER
UPLO
.TP 19
.ti +4
INTEGER
INFO, N
.TP 19
.ti +4
REAL
AP( * )
.SH PURPOSE
SPPTRF computes the Cholesky factorization of a real symmetric
positive definite matrix A stored in packed format.
The factorization has the form
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A = U**T * U, if UPLO = \(aqU\(aq, or
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A = L * L**T, if UPLO = \(aqL\(aq,
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where U is an upper triangular matrix and L is lower triangular.
.SH ARGUMENTS
.TP 8
UPLO (input) CHARACTER*1
= \(aqU\(aq: Upper triangle of A is stored;
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= \(aqL\(aq: Lower triangle of A is stored.
.TP 8
N (input) INTEGER
The order of the matrix A. N >= 0.
.TP 8
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 = \(aqU\(aq, AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = \(aqL\(aq, 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.
.TP 8
INFO (output) INTEGER
= 0: successful exit
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< 0: if INFO = -i, the i-th argument had an illegal value
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> 0: if INFO = i, the leading minor of order i is not
positive definite, and the factorization could not be
completed.
.SH FURTHER DETAILS
The packed storage scheme is illustrated by the following example
when N = 4, UPLO = \(aqU\(aq:
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Two-dimensional storage of the symmetric matrix A:
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a11 a12 a13 a14
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a22 a23 a24
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a33 a34 (aij = aji)
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a44
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Packed storage of the upper triangle of A:
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AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]