function [ r, info ] = r8po_fa ( n, a )
%*****************************************************************************80
%
%% R8PO_FA factors a R8PO matrix.
%
% Discussion:
%
% The R8PO storage format is appropriate for a symmetric positive definite
% matrix and its inverse. (The Cholesky factor of a R8PO matrix is an
% upper triangular matrix, so it will be in R8GE storage format.)
%
% Only the diagonal and upper triangle of the square array are used.
% This same storage scheme is used when the matrix is factored by
% R8PO_FA, or inverted by R8PO_INVERSE. For clarity, the lower triangle
% is set to zero.
%
% The positive definite symmetric matrix A has a Cholesky factorization
% of the form:
%
% A = R' * R
%
% where R is an upper triangular matrix with positive elements on
% its diagonal. This routine overwrites the matrix A with its
% factor R.
%
% Licensing:
%
% This code is distributed under the MIT license.
%
% Modified:
%
% 20 February 2004
%
% Author:
%
% MATLAB version by John Burkardt.
%
% Reference:
%
% Dongarra, Bunch, Moler, Stewart,
% LINPACK User's Guide,
% SIAM, 1979.
%
% Parameters:
%
% Input, integer N, the order of the matrix.
%
% Input, real A(N,N), the matrix in R8PO storage.
%
% Output, real R(N,N), the Cholesky factor R in R8GE storage.
%
% Output, integer INFO, error flag.
% 0, normal return.
% K, error condition. The principal minor of order K is not
% positive definite, and the factorization was not completed.
%
r(1:n,1:n) = a(1:n,1:n);
for j = 1 : n
for k = 1 : j - 1
t = 0.0;
for i = 1 : k-1
t = t + r(i,k) * r(i,j);
end
r(k,j) = ( r(k,j) - t ) / r(k,k);
end
t = 0.0;
for i = 1 : j - 1
t = t + r(i,j)^2;
end
s = r(j,j) - t;
if ( s <= 0.0 )
info = j;
return;
end
r(j,j) = sqrt ( s );
end
info = 0;
%
% Since the Cholesky factor is stored in R8GE format, be sure to
% zero out the lower triangle.
%
for i = 1 : n
for j = 1 : i-1
r(i,j) = 0.0;
end
end
return
end