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% STK_DISTRIB_BIVNORM_CDF [STK internal]
% Copyright Notice
%
% Copyright (C) 2018 CentraleSupelec
% Copyright (C) 2014 SUPELEC
%
% Author: Julien Bect <julien.bect@centralesupelec.fr>
% Copying Permission Statement
%
% This file is part of
%
% STK: a Small (Matlab/Octave) Toolbox for Kriging
% (https://github.com/stk-kriging/stk/)
%
% STK is free software: you can redistribute it and/or modify it under
% the terms of the GNU General Public License as published by the Free
% Software Foundation, either version 3 of the License, or (at your
% option) any later version.
%
% STK is distributed in the hope that it will be useful, but WITHOUT
% ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
% or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
% License for more details.
%
% You should have received a copy of the GNU General Public License
% along with STK. If not, see <http://www.gnu.org/licenses/>.
function [p, q] = stk_distrib_bivnorm_cdf (z, mu1, mu2, sigma1, sigma2, rho)
%--- Split z into [z1, z2] -----------------------------------------------------
s = size (z);
if s(end) ~= 2
stk_error (['Incorrect size: expecting an array with length 2 ' ...
'on its last dimension.'], 'IncorrectSize');
end
S = struct ('type', '()', 'subs', {repmat({':'}, size(s))});
S.subs{end} = 1; z1 = subsref (z, S);
S.subs{end} = 2; z2 = subsref (z, S);
%--- Substract the means -------------------------------------------------------
if ~ isequal (mu1, 0)
z1 = bsxfun (@minus, z1, mu1);
end
if ~ isequal (mu2, 0)
z2 = bsxfun (@minus, z2, mu2);
end
%--- Bring everything to a common size -----------------------------------------
if ~ isequal (size (z1), size (z2), size (sigma1), size (sigma2), size (rho))
[z1, z2, sigma1, sigma2, rho] = stk_commonsize ...
(z1, z2, sigma1, sigma2, rho);
end
p = nan (size (z1));
q = nan (size (z1));
%--- Deal with special cases ---------------------------------------------------
b1 = (sigma1 == 0.0);
if any (b1) % First component is zero a.s.
[p(b1) q(b1)] = handle_singular_case (b1, z1, z2, sigma2);
end
b2 = (~ b1) & (sigma2 == 0.0);
if any (b2) % Second component is zero a.s.
[p(b2) q(b2)] = handle_singular_case (b2, z2, z1, sigma1);
end
%--- Deal with the general case ------------------------------------------------
b0 = ~ (b1 | b2);
if any (b0)
z1 = z1(b0) ./ sigma1(b0);
z2 = z2(b0) ./ sigma2(b0);
[p(b0), q(b0)] = __stk_distrib_bivnorm0_cdf__ ([z1 z2], rho(b0));
end
end % function
function [p q] = handle_singular_case (b1, z1, z2, sigma2)
z1_ = z1(b1);
z2_ = z2(b1);
sigma2_ = sigma2(b1);
% Values for the case z1 < 0
s = size (z1_);
p = zeros (s);
q = ones (s);
b1p = (z1_ >= 0);
if any (b1p)
[p(b1p) q(b1p)] = stk_distrib_normal_cdf (z2_(b1p), 0, sigma2_(b1p));
end
end % function
%!test
%!
%! z1 = [0 1; -1 2];
%! z2 = [0 1; 1 -2];
%!
%! z = cat (3, z1, z2); % 2 x 2 x 2
%!
%! mu1 = 0; % 1 x 1 x 1
%! mu2 = [0 1]; % 1 x 2 x 1
%!
%! sigma1 = [1 3]; % 1 x 2 x 1
%! sigma2 = [1; 2]; % 2 x 1 x 1
%!
%! rho = [0; 0.5]; % 2 x 1 x 1
%!
%! %% BROADCASTING => the result will be a 2 x 2 matrix
%!
%! p = stk_distrib_bivnorm_cdf (z, mu1, mu2, sigma1, sigma2, rho);
%!
%! p11 = 0.25; % mvncdf ([ 0 0], [0 0], [1 0; 0 1]);
%! p12 = 0.315279329909118; % mvncdf ([ 1 1], [0 1], [9 0; 0 1]);
%! p21 = 0.146208349559646; % mvncdf ([-1 1], [0 0], [1 1; 1 4]);
%! p22 = 0.064656239880040; % mvncdf ([ 2 -2], [0 1], [9 3; 3 4]);
%!
%! assert (stk_isequal_tolabs (p, [p11 p12; p21 p22], 1e-14))
%%% [p, q] = stk_distrib_bivnorm_cdf ([inf z], 0, 0, 1, 1, 0) with various z's
%!test
%! [p, q] = stk_distrib_bivnorm_cdf ([inf -inf], 0, 0, 1, 1, 0);
%! assert ((p == 0.0) && (q == 1.0))
%!test
%! [p, q] = stk_distrib_bivnorm_cdf ([inf -10], 0, 0, 1, 1, 0);
%! assert (stk_isequal_tolrel (p, 7.619853024160489e-24, 1e-12))
%! assert (q == 1.0)
%!test
%! [p, q] = stk_distrib_bivnorm_cdf ([inf 0], 0, 0, 1, 1, 0);
%! assert (stk_isequal_tolrel (p, 0.5, 1e-12))
%! assert (stk_isequal_tolrel (q, 0.5, 1e-12))
%!test
%! [p, q] = stk_distrib_bivnorm_cdf ([inf 10], 0, 0, 1, 1, 0);
%! assert (p == 1.0);
%! assert (stk_isequal_tolrel (q, 7.619853024160489e-24, 1e-12))
%!test
%! [p, q] = stk_distrib_bivnorm_cdf ([inf inf], 0, 0, 1, 1, 0);
%! assert ((p == 1.0) && (q == 0.0))
%%% [p, q] = stk_distrib_bivnorm_cdf ([z inf], 0, 0, 1, 1, 0) with various z's
%!test
%! [p, q] = stk_distrib_bivnorm_cdf ([-inf inf], 0, 0, 1, 1, 0);
%! assert ((p == 0.0) && (q == 1.0))
%!test
%! [p, q] = stk_distrib_bivnorm_cdf ([-10 inf], 0, 0, 1, 1, 0);
%! assert (stk_isequal_tolrel (p, 7.619853024160489e-24, 1e-12))
%! assert (q == 1.0)
%!test
%! [p, q] = stk_distrib_bivnorm_cdf ([0 inf], 0, 0, 1, 1, 0);
%! assert (stk_isequal_tolrel (p, 0.5, 1e-12))
%! assert (stk_isequal_tolrel (q, 0.5, 1e-12))
%!test
%! [p, q] = stk_distrib_bivnorm_cdf ([10 inf], 0, 0, 1, 1, 0);
%! assert (p == 1.0);
%! assert (stk_isequal_tolrel (q, 7.619853024160489e-24, 1e-12))
%!test
%! [p, q] = stk_distrib_bivnorm_cdf ([inf inf], 0, 0, 1, 1, 0);
%! assert ((p == 1.0) && (q == 0.0))
%!test % A mixture of singular and non-singular cases
%! p = stk_distrib_bivnorm_cdf ([0 0], 0, 0, [1; 0], 1, 0);
%! assert (isequal (p, [0.25; 0.5]));
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