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HJBE_discretized_univariate_test.m
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%Using the unit testing framework in matlab. See https://www.mathworks.com/help/matlab/matlab_prog/write-simple-test-case-with-functions.html
%To run tests:
% runtests %would run all of them in the current directory
% runtests('my_test') %runs just the my_test.m file
% runtests('my_test/my_function_test') %runs only `my_function_test function in `my_test'.
function tests = HJBE_discretized_univariate_test
tests = functiontests(localfunctions);
end
%This is run at the beginning of the test. Not required.
function setupOnce(testCase)
addpath('../lib/');
testCase.TestData.tolerances.test_tol = 1e-9;
testCase.TestData.tolerances.lower_test_tol = 1e-8; %For huge matrices, the inf norm can get a little different.
testCase.TestData.tolerances.default_csv_precision = '%.10f'; %Should be higher precision than tolerances.test_tol
end
function simple_value_function_test(testCase)
tolerances = testCase.TestData.tolerances;
mu_x = @(x) -0.01 * x;
sigma_bar = 0.1;
sigma_2_x = @(x) (sigma_bar*x).^2;
u_x = @(x) exp(x);
rho = 0.05;
x_min = 1;
x_max = 2;
I = 20;
x = linspace(x_min, x_max, I)';
A = discretize_univariate_diffusion(x, mu_x(x), sigma_2_x(x));
u = u_x(x);
%Solve the simple problem: rho v(x) = u(x) + A v(x) for the above process.
[v, success] = simple_HJBE_discretized_univariate(A, x, u, rho);
%dlmwrite(strcat(mfilename, '_1_v_output.csv'), v, 'precision', tolerances.default_csv_precision); %Uncomment to save again
v_check = dlmread(strcat(mfilename, '_1_v_output.csv'));
verifyTrue(testCase,norm(v - v_check, Inf) < tolerances.test_tol, 'v value no longer matches');
verifyTrue(testCase, success==true, 'unsuccesful');
end
function bigger_value_function_test(testCase)
tolerances = testCase.TestData.tolerances;
mu_x = @(x) -0.01 * x;
sigma_bar = 0.1;
sigma_2_x = @(x) (sigma_bar*x).^2;
u_x = @(x) log(x);
rho = 0.05;
x_min = .01;
x_max = 10;
I = 10000;
x = linspace(x_min, x_max, I)';
A = discretize_univariate_diffusion(x, mu_x(x), sigma_2_x(x));
u = u_x(x);
%Solve the simple problem: rho v(x) = u(x) + A v(x) for the above process.
[v, success] = simple_HJBE_discretized_univariate(A, x, u, rho);
%dlmwrite(strcat(mfilename, '_2_v_output.csv'), v, 'precision', tolerances.default_csv_precision); %Uncomment to save again
v_check = dlmread(strcat(mfilename, '_2_v_output.csv'));
verifyTrue(testCase,norm(v - v_check, Inf) < tolerances.lower_test_tol, 'v value no longer matches');
verifyTrue(testCase, success==true, 'unsuccesful');
end
%
%This will try to jointly solve for the KFE and the value function with linear least squares.
function joint_value_function_KFE_test(testCase)
tolerances = testCase.TestData.tolerances;
mu_x = @(x) -0.01 * ones(numel(x),1);
sigma_bar = 0.1;
sigma_2_x = @(x) (sigma_bar * ones(numel(x),1)).^2;
u_x = @(x) log(x);
rho = 0.05;
x_min = 0.1;
x_max = 2;
I = 1000;
x = linspace(x_min, x_max, I)';
A = discretize_univariate_diffusion(x, mu_x(x), sigma_2_x(x));
u = u_x(x);
%Solve the simple problem: rho v(x) = u(x) + A v(x) for the above process.
disp('Solving HJBE on its own');
tic;
[v, success] = simple_HJBE_discretized_univariate(A, x, u, rho);
toc;
%dlmwrite(strcat(mfilename, '_3_v_output.csv'), v, 'precision', tolerances.default_csv_precision); %Uncomment to save again
v_check = dlmread(strcat(mfilename, '_3_v_output.csv'));
verifyTrue(testCase,norm(v - v_check, Inf) < tolerances.test_tol, 'v value no longer matches');
verifyTrue(testCase, success==true, 'unsuccesful');
%Now find the KFE with linear least squares and the default preconditioner
settings.print_level = 1;
%settings.method = 'LLS';
%settings.method = 'eigenproblem_all';
disp('Solving stationary distribution on its own');
tic;
f = stationary_distribution_discretized_univariate(A, x, settings);
toc;
%dlmwrite(strcat(mfilename, '_3_f_output.csv'), f, 'precision', tolerances.default_csv_precision); %Uncomment to save again
f_check = dlmread(strcat(mfilename, '_3_f_output.csv'));
verifyTrue(testCase,norm(f - f_check, Inf) < tolerances.test_tol, 'f value no longer matches');
%Now, solve as a joint problem with LLS
%settings.preconditioner = 'none';
settings.sparse = 'false';
disp('Solving dense');
tic;
[v, f, success] = simple_joint_HJBE_stationary_distribution_univariate(A, x, u, rho, settings);
verifyTrue(testCase,norm(v - v_check, Inf) < tolerances.test_tol, 'v value no longer matches');
verifyTrue(testCase,norm(f - f_check, Inf) < tolerances.test_tol, 'f value no longer matches');
toc;
%Now try as a sparse system.
disp('Solving sparse with no preconditioner');
settings.sparse = 'true';
tic;
[v, f, success] = simple_joint_HJBE_stationary_distribution_univariate(A, x, u, rho, settings);
toc;
verifyTrue(testCase,norm(v - v_check, Inf) < tolerances.test_tol, 'v value no longer matches');
verifyTrue(testCase,norm(f - f_check, Inf) < tolerances.test_tol, 'f value no longer matches');
%Now try as a sparse system with jacobi preconditioner
disp('Solving sparse with jacobi preconditioner');
settings.sparse = 'jacobi';
tic;
[v, f, success] = simple_joint_HJBE_stationary_distribution_univariate(A, x, u, rho, settings);
toc;
verifyTrue(testCase,norm(v - v_check, Inf) < tolerances.test_tol, 'v value no longer matches');
verifyTrue(testCase,norm(f - f_check, Inf) < tolerances.test_tol, 'f value no longer matches');
end