regressionTest.m

function tests = regressionTest
% This file is part of GPCCA.
%
% Copyright (c) 2018, 2017 Bernhard Reuter
%
% If you use this code or parts of it, cite the following reference:
%
% Reuter, B., Weber, M., Fackeldey, K., R?blitz, S., & Garcia, M. E. (2018). Generalized
% Markov State Modeling Method for Nonequilibrium Biomolecular Dynamics: Exemplified on
% Amyloid beta Conformational Dynamics Driven by an Oscillating Electric Field. Journal of
% Chemical Theory and Computation, 14(7), 3579-3594. https://doi.org/10.1021/acs.jctc.8b00079
%
% GPCCA is free software: you can redistribute it and/or modify
% it under the terms of the GNU Lesser General Public License as published
% by the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% This program 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 Lesser General Public License
% along with this program.  If not, see <http://www.gnu.org/licenses/>.
% -------------------------------------------------------------------------
%   All test functions written by Bernhard Reuter, Theoretical Physics II,
%   University of Kassel, 2017

    tests = functiontests(localfunctions) ;
end
% -------------------------------------------------------------------------
% -------------------------------------------------------------------------
% -------------------------------------------------------------------------
% test for illegal (P, sd, kmin, kmax) empty input
function test_empty_P(testCase)
%       specify the test case data
    matrixfile = 'count.txt' ;
%       get the known test case data
    [ P, sd ] = get_knownInput( matrixfile ) ;
    
    try
        [ ~, ~, ~, ~, ~ ] = gpcca([], sd, 2, 10, [], []) ;
        actVal = 0 ;
    catch ME
        switch ME.identifier
            case 'gpcca:EmptyInput'
                actVal = 1 ;
            otherwise
                rethrow(ME)
        end
    end
    fileID = fopen('test_gpcca_report.txt','w') ;
    fprintf(fileID,'%s',ME.identifier) ;
    fprintf(fileID,'%s',': ') ;
    fprintf(fileID,'%s\n\n',ME.message) ;
    fclose(fileID) ;
    expVal = 1 ;
    verifyEqual(testCase, actVal, expVal)
end

function test_empty_sd(testCase)
%       specify the test case data
    matrixfile = 'count.txt' ;
%       get the known test case data
    [ P, sd ] = get_knownInput( matrixfile ) ;
    
    try
        [ ~, ~, ~, ~, ~ ] = gpcca(P, [], 2, 10, [], []) ;
        actVal = 0 ;
    catch ME
        switch ME.identifier
            case 'gpcca:EmptyInput'
                actVal = 1 ;
            otherwise
                rethrow(ME)
        end
    end
    fileID = fopen('test_gpcca_report.txt','a') ;
    fprintf(fileID,'%s',ME.identifier) ;
    fprintf(fileID,'%s',': ') ;
    fprintf(fileID,'%s\n\n',ME.message) ;
    fclose(fileID) ;
    expVal = 1 ;
    verifyEqual(testCase, actVal, expVal)
end

function test_empty_kmin(testCase)
%       specify the test case data
    matrixfile = 'count.txt' ;
%       get the known test case data
    [ P, sd ] = get_knownInput( matrixfile ) ;
    
    try
        [ ~, ~, ~, ~, ~ ] = gpcca(P, sd, [], 10, [], []) ;
        actVal = 0 ;
    catch ME
        switch ME.identifier
            case 'gpcca:EmptyInput'
                actVal = 1 ;
            otherwise
                rethrow(ME)
        end
    end
    fileID = fopen('test_gpcca_report.txt','a') ;
    fprintf(fileID,'%s',ME.identifier) ;
    fprintf(fileID,'%s',': ') ;
    fprintf(fileID,'%s\n\n',ME.message) ;
    fclose(fileID) ;
    expVal = 1 ;
    expVal = 1 ;
    verifyEqual(testCase, actVal, expVal)
end

function test_empty_kmax(testCase)
%       specify the test case data
    matrixfile = 'count.txt' ;
%       get the known test case data
    [ P, sd ] = get_knownInput( matrixfile ) ;
    
    try
        [ ~, ~, ~, ~, ~ ] = gpcca(P, sd, 2, [], [], []) ;
        actVal = 0 ;
    catch ME
        switch ME.identifier
            case 'gpcca:EmptyInput'
                actVal = 1 ;
            otherwise
                rethrow(ME)
        end
    end
    fileID = fopen('test_gpcca_report.txt','a') ;
    fprintf(fileID,'%s',ME.identifier) ;
    fprintf(fileID,'%s',': ') ;
    fprintf(fileID,'%s\n\n',ME.message) ;
    fclose(fileID) ;
    expVal = 1 ;
    expVal = 1 ;
    verifyEqual(testCase, actVal, expVal)
end

% test for different classes of P and sd
function test_InputDataType(testCase)
%       specify the test case data
    matrixfile = 'count.txt' ;
%       get the known test case data
    [ P, sd ] = get_knownInput( matrixfile ) ;
    
    assumeEqual(testCase, numeric_t, 'mp')
    try
        [ ~, ~, ~, ~, ~ ] = gpcca(double(P), sd, 2, 10, [], []) ;
        actVal = 0 ;
    catch ME
        switch ME.identifier
            case 'gpcca:P_sd_DataTypeError'
                actVal = 1 ;
            otherwise
                rethrow(ME)
        end
    end
    fileID = fopen('test_gpcca_report.txt','a') ;
    fprintf(fileID,'%s',ME.identifier) ;
    fprintf(fileID,'%s',': ') ;
    fprintf(fileID,'%s\n\n',ME.message) ;
    fclose(fileID) ;
    expVal = 1 ;
    expVal = 1 ;
    verifyEqual(testCase, actVal, expVal)
end

% test for kmin, kmax being not integer or kmin>kmax
function test_kmin_input(testCase)
%       specify the test case data
    matrixfile = 'count.txt' ;
%       get the known test case data
    [ P, sd ] = get_knownInput( matrixfile ) ;
    
    try
        [ ~, ~, ~, ~, ~ ] = gpcca(P, sd, 1.1, 10, [], []) ;
        actVal = 0 ;
    catch ME
        switch ME.identifier
            case 'gpcca:k_InputError'
                actVal = 1 ;
            otherwise
                rethrow(ME)
        end
    end
    fileID = fopen('test_gpcca_report.txt','a') ;
    fprintf(fileID,'%s',ME.identifier) ;
    fprintf(fileID,'%s',': ') ;
    fprintf(fileID,'%s\n\n',ME.message) ;
    fclose(fileID) ;
    expVal = 1 ;
    expVal = 1 ;
    verifyEqual(testCase, actVal, expVal)
end

function test_kmax_input(testCase)
%       specify the test case data
    matrixfile = 'count.txt' ;
%       get the known test case data
    [ P, sd ] = get_knownInput( matrixfile ) ;
    
    try
        [ ~, ~, ~, ~, ~ ] = gpcca(P, sd, 2, 10.1, [], []) ;
        actVal = 0 ;
    catch ME
        switch ME.identifier
            case 'gpcca:k_InputError'
                actVal = 1 ;
            otherwise
                rethrow(ME)
        end
    end
    fileID = fopen('test_gpcca_report.txt','a') ;
    fprintf(fileID,'%s',ME.identifier) ;
    fprintf(fileID,'%s',': ') ;
    fprintf(fileID,'%s\n\n',ME.message) ;
    fclose(fileID) ;
    expVal = 1 ;
    expVal = 1 ;
    verifyEqual(testCase, actVal, expVal)
end

function test_k_input(testCase)
%       specify the test case data
    matrixfile = 'count.txt' ;
%       get the known test case data
    [ P, sd ] = get_knownInput( matrixfile ) ;
    
    try
        [ ~, ~, ~, ~, ~ ] = gpcca(P, sd, 3, 2, [], []) ;
        actVal = 0 ;
    catch ME
        switch ME.identifier
            case 'gpcca:k_InputError'
                actVal = 1 ;
            otherwise
                rethrow(ME)
        end
    end
    fileID = fopen('test_gpcca_report.txt','a') ;
    fprintf(fileID,'%s',ME.identifier) ;
    fprintf(fileID,'%s',': ') ;
    fprintf(fileID,'%s\n\n',ME.message) ;
    fclose(fileID) ;
    expVal = 1 ;
    expVal = 1 ;
    verifyEqual(testCase, actVal, expVal)
end

% test for valid initialization of wk in case of empty wk
function test_empty_wk(testCase)
%       set the solver, optional solver and ID-string for file-naming
    wk.solver = 'gauss-newton' ;
    wk.id = 'test_empty_wk' ;
%       specify the test case data
    matrixfile = 'count.txt' ;
%       get the known test case data
    [ P, sd ] = get_knownInput( matrixfile ) ;
    [ T, ~, ~, ~, wk, ~ ] = evalc('gpcca(P, sd, 2, 10, [], [])') ;
    close all
    fileID = fopen('test_gpcca_report.txt','a') ;
    fprintf(fileID,'%s\n\n','test_empty_wk') ;
    fprintf(fileID,'%s\n\n\n',T) ;
    fclose(fileID) ;
    verifyEqual(testCase, isstruct(wk), true)
    verifyEqual(testCase, wk.id, 'gpcca')
    verifyEqual(testCase, wk.schur, 1)
    verifyEqual(testCase, wk.b, 0)
    verifyEqual(testCase, wk.init, 1)
    verifyEqual(testCase, wk.solver, 'gauss-newton')
    verifyEqual(testCase, wk.maxiter, 100)
    verifyEqual(testCase, wk.display, 0)
    verifyEqual(testCase, wk.xtol, 1e-4)
    verifyEqual(testCase, wk.xscale, 1e-06)
end

% test for valid initialization of wk in case of only 
% wk.solver='gauss-newton' defined
function test_wk_gauss_newton(testCase)
%       set the solver, optional solver and ID-string for file-naming
    wk.solver = 'gauss-newton' ;
    wk.id = 'test_wk_gauss_newton' ;
%       specify the test case data
    matrixfile = 'count.txt' ;
%       get the known test case data
    [ P, sd ] = get_knownInput( matrixfile ) ;
    [ T, ~, ~, ~, wk, ~ ] = evalc('gpcca(P, sd, 2, 10, wk, [])') ;
    close all
    fileID = fopen('test_gpcca_report.txt','a') ;
    fprintf(fileID,'%s\n\n','test_wk_gauss_newton') ;
    fprintf(fileID,'%s\n\n\n',T) ;
    fclose(fileID) ;
    verifyEqual(testCase, isstruct(wk), true)
    verifyEqual(testCase, wk.id, 'test_wk_gauss_newton')
    verifyEqual(testCase, wk.schur, 1)
    verifyEqual(testCase, wk.b, 0)
    verifyEqual(testCase, wk.init, 1)
    verifyEqual(testCase, wk.solver, 'gauss-newton')
    verifyEqual(testCase, wk.maxiter, 100)
    verifyEqual(testCase, wk.display, 0)
    verifyEqual(testCase, wk.xtol, 1e-4)
    verifyEqual(testCase, wk.xscale, 1e-06)
end

% test for valid initialization of wk in case of only 
% wk.solver='nelder-mead' defined
function test_wk_nelder_mead(testCase)
%       set the solver, optional solver and ID-string for file-naming
    wk.solver = 'nelder-mead' ;
    wk.id = 'test_wk_nelder_mead' ;
%       specify the test case data
    matrixfile = 'count.txt' ;
%       get the known test case data
    [ P, sd ] = get_knownInput( matrixfile ) ;
    [ T, ~, ~, ~, wk, ~ ] = evalc('gpcca(P, sd, 2, 10, wk, [])') ;
    close all
    fileID = fopen('test_gpcca_report.txt','a') ;
    fprintf(fileID,'%s\n\n','test_wk_nelder_mead') ;
    fprintf(fileID,'%s\n\n\n',T) ;
    fclose(fileID) ;
    verifyEqual(testCase, isstruct(wk), true)
    verifyEqual(testCase, wk.id, 'test_wk_nelder_mead')
    verifyEqual(testCase, wk.schur, 1)
    verifyEqual(testCase, wk.b, 0)
    verifyEqual(testCase, wk.init, 1)
    verifyEqual(testCase, wk.solver, 'nelder-mead')
    verifyEqual(testCase, wk.maxiter, 2000)
    verifyEqual(testCase, wk.display, 0)
    verifyEqual(testCase, wk.tolfun, 1e-4)
    verifyEqual(testCase, wk.tolx, 1e-4)
end

% test for valid initialization of wk in case of only 
% wk.solver='levenberg-marquardt' defined
function test_wk_levenberg_marquardt(testCase)
%       set the solver, optional solver and ID-string for file-naming
    wk.solver = 'levenberg-marquardt' ;
    wk.id = 'test_wk_levenberg_marquardt' ;
%       specify the test case data
    matrixfile = 'count.txt' ;
%       get the known test case data
    [ P, sd ] = get_knownInput( matrixfile ) ;
    [ T, ~, ~, ~, wk, ~ ] = evalc('gpcca(P, sd, 2, 10, wk, [])') ;
    close all
    fileID = fopen('test_gpcca_report.txt','a') ;
    fprintf(fileID,'%s\n\n','test_wk_levenberg_marquardt') ;
    fprintf(fileID,'%s\n\n\n',T) ;
    fclose(fileID) ;
    verifyEqual(testCase, isstruct(wk), true)
    verifyEqual(testCase, wk.id, 'test_wk_levenberg_marquardt')
    verifyEqual(testCase, wk.schur, 1)
    verifyEqual(testCase, wk.b, 0)
    verifyEqual(testCase, wk.init, 1)
    verifyEqual(testCase, wk.solver, 'levenberg-marquardt')
    verifyEqual(testCase, wk.maxiter, 500)
    verifyEqual(testCase, wk.display, 0)
    verifyEqual(testCase, wk.tolfun, 1e-8)
    verifyEqual(testCase, wk.tolx, 1e-10)
end

% test for valid initialization of iopt in case of empty iopt
function test_empty_iopt(testCase)
%       set the solver, optional solver and ID-string for file-naming
    wk.solver = 'gauss-newton' ;
    wk.id = 'test_empty_iopt' ;
%       specify the test case data
    matrixfile = 'count.txt' ;
%       get the known test case data
    [ P, sd ] = get_knownInput( matrixfile ) ;
    [ T, ~, ~, ~, ~, iopt ] = evalc('gpcca(P, sd, 2, 10, wk, [])') ;
    close all
    fileID = fopen('test_gpcca_report.txt','a') ;
    fprintf(fileID,'%s\n\n','test_empty_iopt') ;
    fprintf(fileID,'%s\n\n\n',T) ;
    fclose(fileID) ;
    verifyEqual(testCase, isempty(iopt), true)
end

% test for valid initialization of iopt in case of only 
% iopt.solver='gauss-newton' defined
function test_iopt_gauss_newton(testCase)
%       set the solver, optional solver and ID-string for file-naming
    wk.solver = 'gauss-newton' ;
    iopt.solver = 'gauss-newton' ;
    wk.id = 'test_iopt_gauss_newton' ;
%       specify the test case data
    matrixfile = 'count.txt' ;
%       get the known test case data
    [ P, sd ] = get_knownInput( matrixfile ) ;
    [ T, ~, ~, ~, ~, iopt ] = evalc('gpcca(P, sd, 2, 10, wk, iopt)') ;
    close all
    fileID = fopen('test_gpcca_report.txt','a') ;
    fprintf(fileID,'%s\n\n','test_iopt_gauss_newton') ;
    fprintf(fileID,'%s\n\n\n',T) ;
    fclose(fileID) ;
    verifyEqual(testCase, isstruct(iopt), true)
    verifyEqual(testCase, iopt.solver, 'gauss-newton')
    verifyEqual(testCase, iopt.init, 1)
    verifyEqual(testCase, iopt.parallel, 0)
    verifyEqual(testCase, iopt.maxiter, 100)
    verifyEqual(testCase, iopt.display, 0)
    verifyEqual(testCase, iopt.xtol, 1e-4)
    verifyEqual(testCase, iopt.xscale, 1e-06)
end

% test for valid initialization of iopt in case of only 
% iopt.solver='nelder-mead' defined
function test_iopt_nelder_mead(testCase)
%       set the solver, optional solver and ID-string for file-naming
    wk.solver = 'gauss-newton' ;
    iopt.solver = 'nelder-mead' ;
    wk.id = 'test_iopt_nelder_mead' ;
%       specify the test case data
    matrixfile = 'count.txt' ;
%       get the known test case data
    [ P, sd ] = get_knownInput( matrixfile ) ;
    [ T, ~, ~, ~, ~, iopt ] = evalc('gpcca(P, sd, 2, 10, wk, iopt)') ;
    close all
    fileID = fopen('test_gpcca_report.txt','a') ;
    fprintf(fileID,'%s\n\n','test_iopt_nelder_mead') ;
    fprintf(fileID,'%s\n\n\n',T) ;
    fclose(fileID) ;
    verifyEqual(testCase, isstruct(iopt), true)
    verifyEqual(testCase, iopt.solver, 'nelder-mead')
    verifyEqual(testCase, iopt.init, 1)
    verifyEqual(testCase, iopt.parallel, 0)
    verifyEqual(testCase, iopt.maxiter, 2000)
    verifyEqual(testCase, iopt.display, 0)
    verifyEqual(testCase, iopt.tolfun, 1e-8)
    verifyEqual(testCase, iopt.tolx, 1e-8)
end

% test for valid initialization of iopt in case of only 
% iopt.solver='levenberg-marquardt' defined
function test_iopt_levenberg_marquardt(testCase)
%       set the solver, optional solver and ID-string for file-naming
    wk.solver = 'gauss-newton' ;
    iopt.solver = 'levenberg-marquardt' ;
    wk.id = 'test_iopt_levenberg_marquardt' ;
%       specify the test case data
    matrixfile = 'count.txt' ;
%       get the known test case data
    [ P, sd ] = get_knownInput( matrixfile ) ;
    [ T, ~, ~, ~, ~, iopt ] = evalc('gpcca(P, sd, 2, 10, wk, iopt)') ;
    close all
    fileID = fopen('test_gpcca_report.txt','a') ;
    fprintf(fileID,'%s\n\n','test_iopt_levenberg-marquardt') ;
    fprintf(fileID,'%s\n\n\n',T) ;
    fclose(fileID) ;
    verifyEqual(testCase, isstruct(iopt), true)
    verifyEqual(testCase, iopt.solver, 'levenberg-marquardt')
    verifyEqual(testCase, iopt.init, 1)
    verifyEqual(testCase, iopt.parallel, 0)
    verifyEqual(testCase, iopt.maxiter, 500)
    verifyEqual(testCase, iopt.display, 0)
    verifyEqual(testCase, iopt.tolfun, 1e-8)
    verifyEqual(testCase, iopt.tolx, 1e-10)
end

function test_kmin_vs_koptmin(testCase)
% test the case that iopt.init=2 but koptmin<kmin for the Butane 
% transition count matrix from Marcus Weber.
%       set global variable to indicate testrun (no display output, no
%       interactive input): 'minChiON' indicates that minChi criterion is
%       used and input is taken from testInput_minChiON.mat. 'minChiOFF'
%       indicates that minChi criterion isnt used and input is taken from
%       testInput_minChiOFF.mat.
    global testmode
    testmode = 'minChiON' ;
%       create .mat file used in testmode from inputT() to get the input
%       values normally passed interactively from keyboard
    kmin = 3 ;
    kmax = 5 ;
    koptmin = 2 ;
    koptmax = 3 ;
    oldfileid = 'test_initialize_A_testmatrix' ;
    Switch = 1 ;
    minChi_switch = 1 ;
    name = 'testInput_minChiON.mat' ;
    save(name,'kmin','kmax','koptmin','koptmax','Switch','minChi_switch','oldfileid')
    
    import matlab.unittest.constraints.IsEqualTo;
    import matlab.unittest.constraints.AbsoluteTolerance;
    import matlab.unittest.constraints.RelativeTolerance;
%       set absolute and relative tolerance for verification
    abstol = testCase.TestData.abstolfac * eps ;
    reltol = testCase.TestData.reltolfac * eps ;
%       set the solver, optional solver and ID-string for file-naming
    wk.solver = 'gauss-newton' ;
    wk.id = 'test_kmin_vs_koptmin' ;
    iopt.solver = 'nelder-mead' ;
    iopt.init = 2 ;
%       specify the test case data
    matrixfile = 'count.txt' ;
%       get the known test case data
    [ P, sd ] = get_knownInput( matrixfile ) ;
%       check if the sd calculated by get_knownInput() matches the trusted 
%       testCase.TestData.sd
    [ ~, ~, c ] = verifyAlmostEqual(sd, testCase.TestData.sd, abstol, ...
        reltol, false) ;
    verifyTrue(testCase, c)
%       run gpcca() main function with evalc(): means screen output isnt
%       shown but stored in a output variable T
    try
        [ ~, ~, ~, ~, ~, ~ ] = evalc(['gpcca(P, sd,'...
            ' 2, 10, wk, iopt)']) ;
        actVal = 0 ;
    catch ME
        switch ME.identifier
            case 'gpcca:KeyboardInputError'
                actVal = 1 ;
            otherwise
                rethrow(ME)
        end
    end
%       error output is stored to a file
    fileID = fopen('test_gpcca_report.txt','a') ;
    fprintf(fileID,'%s\n\n','test_kmin_vs_koptmin') ;
    
    fprintf(fileID,'%s',ME.identifier) ;
    fprintf(fileID,'%s',': ') ;
    fprintf(fileID,'%s\n\n',ME.message) ;
    fclose(fileID) ;
    expVal = 1 ;
    verifyEqual(testCase, actVal, expVal)
%       close all open (but invisible) plots
    close all
end

function test_kmax_vs_koptmax(testCase)
% test the case that iopt.init=2 but koptmax>kmax for the Butane 
% transition count matrix from Marcus Weber.
%       set global variable to indicate testrun (no display output, no
%       interactive input): 'minChiON' indicates that minChi criterion is
%       used and input is taken from testInput_minChiON.mat. 'minChiOFF'
%       indicates that minChi criterion isnt used and input is taken from
%       testInput_minChiOFF.mat.
    global testmode
    testmode = 'minChiON' ;
%       create .mat file used in testmode from inputT() to get the input
%       values normally passed interactively from keyboard
    kmin = 2 ;
    kmax = 3 ;
    koptmin = 2 ;
    koptmax = 4 ;
    oldfileid = 'test_initialize_A_testmatrix' ;
    minChi_switch = 1 ;
    Switch = 1 ;
    name = 'testInput_minChiON.mat' ;
    save(name,'kmin','kmax','koptmin','koptmax','Switch','minChi_switch','oldfileid')
    
    import matlab.unittest.constraints.IsEqualTo;
    import matlab.unittest.constraints.AbsoluteTolerance;
    import matlab.unittest.constraints.RelativeTolerance;
%       set absolute and relative tolerance for verification
    abstol = testCase.TestData.abstolfac * eps ;
    reltol = testCase.TestData.reltolfac * eps ;
%       set the solver, optional solver and ID-string for file-naming
    wk.solver = 'gauss-newton' ;
    wk.id = 'test_kmax_vs_koptmax' ;
    iopt.solver = 'nelder-mead' ;
    iopt.init = 2 ;
%       specify the test case data
    matrixfile = 'count.txt' ;
%       get the known test case data
    [ P, sd ] = get_knownInput( matrixfile ) ;
%       check if the sd calculated by get_knownInput() matches the trusted 
%       testCase.TestData.sd
    [ ~, ~, c ] = verifyAlmostEqual(sd, testCase.TestData.sd, abstol, ...
        reltol, false) ;
    verifyTrue(testCase, c)
%       run gpcca() main function with evalc(): means screen output isnt
%       shown but stored in a output variable T
    try
        [ ~, ~, ~, ~, ~, ~ ] = evalc(['gpcca(P, sd,'...
            ' 2, 10, wk, iopt)']) ;
        actVal = 0 ;
    catch ME
        switch ME.identifier
            case 'gpcca:KeyboardInputError'
                actVal = 1 ;
            otherwise
                rethrow(ME)
        end
    end
%       error output is stored to a file
    fileID = fopen('test_gpcca_report.txt','a') ;
    fprintf(fileID,'%s\n\n','test_kmax_vs_koptmax') ;
    
    fprintf(fileID,'%s',ME.identifier) ;
    fprintf(fileID,'%s',': ') ;
    fprintf(fileID,'%s\n\n',ME.message) ;
    fclose(fileID) ;
    expVal = 1 ;
    verifyEqual(testCase, actVal, expVal)
%       close all open (but invisible) plots
    close all
end

function test_IoptInitError(testCase)
% test the case that iopt.init=2 but koptmax>kmax for the Butane 
% transition count matrix from Marcus Weber.
%       set global variable to indicate testrun (no display output, no
%       interactive input): 'minChiON' indicates that minChi criterion is
%       used and input is taken from testInput_minChiON.mat. 'minChiOFF'
%       indicates that minChi criterion isnt used and input is taken from
%       testInput_minChiOFF.mat.
    global testmode
    testmode = 'minChiON' ;
%       create .mat file used in testmode from inputT() to get the input
%       values normally passed interactively from keyboard
    kmin = 2 ;
    kmax = 3 ;
    koptmin = 2 ;
    koptmax = 3 ;
    oldfileid = 'test_initialize_A_testmatrix' ;
    Switch = 1 ;
    minChi_switch = 1 ;
    name = 'testInput_minChiON.mat' ;
    save(name,'kmin','kmax','koptmin','koptmax','Switch','minChi_switch','oldfileid')
    
    import matlab.unittest.constraints.IsEqualTo;
    import matlab.unittest.constraints.AbsoluteTolerance;
    import matlab.unittest.constraints.RelativeTolerance;
%       set absolute and relative tolerance for verification
    abstol = testCase.TestData.abstolfac * eps ;
    reltol = testCase.TestData.reltolfac * eps ;
%       set the solver, optional solver and ID-string for file-naming
    wk.solver = 'gauss-newton' ;
    wk.id = 'test_IoptInitError' ;
    iopt.solver = 'nelder-mead' ;
    iopt.init = 3 ;
%       specify the test case data
    matrixfile = 'count.txt' ;
%       get the known test case data
    [ P, sd ] = get_knownInput( matrixfile ) ;
%       check if the sd calculated by get_knownInput() matches the trusted 
%       testCase.TestData.sd
    [ ~, ~, c ] = verifyAlmostEqual(sd, testCase.TestData.sd, abstol, ...
        reltol, false) ;
    verifyTrue(testCase, c)
%       run gpcca() main function with evalc(): means screen output isnt
%       shown but stored in a output variable T
    try
        [ ~, ~, ~, ~, ~, ~ ] = evalc(['gpcca(P, sd,'...
            ' 2, 10, wk, iopt)']) ;
        actVal = 0 ;
    catch ME
        switch ME.identifier
            case 'gpcca:IoptInitError'
                actVal = 1 ;
            otherwise
                rethrow(ME)
        end
    end
%       error output is stored to a file

    fileID = fopen('test_gpcca_report.txt','a') ;
    fprintf(fileID,'%s\n\n','test_IoptInitError') ;
    fprintf(fileID,'%s',ME.identifier) ;
    fprintf(fileID,'%s',': ') ;
    fprintf(fileID,'%s\n\n',ME.message) ;
    fclose(fileID) ;
    expVal = 1 ;
    verifyEqual(testCase, actVal, expVal)
%       close all open (but invisible) plots
    close all
end

function test_normalCase(testCase)
% test the normal use case for the Butane transition count matrix from
% Marcus Weber.
%       set global variable to indicate testrun (no display output, no
%       interactive input): 'minChiON' indicates that minChi criterion is
%       used and input is taken from testInput_minChiON.mat. 'minChiOFF'
%       indicates that minChi criterion isnt used and input is taken from
%       testInput_minChiOFF.mat.
    global testmode
    testmode = 'minChiON' ;
%       create .mat files used in testmode from inputT() to get the input
%       values normaly passed interactively from keyboard
    kmin = 2 ;
    kmax = 5 ;
    koptmin = 3 ;
    koptmax = 3 ;
    oldfileid = 'test_initialize_A_testmatrix' ;
    Switch = 1 ;
    minChi_switch = 1 ;
    name = 'testInput_minChiON.mat' ;
    save(name,'kmin','kmax','koptmin','koptmax','Switch','minChi_switch','oldfileid')
    
    import matlab.unittest.constraints.IsEqualTo;
    import matlab.unittest.constraints.AbsoluteTolerance;
    import matlab.unittest.constraints.RelativeTolerance;
%       set absolute and relative tolerance for verification
    abstol = testCase.TestData.abstolfac * eps ;
    reltol = testCase.TestData.reltolfac * eps ;
%       set the solver, optional solver and ID-string for file-naming
    wk.solver = 'gauss-newton' ;
    iopt.solver = 'nelder-mead' ;
    wk.id = 'test_normalCase' ;
%       specify the test case data
    matrixfile = 'count.txt' ;
%       get the known test case data
    [ P, sd ] = get_knownInput( matrixfile ) ;
%       check if the sd calculated by get_knownInput() matches the trusted 
%       testCase.TestData.sd
    [ ~, ~, c ] = verifyAlmostEqual(sd, testCase.TestData.sd, abstol, ...
        reltol, false) ;
    verifyTrue(testCase, c)
%       run gpcca() main function with evalc(): means screen output isnt
%       shown but stored in a output variable T
    [ T, Pc_test, chi_test, A_test, wk, iopt ] = evalc('gpcca(P, sd, 2, 10, wk, iopt)') ;
%       close all open (but invisible) plots
    close all
%       T (with all screen output of gpcca()) is stored to a file
    fileID = fopen('test_gpcca_report.txt','a') ;
    fprintf(fileID,'%s\n\n','test_normalCase') ;
    fprintf(fileID,'%s\n\n\n',T) ;
    fclose(fileID) ;
%       verify that wk is fine
    verifyEqual(testCase, isstruct(wk), true)
    verifyEqual(testCase, wk.id, 'test_normalCase')
    verifyEqual(testCase, wk.schur, 1)
    verifyEqual(testCase, wk.b, 0)
    verifyEqual(testCase, wk.init, 1)
    verifyEqual(testCase, wk.solver, 'gauss-newton')
    verifyEqual(testCase, wk.parallel, 0)
    verifyEqual(testCase, wk.maxiter, 100)
    verifyEqual(testCase, wk.display, 0)
    verifyEqual(testCase, wk.xtol, 1e-4)
    verifyEqual(testCase, wk.xscale, 1e-6)
%       verfiy that iopt is fine
    verifyEqual(testCase, isstruct(iopt), true)
    verifyEqual(testCase, iopt.solver, 'nelder-mead')
    verifyEqual(testCase, iopt.init, 1)
    verifyEqual(testCase, iopt.parallel, 0)
    verifyEqual(testCase, iopt.maxiter, 2000)
    verifyEqual(testCase, iopt.display, 0)
    verifyEqual(testCase, iopt.tolfun, 1e-8)
    verifyEqual(testCase, iopt.tolx, 1e-8)
%       test if actual Pc, chi, A are equal (within numerical 
%       errors) to the "good" (correct) values 
    testCase.verifyThat(Pc_test, IsEqualTo(testCase.TestData.Pc, ...
       'Within', AbsoluteTolerance(abstol) | RelativeTolerance(reltol)))
    testCase.verifyThat(chi_test, IsEqualTo(testCase.TestData.chi, ...
       'Within', AbsoluteTolerance(abstol) | RelativeTolerance(reltol)))    
    testCase.verifyThat(A_test, IsEqualTo(testCase.TestData.A, ...
       'Within', AbsoluteTolerance(abstol) | RelativeTolerance(reltol)))
%       load the saved actual Pc, chi, A from files
    fileid = 'test_normalCase-nelder-mead-maxiter_2000-tolfun_1e-08-tolx_1e-08' ;
    fileid = strcat(fileid,'-',testCase.TestData.precision) ;
    Pc_saved = load(strcat(fileid,'-n=3-Pc.txt'),'-ascii') ;
    chi_saved = load(strcat(fileid,'-n=3-chi.txt'),'-ascii') ;
    A_saved = load(strcat(fileid,'-n=3-A.txt'),'-ascii') ;
%       test if the saved actual Pc, chi, A are equal  
%       (within numerical errors) to the "good" (correct) quantities
    testCase.verifyThat(Pc_saved, IsEqualTo(testCase.TestData.Pc, ...
       'Within', AbsoluteTolerance(abstol) | RelativeTolerance(reltol)))
    testCase.verifyThat(chi_saved, IsEqualTo(testCase.TestData.chi, ...
       'Within', AbsoluteTolerance(abstol) | RelativeTolerance(reltol)))    
    testCase.verifyThat(A_saved, IsEqualTo(testCase.TestData.A, ...
       'Within', AbsoluteTolerance(abstol) | RelativeTolerance(reltol)))
%       load the actual saved P, sd, sd_weights from files
    fileid1 = 'test_normalCase-gauss-newton-maxiter_100-xscale_1e-06-xtol_0.0001' ;
    fileid1 = strcat(fileid1,'-',testCase.TestData.precision) ;
    P_saved = load_t(strcat(fileid1,'-P.txt'),'-ascii',numeric_t) ;
    sd_saved = load_t(strcat(fileid1,'-sd.txt'),'-ascii',numeric_t) ;
    sd_weights_saved = load(strcat(fileid,'-n=3-sd_weights.txt'),'-ascii') ;
%       test if actual P, sd have the correct shapes
    verifyTrue(testCase,all(size(P)==size(P_saved)))
    verifyTrue(testCase,all(size(sd)==size(sd_saved)))
%       test if the saved actual P_saved, sd_saved, sd_weights_saved are equal  
%       (within numerical errors) to the "good" (correct) values
    [ ~, ~, c ] = verifyAlmostEqual(P_saved, P, abstol, reltol, false) ;
    verifyTrue(testCase, c)
    [ ~, ~, c ] = verifyAlmostEqual(sd_saved, testCase.TestData.sd, ...
        abstol, reltol, false) ;
    verifyTrue(testCase, c)
    %testCase.verifyThat(sd_saved, IsEqualTo(testCase.TestData.sd, ...
       %'Within', AbsoluteTolerance(abstol) | RelativeTolerance(reltol)))
    testCase.verifyThat(sd_weights_saved, IsEqualTo(testCase.TestData.sd_weights, ...
       'Within', AbsoluteTolerance(abstol) | RelativeTolerance(reltol)))
%       check if crispness-figure was stored after the first optimization
%       loop
    name=strcat(fileid1,'-crispness-figure-n=2-5.pdf') ;
    verifyTrue( testCase, exist(name, 'file')==2 )
    name=strcat(fileid1,'-crispness-figure-n=2-5.fig') ;
    verifyTrue( testCase, exist(name, 'file')==2 )
%       check if val_vec and opt_vec were stored to file after the first 
%       optimization loop
    name=strcat(fileid1,'-val_vec-n=2-5.txt') ;
    verifyTrue( testCase, exist(name, 'file')==2 )
    name=strcat(fileid1,'-opt_vec-n=2-5.txt') ;
    verifyTrue( testCase, exist(name, 'file')==2 )
%       check if the stored val_vec and opt_vec match the trusted values
%       after the first optimization
    val_vec = load(strcat(fileid1,'-val_vec-n=2-5.txt'),'-ascii') ;
    opt_vec = load(strcat(fileid1,'-opt_vec-n=2-5.txt'),'-ascii') ;
    testCase.verifyThat(val_vec, IsEqualTo(testCase.TestData.val_vec, ...
       'Within', AbsoluteTolerance(abstol) | RelativeTolerance(reltol)))
    testCase.verifyThat(opt_vec, IsEqualTo(testCase.TestData.opt_vec, ...
       'Within', AbsoluteTolerance(abstol) | RelativeTolerance(reltol)))
%       check if crispness-figure wasn't stored since koptmin=koptmax,
%       after the optional optimization
    name=strcat(fileid,'-crispness-figure-n=3-3.pdf') ;
    verifyTrue( testCase, exist(name, 'file')==0 )
    name=strcat(fileid,'-crispness-figure-n=3-3.fig') ;
    verifyTrue( testCase, exist(name, 'file')==0 )
%       check if val_vec and opt_vec weren't stored to file since 
%       koptmin=koptmax, after the optional
%       optimization
    name=strcat(fileid,'-val_vec-n=3-3.txt') ;
    verifyTrue( testCase, exist(name, 'file')==0 )
    name=strcat(fileid,'-opt_vec-n=3-3.txt') ;
    verifyTrue( testCase, exist(name, 'file')==0 )
end

function test_normalCase_ioptInit2(testCase)
% test the normal use case for the Butane transition count matrix from
% Marcus Weber, if iopt.init=2.
%       set global variable to indicate testrun (no display output, no
%       interactive input): 'minChiON' indicates that minChi criterion is
%       used and input is taken from testInput_minChiON.mat. 'minChiOFF'
%       indicates that minChi criterion isnt used and input is taken from
%       testInput_minChiOFF.mat.
    global testmode
    testmode = 'minChiON' ;
%       create .mat files used in testmode from inputT() to get the input
%       values normaly passed interactively from keyboard
    kmin = 2 ;
    kmax = 5 ;
    koptmin = 3 ;
    koptmax = 3 ;
    oldfileid = 'test_initialize_A_testmatrix' ;
    Switch = 1 ;
    minChi_switch = 1 ;
    name = 'testInput_minChiON.mat' ;
    save(name,'kmin','kmax','koptmin','koptmax','Switch','minChi_switch','oldfileid')
    
    import matlab.unittest.constraints.IsEqualTo;
    import matlab.unittest.constraints.AbsoluteTolerance;
    import matlab.unittest.constraints.RelativeTolerance;
%       set absolute and relative tolerance for verification
    abstol = testCase.TestData.abstolfac * eps ;
    reltol = testCase.TestData.reltolfac * eps ;
%       we need a softer tolerance here for the quantities derived by
%       optimization, since we perform two optimizations here, with the
%       second one depending on the results of the first... This leads to
%       bigger variations
    abstol1 = 1e-06 ;
    reltol1 = 1e-06 ;
%       set the solver, optional solver and ID-string for file-naming
    wk.solver = 'gauss-newton' ;
    wk.id = 'test_normalCase_ioptInit2' ;
    iopt.solver = 'nelder-mead' ;
    iopt.init = 2 ;
%       specify the test case data
    matrixfile = 'count.txt' ;
%       get the known test case data
    [ P, sd ] = get_knownInput( matrixfile ) ;
%       check if the sd calculated by get_knownInput() matches the trusted 
%       testCase.TestData.sd
    [ ~, ~, c ] = verifyAlmostEqual(sd, testCase.TestData.sd, abstol, ...
        reltol, false) ;
    verifyTrue(testCase, c)
%       run gpcca() main function with evalc(): means screen output isnt
%       shown but stored in a output variable T
    [ T, Pc_test, chi_test, A_test, wk, iopt ] = evalc('gpcca(P, sd, 2, 10, wk, iopt)') ;
%       close all open (but invisible) plots
    close all
%       T (with all screen output of gpcca()) is stored to a file
    fileID = fopen('test_gpcca_report.txt','a') ;
    fprintf(fileID,'%s\n\n','test_normalCase_ioptInit2') ;
    fprintf(fileID,'%s\n\n\n',T) ;
    fclose(fileID) ;
%       verify that wk is fine
    verifyEqual(testCase, isstruct(wk), true)
    verifyEqual(testCase, wk.id, 'test_normalCase_ioptInit2')
    verifyEqual(testCase, wk.schur, 1)
    verifyEqual(testCase, wk.b, 0)
    verifyEqual(testCase, wk.init, 1)
    verifyEqual(testCase, wk.solver, 'gauss-newton')
    verifyEqual(testCase, wk.parallel, 0)
    verifyEqual(testCase, wk.maxiter, 100)
    verifyEqual(testCase, wk.display, 0)
    verifyEqual(testCase, wk.xtol, 1e-4)
    verifyEqual(testCase, wk.xscale, 1e-6)
%       verfiy that iopt is fine
    verifyEqual(testCase, isstruct(iopt), true)
    verifyEqual(testCase, iopt.solver, 'nelder-mead')
    verifyEqual(testCase, iopt.init, 2)
    verifyEqual(testCase, iopt.parallel, 0)
    verifyEqual(testCase, iopt.maxiter, 2000)
    verifyEqual(testCase, iopt.display, 0)
    verifyEqual(testCase, iopt.tolfun, 1e-8)
    verifyEqual(testCase, iopt.tolx, 1e-8)
%       test if actual Pc, chi, A are equal (within numerical 
%       errors) to the "good" (correct) values 
    testCase.verifyThat(Pc_test, IsEqualTo(testCase.TestData.Pc, ...
       'Within', AbsoluteTolerance(abstol1) | RelativeTolerance(reltol1)))
    testCase.verifyThat(chi_test, IsEqualTo(testCase.TestData.chi, ...
       'Within', AbsoluteTolerance(abstol1) | RelativeTolerance(reltol1)))    
    testCase.verifyThat(A_test, IsEqualTo(testCase.TestData.A, ...
       'Within', AbsoluteTolerance(abstol1) | RelativeTolerance(reltol1)))
%       load the saved actual Pc, chi, A from files
    fileid = ['test_normalCase_ioptInit2-nelder-mead-maxiter_2000-'...
        'tolfun_1e-08-tolx_1e-08'] ;
    fileid = strcat(fileid,'-',testCase.TestData.precision) ;
    Pc_saved = load(strcat(fileid,'-n=3-Pc.txt'),'-ascii') ;
    chi_saved = load(strcat(fileid,'-n=3-chi.txt'),'-ascii') ;
    A_saved = load(strcat(fileid,'-n=3-A.txt'),'-ascii') ;
%       test if the saved actual Pc, chi, A are equal  
%       (within numerical errors) to the "good" (correct) quantities
    testCase.verifyThat(Pc_saved, IsEqualTo(testCase.TestData.Pc, ...
       'Within', AbsoluteTolerance(abstol1) | RelativeTolerance(reltol1)))
    testCase.verifyThat(chi_saved, IsEqualTo(testCase.TestData.chi, ...
       'Within', AbsoluteTolerance(abstol1) | RelativeTolerance(reltol1)))    
    testCase.verifyThat(A_saved, IsEqualTo(testCase.TestData.A, ...
       'Within', AbsoluteTolerance(abstol1) | RelativeTolerance(reltol1)))
%       load the actual saved P, sd, sd_weights from files
    fileid1 = ['test_normalCase_ioptInit2-gauss-newton-maxiter_100-'...
        'xscale_1e-06-xtol_0.0001'] ;
    fileid1 = strcat(fileid1,'-',testCase.TestData.precision) ;
    P_saved = load_t(strcat(fileid1,'-P.txt'),'-ascii',numeric_t) ;
    sd_saved = load_t(strcat(fileid1,'-sd.txt'),'-ascii',numeric_t) ;
    sd_weights_saved = load(strcat(fileid,'-n=3-sd_weights.txt'),'-ascii') ;
%       test if actual P, sd have the correct shapes
    verifyTrue(testCase,all(size(P)==size(P_saved)))
    verifyTrue(testCase,all(size(sd)==size(sd_saved)))
%       test if the saved actual P_saved, sd_saved, sd_weights_saved are equal  
%       (within numerical errors) to the "good" (correct) values
    [ ~, ~, c ] = verifyAlmostEqual(P_saved, P, abstol, reltol, false) ;
    verifyTrue(testCase, c)
    [ ~, ~, c ] = verifyAlmostEqual(sd_saved, testCase.TestData.sd, ...
        abstol, reltol, false) ;
    verifyTrue(testCase, c)
    %testCase.verifyThat(sd_saved, IsEqualTo(testCase.TestData.sd, ...
       %'Within', AbsoluteTolerance(abstol) | RelativeTolerance(reltol)))
    testCase.verifyThat(sd_weights_saved, IsEqualTo(testCase.TestData.sd_weights, ...
       'Within', AbsoluteTolerance(abstol1) | RelativeTolerance(reltol1)))
%       check if crispness-figure was stored after the first optimization
%       loop
    name=strcat(fileid1,'-crispness-figure-n=2-5.pdf') ;
    verifyTrue( testCase, exist(name, 'file')==2 )
    name=strcat(fileid1,'-crispness-figure-n=2-5.fig') ;
    verifyTrue( testCase, exist(name, 'file')==2 )
%       check if val_vec and opt_vec were stored to file after the first 
%       optimization loop
    name=strcat(fileid1,'-val_vec-n=2-5.txt') ;
    verifyTrue( testCase, exist(name, 'file')==2 )
    name=strcat(fileid1,'-opt_vec-n=2-5.txt') ;
    verifyTrue( testCase, exist(name, 'file')==2 )
%       check if the stored val_vec and opt_vec match the trusted values
%       after the first optimization
    val_vec = load(strcat(fileid1,'-val_vec-n=2-5.txt'),'-ascii') ;
    opt_vec = load(strcat(fileid1,'-opt_vec-n=2-5.txt'),'-ascii') ;
    testCase.verifyThat(val_vec, IsEqualTo(testCase.TestData.val_vec, ...
       'Within', AbsoluteTolerance(abstol1) | RelativeTolerance(reltol1)))
    testCase.verifyThat(opt_vec, IsEqualTo(testCase.TestData.opt_vec, ...
       'Within', AbsoluteTolerance(abstol1) | RelativeTolerance(reltol1)))
%       check if crispness-figure wasn't stored since koptmin=koptmax,
%       after the optional optimization
    name=strcat(fileid,'-crispness-figure-n=3-3.pdf') ;
    verifyTrue( testCase, exist(name, 'file')==0 )
    name=strcat(fileid,'-crispness-figure-n=3-3.fig') ;
    verifyTrue( testCase, exist(name, 'file')==0 )
%       check if val_vec and opt_vec weren't stored to file since 
%       koptmin=koptmax, after the optional
%       optimization
    name=strcat(fileid,'-val_vec-n=3-3.txt') ;
    verifyTrue( testCase, exist(name, 'file')==0 )
    name=strcat(fileid,'-opt_vec-n=3-3.txt') ;
    verifyTrue( testCase, exist(name, 'file')==0 )
    
end

function test_parallelCase_first(testCase)
% test the parallel use case for the Butane transition count matrix from
% Marcus Weber for the frist optimization only.
%       set global variable to indicate testrun (no display output, no
%       interactive input): 'minChiON' indicates that minChi criterion is
%       used and input is taken from testInput_minChiON.mat. 'minChiOFF'
%       indicates that minChi criterion isnt used and input is taken from
%       testInput_minChiOFF.mat.
    global testmode
    testmode = 'minChiON' ;
%       create .mat files used in testmode from inputT() to get the input
%       values normaly passed interactively from keyboard
    kmin = 2 ;
    kmax = 5 ;
    koptmin = 3 ;
    koptmax = 3 ;
    oldfileid = 'test_initialize_A_testmatrix' ;
    Switch = 1 ;
    minChi_switch = 1 ;
    name = 'testInput_minChiON.mat' ;
    save(name,'kmin','kmax','koptmin','koptmax','Switch','minChi_switch','oldfileid')
    
    import matlab.unittest.constraints.IsEqualTo;
    import matlab.unittest.constraints.AbsoluteTolerance;
    import matlab.unittest.constraints.RelativeTolerance;
%       set absolute and relative tolerance for verification
    abstol = testCase.TestData.abstolfac * eps ;
    reltol = testCase.TestData.reltolfac * eps ;
%       set the solver, optional solver and ID-string for file-naming
    wk.solver = 'nelder-mead' ;
    wk.tolx = 1e-8 ;
    wk.tolfun = 1e-8 ;
    wk.maxiter = 2000 ;
    wk.id = 'test_parallelCase_first_count' ;
    wk.parallel = 1 ;
%       specify the test case data
    matrixfile = 'count.txt' ;
%       get the known test case data
    [ P, sd ] = get_knownInput( matrixfile ) ;
%       check if the sd calculated by get_knownInput() matches the trusted 
%       testCase.TestData.sd
    [ ~, ~, c ] = verifyAlmostEqual(sd, testCase.TestData.sd, abstol, ...
        reltol, false) ;
    verifyTrue(testCase, c)
%       run gpcca() main function with evalc(): means screen output isnt
%       shown but stored in a output variable T
    [ T, ~, ~, ~, wk, ~ ] = evalc('gpcca(P, sd, 2, 5, wk, [])') ;
%       close all open (but invisible) plots
    close all
%       T (with all screen output of gpcca()) is stored to a file
    fileID = fopen('test_gpcca_report.txt','a') ;
    fprintf(fileID,'%s\n\n','test_parallelCase_first') ;
    fprintf(fileID,'%s\n\n\n',T) ;
    fclose(fileID) ;
%       verify that wk is fine
    verifyEqual(testCase, isstruct(wk), true)
    verifyEqual(testCase, wk.id, 'test_parallelCase_first_count')
    verifyEqual(testCase, wk.schur, 1)
    verifyEqual(testCase, wk.b, 0)
    verifyEqual(testCase, wk.init, 1)
    verifyEqual(testCase, wk.solver, 'nelder-mead')
    verifyEqual(testCase, wk.maxiter, 2000)
    verifyEqual(testCase, wk.display, 0)
    verifyEqual(testCase, wk.tolx, 1e-8)
    verifyEqual(testCase, wk.tolfun, 1e-8)
    verifyEqual(testCase, wk.parallel, 1)
%       load the saved actual Pc, chi, A from files
    fileid = ['test_parallelCase_first_count-nelder-mead-maxiter_2000'...
        '-tolfun_1e-08-tolx_1e-08'] ;
    fileid = strcat(fileid,'-',testCase.TestData.precision) ;
    Pc_saved = load(strcat(fileid,'-n=3-Pc.txt'),'-ascii') ;
    chi_saved = load(strcat(fileid,'-n=3-chi.txt'),'-ascii') ;
    A_saved = load(strcat(fileid,'-n=3-A.txt'),'-ascii') ;
%       test if the saved actual Pc, chi, A are equal  
%       (within numerical errors) to the "good" (correct) quantities
    testCase.verifyThat(Pc_saved, IsEqualTo(testCase.TestData.Pc, ...
       'Within', AbsoluteTolerance(abstol) | RelativeTolerance(reltol)))
    testCase.verifyThat(chi_saved, IsEqualTo(testCase.TestData.chi, ...
       'Within', AbsoluteTolerance(abstol) | RelativeTolerance(reltol)))    
    testCase.verifyThat(A_saved, IsEqualTo(testCase.TestData.A, ...
       'Within', AbsoluteTolerance(abstol) | RelativeTolerance(reltol)))
%       load the actual saved P, sd, sd_weights from files
    P_saved = load_t(strcat(fileid,'-P.txt'),'-ascii',numeric_t) ;
    sd_saved = load_t(strcat(fileid,'-sd.txt'),'-ascii',numeric_t) ;
    sd_weights_saved = load(strcat(fileid,'-n=3-sd_weights.txt'),'-ascii') ;
%       test if actual P, sd have the correct shapes
    verifyTrue(testCase,all(size(P)==size(P_saved)))
    verifyTrue(testCase,all(size(sd)==size(sd_saved)))
%       test if the saved actual P_saved, sd_saved, sd_weights_saved are equal  
%       (within numerical errors) to the "good" (correct) values
    [ ~, ~, c ] = verifyAlmostEqual(P_saved, P, abstol, reltol, false) ;
    verifyTrue(testCase, c)
    [ ~, ~, c ] = verifyAlmostEqual(sd_saved, testCase.TestData.sd, ...
        abstol, reltol, false) ;
    verifyTrue(testCase, c)
    %testCase.verifyThat(sd_saved, IsEqualTo(testCase.TestData.sd, ...
       %'Within', AbsoluteTolerance(abstol) | RelativeTolerance(reltol)))
    testCase.verifyThat(sd_weights_saved, IsEqualTo(testCase.TestData.sd_weights, ...
       'Within', AbsoluteTolerance(abstol) | RelativeTolerance(reltol)))
%       check if crispness-figure was stored after the first optimization
%       loop
    name=strcat(fileid,'-crispness-figure-n=2-5.pdf') ;
    verifyTrue( testCase, exist(name, 'file')==2 )
    name=strcat(fileid,'-crispness-figure-n=2-5.fig') ;
    verifyTrue( testCase, exist(name, 'file')==2 )
%       check if val_vec and opt_vec were stored to file after the first 
%       optimization loop
    name=strcat(fileid,'-val_vec-n=2-5.txt') ;
    verifyTrue( testCase, exist(name, 'file')==2 )
    name=strcat(fileid,'-opt_vec-n=2-5.txt') ;
    verifyTrue( testCase, exist(name, 'file')==2 )
%       check if the stored val_vec and opt_vec match the trusted values
%       after the final optimization
    val_vec = load(strcat(fileid,'-val_vec-n=2-5.txt'),'-ascii') ;
    opt_vec = load(strcat(fileid,'-opt_vec-n=2-5.txt'),'-ascii') ;
%       leave opt and val for n=5 out of the check since nelder mead mostly
%       isn't converged after 2000 steps for n=5
    testCase.verifyThat(val_vec(1:3,1:2), IsEqualTo(testCase.TestData.val_vec_nm, ...
       'Within', AbsoluteTolerance(abstol) | RelativeTolerance(reltol)))
    testCase.verifyThat(opt_vec(1:3,1:2), IsEqualTo(testCase.TestData.opt_vec_nm, ...
       'Within', AbsoluteTolerance(abstol) | RelativeTolerance(reltol)))
end

function test_parallelCase_first_and_final(testCase)
% test the parallel use case for the Butane transition count matrix from
% Marcus Weber for the first and final optimization.
%       set global variable to indicate testrun (no display output, no
%       interactive input): 'minChiON' indicates that minChi criterion is
%       used and input is taken from testInput_minChiON.mat. 'minChiOFF'
%       indicates that minChi criterion isnt used and input is taken from
%       testInput_minChiOFF.mat.
    global testmode
    testmode = 'minChiON' ;
%       create .mat file used in testmode from inputT() to get the input
%       values normally passed interactively from keyboard
    kmin = 2 ;
    kmax = 5 ;
    koptmin = 2 ;
    koptmax = 3 ;
    Switch = 1 ;
    minChi_switch = 1 ;
    name = 'testInput_minChiON.mat' ;
    save(name,'kmin','kmax','koptmin','koptmax','Switch','minChi_switch')
    
    import matlab.unittest.constraints.IsEqualTo;
    import matlab.unittest.constraints.AbsoluteTolerance;
    import matlab.unittest.constraints.RelativeTolerance;
%       set absolute and relative tolerance for verification
    abstol = testCase.TestData.abstolfac * eps ;
    reltol = testCase.TestData.reltolfac * eps ;
    
%       set the solver, optional solver and ID-string for file-naming
    wk.solver = 'gauss-newton' ;
    wk.id = 'test_parallelCase_first_and_final_count' ;
    wk.parallel = 1 ;
    iopt.solver = 'nelder-mead' ;
    iopt.tolx = 1e-8 ;
    iopt.tolfun = 1e-8 ;
    iopt.maxiter = 2000 ;
    iopt.parallel = 1 ;
%       specify the test case data
    matrixfile = 'count.txt' ;
%       get the known test case data
    [ P, sd ] = get_knownInput( matrixfile ) ;
%       check if the sd calculated by get_knownInput() matches the trusted 
%       testCase.TestData.sd
    [ ~, ~, c ] = verifyAlmostEqual(sd, testCase.TestData.sd, abstol, ...
        reltol, false) ;
    verifyTrue(testCase, c)
%       run gpcca() main function with evalc(): means screen output isnt
%       shown but stored in a output variable T
    [ T, Pc_test, chi_test, A_test, wk, iopt ] = evalc('gpcca(P, sd, 2, 10, wk, iopt)') ;
%       close all open (but invisible) plots
    close all
%       T (with all screen output of gpcca()) is stored to a file
    fileID = fopen('test_gpcca_report.txt','a') ;
    fprintf(fileID,'%s\n\n','test_parallelCase_first_and_final') ;
    fprintf(fileID,'%s\n\n\n',T) ;
    fclose(fileID) ;
%       verify that wk is fine
    verifyEqual(testCase, isstruct(wk), true)
    verifyEqual(testCase, wk.id, 'test_parallelCase_first_and_final_count')
    verifyEqual(testCase, wk.schur, 1)
    verifyEqual(testCase, wk.b, 0)
    verifyEqual(testCase, wk.init, 1)
    verifyEqual(testCase, wk.solver, 'gauss-newton')
    verifyEqual(testCase, wk.parallel, 1)
    verifyEqual(testCase, wk.maxiter, 100)
    verifyEqual(testCase, wk.display, 0)
    verifyEqual(testCase, wk.xtol, 1e-4)
    verifyEqual(testCase, wk.xscale, 1e-6)
%       verfiy that iopt is fine
    verifyEqual(testCase, isstruct(iopt), true)
    verifyEqual(testCase, iopt.solver, 'nelder-mead')
    verifyEqual(testCase, iopt.init, 1)
    verifyEqual(testCase, iopt.parallel, 1)
    verifyEqual(testCase, iopt.maxiter, 2000)
    verifyEqual(testCase, iopt.display, 0)
    verifyEqual(testCase, iopt.tolfun, 1e-8)
    verifyEqual(testCase, iopt.tolx, 1e-8)
%       test if actual Pc, chi, A are equal (within numerical 
%       errors) to the "good" (correct) values 
    testCase.verifyThat(Pc_test, IsEqualTo(testCase.TestData.Pc, ...
       'Within', AbsoluteTolerance(abstol) | RelativeTolerance(reltol)))
    testCase.verifyThat(chi_test, IsEqualTo(testCase.TestData.chi, ...
       'Within', AbsoluteTolerance(abstol) | RelativeTolerance(reltol)))    
    testCase.verifyThat(A_test, IsEqualTo(testCase.TestData.A, ...
       'Within', AbsoluteTolerance(abstol) | RelativeTolerance(reltol)))
%       load the saved actual Pc, chi, A from files
    fileid = ['test_parallelCase_first_and_final_count-nelder-mead-'...
        'maxiter_2000-tolfun_1e-08-tolx_1e-08'] ;
    fileid = strcat(fileid,'-',testCase.TestData.precision) ;
    Pc_saved = load(strcat(fileid,'-n=3-Pc.txt'),'-ascii') ;
    chi_saved = load(strcat(fileid,'-n=3-chi.txt'),'-ascii') ;
    A_saved = load(strcat(fileid,'-n=3-A.txt'),'-ascii') ;
%       test if the saved actual Pc, chi, A are equal  
%       (within numerical errors) to the "good" (correct) quantities
    testCase.verifyThat(Pc_saved, IsEqualTo(testCase.TestData.Pc, ...
       'Within', AbsoluteTolerance(abstol) | RelativeTolerance(reltol)))
    testCase.verifyThat(chi_saved, IsEqualTo(testCase.TestData.chi, ...
       'Within', AbsoluteTolerance(abstol) | RelativeTolerance(reltol)))    
    testCase.verifyThat(A_saved, IsEqualTo(testCase.TestData.A, ...
       'Within', AbsoluteTolerance(abstol) | RelativeTolerance(reltol)))
%       load the actual saved P, sd, sd_weights from files
    fileid1 = ['test_parallelCase_first_and_final_count-gauss-newton-'...
        'maxiter_100-xscale_1e-06-xtol_0.0001'] ;
    fileid1 = strcat(fileid1,'-',testCase.TestData.precision) ;
    P_saved = load_t(strcat(fileid1,'-P.txt'),'-ascii',numeric_t) ;
    sd_saved = load_t(strcat(fileid1,'-sd.txt'),'-ascii',numeric_t) ;
    sd_weights_saved = load(strcat(fileid,'-n=3-sd_weights.txt'),'-ascii') ;
%       test if actual P, sd have the correct shapes
    verifyTrue(testCase,all(size(P)==size(P_saved)))
    verifyTrue(testCase,all(size(sd)==size(sd_saved)))
%       test if the saved actual P_saved, sd_saved, sd_weights_saved are equal  
%       (within numerical errors) to the "good" (correct) values
    [ ~, ~, c ] = verifyAlmostEqual(P_saved, P, abstol, reltol, false) ;
    verifyTrue(testCase, c)
    [ ~, ~, c ] = verifyAlmostEqual(sd_saved, testCase.TestData.sd, ...
        abstol, reltol, false) ;
    verifyTrue(testCase, c)
    %testCase.verifyThat(sd_saved, IsEqualTo(testCase.TestData.sd, ...
       %'Within', AbsoluteTolerance(abstol) | RelativeTolerance(reltol)))
    testCase.verifyThat(sd_weights_saved, IsEqualTo(testCase.TestData.sd_weights, ...
       'Within', AbsoluteTolerance(abstol) | RelativeTolerance(reltol)))
%       check if crispness-figure was stored after the first optimization
%       loop
    name=strcat(fileid1,'-crispness-figure-n=2-5.pdf') ;
    verifyTrue( testCase, exist(name, 'file')==2 )
    name=strcat(fileid1,'-crispness-figure-n=2-5.fig') ;
    verifyTrue( testCase, exist(name, 'file')==2 )
%       check if val_vec and opt_vec were stored to file after the first 
%       optimization loop
    name=strcat(fileid1,'-val_vec-n=2-5.txt') ;
    verifyTrue( testCase, exist(name, 'file')==2 )
    name=strcat(fileid1,'-opt_vec-n=2-5.txt') ;
    verifyTrue( testCase, exist(name, 'file')==2 )
%       check if the stored val_vec and opt_vec match the trusted values
%       after the first optimization
    val_vec = load(strcat(fileid1,'-val_vec-n=2-5.txt'),'-ascii') ;
    opt_vec = load(strcat(fileid1,'-opt_vec-n=2-5.txt'),'-ascii') ;
    testCase.verifyThat(val_vec, IsEqualTo(testCase.TestData.val_vec, ...
       'Within', AbsoluteTolerance(abstol) | RelativeTolerance(reltol)))
    testCase.verifyThat(opt_vec, IsEqualTo(testCase.TestData.opt_vec, ...
       'Within', AbsoluteTolerance(abstol) | RelativeTolerance(reltol)))
%       check if crispness-figure was stored 
%       after the optional optimization
    name=strcat(fileid,'-crispness-figure-n=2-3.pdf') ;
    verifyTrue( testCase, exist(name, 'file')==2 )
    name=strcat(fileid,'-crispness-figure-n=2-3.fig') ;
    verifyTrue( testCase, exist(name, 'file')==2 )
%       check if val_vec and opt_vec were stored to file
%       after the optional optimization
    name=strcat(fileid,'-val_vec-n=2-3.txt') ;
    verifyTrue( testCase, exist(name, 'file')==2 )
    name=strcat(fileid,'-opt_vec-n=2-3.txt') ;
    verifyTrue( testCase, exist(name, 'file')==2 )
%       check if the stored val_vec and opt_vec match the trusted values
%       after the final optimization
    val_vec = load(strcat(fileid,'-val_vec-n=2-3.txt'),'-ascii') ;
    opt_vec = load(strcat(fileid,'-opt_vec-n=2-3.txt'),'-ascii') ;
    testCase.verifyThat(val_vec, IsEqualTo(testCase.TestData.val_vec_nm(1:2,1:2), ...
       'Within', AbsoluteTolerance(abstol) | RelativeTolerance(reltol)))
    testCase.verifyThat(opt_vec, IsEqualTo(testCase.TestData.opt_vec_nm(1:2,1:2), ...
       'Within', AbsoluteTolerance(abstol) | RelativeTolerance(reltol)))
end

function test_parallelCase_first_and_final_ioptInit2(testCase)
% test the parallel use case for the Butane transition count matrix from
% Marcus Weber for the first and final optimization, if iopt.init=2.
%       set global variable to indicate testrun (no display output, no
%       interactive input): 'minChiON' indicates that minChi criterion is
%       used and input is taken from testInput_minChiON.mat. 'minChiOFF'
%       indicates that minChi criterion isnt used and input is taken from
%       testInput_minChiOFF.mat.
    global testmode
    testmode = 'minChiON' ;
%       create .mat file used in testmode from inputT() to get the input
%       values normally passed interactively from keyboard
    kmin = 2 ;
    kmax = 5 ;
    koptmin = 2 ;
    koptmax = 3 ;
    Switch = 1 ;
    minChi_switch = 1 ;
    name = 'testInput_minChiON.mat' ;
    save(name,'kmin','kmax','koptmin','koptmax','Switch','minChi_switch')
    
    import matlab.unittest.constraints.IsEqualTo;
    import matlab.unittest.constraints.AbsoluteTolerance;
    import matlab.unittest.constraints.RelativeTolerance;
%       set absolute and relative tolerance for verification
    abstol = testCase.TestData.abstolfac * eps ;
    reltol = testCase.TestData.reltolfac * eps ;
%       we need a softer tolerance here for the quantities derived by
%       optimization, since we perform two optimizations here, with the
%       second one depending on the results of the first... This leads to
%       bigger variations
    abstol1 = 1e-06 ;
    reltol1 = 1e-06 ;
    
%       set the solver, optional solver and ID-string for file-naming
    wk.solver = 'gauss-newton' ;
    wk.id = 'test_parallelCase_first_and_final_ioptInit2_count' ;
    wk.parallel = 1 ;
    iopt.solver = 'nelder-mead' ;
    iopt.tolx = 1e-8 ;
    iopt.tolfun = 1e-8 ;
    iopt.maxiter = 2000 ;
    iopt.parallel = 1 ;
    iopt.init = 2 ;
%       specify the test case data
    matrixfile = 'count.txt' ;
%       get the known test case data
    [ P, sd ] = get_knownInput( matrixfile ) ;
%       check if the sd calculated by get_knownInput() matches the trusted 
%       testCase.TestData.sd
    [ ~, ~, c ] = verifyAlmostEqual(sd, testCase.TestData.sd, abstol, ...
        reltol, false) ;
    verifyTrue(testCase, c)
%       run gpcca() main function with evalc(): means screen output isnt
%       shown but stored in a output variable T
    [ T, Pc_test, chi_test, A_test, wk, iopt ] = evalc('gpcca(P, sd, 2, 10, wk, iopt)') ;
%       close all open (but invisible) plots
    close all
%       T (with all screen output of gpcca()) is stored to a file
    fileID = fopen('test_gpcca_report.txt','a') ;
    fprintf(fileID,'%s\n\n','test_parallelCase_first_and_final_ioptInit2') ;
    fprintf(fileID,'%s\n\n\n',T) ;
    fclose(fileID) ;
%       verify that wk is fine
    verifyEqual(testCase, isstruct(wk), true)
    verifyEqual(testCase, wk.id, 'test_parallelCase_first_and_final_ioptInit2_count')
    verifyEqual(testCase, wk.schur, 1)
    verifyEqual(testCase, wk.b, 0)
    verifyEqual(testCase, wk.init, 1)
    verifyEqual(testCase, wk.solver, 'gauss-newton')
    verifyEqual(testCase, wk.parallel, 1)
    verifyEqual(testCase, wk.maxiter, 100)
    verifyEqual(testCase, wk.display, 0)
    verifyEqual(testCase, wk.xtol, 1e-4)
    verifyEqual(testCase, wk.xscale, 1e-6)
%       verfiy that iopt is fine
    verifyEqual(testCase, isstruct(iopt), true)
    verifyEqual(testCase, iopt.solver, 'nelder-mead')
    verifyEqual(testCase, iopt.init, 2)
    verifyEqual(testCase, iopt.parallel, 1)
    verifyEqual(testCase, iopt.maxiter, 2000)
    verifyEqual(testCase, iopt.display, 0)
    verifyEqual(testCase, iopt.tolfun, 1e-8)
    verifyEqual(testCase, iopt.tolx, 1e-8)
%       test if actual Pc, chi, A are equal (within numerical 
%       errors) to the "good" (correct) values 
    testCase.verifyThat(Pc_test, IsEqualTo(testCase.TestData.Pc, ...
       'Within', AbsoluteTolerance(abstol1) | RelativeTolerance(reltol1)))
    testCase.verifyThat(chi_test, IsEqualTo(testCase.TestData.chi, ...
       'Within', AbsoluteTolerance(abstol1) | RelativeTolerance(reltol1)))    
    testCase.verifyThat(A_test, IsEqualTo(testCase.TestData.A, ...
       'Within', AbsoluteTolerance(abstol1) | RelativeTolerance(reltol1)))
%       load the saved actual Pc, chi, A from files
    fileid = ['test_parallelCase_first_and_final_ioptInit2_count-nelder-mead-'...
        'maxiter_2000-tolfun_1e-08-tolx_1e-08'] ;
    fileid = strcat(fileid,'-',testCase.TestData.precision) ;
    Pc_saved = load(strcat(fileid,'-n=3-Pc.txt'),'-ascii') ;
    chi_saved = load(strcat(fileid,'-n=3-chi.txt'),'-ascii') ;
    A_saved = load(strcat(fileid,'-n=3-A.txt'),'-ascii') ;
%       test if the saved actual Pc, chi, A are equal  
%       (within numerical errors) to the "good" (correct) quantities
    testCase.verifyThat(Pc_saved, IsEqualTo(testCase.TestData.Pc, ...
       'Within', AbsoluteTolerance(abstol1) | RelativeTolerance(reltol1)))
    testCase.verifyThat(chi_saved, IsEqualTo(testCase.TestData.chi, ...
       'Within', AbsoluteTolerance(abstol1) | RelativeTolerance(reltol1)))    
    testCase.verifyThat(A_saved, IsEqualTo(testCase.TestData.A, ...
       'Within', AbsoluteTolerance(abstol1) | RelativeTolerance(reltol1)))
%       load the actual saved P, sd, sd_weights from files
    fileid1 = ['test_parallelCase_first_and_final_ioptInit2_count-gauss-newton-'...
        'maxiter_100-xscale_1e-06-xtol_0.0001'] ;
    fileid1 = strcat(fileid1,'-',testCase.TestData.precision) ;
    P_saved = load_t(strcat(fileid1,'-P.txt'),'-ascii',numeric_t) ;
    sd_saved = load_t(strcat(fileid1,'-sd.txt'),'-ascii',numeric_t) ;
    sd_weights_saved = load(strcat(fileid,'-n=3-sd_weights.txt'),'-ascii') ;
%       test if actual P, sd have the correct shapes
    verifyTrue(testCase,all(size(P)==size(P_saved)))
    verifyTrue(testCase,all(size(sd)==size(sd_saved)))
%       test if the saved actual P_saved, sd_saved, sd_weights_saved are equal  
%       (within numerical errors) to the "good" (correct) values
    [ ~, ~, c ] = verifyAlmostEqual(P_saved, P, abstol, reltol, false) ;
    verifyTrue(testCase, c)
    [ ~, ~, c ] = verifyAlmostEqual(sd_saved, testCase.TestData.sd, ...
        abstol, reltol, false) ;
    verifyTrue(testCase, c)
    %testCase.verifyThat(sd_saved, IsEqualTo(testCase.TestData.sd, ...
       %'Within', AbsoluteTolerance(abstol) | RelativeTolerance(reltol)))
    testCase.verifyThat(sd_weights_saved, IsEqualTo(testCase.TestData.sd_weights, ...
       'Within', AbsoluteTolerance(abstol1) | RelativeTolerance(reltol1)))
%       check if crispness-figure was stored after the first optimization
%       loop
    name=strcat(fileid1,'-crispness-figure-n=2-5.pdf') ;
    verifyTrue( testCase, exist(name, 'file')==2 )
    name=strcat(fileid1,'-crispness-figure-n=2-5.fig') ;
    verifyTrue( testCase, exist(name, 'file')==2 )
%       check if val_vec and opt_vec were stored to file after the first 
%       optimization loop
    name=strcat(fileid1,'-val_vec-n=2-5.txt') ;
    verifyTrue( testCase, exist(name, 'file')==2 )
    name=strcat(fileid1,'-opt_vec-n=2-5.txt') ;
    verifyTrue( testCase, exist(name, 'file')==2 )
%       check if the stored val_vec and opt_vec match the trusted values
%       after the first optimization
    val_vec = load(strcat(fileid1,'-val_vec-n=2-5.txt'),'-ascii') ;
    opt_vec = load(strcat(fileid1,'-opt_vec-n=2-5.txt'),'-ascii') ;
    testCase.verifyThat(val_vec, IsEqualTo(testCase.TestData.val_vec, ...
       'Within', AbsoluteTolerance(abstol1) | RelativeTolerance(reltol1)))
    testCase.verifyThat(opt_vec, IsEqualTo(testCase.TestData.opt_vec, ...
       'Within', AbsoluteTolerance(abstol1) | RelativeTolerance(reltol1)))
%       check if crispness-figure was stored 
%       after the optional optimization
    name=strcat(fileid,'-crispness-figure-n=2-3.pdf') ;
    verifyTrue( testCase, exist(name, 'file')==2 )
    name=strcat(fileid,'-crispness-figure-n=2-3.fig') ;
    verifyTrue( testCase, exist(name, 'file')==2 )
%       check if val_vec and opt_vec were stored to file
%       after the optional optimization
    name=strcat(fileid,'-val_vec-n=2-3.txt') ;
    verifyTrue( testCase, exist(name, 'file')==2 )
    name=strcat(fileid,'-opt_vec-n=2-3.txt') ;
    verifyTrue( testCase, exist(name, 'file')==2 )
%       check if the stored val_vec and opt_vec match the trusted values
%       after the final optimization
    val_vec = load(strcat(fileid,'-val_vec-n=2-3.txt'),'-ascii') ;
    opt_vec = load(strcat(fileid,'-opt_vec-n=2-3.txt'),'-ascii') ;
    testCase.verifyThat(val_vec, IsEqualTo(testCase.TestData.val_vec_nm(1:2,1:2), ...
       'Within', AbsoluteTolerance(abstol1) | RelativeTolerance(reltol1)))
    testCase.verifyThat(opt_vec, IsEqualTo(testCase.TestData.opt_vec_nm(1:2,1:2), ...
       'Within', AbsoluteTolerance(abstol1) | RelativeTolerance(reltol1)))   
end

 % write a second normal case test function based on the example_matrix
 % from Roeblitz
 
% -------------------------------------------------------------------------
% -------------------------------------------------------------------------
% -------------------------------------------------------------------------
function setupOnce(testCase)
% test environment setup
%   Written by Bernhard Reuter, Theoretical Physics II,
%   University of Kassel, 2017
%       set global variable to indicate testrun (no display output, no
%       interactive input): 'minChiON' indicates that minChi criterion is
%       used and input is taken from testInput_minChiON.mat. 'minChiOFF'
%       indicates that minChi criterion isnt used and input is taken from
%       testInput_minChiOFF.mat.
    global testmode
    testmode = 'minChiON' ;
%       set global variable to make all plots invisible but still store
%       them
    global figureVisible
    figureVisible = false ;
%       request precision from user
    disp('You can choose in which precision the test is performed: ')
    disp('Either double precision (16 significant digits, Matlab ')
    disp('standard) or multi-precision with 50 significant digits. ')
    disp('The multi-precision mode is only applicable, if you have ')
    disp('the Matlab multiprecision toolbox from Advanpix installed!')
    testCase.TestData.precision = input(['Enter the precision to use ', ...
    'during the test IN QUOTES (mp or double): ']) ;
    prec = testCase.TestData.precision ;
    assert(ischar(prec),'setupOnce:InputError', ...
        'The precision you passed is not a string!')
    if ~strcmpi(prec,'mp') && ~strcmpi(prec,'double')
        error('setupOnce:InputError','The precision you passed is invalid!')
    end
%       create and change to temporary folder
    testCase.TestData.origPath = pwd ;
    testCase.TestData.tmpFolder = strcat('regressionTestsFolder_',prec) ;
    tmp = testCase.TestData.tmpFolder ;
    if exist(tmp, 'dir') == 7
        rmdir(tmp, 's')
    end
    mkdir(testCase.TestData.tmpFolder)
    copyfile('cluster_by_isa.m', tmp)
    copyfile('count.txt', tmp)
    copyfile('do_schur.m', tmp)
    copyfile('fillA.m', tmp)
    copyfile('find_twoblocks.m', tmp)
    copyfile('getopt.m', tmp)
    copyfile('gram_schmidt_mod.m', tmp)
    copyfile('indexsearch.m', tmp)
    copyfile('initialize_A.m', tmp)
    copyfile('initialize_optional.m', tmp)
    copyfile('initialize_workspace.m', tmp)
    copyfile('inputT.m', tmp)
    copyfile('load_t.m', tmp)
    copyfile('main_nlscon.m', tmp)
    copyfile('nearly_equal.m', tmp)
    copyfile('nlscon.m', tmp)
    copyfile('numeric_t.m', tmp)
    copyfile('objective.m', tmp)
    copyfile('opt_soft.m', tmp)
    copyfile('optimization_loop.m', tmp)
    copyfile('gpcca.m', tmp)
    copyfile('plotmatrix.m',tmp)
    copyfile('postprocess.m', tmp)
    copyfile('problem_pcca_nlscon.m', tmp)
    copyfile('save_t.m', tmp)
    copyfile('SRSchur_num_t.m', tmp)
    copyfile('use_minChi.m', tmp)
    cd(testCase.TestData.tmpFolder)
%       factor abstolfac to multiply eps with for use as absolute tolerance 
%       abstol=abstolfac*eps in many (not all) comparisons 
    testCase.TestData.abstolfac = 1e10 ;
%       factor reltolfac to multiply eps with for use as relative tolerance 
%       reltol=reltolfac*eps in many (not all) comparisons 
    testCase.TestData.reltolfac = 1e10 ;
%       global variable to define precision to use
    global class_t ;
%       set precision of variables or expressions wrapped by numeric_t(),
%       i.e. 'double' or 'mp' for multipresicion (with multiprecision toolbox)
    if strcmpi(testCase.TestData.precision,'mp')
        mp.Digits(50) ;
        class_t = 'mp' ;
    elseif strcmpi(testCase.TestData.precision,'double')
        class_t = 'double' ;
    else
        error('knownInput:PrecisionError','Unknown Precision')
    end
%       create .mat files used in testmode from inputT() to get the input
%       values normaly passed interactively from keyboard
    kmin = 2 ;
    kmax = 5 ;
    koptmin = 3 ;
    koptmax = 3 ;
    Switch = 1 ;
    minChi_switch = 0 ;
    oldfileid = 'test_initialize_A_testmatrix' ;
    name = 'testInput_minChiOFF.mat' ;
    save(name,'kmin','kmax','koptmin','koptmax','Switch','minChi_switch','oldfileid')
    minChi_switch = 1 ;
    name = 'testInput_minChiON.mat' ;
    save(name,'kmin','kmax','koptmin','koptmax','Switch','minChi_switch','oldfileid')
    e1 = [0,1,0] ;
    e2 = [0,1,0] ;
    e3 = [0,1,0] ;
    e4 = [0,1,0] ;
    A = [ e1; e2; e3 ; e4 ] ;
    name = 'test_initialize_A_testmatrix-n=3-A.mat' ;
    save(name,'A')
    clearvars kmin kmax kopt minChi_switch oldfileid A
%   -----------------------------------------------------------------------    
%   -----------------------------------------------------------------------
%   Trusted results from Markov modeling in multi-precision (mp.Digits=50:  
%   50 digits) with program version PCCAwww_Schur_8 for the count.txt 
%   Butane transition count matrix from Marcus Weber, 
%   Zuse Institute Berlin, 2017.
%   First optimization was performed with gauss-newton, maxiter=100,
%   xscale=1e-06, xtol=0.0001; second (final) optional optimization was
%   performed with nelder-mead, maxiter=2000, tolfun=1e-08, tolx=1e-08.
    if strcmp(testCase.TestData.precision,'mp')

%           trusted pi vector
%         pi = mp(['[' ...
%             '2.187571738471187133902010209426431107370120314283084e-03 '...    
%             '5.423036997059156482442849543364912557266841765301612e-03 '...   
%             '2.342044854329907260168349964151761987284772748464778e-02 '...   
%             '5.82857795969564539526224197339871353172023700420376e-02 '...   
%             '7.249429129236546999640676258221933776081948593780891e-02 '...    
%             '5.405254454504247218578406828743684371598311397463422e-02 '...   
%             '2.835011453613026984410550759359357413416088406624178e-02 '...   
%             '1.464966954395519941769762620611903248173040191869405e-02 '...   
%             '9.497264358463482494311324131462901182375049908834072e-03 '...   
%             '5.873112283083479772803973321317160093259194654200614e-03 '...   
%             '5.11881979629663654152847775468251262673084951647561e-03 '...   
%             '4.124483560128425064871186093010587059163505318218241e-03 '...   
%             '3.571750407440842955112976496339522747320363072257662e-03 '...   
%             '3.692062289670242853883241202001993248407862279938365e-03 '...   
%             '4.407199335201498052321600670009464455227404169163185e-03 '...   
%             '5.574449257298707584836971904564222834389840901133797e-03 '...   
%             '7.342640276733900326651045301307644057934297857129383e-03 '...   
%             '1.399329698364030539576898074002627013807852032174395e-02 '...   
%             '3.046962550162387511970164593953755562709520736344117e-02 '...   
%             '5.972086356741853855741812980868204329718853313486307e-02 '...   
%             '8.726492361387920248951755364896302567171102784491492e-02 '...   
%             '8.835621020173257643148704284922560801469083260596333e-02 '...   
%             '6.072468748794412023536952401498073278891664703008955e-02 '...   
%             '2.987120408479456813169795751542147880384980005856268e-02 '...   
%             '1.386374881950864541426139670828217022628172043490721e-02 '...   
%             '7.769216656478180839450417795830069882525660099732915e-03 '...   
%             '5.324104870327474208926669153463147380787585372678127e-03 '...   
%             '3.955418928941523649879773437730092147573557883468659e-03 '...   
%             '4.027280031456316269729737741278624605202506059657095e-03 '...   
%             '3.218799581014319343245023602445808184554096362520484e-03 '...   
%             '3.745858750020438513052979905013613620747426334531594e-03 '...   
%             '5.387966522927750746553881183087983429716988885592274e-03 '...   
%             '5.832573831546526856354722524286525993642042410187094e-03 '...   
%             '7.677029504691290542091061441459794707642367788514225e-03 '...   
%             '1.459368537031396585424615476070039944096715840641644e-02 '...   
%             '2.783266461995124875161728265907097088549624852133055e-02 '...   
%             '5.38541628666812454950482564318821030607325668855242e-02 '...   
%             '7.425019666813391557063689249535295617657414516216497e-02 '...   
%             '5.855544688937754390450142827946923895255202586768602e-02 '...   
%             '2.262922654046515828530060428980232174540805949777298e-02 '...   
%             '5.929305078819016054013734113714815933195344238828693e-03 '...   
%             '3.087264670715756079163608287931754032680618247919858e-03 ]']) ;
%         pi = pi' ;
%         testCase.TestData.pi = pi ;
%           trusted pi_weights
%         pi_weights = [ 2.8409817970251405e-01 ; ...
%                        2.8737681725227660e-01 ; ...
%                        4.2852500304520924e-01 ] ;
%         testCase.TestData.pi_weights = pi_weights ;
%           trusted sd vector
        sd = mp(['['...
        '2.119682047692846073089036644503324501324801279808036e-03 '...    
        '5.449182622606609008648702694595810628405739139129141e-03 '...    
        '2.342648602709593560965855121731740238964155376693496e-02 '...    
        '5.822126680997850322451632255161725741138829175623657e-02 '...    
        '7.247912813078038294255861620756886467029945508173788e-02 '...    
        '5.404189371594260860870869369594560815877618357246411e-02 '...
        '2.835574663800429935509673548967654851772234164875261e-02 '...    
        '1.468779683047542868569714542818577213417987301904714e-02 '...    
        '9.46857971304304354346847972804079388091786232065187e-03 '...    
        '5.879118132280157976303554466829975503674448832675084e-03 '...    
        '5.129230615407688846672999050142478628205769134629806e-03 '...    
        '4.149377593360995850622406639004149377593360995850611e-03 '...    
        '3.609458581212818077288406738989151627255911613258018e-03 '...   
        '3.709443583462480627905814127880817877318402239664052e-03 '...   
        '4.409338599210118482227665850122481627755836624506334e-03 '...   
        '5.579163125531170324451332300154976753486976953456981e-03 '...   
        '7.31890216467529870519422086686996950457431385292207e-03  '...  
        '1.396790481427785832125181222816577513372994050892362e-02 '...   
        '3.044543318502224666300054991751237314402839574063884e-02 '...   
        '5.97510373443983402489626556016597510373443983402488e-02 '...   
        '8.726690996350547417887316902464630305454181872719118e-02 '...   
        '8.83067539869019647052942058691196320551917212418139e-02 '...   
        '6.067089936509523571464280357946308053791931210318447e-02 '...   
        '2.982552617107433884917262410638404239364095385692149e-02 '...   
        '1.385792131180322951557266410038494225866120081987701e-02 '...   
        '7.748837674348847672849072639104134379843023546468013e-03 '...   
        '5.379193121031845223216517522371644253361995700644913e-03 '...   
        '3.959406089086637004449332600109983502474628805679159e-03 '...   
        '4.009398590211468279758036294555816627505874118882155e-03 '...   
        '3.239514072889066640003999400089986502024696295555666e-03 '...   
        '3.769434584812278158276258561215817627355896615507664e-03 '...   
        '5.369194620806878968154776783482477628355746638004297e-03 '...   
        '5.809128630705394190871369294605809128630705394190856e-03 '...   
        '7.678848172774083887416887466879968004799280107983785e-03 '...   
        '1.461780732890066490026496025596160575913612958056291e-02 '...   
        '2.78658201269809528570714392841073838924161375793631e-02 '...   
        '5.38919162125681147827825826126081087836824476328552e-02 '...   
        '7.429885517172424136379543068539719042143678448232798e-02 '...   
        '5.8661200819877018447232915062740588911663250512423e-02 '...   
        '2.265660150977353396990451432285157226416037594360853e-02 '...   
        '5.929110633404989251612258161275808628705694145878122e-03 '... 
        '2.989551567264910263460480927860820876868469729540559e-03]']) ;
        sd = sd' ;
        testCase.TestData.sd = sd ;
        name = strcat('count-sd.txt') ;
        mp.write(sd,name)
%           trusted A (3 clusters)
        A = [ ...
            2.8405568184913027e-01   2.8755576853720499e-01 ...
            4.2838854961366463e-01 ; ...
           -3.7905560917703573e-01   3.3892409425378806e-01 ...
            4.0131514923247673e-02 ; ...
           -1.9965336957536015e-01  -2.7103148561325063e-01 ...
            4.7068485518861081e-01 ] ;
        testCase.TestData.A = A ;
        name = strcat('count-A.txt') ;
        save(name,'A','-ascii','-double')
%           trusted chi (3 clusters)
        chi = [ ... 
            8.5043523873880167e-01   4.3889650578342830e-11 ...
            1.4956476121730866e-01 ; ...
            8.8090007542005921e-01   2.5589115375343415e-02 ...
            9.3510809204597284e-02 ; ...
            9.6495990190978398e-01   1.1558207813298174e-02 ...
            2.3481890276917761e-02 ; ...
            9.7558793310460756e-01   1.5709140129768342e-02 ...
            8.7029267656239927e-03 ; ...
            9.7963327053545801e-01   1.4060862546032220e-02 ...
            6.3058669185096176e-03 ; ...
            9.8568851438933369e-01   1.4311485610666249e-02 ...
            2.8588715185016204e-18 ; ...
            9.6791270535282714e-01   1.7471491809863966e-02 ...
            1.4615802837308787e-02 ; ...
            9.4601281012257943e-01   1.7835098543345616e-02 ...
            3.6152091334074828e-02 ; ...
            9.2448952433822884e-01   1.8479564079043900e-02 ...
            5.7030911582727190e-02 ; ...
            8.8318556579259355e-01   2.4948552633467999e-02 ...
            9.1865881573938366e-02 ; ...
            7.5874311920722926e-01   2.5407453476173496e-02 ...
            2.1584942731659709e-01 ; ...
            6.8245807053420782e-01   5.4751908940179971e-02 ...
            2.6279002052561207e-01 ; ...
            5.3234840569967345e-01   6.3068044907414536e-02 ...
            4.0458354939291197e-01 ; ...
            3.1537515699639257e-01   5.2337908021708332e-02 ...
            6.3228693498189903e-01 ; ...
            2.2250786517110874e-01   7.6139414102714117e-02 ...
            7.0135272072617705e-01 ; ...
            1.2375934853700991e-01   5.4508417089852046e-02 ...
            8.2173223437313792e-01 ; ...
            4.9653667316515840e-02   2.9603583297964756e-02 ...
            9.2074274938551937e-01 ; ...
            2.5736159571560040e-02   1.2561644103436354e-02 ...
            9.6170219632500353e-01 ; ...
            1.1894344993512617e-02   6.3139005313609343e-03 ...
            9.8179175447512634e-01 ; ...
            4.8084968892437262e-03   3.6671524338924661e-03 ...
            9.9152435067686373e-01 ; ...
            3.1536353492936761e-03   7.1221730872170121e-04 ...
            9.9613414734198447e-01 ; ...
            1.7064014946817492e-17   4.7395675902214775e-17 ...
            9.9999999999999978e-01 ; ...
            8.2726996336765120e-03   3.0940472642748782e-04 ...
            9.9141789563989591e-01 ; ...
            1.2722881126783015e-02   5.9164159394738403e-03 ...
            9.8136070293374311e-01 ; ...
            2.2122528189377780e-02   1.3902592390826123e-02 ...
            9.6397487941979598e-01 ; ...
            4.0589834059942542e-02   3.7980881743778290e-02 ...
            9.2142928419627912e-01 ; ...
            8.0588740622014418e-02   1.1344669076732349e-01 ...
            8.0596456861066201e-01 ; ...
            1.0568119504467928e-01   2.0230326690849965e-01 ...
            6.9201553804682103e-01 ; ...
            8.3281552679900978e-02   3.4042640424725945e-01 ...
            5.7629204307283954e-01 ; ...
            5.8911161575871167e-02   4.8967335413071073e-01 ...
            4.5141548429341805e-01 ; ...
            4.3770917595154141e-02   6.6193931626137481e-01 ...
            2.9428976614347097e-01 ; ...
            2.9817138929275813e-02   8.0565415247849947e-01 ...
            1.6452870859222457e-01 ; ...
            1.4136303417923221e-02   8.8989778149855503e-01 ...
            9.5965915083521605e-02 ; ...
            1.3671381908781288e-02   9.4419514302533569e-01 ...
            4.2133475065882837e-02 ; ...
            7.5795321139196827e-03   9.6824758368408359e-01 ...
            2.4172884201996588e-02 ; ...
            1.0405260238826743e-02   9.8297752755905710e-01 ...
            6.6172122021160209e-03 ; ...
            4.5138347223811137e-03   9.8998687175067512e-01 ...
            5.4992935269436351e-03 ; ...
            8.4518297221101869e-03   9.9154817000192241e-01 ...
            2.7596725564344715e-10 ; ...
            6.5843351926753247e-03   9.8840580521018662e-01 ...
            5.0098595971378411e-03 ; ...
            9.2202981926287932e-03   9.7351230297269720e-01 ...
            1.7267398834673802e-02 ; ...
            1.6299801690322059e-02   9.2119142752842509e-01 ...
            6.2508770781252748e-02 ; ...
            4.5801965122805573e-10   9.1035357717143850e-01 ...
            8.9646422370541698e-02] ;
        testCase.TestData.chi = chi ;
        name = strcat('count-chi.txt') ;
        save(name,'chi','-ascii','-double')
%           trusted sd_weights (3 clusters)
        sd_weights = [ 2.8405568184913021e-01 ; ... 
                       2.8755576853720499e-01 ; ...
                       4.2838854961366463e-01 ] ;
        testCase.TestData.sd_weights = sd_weights ;
        name = strcat('count-sd_weights.txt') ;
        save(name,'sd_weights','-ascii','-double')
%           trusted Pc (3 clusters)
        Pc = [ 9.5104510750059468e-01   1.8354056625839634e-02 ...
               3.0600835873566212e-02 ; ...
               1.8594617368171678e-02   9.5127058926326458e-01 ...
               3.0134793368563506e-02 ; ...
               1.9985610707576054e-02   2.0510702582310622e-02 ...
               9.5950368671011355e-01 ] ;
        testCase.TestData.Pc = Pc ;
        name = strcat('count-Pc.txt') ;
        save(name,'Pc','-ascii','-double')
%           trusted index vector
        idx_vec = [ 1.0000000000000000e+00 ; ...
                    2.0000000000000000e+00 ; ...
                    3.0000000000000000e+00 ; ...
                    4.0000000000000000e+00 ; ...
                    5.0000000000000000e+00 ; ...
                    6.0000000000000000e+00 ; ...
                    7.0000000000000000e+00 ; ...
                    8.0000000000000000e+00 ; ...
                    9.0000000000000000e+00 ; ...
                    1.0000000000000000e+01 ; ...
                    1.1000000000000000e+01 ; ...
                    1.2000000000000000e+01 ; ...
                    1.3000000000000000e+01 ; ...
                    3.0000000000000000e+01 ; ...
                    3.1000000000000000e+01 ; ...
                    3.2000000000000000e+01 ; ...
                    3.3000000000000000e+01 ; ...
                    3.4000000000000000e+01 ; ...
                    3.5000000000000000e+01 ; ...
                    3.6000000000000000e+01 ; ...
                    3.7000000000000000e+01 ; ...
                    3.8000000000000000e+01 ; ...
                    3.9000000000000000e+01 ; ...
                    4.0000000000000000e+01 ; ...
                    4.1000000000000000e+01 ; ...
                    4.2000000000000000e+01 ; ...
                    1.4000000000000000e+01 ; ...
                    1.5000000000000000e+01 ; ...
                    1.6000000000000000e+01 ; ...
                    1.7000000000000000e+01 ; ...
                    1.8000000000000000e+01 ; ...
                    1.9000000000000000e+01 ; ...
                    2.0000000000000000e+01 ; ...
                    2.1000000000000000e+01 ; ...
                    2.2000000000000000e+01 ; ...
                    2.3000000000000000e+01 ; ...
                    2.4000000000000000e+01 ; ...
                    2.5000000000000000e+01 ; ...
                    2.6000000000000000e+01 ; ...
                    2.7000000000000000e+01 ; ...
                    2.8000000000000000e+01 ; ...
                    2.9000000000000000e+01 ] ;
        testCase.TestData.idx_vec = idx_vec ;
%           trusted val_vec (gauss-newton, 2-5 clusters)
        val_vec = [ 2.0000000000000000e+00 ,  4.5068631407622628e-01 ; ...
                    3.0000000000000000e+00 ,  2.0412629223762790e-01 ; ...
                    4.0000000000000000e+00 ,  2.0497574271481929e+00 ; ...
                    5.0000000000000000e+00 ,  2.7047258063177479e+00 ] ;
        testCase.TestData.val_vec = val_vec ;
%           trusted opt_vec (gauss-newton, 2-5 clusters)
        opt_vec = [ 2.0000000000000000e+00 ,  7.7465684296188686e-01 ; ...
                    3.0000000000000000e+00 ,  9.3195790258745737e-01 ; ...
                    4.0000000000000000e+00 ,  4.8756064321295178e-01 ; ...
                    5.0000000000000000e+00 ,  4.5905483873645042e-01 ] ;
        testCase.TestData.opt_vec = opt_vec ;
%           trusted val_vec (nelder-mead, 2-4 clusters)
        val_vec = [ 2.0000000000000000e+00 ,  4.5068631407622628e-01 ;
                    3.0000000000000000e+00 ,  1.7800054504655316e-01 ;
                    4.0000000000000000e+00 ,  1.1742290998095775e+00 ] ;
        testCase.TestData.val_vec_nm = val_vec ;
%           trusted opt_vec (nelder-mead, 2-4 clusters)
        opt_vec = [ 2.0000000000000000e+00 ,  7.7465684296188686e-01 ;
                    3.0000000000000000e+00 ,  9.4066648498448224e-01 ;
                    4.0000000000000000e+00 ,  7.0644272504760564e-01 ] ;
        testCase.TestData.opt_vec_nm = opt_vec ;
%   -----------------------------------------------------------------------
%   Trusted results from Markov modeling in double precision with program 
%   version PCCAwww_Schur_8 for the count.txt Butane transition matrix 
%   from Marcus Weber, Zuse Institute Berlin, 2017.
%   First optimization was performed with gauss-newton, maxiter=100,
%   xscale=1e-06, xtol=0.0001; second (final) optional optimization was
%   performed with nelder-mead, maxiter=2000, tolfun=1e-08, tolx=1e-08.
    elseif strcmp(testCase.TestData.precision,'double')

%           trusted pi vector
%         pi = [ 2.1875717384711871e-03 ; ...
%                5.4230369970591575e-03 ; ...
%                2.3420448543299083e-02 ; ...
%                5.8285779596956473e-02 ; ...
%                7.2494291292365468e-02 ; ...
%                5.4052544545042477e-02 ; ...
%                2.8350114536130275e-02 ; ...
%                1.4649669543955196e-02 ; ...
%                9.4972643584634829e-03 ; ...
%                5.8731122830834818e-03 ; ...
%                5.1188197962966381e-03 ; ...
%                4.1244835601284245e-03 ; ...
%                3.5717504074408435e-03 ; ...
%                3.6920622896702438e-03 ; ...
%                4.4071993352014999e-03 ; ...
%                5.5744492572987097e-03 ; ...
%                7.3426402767339024e-03 ; ...
%                1.3993296983640316e-02 ; ...
%                3.0469625501623895e-02 ; ...
%                5.9720863567418590e-02 ; ...
%                8.7264923613879344e-02 ; ...
%                8.8356210201732663e-02 ; ...
%                6.0724687487944184e-02 ; ...
%                2.9871204084794590e-02 ; ...
%                1.3863748819508656e-02 ; ...
%                7.7692166564781867e-03 ; ...
%                5.3241048703274755e-03 ; ...
%                3.9554189289415257e-03 ; ...
%                4.0272800314563153e-03 ; ...
%                3.2187995810143183e-03 ; ...
%                3.7458587500204367e-03 ; ...
%                5.3879665229277446e-03 ; ...
%                5.8325738315465198e-03 ; ...
%                7.6770295046912742e-03 ; ...
%                1.4593685370313933e-02 ; ...
%                2.7832664619951177e-02 ; ...
%                5.3854162866681099e-02 ; ...
%                7.4250196668133692e-02 ; ...
%                5.8555446889377381e-02 ; ...
%                2.2629226540465116e-02 ; ...
%                5.9293050788190088e-03 ; ...
%                3.0872646707157544e-03 ] ;
%         testCase.TestData.pi = pi ;
%           trusted pi_weights
%         pi_weights = [ 2.8409817970251633e-01 ; ...
%                        2.8737681725227632e-01 ; ...
%                        4.2852500304520702e-01 ] ;
%         testCase.TestData.pi_weights = pi_weights ;
%           trusted sd vector
        sd = [ 2.1196820476928461e-03 ; ...
               5.4491826226066090e-03 ; ...
               2.3426486027095936e-02 ; ...
               5.8221266809978502e-02 ; ...
               7.2479128130780376e-02 ; ...
               5.4041893715942611e-02 ; ...
               2.8355746638004300e-02 ; ...
               1.4687796830475429e-02 ; ...
               9.4685797130430443e-03 ; ...
               5.8791181322801582e-03 ; ...
               5.1292306154076886e-03 ; ...
               4.1493775933609959e-03 ; ...
               3.6094585812128182e-03 ; ...
               3.7094435834624808e-03 ; ...
               4.4093385992101186e-03 ; ...
               5.5791631255311704e-03 ; ...
               7.3189021646752990e-03 ; ...
               1.3967904814277858e-02 ; ...
               3.0445433185022245e-02 ; ...
               5.9751037344398343e-02 ; ...
               8.7266909963505473e-02 ; ...
               8.8306753986901965e-02 ; ...
               6.0670899365095239e-02 ; ...
               2.9825526171074340e-02 ; ...
               1.3857921311803230e-02 ; ...
               7.7488376743488473e-03 ; ...
               5.3791931210318451e-03 ; ...
               3.9594060890866369e-03 ; ...
               4.0093985902114682e-03 ; ...
               3.2395140728890665e-03 ; ...
               3.7694345848122784e-03 ; ...
               5.3691946208068789e-03 ; ...
               5.8091286307053944e-03 ; ...
               7.6788481727740835e-03 ; ...
               1.4617807328900665e-02 ; ...
               2.7865820126980953e-02 ; ...
               5.3891916212568114e-02 ; ...
               7.4298855171724243e-02 ; ...
               5.8661200819877017e-02 ; ...
               2.2656601509773534e-02 ; ...
               5.9291106334049895e-03 ; ...
               2.9895515672649104e-03 ] ;
        testCase.TestData.sd = sd ;
        name = strcat('count-sd.txt') ;
        save(name,'sd','-ascii','-double')
%           trusted A (3 clusters)
        A = [ 2.8405568184913244e-01   2.8755576853720538e-01 ...
              4.2838854961366207e-01 ; ...
              3.7905560917700676e-01  -3.3892409425382630e-01 ...
             -4.0131514923180477e-02 ; ...
             -1.9965336957541363e-01  -2.7103148561320506e-01 ...
              4.7068485518861869e-01 ] ;
        testCase.TestData.A = A ;
        name = strcat('count-A.txt') ;
        save(name,'A','-ascii','-double')
%           trusted chi (3 clusters)
        chi = [ 8.5043523873879956e-01   4.3886683668813712e-11 ...
                1.4956476121731360e-01 ; ...
                8.8090007542006055e-01   2.5589115375342489e-02 ...
                9.3510809204596937e-02 ; ...
                9.6495990190978509e-01   1.1558207813296294e-02 ...
                2.3481890276918493e-02 ; ...
                9.7558793310460945e-01   1.5709140129765899e-02 ...
                8.7029267656243241e-03 ; ...
                9.7963327053545934e-01   1.4060862546031219e-02 ...
                6.3058669185093305e-03 ; ...
                9.8568851438933425e-01   1.4311485610665552e-02 ...
                2.8071248236694572e-17 ; ...
                9.6791270535282792e-01   1.7471491809863252e-02 ...
                1.4615802837308636e-02 ; ...
                9.4601281012257998e-01   1.7835098543344384e-02 ...
                3.6152091334075327e-02 ; ...
                9.2448952433822940e-01   1.8479564079042093e-02 ...
                5.7030911582728390e-02 ; ...
                8.8318556579259333e-01   2.4948552633467080e-02 ...
                9.1865881573939379e-02 ; ...
                7.5874311920722926e-01   2.5407453476171762e-02 ...
                2.1584942731659873e-01 ; ...
                6.8245807053420782e-01   5.4751908940178097e-02 ...
                2.6279002052561395e-01 ; ...
                5.3234840569967190e-01   6.3068044907413703e-02 ...
                4.0458354939291430e-01 ; ...
                3.1537515699639085e-01   5.2337908021706729e-02 ...
                6.3228693498190214e-01 ; ...
                2.2250786517110696e-01   7.6139414102712424e-02 ...
                7.0135272072618049e-01 ; ...
                1.2375934853700912e-01   5.4508417089850582e-02 ...
                8.2173223437314014e-01 ; ...
                4.9653667316514778e-02   2.9603583297963372e-02 ...
                9.2074274938552181e-01 ; ...
                2.5736159571559877e-02   1.2561644103436256e-02 ...
                9.6170219632500376e-01 ; ...
                1.1894344993512570e-02   6.3139005313615033e-03 ...
                9.8179175447512568e-01 ; ...
                4.8084968892439985e-03   3.6671524338928122e-03 ...
                9.9152435067686306e-01 ; ...
                3.1536353492936597e-03   7.1221730872186764e-04 ...
                9.9613414734198436e-01 ; ...
               -3.0507380398593992e-18  -6.5549521997357121e-18 ...
                9.9999999999999989e-01 ; ...
                8.2726996336765744e-03   3.0940472642753200e-04 ...
                9.9141789563989580e-01 ; ...
                1.2722881126783353e-02   5.9164159394744483e-03 ...
                9.8136070293374211e-01 ; ...
                2.2122528189377291e-02   1.3902592390825667e-02 ...
                9.6397487941979698e-01 ; ...
                4.0589834059942057e-02   3.7980881743777700e-02 ...
                9.2142928419628023e-01 ; ...
                8.0588740622014210e-02   1.1344669076732210e-01 ...
                8.0596456861066357e-01 ; ...
                1.0568119504467953e-01   2.0230326690849842e-01 ...
                6.9201553804682192e-01 ; ...
                8.3281552679901921e-02   3.4042640424725878e-01 ...
                5.7629204307283921e-01 ; ...
                5.8911161575873422e-02   4.8967335413071028e-01 ...
                4.5141548429341599e-01 ; ...
                4.3770917595157881e-02   6.6193931626137592e-01 ...
                2.9428976614346619e-01 ; ...
                2.9817138929281523e-02   8.0565415247850192e-01 ...
                1.6452870859221638e-01 ; ...
                1.4136303417928717e-02   8.8989778149855780e-01 ...
                9.5965915083513417e-02 ; ...
                1.3671381908787954e-02   9.4419514302533858e-01 ...
                4.2133475065873442e-02 ; ...
                7.5795321139255963e-03   9.6824758368408681e-01 ...
                2.4172884201987460e-02 ; ...
                1.0405260238833199e-02   9.8297752755905998e-01 ...
                6.6172122021064947e-03 ; ...
                4.5138347223880404e-03   9.8998687175067734e-01 ...
                5.4992935269345851e-03 ; ...
                8.4518297221162914e-03   9.9154817000192508e-01 ...
                2.7595845559331095e-10 ; ...
                6.5843351926822497e-03   9.8840580521018928e-01 ...
                5.0098595971283938e-03 ; ...
                9.2202981926351631e-03   9.7351230297269997e-01 ...
                1.7267398834664754e-02 ; ...
                1.6299801690329144e-02   9.2119142752842731e-01 ...
                6.2508770781243561e-02 ; ...
                4.5803069549102952e-10   9.1035357717144483e-01 ...
                8.9646422370524254e-02 ] ;
        testCase.TestData.chi = chi ;
        name = strcat('count-chi.txt') ;
        save(name,'chi','-ascii','-double')
%           trusted sd_weights (3 clusters)
        sd_weights = [ 2.8405568184913244e-01 ; ...
                       2.8755576853720533e-01 ; ...
                       4.2838854961366213e-01 ] ;
        testCase.TestData.sd_weights = sd_weights ;
        name = strcat('count-sd_weights.txt') ;
        save(name,'sd_weights','-ascii','-double')
%           trusted Pc (3 clusters)
        Pc = [ 9.5104510750059479e-01   1.8354056625839690e-02 ...
               3.0600835873566056e-02 ; ...
               1.8594617368171685e-02   9.5127058926326480e-01 ...
               3.0134793368563478e-02 ; ...
               1.9985610707576221e-02   2.0510702582310643e-02 ...
               9.5950368671011388e-01 ] ;
        testCase.TestData.Pc = Pc ;
        name = strcat('count-Pc.txt') ;
        save(name,'Pc','-ascii','-double')
%           trusted index vector
        idx_vec = [ 1.0000000000000000e+00 ; ...
                    2.0000000000000000e+00 ; ...
                    3.0000000000000000e+00 ; ...
                    4.0000000000000000e+00 ; ...
                    5.0000000000000000e+00 ; ...
                    6.0000000000000000e+00 ; ...
                    7.0000000000000000e+00 ; ...
                    8.0000000000000000e+00 ; ...
                    9.0000000000000000e+00 ; ...
                    1.0000000000000000e+01 ; ...
                    1.1000000000000000e+01 ; ...
                    1.2000000000000000e+01 ; ...
                    1.3000000000000000e+01 ; ...
                    3.0000000000000000e+01 ; ...
                    3.1000000000000000e+01 ; ...
                    3.2000000000000000e+01 ; ...
                    3.3000000000000000e+01 ; ...
                    3.4000000000000000e+01 ; ...
                    3.5000000000000000e+01 ; ...
                    3.6000000000000000e+01 ; ...
                    3.7000000000000000e+01 ; ...
                    3.8000000000000000e+01 ; ...
                    3.9000000000000000e+01 ; ...
                    4.0000000000000000e+01 ; ...
                    4.1000000000000000e+01 ; ...
                    4.2000000000000000e+01 ; ...
                    1.4000000000000000e+01 ; ...
                    1.5000000000000000e+01 ; ...
                    1.6000000000000000e+01 ; ...
                    1.7000000000000000e+01 ; ...
                    1.8000000000000000e+01 ; ...
                    1.9000000000000000e+01 ; ...
                    2.0000000000000000e+01 ; ...
                    2.1000000000000000e+01 ; ...
                    2.2000000000000000e+01 ; ...
                    2.3000000000000000e+01 ; ...
                    2.4000000000000000e+01 ; ...
                    2.5000000000000000e+01 ; ...
                    2.6000000000000000e+01 ; ...
                    2.7000000000000000e+01 ; ...
                    2.8000000000000000e+01 ; ...
                    2.9000000000000000e+01 ] ;
        testCase.TestData.idx_vec = idx_vec ;
%           trusted val_vec (gauss-newton, 2-5 clusters)
        val_vec = [ 2.0000000000000000e+00 ,  4.5068631407624360e-01 ; ...
                    3.0000000000000000e+00 ,  2.0412629225068146e-01 ; ...
                    4.0000000000000000e+00 ,  2.0497563172193218e+00 ; ...
                    5.0000000000000000e+00 ,  2.7047259529717986e+00 ] ;
        testCase.TestData.val_vec = val_vec ;
%           trusted opt_vec (gauss-newton, 2-5 clusters)
        opt_vec = [ 2.0000000000000000e+00 ,  7.7465684296187820e-01 ; ...
                    3.0000000000000000e+00 ,  9.3195790258310618e-01 ; ...
                    4.0000000000000000e+00 ,  4.8756092069516954e-01 ; ...
                    5.0000000000000000e+00 ,  4.5905480940564025e-01 ] ;
        testCase.TestData.opt_vec = opt_vec ; 
%           trusted val_vec (nelder-mead, 2-4 clusters)
        val_vec = [ 2.0000000000000000e+00 ,  4.5068631407624360e-01 ;
                    3.0000000000000000e+00 ,  1.7800054504654916e-01 ;
                    4.0000000000000000e+00 ,  1.1742290998137550e+00 ] ;
        testCase.TestData.val_vec_nm = val_vec ;
%           trusted opt_vec (nelder-mead, 2-4 clusters)
        opt_vec = [ 2.0000000000000000e+00 ,  7.7465684296187820e-01 ;
                    3.0000000000000000e+00 ,  9.4066648498448358e-01 ;
                    4.0000000000000000e+00 ,  7.0644272504656125e-01 ] ;
        testCase.TestData.opt_vec_nm = opt_vec ;        
    end
%   -----------------------------------------------------------------------
%   example transition matrix from Susanna Roeblitz,
%   Zuse Institute Berlin, 2017.
    for i = [ 0, 10, 50, 100, 200, 500, 1000 ]
        mu = i ;
        W =[1000 100 100 10 0 0 0 0 0;...
            100 1000 100 0 0 0 0 0 0;...
            100 100 1000 0 mu 0 0 0 0;...
            10 0 0 1000 100 100 10 0 0;...
            0 0 mu 100 1000 100 0 0 0;...
            0 0 0 100 100 1000 0 mu 0;...
            0 0 0 10 0 0 1000 100 100;...
            0 0 0 0 0 mu 100 1000 100;...
            0 0 0 0 0 0 100 100 1000];
        name = strcat('example_matrix_mu',num2str(i),'.txt') ;
        save(name,'-ascii','W','-double')
    end

    if strcmp(testCase.TestData.precision,'mp')
%       Trusted results from testing with test_fillA(testCase) in   
%       multi-precision (mp.Digits=50: 50 digits) with program version   
%       PCCAwww_Schur_9 for the example transition matrix with mu=0 from 
%       Susanna Roeblitz, Zuse Institute Berlin, 2017.
%           trusted initial A (3,3)-matrix
        testCase.TestData.A_mu0_init = [ 3.3390904470272770e-01 ...
            3.3304547764863618e-01   3.3304547764863618e-01 ; ...
           -7.6900386296779886e-49   4.0366140439774489e-01 ...
           -4.0366140439774489e-01 ; ...
            4.5730890701570093e-01  -2.2865445350785046e-01 ...
           -2.2865445350785046e-01 ] ;
%           trusted A (3,3)-matrix after using fillA() on A_init
        testCase.TestData.A_mu0 = [ 3.3390904470272770e-01 ...
            3.3304547764863618e-01   3.3304547764863618e-01 ; ...
           -0.0000000000000000e+00   4.0366140439774489e-01 ...
           -4.0366140439774489e-01 ; ...
            4.5730890701570093e-01  -2.2865445350785046e-01 ...
           -2.2865445350785046e-01 ] ;
%           trusted (cut to double precision by double()) schur vector (9,3)-matrix
        v1 = [ 1.0000000000000000e+00   1.1983873824613118e+00 ...
              -6.6212084649124303e-01 ] ;
        v2 = [ 1.0000000000000000e+00   1.2386618947283068e+00 ...
              -7.3016081598267124e-01 ] ;
        v3 = [ 1.0000000000000000e+00   1.2386618947283068e+00 ...
              -7.3016081598267124e-01 ] ;
        v4 = [ 1.0000000000000000e+00  -2.2437686940366006e-48 ...
               1.3208168935772102e+00 ] ;
        v5 = [ 1.0000000000000000e+00  -2.4972075324166187e-48 ...
               1.4565448979422639e+00 ] ;
        v6 = [ 1.0000000000000000e+00  -2.4731316796753597e-48 ...
               1.4565448979422639e+00 ] ;
        v7 = [ 1.0000000000000000e+00  -1.1983873824613118e+00 ...
              -6.6212084649124303e-01 ] ;
        v8 = [ 1.0000000000000000e+00  -1.2386618947283068e+00 ...
              -7.3016081598267124e-01 ] ;
        v9 = [ 1.0000000000000000e+00  -1.2386618947283068e+00 ...
              -7.3016081598267124e-01 ] ;
        testCase.TestData.svecs_mu0 = [ v1; v2; v3; v4; v5; v6; v7; v8; v9 ] ; 
%       Trusted results from testing with test_fillA(testCase) in   
%       multi-precision (mp.Digits=50: 50 digits) with program version   
%       PCCAwww_Schur_9 for the example transition matrix with mu=1000 from 
%       Susanna Roeblitz, Zuse Institute Berlin, 2017.
%           trusted initial A (5,5)-matrix
        testCase.TestData.A_mu1000_init = [ ...
            9.1894070188323768e-02   1.7530349447685256e-01 ...
            1.7530349447685256e-01   2.7874947042898557e-01 ...
            2.7874947042898557e-01 ; ...
            9.5617462375120710e-51   2.3004217991775647e-01 ...
           -2.3004217991775647e-01   2.4680580481257491e-01 ...
           -2.4680580481257491e-01 ; ...
           -8.2063944467677397e-02   2.1685904674531994e-01 ...
            2.1685904674531994e-01  -1.7582707451148125e-01 ...
           -1.7582707451148125e-01 ; ...
            1.2649128975068150e-51  -1.5813354667522092e-01 ...
            1.5813354667522092e-01   3.0646480920422281e-01 ...
           -3.0646480920422281e-01 ; ...
           -2.6659946136620422e-01  -4.6750705493354562e-02 ...
           -4.6750705493354562e-02   1.8005043617645666e-01 ...
            1.8005043617645666e-01 ] ;
%           trusted A (5,5)-matrix after using fillA() on A_init
        testCase.TestData.A_mu1000 = [ ...
            1.1624352928638547e-01   1.4701250216352996e-01 ...
            1.4701250216352996e-01   2.9486573319327730e-01 ...
            2.9486573319327730e-01 ; ...
           -0.0000000000000000e+00   1.9291729793400017e-01 ...
           -1.9291729793400017e-01   2.0697555985554739e-01 ...
           -2.0697555985554739e-01 ; ...
           -6.8820224317862874e-02   1.8186169747481573e-01 ...
            1.8186169747481573e-01  -1.4745158531588429e-01 ...
           -1.4745158531588429e-01 ; ...
           -0.0000000000000000e+00  -1.3261349091810171e-01 ...
            1.3261349091810171e-01   2.5700661906731492e-01 ...
           -2.5700661906731492e-01 ; ...
           -2.2357485803610264e-01  -3.9205939465147714e-02 ...
           -3.9205939465147714e-02   1.5099336848319903e-01 ...
            1.5099336848319903e-01 ] ;
%           trusted (cut to double precision by double()) schur vector (9,5)-matrix
        testCase.TestData.svecs_mu1000 = [ 1.0000000000000000e+00 ...
           -1.3488263927262389e+00   1.3104358647426715e+00 ...
            1.0433110064103206e+00  -6.0005035322490063e-01 ; ...
            1.0000000000000000e+00  -1.3990235434236398e+00 ...
            1.4737789968291537e+00   1.1266779128181024e+00 ...
           -1.0896513975018773e-01 ; ...
            1.0000000000000000e+00  -8.8508490246081217e-01 ...
           -4.3510374799711482e-01  -9.8936037088281537e-01 ...
            6.5386362361676453e-01 ; ...
            1.0000000000000000e+00   2.4862023997663969e-49 ...
           -1.4466972854287909e+00  -2.2942203823682567e-49 ...
           -2.9609371304557914e+00 ; ...
            1.0000000000000000e+00  -7.2188567221853384e-01 ...
           -6.8838572855836444e-01  -1.0501513257627346e+00 ...
            5.5658671487432088e-01 ; ...
            1.0000000000000000e+00   7.2188567221853384e-01 ...
           -6.8838572855836444e-01   1.0501513257627346e+00 ...
            5.5658671487432088e-01 ; ...
            1.0000000000000000e+00   1.3488263927262389e+00 ...
            1.3104358647426715e+00  -1.0433110064103206e+00 ...
           -6.0005035322490063e-01 ; ...
            1.0000000000000000e+00   8.8508490246081217e-01 ...
           -4.3510374799711482e-01   9.8936037088281537e-01 ...
            6.5386362361676453e-01 ; ...
            1.0000000000000000e+00   1.3990235434236398e+00 ...
            1.4737789968291537e+00  -1.1266779128181024e+00 ...
           -1.0896513975018773e-01 ] ; 
%       Trusted results from testing with test_use_minChi(testCase) in   
%       multi-precision (mp.Digits=50: 50 digits) with program version   
%       PCCAwww_Schur_9 for the example transition matrix with mu=0 from 
%       Susanna Roeblitz, Zuse Institute Berlin, 2017.
%       The results are trusted since they are (visually) similar to the
%       results (for the same test matrix but obtained by - more precise -
%       Nelder-Mead (instead of unoptimized calculation by the Inner 
%       Simplex Algorithm as in use_minChi() and cluster_by_isa()) 
%       optimization) published in Fig. 4 a) from
%       (1) Roeblitz, S.; Weber, M. Fuzzy Spectral Clustering by PCCA+:
%       Application to Markov State Models and Data Classification. Adv.
%       Data Anal. Classif. 2013, 7 (2), 147?179.
%           trusted chi by ISA for n_cluster=3
        testCase.TestData.chi_isa_mu0_n3 = [ ...
            3.1115284081506680e-02   9.6818509177611722e-01   6.9962414237611918e-04 ; ...
            1.8709352970645370e-50   1.0000000000000000e+00  -9.6219529563319043e-50 ; ...
            3.2073176521106348e-50   1.0000000000000000e+00  -9.7555911918365141e-50 ; ...
            9.3793037467239504e-01   3.1034812663802466e-02   3.1034812663802466e-02 ; ...
            1.0000000000000000e+00  -1.8976629441654589e-49   2.0313011796700687e-49 ; ...
            1.0000000000000000e+00  -1.8442076499636150e-49   1.9243905912663809e-49 ; ...
            3.1115284081506680e-02   6.9962414237611918e-04   9.6818509177611722e-01 ; ...
            1.3363823550460978e-50   8.9537617788088554e-50   1.0000000000000000e+00 ; ...
            1.3363823550460978e-50   8.9537617788088554e-50   1.0000000000000000e+00  ] ;
%       Trusted results from testing with test_use_minChi(testCase) in   
%       multi-precision (mp.Digits=50: 50 digits) with program version   
%       PCCAwww_Schur_9 for the example transition matrix with mu=100 from 
%       Susanna Roeblitz, Zuse Institute Berlin, 2017.
%       The results are trusted since they are (visually) similar to the
%       results (for the same test matrix but obtained by - more precise -
%       Nelder-Mead (instead of unoptimized calculation by the Inner 
%       Simplex Algorithm as in use_minChi() and cluster_by_isa()) 
%       optimization) published in Fig. 4 b) from
%       (1) Roeblitz, S.; Weber, M. Fuzzy Spectral Clustering by PCCA+:
%       Application to Markov State Models and Data Classification. Adv.
%       Data Anal. Classif. 2013, 7 (2), 147?179.
%           trusted chi by ISA for n_cluster=3
        testCase.TestData.chi_isa_mu100_n3 = [ ...
           -4.2580228676557226e-03   4.2801027432807288e-02   9.6145699543484842e-01 ; ...
           -9.3546764853226848e-51  -1.0691058840368783e-50   1.0000000000000000e+00 ; ...
           -2.7309451028470270e-02   2.5981853655796699e-01   7.6749091447050322e-01 ; ...
           -5.3455294201843913e-51   1.0000000000000000e+00  -2.4054882390829761e-50 ; ...
           -2.3685358779865925e-02   8.3488897155844621e-01   1.8879638722141970e-01 ; ...
            1.8879638722141970e-01   8.3488897155844621e-01  -2.3685358779865925e-02 ; ...
            9.6145699543484842e-01   4.2801027432807288e-02  -4.2580228676557226e-03 ; ...
            7.6749091447050322e-01   2.5981853655796699e-01  -2.7309451028470270e-02 ; ...
            1.0000000000000000e+00  -8.0182941302765869e-51  -4.0091470651382935e-51 ] ;
    elseif strcmp(testCase.TestData.precision,'double')
%       Trusted results from testing with test_fillA(testCase) in   
%       double precision with program version   
%       PCCAwww_Schur_9 for the example transition matrix with mu=0 from 
%       Susanna Roeblitz, Zuse Institute Berlin, 2017.
%           trusted initial A (3,3)-matrix
        testCase.TestData.A_mu0_init = [ ...
            3.3390904470272748e-01   3.3304547764863601e-01 ...
            3.3304547764863596e-01 ; ...
            1.1824450993798861e-14  -4.0366140439775017e-01 ...
            4.0366140439773823e-01 ; ...
           -4.5730890701570082e-01   2.2865445350784039e-01 ...
            2.2865445350786040e-01 ] ;
%           trusted A (3,3)-matrix after using fillA() on A_init
        testCase.TestData.A_mu0 = [ ...
            3.3390904470272720e-01   3.3304547764863651e-01 ...
            3.3304547764863612e-01 ; ...
            1.1934897514720417e-14  -4.0366140439774961e-01 ...
            4.0366140439773768e-01 ; ...
           -4.5730890701570021e-01   2.2865445350784008e-01 ...
            2.2865445350786009e-01 ] ;
%           trusted (cut to double precision by double()) schur vector (9,3)-matrix
        testCase.TestData.svecs_mu0 = [ ...
            1.0000000000000002e+00   1.1983873824612949e+00 ...
            6.6212084649127290e-01 ; ...
            1.0000000000000002e+00   1.2386618947282897e+00 ...
            7.3016081598270310e-01 ; ...
            1.0000000000000002e+00   1.2386618947282877e+00 ...
            7.3016081598270255e-01 ; ...
            1.0000000000000002e+00   2.9934085326177830e-14 ...
           -1.3208168935772115e+00 ; ...
            1.0000000000000002e+00   3.8344472783066848e-14 ...
           -1.4565448979422635e+00 ; ...
            1.0000000000000002e+00   3.8841087123289861e-14 ...
           -1.4565448979422631e+00 ; ...
            1.0000000000000002e+00  -1.1983873824613247e+00 ...
            6.6212084649121505e-01 ; ...
            1.0000000000000002e+00  -1.2386618947283270e+00 ...
            7.3016081598263805e-01 ; ...
            1.0000000000000002e+00  -1.2386618947283281e+00 ...
            7.3016081598263893e-01 ] ; 
%       Trusted results from testing with test_fillA(testCase) in   
%       double precision with program version   
%       PCCAwww_Schur_9 for the example transition matrix with mu=1000 from 
%       Susanna Roeblitz, Zuse Institute Berlin, 2017.
%           trusted initial A (5,5)-matrix
        testCase.TestData.A_mu1000_init = [ ...
            9.1894070188323573e-02   1.7530349447685195e-01 ...
            1.7530349447685301e-01   2.7874947042898623e-01 ...
            2.7874947042898501e-01 ; ...
           -1.9968968873256783e-16   2.3004217991775602e-01 ...
           -2.3004217991775622e-01   2.4680580481257552e-01 ...
           -2.4680580481257508e-01 ; ...
            8.2063944467677424e-02  -2.1685904674531978e-01 ...
           -2.1685904674531978e-01   1.7582707451147850e-01 ...
            1.7582707451148361e-01 ; ...
           -2.6690050013010803e-16  -1.5813354667522189e-01 ...
            1.5813354667521951e-01   3.0646480920422386e-01 ...
           -3.0646480920422126e-01 ; ...
           -2.6659946136620399e-01  -4.6750705493354333e-02 ...
           -4.6750705493354631e-02   1.8005043617645519e-01 ...
            1.8005043617645786e-01 ] ;
%           trusted A (5,5)-matrix after using fillA() on A_init
        testCase.TestData.A_mu1000 = [ ...
            1.1624352928638476e-01   1.4701250216352987e-01 ...
            1.4701250216353140e-01   2.9486573319327480e-01 ...
            2.9486573319327908e-01 ; ...
           -2.0948669444255076e-16   1.9291729793399881e-01 ...
           -1.9291729793399898e-01   2.0697555985554686e-01 ...
           -2.0697555985554650e-01 ; ...
            6.8820224317862555e-02  -1.8186169747481468e-01 ...
           -1.8186169747481468e-01   1.4745158531588126e-01 ...
            1.4745158531588554e-01 ; ...
           -1.8621039506004511e-16  -1.3261349091810185e-01 ...
            1.3261349091809985e-01   2.5700661906731453e-01 ...
           -2.5700661906731237e-01 ; ...
           -2.2357485803610139e-01  -3.9205939465147326e-02 ...
           -3.9205939465147575e-02   1.5099336848319703e-01 ...
            1.5099336848319928e-01 ] ;
%           trusted (cut to double precision by double()) schur vector (9,5)-matrix
        testCase.TestData.svecs_mu1000 = [ ...
            1.0000000000000002e+00   1.3488263927262381e+00 ...
           -1.3104358647426639e+00  -1.0433110064103177e+00 ...
           -6.0005035322489464e-01 ; ...
            1.0000000000000002e+00   1.3990235434236424e+00 ...
           -1.4737789968291495e+00  -1.1266779128181197e+00 ...
           -1.0896513975018769e-01 ; ...
            1.0000000000000002e+00   8.8508490246081195e-01 ...
            4.3510374799711093e-01   9.8936037088282069e-01 ...
            6.5386362361676154e-01 ; ...
            1.0000000000000002e+00  -1.5699540956179371e-15 ...
            1.4466972854287901e+00  -2.8905778341536754e-15 ...
           -2.9609371304557919e+00 ; ...
            1.0000000000000002e+00   7.2188567221853306e-01 ...
            6.8838572855835944e-01   1.0501513257627397e+00 ...
            5.5658671487431721e-01 ; ...
            1.0000000000000002e+00  -7.2188567221853406e-01 ...
            6.8838572855836977e-01  -1.0501513257627297e+00 ...
            5.5658671487432432e-01 ; ...
            1.0000000000000002e+00  -1.3488263927262389e+00 ...
           -1.3104358647426779e+00   1.0433110064103133e+00 ...
           -6.0005035322490197e-01 ; ...
            1.0000000000000002e+00  -8.8508490246081095e-01 ...
            4.3510374799711915e-01  -9.8936037088281159e-01 ...
            6.5386362361676742e-01 ; ...
            1.0000000000000002e+00  -1.3990235434236402e+00 ...
           -1.4737789968291592e+00   1.1266779128180928e+00 ...
           -1.0896513975019061e-01 ] ; 
%       Trusted results from testing with test_use_minChi(testCase) in   
%       double precision with program version   
%       PCCAwww_Schur_9 for the example transition matrix with mu=0 from 
%       Susanna Roeblitz, Zuse Institute Berlin, 2017. 
%       The results are trusted since they are (visually) similar to the
%       results (for the same test matrix but obtained by - more precise -
%       Nelder-Mead (instead of unoptimized calculation by the Inner 
%       Simplex Algorithm as in use_minChi() and cluster_by_isa()) 
%       optimization) published in Fig. 4 a) from
%       (1) Roeblitz, S.; Weber, M. Fuzzy Spectral Clustering by PCCA+:
%       Application to Markov State Models and Data Classification. Adv.
%       Data Anal. Classif. 2013, 7 (2), 147?179.
%           trusted chi by ISA for n_cluster=3
        testCase.TestData.chi_isa_mu0_n3 = [ ...
            3.1115284081507055e-02   6.9962414237666952e-04   9.6818509177611567e-01 ; ...
           -2.2306101257299255e-17   2.7238701370796497e-16   9.9999999999999922e-01 ; ...
            2.3155133771019864e-16   9.5036998707745997e-16   9.9999999999999833e-01 ; ...
            9.3793037467239537e-01   3.1034812663803282e-02   3.1034812663800999e-02 ; ...
            9.9999999999999956e-01  -8.3121127279257571e-16   9.4045844324124387e-16 ; ...
            9.9999999999999933e-01  -8.9620175089935441e-16   1.2085348725220209e-15 ; ...
            3.1115284081505195e-02   9.6818509177611567e-01   6.9962414237894190e-04 ; ...
            4.1989789562932371e-16   9.9999999999999956e-01  -3.2491549094043100e-16 ; ...
            1.3725993281327047e-17   1.0000000000000002e+00  -5.6591874961648636e-16 ] ;
%       Trusted results from testing with test_use_minChi(testCase) in   
%       double precision with program version   
%       PCCAwww_Schur_9 for the example transition matrix with mu=100 from 
%       Susanna Roeblitz, Zuse Institute Berlin, 2017.
%       The results are trusted since they are (visually) similar to the
%       results (for the same test matrix but obtained by - more precise -
%       Nelder-Mead (instead of unoptimized calculation by the Inner 
%       Simplex Algorithm as in use_minChi() and cluster_by_isa()) 
%       optimization) published in Fig. 4 b) from
%       (1) Roeblitz, S.; Weber, M. Fuzzy Spectral Clustering by PCCA+:
%       Application to Markov State Models and Data Classification. Adv.
%       Data Anal. Classif. 2013, 7 (2), 147?179.
%           trusted chi by ISA for n_cluster=3
        testCase.TestData.chi_isa_mu100_n3 = [ ... 
           -4.2580228676599614e-03   4.2801027432808406e-02   9.6145699543485141e-01 ; ...
           -1.4772846838530374e-15   5.0378037267330542e-17   1.0000000000000013e+00 ; ...
           -2.7309451028471876e-02   2.5981853655796916e-01   7.6749091447050255e-01 ; ...
            2.5476043241765107e-15   1.0000000000000000e+00  -2.7488885789634078e-15 ; ...
           -2.3685358779863556e-02   8.3488897155844455e-01   1.8879638722141870e-01 ; ...
            1.8879638722141809e-01   8.3488897155844921e-01  -2.3685358779867570e-02 ; ...
            9.6145699543484642e-01   4.2801027432807524e-02  -4.2580228676540859e-03 ; ...
            7.6749091447050422e-01   2.5981853655796533e-01  -2.7309451028469895e-02 ; ...
            9.9999999999999867e-01   1.8729778932510503e-17   1.1929305952124212e-15 ] ;
    end
%   -----------------------------------------------------------------------
end
% -------------------------------------------------------------------------
% -------------------------------------------------------------------------
% -------------------------------------------------------------------------
function teardownOnce(testCase)
% test environment tear down
%   Written by Bernhard Reuter, Theoretical Physics II,
%   University of Kassel, 2017 
    cd(testCase.TestData.origPath)
%       clear all variables, globals and functions from workspace
    clear all
    %rmdir(testCase.TestData.tmpFolder)
end
% -------------------------------------------------------------------------
% -------------------------------------------------------------------------
% -------------------------------------------------------------------------
function [ P, sd ] = get_knownInput( matrixfile )
% Load the count transition matrix for Butane from Marcus Weber and
% calculate the stochastic transition matrix and the "initial distribution"
% from it. 
%   The loading and calculations are performed in double or
%   multiprecision, depending on the user input from keyboard (see
%   setupOnce() function).
%   Written by Bernhard Reuter, Theoretical Physics II,
%   University of Kassel, 2017
%   ------------------------------------------------------------
%   read the count matrix from file, calculate the stochastic matrix,
    Tc = load_t(matrixfile,'-ascii',numeric_t) ;
    dummy = (mod(Tc,1) ~= 0) ;
    assert(~any(dummy(:)), ...
        'main:Tc_DataError','Tc doesnt seem to be a count matrix')
    clearvars dummy
    assert(isa(Tc,numeric_t),'main:Tc_DataTypeError', ...
        'Variable is type %s not %s',class(Tc),numeric_t)
    assert(size(Tc,1)==size(Tc,2),'main:Tc_MatrixShapeError', ...
        'Matrix is not quadratic but %d x %d',size(Tc,1),size(Tc,2))
%       find rows of the count matrix Tc with nonzero rowsum
    [row, ~] = find(sum(Tc,2) > numeric_t('0.0001')) ;
%       calculate stochastic matrix P from the count matrix Tc
%       while accounting for rows in Tc with zero rowsum
    P = Tc ;
    Ts = Tc(row, :) ;
    P(row, :) = diag(numeric_t('1.0')./sum(Ts,2))*Ts ;
    assert(isa(P,numeric_t),'main:P_DataTypeError', ...
        'Variable is type %s not %s',class(P),numeric_t)
    %   calculate "initial distribution"
    sd = sum(Tc,2) ; sd=sd/sum(sd) ;
    assert(isa(sd,numeric_t),'main:sd_DataTypeError', ...
        'Variable is type %s not %s',class(sd),numeric_t)
end
% -------------------------------------------------------------------------
% -------------------------------------------------------------------------
% -------------------------------------------------------------------------
function [ actVal, expVal, c ] = verifyAlmostEqual(actVal, expVal, ...
    abstol, reltol, varargin)
% Checks if an actual value actVal and an expected value expVal are almost 
%   equal with respect to a given absolute or relative tolerance or both. 
%   The precision can bei either mp or double.
%   Written by Bernhard Reuter, Theoretical Physics II, University of
%   Kassel, 2017
%
%   Input:
%       actVal      the actual value
%       expVal      the expected value
%       abstol      the absolute tolerance, will be used only if abstol>0
%       reltol      the relative tolerance, will be used only if reltol>0
%       varargin:
%       combi       logical; if true, both abstol and reltol have to be
%                   fullfilled; if false, either abstol or reltol have to
%                   be fullfilled
%   -----------------------------------------------------------------------   
%       catch inappropriate use
    assert( (isa(actVal,'mp') || isa(actVal,'double')), ...
        'verifyAlmostEqual:DataTypeError1', ...
        'actVal is neither mp nor double')
    assert( (isa(expVal,'mp') || isa(expVal,'double')), ...
        'verifyAlmostEqual:DataTypeError2', ...
        'expVal is neither mp nor double')
    assert(all(size(actVal)==size(expVal)), ...
        'verifyAlmostEqual:MatchError', ...
        'expVal and actVal do not have the same shape')
%   -----------------------------------------------------------------------
    class_t1 = class(actVal);
    class_t2 = class(expVal);
    if (strcmp(class_t1,class_t2)) % l2
        class_t = class_t1;
    else % l1
        disp(['class(actVal)=' class_t1 ' is not equal class(expVal)=' class_t2 '!'])
        disp('will convert to datatype double before comparison ')
        actVal = double(actVal) ;
        expVal = double(expVal) ;
        class_t = 'double' ;
    end
%   -----------------------------------------------------------------------
    function r = num_t(expression)
        if (nargin > 0)
            if(strcmp(class_t,'mp')), r = mp(expression);
            else
                if isnumeric(expression)
                    r = expression;
                else
                    r = eval(expression);
                end;
            end;
        else
            r = class_t;
        end;
    end  % num_t
%   -----------------------------------------------------------------------
%   check for correct use of varargin
    if nargin == 5 % l3
        assert(isa(varargin{1}, 'logical'), 'verifyAlmostEqual:DataTypeError3', ...
        'combi is not of class logical')
        combi = varargin{1} ;
    elseif nargin > 5 % l4
        error('verifyAlmostEqual:InputError','Too many input arguments!')
    end
%   -----------------------------------------------------------------------
    absA = abs(actVal) ;
    absB = abs(expVal) ;
	diff = abs(actVal - expVal) ;
    idx = (actVal == expVal) ; % to handle elementwise infinities/equalities
    diff(idx) = num_t('0') ; % to handle elementwise infinities/equalities
    

%       shortcut, handles infinities/equalities, if ALL elements of actVal
%       and expVal are infinite or equal
    if (actVal == expVal) % l5
        c = true ;
        return
    elseif nargin == 5 % l6
%           use absolute and relative error, almost equal if both are
%           fullfilled
        if ( (combi == true) && (abstol > num_t('0'))  && (reltol > num_t('0')) ) % l7+l8+l9
            c1 = ( diff < abstol ) ;
            c1 = all(c1(:)) ;
            relerr = diff ./ min(absA + absB, realmax(num_t)) ;
            idx = (actVal == expVal) ; % to handle elementwise infinities/equalities
            relerr(idx) = num_t('0') ; % to handle elementwise infinities/equalities
            c2 = ( relerr < reltol ) ;
            c2 = all(c2(:)) ;
            c = ( c1 == true && c2 == true ) ;
            if c == false % l10
                disp('Expected value:')
                disp(expVal)
                disp('Actual value:')
                disp(actVal)
                disp('abstol:')
                disp(abstol)
                disp('reltol:')
                disp(reltol)
                disp('absolute error:')
                disp(diff)
                disp('relative error:')
                disp(relerr)
            end 
            return
        % use absolute and relative error, almost equal if at least one is
        % fullfilled
        elseif ( (combi == false) && (abstol > num_t('0'))  && (reltol > num_t('0')) ) % l11+l12+l13
            c1 = ( diff < abstol ) ;
            c1 = all(c1(:)) ;
            relerr = diff ./ min(absA + absB, realmax(num_t)) ;
            idx = (actVal == expVal) ; % to handle elementwise infinities/equalities
            relerr(idx) = num_t('0') ; % to handle elementwise infinities/equalities
            c2 = ( relerr < reltol ) ;
            c2 = all(c2(:)) ;
            c = ( c1 == true || c2 == true ) ;
            if c == false % l14
                disp('Expected value:')
                disp(expVal)
                disp('Actual value:')
                disp(actVal)
                disp('abstol:')
                disp(abstol)
                disp('reltol:')
                disp(reltol)
                disp('absolute error:')
                disp(diff)
                disp('relative error:')
                disp(relerr)
            end
            return
        else % l6
            error('verifyAlmostEqual:FatalError1','Nothing applied (1)!')
        end
%       use absolute error 
    elseif abstol > num_t('0') % l15
        c = ( diff < abstol ) ;
        c = all(c(:)) ;
        if c == false % l16
            disp('Expected value:')
            disp(expVal)
            disp('Actual value:')
            disp(actVal)
            disp('abstol:')
            disp(abstol)
            disp('absolute error:')
            disp(diff)
        end
        return
%       use relative error 
    elseif reltol > num_t('0') % l17
        relerr = diff ./ min(absA + absB, realmax(num_t)) ;
        idx = (actVal == expVal) ; % to handle elementwise infinities/equalities
        relerr(idx) = num_t('0') ; % to handle elementwise infinities/equalities
        c = ( relerr < reltol ) ;
        c = all(c(:)) ;
        if c == false % l18
            disp('Expected value:')
            disp(expVal)
            disp('Actual value:')
            disp(actVal)
            disp('reltol:')
            disp(reltol)
            disp('relative error:')
            disp(relerr)
        end
        return
    else % l2
        error('verifyAlmostEqual:FatalError2','Nothing applied (2)!')
    end
end
% end of function verifyAlmostEqual()
% -------------------------------------------------------------------------
% -------------------------------------------------------------------------
% -----------------------------------------------------------------------