function score = validate3(whichstart, x)
% VALIDATE3 : Validate output from Homework 3
%
% score = validate3(whichstart, x);
%
% Check the one- and two-norms of a solution vector "x"
% to the linear system in CS 240A Homework 3.  Return:
%   1: success, correct answer
%   0: failure, wrong answer
%  -1: unknown, don't have a validation for this problem size.
%
% John R. Gilbert    12 Feb 2006

%   whichstart = 0:  A = identity matrix, b = (1:n)'
%   whichstart = 1:  A = 3D model problem, b = (1:n)'

n = length(x);

if whichstart == 0
    score = norm(x - (1:n)') < 1e-3/norm((1:n)');
    return;
end;

if whichstart == 1
    % values of n for which we can validate with whichstart=1
    sizes =   [            1
                           8
                          27
                          64
                         125
                         216
                         343
                         512
                         729
                        1000
                        1331
                        1728
                        2197
                        2744
                        3375
                        4096
                        4913
                        5832
                        6859
                        8000];
    norm1 = 1.0e8 *   [0.00000000166667
                       0.00000012000000
                       0.00000203960784
                       0.00001632982456
                       0.00008427151515
                       0.00032690763847
                       0.00103809093064
                       0.00284236743332
                       0.00694260026760
                       0.01548630388510
                       0.03208372492816
                       0.06251477176100
                       0.11566596067841
                       0.20474261275177
                       0.34880560123076
                       0.57468601538073
                       0.91933517259960
                       1.43267147662368
                       2.18098968559791
                       3.25100221975350];
    norm2 = 1.0e+6 *  [0.00000016666667
                       0.00000443621460
                       0.00004180345581
                       0.00022091898732
                       0.00082777417437
                       0.00247448998919
                       0.00630606378618
                       0.01427117250277
                       0.02946259283900
                       0.05653238399832
                       0.10218664488534
                       0.17576438168196
                       0.28990478851359
                       0.46130704344037
                       0.71158654724393
                       1.06823137835436
                       1.56566260000087
                       2.24640193240096
                       3.16235019129708
                       4.37617979264501];
    i = find(sizes == n);
    if isempty(i)
        fprintf('Sorry, no validation available for n=%d\n',n);
        score = -1;
        return;
    end;
    check1 = abs((norm(x,1)-norm1(i))/norm1(i));
    check2 = abs((norm(x,2)-norm2(i))/norm2(i));
    score = (check1 < 1e-3) && (check2 < 1e-3);
    return;
end;

fprintf('Sorry, no validation available for whichstart=%d\n',whichstart);
return;