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# spikes

## (PublicToolbox/regutools/spikes.m in BrainStorm 2.0 (Alpha))

### Function Synopsis

    [A,b,x] = spikes(n,t_max)

### Help Text

    SPIKES Test problem with a "spiky" solution.

     [A,b,x] = spikes(n,t_max)

     Artificially generated discrete ill-posed problem.

     The solution x consists of a unit step at t = .5, and a pulse train
     of spikes of decrasing magnitude at t = .5, 1.5, 2.5, ...

     The parameter t_max is optional; its default value is 5.
     It controls the length of the pulse train.

### Listing of function C:\BrainStorm_2001\PublicToolbox\regutools\spikes.m

    function [A,b,x] = spikes(n,t_max)
    %SPIKES Test problem with a "spiky" solution.
    %
    % [A,b,x] = spikes(n,t_max)
    %
    % Artificially generated discrete ill-posed problem.
    %
    % The solution x consists of a unit step at t = .5, and a pulse train
    % of spikes of decrasing magnitude at t = .5, 1.5, 2.5, ...
    %
    % The parameter t_max is optional; its default value is 5.
    % It controls the length of the pulse train.

    % Per Christian Hansen, UNI-C, 06/24/91.

    % Initialization.
    if (nargin == 1), t_max = 5; end
    t = t_max*[1:n]/n; del = t_max/n;

    % Compute the matrix A.
    [t,sigma] = meshdom(del:del:t_max,del:del:t_max); sigma = flipud(sigma);
    A = sigma./(2*sqrt(pi*t.^3)).*exp(-(sigma.^2)./(4*t));

    % Compute the right-hand side b and the solution x.
    if (nargout > 1)
      heights = 2*ones(t_max,1); heights(1) = 25;
      heights(2) = 9; heights(3) = 5; heights(4) = 4; heights(5) = 3;
      x = zeros(n,1); n_h = 1;
      peak = 0.5/t_max; peak_dist = 1/t_max;
      if (peak < 1)
        n_peak = round(peak*n); x(n_peak) = heights(n_h);
        x(n_peak+1:n) = ones(n-n_peak,1);
        peak = peak + peak_dist; n_h = n_h + 1;
      end
      while (peak < 1)
        x(round(peak*n)) = heights(n_h);
        peak = peak + peak_dist; n_h = n_h + 1;
      end
      b = A*x;
    end

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