function demprior(action);%DEMPRIOR Demonstrate sampling from a multi-parameter Gaussian prior.%%	Description%	This function plots the functions represented by a multi-layer%	perceptron network when the weights are set to values drawn from a%	Gaussian prior distribution. The parameters AW1, AB1 AW2 and AB2%	control the inverse variances of the first-layer weights, the hidden%	unit  biases, the second-layer weights and the output unit biases%	respectively.  Their values can be adjusted on a logarithmic scale%	using the sliders, or  by typing values into the text boxes and%	pressing the return key.%%	See also%	MLP%%	Copyright (c) Ian T Nabney (1996-2001)if nargin<1,    action='initialize';end;if strcmp(action,'initialize')    aw1 = 0.01;  ab1 = 0.1;  aw2 = 1.0;  ab2 = 1.0;    % Create FIGURE  fig=figure( ...    'Name','Sampling from a Gaussian prior', ...    'Position', [50 50 480 380], ...    'NumberTitle','off', ...    'Color', [0.8 0.8 0.8], ...    'Visible','on');  % The TITLE BAR frame  uicontrol(fig,  ...    'Style','frame', ...    'Units','normalized', ...    'HorizontalAlignment', 'center', ...    'Position', [0.5 0.82 0.45 0.1], ...    'BackgroundColor',[0.60 0.60 0.60]);    % The TITLE BAR text  uicontrol(fig, ...    'Style', 'text', ...    'Units', 'normalized', ...    'BackgroundColor', [0.6 0.6 0.6], ...    'Position', [0.54 0.85 0.40 0.05], ...    'HorizontalAlignment', 'left', ...    'String', 'Sampling from a Gaussian prior');    % Frames to enclose sliders  uicontrol(fig, ...    'Style', 'frame', ...    'Units', 'normalized', ...    'BackgroundColor', [0.6 0.6 0.6], ...    'Position', [0.05 0.08 0.35 0.18]);    uicontrol(fig, ...    'Style', 'frame', ...    'Units', 'normalized', ...    'BackgroundColor', [0.6 0.6 0.6], ...    'Position', [0.05 0.3 0.35 0.18]);     uicontrol(fig, ...    'Style', 'frame', ...    'Units', 'normalized', ...    'BackgroundColor', [0.6 0.6 0.6], ...    'Position', [0.05 0.52 0.35 0.18]);     uicontrol(fig, ...    'Style', 'frame', ...    'Units', 'normalized', ...    'BackgroundColor', [0.6 0.6 0.6], ...    'Position', [0.05 0.74 0.35 0.18]);     % Frame text  uicontrol(fig, ...    'Style', 'text', ...    'Units', 'normalized', ...    'HorizontalAlignment', 'left', ...    'BackgroundColor', [0.6 0.6 0.6], ...    'Position', [0.07 0.17 0.06 0.07], ...    'String', 'aw1');  % Frame text  uicontrol(fig, ...    'Style', 'text', ...    'Units', 'normalized', ...    'HorizontalAlignment', 'left', ...    'BackgroundColor', [0.6 0.6 0.6], ...    'Position', [0.07 0.39 0.06 0.07], ...    'String', 'ab1');  % Frame text  uicontrol(fig, ...    'Style', 'text', ...    'Units', 'normalized', ...    'HorizontalAlignment', 'left', ...    'BackgroundColor', [0.6 0.6 0.6], ...    'Position', [0.07 0.61 0.06 0.07], ...    'String', 'aw2');  % Frame text  uicontrol(fig, ...    'Style', 'text', ...    'Units', 'normalized', ...    'HorizontalAlignment', 'left', ...    'BackgroundColor', [0.6 0.6 0.6], ...    'Position', [0.07 0.83 0.06 0.07], ...    'String', 'ab2');     % Slider  minval = -5; maxval = 5;  aw1slide = uicontrol(fig, ...    'Style', 'slider', ...    'Units', 'normalized', ...    'Value', log10(aw1), ...    'BackgroundColor', [0.8 0.8 0.8], ...    'Position', [0.07 0.1 0.31 0.05], ...    'Min', minval, 'Max', maxval, ...    'Callback', 'demprior update');    % Slider  ab1slide = uicontrol(fig, ...    'Style', 'slider', ...    'Units', 'normalized', ...    'Value', log10(ab1), ...    'BackgroundColor', [0.8 0.8 0.8], ...    'Position', [0.07 0.32 0.31 0.05], ...    'Min', minval, 'Max', maxval, ...    'Callback', 'demprior update');    % Slider  aw2slide = uicontrol(fig, ...    'Style', 'slider', ...    'Units', 'normalized', ...    'Value', log10(aw2), ...    'BackgroundColor', [0.8 0.8 0.8], ...    'Position', [0.07 0.54 0.31 0.05], ...    'Min', minval, 'Max', maxval, ...    'Callback', 'demprior update');    % Slider  ab2slide = uicontrol(fig, ...    'Style', 'slider', ...    'Units', 'normalized', ...    'Value', log10(ab2), ...    'BackgroundColor', [0.8 0.8 0.8], ...    'Position', [0.07 0.76 0.31 0.05], ...    'Min', minval, 'Max', maxval, ...    'Callback', 'demprior update');    % The graph box  haxes = axes('Position', [0.5 0.28 0.45 0.45], ...    'Units', 'normalized', ...    'Visible', 'on');    % Text display of hyper-parameter values    format = '%8f';    aw1val = uicontrol(fig, ...    'Style', 'edit', ...    'Units', 'normalized', ...    'Position', [0.15 0.17 0.23 0.07], ...    'String', sprintf(format, aw1), ...    'Callback', 'demprior newval');    ab1val = uicontrol(fig, ...    'Style', 'edit', ...    'Units', 'normalized', ...    'Position', [0.15 0.39 0.23 0.07], ...    'String', sprintf(format, ab1), ...    'Callback', 'demprior newval');    aw2val = uicontrol(fig, ...    'Style', 'edit', ...    'Units', 'normalized', ...    'Position', [0.15 0.61 0.23 0.07], ...    'String', sprintf(format, aw2), ...    'Callback', 'demprior newval');    ab2val = uicontrol(fig, ...    'Style', 'edit', ...    'Units', 'normalized', ...    'Position', [0.15 0.83 0.23 0.07], ...    'String', sprintf(format, ab2), ...    'Callback', 'demprior newval');     % The SAMPLE button  uicontrol(fig, ...    'Style','push', ...    'Units','normalized', ...    'BackgroundColor', [0.6 0.6 0.6], ...    'Position',[0.5 0.08 0.13 0.1], ...    'String','Sample', ...    'Callback','demprior replot');    % The CLOSE button  uicontrol(fig, ...    'Style','push', ...    'Units','normalized', ...    'BackgroundColor', [0.6 0.6 0.6], ...    'Position',[0.82 0.08 0.13 0.1], ...    'String','Close', ...    'Callback','close(gcf)');    % The HELP button  uicontrol(fig, ...    'Style','push', ...    'Units','normalized', ...    'BackgroundColor', [0.6 0.6 0.6], ...    'Position',[0.66 0.08 0.13 0.1], ...    'String','Help', ...    'Callback','demprior help');     % Save handles to objects    hndlList=[fig aw1slide ab1slide aw2slide ab2slide aw1val ab1val aw2val ...      ab2val haxes];  set(fig, 'UserData', hndlList);    demprior('replot')    elseif strcmp(action, 'update'),    % Update when a slider is moved.    hndlList   = get(gcf, 'UserData');  aw1slide   = hndlList(2);  ab1slide = hndlList(3);  aw2slide  = hndlList(4);  ab2slide = hndlList(5);  aw1val = hndlList(6);  ab1val = hndlList(7);  aw2val = hndlList(8);  ab2val = hndlList(9);  haxes = hndlList(10);    aw1 = 10^get(aw1slide, 'Value');  ab1 = 10^get(ab1slide, 'Value');  aw2 = 10^get(aw2slide, 'Value');  ab2 = 10^get(ab2slide, 'Value');      format = '%8f';  set(aw1val, 'String', sprintf(format, aw1));  set(ab1val, 'String', sprintf(format, ab1));  set(aw2val, 'String', sprintf(format, aw2));  set(ab2val, 'String', sprintf(format, ab2));    demprior('replot');  elseif strcmp(action, 'newval'),    % Update when text is changed.    hndlList   = get(gcf, 'UserData');  aw1slide   = hndlList(2);  ab1slide = hndlList(3);  aw2slide  = hndlList(4);  ab2slide = hndlList(5);  aw1val = hndlList(6);  ab1val = hndlList(7);  aw2val = hndlList(8);  ab2val = hndlList(9);  haxes = hndlList(10);      aw1 = sscanf(get(aw1val, 'String'), '%f');  ab1 = sscanf(get(ab1val, 'String'), '%f');  aw2 = sscanf(get(aw2val, 'String'), '%f');  ab2 = sscanf(get(ab2val, 'String'), '%f');    set(aw1slide, 'Value', log10(aw1));  set(ab1slide, 'Value', log10(ab1));  set(aw2slide, 'Value', log10(aw2));  set(ab2slide, 'Value', log10(ab2));    demprior('replot');  elseif strcmp(action, 'replot'),    % Re-sample from the prior and plot graphs.   oldFigNumber=watchon;  hndlList   = get(gcf, 'UserData');  aw1slide   = hndlList(2);  ab1slide = hndlList(3);  aw2slide  = hndlList(4);  ab2slide = hndlList(5);  haxes = hndlList(10);    aw1 = 10^get(aw1slide, 'Value');  ab1 = 10^get(ab1slide, 'Value');  aw2 = 10^get(aw2slide, 'Value');  ab2 = 10^get(ab2slide, 'Value');   axes(haxes);  cla  set(gca, ...    'Box', 'on', ...    'Color', [0 0 0], ...    'XColor', [0 0 0], ...    'YColor', [0 0 0], ...    'FontSize', 14);  axis([-1 1 -10 10]);    set(gca,'DefaultLineLineWidth', 2);  nhidden = 12;  prior = mlpprior(1, nhidden, 1, aw1, ab1, aw2, ab2);  xvals = -1:0.005:1;  nsample = 10;    % Number of samples from prior.  hold on  plot([-1 0; 1 0], [0 -10; 0 10], 'b--');  net = mlp(1, nhidden, 1, 'linear', prior);  for i = 1:nsample    net = mlpinit(net, prior);    yvals = mlpfwd(net, xvals');    plot(xvals', yvals, 'y');  end      watchoff(oldFigNumber); elseif strcmp(action, 'help'),    % Provide help to user.  oldFigNumber=watchon;  helpfig = figure('Position', [100 100 480 400], ...    'Name', 'Help', ...    'NumberTitle', 'off', ...    'Color', [0.8 0.8 0.8], ...    'Visible','on');      % The HELP TITLE BAR frame  uicontrol(helpfig,  ...    'Style','frame', ...    'Units','normalized', ...    'HorizontalAlignment', 'center', ...    'Position', [0.05 0.82 0.9 0.1], ...    'BackgroundColor',[0.60 0.60 0.60]);    % The HELP TITLE BAR text  uicontrol(helpfig, ...    'Style', 'text', ...    'Units', 'normalized', ...    'BackgroundColor', [0.6 0.6 0.6], ...    'Position', [0.26 0.85 0.6 0.05], ...    'HorizontalAlignment', 'left', ...    'String', 'Help: Sampling from a Gaussian Prior');    helpstr1 = strcat( ...    'This demonstration shows the effects of sampling from a Gaussian', ...     ' prior over weights for a two-layer feed-forward network. The', ...     ' parameters aw1, ab1, aw2 and ab2 control the inverse variances of', ...     ' the first-layer weights, the hidden unit biases, the second-layer', ...     ' weights and the output unit biases respectively. Their values can', ...     ' be adjusted on a logarithmic scale using the sliders, or by', ...     ' typing values into the text boxes and pressing the return key.', ...     '  After setting these values, press the ''Sample'' button to see a', ...     ' new sample from the prior. ');   helpstr2 = strcat( ...     'Observe how aw1 controls the horizontal length-scale of the', ...     ' variation in the functions, ab1 controls the input range over', ...     ' such variations occur, aw2 sets the vertical scale of the output', ...     ' and ab2 sets the vertical off-set of the output. The network has', ...     ' 12 hidden units. ');   hstr(1) = {helpstr1};   hstr(2) = {''};   hstr(3) = {helpstr2};  % The HELP text  helpui = uicontrol(helpfig, ...    'Style', 'edit', ...    'Units', 'normalized', ...    'ForegroundColor', [0 0 0], ...    'HorizontalAlignment', 'left', ...    'BackgroundColor', [1 1 1], ...    'Min', 0, ...    'Max', 2, ...    'Position', [0.05 0.2 0.9 0.8]);      [hstrw , newpos] = textwrap(helpui, hstr, 70);   set(helpui, 'String', hstrw, 'Position', [0.05, 0.2, 0.9, newpos(4)]);        % The CLOSE button  uicontrol(helpfig, ...    'Style','push', ...    'Units','normalized', ...    'BackgroundColor', [0.6 0.6 0.6], ...    'Position',[0.4 0.05 0.2 0.1], ...    'String','Close', ...    'Callback','close(gcf)');   watchoff(oldFigNumber);end;