From f5c3bb6139fa2ec7ca5cfeab6544a4c8b4d99850 Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Mon, 21 Dec 2020 19:58:19 +0100 Subject: [PATCH] [regression] finished exercise --- regression/code/gradientDescent.m | 9 +- regression/exercises/exp2errorsurface.m | 15 ++++ regression/exercises/exp2fit.m | 15 ++++ regression/exercises/exp2fit.pdf | Bin 0 -> 29836 bytes regression/exercises/exp2func.m | 4 + regression/exercises/exp2plot.m | 27 ++++++ regression/exercises/exp2plot.pdf | Bin 0 -> 185733 bytes regression/exercises/expdecaydata.m | 2 +- regression/exercises/expdecayplot.m | 10 +-- regression/exercises/expdecayplot.pdf | Bin 0 -> 179679 bytes regression/exercises/gradientdescent-1.tex | 96 +++++++++++++++++---- regression/exercises/gradientdescent.m | 39 +++++++++ regression/exercises/savefigpdf.m | 28 ++++++ 13 files changed, 217 insertions(+), 28 deletions(-) create mode 100644 regression/exercises/exp2errorsurface.m create mode 100644 regression/exercises/exp2fit.m create mode 100644 regression/exercises/exp2fit.pdf create mode 100644 regression/exercises/exp2func.m create mode 100644 regression/exercises/exp2plot.m create mode 100644 regression/exercises/exp2plot.pdf create mode 100644 regression/exercises/expdecayplot.pdf create mode 100644 regression/exercises/gradientdescent.m create mode 100644 regression/exercises/savefigpdf.m diff --git a/regression/code/gradientDescent.m b/regression/code/gradientDescent.m index 20e0b90..3fb9643 100644 --- a/regression/code/gradientDescent.m +++ b/regression/code/gradientDescent.m @@ -13,7 +13,7 @@ function [p, ps, mses] = gradientDescent(x, y, func, p0, epsilon, threshold) % mses: vector with the corresponding mean squared errors p = p0; - gradient = ones(1, length(p0)) * 1000.0; + gradient = ones(size(p0)) * 1000.0; ps = []; mses = []; while norm(gradient) > threshold @@ -29,13 +29,12 @@ function mse = meanSquaredError(x, y, func, p) end function gradmse = meanSquaredGradient(x, y, func, p) - gradmse = zeros(size(p, 1), size(p, 2)); + gradmse = zeros(size(p)); h = 1e-7; % stepsize for derivatives + ph = eye(length(p))*h; % ... for each parameter mse = meanSquaredError(x, y, func, p); for i = 1:length(p) % for each coordinate ... - pi = p; - pi(i) = pi(i) + h; % displace i-th parameter - msepi = meanSquaredError(x, y, func, pi); + msepi = meanSquaredError(x, y, func, p + ph(:,i)); gradmse(i) = (msepi - mse)/h; end end diff --git a/regression/exercises/exp2errorsurface.m b/regression/exercises/exp2errorsurface.m new file mode 100644 index 0000000..7dc4e4f --- /dev/null +++ b/regression/exercises/exp2errorsurface.m @@ -0,0 +1,15 @@ +expdecaydata; % generate data +close all; + +cs = 0.5:0.02:1.5; % range of c values +taus = 4.0:0.2:16.0; % range of tau values +msesurf = zeros(length(taus), length(cs)); % mean squared error +for i = 1:length(taus) + for k = 1:length(cs) + msesurf(i, k) = mean((voltage - ... + exp2func(time, [cs(k), taus(i)])).^2); + end +end +%surface(cs, taus, mses) +%contour(cs, taus, mses) +contourf(cs, taus, log10(msesurf)) diff --git a/regression/exercises/exp2fit.m b/regression/exercises/exp2fit.m new file mode 100644 index 0000000..47e833a --- /dev/null +++ b/regression/exercises/exp2fit.m @@ -0,0 +1,15 @@ +expdecaydata; +close all; + +p0 = [0.5, 6.0]; +pest = lsqcurvefit(@(p, x) exp2func(x, p), p0, time, voltage); +fprintf('c=%4.1fmV, tau=%4.1fms\n', pest(1), pest(2)); + +hold on; +plot(time, voltage) +plot(time, exp2func(time, pest), 'LineWidth', 2) +hold off; +xlabel('time [ms]') +ylabel('voltage [mv]') +savefigpdf(gcf, 'exp2fit.pdf', 15, 8.5); + diff --git a/regression/exercises/exp2fit.pdf b/regression/exercises/exp2fit.pdf new file mode 100644 index 0000000000000000000000000000000000000000..de17294b7c8755e89799fd65bbb17b8790ffe583 GIT binary patch literal 29836 zcmX_nbzD@>_czM|OD`?W5)uN^-G~YwQa~g`mae5k8kX)51*Abjx3gbU7Ei13U7l80XoXqU-rKR!tv|ODmJj^X! zA)E@%rsg)5kT;rI5Isv*H(Mu1h~P`%m;Ags8VXuE%9^^8kS8%pPUapCmX7XkT}_>B 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+function x = exp2func(t, p) +% return the exponential function x = c*e^{-t/tau} + x = p(1)*exp(-t./p(2)); +end diff --git a/regression/exercises/exp2plot.m b/regression/exercises/exp2plot.m new file mode 100644 index 0000000..cc2dd91 --- /dev/null +++ b/regression/exercises/exp2plot.m @@ -0,0 +1,27 @@ +... + +p0 = [0.5, 6.0]; +[pest, ps, mses] = gradientdescent(time, voltage, @exp2func, p0, 1.0, 0.00001); +fprintf('c=%4.1fmV, tau=%4.1fms\n', pest(1), pest(2)); + +subplot(1, 2, 1); +hold on; +%surface(cs, taus, msesurf); +%plot3(ps(1,:), ps(2,:), mses, '.r'); +%view(80, 35); +contourf(cs, taus, log10(msesurf)); +plot(ps(1,:), ps(2,:), '.r'); +hold off; +xlabel('c [mV]') +ylabel('tau [ms]') +zlabel('mse [mV^2]') + +subplot(1, 2, 2); +hold on; +plot(time, voltage) +plot(time, exp2func(time, pest), 'LineWidth', 2) +hold off; +xlabel('time [ms]') +ylabel('voltage [mv]') +savefigpdf(gcf, 'exp2plot.pdf', 15, 8.5); + diff --git a/regression/exercises/exp2plot.pdf 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sampling interval in ms noisesd = 0.05; % measurement noise in mV -time = 0.0:dt:5*tau; % time vector +time = 0.0:dt:6*tau; % time vector voltage = expdecay(time, tau); % exponential decay voltage = voltage + noisesd*randn(1, length(voltage)); % plus noise diff --git a/regression/exercises/expdecayplot.m b/regression/exercises/expdecayplot.m index fac8bfe..68ea89b 100644 --- a/regression/exercises/expdecayplot.m +++ b/regression/exercises/expdecayplot.m @@ -8,7 +8,7 @@ thresh = 0.00001; subplot(2, 2, 1); % top left panel hold on; plot(taus, '-o'); -plot([1, length(taus)], [tau, tau], 'k'); % line indicating true tau value +plot([1, length(taus)], [tau, tau], 'k'); % line indicating true tau hold off; xlabel('Iteration'); ylabel('tau'); @@ -19,11 +19,9 @@ ylabel('MSE'); subplot(1, 2, 2); % right panel hold on; % generate x-values for plottig the fit: -tt = 0.0:0.01:max(time); -xx = expdecay(tt, tauest); -plot(time, voltage, '.'); % plot original data -plot(tt, xx, '-r'); % plot fit 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zqpl81c$FjHN<#MZflUl@H^teo$C0{J+3zYP4Kjk}zaQU|6s_GK5RvxYjWU9(f1JC28*Jg*?79L3((*Y6V7cA*8?x zax(Hz^cQyN0^@1$rF=ju{*B-#s;U1?doq5DyFR4G6p&Ap9RB9FNGqN%%)E z)YP~n^`yCuc>n_uf^7u{x?3Vcxe$`(I(l4^hW=pNTL1dj25}=JLjRMph+w2AtrVBE z6s^>M{kRn5nTZr^#0%V zlx1YWas7W_(o+AkJ!R$p`K+{p^nX7a8tm%rhYbFgIKTn}L%ELG{|`Af4Dbx(0_* threshold + ps = [ps, p(:)]; + mses = [mses, meansquarederror(t, x, func, p)]; + gradient = msegradient(t, x, func, p); + p = p - epsilon * gradient; + end +end + +function mse = meansquarederror(t, x, func, p) + mse = mean((x - func(t, p)).^2); +end + +function gradmse = msegradient(t, x, func, p) + gradmse = zeros(size(p)); + h = 1e-3; % stepsize for derivative + ph = eye(length(p))*h; % ... for each parameter + mse = meansquarederror(t, x, func, p); + for i = 1:length(p) % for each coordinate ... + msepi = meansquarederror(t, x, func, p(:) + ph(:,i)); + gradmse(i) = (msepi - mse)/h; + end +end diff --git a/regression/exercises/savefigpdf.m b/regression/exercises/savefigpdf.m new file mode 100644 index 0000000..97a28a3 --- /dev/null +++ b/regression/exercises/savefigpdf.m @@ -0,0 +1,28 @@ +function savefigpdf(fig, name, width, height) +% Saves figure fig in pdf file name.pdf with appropriately set page size +% and fonts + + % default width: + if nargin < 3 + width = 11.7; + end + % default height: + if nargin < 4 + height = 9.0; + end + + % paper: + set(fig, 'PaperUnits', 'centimeters'); + set(fig, 'PaperSize', [width height]); + set(fig, 'PaperPosition', [0.0 0.0 width height]); + set(fig, 'Color', 'white') + + % font: + set(findall(fig, 'type', 'axes'), 'FontSize', 12) + set(findall(fig, 'type', 'text'), 'FontSize', 12) + + % save: + saveas(fig, name, 'pdf') + +end +