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[linalg] added covar examples

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This commit is contained in:
Jan Benda 2019-01-06 19:30:23 +01:00
parent b0decc7df2
commit 072b9a7053
7 changed files with 72 additions and 12 deletions
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3
linearalgebra/code/coordinatetrafo.m
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@ -2,8 +2,9 @@
x=[-1:0.02:1]'; % column vector!
y=4*x/3 + 0.1*randn( size( x ) );
plot( x, y, '.b' );
axis( 'equal' );
hold on;
plot( x(1), y(1), '.b' );
axis( 'equal' );
% new coordinate system:
% e1 = [ 3 4 ]

28
linearalgebra/code/covarmatrix.m Normal file
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@ -0,0 +1,28 @@
% covariance in 2D:
x = 2.0*randn(1000, 1);
y = 0.5*x + 0.2*randn(1000, 1);
scatter(x, y)
var(x)
var(y)
cov( [x, y] )
pause(1.0)
% covariance of independent coordinates in 2D:
x = 2.0*randn(1000, 1);
y = 0.5*randn(1000, 1);
scatter(x, y)
var(x)
var(y)
cov( [x, y] )
pause(1.0)
% covariance in 3D:
x = 2.0*randn(1000, 1);
y = -0.5*x + 0.2*randn(1000, 1);
z = 2.0*x + 0.6*y + 2.0*randn(1000, 1);
scatter3(x, y, z, 'filled')
var(x)
var(y)
var(z)
cov( [x, y, z] )
pause()

36
linearalgebra/code/covarmatrixeigen.m Normal file
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@ -0,0 +1,36 @@
% covariance in 2D:
x = 2.0*randn(1000, 1);
y = 0.5*x + 0.6*randn(1000, 1);
scatter(x, y)
cv = cov( [x, y] );
[v d] = eig(cv);
hold on
quiver([0 0], [0 0], v(1,:).*sqrt(diag(d))', v(2,:).*sqrt(diag(d))', 'r', 'LineWidth', 2);
axis( 'equal' );
hold off
pause
% covariance of independent coordinates in 2D:
x = 1.5*randn(1000, 1);
y = 0.8*randn(1000, 1);
scatter(x, y)
cv = cov( [x, y] );
[v d] = eig(cv);
hold on
quiver([0 0], [0 0], v(1,:).*sqrt(diag(d))', v(2,:).*sqrt(diag(d))', 'r', 'LineWidth', 2);
axis( 'equal' );
hold off
pause
% covariance in 3D:
x = 2.0*randn(1000, 1);
y = -0.5*x + 0.2*randn(1000, 1);
z = 2.0*x + 0.6*y + 2.0*randn(1000, 1);
scatter3(x, y, z)
cv = cov( [x, y, z] );
[v d] = eig(cv);
hold on
quiver3([0 0 0], [0 0 0], [0 0 0], v(1,:).*sqrt(diag(d))', v(2,:).*sqrt(diag(d))', v(3,:).*sqrt(diag(d))', 'r', 'LineWidth', 2);
axis( 'equal' );
hold off
pause()

2
linearalgebra/code/pca2d.m
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@ -43,7 +43,7 @@ function pca2d( x, y, pm, w, h )
end
% plot eigenvectors:
quiver( ones( 1, 2 ).*mean( x ), ones( 1, 2 )*mean(y), v(1,:).*sqrt(diag(d))', v(2,:).*sqrt(diag(d))', 'r', 'LineWidth', 3, 'AutoScale', 'off', 'AutoScaleFactor', 1.0, 'MaxHeadSize', 0.7 )
quiver( ones( 1, 2 ).*mean( x ), ones( 1, 2 )*mean(y), v(1,:).*sqrt(diag(d))', v(2,:).*sqrt(diag(d))', 'r' ); %, 'LineWidth', 3, 'AutoScale', 'off', 'AutoScaleFactor', 1.0, 'MaxHeadSize', 0.7 )
xlabel( 'x' );
ylabel( 'y' );

10
linearalgebra/code/pca2dexamples.m
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@ -7,7 +7,7 @@ for r = 0.01:0.19:1
clf( f );
y = r*x + sqrt(1-r^2)*randn( n, 1 );
pca2d( x, y, 0, 5.0, 3.0 );
waitforbuttonpress;
pause( 1.0 );
end
% two distributions:
@ -17,13 +17,11 @@ y1 = randn( n/2, 1 );
x2 = randn( n/2, 1 );
y2 = randn( n/2, 1 );
f = figure( 1 );
pause( 'on' );
for d = 0:1:5
fprintf( 'Distance = %g\n', d );
clf( f );
d2 = d / sqrt( 2.0 );
x = [ x1; x2 ];
y = [ y1+d2; y2-d2 ];
x = [ x1+d; x2-d ];
y = [ y1+d; y2-d ];
pca2d( x, y, 0, 10.0, 7.0 );
waitforbuttonpress;
pause( 1.0 );
end

2
linearalgebra/code/pca3d.m
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@ -15,7 +15,7 @@ function pca3d( x, y, z )
% scatter plot:
view( 3 );
scatter3( x, y, z ); % , 0.1, 'b', 'filled', 'MarkerEdgeColor', 'blue' );
scatter3( x, y, z ); % , 1.0, 'b', 'filled' ); %, 'MarkerEdgeColor', 'blue' );
xlabel( 'x' );
ylabel( 'y' );
zlabel( 'z' );

3
linearalgebra/code/pca3dexamples.m
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@ -1,6 +1,3 @@
scrsz = get( 0, 'ScreenSize' );
set( 0, 'DefaultFigurePosition', [ scrsz(3)/2 scrsz(4)/2 scrsz(3)/2 scrsz(4)/2 ] );
n = 10000;
% three distributions: