I wrote a program implementing Gaussian Elimination with Complete Pivoting:
function x = gecp(A,b)
x = b;
n = length(A);
p = 1:n;
l = b;
for k = 1:n
[i,j] = find(A(k:n,k:n)==max(abs(A(k:n,k:n)),[],'all'));
i = i+k-1;
j = j+k-1;
[A(k,:),A(i,:)] = deal(A(i,:),A(k,:));
[A(:,j),A(:,k)] = deal(A(:,k),A(:,j));
[b(i),b(k)] = deal(b(k),b(i));
[p(k),p(j)] = deal(p(j),p(k));
temp = (k+1):n;
l(temp) = A(temp,k)/A(k,k);
b(temp) = b(temp)-l(temp).*b(k);
A(temp,temp) = A(temp,temp)-l(temp).*A(k,temp);
end
x(n) = b(n)/A(n,n);
for k = (n-1):-1:1
s = 0;
for h = (k+1):n
s = s+A(k,h)*x(h);
end
x(k) = (b(k)-s)/A(k,k);
end
x(p) = x;
And it is called like this:
N = 5; A = randn(N); b = randn(N,1); x = gecp(A,b)
Unfortunately all lines containing deal function (used for swapping rows of columns of matrices), give me following (or similar) error: "Unable to perform assignment because the size of the left side is 1-by-5 and the size of the right side is 0-by-5."
Unfortunately I have no idead why would the width of these vectors be changed to 0 as I wrote excatly the same thing on both sides.
Related
Trying to find the optimal hyperparameters for my svm model using a grid search, but it simply returns 1 for the hyperparameters.
function evaluations = inner_kfold_trainer(C,q,k,features_xy,labels)
features_xy_flds = kdivide(features_xy, k);
labels_flds = kdivide(labels, k);
evaluations = zeros(k,3);
for i = 1:k
fprintf('Fold %i of %i\n',i,k);
train_data = cell2mat(features_xy_flds(1:end ~= i));
train_labels = cell2mat(labels_flds(1:end ~= i));
test_data = cell2mat(features_xy_flds(i));
test_labels = cell2mat(labels_flds(i));
%AU1
train_labels = train_labels(:,1);
test_labels = test_labels(:,1);
[k,~] = size(test_labels);
%train
sv = fitcsvm(train_data,train_labels, 'KernelFunction','polynomial', 'PolynomialOrder',q,'BoxConstraint',C);
sv.predict(test_data);
%Calculate evaluative measures
%svm_outputs = zeros(k,1);
sv_predictions = sv.predict(test_data);
[precision,recall,F1] = evaluation(sv_predictions,test_labels);
evaluations(i,1) = precision;
evaluations(i,2) = recall;
evaluations(i,3) = F1;
end
save('eval.mat', 'evaluations');
end
an inner-fold cross validation function
and below the grid function where something seems to be going wrong
function [q,C] = grid_search(features_xy,labels,k)
% n x n grid
n = 3;
q_grid = linspace(1,19,n);
C_grid = linspace(1,59,n);
tic
evals = zeros(n,n,3);
for i = 1:n
for j = 1:n
fprintf('## i=%i, j=%i ##\n', i, j);
svm_results = inner_kfold_trainer(C_grid(i), q_grid(j),k,features_xy,labels);
evals(i,j,:) = mean(svm_results(:,:));
% precision only
%evals(i,j,:) = max(svm_results(:,1));
toc
end
end
f = evals;
% retrieving the best value of the hyper parameters, to use in the outer
% fold
[M1,I1] = max(f);
[~,I2] = max(M1(1,1,:));
index = I1(:,:,I2);
C = C_grid(index(1))
q = q_grid(index(2))
end
When I run grid_search(features_xy,labels,8) for example, I get C=1 and q=1, for any k(the no. of folds) value. Also features_xy is a 500*98 matrix.
This is my Approximate entropy Calculator in MATLAB. https://en.wikipedia.org/wiki/Approximate_entropy
I'm not sure why it isn't working. It's returning a negative value.Can anyone help me with this? R1 being the data.
FindSize = size(R1);
N = FindSize(1);
% N = input ('insert number of data values');
%if you want to put your own N in, take away the % from the line above
and
%insert the % before the N = FindSize(1)
%m = input ('insert m: integer representing length of data, embedding
dimension ');
m = 2;
%r = input ('insert r: positive real number for filtering, threshold
');
r = 0.2*std(R1);
for x1= R1(1:N-m+1,1)
D1 = pdist2(x1,x1);
C11 = (D1 <= r)/(N-m+1);
c1 = C11(1);
end
for i1 = 1:N-m+1
s1 = sum(log(c1));
end
phi1 = (s1/(N-m+1));
for x2= R1(1:N-m+2,1)
D2 = pdist2(x2,x2);
C21 = (D2 <= r)/(N-m+2);
c2 = C21(1);
end
for i2 = 1:N-m+2
s2 = sum(log(c2));
end
phi2 = (s2/(N-m+2));
Ap = phi1 - phi2;
Apen = Ap(1)
Following the documentation provided by the Wikipedia article, I developed this small function that calculates the approximate entropy:
function res = approximate_entropy(U,m,r)
N = numel(U);
res = zeros(1,2);
for i = [1 2]
off = m + i - 1;
off_N = N - off;
off_N1 = off_N + 1;
x = zeros(off_N1,off);
for j = 1:off
x(:,j) = U(j:off_N+j);
end
C = zeros(off_N1,1);
for j = 1:off_N1
dist = abs(x - repmat(x(j,:),off_N1,1));
C(j) = sum(~any((dist > r),2)) / off_N1;
end
res(i) = sum(log(C)) / off_N1;
end
res = res(1) - res(2);
end
I first tried to replicate the computation shown the article, and the result I obtain matches the result shown in the example:
U = repmat([85 80 89],1,17);
approximate_entropy(U,2,3)
ans =
-1.09965411068114e-05
Then I created another example that shows a case in which approximate entropy produces a meaningful result (the entropy of the first sample is always less than the entropy of the second one):
% starting variables...
s1 = repmat([10 20],1,10);
s1_m = mean(s1);
s1_s = std(s1);
s2_m = 0;
s2_s = 0;
% datasample will not always return a perfect M and S match
% so let's repeat this until equality is achieved...
while ((s1_m ~= s2_m) && (s1_s ~= s2_s))
s2 = datasample([10 20],20,'Replace',true,'Weights',[0.5 0.5]);
s2_m = mean(s2);
s2_s = std(s2);
end
m = 2;
r = 3;
ae1 = approximate_entropy(s1,m,r)
ae2 = approximate_entropy(s2,m,r)
ae1 =
0.00138568170752751
ae2 =
0.680090884817465
Finally, I tried with your sample data:
fid = fopen('O1.txt','r');
U = cell2mat(textscan(fid,'%f'));
fclose(fid);
m = 2;
r = 0.2 * std(U);
approximate_entropy(U,m,r)
ans =
1.08567461184858
I have a linear system Ay = b, which is created by matrix looks like this:
Here attempt to find the curves based on the matrix in the image description:
n = 10;
x0 = 0;
xn = 1;
h = 1/n;
y0 = 0;
y1 = 0;
x = zeros(1:n-1);
for i = 1:n-1;
x(i) = i*h
end
A =zeros(n-1);
for j = 1:n-2;
A(j,j+1) = (1+h/2);
A(j,j) = (h*exp(x(j))-2);
A(j+1,j) = (1-h/2);
end
A(n-1,n-1) = (h*exp(x(n-1))-2);
b = zeros(1,n-1); %Right-hand side vector
for i = 1:n-1
b(i)=h^2*((exp(x(i))-pi^2)*sin(pi*x(i))+pi*cos(pi*x(i)));
end
b=b';
y = zeros(1,n-1);
y = inv(A)*b % Solving for y
figure
plot(x,y,x,sin(x))
This is code that I create but the curves disappear, anyone can help me to check my code?
I executed this code using Feature Matrix 517*11 and Label Matrix 517*1. But once the dimensions of matrices change the code cant be run. How can I fix this?
The error is:
Subscripted assignment dimension mismatch.
in this line :
edges(k,j) = quantlevels(a);
Here is my code:
function [features,weights] = MI(features,labels,Q)
if nargin <3
Q = 12;
end
edges = zeros(size(features,2),Q+1);
for k = 1:size(features,2)
minval = min(features(:,k));
maxval = max(features(:,k));
if minval==maxval
continue;
end
quantlevels = minval:(maxval-minval)/500:maxval;
N = histc(features(:,k),quantlevels);
totsamples = size(features,1);
N_cum = cumsum(N);
edges(k,1) = -Inf;
stepsize = totsamples/Q;
for j = 1:Q-1
a = find(N_cum > j.*stepsize,1);
edges(k,j) = quantlevels(a);
end
edges(k,j+2) = Inf;
end
S = zeros(size(features));
for k = 1:size(S,2)
S(:,k) = quantize(features(:,k),edges(k,:))+1;
end
I = zeros(size(features,2),1);
for k = 1:size(features,2)
I(k) = computeMI(S(:,k),labels,0);
end
[weights,features] = sort(I,'descend');
%% EOF
function [I,M,SP] = computeMI(seq1,seq2,lag)
if nargin <3
lag = 0;
end
if(length(seq1) ~= length(seq2))
error('Input sequences are of different length');
end
lambda1 = max(seq1);
symbol_count1 = zeros(lambda1,1);
for k = 1:lambda1
symbol_count1(k) = sum(seq1 == k);
end
symbol_prob1 = symbol_count1./sum(symbol_count1)+0.000001;
lambda2 = max(seq2);
symbol_count2 = zeros(lambda2,1);
for k = 1:lambda2
symbol_count2(k) = sum(seq2 == k);
end
symbol_prob2 = symbol_count2./sum(symbol_count2)+0.000001;
M = zeros(lambda1,lambda2);
if(lag > 0)
for k = 1:length(seq1)-lag
loc1 = seq1(k);
loc2 = seq2(k+lag);
M(loc1,loc2) = M(loc1,loc2)+1;
end
else
for k = abs(lag)+1:length(seq1)
loc1 = seq1(k);
loc2 = seq2(k+lag);
M(loc1,loc2) = M(loc1,loc2)+1;
end
end
SP = symbol_prob1*symbol_prob2';
M = M./sum(M(:))+0.000001;
I = sum(sum(M.*log2(M./SP)));
function y = quantize(x, q)
x = x(:);
nx = length(x);
nq = length(q);
y = sum(repmat(x,1,nq)>repmat(q,nx,1),2);
I've run the function several times without getting any error.
I've used as input for "seq1" and "seq2" arrays such as 1:10 and 11:20
Possible error might rise in the loops
for k = 1:lambda1
symbol_count1(k) = sum(seq1 == k);
end
if "seq1" and "seq2" are defined as matrices since sum will return an array while
symbol_count1(k)
is expected to be single value.
Another possible error might rise if seq1 and seq2 are not of type integer since they are used as indexes in
M(loc1,loc2) = M(loc1,loc2)+1;
Hope this helps.
I am writing a graphical representation of numerical stability of differential operators and I am having trouble removing a nested for loop. The code loops through all entries in the X,Y, plane and calculates the stability value for each point. This is done by finding the roots of a polynomial of a size dependent on an input variable (length of input vector results in a polynomial 3d matrix of size(m,n,(lenght of input vector)). The main nested for loop is as follows.
for m = 1:length(z2)
for n = 1:length(z1)
pointpoly(1,:) = p(m,n,:);
r = roots(pointpoly);
if isempty(r),r=1e10;end
z(m,n) = max(abs(r));
end
end
The full code of an example numerical method (Trapezoidal Rule) is as follows. Any and all help is appreciated.
alpha = [-1 1];
beta = [.5 .5];
Wind = 2;
Wsize = 500;
if numel(Wind) == 1
Wind(4) = Wind(1);
Wind(3) = -Wind(1);
Wind(2) = Wind(4);
Wind(1) = Wind(3);
end
if numel(Wsize) == 1
Wsize(2) = Wsize;
end
z1 = linspace(Wind(1),Wind(2),Wsize(1));
z2 = linspace(Wind(3),Wind(4),Wsize(2));
[Z1,Z2] = meshgrid(z1,z2);
z = Z1+1i*Z2;
p = zeros(Wsize(2),Wsize(1),length(alpha));
for n = length(alpha):-1:1
p(:,:,(length(alpha)-n+1)) = alpha(n)-z*beta(n);
end
for m = 1:length(z2)
for n = 1:length(z1)
pointpoly(1,:) = p(m,n,:);
r = roots(pointpoly);
if isempty(r),r=1e10;end
z(m,n) = max(abs(r));
end
end
figure()
surf(Z1,Z2,z,'EdgeColor','None');
caxis([0 2])
cmap = jet(255);
cmap((127:129),:) = 0;
colormap(cmap)
view(2);
title(['Alpha Values (',num2str(alpha),') Beta Values (',num2str(beta),')'])
EDIT::
I was able to remove one of the for loops using the reshape command. So;
for m = 1:length(z2)
for n = 1:length(z1)
pointpoly(1,:) = p(m,n,:);
r = roots(pointpoly);
if isempty(r),r=1e10;end
z(m,n) = max(abs(r));
end
end
has now become
gg = reshape(p,[numel(p)/length(alpha) length(alpha)]);
r = zeros(numel(p)/length(alpha),1);
for n = 1:numel(p)/length(alpha)
temp = roots(gg(n,:));
if isempty(temp),temp = 0;end
r(n,1) = max(abs(temp));
end
z = reshape(r,[Wsize(2),Wsize(1)]);
This might be one for loop, but I am still going through the same number of elements. Is there a way to use the roots command on all of my rows at the same time?