My main problem with this code is efficiency,I want to vectorise this section of my code:
for x = 1:N
for c = 1:L
Z = in(x,1:Ks(c,1);
Cpreds(x,c) = mode(Ctrn(Z));
end
end
Below is my implementation in detail:
function [Cpreds] = my_knn_classify(Xtrn,Ctrn, Xtst, Ks)
% Input:
% Xtrn : M-by-D training data matrix
% Ctrn : M-by-1 label vector for Xtrn
% Xtst : N-by-D test data matrix
% Ks : L-by-1 vector of the numbers of nearest neighbours in Xtrn
% Output:
% Cpreds : N-by-L matrix of predicted labels for Xtst
[N,~] = size(Xtst);
B = Xtrn;
Ctrn = Ctrn';
[L,~] = size(Ks);
Cpreds = zeros(N, L);
DI = myfn(Xtst, B); %Vectorising euclidean distance method
[~,in] = sort(DI,2,'ascend');
for x = 1:N
for c = 1:L
Z = in(x,1:Ks(c,1));
Cpreds(x,c) = mode(Ctrn(Z));
end
end
The outer loop is straightforward to vectorise, but the inner loop changes the number of elements passed to mode on each iteration, so is probably unavoidable.
Here is a vectorised version of the outer loop:
for c = 1:L
Z = in(:,1:Ks(c,1));
Cpreds(:,c) = mode(Ctrn(Z),2);
end
Related
I am very new to Scilab, but so far have not been able to find an answer (either here or via google) to my question. I'm sure it's a simple solution, but I'm at a loss. I have a lot of MATLAB scripts I wrote in grad school, but now that I'm out of school, I no longer have access to MATLAB (and can't justify the cost). Scilab looked like the best open alternative. I'm trying to convert my .m files to Scilab compatible versions using mfile2sci, but when running the mfile2sci GUI, I get the error/message shown below. Attached is the original code from the M-file, in case it's relevant.
I Searched Stack Overflow and companion sites, Google, Scilab documentation.
The M-file code follows (it's a super basic MATLAB script as part of an old homework question -- I chose it as it's the shortest, most straightforward M-file I had):
Mmax = 15;
N = 20;
T = 2000;
%define upper limit for sparsity of signal
smax = 15;
mNE = zeros(smax,Mmax);
mESR= zeros(smax,Mmax);
for M = 1:Mmax
aNormErr = zeros(smax,1);
aSz = zeros(smax,1);
ESR = zeros(smax,1);
for s=1:smax % for-loop to loop script smax times
normErr = zeros(1,T);
vESR = zeros(1,T);
sz = zeros(1,T);
for t=1:T %for-loop to carry out 2000 trials per s-value
esr = 0;
A = randn(M,N); % generate random MxN matrix
[M,N] = size(A);
An = zeros(M,N); % initialize normalized matrix
for h = 1:size(A,2) % normalize columns of matrix A
V = A(:,h)/norm(A(:,h));
An(:,h) = V;
end
A = An; % replace A with its column-normalized counterpart
c = randperm(N,s); % create random support vector with s entries
x = zeros(N,1); % initialize vector x
for i = 1:size(c,2)
val = (10-1)*rand + 1;% generate interval [1,10]
neg = mod(randi(10),2); % include [-10,-1]
if neg~=0
val = -1*val;
end
x(c(i)) = val; %replace c(i)th value of x with the nonzero value
end
y = A*x; % generate measurement vector (y)
R = y;
S = []; % initialize array to store selected columns of A
indx = []; % vector to store indices of selected columns
coeff = zeros(1,s); % vector to store coefficients of approx.
stop = 10; % init. stop condition
in = 0; % index variable
esr = 0;
xhat = zeros(N,1); % intialize estimated x signal
while (stop>0.5 && size(S,2)<smax)
%MAX = abs(A(:,1)'*R);
maxV = zeros(1,N);
for i = 1:size(A,2)
maxV(i) = abs(A(:,i)'*R);
end
in = find(maxV == max(maxV));
indx = [indx in];
S = [S A(:,in)];
coeff = [coeff R'*S(:,size(S,2))]; % update coefficient vector
for w=1:size(S,2)
r = y - ((R'*S(:,w))*S(:,w)); % update residuals
if norm(r)<norm(R)
index = w;
end
R = r;
stop = norm(R); % update stop condition
end
for j=1:size(S,2) % place coefficients into xhat at correct indices
xhat(indx(j))=coeff(j);
end
nE = norm(x-xhat)/norm(x); % calculate normalized error for this estimate
%esr = 0;
indx = sort(indx);
c = sort(c);
if isequal(indx,c)
esr = esr+1;
end
end
vESR(t) = esr;
sz(t) = size(S,2);
normErr(t) = nE;
end
%avsz = sum(sz)/T;
aSz(s) = sum(sz)/T;
%aESR = sum(vESR)/T;
ESR(s) = sum(vESR)/T;
%avnormErr = sum(normErr)/T; % produce average normalized error for these run
aNormErr(s) = sum(normErr)/T; % add new avnormErr to vector of all av norm errors
end
% just put this here to view the vector
mNE(:,M) = aNormErr;
mESR(:,M) = ESR;
% had an 'end' placed here, might've been unmatched
mNE%reshape(mNE,[],Mmax)
mESR%reshape(mESR,[],Mmax)]
figure
dimx = [1 Mmax];
dimy = [1 smax];
imagesc(dimx,dimy,mESR)
colormap gray
strESR = sprintf('Average ESR, N=%d',N);
title(strESR);
xlabel('M');
ylabel('s');
strNE = sprintf('Average Normed Error, N=%d',N);
figure
imagesc(dimx,dimy,mNE)
colormap gray
title(strNE)
xlabel('M');
ylabel('s');
The command used (and results) follow:
--> mfile2sci
ans =
[]
****** Beginning of mfile2sci() session ******
File to convert: C:/Users/User/Downloads/WTF_new.m
Result file path: C:/Users/User/DOWNLO~1/
Recursive mode: OFF
Only double values used in M-file: NO
Verbose mode: 3
Generate formatted code: NO
M-file reading...
M-file reading: Done
Syntax modification...
Syntax modification: Done
File contains no instruction, no translation made...
****** End of mfile2sci() session ******
To convert the foo.m file one has to enter
mfile2sci <path>/foo.m
where stands for the path of the directoty where foo.m is. The result is written in /foo.sci
Remove the ```` at the begining of each line, the conversion will proceed normally ?. However, don't expect to obtain a working .sci file as the m2sci converter is (to me) still an experimental tool !
I have a 3d array A, e.g. A=rand(N,N,K).
I need an array B s.t.
B(n,m) = norm(A(:,:,n)*A(:,:,m)' - A(:,:,m)*A(:,:,n)','fro')^2 for all indices n,m in 1:K.
Here's the looping code:
B = zeros(K,K);
for n=1:K
for m=1:K
B(n,m) = norm(A(:,:,n)*A(:,:,m)' - A(:,:,m)*A(:,:,n)','fro')^2;
end
end
I don't want to loop through 1:K.
I can create an array An_x_mt of size NK x NK s.t.
An_x_mt equals A(:,:,n)*A(:,:,m)' for all n,m in 1:K by
An_x_mt = Ar*Ac_t;
with
Ac_t=reshape(permute(A,[2 1 3]),size(A,1),[]);
Ar=Ac_t';
How do I create an array Am_x_nt also of size NK x NK s.t.
Am_x_nt equals A(:,:,m)*A(:,:,n)' for all n,m in 1:K
so that I could do
B = An_x_mt - Am_x_nt
B = reshape(B,N,N,[]);
B = reshape(squeeze(sum(sum(B.^2,1),2)),K,K);
Thx
For those who can't/won't use mmx and want to stick to pure Matlab code, here's how you could do it. mat2cell and cell2mat functions are your friends:
[N,~,nmat]=size(A);
Atc = reshape(permute(A,[2 1 3]),N,[]); % A', N x N*nmat
Ar = Atc'; % A, N*nmat x N
Anmt_2d = Ar*Atc; % An*Am'
Anmt_2d_cell = mat2cell(Anmt_2d,N*ones(nmat,1),N*ones(nmat,1));
Amnt_2d_cell = Anmt_2d_cell'; % ONLY products transposed, NOT their factors
Amnt_2d = cell2mat(Amnt_2d_cell); % Am*An'
Anm = Anmt_2d - Amnt_2d;
Anm = Anm.^2;
Anm_cell = mat2cell(Anm,N*ones(nmat,1),N*ones(nmat,1));
d = cellfun(#(c) sum(c(:)), Anm_cell); % squared Frobenius norm of each product; nmat x nmat
Alternatively, after computing Anmt_2d_cell and Amnt_2d_cell, you could convert them to 3d with the 3rd dimension encoding the (n,m) and (m,n) indices and then do the rest of the computations in 3d. You would need the permn() utility from here https://www.mathworks.com/matlabcentral/fileexchange/7147-permn-v-n-k
Anmt_3d = cat(3,Anmt_2d_cell);
Amnt_3d = cat(3,Amnt_2d_cell);
Anm_3d = Anmt_3d - Amnt_3d;
Anm_3d = Anm_3d.^2;
Anm = squeeze(sum(sum(Anm_3d,1),2));
d = zeros(nmat,nmat);
nm=permn(1:nmat, 2); % all permutations (n,m) with repeat, by-row order
d(sub2ind([nmat,nmat],nm(:,1),nm(:,2))) = Anm;
For some reason, the 2nd option (3D arrays) is twice faster.
Hopes this helps.
Let's say I have a matrix over GF(2) , i.e. a binary matrix. Now how do I go about computing the left null space of the given matrix over the finite field of 2?
Does MATLAB provide an in-built function for this?
I don't know of Matlab packages for linear algebra in finite space, but I programmed a simple
function that calculates LU-factorizations of matrices modulo a prime p (for example, 2):
function [L,D,U,rows,cols] = ModLU(A,p)
%
% LU-factorization of A, modulo p:
% A(rows,cols) - mod(L * diag(D)*U,p)
%
[m,n] = size(A);
% inverses in mod-p:
% mod(k*invp(k+1)) = 0 if k==0; 1 otherwise
invp = 2:p-2;
for i = 2:p-2; invp = mod(invp.*[2:p-2],p); end
invp = [0,1,invp,p-1];
% Initialize outputs:
L = eye(m); U = A;
rows = 1:m;
cols = 1:n;
% Sweep
for i = 1:m
% Pivoting
[row,col] = find(U(i:end,:));
if isempty(row); break; end
row = row(1)+i-1; col = col(1);
r = 1:m; r(i) = row; r(row) = i;
c = 1:n; c(i) = col; c(col) = i;
ri = rows(i); rows(i) = rows(row); rows(row)=ri;
ci = cols(i); cols(i) = cols(col); cols(col)=ci;
rinv = 1:m; rinv(r) = 1:m;
U = U(r,c); L=L(r,r);
% Gaussian elimination
L(i+1:end,i ) = mod(invp(U(i,i)+1) * U(i+1:end,i),p);
U(i+1:end,i:end) = mod(U(i+1:end,i:end) + (p-L(i+1:end,i)) * U(i,i:end),p);
end
% Factorize diagonal
D = zeros(m,1); D(1:min(m,n)) = diag(U);
U = mod(diag(invp(D+1)) * U,p );
Also, for an upper triangular matrix with ones on the diagonal, a function that calculates
the right-null space modulo p:
function N = NullPU(U,p)
% for an upper triangular matrix, calculate a base for the null space modulo p:
% U * N = 0
n = size(U,2);
rank = size(find(diag(U)),1);
A = U(1:rank,:);
for i=rank:-1:2
A(1:i-1,:) = mod(A(1:i-1,:) + (p-1) * A(1:i-1,i) * A(i,:),p);
end
N = [mod(p-A(:,rank+1:end),p); eye(n-rank)];
These functions are simply combined into a function that calculates the null space of
matrix A, modulo p:
function N = NullP(A,p)
% Calculate a basis for the null space of A, modulo p:
% mod(A*N,p) = 0
[L,D,U,rows,cols] = ModLU(A,p);
N = NullPU(U,p);
N(cols,:) = N;
Note that this function calculates a base for the right null space of A, modulo p. The left
null space is found using
N = NullP(A',p)';
This is a part of my code in Matlab. I tried to make it parallel but there is an error:
The variable gax in a parfor cannot be classified.
I know why the error occurs. because I should tell Matlab that v is an incresing vector which doesn't contain repeated elements. Could anyone help me to use this information to parallelize the code?
v=[1,3,6,8];
ggx=5.*ones(15,14);
gax=ones(15,14);
for m=v
if m > 1
parfor j=1:m-1
gax(j,m-1) = ggx(j,m-1);
end
end
if m<nn
parfor jo=m+1:15
gax(jo,m) = ggx(jo,m);
end
end
end
Optimizing a code should be closely related to its purpose, especially when you use parfor. The code you wrote in the question can be written in a much more efficient way, and definitely, do not need to be parallelized.
However, I understand that you tried to simplify the problem, just to get the idea of how to slice your variables, so here is a fixed version the can run with parfor. But this is surely not the way to write this code:
v = [1,3,6,8];
ggx = 5.*ones(15,14);
gax = ones(15,14);
nn = 5;
for m = v
if m > 1
temp_end = m-1;
temp = ggx(:,temp_end);
parfor ja = 1:temp_end
gax(ja,temp_end) = temp(ja);
end
end
if m < nn
temp = ggx(:,m);
parfor jo = m+1:15
gax(jo,m) = temp(jo);
end
end
end
A vectorized implementation will look like this:
v = [1,3,6,8];
ggx = 5.*ones(15,14);
gax = ones(15,14);
nn = 5;
m1 = v>1; % first condition with logical indexing
temp = v(m1)-1; % get the values from v
r = ones(1,sum(temp)); % generate a vector of indicies
r(cumsum(temp)) = -temp+1; % place the reseting locations
r = cumsum(r); % calculate the indecies
r(cumsum(temp)) = temp; % place the ending points
c = repelem(temp,temp); % create an indecies vector for the columns
inds1 = sub2ind(size(gax),r,c); % convert the indecies to linear
mnn = v<nn; % second condition with logical indexing
temp = v(mnn)+1; % get the values from v
r_max = size(gax,1); % get the height of gax
r_count = r_max-temp+1; % calculate no. of rows per value in v
r = ones(1,sum(r_count)); % generate a vector of indicies
r([1 r_count(1:end-1)+1]) = temp; % set the t indicies
r(cumsum(r_count)+1) = -(r_count-temp)+1; % place the reseting locations
r = cumsum(r(1:end-1)); % calculate the indecies
c = repelem(temp-1,r_count); % create an indecies vector for the columns
inds2 = sub2ind(size(gax),r,c); % convert the indecies to linear
gax([inds1 inds2]) = ggx([inds1 inds2]); % assgin the relevant values
This is indeed quite complicated, and not always necessary. A good thing to remember, though, is that nested for loop are much slower than a single loop, so in some cases (depend on the size of the output), this will may be the fastest solution:
for m = v
if m > 1
gax(1:m-1,m-1) = ggx(1:m-1,m-1);
end
if m<nn
gax(m+1:15,m) = ggx(m+1:15,m);
end
end
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?