I have a vector. I want to remove outliers. I got bin and no of values in that bin. I want to remove all points based on the number of elements in each bin.
Data:
d1 =[
360.471912914169
505.084636471948
514.39429429184
505.285068055647
536.321181755858
503.025854206322
534.304229816684
393.387035881967
396.497969729985
520.592172434431
421.284713703215
420.401106087984
537.05330275495
396.715779872694
514.39429429184
404.442344469518
476.846474245118
599.020867750031
429.163139144079
514.941744277933
445.426761656729
531.013596812737
374.977332648255
364.660115724218
538.306752697753
519.042387479096
1412.54699036882
405.571202133485
516.606049132218
2289.49623498271
378.228766753667
504.730621222846
358.715764917016
462.339366699398
512.429858614816
394.778786157514
366
498.760463549388
366.552861126468
355.37022947906
358.308526273099
376.745272034036
366.934599077274
536.0901883079
483.01740134285
508.975480745389
365.629593988233
536.368800360349
557.024236456548
366.776498701866
501.007025898839
330.686029339009
508.395475983019
429.563732174866
2224.68806802212
534.655786464525
518.711297351426
534.304229816684
514.941744277933
420.32368479542
367.129404978681
525.626188464768
388.329756778952
1251.30895065927
525.626188464768
412.313764019587
513.697381733643
506.675438520558
1517.71183364959
550.276294237722
543.359917550053
500.639590923451
395.129864728041];
Histogram computation:
[nelements,centers] = hist(d1);
nelements=55 13 0 0 1 1 1 0 0 2
I want to remove all points apearing less than 5 (in nelements). It means only first 2 elements in nelements( 55, 13 ) remains.
Is there any function in matlab.
You can do it along these lines:
threshold = 5;
bin_halfwidth = (centers(2)-centers(1))/2;
keep = ~any(abs(bsxfun(#minus, d1, centers(nelements<threshold))) < bin_halfwidth , 2);
d1_keep = d1(keep);
Does this do what you want?
binwidth = centers(2)-centers(1);
centersOfRemainingBins = centers(nelements>5);
remainingvals = false(length(d1),1);
for ii = 1:length(centersOfRemainingBins )
remainingvals = remainingvals | (d1>centersOfRemainingBins (ii)-binwidth/2 & d1<centersOfRemainingBins (ii)+binwidth/2);
end
d_out = d1(remainingvals);
I don't know Matlab function for this problem, but I think, that function with follow code is what are you looking for:
sizeData = size(data);
function filter_hist = filter_hist(data, binCountRemove)
if or(max(sizeData) == 0, binCountRemove < 1)
disp('Error input!');
filter_hist = [];
return;
end
[n, c] = hist(data);
sizeN = size(n);
intervalSize = c(2) - c(1);
if sizeData(1) > sizeData(2)
temp = transpose(data);
else
temp = data;
end
for i = 1:1:max(sizeN)
if n(i) < binCountRemove
a = c(i) - intervalSize / 2;
b = c(i) + intervalSize / 2;
sizeTemp = size(temp);
removeInds = [];
k = 0;
for j = 1:1:max(sizeTemp)
if and(temp(j) > a, less_equal(temp(j), b) == 1)
k = k + 1;
removeInds(k) = j;
end
end
temp(removeInds) = [];
end
end
filter_hist = transpose(temp);
%Determines when 'a' less or equal to 'b' by accuracy
function less_equal = less_equal(a, b)
delta = 10^-6; %Accuracy
if a < b
less_equal = 1;
return;
end
if abs(b - a) < delta
less_equal = 1;
return;
end
less_equal = 0;
You can do something like this
nelements=nelements((nelements >5))
Related
I have two Xval(Predicted values) and Sv(validation test) matrices, one with the classifier output data and the other with the validation data for the same samples. Each column represents the predicted value, eg [0 0 1 0 0 0 0 0 0 0] represents digit 3 (1 in the digit that is). I would like to know if it is possible to calculate the confusion matrix in a vectorized way or with a built in function, the sizes of both matrices are 12000x10. The code who generates both matrices are this
load data;
load test;
[N, m] = size(X);
X = [ones(N, 1) X];
[Nt, mt] = size(Xt);
Xt = [ones(Nt, 1) Xt];
new_order = randperm(N);
X = X(new_order,: );
S = S(new_order,: );
part = 0.8;
Xtr = X(1: (part * N),: );
Xv = X((part * N + 1): N,: );
Str = S(1: (part * N),: );
Sv = S((part * N + 1): N,: );
v_c = [];
v_tx_acerto = [];
tx_acerto_max = 0;
c = 250;
w = (X'*X+c*eye(m+1))\X' * S;
Xval = Xv*w;
for i=1:12000
aux = Xval(i,:);
aux(aux == max(aux)) = 1;
aux(aux<1) = 0;
Xval(i,:) = aux;
end
There are build-in functions confusionmat or plotconfusion. But if you want to have full control, you can just write a simple function yourself, e.g:
function [CMat_rel,CMat_abs] = ConfusionMatrix(Cprd,Cact)
Cprd_uq = unique(Cprd);
Cact_uq = unique(Cact);
NumPrd = length(Cprd_uq);
NumAct = length(Cact_uq);
% assert(NumPrd == NumAct)
% allocate memory
CMat_abs = NaN(NumPrd,NumAct);
CMat_rel = NaN(NumPrd,NumAct);
for j = 1:NumAct
lgAct = Cact == Cact_uq(j);
SumAct = sum(lgAct);
for i = 1:NumAct
lgPrd = Cprd == Cact_uq(i);
Num = sum( lgPrd(lgAct) == true );
CMat_abs(i,j) = Num;
CMat_rel(i,j) = Num/SumAct;
end
end
end
Basically I have a code where it produces a plot of all possible permutations between Cost and Reliability. There's a total of 864 data points split up between 8 rows. Five of the rows have 2 options and three of them 3 options.
Given here is a copy of my code. I'm trying to have the permutations of 'Other Cameras' and 'Depth & Structure Testing' have a different color with the other six possibilities. I tried using the 'gscatter' command but didn't have much luck with it.
I believe I need to have the scatter command in the if/else statements themselves, although I'm not too sure what to plot in the 'X' and 'Y' for the 'scatter' command. Currently my code is set up for plotting all the data in one color. I deleted my code with the 'gscatter' because I got many errors and when I tried to fix them the plot ultimately didn't work as planned.
% Pareto_Eval
baseline_cost = 45;
nrows = 8;
%Initialize Variables
for aa = 1:nrows
cost_delta(aa) = 0;
reliability(aa) = 1;
end
icount = 1;
%Propulsion
for row1 = 1:2
if row1 == 1
cost_delta(1)= -7;
reliability(1) = 0.995;
elseif row1==2
cost_delta(1)=0;
reliability(1)=.99;
end
%Entry Mode
for row2 = 1:2
if row2 == 1
cost_delta(2) = -3;
reliability(2) = .99;
else
cost_delta(2) = 0;
reliability(2) = .98;
end
%Landing Method
for row3 = 1:3
if row3 == 1 %if needs declaration
cost_delta(3)= 0;
reliability(3) = .99;
elseif row3 == 2 %elseif needs declaration
cost_delta(3) = 4;
reliability(3) = .995;
else %else does not need declaration
cost_delta(3) = -2;
reliability(3) = .95;
end
%Lander Type
for row4 = 1:3
if row4 == 1
cost_delta(4)= 10;
reliability(4) = .99;
elseif row4 == 2
cost_delta(4) = 0;
reliability(4) = .99;
else
cost_delta(4) = 15;
reliability(4) = .95;
end
%Rover Type
for row5 = 1:2
if row5 == 1
cost_delta(5)= -2;
reliability(5) = .98;
else
cost_delta(5) = 0;
reliability(5) = .975;
end
%Power Source
for row6 = 1:2
if row6 == 1
cost_delta(6) = -3;
reliability(6) = .95;
else
cost_delta(6) = 0;
reliability(6) = .995;
end
%Depth & Structure Testing
for row7 = 1:2
if row7 == 1
cost_delta(7) = 0;
reliability(7) = .99;
else
cost_delta(7) = 2;
reliability(7) = .85;
end
%Other Cameras
for row8 = 1:3
if row8 == 1
cost_delta(8)= -1;
reliability(8) = .99;
elseif row8 == 2
cost_delta(8) = -1;
reliability(8) = .99;
else
cost_delta(8) = 0;
reliability(8) = .9801;
end
cost_delta_total = 0;
reliability_product = 1;
for bb=1:nrows
cost_delta_total = cost_delta_total + cost_delta(bb);
reliability_product = reliability_product*reliability(bb);
end
total_cost(icount) = baseline_cost + cost_delta_total;
total_reliability(icount) = reliability_product;
icount = icount + 1;
end; end; end; %Rows 1,2,3
end; end; end; %Rows 4,5,6
end; end; %Rows 7,8
%Plot the Pareto Evaluation
fignum=1;
figure(fignum)
sz = 5;
scatter(total_reliability, total_cost, sz, 'blue')
xlabel('Reliability')
ylabel('Cost')
title('Pareto Plot')
Any help is appreciated. I don't have a lot of experience with Matlab and I've tried looking around for help but nothing really worked.
Here is a sample code to make questions easier I created:
% Pareto_Eval
baseline_cost = 55;
nrows = 3;
%Initialize Variables
for aa = 1:nrows
cost_delta(aa) = 0;
reliability(aa) = 1;
end
icount = 1;
%Group 1
for row1 = 1:2
if row1 == 1
cost_delta(1)= 5;
reliability(1) = 0.999;
elseif row1==2
cost_delta(1) = 0;
reliability(1) = .995;
end
%Group 2
for row2 = 1:2
if row2 == 1
cost_delta(2) = 0;
reliability(2) = .98;
else
cost_delta(2) = -2;
reliability(2) = .95;
end
%Group 3
for row3 = 1:2
if row3 == 1
cost_delta(3) = 3;
reliability(3) = .997;
else
cost_delta(3) = 0;
reliability(3) = .96;
end
%initializing each row
cost_delta_total = 0;
reliability_product = 1;
for bb = 1:nrows
cost_delta_total = cost_delta_total + cost_delta(bb);
reliability_product = reliability_product*reliability(bb);
end
total_cost(icount) = baseline_cost + cost_delta_total;
total_reliability(icount) = reliability_product;
icount = icount + 1;
end
end
end
fignum=1;
figure(fignum)
sz = 25;
scatter(total_reliability, total_cost, sz)
xlabel('Reliability')
ylabel('Cost')
title('Pareto Plot')
Basically I need to make a plot in each if-loop, but I'm not sure how to do it and have them all on the same plot
sounds like an interesting project! Not sure if I understood your intended plots correctly, but hopefully the code below gets you a bit closer to what you are looking for.
I've started off with a rather deep mess of nested for loops (as you did) but kept it more concise bybuilding a permutations matrix.
counter = 0;
for propulsion_options = 1:2
for entry_mode = 1:2
for landing_method = 1:3
for lander_type = 1:3
for rover_type = 1:2
for power_source = 1:2
for depth_testing = 1:2
for other_cameras = 1:3
counter = counter +1
permutations(counter,:) = [...
propulsion_options,...
entry_mode,...
landing_method,...
lander_type,...
rover_type,...
power_source,...
depth_testing,...
other_cameras];
end
end
end
end
end
end
end
end
This way I kept the actual scoring out of the loops, and perhaps easier to tweak the values. I initialised the cost and reliabiltiy arrays to be the same size as the permutations array:
cost_delta = zeros(size(permutations));
reliability = zeros(size(permutations));
Then for each metric, I searched the permutations array for all occurances of each possible value and assigned the appropriate score:
%propulsion
propertyNo = 1;
cost_delta(find(permutations(:,propertyNo)==1),propertyNo) = -7;
cost_delta(find(permutations(:,propertyNo)==2),propertyNo) = 0;
reliability(find(permutations(:,propertyNo)==1),propertyNo) = 0.995;
reliability(find(permutations(:,propertyNo)==2),propertyNo) = 0.99;
%entry_mode (2)
propertyNo = 2;
cost_delta(find(permutations(:,propertyNo)==1),propertyNo) = -3;
cost_delta(find(permutations(:,propertyNo)==2),propertyNo) = 0;
reliability(find(permutations(:,propertyNo)==1),propertyNo) = 0.99;
reliability(find(permutations(:,propertyNo)==2),propertyNo) = 0.98;
%landing_method (3)
propertyNo = 3;
cost_delta(find(permutations(:,propertyNo)==1),propertyNo) = 0;
cost_delta(find(permutations(:,propertyNo)==2),propertyNo) = 4;
cost_delta(find(permutations(:,propertyNo)==3),propertyNo) = -2;
reliability(find(permutations(:,propertyNo)==1),propertyNo) = 0.99;
reliability(find(permutations(:,propertyNo)==2),propertyNo) = 0.995;
reliability(find(permutations(:,propertyNo)==3),propertyNo) = 0.95;
%lander_type (3)
propertyNo = 4;
cost_delta(find(permutations(:,propertyNo)==1),propertyNo) = 10;
cost_delta(find(permutations(:,propertyNo)==2),propertyNo) = 0;
cost_delta(find(permutations(:,propertyNo)==3),propertyNo) = 15;
reliability(find(permutations(:,propertyNo)==1),propertyNo) = 0.99;
reliability(find(permutations(:,propertyNo)==2),propertyNo) = 0.99;
reliability(find(permutations(:,propertyNo)==3),propertyNo) = 0.95;
%rover_type (2)
propertyNo = 5;
cost_delta(find(permutations(:,propertyNo)==1),propertyNo) = -2;
cost_delta(find(permutations(:,propertyNo)==2),propertyNo) = 0;
reliability(find(permutations(:,propertyNo)==1),propertyNo) = 0.98;
reliability(find(permutations(:,propertyNo)==2),propertyNo) = 0.975;
%power_source (2)
propertyNo = 6;
cost_delta(find(permutations(:,propertyNo)==1),propertyNo) = -3;
cost_delta(find(permutations(:,propertyNo)==2),propertyNo) = 0;
reliability(find(permutations(:,propertyNo)==1),propertyNo) = 0.95;
reliability(find(permutations(:,propertyNo)==2),propertyNo) = 0.995;
%depth_testing (2)
propertyNo = 7;
cost_delta(find(permutations(:,propertyNo)==1),propertyNo) = 0;
cost_delta(find(permutations(:,propertyNo)==2),propertyNo) = 2;
reliability(find(permutations(:,propertyNo)==1),propertyNo) = 0.99;
reliability(find(permutations(:,propertyNo)==2),propertyNo) = 0.85;
%other_cameras (3)
propertyNo = 8;
cost_delta(find(permutations(:,propertyNo)==1),propertyNo) = -1;
cost_delta(find(permutations(:,propertyNo)==2),propertyNo) = -1;
cost_delta(find(permutations(:,propertyNo)==3),propertyNo) = 0;
reliability(find(permutations(:,propertyNo)==1),propertyNo) = 0.99;
reliability(find(permutations(:,propertyNo)==2),propertyNo) = 0.99;
reliability(find(permutations(:,propertyNo)==3),propertyNo) = 0.9801;
Then each permutation can have a total cost / reliabiltiy score by summing and takign the product along the second dimension:
cost_delta_total = sum(cost_delta,2);
reliability_product = prod(reliability,2);
Finally, you can plot all points (as per your original):
%Plot the Pareto Evaluation
fignum=1;
figure(fignum)
sz = 5;
scatter(reliability_product, cost_delta_total, sz, 'b')
xlabel('Reliability')
ylabel('Cost')
title('Pareto Plot')
or you can create an index into the permutations by searching for specific property values and plot these different colours (actually this bit answers your most specific question of how to plot two things on the same axes - you just need the hold on; command):
propertyNo = 7;
indexDepth1 = find(permutations(:,propertyNo)==1);
indexDepth2 = find(permutations(:,propertyNo)==2);
fignum=2;
figure(fignum)
sz = 5;
scatter(reliability_product(indexDepth1), cost_delta_total(indexDepth1), sz, 'k');
hold on;
scatter(reliability_product(indexDepth2), cost_delta_total(indexDepth2), sz, 'b');
xlabel('Reliability')
ylabel('Cost')
title('Pareto Plot')
legend('Depth & Structure Test 1','Depth & Structure Test 2')
propertyNo = 8;
indexCam1 = find(permutations(:,propertyNo)==1);
indexCam2 = find(permutations(:,propertyNo)==2);
indexCam3 = find(permutations(:,propertyNo)==3);
fignum=3;
figure(fignum)
sz = 5;
scatter(reliability_product(indexCam1), cost_delta_total(indexCam1), sz, 'k');
hold on;
scatter(reliability_product(indexCam2), cost_delta_total(indexCam2), sz, 'b');
scatter(reliability_product(indexCam3), cost_delta_total(indexCam3), sz, 'g');
xlabel('Reliability')
ylabel('Cost')
title('Pareto Plot')
legend('Other Camera 1','Other Camera 2','Other Camera 3')
Good luck with the mission! When is launch day?
I would like to divide an image into 8 by 6 blocks and then from each block would like to get the average of red, green and blue values then store the average values from each block into an array. Say that if I have image divided into 4 blocks the result array would be:
A = [average_red, average_green, average_blue,average_red, ...
average_green, average_blue,average_red, average_green, ...
average_blue,average_red, average_green, average_blue,...
average_red, average_green, average_blue,]
The loop I have created looks very complicated, takes a long time to run and I'm not even sure if it's working properly or not as I have no clue how to check. Is there any simpler way to implement this.
Here is the loop:
[rows, columns, ~] = size(img);
[rows, columns, ~] = size(img);
rBlock = 6;
cBlock = 8;
NumberOfBlocks = rBlock * cBlock;
bRow = ceil(rows/rBlock);
bCol = ceil(columns/cBlock);
row = bRow;
col = bCol;
r = zeros(row*col,1);
g = zeros(row*col,1);
b = zeros(row*col,1);
n = 1;
cl = 1;
rw = 1;
for x = 1:NumberOfBlocks
for i = cl : col
for j = rw : row
% some code
end
end
%some code
if i == columns && j ~= rows
cl = 1;
rw = j - (bRow -1);
col = (col - col) + bCol;
row = row + bRaw;
elseif a == columns && c == rows
display('done');
else
cl = i + 1;
rw = j - (bRow -1);
col = col + col;
row = row + row;
end
end
Because there are only 48 block, you may use simple for loop iterating blocks. (I think it's going to be fast enough).
Here is my code:
%Build test image
img = double(imresize(imread('peppers.png'), [200, 300]));
[rows, columns, ~] = size(img);
rBlock = 6;
cBlock = 8;
NumberOfBlocks = rBlock * cBlock;
bRow = ceil(rows/rBlock);
bCol = ceil(columns/cBlock);
idx = 1;
A = zeros(1, rBlock*cBlock*3);
for y = 0:rBlock-1
for x = 0:cBlock-1
%Block (y,x) boundaries: (x0,y0) to (x1,y1)
x0 = x*bCol+1;
y0 = y*bRow+1;
x1 = min(x0+bCol-1, columns); %Limit x1 to columns
y1 = min(y0+bRow-1, rows); %Limit y1 to rows
redMean = mean2(img(y0:y1, x0:x1, 1)); %Mean of red pixel in block (y,x)
greenMean = mean2(img(y0:y1, x0:x1, 2)); %Mean of green pixel in block (y,x)
blueMean = mean2(img(y0:y1, x0:x1, 3)); %Mean of blue pixel in block (y,x)
%Fill 3 elements of array A.
A(idx) = redMean;
A(idx+1) = greenMean;
A(idx+2) = blueMean;
%Advance index by 3.
idx = idx + 3;
end
end
I have written a small Matlab funcion which takes an image in RGB and converts it to HSV according to the conversion formulas found here.
The problem is that when I apply this to a color spectrum there is a cut in the spectrum and some values are wrong, see images (to make the comparison easier I have used the internal hsv2rgb() function to convert back to RGB. This does not happen with Matlabs own function rgb2hsv() but I can not find what I have done wrong.
This is my function
function [ I_HSV ] = RGB2HSV( I_RGB )
%UNTITLED3 Summary of this function goes here
% Detailed explanation goes here
[MAX, ind] = max(I_RGB,[],3);
if max(max(MAX)) > 1
I_r = I_RGB(:,:,1)/255;
I_g = I_RGB(:,:,2)/255;
I_b = I_RGB(:,:,3)/255;
MAX = max(cat(3,I_r, I_g, I_b),[],3);
else
I_r = I_RGB(:,:,1);
I_g = I_RGB(:,:,2);
I_b = I_RGB(:,:,3);
end
MIN = min(cat(3,I_r, I_g, I_b),[],3);
d = MAX - MIN;
I_V = MAX;
I_S = (MAX - MIN) ./ MAX;
I_H = zeros(size(I_V));
a = 1/6*mod(((I_g - I_b) ./ d),1);
b = 1/6*(I_b - I_r) ./ d + 1/3;
c = 1/6*(I_r - I_g) ./ d + 2/3;
H = cat(3, a, b, c);
for m=1:size(H,1);
for n=1:size(H,2);
if d(m,n) == 0
I_H(m,n) = 0;
else
I_H(m,n) = H(m,n,ind(m,n));
end
end
end
I_HSV = cat(3,I_H,I_S,I_V);
end
Original spectrum
Converted spectrum
The error was in my simplification of the calculations of a, b, and c. Changing it to the following solved the problem.
function [ I_HSV ] = RGB2HSV( I_RGB )
%UNTITLED3 Summary of this function goes here
% Detailed explanation goes here
[MAX, ind] = max(I_RGB,[],3);
if max(max(MAX)) > 1
I_r = I_RGB(:,:,1)/255;
I_g = I_RGB(:,:,2)/255;
I_b = I_RGB(:,:,3)/255;
MAX = max(cat(3,I_r, I_g, I_b),[],3);
else
I_r = I_RGB(:,:,1);
I_g = I_RGB(:,:,2);
I_b = I_RGB(:,:,3);
end
MIN = min(cat(3,I_r, I_g, I_b),[],3);
D = MAX - MIN;
I_V = MAX;
I_S = D ./ MAX;
I_H = zeros(size(I_V));
a = 1/6*mod(((I_g - I_b) ./ D),6);
b = 1/6*((I_b - I_r) ./ D + 2);
c = 1/6*((I_r - I_g) ./ D + 4);
H = cat(3, a, b, c);
for m=1:size(H,1);
for n=1:size(H,2);
if D(m,n) == 0
I_H(m,n) = 0;
else
I_H(m,n) = H(m,n,ind(m,n));
end
if MAX(m,n) == 0
S(m,n) = 0;
end
end
end
I_HSV = cat(3,I_H,I_S,I_V);
end
I'm trying to vectorize the 2 inner nested for loops, but I can't come up with a way to do this. The FS1 and FS2 functions have been written to accept argument for N_theta and N_e, which is what the loops are iterating over
%% generate regions
for raw_r=1:visual_field_width
for raw_c=1:visual_field_width
r = raw_r - center_r;
c = raw_c - center_c;
% convert (r,c) to polar: (eccentricity, angle)
e = sqrt(r^2+c^2)*deg_per_pixel;
a = mod(atan2(r,c),2*pi);
for nt=1:N_theta
for ne=1:N_e
regions(raw_r, raw_c, nt, ne) = ...
FS_1(nt-1,a,N_theta) * ...
FS_2(ne-1,e,N_e,e0_in_deg, e_max);
end
end
end
end
Ideally, I could replace the two inner nested for loops by:
regions(raw_r,raw_c,:,:) = FS_1(:,a,N_theta) * FS_2(:,N_e,e0_in_deg,e_max);
But this isn't possible. Maybe I'm missing an easy fix or vectorization technique? e0_in_deg and e_max are parameters.
The FS_1 function is
function h = FS_1(n,theta,N,t)
if nargin==2
N = 9;
t=1/2;
elseif nargin==3
t=1/2;
end
w = (2*pi)/N;
theta = theta + w/4;
if n==0 && theta>(3/2)*pi
theta = theta - 2*pi;
end
h = FS_f((theta - (w*n + 0.5*w*(1-t)))/w);
the FS_2 function is
function g = FS_gne(n,e,N,e0, e_max)
if nargin==2
N = 10;
e0 = .5;
elseif nargin==3
e0 = .5;
end
w = (log(e_max) - log(e0))/N;
g = FS_f((log(e)-log(e0)-w*(n+1))/w);
and the FS_f function is
function f = FS_f(x, t)
if nargin<2
t = 0.5;
end
f = zeros(size(x));
% case 1
idx = x>-(1+t)/2 & x<=(t-1)/2;
f(idx) = (cos(0.5*pi*((x(idx)-(t-1)/2)/t))).^2;
% case 2
idx = x>(t-1)/2 & x<=(1-t)/2;
f(idx) = 1;
% case 3
idx = x>(1-t)/2 & x<=(1+t)/2;
f(idx) = -(cos(0.5*pi*((x(idx)-(1+t)/2)/t))).^2+1;
I had to assume values for the constants, and then used ndgrid to find the possible configurations and sub2ind to get the indices. Doing this I removed all loops. Let me know if this produced the correct values.
function RunningFunction
%% generate regions
visual_field_width = 10;
center_r = 2;
center_c = 3;
deg_per_pixel = 17;
N_theta = 2;
N_e = 5;
e0_in_deg = 35;
e_max = 17;
[raw_r, raw_c, nt, ne] = ndgrid(1:visual_field_width, 1:visual_field_width, 1:N_theta, 1:N_e);
ind = sub2ind(size(raw_r), raw_r, raw_c, nt, ne);
r = raw_r - center_r;
c = raw_c - center_c;
% convert (r,c) to polar: (eccentricity, angle)
e = sqrt(r.^2+c.^2)*deg_per_pixel;
a = mod(atan2(r,c),2*pi);
regions(ind) = ...
FS_1(nt-1,a,N_theta) .* ...
FS_2(ne-1,e,N_e,e0_in_deg, e_max);
regions = reshape(regions, size(raw_r));
end
function h = FS_1(n,theta,N,t)
if nargin==2
N = 9;
t=1/2;
elseif nargin==3
t=1/2;
end
w = (2*pi)./N;
theta = theta + w/4;
theta(n==0 & theta>(3/2)*pi) = theta(n==0 & theta>(3/2)*pi) - 2*pi;
h = FS_f((theta - (w*n + 0.5*w*(1-t)))/w);
end
function g = FS_2(n,e,N,e0, e_max)
if nargin==2
N = 10;
e0 = .5;
elseif nargin==3
e0 = .5;
end
w = (log(e_max) - log(e0))/N;
g = FS_f((log(e)-log(e0)-w*(n+1))/w);
end
function f = FS_f(x, t)
if nargin<2
t = 0.5;
end
f = zeros(size(x));
% case 1
idx = x>-(1+t)/2 & x<=(t-1)/2;
f(idx) = (cos(0.5*pi*((x(idx)-(t-1)/2)/t))).^2;
% case 2
idx = x>(t-1)/2 & x<=(1-t)/2;
f(idx) = 1;
% case 3
idx = x>(1-t)/2 & x<=(1+t)/2;
f(idx) = -(cos(0.5*pi*((x(idx)-(1+t)/2)/t))).^2+1;
end