Last plot in subplot becomes over-sized - matlab

I am using subplot function of MATLAB. Surprisingly the last plot in each subplot set becomes over-sized. Can anybody help me to resolve this issue? I have experimented with the parameters a little, but no luck. I am not able to post the plot figure.
function plotFluxVariabilityByGene(cRxn,KeggID,geneName)
load iJO1366; % Load the model iJO1366
%Find 'Gene' associated reactions from 'model'
reactions = rxnNamesFromKeggID(model,KeggID);
nCheck = 0; % Initialize counter
% Determine initial subplot dimensions
[R C setSize] = subplotSize(numel(reactions));
for n = 1 : numel(reactions)
% Get the name of nth reaction
rxn = reactions{n};
% Define the array for control reaction fluxes
cRxnArray = getCrxnArray(model,cRxn);
% Initialize storage for lower and upper limit-values
L = []; U = []; Avg = [];
% Get the fluxVariability values
for i = 1 : numel(cRxnArray)
modelMod = changeRxnBounds(model,cRxn,cRxnArray(i),'b');
[L(i) U(i)] = fluxVariability(modelMod,100,'max',{rxn});
Avg(i) = (L(i) + U(i))/2;
%fprintf('mthfcFlux = %f; Li = %f; Ui = %f\n',array(i),L(i),U(i));
end
% adjust the subplot number
nCheck = nCheck + 1;
% Determine the range of n to be saved in one file
if nCheck == 1
start = n;
elseif nCheck == setSize;
stop = n;
end
subplot(R,C,nCheck)
plot(cRxnArray,L,'-r','LineWidth',1); hold on;
plot(cRxnArray,L,'^r','MarkerSize',3,'LineWidth',2);
plot(cRxnArray,U,'-.b','LineWidth',1);
plot(cRxnArray,U,'^b','MarkerSize',2,'LineWidth',2);
plot(cRxnArray,Avg,'-','Color',[0.45,0.45,0.45],'LineWidth',2.5);
% Label X and Y axes
%xlabel([cRxn ' Flux']);
%ylabel(['fluxVariability ' char(rxn)]);
xlabel('Flux');
ylabel('fluxVariability');
hold off;
% Adjust X and Y axes limits
%xmn = min(cRxnArray) - ((max(cRxnArray) - min(cRxnArray))*0.05);
%xmx = max(cRxnArray) + ((max(cRxnArray) - min(cRxnArray))*0.05);
%ymn = min([U L]) - ((max([U L]) - min([U L]))*0.05);
%ymx = max([U L]) + ((max([U L]) - min([U L]))*0.05);
%if xmn ~= xmx
% xlim([xmn xmx]);
%end
%if ymn ~= ymx
% ylim([ymn ymx]);
%end
% Print which reactions are done
fprintf('\n......done for %s',char(rxn));
% If 'setSize' subplots are done then save the set in a file
if nCheck == setSize
saveas(gcf,['TEST/' cRxn 'flux-Vs-' geneName '_fluxVariability' num2str(start) '-' num2str(stop) '.fig']);
saveas(gcf,['TEST/' cRxn 'flux-Vs-' geneName '_fluxVariability' num2str(start) '-' num2str(stop) '.eps']); close(gcf);
% Determine initial subplot dimensions
[R C setSize] = subplotSize(numel(reactions)-n);
% Return nCheck to zero;
nCheck = 0;
end
end
% If nCheck is not equal to 16 then there are subplot that is not saved
% inside the for loop. Let's save it here.
if nCheck ~= setSize
stop = n;
saveas(gcf,['TEST/' cRxn 'flux-Vs-' geneName '_fluxVariability' num2str(start) '-' num2str(stop) '.fig']);
saveas(gcf,['TEST/' cRxn 'flux-Vs-' geneName '_fluxVariability' num2str(start) '-' num2str(stop) '.eps']); close(gcf);
end
fprintf('\nAll done\n');
end
%####################################################
%# Other functions ##
%####################################################
function rxnNames = rxnNamesFromKeggID(model,KeggID)
% Find 'Gene' associated reactions from 'model'
associatedRxns = findRxnsFromGenes(model,KeggID);
% Extract the reaction details from the structure to a cell
rxnDetails = eval(sprintf('associatedRxns.%s',KeggID));
% Extract only the reaction names from the cell
rxnNames = rxnDetails(:,1);
end
%####################################################
function cRxnArray = getCrxnArray(model,cRxn)
% Define the solver
changeCobraSolver('glpk');
% Find solution for the model
sol = optimizeCbModel(model);
% Change the objective of the default model to 'cRxn'
tmpModel = changeObjective(model,cRxn);
% Find slution for the changed model. This gives the maximum and
% minimum possible flux through the reaction 'cRxn' when the model is
% still viable
%solMax = optimizeCbModel(tmpModel,'max');
solMin = optimizeCbModel(tmpModel,'min');
% Create an array of 20 euqally spaced flux values between 'solMin' and
% 'sol.x'
%array = linspace(solMin.f,solMax.f,10);
cRxnArray = linspace(solMin.f,sol.x(findRxnIDs(model,cRxn)),20);
end
%####################################################
function [R C setSize] = subplotSize(remainingPlots)
% Sets number of columns and rows to 3 if total subplot >= 9
if remainingPlots > 7
R = 3; C = 3; setSize = 9;
elseif remainingPlots < 7
R = 2; C = 3; setSize = 6;
elseif remainingPlots < 5
R = 2; C = 2; setSize = 4;
elseif remainingPlots < 4
R = 1; C = 3; setSize = 3;
elseif remainingPlots < 3
R = 1; C = 2; setSize = 2;
end
end
%####################################################
My subplot looks like this:

I suspect its because you are calling subplotSize a second time inside your loop. This could be changing your R and C variables.
I would advise to check the R and C variables at the subplot command on each loop.

Related

Use a variable outside the function in matlab

I've written the following function:
% This function plots the contours of likelihood values on the scatter plot of a 2 dimensional data.
function [xgrid,ygrid,Z,xy_matrix] = biVariateContourPlotsGMMCopula(givenData,gmmObject,~,numMeshPoints,x_dim,y_dim)
%INPUT: givenData (MxN, M=number of points, N=Dimension)
% : plo = binary variable (1 plot contour plot, 0 do not plot)
%OUTPUT: xgrid,ygrid,Z ( Z contains the likelihood values of the points defined by xgrid and ygrid)
%load general_info;
d = 2;
if nargin < 5
x_dim = 1;
y_dim = 2;
end
if x_dim == y_dim
hist(givenData(:,x_dim),10);
return;
end
numMeshPoints = min(numMeshPoints,256);
givenData = givenData(:,[x_dim y_dim]);
alpha = gmmObject.alpha;
mu = gmmObject.mu(:,[x_dim y_dim]);
sigma = gmmObject.sigma([x_dim y_dim],[x_dim y_dim],:) + 0.005*repmat(eye(d),[1 1 numel(alpha)]);
gmmObject = gmdistribution(mu,sigma,alpha);
bin_num = 256;
for j = 1:2
l_limit = min(gmmObject.mu(:,j))-3*(max(gmmObject.Sigma(j,j,:))^0.5);
u_limit = max(gmmObject.mu(:,j))+3*(max(gmmObject.Sigma(j,j,:))^0.5);
xmesh_inverse_space{j} = (l_limit:(u_limit-l_limit)/(bin_num-1):u_limit);
end
%if isempty(xmesh)||isempty(pdensity)||isempty(cdensity)
% Following for loop does the non-parameteric estimation of marginal % densities if not provided
for i = 1:d
currentVar = givenData(:,i);
[~,pdensity{i},xmesh{i}]=kde(currentVar,numMeshPoints);
pdensity{i}(pdensity{i}<0) = 0;
cdensity{i} = cumsum(pdensity{i});
cdensity{i} = (cdensity{i}-min(cdensity{i}))/(max(cdensity{i})-min(cdensity{i})); % scaling the cdensity value to be between [0 1]
end
[xgrid,ygrid] = meshgrid(xmesh{1}(2:end-1),xmesh{2}(2:end-1));
for k = 1:d
marginalLogLikelihood_grid{k} = log(pdensity{k}(2:end-1)+eps);
marginalCDFValues_grid{k} = cdensity{k}(2:end-1);
end
[marg1,marg2] = meshgrid(marginalLogLikelihood_grid{1},marginalLogLikelihood_grid{2});
[xg,yg] = meshgrid(marginalCDFValues_grid{1},marginalCDFValues_grid{2});
inputMatrix = [reshape(xg,numel(xg),1) reshape(yg,numel(yg),1)];
clear xg yg;
copulaLogLikelihoodVals = gmmCopulaPDF(inputMatrix,gmmObject,xmesh_inverse_space);
Z = reshape(copulaLogLikelihoodVals,size(marg1,1),size(marg1,2));
Z = Z+marg1+marg2;
Z = exp(Z);
% Getting the likelihood value from the log-likelihood
plot(givenData(:,1),givenData(:,2),'b.','MarkerSize',5);hold
[~,h] = contour(xgrid,ygrid,Z,[4e-6,4e-6]);
% Extract the (x, y) coordinates of the contour and concatenate them along the first dimension
xy_matrix = [];
for i = 1:length(h)
xy = get(h(i), 'XData');
x = xy(1, :);
y = xy(2, :);
xy_matrix = [xy_matrix, [x; y]];
end
% Print the concatenated matrix
disp(xy_matrix);
%title_string = ['GMCM fit (Log-Likelihood = ',num2str(logLikelihoodVal), ')'];
%title(title_string,'FontSize',12,'FontWeight','demi');
axis tight
however xy_matrix is not shown on the workspace.
How do I return the variable xy_matrix so that I can use it in another function?
Function call is inside a for loop as in below:
for i = 1:d
for j = 1:d
subplot(d,d,count); count = count+1;
[xgrid,ygrid,Z,xy_matrix] = biVariateContourPlotsGMMCopula(power_curve_reference_build_T2,gmcObject_bestfit,0,256,i,j);
end
end
So, when I'm including xy_matrix as a params in the function call, it generates the following error:
Have I missed anything here?
When you're calling the function with i==j==1 as parameters x_dim and y_dim, the function ends in the following if:
if x_dim == y_dim
hist(givenData(:,x_dim),10);
return;
end
The return values aren't defined at that point. If you define them in the beginning of the function, you won't get the error message.
function [xgrid,ygrid,Z,xy_matrix] = biVariateContourPlotsGMMCopula(givenData,gmmObject,~,numMeshPoints,x_dim,y_dim)
%INPUT: givenData (MxN, M=number of points, N=Dimension)
% : plo = binary variable (1 plot contour plot, 0 do not plot)
%OUTPUT: xgrid,ygrid,Z ( Z contains the likelihood values of the points defined by xgrid and ygrid)
%load general_info;
xgrid=0;
ygrid=0;
Z=0;
xy_matrix=0;
d = 2;
if nargin < 5
x_dim = 1;
y_dim = 2;
end
Below is a suggestion of some changes of your function call. The return values are saved in cells so that you don't overwrite them in the next iteration. The function is also not called when i==j==x_dim==y_dim.
xgrids={};
ygrids={};
Zs={};
xy_matrices={};
for i = 1:d
for j = 1:d
if i~=j
subplot(d,d,count); count = count+1;
[xgrids{i,j},ygrids{i,j},Zs{i,j},xy_matrices{i,j}] = biVariateContourPlotsGMMCopula(power_curve_reference_build_T2,gmcObject_bestfit,0,256,i,j);
end
end
end

Berlekamp Massey Algorithm for BCH simplified binary version

I am trying to follow Lin, Costello's explanation of the simplified BM algorithm for the binary case in page 210 of chapter 6 with no success on finding the error locator polynomial.
I'm trying to implement it in MATLAB like this:
function [locator_polynom] = compute_error_locator(syndrome, t, m, field, alpha_powers)
%
% Initial conditions for the BM algorithm
polynom_length = 2*t;
syndrome = [syndrome; zeros(3, 1)];
% Delta matrix storing the powers of alpha in the corresponding place
delta_rho = uint32(zeros(polynom_length, 1)); delta_rho(1)=1;
delta_next = uint32(zeros(polynom_length, 1));
% Premilimnary values
n_max = uint32(2^m - 1);
% Initialize step mu = 1
delta_next(1) = 1; delta_next(2) = syndrome(1); % 1 + S1*X
% The discrepancy is stored in polynomial representation as uint32 numbers
value = gf_mul_elements(delta_next(2), syndrome(2), field, alpha_powers, n_max);
discrepancy_next = bitxor(syndrome(3), value);
% The degree of the locator polynomial
locator_degree_rho = 0;
locator_degree_next = 1;
% Update all values
locator_polynom = delta_next;
delta_current = delta_next;
discrepancy_rho = syndrome(1);
discrepancy_current = discrepancy_next;
locator_degree_current = locator_degree_next;
rho = 0; % The row with the maximum value of 2mu - l starts at 1
for i = 1:t % Only the even steps are needed (so make t out of 2*t)
if discrepancy_current ~= 0
% Compute the correction factor
correction_factor = uint32(zeros(polynom_length, 1));
x_exponent = 2*(i - rho);
if (discrepancy_current == 1 || discrepancy_rho == 1)
d_mu_times_rho = discrepancy_current * discrepancy_rho;
else
alpha_discrepancy_mu = alpha_powers(discrepancy_current);
alpha_discrepancy_rho = alpha_powers(discrepancy_rho);
alpha_inver_discrepancy_rho = n_max - alpha_discrepancy_rho;
% The alpha power for dmu * drho^-1 is
alpha_d_mu_times_rho = alpha_discrepancy_mu + alpha_inver_discrepancy_rho;
% Equivalent to aux mod(2^m - 1)
alpha_d_mu_times_rho = alpha_d_mu_times_rho - ...
n_max * uint32(alpha_d_mu_times_rho > n_max);
d_mu_times_rho = field(alpha_d_mu_times_rho);
end
correction_factor(x_exponent+1) = d_mu_times_rho;
correction_factor = gf_mul_polynoms(correction_factor,...
delta_rho,...
field, alpha_powers, n_max);
% Finally we add the correction factor to get the new delta
delta_next = bitxor(delta_current, correction_factor(1:polynom_length));
% Update used data
l = polynom_length;
while delta_next(l) == 0 && l>0
l = l - 1;
end
locator_degree_next = l-1;
% Update previous maximum if the degree is higher than recorded
if (2*i - locator_degree_current) > (2*rho - locator_degree_rho)
locator_degree_rho = locator_degree_current;
delta_rho = delta_current;
discrepancy_rho = discrepancy_current;
rho = i;
end
else
% If the discrepancy is 0, the locator polynomial for this step
% is passed to the next one. It satifies all newtons' equations
% until now.
delta_next = delta_current;
end
% Compute the discrepancy for the next step
syndrome_start_index = 2 * i + 3;
discrepancy_next = syndrome(syndrome_start_index); % First value
for k = 1:locator_degree_next
value = gf_mul_elements(delta_next(k + 1), ...
syndrome(syndrome_start_index - k), ...
field, alpha_powers, n_max);
discrepancy_next = bitxor(discrepancy_next, value);
end
% Update all values
locator_polynom = delta_next;
delta_current = delta_next;
discrepancy_current = discrepancy_next;
locator_degree_current = locator_degree_next;
end
end
I'm trying to see what's wrong but I can't. It works for the examples in the book, but not always. As an aside, to compute the discrepancy S_2mu+3 is needed, but when I have only 24 syndrome coefficients how is it computed on step 11 where 2*11 + 3 is 25?
Thanks in advance!
It turns out the code is ok. I made a different implementation from Error Correction and Coding. Mathematical Methods and gives the same result. My problem is at the Chien Search.
Code for the interested:
function [c] = compute_error_locator_v2(syndrome, m, field, alpha_powers)
%
% Initial conditions for the BM algorithm
% Premilimnary values
N = length(syndrome);
n_max = uint32(2^m - 1);
polynom_length = N/2 + 1;
L = 0; % The curent length of the LFSR
% The current connection polynomial
c = uint32(zeros(polynom_length, 1)); c(1) = 1;
% The connection polynomial before last length change
p = uint32(zeros(polynom_length, 1)); p(1) = 1;
l = 1; % l is k - m, the amount of shift in update
dm = 1; % The previous discrepancy
for k = 1:2:N % For k = 1 to N in steps of 2
% ========= Compute discrepancy ==========
d = syndrome(k);
for i = 1:L
aux = gf_mul_elements(c(i+1), syndrome(k-i), field, alpha_powers, n_max);
d = bitxor(d, aux);
end
if d == 0 % No change in polynomial
l = l + 1;
else
% ======== Update c ========
t = c;
% Compute the correction factor
correction_factor = uint32(zeros(polynom_length, 1));
% This is d * dm^-1
dd_sum = modulo(alpha_powers(d) + n_max - alpha_powers(dm), n_max);
for i = 0:polynom_length - 1
if p(i+1) ~= 0
% Here we compute d*d^-1*p(x_i)
ddp_sum = modulo(dd_sum + alpha_powers(p(i+1)), n_max);
if ddp_sum == 0
correction_factor(i + l + 1) = 1;
else
correction_factor(i + l + 1) = field(ddp_sum);
end
end
end
% Finally we add the correction factor to get the new locator
c = bitxor(c, correction_factor);
if (2*L >= k) % No length change in update
l = l + 1;
else
p = t;
L = k - L;
dm = d;
l = 1;
end
end
l = l + 1;
end
end
The code comes from this implementation of the Massey algorithm

How to find Orientation of axis of contour in matlab?

I want to find Orientation, MajorAxisLengthand MinorAxisLength of contour which is plotted with below code.
clear
[x1 , x2] = meshgrid(linspace(-10,10,100),linspace(-10,10,100));
mu = [1,3];
sigm = [2,0;0,2];
xx_size = length(mu);
tem_matrix = ones(size(x1));
x_mesh= cell(1,xx_size);
for i = 1 : xx_size
x_mesh{i} = tem_matrix * mu(i);
end
x_mesh= {x1,x2};
temp_mesh = [];
for i = 1 : xx_size
temp_mesh = [temp_mesh x_mesh{i}(:)];
end
Z = mvnpdf(temp_mesh,mu,sigm);
z_plat = reshape(Z,size(x1));
figure;contour(x1, x2, z_plat,3, 'LineWidth', 2,'color','m');
% regionprops(z_plat,'Centroid','Orientation','MajorAxisLength','MinorAxisLength');
In my opinion, I may have to use regionprops command but I don't know how to do this. I want to find direction of axis of contour and plot something like this
How can I do this task? Thanks very much for your help
Rather than trying to process the graphical output of contour, I would instead recommend using contourc to compute the ContourMatrix and then use the x/y points to estimate the major and minor axes lengths as well as the orientation (for this I used this file exchange submission)
That would look something like the following. Note that I have modified the inputs to contourc as the first two inputs should be the vector form and not the output of meshgrid.
% Compute the three contours for your data
contourmatrix = contourc(linspace(-10,10,100), linspace(-10,10,100), z_plat, 3);
% Create a "pointer" to keep track of where we are in the output
start = 1;
count = 1;
% Now loop through each contour
while start < size(contourmatrix, 2)
value = contourmatrix(1, start);
nPoints = contourmatrix(2, start);
contour_points = contourmatrix(:, start + (1:nPoints));
% Now fit an ellipse using the file exchange
ellipsedata(count) = fit_ellipse(contour_points(1,:), contour_points(2,:));
% Increment the start pointer
start = start + nPoints + 1;
count = count + 1;
end
orientations = [ellipsedata.phi];
% 0 0 0
major_length = [ellipsedata.long_axis];
% 4.7175 3.3380 2.1539
minor_length = [ellipsedata.short_axis];
% 4.7172 3.3378 2.1532
As you can see, the contours are actually basically circles and therefore the orientation is zero and the major and minor axis lengths are almost equal. The reason that they look like ellipses in your post is because your x and y axes are scaled differently. To fix this, you can call axis equal
figure;contour(x1, x2, z_plat,3, 'LineWidth', 2,'color','m');
axis equal
Thank you #Suever. It help me to do my idea.
I add some line to code:
clear
[X1 , X2] = meshgrid(linspace(-10,10,100),linspace(-10,10,100));
mu = [-1,0];
a = [3,2;1,4];
a = a * a';
sigm = a;
xx_size = length(mu);
tem_matrix = ones(size(X1));
x_mesh= cell(1,xx_size);
for i = 1 : xx_size
x_mesh{i} = tem_matrix * mu(i);
end
x_mesh= {X1,X2};
temp_mesh = [];
for i = 1 : xx_size
temp_mesh = [temp_mesh x_mesh{i}(:)];
end
Z = mvnpdf(temp_mesh,mu,sigm);
z_plat = reshape(Z,size(X1));
figure;contour(X1, X2, z_plat,3, 'LineWidth', 2,'color','m');
hold on;
% Compute the three contours for your data
contourmatrix = contourc(linspace(-10,10,100), linspace(-10,10,100), z_plat, 3);
% Create a "pointer" to keep track of where we are in the output
start = 1;
count = 1;
% Now loop through each contour
while start < size(contourmatrix, 2)
value = contourmatrix(1, start);
nPoints = contourmatrix(2, start);
contour_points = contourmatrix(:, start + (1:nPoints));
% Now fit an ellipse using the file exchange
ellipsedata(count) = fit_ellipse(contour_points(1,:), contour_points(2,:));
% Increment the start pointer
start = start + nPoints + 1;
count = count + 1;
end
orientations = [ellipsedata.phi];
major_length = [ellipsedata.long_axis];
minor_length = [ellipsedata.short_axis];
tet = orientations(1);
x1 = mu(1);
y1 = mu(2);
a = sin(tet) * sqrt(major_length(1));
b = cos(tet) * sqrt(major_length(1));
x2 = x1 + a;
y2 = y1 + b;
line([x1, x2], [y1, y2],'linewidth',2);
tet = ( pi/2 + orientations(1) );
a = sin(tet) * sqrt(minor_length(1));
b = cos(tet) * sqrt(minor_length(1));
x2 = x1 + a;
y2 = y1 + b;
line([x1, x2], [y1, y2],'linewidth',2);

Error in FDM for a coupled PDEs

Here is the code which is trying to solve a coupled PDEs using finite difference method,
clear;
Lmax = 1.0; % Maximum length
Wmax = 1.0; % Maximum wedth
Tmax = 2.; % Maximum time
% Parameters needed to solve the equation
K = 30; % Number of time steps
n = 3; % Number of space steps
m =30; % Number of space steps
M = 2;
N = 1;
Pr = 1;
Re = 1;
Gr = 5;
maxn=20; % The wave-front: intermediate point from which u=0
maxm = 20;
maxk = 20;
dt = Tmax/K;
dx = Lmax/n;
dy = Wmax/m;
%M = a*B1^2*l/(p*U)
b =1/(1+M*dt);
c =dt/(1+M*dt);
d = dt/((1+M*dt)*dy);
%Gr = gB*(T-T1)*l/U^2;
% Initial value of the function u (amplitude of the wave)
for i = 1:n
if i < maxn
u(i,1)=1.;
else
u(i,1)=0.;
end
x(i) =(i-1)*dx;
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
for j = 1:m
if j < maxm
v(j,1)=1.;
else
v(j,1)=0.;
end
y(j) =(j-1)*dy;
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
for k = 1:K
if k < maxk
T(k,1)=1.;
else
T(k,1)=0.;
end
z(k) =(k-1)*dt;
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Value at the boundary
%for k=0:K
%end
% Implementation of the explicit method
for k=0:K % Time loop
for i=1:n % Space loop
for j=1:m
u(i,j,k+1) = b*u(i,j,k)+c*Gr*T(i,j,k+1)+d*[((u(i,j+1,k)-u(i,j,k))/dy)^(N-1)*((u(i,j+1,k)-u(i,j,k))/dy)]-d*[((u(i,j,k)-u(i,j-1,k))/dy)^(N-1)*((u(i,j,k)-u(i,j-1,k))/dy)]-d*[u(i,j,k)*((u(i,j,k)-u(i-1,j,k))/dx)+v(i,j,k)*((u(i,j+1,k)-u(i,j,k))/dy)];
v(i,j,k+1) = dy*[(u(i-1,j,k+1)-u(i,j,k+1))/dx]+v(i,j-1,k+1);
T(i,j,k+1) = T(i,j,k)+(dt/(Pr*Re))*{(T(i,j+1,k)-2*T(i,j,k)+T(i,j-1,k))/dy^2-Pr*Re{u(i,j,k)*((T(i,j,k)-T(i-1,j,k))/dx)+v(i,j,k)*((T(i,j+1,k)-T(i,j,k))/dy)}};
end
end
end
% Graphical representation of the wave at different selected times
plot(x,u(:,1),'-',x,u(:,10),'-',x,u(:,50),'-',x,u(:,100),'-')
title('graphs')
xlabel('X')
ylabel('Y')
But I am getting this error
Subscript indices must either be real positive integers or logicals.
I am trying to implement this
with boundary conditions
Can someone please help me out!
Thanks
To be quite honest, it looks like you started with something that's way over your head, just typed everything down in one go without thinking much, and now you are surprised that it doesn't work...
In the future, please break down problems like these into waaaay smaller chunks that you can individually plot, check, test, etc. Better yet, try simpler problems first (wave equation, heat equation, ...), gradually working your way up to this.
I say this so harshly, because there were quite a number of fairly basic things wrong with your code:
you've used braces ({}) and brackets ([]) exactly as they are written in the equation. In MATLAB, braces are a constructor for a special container object called a cell array, and brackets are used to construct arrays and matrices. To group things like in the equation, you always have to use parentheses (()).
You had quite a number of parentheses wrong, which became apparent when I re-grouped and broke up those huge unintelligible lines into multiple lines that humans can actually read with understanding
you forgot to take the absolute values in the 3rd and 4th terms of u
you looped over k = 0:K and j = 1:m and then happily index everything with k and j-1. MATLAB is 1-based, meaning, the first element of anything is element 1, and indexing with 0 is an error
you've initialized 3 vectors u, v and T, but then index those in the loop as if they are 3D arrays
Now, I've managed to come up with the following code, which runs OK and at least more or less agrees with the equations shown. But I think it still doesn't make much sense because I get only zeros out (except for the initial values).
But, with this feedback, you should be able to correct any problems left.
Lmax = 1.0; % Maximum length
Wmax = 1.0; % Maximum wedth
Tmax = 2.; % Maximum time
% Parameters needed to solve the equation
K = 30; % Number of time steps
n = 3; % Number of space steps
m = 30; % Number of space steps
M = 2;
N = 1;
Pr = 1;
Re = 1;
Gr = 5;
maxn = 20; % The wave-front: intermediate point from which u=0
maxm = 20;
maxk = 20;
dt = Tmax/K;
dx = Lmax/n;
dy = Wmax/m;
%M = a*B1^2*l/(p*U)
b = 1/(1+M*dt);
c = dt/(1+M*dt);
d = dt/((1+M*dt)*dy);
%Gr = gB*(T-T1)*l/U^2;
% Initial value of the function u (amplitude of the wave)
u = zeros(n,m,K+1);
x = zeros(n,1);
for i = 1:n
if i < maxn
u(i,1)=1.;
else
u(i,1)=0.;
end
x(i) =(i-1)*dx;
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
v = zeros(n,m,K+1);
y = zeros(m,1);
for j = 1:m
if j < maxm
v(1,j,1)=1.;
else
v(1,j,1)=0.;
end
y(j) =(j-1)*dy;
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
T = zeros(n,m,K+1);
z = zeros(K,1);
for k = 1:K
if k < maxk
T(1,1,k)=1.;
else
T(1,1,k)=0.;
end
z(k) =(k-1)*dt;
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Value at the boundary
%for k=0:K
%end
% Implementation of the explicit method
for k = 2:K % Time loop
for i = 2:n % Space loop
for j = 2:m-1
u(i,j,k+1) = b*u(i,j,k) + ...
c*Gr*T(i,j,k+1) + ...
d*(abs(u(i,j+1,k) - u(i,j ,k))/dy)^(N-1)*((u(i,j+1,k) - u(i,j ,k))/dy) - ...
d*(abs(u(i,j ,k) - u(i,j-1,k))/dy)^(N-1)*((u(i,j ,k) - u(i,j-1,k))/dy) - ...
d*(u(i,j,k)*((u(i,j ,k) - u(i-1,j,k))/dx) +...
v(i,j,k)*((u(i,j+1,k) - u(i ,j,k))/dy));
v(i,j,k+1) = dy*(u(i-1,j,k+1)-u(i,j,k+1))/dx + ...
v(i,j-1,k+1);
T(i,j,k+1) = T(i,j,k) + dt/(Pr*Re) * (...
(T(i,j+1,k) - 2*T(i,j,k) + T(i,j-1,k))/dy^2 - Pr*Re*(...
u(i,j,k)*((T(i,j,k) - T(i-1,j,k))/dx) + v(i,j,k)*((T(i,j+1,k) - T(i,j,k))/dy))...
);
end
end
end
% Graphical representation of the wave at different selected times
figure, hold on
plot(x, u(:, 1), '-',...
x, u(:, 10), '-',...
x, u(:, 50), '-',...
x, u(:,100), '-')
title('graphs')
xlabel('X')
ylabel('Y')

Finding the coordinates of a sub-image in an image in Matlab

I need to find the coordinates of a 3D sub-image location residing in a 3D image in Matlab. Can anyone help me?
Thanks,
The following code essentially scans through the large array A and compare each element against the first one in the small array B. If an equal is found, a part of A, of which the size is same as of B, is picked out and compared against B.
clear;clc
% reproduce your scenario
A = randi(100, [30, 20, 10]);
B = A(20:30, 1:18, 4:end);
% counter-case verification
% B(end)=200;
% speed up
lenA = numel(A);
[sa1,sa2,sa3] = size(A);
[sb1,sb2,sb3] = size(B);
% a cumbersome method
eqflag = 0;
counterA = 1;
while (counterA <= lenA)
if A(counterA) == B(1)
[subA1,subA2,subA3] = ind2sub([sa1,sa2,sa3],counterA);
if ( (subA1+sb1-1)<=sa1 ) && ( (subA2+sb2-1)<=sa2 ) ...
&& ( (subA3+sb3-1)<=sa3 ) && isequal( B, ...
A(subA1+(1:sb1)-1,subA2+(1:sb2)-1,subA3+(1:sb3)-1) )
eqflag = 1;
break;
end
end
counterA = counterA + 1;
end
if eqflag
fprintf('found matching starting at A(%d, %d, %d).\n', ...
subA1, subA2, subA3);
fprintf('matching region A(%d:%d, %d:%d, %d:%d).\n', ...
subA1, subA1+sb1-1, subA2, subA2+sb2-1, subA3, subA3+sb3-1);
else
fprintf('no matching found.\n');
end
clearvars sa* lenA counterA
% --------------
% a parallel way
[sa1,sa2,sa3] = size(A);
match_first = find(A==B(1));
[m1,m2,m3] = ind2sub([sa1,sa2,sa3],match_first);
region_first_ind = intersect( intersect(find(m1+sb1-1<=sa1), ...
find(m2+sb2-1<=sa2)),find(m3+sb3-1<=sa3)); % array size issue
region_first = num2cell( [m1(region_first_ind),m2(region_first_ind),...
m3(region_first_ind)], 2);
region = cellfun(#(v) [v;v+[sb1,sb2,sb3]-1], region_first, ...
'UniformOutput', false);
region_match = cellfun(#(v) isequal(A(v(1):v(2), v(3):v(4), v(5):v(6)),...
B), region, 'UniformOutput', false);
match = cell2mat(region([region_match{:}]));
if ~isempty(match)
fprintf('found matching starting at A(%d, %d, %d).\n', ...
match(1), match(3), match(5));
fprintf('matching region A(%d:%d, %d:%d, %d:%d).\n', ...
match(1), match(2), match(3), match(4), match(5), match(6));
else
fprintf('no matching found.\n');
end