Trapz error in calculating 2D integrals: ORDER contains an invalid permutation index

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Tsz Tsun
Tsz Tsun on 25 Aug 2022
Commented: Tsz Tsun on 25 Aug 2022
Hi all, I am very new to matlab and I need to use trapz or cumtrapz to calculate a double integral. Part I of the code calculates the the eigenvalue and eigenvectors of a given Hamiltonian matrix at each point of x and y, and stores them into a harsh map container, this parts run perfectly fine. Part II uses the result I stored in the container to calculate the Berry curvature using the complicated formula. So now at each point of x and y in the grid, I have MBerry("1,1") , MBerry("1,2") ,MBerry("1,3") etc MBerry("2,1") ,MBerry("2,2") etc up to M("98,98") values. And I would like to calculate the trapz Integral of this 3D plot. However I get an error :
Error using permute
ORDER contains an invalid permutation index.
I should get an answer of I is equal around 25.
%q =4 case
%Part I of the code
a=0.25;
N=100;
q=1;
Eigenvector=[];
M = containers.Map();
ChernNumber = 0;
for u=0:99
for v= 0:99
disp(u);
disp(v);
x=(2*pi*u)/(q*N);
y=(2*pi*v)/(q*N);
%K is the Hamiltonian matrix
K=[-2*cos(2*pi*a-y) -exp(i*x) 0 -exp(-i*x); -exp(-i*x) -2*cos(2*pi*2*a-y) -exp(i*x) 0; 0 -exp(-i*x) -2*cos(2*pi*3*a-y) -exp(i*x); -exp(i*x) 0 -exp(-i*x) -2*cos(2*pi*4*a-y)];
%find eigenvalue
e=eig(K)
%find eigenvector
[V,D]=eig(K);
%Store eigenvector in a container hash map
keySet = sprintf("%u,%u", u, v)
Eigenvector=V(:,1)
valueSet = Eigenvector
M(keySet) = valueSet
end
end
%The above part runs perfectly fine
%Part II of the code
%This part calculates the Berry curvature using the eigenvectors calculated
%in the above code
%Define an empty container MBerry
MBerry = containers.Map();
for u=0:98
for v=0:98
keySet = sprintf("%d,%d", u, v)
%Calculation of Berry Curvature for each point of the momentum
%space grid
BerryCurvature=...
log((dot(M(sprintf('%d,%d',u,v)),M(sprintf('%d,%d',u+1,v)))/abs(dot(M(sprintf('%d,%d',u,v)),M(sprintf('%d,%d',u+1,v)))))*...
(dot(M(sprintf('%d,%d',u+1,v)),M(sprintf('%d,%d',u+1,v+1)))/abs(dot(M(sprintf('%d,%d',u+1,v)),M(sprintf('%d,%d',u+1,v+1)))))*...
(dot(M(sprintf('%d,%d',u+1,v+1)),M(sprintf('%d,%d',u,v+1)))/abs(dot(M(sprintf('%d,%d',u+1,v+1)),M(sprintf('%d,%d',u,v+1)))))*...
(dot(M(sprintf('%d,%d',u,v+1)),M(sprintf('%d,%d',u,v)))/abs(dot(M(sprintf('%d,%d',u,v+1)),M(sprintf('%d,%d',u,v))))))
MBerry(keySet) = BerryCurvature
%Calucation of the Chern number
ChernNumber= ChernNumber + sum(MBerry(keySet))
%All of the above code work fine
%Using cumtrapz to calculate the Chern Number
x=(2*pi*u)/(q*N);
y=(2*pi*v)/(q*N);
MBerry(keySet);
I = cumtrapz(y,cumtrapz(x,MBerry(keySet),2))
end
end

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Accepted Answer

Torsten
Torsten on 25 Aug 2022
Edited: Torsten on 25 Aug 2022
Ran in:
Although I have no idea of what you are doing in your code ...
%q =4 case
%Part I of the code
a=0.25;
N=100;
q=1;
Eigenvector=[];
M = cell(100); %containers.Map();
ChernNumber = 0;
for u=0:99
for v= 0:99
%disp(u);
%disp(v);
x=(2*pi*u)/(q*N);
y=(2*pi*v)/(q*N);
%K is the Hamiltonian matrix
K=[-2*cos(2*pi*a-y) -exp(i*x) 0 -exp(-i*x); -exp(-i*x) -2*cos(2*pi*2*a-y) -exp(i*x) 0; 0 -exp(-i*x) -2*cos(2*pi*3*a-y) -exp(i*x); -exp(i*x) 0 -exp(-i*x) -2*cos(2*pi*4*a-y)];
%find eigenvalue
e=eig(K);
%find eigenvector
[V,D]=eig(K);
%Store eigenvector in a container hash map
%keySet = sprintf("%u,%u", u, v);
Eigenvector=V(:,1);
valueSet = Eigenvector;
%M(keySet) = valueSet;
M{u+1,v+1} = valueSet;
%M(keySet)
end
end
%class(M)
%size(M)
%M
%The above part runs perfectly fine
%Part II of the code
%This part calculates the Berry curvature using the eigenvectors calculated
%in the above code
%Define an empty container MBerry
%MBerry = containers.Map();
MBerry = zeros(99);
for u=0:98
for v=0:98
%keySet = sprintf("%d,%d", u, v)
%Calculation of Berry Curvature for each point of the momentum
%space grid
%BerryCurvature=...
%log((dot(M(sprintf('%d,%d',u,v)),M(sprintf('%d,%d',u+1,v)))/abs(dot(M(sprintf('%d,%d',u,v)),M(sprintf('%d,%d',u+1,v)))))*...
%(dot(M(sprintf('%d,%d',u+1,v)),M(sprintf('%d,%d',u+1,v+1)))/abs(dot(M(sprintf('%d,%d',u+1,v)),M(sprintf('%d,%d',u+1,v+1)))))*...
%(dot(M(sprintf('%d,%d',u+1,v+1)),M(sprintf('%d,%d',u,v+1)))/abs(dot(M(sprintf('%d,%d',u+1,v+1)),M(sprintf('%d,%d',u,v+1)))))*...
%(dot(M(sprintf('%d,%d',u,v+1)),M(sprintf('%d,%d',u,v)))/abs(dot(M(sprintf('%d,%d',u,v+1)),M(sprintf('%d,%d',u,v))))))
BerryCurvature = ...
log((dot(M{u+1,v+1},M{u+2,v+1})/abs(dot(M{u+1,v+1},M{u+2,v+1})))*...
(dot(M{u+2,v+1},M{u+2,v+2})/abs(dot(M{u+2,v+1},M{u+2,v+2})))*...
(dot(M{u+2,v+2},M{u+1,v+2})/abs(dot(M{u+2,v+2},M{u+1,v+2})))*...
(dot(M{u+1,v+2},M{u+1,v+1})/abs(dot(M{u+1,v+2},M{u+1,v+1}))));
MBerry(u+1,v+1) = BerryCurvature;
%Calucation of the Chern number
%ChernNumber= ChernNumber + sum(MBerry(keySet))
%All of the above code work fine
%Using cumtrapz to calculate the Chern Number
%x=(2*pi*u)/(q*N);
%y=(2*pi*v)/(q*N);
%MBerry(keySet);
%I = cumtrapz(y,cumtrapz(x,MBerry(keySet),2))
end
end
x = (2*pi*(0:98))/(q*N);
y = (2*pi*(0:98))/(q*N);
I = cumtrapz(y,cumtrapz(x,MBerry,2))
I =
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More Answers (1)

Christine Tobler
Christine Tobler on 25 Aug 2022
Ran in:
Replace the line
I = cumtrapz(y,cumtrapz(x,MBerry(keySet),2));
with
I = cumtrapz(y,cumtrapz(x,MBerry(keySet),2), 1);
Here's what happens to cause the error: MBerry(keySet) in one iteration returns a scalar, and then the above line becomes
x = 1.234; % Just using some scalars here, the values don't matter
y = 2.345;
MBerry_keySet = 3.456;
tmp = cumtrapz(x, MBerry_keySet, 2)
tmp = 0
I = cumtrapz(y, tmp)
Error using permute
ORDER contains an invalid permutation index.

Error in cumtrapz (line 56)
y = permute(y,perm);
This last call takes two scalars, and in this case CUMTRAPZ goes into the cumtrapz(y, dim) syntax instead of the cumtrapz(x, y) branch. The error message is because 0 is not a valid dimension input.
It's not great of course that we have two overlapping syntaxes like this here. The best workaround is to just use the three-input syntax which has no ambiguity as to which input is treated how.
I'll make a note to improve the error message here so it mentions the DIM argument.
  1 Comment
Tsz Tsun
Tsz Tsun on 25 Aug 2022
Do you mean like this ?
%q =4 case
%Part I of the code
a=0.25;
N=100;
q=1;
Eigenvector=[];
M = containers.Map();
ChernNumber = 0;
for u=0:99
for v= 0:999
disp(u);
disp(v);
x=(2*pi*u)/(q*N);
y=(2*pi*v)/(q*N);
%K is the Hamiltonian matrix
K=[-2*cos(2*pi*a-y) -exp(i*x) 0 -exp(-i*x); -exp(-i*x) -2*cos(2*pi*2*a-y) -exp(i*x) 0; 0 -exp(-i*x) -2*cos(2*pi*3*a-y) -exp(i*x); -exp(i*x) 0 -exp(-i*x) -2*cos(2*pi*4*a-y)];
%find eigenvalue
e=eig(K)
%find eigenvector
[V,D]=eig(K);
%Store eigenvector in a container hash map
keySet = sprintf("%u,%u", u, v)
Eigenvector=V(:,1)
valueSet = Eigenvector
M(keySet) = valueSet
end
end
%The above part runs perfectly fine
%Part II of the code
%This part calculates the Berry curvature using the eigenvectors calculated
%in the above code
%Define an empty container MBerry
MBerry = containers.Map();
for u=0:98
for v=0:98
keySet = sprintf("%d,%d", u, v)
%Calculation of Berry Curvature for each point of the momentum
%space grid
BerryCurvature=...
log((dot(M(sprintf('%d,%d',u,v)),M(sprintf('%d,%d',u+1,v)))/abs(dot(M(sprintf('%d,%d',u,v)),M(sprintf('%d,%d',u+1,v)))))*...
(dot(M(sprintf('%d,%d',u+1,v)),M(sprintf('%d,%d',u+1,v+1)))/abs(dot(M(sprintf('%d,%d',u+1,v)),M(sprintf('%d,%d',u+1,v+1)))))*...
(dot(M(sprintf('%d,%d',u+1,v+1)),M(sprintf('%d,%d',u,v+1)))/abs(dot(M(sprintf('%d,%d',u+1,v+1)),M(sprintf('%d,%d',u,v+1)))))*...
(dot(M(sprintf('%d,%d',u,v+1)),M(sprintf('%d,%d',u,v)))/abs(dot(M(sprintf('%d,%d',u,v+1)),M(sprintf('%d,%d',u,v))))))
MBerry(keySet) = BerryCurvature
%Calucation of the Chern number
ChernNumber= ChernNumber + sum(MBerry(keySet))
%All of the above code work fine
%Using cumtrapz to calculate the Chern Number
x=(2*pi*u)/(q*N);
y=(2*pi*v)/(q*N);
MBerry(keySet);
I = cumtrapz(y,cumtrapz(x,MBerry(keySet),2), 1)
end
end
The error messages go away, however, I obtain I = 0 for all entries when I run it. I should obtain a value close to ChernNumber (i.e. around 25) as above.

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