I have been trying to figure out this integral for some time, but have come up short. I have tried doing a symbolic integration, but I get it shot back out at me, so I am assuming there is not solution that way. I have resolved to solve it with a definite integral, but still keep getting errors:
clear
clc
x = 1;
y = 1;
z = 1;
R = 2;
b =#(theta) y.*cos(theta)/((x-R.*cos(theta)).^2+y.^2+(z -
R.*sin(theta)).^2).^(3/2)
integral(b,1,2)
My current error is:
Error using integralCalc/finalInputChecks (line 515)
Output of the function must be the same size as the input. If FUN is an array-valued
integrand, set the 'ArrayValued' option to true.
Error in integralCalc/iterateScalarValued (line 315)
finalInputChecks(x,fx);
Error in integralCalc/vadapt (line 132)
[q,errbnd] = iterateScalarValued(u,tinterval,pathlen);
Error in integralCalc (line 75)
[q,errbnd] = vadapt(#AtoBInvTransform,interval);
Error in integral (line 88)
Q = integralCalc(fun,a,b,opstruct);
Any help would be very appreciated!
You need to change the division sign in the first term from / to ./ to ensure that you are doing element-wise division and not matrix right division:
b = #(theta) y.*cos(theta)./((x-R.*cos(theta)).^2+y.^2+(z - ...
R.*sin(theta)).^2).^(3/2);
integral(b,1,2)
ans =
0.055781612354862
Related
I am trying to write the program in MATLAB to perform sequential integration. First I define the first integral n_array_exact{1}() and save it as function handle in the array. This first integral becomes a function of x only after the integration. As a next step I use this function to calculate next double integral (call it n_array_exact{2}(x)) w.r.t mu1 and s. Before substituting n_array_exact{1}(x) to calculate n_array_exact{2}(x), I replace x in n_array_exact{1}(x) to a function called xp(x, mu1,s) instead.
% Ordinary integration
n_array_exact{1} = #(x) integral(#(mu) exp((x.*mu)), -1,1)/2;
xp2= #(x,mu1,s) sqrt(x*x +s*s +2*x*mu1*s);
for i=2:3
n_array_exact{i} = #(x) integral2(#(mu1,s) exp(-s.*mu1.*x).*n_array_exact{1}(xp2(x,mu1,s)), 0,1,-1,1);
end
n_array_exact{2}(0.05)
%n_array_exact{3}(0.05)
%n_array_exact{4}(0.05)
After performing the integration and trying to evaluate n_array_exact{2}0.05) I got the following errors:
Error using .*
Matrix dimensions must agree.
Error in #(mu)exp((x.*mu))
Error in integralCalc/iterateScalarValued (line 315)
fx = FUN(t);
Error in integralCalc/vadapt (line 133)
[q,errbnd] = iterateScalarValued(u,tinterval,pathlen);
Error in integralCalc (line 76)
[q,errbnd] = vadapt(#AtoBInvTransform,interval);
Error in integral (line 88)
Q = integralCalc(fun,a,b,opstruct);
Error in #(x)integral(#(mu)exp((x.*mu)),-1,1)/2
Error in #(mu1,s)exp(-s.*mu1.*x).*n_array_exact{1}(xp2(x,mu1,s))
Error in integral2Calc>integral2t/tensor (line 229)
Z = FUN(X,Y); NFE = NFE + 1;
Error in integral2Calc>integral2t (line 56)
[Qsub,esub] = tensor(thetaL,thetaR,phiB,phiT);
Error in integral2Calc (line 10)
[q,errbnd] = integral2t(fun,xmin,xmax,ymin,ymax,optionstruct);
Error in integral2 (line 106)
Q = integral2Calc(fun,xmin,xmax,yminfun,ymaxfun,opstruct);
Error in #(x)integral2(#(mu1,s)exp(-s.*mu1.*x).*n_array_exact{1}(xp2(x,mu1,s)),0,1,-1,1)
Error in test (line 10)
n_array_exact{2}(0.05)
Starting from the vector Psi_0 I define the propagated vector as Psi (t) = exp{-iHt} Psi_0, where H is the Adjacency matrix (but I think it is irrelevant to my problem here). I need to calculate
1/tau * int^tau_0 |<j|psi(t)>|^2 dt
I tried to do this in the following way but it doesn't work
psi_0 = diag(eye(N))/N;
Psi_t = zeros(N);
Psi_sqared = #(t) (expm(1j*A*t)*psi_0).*(expm(-1j*A*t)*psi_0);
c_tqw = integral(Psi_sqared, 0, 10000)/10000;
The error is the following
Error using *
Incorrect dimensions for matrix multiplication. Check that the number of columns in the first matrix matches the number of rows in the
second matrix. To perform elementwise multiplication, use '.*'.
Error in centrality_measure>#(t)(expm(1j*A*t)*psi_0).*(expm(-1j*A*t)*psi_0)
Error in integralCalc/iterateScalarValued (line 314)
fx = FUN(t);
Error in integralCalc/vadapt (line 132)
[q,errbnd] = iterateScalarValued(u,tinterval,pathlen);
Error in integralCalc (line 75)
[q,errbnd] = vadapt(#AtoBInvTransform,interval);
Error in integral (line 88)
Q = integralCalc(fun,a,b,opstruct);
Error in centrality_measure (line 75)
c_tqw = integral(Psi_sqared, 0, 10000)/10000;
Any suggestion to avoid this error?
I need to evaluate the following integral in MATLAB (numerically):
I already tried various things but I can't figure out how to solve this! Following is my last try:
Fdx = #(x) integral(#(y)1./(1+sqrt(y.^2))*(1-pi^2),0,x);
dFdx(1)
F = 8 * integral(dFdx,0,10)
As a result MATLAB gives me this error message:
Error using integral (line 85)
A and B must be floating-point scalars.
Error in #(x)integral(#(y)1./(1+sqrt(y.^2))*(1-pi^2),0,x)
Error in integralCalc/iterateScalarValued (line 314)
fx = FUN(t);
Error in integralCalc/vadapt (line 132)
[q,errbnd] = iterateScalarValued(u,tinterval,pathlen);
Error in integralCalc (line 75)
[q,errbnd] = vadapt(#AtoBInvTransform,interval);
Error in integral (line 88)
Q = integralCalc(fun,a,b,opstruct);
Error in test (line 7)
F=8 * integral(dFdx,0,10)
Try using integral2 instead. See example 2 in the documentation:
http://www.mathworks.com/help/matlab/ref/integral2.html
Hope it helps.
I have an issue with Matlab integration. It tells me that there is an error about dimensions. However they do agree and operations are properly done using vectorized operators (.^ .* etc...). It is simple code yet I am stuck
A = 1:10;
B = 1:10;
K_fun = #(x) (x ./ sqrt((x + A.^2 ) .* (x + B.^2) .* (x + B.^2)) );
K = integral( K_fun, 0,Inf );
and here the error message in the command window:
Error using +
Matrix dimensions must agree.
Error in #(x)(x./sqrt((x+A.^2).*(x+B.^2).*(x+B.^2)))
Error in integralCalc/iterateScalarValued (line 314)
fx = FUN(t);
Error in integralCalc/vadapt (line 133)
[q,errbnd] = iterateScalarValued(u,tinterval,pathlen);
Error in integralCalc (line 84)
[q,errbnd] = vadapt(#AToInfInvTransform,interval);
Error in integral (line 89)
Q = integralCalc(fun,a,b,opstruct);
Error in PROVA_New_Drag3 (line 21)
K = integral( K_fun , 0 , Inf);
Thank you in advance
It evaluates both your integration limits in a vector, so effectively your xin the function is [0 Inf], which is why the lengths don't agree.
You can set the 'ArrayValued' flag to true in the integral call
K = integral( K_fun, 0,Inf,'ArrayValued', true );
to get it to evaluate them separately.
I got another warning about a singularity but this is likely because you're using 0, infinity and division so it's related more to your function than the integration call. It might help to to sprinkle some eps around in K_fun.
UPDATE: Please see Troy's explanation of the singularity warning and note that eps won't actually help with that.
I try to get an integral of two function handles in Matlab. The first function handle would be a weibull probability density function and the second function handle is based on a cfit I created with linear interpolation of single points.
x = 0:0.1:35;
fun1 = #(x) wblpdf(x,weibullAlpha,weibullBeta);
fun2 = #(x) feval(cfitObject,x);
fun3 = #(x) (fun(x).*fun2(x));
y = integral(fun3,0,35); % Using quad(fun3,0,35) doesn't work either.
I receive the following error:
Error using integralCalc/finalInputChecks (line 515)
Output of the function must be the same size as the input. If FUN is an array-valued integrand,
set the 'ArrayValued' option to true.
Error in integralCalc/iterateScalarValued (line 315)
finalInputChecks(x,fx);
Error in integralCalc/vadapt (line 132)
[q,errbnd] = iterateScalarValued(u,tinterval,pathlen);
Error in integralCalc (line 75)
[q,errbnd] = vadapt(#AtoBInvTransform,interval);
Error in integral (line 88)
Q = integralCalc(fun,a,b,opstruct);
Error in test (line 7) % "test" is the name of the script file.
y = integral(fun3,0,35);
The problem must have to do something with "fun2" since the code works just fine with e.g.
fun2 = x.^2;
Note: if I plot fun2 with the cfitObject I don't get an error. It's also possible to integrate the function using quad().
x = 0:0.1:35;
fun2 = #(x) feval(cfitObject,x);
y = quad(fun2,0,35);
plot(x, fun2(x))
Any help is greatly appreciated!
Your code seems to be ok. Probably the problem is that fun2 cannot take vectorized input, it could be resolved by modifying fun2 (cfitObject) to be able to handle vector input or telling the software that the function in the integral is array valued:
y = integral(fun3, 0, 35, 'ArrayValued', 1);