MATLAB: Function handle integration with several variable, matrix dimension error

dimensiondirachandlesMATLAB

Hi! I am using function handles to integrate with several variables (note: I made the same program using symbolic integration, but it takes a really long time). However, I keep getting an error in matrix dimensions in the last line of my when I plug in R(1) and I really can't figure out what is wrong. Any tips would be greatly appreciated!

FUN_1 = @(y_1,y_2,x_1,x_2)sum(heaviside(y_1-1)).*dirac(1,y_2-1).*(-1/2*log((x_1-y_1).^2+(x_2-y_2).^2))+sum(dirac(y_1-1).*dirac(y_2-1));
  Q_1 = @(x_1,x_2)integral2(@(y_1,y_2)FUN_1(y_1,y_2,x_1,x_2),1,2,1,2);
FUN_2 = @(y_1,y_2,x_1,x_2)sum(heaviside(y_1-1).*dirac(1,y_2-1))+sum(dirac(y_1-1).*dirac(y_2-1))*(-1/2*log((x_1-y_1).^2+(x_2-y_2).^2));
Q_2 = @(x_1,x_2)integral2(@(y_1,y_2)FUN_1(y_1,y_2,x_1,x_2),1,2,1,2);
S = @(x_1,x_2)Q_1(x_1,x_2)+Q_2(x_1,x_2);
R = @(x_2)integral(@(x_1)S(x_1,x_2),1,2);
b = R(1);
disp(b)

Best Answer

integral() calls the function passing in a vector of values. So your S will be called with a vector x_1, so your Q_1 will be called with a vector x_1. Your Q_1 calls integral2, which is going to call FUN_1 with array y_1 and y_2 (the same size) and the vector x_1 (of different size). Your FUN_1 expects x_1 and y_1 to be compatible size for subtraction, but the two are not compatible.

You could use the 'ArrayValued' option of integral so that it only passes in a scalar for x_1, at a cost to efficiency. You should look more carefully at which operations can be vectorized. Sometimes it helps to use arrayfun() along the way.

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MATLAB: Multiplication of two polynomials having different variables

The simple answer is to use the symbolic toolbox. If you have it, I cannnot think of a good reason why you would not use it.

syms X Y
(X^3 + X^2+ X+1)*(Y^3 +Y^2 +Y+1)
ans =
(X^3 + X^2 + X + 1)*(Y^3 + Y^2 + Y + 1)
expand(ans)
ans =
X^3*Y^3 + X^3*Y^2 + X^3*Y + X^3 + X^2*Y^3 + X^2*Y^2 + X^2*Y + X^2 + X*Y^3 + X*Y^2 + X*Y + X + Y^3 + Y^2 + Y + 1

Lacking that, you can download my sympoly toolbox. It is on the file exchange. So I can do this:

sympoly X Y
(X^3 + X^2+ X+1)*(Y^3 +Y^2 +Y+1)
ans =
    1 + Y + Y^2 + Y^3 + X + X*Y + X*Y^2 + X*Y^3 + X^2 + X^2*Y + X^2*Y^2 + X^2*Y^3 + X^3 + X^3*Y + X^3*Y^2 + X^3*Y^3

So at least for basic polynomial manipulations, it works quite well.

Lacking that, can you solve the problem with neither tool present? Of course. Since you wanted to use conv...

xpoly = [1 1 1 0];
ypoly = [1 1 1 1];

Effectively, you know these are the coefficients of polynomials in x and y, such that the ith element of xpoly is the coefficient of X^(4- i).

xypoly = xpoly'*ypoly
xypoly =
     1     1     1     1
     1     1     1     1
     1     1     1     1
     0     0     0     0

So the (i,j) element of xypoly is the coefficient of x^(4 - i) * y^(4 - j).

MATLAB: Integrate multivariate fuction with respect to one variable and pass the result to another function for integration.

Notice you have:

fun= @(x, y) x.*exp(-y.*x);

which is a function of two variables. But you try

c= @(y)integral(@(x) fun, 0,1);

which does not pass any parameters to the function. You probably intended

c= @(y)integral(@(x) fun(x), 0,1);

But notice that you are not passing y, so you would need

c= @(y) integral(@(x) fun(x, y), 0,1);

Then you have

fun1= @(y) 1/2-(1/pi).*y.*c;
c1 = integral(fun1, 0,1);

this attempts to invoke c, but c is a function handle. You have to pass a value to the handle:

fun1 = @(y) 1/2-(1/pi).*y.*c(y);
c1 = integral(fun1, 0,1);

I think that should work.

Best Answer

Related Solutions

MATLAB: Multiplication of two polynomials having different variables

MATLAB: Integrate multivariate fuction with respect to one variable and pass the result to another function for integration.

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