Octave：For循环错误表示A（I）= X：X必须与I具有相同的大小

Question

I need to evaluate the integral from x=-1 to x=1 for the function x*e^(x)*sin(pi*x) . To do so, I'm using the Gaussian Quadrature method. This method can be summarized as the summation of the (weights)*(function evaluated at given roots) from k=1 to k=n where n=30 .

In my code below, the roots are found in the column vector LegendreGaussQuadratureConstants(n).x . I'm taking the transpose because I want to perform element by element multiplication on the weights, which are stored in the row vector LegendreGaussQuadratureConstants(n).w

My code:

fx = @(x) x .* e.^(-x) .* sin(pi .* x);

  for k = 1:50

    Leg(k) = (fx(LegendreGaussQuadratureConstants(k).x))' .* LegendreGaussQuadratureConstants(k).w;

  endfor

The problem is that it's giving me the error in the title, implying that there is some problem with using a scalar value of k and that it should match up with the size of values being multiplied, but that makes no sense...

Answer 1

You said it yourself in your question

the roots are found in the column vector LegendreGaussQuadratureConstants(n).x . I'm taking the transpose because I want to perform element by element multiplication on the weights, which are stored in the row vector LegendreGaussQuadratureConstants(n).w .

You're taking the element-wise product of two vectors and the result is also going to be a vector. However, you then try to assign it to a scalar, Leg(k) which produces your error.

You either need to store these vectors in a 2D version of Leg

for k = 1:50
    Leg(k,:) = (fx(LegendreGaussQuadratureConstants(k).x))' .* LegendreGaussQuadratureConstants(k).w;
endfor

or perform some other operation on the element-wise multiplication result to get it to be a scalar.

for k = 1:50
    Leg(k) = sum((fx(LegendreGaussQuadratureConstants(k).x))' .* LegendreGaussQuadratureConstants(k).w);
endfor