How to generate a function of two variables without using any loop?

Question

Suppose I have a function y (t, x) = exp (-t) * sin (x)

In matlab, I define

t = [0: 0.5: 5]; x = [0: 0.1: 10*2*pi]; y = zeros(length(t), length(x)); % empty matrix init 

Now, how do I determine the matrix y without using any loop , so that each element y (i, j) contains the value of the desired function y at (t(i), x(j)) ? The following shows how I did this using a for loop.

 for i = 1:length(t) y(i,:) = exp(-t(i)) .* sin(x); end 

Answer 1

Your input vectors are x - 1xN and t - 1xM , the output matrix y is MxN . To vectorize the code, both x and t must be the same size as y .

 [x_,t_] = meshgrid(x,t); y_ = exp(-t_) .* sin(x_); 

Your example is a simple 2D case. The meshgrid() function also works 3D. Sometimes you cannot avoid a loop, in cases where your loop can go either 1: N or 1: M, choose the shortest. Another function that I use to prepare the vector for the vectorized equation (vector multiplication of the matrix x) is diag() .

Answer 2

no meshgrid ; just use:

 y = exp(-t(:)) * sin(x(:)'); %multiplies a column vector times a row vector. 

Answer 3

This may be useful:
http://www.mathworks.com/access/helpdesk/help/techdoc/ref/meshgrid.html

http://www.mathworks.com/company/newsletters/digest/sept00/meshgrid.html

Good luck.