How to write in Matlab a matrix whose coefficients depend on a real alpha parameter

A(i,j) = (1+alpha*x(i)*y(j))*exp(x(i)*y(j))

where almpha is a real parameter, x(i) and y(j) points in [0 , 1] with i , j = 1, ..., N

Answer 1

[John D'Errico]

Many ways. It seems unclear exactly what is your goal. And what are x and y? Are they just a list of numbers? Or a sequence as linspace would provide?

For example, you might do this:

N = 4;
x = linspace(0,1,N);
y = linspace(0,1,N);
syms alpha
A = (1+alpha*x.'*y)*exp(x.'*y)

A = 

vpa(A,5)

ans = 

Of course, x and y might be just any arbitrary vectors of numbers.

Another approach would be to write it as a function handle. This time I'll use random vectors for x and y.

x = sort(rand(1,N))

x = 1x4

0.0962 0.1445 0.9101 0.9192

y = sort(rand(1,N))

y = 1x4

0.0370 0.2099 0.4181 0.4717

Afun = @(alph) (1+alph*x.'*y)*exp(x.'*y);

And now we can evaluate Afun for any value of the parameter.

Afun(0.3)

ans = 4x4

4.1115 4.5130 5.0803 5.2430 4.1284 4.5323 5.1030 5.2666 4.3969 4.8383 5.4627 5.6418 4.4000 4.8419 5.4670 5.6462

[Djamel]

Thank you so much John D'Errico. Both script suggestions work.

Answer 2

[Voss]

Here's an example:

alpha = 0.4;
N = 9;
x = linspace(0,1,N);
y = linspace(0,1,N);

xy = x(:).*y(:).' % column x * row y

xy = 9x9

0 0 0 0 0 0 0 0 0 0 0.0156 0.0312 0.0469 0.0625 0.0781 0.0938 0.1094 0.1250 0 0.0312 0.0625 0.0938 0.1250 0.1562 0.1875 0.2188 0.2500 0 0.0469 0.0938 0.1406 0.1875 0.2344 0.2812 0.3281 0.3750 0 0.0625 0.1250 0.1875 0.2500 0.3125 0.3750 0.4375 0.5000 0 0.0781 0.1562 0.2344 0.3125 0.3906 0.4688 0.5469 0.6250 0 0.0938 0.1875 0.2812 0.3750 0.4688 0.5625 0.6562 0.7500 0 0.1094 0.2188 0.3281 0.4375 0.5469 0.6562 0.7656 0.8750 0 0.1250 0.2500 0.3750 0.5000 0.6250 0.7500 0.8750 1.0000

A = (1+alpha.*xy).*exp(xy)

A = 9x9

1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0221 1.0446 1.0676 1.0911 1.1150 1.1395 1.1644 1.1898 1.0000 1.0446 1.0911 1.1395 1.1898 1.2422 1.2967 1.3534 1.4124 1.0000 1.0676 1.1395 1.2157 1.2967 1.3826 1.4738 1.5706 1.6732 1.0000 1.0911 1.1898 1.2967 1.4124 1.5377 1.6732 1.8199 1.9785 1.0000 1.1150 1.2422 1.3826 1.5377 1.7088 1.8976 2.1058 2.3353 1.0000 1.1395 1.2967 1.4738 1.6732 1.8976 2.1499 2.4335 2.7521 1.0000 1.1644 1.3534 1.5706 1.8199 2.1058 2.4335 2.8089 3.2385 1.0000 1.1898 1.4124 1.6732 1.9785 2.3353 2.7521 3.2385 3.8056