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

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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

Respuesta aceptada

John D'Errico
John D'Errico el 26 de Mzo. de 2024
Editada: John D'Errico el 26 de Mzo. de 2024
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

Más respuestas (1)

Voss
Voss el 26 de Mzo. de 2024
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

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