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

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Djamel 2024-3-26

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https://ww2.mathworks.cn/matlabcentral/answers/2099161-how-to-write-in-matlab-a-matrix-whose-coefficients-depend-on-a-real-alpha-parameter

评论： Djamel 2024-4-2，14:33

采纳的回答： John D'Errico

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

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Answer 1

John D'Errico 2024-3-26

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编辑：John D'Errico 2024-3-26

在 MATLAB Online 中打开

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

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Djamel 2024-4-2，14:33

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

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Answer 2

Voss 2024-3-26

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在 MATLAB Online 中打开

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