Looping through a cell array to differentiate and integrate

Question

William 2024-2-24

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2086183-looping-through-a-cell-array-to-differentiate-and-integrate

回答： Walter Roberson 2024-2-24

I am trying to build a matrix which is generated by integrating the sum of a set of derivatives of functions defined in a cell array. When I run the below code, it says there's an error in the 15th line saying that the variable x is not recognized. Any help would be greatly appreciated!

a = [0 1 1 0 0 1 1 0];
b = [0 0 1 1 0 0 1 1];
c = [0 0 0 0 1 1 1 1];
H = {@(x,y,z) (1/8).*(1-x).*(1-y).*(1-z), @(x,y,z) (1/8).*(1+x).*(1-y).*(1-z), @(x,y,z) (1/8).*(1+x).*(1+y).*(1-z), @(x,y,z) (1/8).*(1-x).*(1+y).*(1-z), @(x,y,z) (1/8).*(1-x).*(1-y).*(1+z),  @(x,y,z) (1/8).*(1+x).*(1-y).*(1+z), @(x,y,z) (1/8).*(1+x).*(1+y).*(1+z), @(x,y,z) (1/8).*(1-x).*(1+y).*(1+z)};
for i = 1:8
    for j = 1:8
        f(i,j) = @(x,y,z) diff(H{1,i},x).*diff(H{1,j},x) + diff(H{1,i},y).*diff(H{1,j},y) + diff(H{1,i},z).*diff(H{1,j},z);
        k(i,j) = integral3(f(i,j),min(a),max(a),min(b),max(b),min(c),max(c));
    end
end
Incorrect number or types of inputs or outputs for function diff.

Error in solution>@(x,y,z)diff(H{1,i},x).*diff(H{1,j},x)+diff(H{1,i},y).*diff(H{1,j},y)+diff(H{1,i},z).*diff(H{1,j},z) (line 7)
        f(i,j) = @(x,y,z) diff(H{1,i},x).*diff(H{1,j},x) + diff(H{1,i},y).*diff(H{1,j},y) + diff(H{1,i},z).*diff(H{1,j},z);

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Answer 1

Walter Roberson 2024-2-24

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2086183-looping-through-a-cell-array-to-differentiate-and-integrate#answer_1415528

在 MATLAB Online 中打开

There are two major functions diff()

When at least one of the parameters to diff() is a symbolic expression, or a symbolic function, or a symbolic array, then the result of diff() is symbolic differentiation .

If none of the parameters to diff() are symbolic expressions, or symbolic functions, or symbolic arrays, then the operation of diff is along the lines of A(2:end) - A(1:end-1) (but possibly repeated several times, depending on the parameters.)

You are attempting to take diff(H{1,i},x) where H{1,i} is an anonymous function, and x is a numeric parameter. That fails.

a = [0 1 1 0 0 1 1 0];
b = [0 0 1 1 0 0 1 1];
c = [0 0 0 0 1 1 1 1];
syms x y z
H = {(1/8).*(1-x).*(1-y).*(1-z), (1/8).*(1+x).*(1-y).*(1-z), (1/8).*(1+x).*(1+y).*(1-z), (1/8).*(1-x).*(1+y).*(1-z), (1/8).*(1-x).*(1-y).*(1+z),  (1/8).*(1+x).*(1-y).*(1+z), (1/8).*(1+x).*(1+y).*(1+z), (1/8).*(1-x).*(1+y).*(1+z)};
for i = 1:8
    for j = 1:8
        f{i,j} = matlabFunction(diff(H{1,i},x).*diff(H{1,j},x) + diff(H{1,i},y).*diff(H{1,j},y) + diff(H{1,i},z).*diff(H{1,j},z), 'vars', [x, y, z]);
        k(i,j) = integral3(f{i,j},min(a),max(a),min(b),max(b),min(c),max(c));
    end
end