How to evaluate a symbolic expression having `max` and `diff`?

Question

Rounak Saha Niloy 2024-1-1

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https://ww2.mathworks.cn/matlabcentral/answers/2065431-how-to-evaluate-a-symbolic-expression-having-max-and-diff

评论： Walter Roberson 2024-1-4

I have calculated the jacobian of two functions where variables are x1, x2, x3.

The jacobian is as follows-

JacobianF =
 
[                                            diff(max([0, (7*sin(4*pi*x1))/10], [], 2, 'omitnan', ~in(x1, 'real')), x1) + 96*pi*cos(6*pi*x1)*(x3 + sin(6*pi*x1)) + 160*3^(1/2)*pi^2*cos(6*pi*x1)*sin((3^(1/2)*pi*(20*x3 + 20*sin(6*pi*x1)))/3) + 1,                                                                                                                                                                                        0, 16*x3 + 16*sin(6*pi*x1) + diff(max([0, (7*sin(4*pi*x1))/10], [], 2, 'omitnan', ~in(x1, 'real')), x3) + (80*3^(1/2)*pi*sin((3^(1/2)*pi*(20*x3 + 20*sin(6*pi*x1)))/3))/3]
[diff(max([0, (7*sin(4*pi*x1))/10], [], 2, 'omitnan', ~in(x1, 'real')), x1) - 96*pi*cos((2*pi)/3 + 6*pi*x1)*(x2 - sin((2*pi)/3 + 6*pi*x1)) - 240*2^(1/2)*pi^2*cos((2*pi)/3 + 6*pi*x1)*sin((2^(1/2)*pi*(20*x2 - 20*sin((2*pi)/3 + 6*pi*x1)))/2) - 1, 16*x2 - 16*sin((2*pi)/3 + 6*pi*x1) + diff(max([0, (7*sin(4*pi*x1))/10], [], 2, 'omitnan', ~in(x1, 'real')), x2) + 40*2^(1/2)*pi*sin((2^(1/2)*pi*(20*x2 - 20*sin((2*pi)/3 + 6*pi*x1)))/2),                                                                                                                                                                      0]

Now, I need to evaluate this JacobianF at

X = [0.2703 0.6193 0.9370];

where X(1) is x1 and so on.

To evaluate this JacobianF, I have used the following code-

Var_List = sym('x', [1, 3]);
df=double(subs(JacobianF, Var_List, X));

However, I get the following error. What is the cause of this error? How to resolve it and calculate the JacobianF at the specified position?

Error using symengine
Unable to convert expression containing remaining symbolic function calls into double array. Argument must be
expression that evaluates to number.
Error in sym/double (line 872)
Xstr = mupadmex('symobj::double', S.s, 0);

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Dyuman Joshi 2024-1-1

在 MATLAB Online 中打开

"What is the cause of this error?"

You can't use double() on a symolic expression -

syms x1 x2 x3

JacobianF = [diff(max([0, (7*sin(4*pi*x1))/10], [], 2, 'omitnan', ~in(x1, 'real')), x1) + 96*pi*cos(6*pi*x1)*(x3 + sin(6*pi*x1)) + 160*3^(1/2)*pi^2*cos(6*pi*x1)*sin((3^(1/2)*pi*(20*x3 + 20*sin(6*pi*x1)))/3) + 1, 0, 16*x3 + 16*sin(6*pi*x1) + diff(max([0, (7*sin(4*pi*x1))/10], [], 2, 'omitnan', ~in(x1, 'real')), x3) + (80*3^(1/2)*pi*sin((3^(1/2)*pi*(20*x3 + 20*sin(6*pi*x1)))/3))/3;

diff(max([0, (7*sin(4*pi*x1))/10], [], 2, 'omitnan', ~in(x1, 'real')), x1) - 96*pi*cos((2*pi)/3 + 6*pi*x1)*(x2 - sin((2*pi)/3 + 6*pi*x1)) - 240*2^(1/2)*pi^2*cos((2*pi)/3 + 6*pi*x1)*sin((2^(1/2)*pi*(20*x2 - 20*sin((2*pi)/3 + 6*pi*x1)))/2) - 1, 16*x2 - 16*sin((2*pi)/3 + 6*pi*x1) + diff(max([0, (7*sin(4*pi*x1))/10], [], 2, 'omitnan', ~in(x1, 'real')), x2) + 40*2^(1/2)*pi*sin((2^(1/2)*pi*(20*x2 - 20*sin((2*pi)/3 + 6*pi*x1)))/2), 0]

JacobianF =

X = [0.2703 0.6193 0.9370];

df= subs(JacobianF, [x1 x2 x3], X)

df =

Dyuman Joshi 2024-1-1

在 MATLAB Online 中打开

As for why the expression is not evaluated to a numeric value, I am not so sure.

If I had to guess, I'd say it is because you have assumed x1, x2 and x3 to be not-real i.e. complex, yet you have provided a real value.

But then, the Sym engine is unable to evaluate the expression for complex numbers as well -

syms x1 x2 x3

JacobianF = [diff(max([0, (7*sin(4*pi*x1))/10], [], 2, 'omitnan', ~in(x1, 'real')), x1) + 96*pi*cos(6*pi*x1)*(x3 + sin(6*pi*x1)) + 160*3^(1/2)*pi^2*cos(6*pi*x1)*sin((3^(1/2)*pi*(20*x3 + 20*sin(6*pi*x1)))/3) + 1, 0, 16*x3 + 16*sin(6*pi*x1) + diff(max([0, (7*sin(4*pi*x1))/10], [], 2, 'omitnan', ~in(x1, 'real')), x3) + (80*3^(1/2)*pi*sin((3^(1/2)*pi*(20*x3 + 20*sin(6*pi*x1)))/3))/3;

diff(max([0, (7*sin(4*pi*x1))/10], [], 2, 'omitnan', ~in(x1, 'real')), x1) - 96*pi*cos((2*pi)/3 + 6*pi*x1)*(x2 - sin((2*pi)/3 + 6*pi*x1)) - 240*2^(1/2)*pi^2*cos((2*pi)/3 + 6*pi*x1)*sin((2^(1/2)*pi*(20*x2 - 20*sin((2*pi)/3 + 6*pi*x1)))/2) - 1, 16*x2 - 16*sin((2*pi)/3 + 6*pi*x1) + diff(max([0, (7*sin(4*pi*x1))/10], [], 2, 'omitnan', ~in(x1, 'real')), x2) + 40*2^(1/2)*pi*sin((2^(1/2)*pi*(20*x2 - 20*sin((2*pi)/3 + 6*pi*x1)))/2), 0];

X = [0.2703 0.6193 0.9370];

Y = X + X*i;

%Real

df1 = subs(JacobianF, [x1 x2 x3], X);

vpa(df1)

ans =

%Complex

df2 = subs(JacobianF, [x1 x2 x3], Y);

vpa(df2)

ans =

Rounak Saha Niloy 2024-1-2

在 MATLAB Online 中打开

I have sorted the max function. But I am having trouble with min functions.

I have the following function which needs to be converted-

function Output = b_flat(y,A,B,C)
    Output = A+min(0,floor(y-B))*A.*(B-y)/B-min(0,floor(C-y))*(1-A).*(y-C)/(1-C);
    Output = round(Output*1e4)/1e4;
end

I have converted it as-

function Output = b_flat(y,A,B,C)
    Output = A+piecewise(0<=floor(y-B),0,floor(y-B))*A.*(B-y)/B-piecewise(0<=floor(C-y),0,floor(C-y))*(1-A).*(y-C)/(1-C);
    Output = round(Output*1e4)/1e4;
end

But this gives me the following error. What might be causing the issue?

Output = A+piecewise(0<=floor(y-B),0,floor(y-B))*A.*(B-y)/B-piecewise(0<=floor(C-y),0,floor(C-y))*(1-A).*(y-C)/(1-C);

Error using mupadengine/feval_internal

First argument must be a condition.

Error in sym/piecewise (line 49)

pw = feval_internal(symengine, 'piecewise', lists{:}, 'ExclusiveConditions');

Error in CalculateJacobianF>b_flat (line 364)

Output = A+piecewise(0<=floor(y-B),0,floor(y-B))*A.*(B-y)/B-piecewise(0<=floor(C-y),0,floor(C-y))*(1-A).*(y-C)/(1-C);

Torsten 2024-1-2

在 MATLAB Online 中打开

Use

min(x,0) = 0.5*(x-abs(x))

as I used

max(x,0) = 0.5*(x+abs(x))

below.

Walter Roberson 2024-1-4

在 MATLAB Online 中打开

Looks like it works for me when y is symbolic.

syms y

b_flat(y, 1, 2, 3)

ans =

b_flat(y, -10, 5, 17)

ans =

function Output = b_flat(y,A,B,C)

Output = A+piecewise(0<=floor(y-B),0,floor(y-B))*A.*(B-y)/B-piecewise(0<=floor(C-y),0,floor(C-y))*(1-A).*(y-C)/(1-C);

Output = round(Output*1e4)/1e4;

end

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Answer 1

Walter Roberson 2024-1-1

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2065431-how-to-evaluate-a-symbolic-expression-having-max-and-diff#answer_1381176

The derivative of max() is not generally defined.

You would probably have more success if you defined in terms of piecewise() instead of in terms of max()

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Dyuman Joshi 2024-1-4

I guess the Sym engine does not have the ability to recognise that the definition of max() can be broken into a piecewise definition, than a derivative can be calculated.

I wonder if that is possible to implement or not.

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Answer 2

Torsten 2024-1-1

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2065431-how-to-evaluate-a-symbolic-expression-having-max-and-diff#answer_1381181

编辑：Torsten 2024-1-2

在 MATLAB Online 中打开

Use

max(x,0) = 0.5*(abs(x)+x)

for real x.

syms x1

f1 = max([0, (7*sin(4*pi*x1))/10], [], 2, 'omitnan', ~in(x1, 'real'))

f1 =

f2 = 0.5*(abs(7*sin(4*pi*x1)/10)+7*sin(4*pi*x1)/10)

f2 =

figure(1)

hold on

fplot(f1,[-0.5 0.25])

fplot(f2,[-0.5 0.25])

hold off

df1 = diff(f1,x1)

df1 =

df2 = diff(f2,x1)

df2 =

figure(2)

%fplot(df1,[-0.5 0.25])

fplot(df2,[-0.5 0.25])

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How to evaluate a symbolic expression having `max` and `diff`?

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How to evaluate a symbolic expression having `max` and `diff`?

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