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

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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);
  12 Comments
Torsten
Torsten on 2 Jan 2024
Use
min(x,0) = 0.5*(x-abs(x))
as I used
max(x,0) = 0.5*(x+abs(x))
below.
Walter Roberson
Walter Roberson on 4 Jan 2024
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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Answers (2)

Walter Roberson
Walter Roberson on 1 Jan 2024
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()
  1 Comment
Dyuman Joshi
Dyuman Joshi on 4 Jan 2024
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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Torsten
Torsten on 1 Jan 2024
Edited: Torsten on 2 Jan 2024
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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