while iam trying to execute my code iam getting error

x = sym('x');

y=2*x-1

h(1)=1;

h(2)=2*y;

n=input('enter number of polynomials required ');

for i=3:n

h(i)=2*y*h(i-1)-2*(i-2)*h(i-2);

end

disp(h);

for i=1:n

k(i)=(2/sqrt(pi))*h(i);

end

disp(k)

error is

Error in hermite (line 4)

h(2)=2*y;

Caused by:

Error using symengine

Unable to convert expression containing symbolic variables into double array. Apply 'subs' function first to substitute values for

variables.

Answer 1

[Rishi]

Hi prithvi,

I understan that you want to know why you are getting the given error.

The error you're encountering is due to trying to perform an operation that mixes symbolic and numeric computations in MATLAB. You are using 'sym' to define 'x' as symbolic variable and then defining 'y' as a symbolic expression in terms of 'x'. The variable 'h' is being used as a numeric array, but you're trying to assign a symbolic expression, 'y', to 'h(2)'.

To fix this error, you can define 'h' as a symbolic array from the start. Here is the edited code:

syms x; % Define x as a symbolic variable
y = 2*x - 1; % Define y as a symbolic expression

n = input('Enter the number of polynomials required: '); % Get the number of polynomials from the user
h = sym('h', [1 n]); % Initialize h as a symbolic array of size n

h(1) = 1; % Set the first Hermite polynomial
h(2) = 2*y; % Set the second Hermite polynomial

for i = 3:n
    h(i) = 2*y*h(i-1) - 2*(i-2)*h(i-2); % Recurrence relation for Hermite polynomials
end

disp(h); % Display the Hermite polynomials

k = sym('k', [1 n]); % Initialize k as a symbolic array of size n

for i = 1:n
    k(i) = (2/sqrt(pi))*h(i); % Scale the Hermite polynomials
end

disp(k); % Display the scaled Hermite polynomials

This will result in 'h' and 'k' both being a symbolic array. If you wish to evaluate these polynomials at specific numeric values, you can use the 'subs' function to substitute a numeric value for 'x'.

You can learn more about the 'subs' function here:

https://www.mathworks.com/help/symbolic/subs.html

Hope this helps!

[prithvi]

Thank you so much 🙏🙏🙏

Answer 2

[Dyuman Joshi]

Numeric arrays in MATLAB are homogenous.

When you initialize h(1) as a double array, then any elements to be added to it are expected to be double or something that can be converted to a double (of course, of compatible size for concatenation).

But since 2*y is a symbolic variable, it can't be converted to a double array, thus you get the error, which states the same as well.

What can you do now?

You can preallocate the array h as a symbolic array -

x = sym('x');
y = 2*x-1;

y = 

n = 5; %input('enter number of polynomials required ');

%One of the option is to preallocate the arrays as with zeros()
h = zeros(1, n, 'sym')

h = 

h(1) = 1;
h(2) = 2*y;

for i=3:n
    h(i) = 2*y*h(i-1)-2*(i-2)*h(i-2);
end
disp(h);

Also, you can write k as follows -

%Vectorized form
k = (2/sqrt(sym('pi')))*h;
disp(k)

[prithvi]

Thank you so much 🙏🙏🙏