## Substituting an expression not giving intended result

### John (view profile)

on 7 Jan 2019
Latest activity Commented on by Star Strider

on 7 Jan 2019

### Star Strider (view profile)

I'm trying to simplify the following expression using the subs function. In the code below, I was expecting Asubs = 3*Phi. Any ideas on what might be wrong in my code?
clear all;
clc;
syms phi(c,cbar,sigma) Phi(c,cbar,sigma) A(csol,cbar,sigma)
assumeAlso(sigma,'real')
assumeAlso(sigma>0)
phi(c,cbar,sigma)= (1/sqrt(2*sym(pi)*sigma^2))*exp(-(c-cbar)^2/(2*sigma^2))
A(csol,cbar,sigma)=3*int(phi(c,cbar,sigma),c,-inf,csol)
Phi(csol,cbar,sigma) = 1/2 + 1/2*erf(sqrt(2)*(csol-cbar)/(2*sigma))
%Phi(x,sigma) = 1/2 + 1/2*erf(sqrt(2)*(x)/(2*sigma))
Asubs = subs(A,Phi)

### Star Strider (view profile)

on 7 Jan 2019

Since ‘Phi’ does not appear as such specifically in ‘A’, the substitution will fail.
Perhaps this is closer to what you want:
As = simplify(A/Phi)
prodcing:
As(csol, cbar, sigma) =
3

John

### John (view profile)

on 7 Jan 2019
I see. The code in the question is a kind of mwe for the following problem. The normal distribution CDF and PDF appear in many of the formulas that I'm working. I wanted to shorten those formulas by using $\Phi$ and $\phi$ to represent them in the expressions. In case you know of a workaround, I'd love to hear.
Star Strider

### Star Strider (view profile)

on 7 Jan 2019
I am still at a loss to understand what you are doing.
I would not use the Symbolic Math Toolbox for such calculations. It is primarily designed for derivations and other such. Use the matlabFunction (link) function to create anonymous functions from your symbolic functions. Then use them in your calculations.

on 7 Jan 2019

syms c cbar sigma Phi A csol
assumeAlso(sigma,'real')
assumeAlso(sigma>0)
phi(c,cbar,sigma)= (1/sqrt(2*sym(pi)*sigma^2))*exp(-(c-cbar)^2/(2*sigma^2))
A(csol,cbar,sigma)=3*int(phi(c,cbar,sigma),c,-inf,csol)
Phi(csol,cbar,sigma) = 1/2 + 1/2*erf(sqrt(2)*(csol-cbar)/(2*sigma))
%Phi(x,sigma) = 1/2 + 1/2*erf(sqrt(2)*(x)/(2*sigma))
Asubs = vpa(subs(A,Phi)) % cbar csol and sigma values are not known

John

### John (view profile)

on 7 Jan 2019
This doesn't make the substitution. It only evaluates the square roots, pi, etc