Cannot integrate the function. double to sym

Question

I'm trying to integrate the function. I'm getting the error Undefined function 'int' for input arguments of type 'double'. Here is my code:

P = @(m,sigma,t,C) (normcdf((C-m/sigma)/sqrt(t),0,1) - exp(2*C*m/sigma)*normcdf((-C-m/sigma)/sqrt(t),0,1));
Pr = @(m1,m2,sigma_1, sigma_2,t,C) (P(m1,sigma_1,t,C)*P(m2,sigma_2,t,C));
P_S = @(m1,m2,sigma_1,sigma_2,C) (1 - int(Pr(m1,m2,sigma_1,sigma_2,t,C), t, 0, inf));

What am I doing wrong and how to integrate this function?

horchler horchler · Accepted Answer · 2013-06-05T21:56:48

normcdf is used for floating point calculations and does not support symbolic input. You need to write your own. Luckily that's pretty easy. Try replacing normcdf with this:

normcdf_sym = @(x,mu,sig) (1./(sig*sqrt(2*sym('pi'))))*int(exp(-(t-mu).^2./(2*sig.^2)),t,-Inf,x);

Or with this, which is is equivalent to the above:

normcdf_sym = @(x,mu,sig) (1+erf((x-mu)./(sig*sqrt(2))))/2;

Also, you'll likely want to define your symbolic variables as real: syms m sigma t C real;. Or use the assume and assumeAlso functions.

All this is assuming you want to use symbolic integration in the first place, as opposed to numeric integration.

Cannot integrate the function. double to sym

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