MATLAB: Problems using the equality indicator. Matlab returns 0 when I check the equality of 2 terms. At the same time it returns 1 for the ratio of the same terms.

equationssymbolic

mu1 =

(k^psi*(b – 1)*(psi – 1))/(y2 + k^psi – b*k^psi – b*psi*y2)

>> mu2

mu2 =

-(psi – 1)/((y2*(b*psi – 1))/(k^psi*(b – 1)) + 1)

>> simplify(mu1)==simplify(mu2)

ans =

>> simplify(mu1/mu2)

ans =

Best Answer

factor(mu1) == factor(mu2)

Related Solutions

MATLAB: Find intersection of 2 normal distribution

The ‘val’ value is the x-value of the intersection, however you need to start fzero in the correct region for it to return the correct value. It is then straightforward to calculate the y-value from either Gaussian function, since they are both approximately the same at that point.

I changed your code slightly so it returns the correct results:

mu1 = 160;  
var1 = 20;
mu2 = 175;
var2 = 15;
yfun = @(mu,var, x)(2*pi*(var))^(-0.5)* exp(-((x-mu).^2)/(2*(var)));
val = fzero(@(x) yfun(mu1, var1, x) - yfun(mu2, var2, x), mean([mu1,mu2]))
yval = yfun(mu1, var1, val)

producing:

val =
          167.872647061767
yval =
        0.0189439821229373

Experiment to get the result you want.

MATLAB: Solve returns different answers to the same question

It is possible to demonstrate that one of the roots you are seeing imaginary portions for has a closed form value of

 10/63 * sqrt(3) * sqrt(499) * cos(atan(63/1596949 * sqrt(3) * sqrt(203226157))/3 + pi/6) - 110/63 - 10/63 * sqrt(499) * sin(atan(63/1596949 * sqrt(3) * sqrt(203226157))/3 + pi/6)

That involves two arctan of the same expression 63*sqrt(3)*sqrt(203226157)*(1/1596949) . You can evaluate that expression and see that it is a number between 0 and 1; therefore the arctan is real-valued. Therefore the expression as a whole is real valued.

The imaginary components you see do not exist and are due to round-off error. If you increase the number of digits in the vpa then the imaginary components will get smaller and smaller.

... actually I need to revise that closed form solution, as I was not paying attention to the way the variables get renamed. I will come back to this with a correction; I need to do something else for now.

Best Answer

Related Solutions

MATLAB: Find intersection of 2 normal distribution

MATLAB: Solve returns different answers to the same question

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