I am working with a curve with two parameters (α,β), in addition to the independent (x between 0 and 1) and dependent (y) variables. I have a function which takes a value for the independent variable and the two parameters
function(x,α,β) and returns the slope and y-intercept (
[m,b]) for the tangent of the curve at the given x.
I need to find values of x with the same tangent line, i.e.
x[n]. Is there a solver I can use for this?
For reference/experimentation, here is the function:
def tan_Gmix_van_Laar(x,α,β): if x>1 or x<0: print("for tan_Gmix_van_Laar: x out of bounds") return G = (x-x**2)*α*β/(β+(α-β)*x) + x*np.log(x)+(1-x)*np.log(1-x) m = α*β/(β+(α-β)*x)*(1-2*x) - α*β*(α-β)/((α-β)*x+β)**2*(x-x**2) + np.log(x/(1-x)) b = G-m*x tanparams = np.array([m,b]) return tanparams