question

[avnerbarr]

How can i add a customized error function?

[claudejrogers]

Do you mean you want to fit data to an equation of the form erf(x)=\frac{2}{\sqrt{\pi}}\int^{x}_{0}e^{-z^{2}}dz, or something similar?

[avnerbarr]

I have a graph and I want to solve for points : the form of the minimization I am trying to solve for is as follows:

E(q1,q2,...qn) = SIGMA(e i,j) [ a(i,j) ( || qi -q j|| ^2 - dij)^2]

where qi's are the coordinates (x,y) e(i,j) are the edge from qi to qj and a(i,j) , d(i,j) are empericil values.

[claudejrogers]

I might not understand you correctly, so forgive me if this doesn't answer the question. This program doesn't provide a general minimization algorithm, but instead attempts to solve a very specific least squares problem:

minimize || f ( x ) ||, or equivalently find x* = argmin_x{F( x )}, where (in latex)

F(\mathbf{x}) = \frac{1}{2}\sum_{i = 1}^{m}(f_i(\mathbf{x}))^2 = \frac{1}{2}||\mathbf{f}(\mathbf{x})|| = \frac{1}{2}\mathbf{f}(\mathbf{x})^\top\mathbf{f}(\mathbf{x})

and

f_i(\mathbf{x}) = m_i(\mathbf{x}, t) - y_i

In other words, if one has a model equation m( x, t) that is expected to fit to data y, this program tries to find values for the parameters given in x to minimize the sum of squares of the residuals for each data point. The algorithm assumes that f has continuous second partial derivatives. Changing the form of F( x ) would probably require rewriting the program.

[avnerbarr]

ok. so in other words only the supplied functions will work? (in the big case statement) I'm looking for a general least squares solver for ios/mac if you know of one.

On Oct 28, 2012, at 10:28 PM, claudejrogers notifications@github.com wrote:

I might not understand you correctly, so forgive me if this doesn't answer the question. This program doesn't provide a general minimization algorithm, but instead attempts to solve a very specific least squares problem:

minimize || f ( x ) ||, or equivalently find x* = argmin_x{F( x )}, where (in latex)

F(\mathbf{x}) = \frac{1}{2}\sum_{i = 1}^{m}(f_i(\mathbf{x}))^2 = \frac{1}{2}||\mathbf{f}(\mathbf{x})|| = \frac{1}{2}\mathbf{f}(\mathbf{x})^\top\mathbf{f}(\mathbf{x}) and

f_i(\mathbf{x}) = m_i(\mathbf{x}, t) - y_i In other words, if one has a model equation m( x, t) that is expected to fit to data y, this program tries to find values for the parameters given in x to minimize the sum of squares of the residuals for each data point. The algorithm assumes that f has continuous second partial derivatives. Changing the form of F( x ) would probably require rewriting the program.

— Reply to this email directly or view it on GitHub.

[claudejrogers]

Oh, sorry, I did misunderstand you. Yes, you can add additional functions. I'll update the readme with instructions shortly.

You are talking about changing m(x, t), which is fine.

[claudejrogers]

Ok, I updated the readme. Let me know if you have additional questions.