260

[cwhanse]

Fix typing, add whatsnew note

[mikofski]

@cwhanse why not use scipy.optimize.newton here in pvsystem.v_from_i on line 1846?

from scipy.optimize import newton
# Three iterations of Newton-Raphson method to solve
# w+log(w)=logargW. The initial guess is w=logargW. Where direct
# evaluation (above) results in NaN from overflow, 3 iterations
# of Newton's method gives approximately 8 digits of precision.
lambertwterm_log = newton(lambda w: w + np.log(w) - logargW, logargW, lambda w: 1 + 1/w)

[cwhanse]

This was transcribed from Matlab. No reason not to use the scipy function, but I doubt there's any performance advantage - after I fix the failed checks, of course.

[mikofski]

True, I checked, performance at least for the test case is exactly the same. But IMO scipy.optimize.newton will be easier to maintain. For example, you wouldn't have to update the number of iterations to depend on order as you did in #260

[wholmgren]

I think the newton function will only work with scalar inputs. I'm guessing that it's more efficient to do it Cliff's original way for array input of non-trivial length.

I did not know you could highlight a block of code like that in a github link!

[mikofski]

I chose newton specifically because this example uses scalar inputs. The equivalent multivariate solver is scipy.optimize.fsolve based on MINPACK’s hybrd and hybrj which is a modified version of Powell's method and the Newton-Raphson methods.

From the GNU Scientific Library:

This is a modified version of Powell’s Hybrid method as implemented in the HYBRJ algorithm in MINPACK. Minpack was written by Jorge J. Moré, Burton S. Garbow and Kenneth E. Hillstrom. The Hybrid algorithm retains the fast convergence of Newton’s method but will also reduce the residual when Newton’s method is unreliable. The algorithm uses a generalized trust region to keep each step under control.

from scipy import optimize
# Three iterations of Newton-Raphson method to solve
# w+log(w)=logargW. The initial guess is w=logargW. Where direct
# evaluation (above) results in NaN from overflow, 3 iterations
# of Newton's method gives approximately 8 digits of precision.
lambertwterm_log = optimize.fsolve(
    func=lambda w: w + np.log(w) - logargW,
    x0=logargW,
    fprime=lambda w: 1 + 1/w)

If even more flexibility is needed, then scipy.optimize.root is the general interface to multivariate equation solvers. You can specify the method argument, EG: lm is Levenberg-Marquardt for least square fitting of non-square systems of equations.

@cwhanse the equivalent of this in MATLAB would be the Optimization Toolbox's fsolve which I re-implemented in the MATLAB FEX Newton-Raphson solver for times when I didn't have access to the expensive toolbox.

[mikofski]

I'm okay with it as it is:

1. I don't want to block merging it,
2. it is working well and is identical to the SciPy methods,
3. and it's already quite compact and short,

but IMO I think that mature, well established, easily available methods are usually more transparent to users and easier to maintain than custom re-implementations.

[cwhanse]

Closing this to submit a clean pull request