c-f-h / baryrat Goto Github PK

If I want to calculate the AAA with complex numbers it gets a wrong solution.
I think this is due to the fact, that scipys SVD does calculate U,S,V^H whereas Matlab calculates U,S,V.
This should be solved by editing line

to
wj = Vh[-1, :].conj()

I'm trying to use BRASIL for function approximation with a fraction of polynomials.

Once I approximated a function and got a BarycentricRational object, how do I represent this object as a fraction of polynomials, e.g. (c0 + c1 * x + c2 * x^2) / (k0 + k1 * x + k2 * x^2)? How do I get c0, c1, c2, k0, k1, k2 from the barycentric representation?

Hello and thanks for making this package available! I get an error trying to use BRASIL with mpmath. This is my sample code:

from baryrat import brasil
import mpmath as mp

mp.dps = 150

r = brasil(lambda x: mp.sqrt(x), interval=[0.0, 1.0], deg=(7,7))

and the error:

TypeError: cannot create mpf from array([0.00273905, 0.02447174, 0.0669873 , 0.12842759, 0.20610737,
       0.29663168, 0.39604415, 0.5       , 0.60395585, 0.70336832,
       0.79389263, 0.87157241, 0.9330127 , 0.97552826, 0.99726095])

Is this not possible? Or am I doing something wrong?

Hello,

I'm trying to fit a multivariate function. While I've had success with PolyRat, implementing the resulting fit in embedded code is rather ... complex. (And using a rational function converted from that unfortunately fails hard in numerical instability.)

After some digging, it seems that the baricentric formulae used in BaryRat are much more friendly to have a go at, while still offering (hopefully) enough numerical stability.

Q: May I ask if it is possible to do such a thing with BaryRat? And if so, how?

Q: The function I'm working with takes 2 real-valued inputs, for one output. Could it perhaps be possible to treat the inputs as a complex number and fit that?

Thank you,
Tom

Hi,

I have attempted to approximate a univariate complex function with a complex argument using BRASIL. However, it appears that the BRASIL method does not support this type of approximation. Can you provide guidance on the implementation of this functionality? If so, I would be really happy to help and attempt to contribute a little something back to this nice project.

Hello,

I want to generate rational approximation of degree (m,n) m!=n.

I invoke brasil with:
eps = np.finfo(np.double).eps
r = brasil(lambda x: x**args.alpha, (0, 1), (7,6), tol=eps, npi=-30, maxiter=10000)

where alpha is the fractional power.

I get the following error:

Traceback (most recent call last):
File "./python_code/./bura_mul_k1.py", line 20, in
r = brasil(lambda x: x**args.alpha, (0, 1), (m,n), tol=eps, npi=-30, maxiter=10000)
File "./python_code/baryrat.py", line 513, in brasil
n = 2 * deg + 1 # number of interpolation nodes
TypeError: can only concatenate tuple (not "int") to tuple

Best Regards,
Dimitar

Some other packages have derivatives and I'm not sure if integrals have a efficient representation.