The vectfit
function approximates a response
(generally a vector) with a rational function:
where and
are poles and residues in
the complex plane and
are
the polynomial coefficients.
When
is a vector, all
elements become fitted with a common pole set.
The identification is done using the pole relocating method known as Vector Fitting [1] with relaxed non-triviality constraint for faster convergence and smaller fitting errors [2], and utilization of matrix structure for fast solution of the pole identifion step [3].
- [1] B. Gustavsen and A. Semlyen, "Rational approximation of frequency domain responses by Vector Fitting", IEEE Trans. Power Delivery, vol. 14, no. 3, pp. 1052-1061, July 1999.
- [2] B. Gustavsen, "Improving the pole relocating properties of vector fitting", IEEE Trans. Power Delivery, vol. 21, no. 3, pp. 1587-1592, July 2006.
- [3] D. Deschrijver, M. Mrozowski, T. Dhaene, and D. De Zutter, "Macromodeling of Multiport Systems Using a Fast Implementation of the Vector Fitting Method", IEEE Microwave and Wireless Components Letters, vol. 18, no. 6, pp. 383-385, June 2008.
All credit goes to Bjorn Gustavsen for his MATLAB implementation. (http://www.sintef.no/Projectweb/VECTFIT/)
The vectfit
functions are implemented in C++, using xtensor
for multi-dimensional arrays and xtensor-blas
for linear-algebra operations.
The C++ functions are wrapped into a Python extension module through
xtensor-python
and
pybind11
.
import vectfit as m
import numpy as np
s = np.array([3., 3.5, 4., 4.5, 5., 5.5, 6.])
f = np.array([[4.98753117e-02, 3.09734513e-01, 1.18811881e+00,
6.53846154e+00, 2.20000000e+02, 1.03846154e+01,
3.16831683e+00],
[-4.98753117e-01,-2.21238938e-01, 9.90099010e-01,
9.61538462e+00, 4.00000000e+02, 2.11538462e+01,
6.93069307e+00]])
weight = 1.0/f
init_poles = [4.5 + 0.045j, 4.5 - 0.045j]
poles, residues, cf, fit, rms = m.vectfit(f, s, init_poles, weight)
-
C++ compiler such as g++
sudo apt install g++
-
Necessary libraries including
xtensor
,xtensor-blas
(>=0.15),xtensor-python
, andpybind11
Refer to 'installation steps on Ubuntu' for building necessary libraries from source, or, it is convenient to install all the libraries through conda package manager:
conda install -c conda-forge xtensor-blas xtensor-python
On Unix (Linux, OS X)
- clone this repository
git clone https://github.com/liangjg/vectfit.git
pip install ./vectfit
On Windows (Requires Visual Studio 2015)
-
For Python 3.5:
- clone this repository
pip install ./vectfit
-
For earlier versions of Python, including Python 2.7:
xtensor requires a C++14 compliant compiler (i.e. Visual Studio 2015 on Windows). Running a regular
pip install
command will detect the version of the compiler used to build Python and attempt to build the extension with it. We must force the use of Visual Studio 2015.- clone this repository
"%VS140COMNTOOLS%\..\..\VC\vcvarsall.bat" x64
set DISTUTILS_USE_SDK=1
set MSSdk=1
pip install ./vectfit
Note that this requires the user building
vectfit
to have registry edition rights on the machine, to be able to run thevcvarsall.bat
script.
On Windows, the Visual C++ 2015 redistributable packages are a runtime requirement for this project. It can be found here.
If you use the Anaconda python distribution, you may require the Visual Studio runtime as a platform-dependent runtime requirement for you package:
requirements:
build:
- python
- setuptools
- pybind11
run:
- python
- vs2015_runtime # [win]
Documentation for the example project is generated using Sphinx. Sphinx has the ability to automatically inspect the signatures and documentation strings in the extension module to generate beautiful documentation in a variety formats. The following command generates HTML-based reference documentation; for other formats please refer to the Sphinx manual:
cd vectfit/docs
make html
Running the tests requires pytest
.
py.test .