The fc_linalg3D Python package is an experimental package which contains all the code used in the report
Efficient algorithms to perform linear algebra operations on 3D arrays in vector languages, April 2018, F. Cuvelier.
Introduction:
More documentation is available on fc_linalg3D Python package dedicated web page with an User's Guide (pdf).
This package was tested under:
- CentOS 7, Fedora 27
- with Python 2.7.14 compiled from source (www.python.org)
- with Python 3.5.5 compiled from source (www.python.org)
- with Python 3.6.4 compiled from source (www.python.org)
- MacOS High Sierra
- with Miniconda Python 2.7 distribution (release 2.7.14)
- with Miniconda Python 3.6 distribution (release 3.6.4)
- with Python 2.7.14 (www.python.org)
- with Python 3.5.4 (www.python.org)
- with Python 3.6.5 (www.python.org)
- openSUSE Leap 42.3 7
- with Python 2.7.14 compiled from source (www.python.org)
- with Python 3.4.8 compiled from source (www.python.org)
- with Python 3.5.5 compiled from source (www.python.org)
- with Python 3.6.5 compiled from source (www.python.org)
- Ubuntu 18.04 LTS, 17.10, 16.04 LTS
- with Python 2.7.x (x=13,14,15) compiled from source (www.python.org)
- with Python 3.6.x (x=3,4,5) compiled from source (www.python.org)
- with Python 3.5.5 compiled from source (www.python.org)
- Windows 10
- with Miniconda Python 2.7 distribution (release 2.7.14)
- with Miniconda Python 3.6 distribution (release 3.6.4)
- with Python 2.7.15 (www.python.org)
- with Python 3.5.4 (www.python.org)
- with Python 3.6.5 (www.python.org)
Installation:
The fc_linalg3D Python package is available from the Python Package Index, so to install/upgrade simply type
pip install fc_linalg3D-0.0.1.tar.gz -U
Testing :
There are demos functions in the fc_linalg3D.demos module named linalg3D_*. For example, run the following code under Python:
from fc_linalg3D import demos demos.linalg3D_Lagrange()The output of this code is:
#--------------------------------------------------------------------------- # Benchmarking functions: # fun[0], Lag: fc_linalg3D.demos.Lagrange # fun[1], lagint: fc_linalg3D.demos.lagint # cmpErr[i], error between fun[0] and fun[i] outputs computed with function # lambda o1,o2: np.linalg.norm(o1-o2,np.inf) # where # - 1st input parameter is the output of fun[0] # - 2nd input parameter is the output of fun[i] #--------------------------------------------------------------------------- # Setting inputs of Lagrange polynomial functions: y=LAGRANGE(X,Y,x) # where X is numpy.linspace(a,b,n+1), Y=fun(X) and x is random values on [a,b] # n is the order of the Lagrange polynomial # fun function is: lambda x: np.sin(x) # [a,b]=[-1,1] # X: (n+1,) numpy array # Y: (n+1,) numpy array # x: (m,) numpy array # Error[i] computed with fun[i] output: # lambda y: np.linalg.norm(y-fun(x),np.inf) #--------------------------------------------------------------------------- #date:2018/05/03 10:16:55 #nbruns:5 #numpy: i4 i4 f4 f4 f4 f4 f4 #format: {:>5} {:>5} {:8.3f} {:10.3e} {:11.3f} {:10.3e} {:11.3e} #labels: m n Lag(s) Error[0] lagint(s) Error[1] cmpErr[1] 100 5 0.012 1.163e-05 0.014 1.163e-05 3.331e-16 100 9 0.020 2.859e-10 0.023 2.859e-10 8.882e-16 100 15 0.036 2.143e-14 0.038 2.143e-14 2.565e-14 500 5 0.056 1.162e-05 0.071 1.162e-05 5.551e-16 500 9 0.102 2.901e-10 0.118 2.901e-10 1.443e-15 500 15 0.178 2.232e-14 0.188 2.232e-14 2.287e-14 1000 5 0.111 1.163e-05 0.146 1.163e-05 5.551e-16 1000 9 0.202 2.902e-10 0.235 2.902e-10 1.554e-15 1000 15 0.361 2.576e-14 0.377 2.576e-14 2.620e-14