Introduction:

More documentation is available on fc_bench Python package dedicated web page with an User’s Guide (pdf).

Installation:

The fc_bench Python package is available from the Python Package Index, so to install/upgrade simply type

pip install fc_bench -U

Testing :

There are demos functions in the fc_bench.demos module named bench_*. For example, run the following code under Python:

from fc_bench import demos
demos.bench_Lagrange()

The output of this code is:

#---------------------------------------------------------------------------
# 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)
#---------------------------------------------------------------------------
# Benchmarking functions:
#   fun[0],            Lag: fc_bench.demos.Lagrange
#   fun[1],         lagint: fc_bench.demos.lagint
#---------------------------------------------------------------------------
# Comparative functions:
#   comp[i-1,0], compares outputs of fun[0] and fun[i]
#       lambda o1,o2: np.linalg.norm(o1-o2,np.inf)
#    For each comparative function:
#      - 1st input parameter is the output of fun[0]
#      - 2nd input parameter is the output of fun[i]
#---------------------------------------------------------------------------
#date:2019-12-21_16-56-34
#nbruns:5
#numpy:     <i8    <i8       f8           f8          f8           f8          f8
#format:  {:>5}  {:>5}  {:6.3f}     {:10.3e}     {:9.3f}     {:10.3e}     {:9.3e}
#labels:      m      n   Lag(s)     Error[0]   lagint(s)     Error[1]     comp[0]
            100      3    0.014    1.218e-03       0.019    1.218e-03   2.220e-16
            100      5    0.021    1.162e-05       0.028    1.162e-05   4.441e-16
            100      7    0.030    6.999e-08       0.037    6.999e-08   3.331e-16
            100     11    0.048    8.699e-13       0.056    8.689e-13   2.554e-15
            500      3    0.068    1.218e-03       0.095    1.218e-03   3.331e-16
            500      5    0.108    1.163e-05       0.144    1.163e-05   6.661e-16
            500      7    0.152    7.004e-08       0.190    7.004e-08   8.882e-16
            500     11    0.244    8.766e-13       0.282    8.766e-13   2.887e-15