Smooth Transition Between Functions

 Stitching together two functions is sometimes required as a way to transition from one dependence to another. The following schematic describes the idea pictorially:

Two different approaches are considered in this PDF (or this Jupyter Notebook).

Trapezoidal rule in log-log space

Consider the problem described in this StackOverFlow post. You have a function with certain smoothness properties that are apparent on a log-log plot. This is often accompanied by a large domain of integration. It seems worthwhile to "integrate in logspace", whatever that means. 

This Jupyter notebook probes this question and makes some recommendations.

Quicktip: Reindent Python Scripts

Suppose part of a python file uses spaces for indentation, while another part uses tabs. This will throw up exceptions at runtime. So the question is how to fix it.

One answer is to use the python script reindent.py. Stick it in some folder (~/bin/) in the default path and make it executable (chmod +x reindent.py).

The usage is straightforward:

reindent -n file.py

modifies the original file in place.

Matplotlib: Saving TIFF and JPG formats

With pillow installed, on my LinuxMint installation:

import matplotlib
matplotlib.use('TkAgg') # backend

x = np.linspace(0,1)
plt.plot(x, x**2)
plt.savefig('test.tiff', dpi=300, fmt="tiff", pil_kwargs={"compression": "tiff_lzw"})

QuickTip: Catching array bounds violations in Fortran 90

With gfortran, you can check if array bounds are violated during runtime by,

gfortran -fbounds-check myProg.f90