Viewing posts by christian
Visualizing Kaczmarz's Algorithm
Posted by: christian in Featured on frontpage on 18 Mar 2022
Kaczmarz's algorithm is an iterative algorithm for solving a system of linear equations. In its simplest form, the equations are written in matrix form, $\boldsymbol{A}\boldsymbol{x} = \boldsymbol{b}$ and, starting with the initial guess for the solution, $\boldsymbol{x}_1 = \boldsymbol{0}$, the zero vector, successive approximations are generated by projecting $\boldsymbol{x}_k$ onto the hyperplanes defined by the rows of $\boldsymbol{A}$: $\boldsymbol{a}_1, \boldsymbol{a}_2, \ldots$. $$ \boldsymbol{x}_{k+1} = \boldsymbol{x}_{k} + \frac{b_{i} - \boldsymbol{a}_i.\boldsymbol{x}_k}{|\boldsymbol{a}_i|^2} \boldsymbol{a}_i $$
ASCII art
Posted by: christian on 17 Mar 2022
This is just a simple script that takes an image and renders it as a grid of ASCII characters in the console. The character chosen depends on the brightness of each pixel in the image: the following sequence (from densest (brightest) to least dense) is used:
Raincloud plots comparing rainfall in Wales and East Anglia
Posted by: christian on 8 Feb 2022
As a companion script to this one on UK monthly temperatures the Met Office's data on rainfall can be compared in a similar way. The script below produces "raincloud" plots of the monthly rainfall since 1891 for two regions of the UK: East Anglia (relatively dry) and Wales (notoriously wet). The "cloud" for each month is a kernel density estimate of the distribution of the number of days on which at least 1mm of rain falls; the "rain" is a histogram of the same data.
Ridgeline plots of monthly UK temperatures
Posted by: christian in Featured on frontpage on 5 Feb 2022
The UK Meteorological Office offers historical data of mean monthly temperatures in different regions of the UK for download. For the purposes of this blog post, I downloaded the data corresponding to two regions: Scotland.txt and South_England.txt.
Linear least squares fitting of a two-dimensional data
Posted by: christian in Featured on frontpage on 30 Jan 2022
This earlier blog post presented a way of performing a non-linear least squares fit on two-dimensional data using a sum of (2D) Gaussian functions.