R9482/Homework2b8f024d4069dmaster
Homework2
README.md
SP4E - Homework 2
General Info
This file provides a brief documentation and information related to the second Homework of the course "Scientific Programming for Engineers", fall 2019.
This homework is done by O. Ashtari and A. Sieber.
Last update: 10.30.2019
Project Description
The aim of this project is to implement a familly of objects intended to compute two types of series: an arithmetic series and a series to approximate the value of pi number. The user can then decide how to dump the results by either printing them to the screen or writing them to a file. If the later option is chosen, a python file is available to plot the results stored in the file.
Requirements
- CMake: minimum version 2.6
- Python
- numpy
- argparse
- matplotlib
Installation
Running
Series calculation in C++
Post-Processing with Python
A output_reader.py post-processing routine is implemented in the src folder. It is intended to plot the series data written to file. This python script is written with Python 3.7 and requires the libraries matplotlib, numpy and argparse to be installed. The program works with the simple following command line.
$ python output_reader.py -f path_to_file -s separator
The argument path_to_file refers the path to the file containing the data to be plotted (the path is to be taken from the location of the python file). The argument separator refers to the type of delimiter used in the data file to separate the different quantities. This second argument can either be tab, comma or pipe.
Work separtion between the authors
The idea was writing mother classes as interfaces first. This task was done at the exercise session: structure of two classes Series and DumperSeries, including their virtual functions, was formed and written. To be abale to work remotely, each of us took one of the daughters of Series (namely compute_arithmetic and compute_pi) and one of the daughters of DumperSeries (namely PrintSeries and WriteSeries) to work on. Moreover, two other major tasks of writing a python script for visualization and modifying Series class to avoid re-calculations were split between authors. Each of us developed his own part and worked on his own main.cc. Finally, mains were merged and the project reviewed.
Concluding remarks
Complexity of the program
Arithmetic Series
In the arithmetic series, summing from 1 to N needs N adding (+) operations, thus to print or write the result for different values of N from 1 to m, number of operations will be:
write num. of operations --- ------------------ 1 1 2 2 3 3 4 4 m m --- ------------------ sum1: m*(m+1)/2
However, if we keep track of the latest N as well as the corresponding value of summation, the program needs to only add one term to the available value. So, number of operations will be:
write num. of operations --- ------------------ 1 1 2 1 3 1 4 1 m 1 --- ------------------ sum2: m
Therefore, for a large m the ratio sum1/sum2 tends to 0.5*m.
PI Series
For pi calculation, the problem is more complicated. to add each term like 1.0/(i*i) to the summation, one multiplying operation (*), one inversion operation (/), and one adding operation (+) (totally three operations) is required. Finally, to clculate the approximation for pi, square root of the summation multiplied by 6 is returned, which means two more operations. Hence, number of operations will be:
write num. of operations --- ------------------ 1 1*(3)+2 2 2*(3)+2 3 3*(3)+2 4 4*(3)+2 m m*(3)+2 --- ------------------ sum2: m*(3*m+7)/2
However, if we keep track of the latest N as well as the corresponding value of summation (without square root), the program needs to only add one term to the available value (three operations), multiply the result by 6, then claculate the square root. So, number of operations will be:
write num. of operations --- ------------------ 1 3+2=5 2 3+2=5 3 3+2=5 4 3+2=5 m 3+2=5 --- ------------------ sum2: 5*m
Therefore, for a large m the ratio of sum1/sum2 tends to 0.3*m.