R9482/Homework2e53b138a67a2master
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
Installation
Running
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. 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.
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-1 adding (+) operations. So, to print or write the result for different values of N from 1 to say m, number of operations will be:
N 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:
N num. of operations --- ------------------ 1 1 2 1 3 1 4 1 m 1 --- ------------------ sum2: m
Therefore, for a large m the ratio of sum1/sum2 tends to 0.5*m.
PI Series
For pi calculation, the problem is more complicated. to add each term 1.0/(i*i), one multiplying operation (*), one inversion operation (/), and one adding operation (+) is required. Finally, square root of the summation multiplied by 6 is returned. So, number of operations will be:
N num. of operations --- ------------------ 1 1*(1+1+1)+1+1=5 2 2*(1+1+1)+1+1=8 3 3*(1+1+1)+1+1=11 4 4*(1+1+1)+1+1=14 m m*(1+1+1)+1+1=3m+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, multiply the result by 6, then claculate the square roo. So, number of operations will be:
N num. of operations --- ------------------ 1 (1+1+1)+1+1=5 2 (1+1+1)+1+1=5 3 (1+1+1)+1+1=5 4 (1+1+1)+1+1=5 m (1+1+1)+1+1=5 --- ------------------ sum2: 5*m
Therefore, for a large m the ratio of sum1/sum2 tends to 0.3*m.