Function a Newton Scanner - ScanForRoot - Newton's Algorithms - Multiplication of Matrices Using Software Components - C++ Project - Engineering Assignment Help

Assignment Task

Task 1
Please develop the function ScanForRoots to scan a given function f(x) for its roots using the newton’s algorithm.

The Interface
The program should read the following input parameters from an input file. The file’s format is given as follows.

1. [max number of roots to find]
2. [lower bound: lb] [upper bound: up] [step width: sw]
3. [precision eps] [stepwidth h] [max iteration: ix]

The program should search the root of a function with the starting position x0. The starting position x0 should be taken from the interval which is described by the parameters ub, lb and sw read from the input
file. The found roots of the function should be saved in a dynamical array, which should be a parameter of the function ScanForRoots The size of the array should be set by a parameter, which is read from the input file.
An example data file is given below.

1. 10
2. -10. +10. 0.1
3. 1.e-7 0.01 100

In the project, a reasonable interval should be selected to be able to check the quality of the developed software.

The Function ScanForRoots
So the interface to ScanForRoots is the following.

The return value of ScanForRoots should give the number of found roots. The roots should not be stored multiple.
The main program which should call ScanForRoots should do the following.

• open, read and close the input file ScanForRoots.inp.
• call ScanForRoots1 to search for the function’s roots.
• write a little report which gives a list of the found roots

Task 2

Please write a program based on the software components we have developed in our lecture for the
multiplication of some matrices as given in the equation ??.
S = A1 . A2 . . . An
The User Interface
The problem should be described in an input file with the following format. The first line contents the number of matrices to multiply. The second line contents the number of rows and columns of the first matrix. The following lines contain the values of the first matrix. The next line contents the dimension of the next matrix and the following lines contain the data of the matrix. The problem should be scalable, which means you should use dynamically allocatable arrays to implement the program variables. To hold the matrix data in memory you should minimize the allocated memory to make the program as efficient as possible. Step by step the read matrices should be printed to an output file and in the end, the product matrix should be given in the output file. The format and the values of the used matrix data are given in a text input file of the following format
as discussed above.

1. [number of matrices]
2. [rows 1] [columns 1]
3. [data of matrix 1]
4. [rows 2] [columns 2]
5. [data of matrix 2]
6. ...
7. [rows of the last matrix] [columns of the last matrix]
8. [data of the last matrix]

An example data file to multiply three matrices is given below.

1. 3
2. 3 4
3. 1. 2. 3. 4.
4. 5. 6. 7. 8.
5. 9. 10. 11. 12.
6. 4 2
7. 0.1 0.2
8. 0.3 0.4
9. 0.5 0.6
10. 0.7 0.8
11. 2 1
12. -1.
13. -2.

Task 3

The third project implements a new C++ class for a combined profile. The class to calculate the section values for the combined profile should be implemented like the H- or U-profile of our lecture CLFE.

Combined Profile
The combined profile is a linked group of standard profiles given in the standard table book of European profiles. So every part of the combined profile comes with it’s set of parameters (like h=height, w=width, t=thickness and so on). Our combined profile therefor is the aggregation of all these profile parameters.

Our Goal
The goal of this project is, to compare the result of the thin-walled approximation with the exact values of the profile’s area and moment of inertia. To do this, the exact values should be calculated in a testable form using the exact values of the single profiles from the table book. The results should be discussed and evaluated. The deviations should be given in percent.

The Code
It’s recommended to use parts of the code we have developed in the lecture. Please don’t forget the error checking in the code. The code should be able to detect wrong input data and should also be able to handle the special cases we have discussed in the lecture. The code should be commented on.All classes should be discussed using UML diagrams (see the script). Algorithms should be discussed using flow charts.

The Report
The report for this project should contain a section, which describes the theory of the problem. One section should describe the usage of the developed program (like a user manual) and one section should describe the code (like a programmer guide). Here we need a description of the interfaces (parameters) of the used functions and subprograms. Algorithms should be discussed using flow charts. And don’t forget the layout. The calculation of the analytical i.e. the exact section values (area and moment of inertia) have to be shown in detail step by step in a verifiable way, using the section values of the tables. The evaluated error should be discussed.

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