4 by 4 Matrix Inversion

7/31/2019 4 by 4 Matrix Inversion

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4 by 4 MATRIX INVERSION

&BACKWARD COMPUTATION

Using Visual Basic 6.0

COURSE: SVY 312

COURSE TITLE: COMPUTERAPPLICATIONS IN SURVEYING

BY

GROUP

Lecturer: BADEJO (DR)

October, 2009


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GROUP MEMBERS

Name

Matric No

Obey Ife Akin

060405026

Oluwo Abisoye .I.T

070405027

Ufan Iboro Anietie

060405019

Falade


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Introduction

Before we can talk of programming, a certain problem has to exist and inorder to solve this problem there are some certain stages which one must

go through. These stages include:

- Existence of a problem to be solved

- Understanding the problem

- Planning the solution- Preparing flowchart or algorithm

- Coding

- Inputting program into the computer

- Program run and testing

- Documentation.

We have two problems to be dealt with so we are going to take a look at

how these problems can be solved using Visual Basic 6.0 application.


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ABOUT Visual Basic 6.0

Visual Basic is a tool that allows you to develop Windows (Graphic User

Interface - GUI) applications. The applications have a familiar appearance to

the user.

Visual Basic is an object-oriented programming development system for

creating applications that run under any of the Microsoft Windows

environments. It has the following two major components:

1. An extensive collection of prewritten tools, called controls. These controlsare accessible as icons within a graphical programming environment for

creating customized windows components (e.g., menus, dialog boxes, text

boxes, slide bars, etc.).

2. A complete set of program commands, derived from Microsofts

implementation of the classical Basic programming language. The

command set includes features that embrace contemporary programming

practices.

The overall approach to Visual Basic programming is twofold:

1. Create a user interface that is appropriate to the particular application athand.

2. Add a group of Basic instructions to carry out the actions associated with

each of the controls.

Visual Basic is event-driven, meaning code remains idle until called upon

to respond to some event (button pressing, menu selection etc). Visual

Basic is governed by an event processor. Nothing happens until an event is

detected. Once an event is detected, the code corresponding to that event

(event procedure) is executed. Program control is then returned to the

event processor.


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Some Features of Visual Basic include:

- Full set of objects - you 'draw' the application

- Lots of icons and pictures for your use

- Response to mouse and keyboard actions

- Clipboard and printer access- Full array of mathematical, string handling, and graphics functions

- Can handle fixed and dynamic variable and control arrays

- Sequential and random access file support

- Useful debugger and error-handling facilities

- Powerful database access tools

- ActiveX support

- Package & Deployment Wizard makes distributing your applications

simple

Structure of a Visual Basic Application

Application (Project) interface is made up of:

a) Forms - Windows that you create for user interface

b) Controls - Graphical features drawn on forms to allow user interaction(textboxes, labels, scroll bars, command buttons, etc.) (Forms and

Controls are objects.)

c) Properties - Every characteristic of a form or control is specified by a

property. Example properties include names, captions, size, color,

position, and contents. Visual Basic applies default properties. You can

change properties at design time or run time.

d) Methods - Built-in procedure that can be invoked to impart some action

to a particular object.

e) Event Procedures - Code related to some object. This is the code that isexecuted when a certain event occurs.


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f) General Procedures - Code not related to objects. This code must be

invoked by the application.

g) Modules - Collection of general procedures, variable declarations, and

constant definitions used by application.

Steps in Developing a Visual Basic

ApplicationThere are three primary steps involved in building a Visual Basic

application:

1. Draw the user interface

2. Assign properties to controls

3. Attach code to controls

4 by 4 MATRIX INVERSION

For this particular problem, we used the adjoint/co-factormethod to

create a program which can be used to solve the 4 by 4 matrix.

We started off by creating the user interface which looks like the one

below;


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Afterwards, we went on to write the codes for the program. The program

codes are written below;

Private Sub Command1_Click()

Dim a11 As Double, a12 As Double, a13 As Double, a14 As Double, a21 As

Double, a22 As Double, a23 As Double, a24 As Double, a31 As Double, a32

As Double, a33 As Double, a34 As Double, a41 As Double, a42 As Double,

a43 As Double, a44 As Double

Dim b11 As Double, b12 As Double, b13 As Double, b14 As Double, b21 As

Double, b22 As Double, b23 As Double, b24 As Double, b31 As Double, b32

As Double, b33 As Double, b34 As Double, b41 As Double, b42 As Double,b43 As Double, b44 As Double

Dim detA As Double

Dim c11, c12, c13, c14, c21, c22, c23, c24, c31, c32, c33, c34, c41, c42,

c43, c44 As Double

a11 = Val(e1.Text)


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a12 = Val(e2.Text)

a13 = Val(e3.Text)

a14 = Val(e4.Text)

a21 = Val(e5.Text)

a22 = Val(e6.Text)

a23 = Val(e7.Text)

a24 = Val(e8.Text)

a31 = Val(e9.Text)

a32 = Val(e10.Text)

a33 = Val(e11.Text)

a34 = Val(e12.Text)

a41 = Val(e13.Text)

a42 = Val(e14.Text)

a43 = Val(e15.Text)

a44 = Val(e16.Text)

detA = -a41 * (a12 * ((a23 * a34) - (a24 * a33)) - a13 * ((a22 * a34) - (a24 *

a32)) + a14 * ((a22 * a33) - (a23 * a32))) + a42 * (a11 * ((a23 * a34) - (a24

* a33)) - a13 * ((a21 * a34) - (a24 * a31)) + a14 * ((a21 * a33) - (a23 *

a31))) - a43 * (a11 * ((a22 * a34) - (a24 * a32)) - a12 * ((a21 * a34) - (a24 *

a31)) + a14 * ((a21 * a32) - (a22 * a31))) + a44 * (a11 * ((a22 * a33) - (a23* a32)) - a12 * ((a21 * a33) - (a23 * a31)) + a13 * ((a21 * a32) - (a22 *

a31)))

dA.Text= detA

c11 = a22 * ((a33 * a44) - (a43 * a34)) - a23 * ((a32 * a44) - (a34 * a42)) +

a24 * ((a32 * a43) - (a33 * a42))


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c12 = -(a21 * ((a33 * a44) - (a34 * a43)) - a23 * ((a31 * a44) - (a41 * a34))

+ a24 * ((a31 * a43) - (a33 * a41)))

c13 = a21 * ((a32 * a44) - (a34 * a42)) - a22 * ((a31 * a44) - (a41 * a34)) +

a24 * ((a31 * a42) - (a32 * a41))

c14 = -(a21 * ((a32 * a43) - (a33 * a42)) - a22 * ((a31 * a43) - (a41 * a33))

+ a23 * ((a31 * a42) - (a32 * a41)))

c21 = -(a12 * ((a33 * a44) - (a43 * a34)) - a13 * ((a32 * a44) - (a34 * a42))

+ a14 * ((a32 * a43) - (a42 * a33)))

c22 = a11 * ((a33 * a44) - (a43 * a34)) - a13 * ((a31 * a44) - (a34 * a41)) +a14 * ((a31 * a43) - (a41 * a33))

c23 = -(a11 * ((a32 * a44) - (a42 * a34)) - a12 * ((a31 * a44) - (a34 * a41))

+ a14 * ((a31 * a42) - (a41 * a32)))

c24 = a11 * ((a32 * a43) - (a33 * a42)) - a12 * ((a31 * a43) - (a33 * a41)) +

a13 * ((a31 * a42) - (a32 * a41))

c31 = a12 * ((a23 * a44) - (a43 * a24)) - a13 * ((a22 * a44) - (a42 * a24)) +

a14 * ((a22 * a43) - (a42 * a23))

c32 = -(a11 * ((a23 * a44) - (a43 * a24)) - a13 * ((a21 * a44) - (a41 * a24))

+ a14 * ((a21 * a43) - (a41 * a23)))

c33 = a11 * ((a22 * a44) - (a42 * a24)) - a12 * ((a21 * a44) - (a41 * a24)) +

a14 * ((a21 * a42) - (a41 * a22))

c34 = -(a11 * ((a22 * a43) - (a42 * a23)) - a12 * ((a21 * a43) - (a41 * a23))

+ a13 * ((a21 * a42) - (a22 * a41)))

c41 = -(a12 * ((a23 * a34) - (a33 * a24)) - a13 * ((a22 * a34) - (a32 * a24))

+ a14 * ((a22 * a33) - (a32 * a23)))

c42 = a11 * ((a23 * a34) - (a33 * a24)) - a13 * ((a21 * a34) - (a31 * a24)) +

a14 * ((a21 * a33) - (a31 * a23))


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c43 = -(a11 * ((a22 * a34) - (a32 * a24)) - a12 * ((a21 * a34) - (a31 * a24))

+ a14 * ((a21 * a32) - (a31 * a22)))

c44 = a11 * ((a22 * a33) - (a32 * a23)) - a12 * ((a21 * a33) - (a31 * a23)) +

a13 * ((a21 * a32) - (a31 * a22))

b11 = c11 / detA

b12 = c12 / detA

b13 = c13 / detA

b14 = c14 / detA

b21 = c21 / detA

b22 = c22 / detA

b23 = c23 / detA

b24 = c24 / detA

b31 = c31 / detA

b32 = c32 / detA

b33 = c33 / detA

b34 = c34 / detA

b41 = c41 / detA

b42 = c42 / detA

b43 = c43 / detA

b44 = c44 / detA

d1.Text= b11

d2.Text= b21


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d3.Text= b31

d4.Text= b41

d5.Text= b12

d6.Text= b22

d7.Text= b32

d8.Text= b42

d9.Text= b13

d10.Text= b23

d11.Text= b33

d12.Text= b43

d13.Text= b14

d14.Text= b24

d15.Text= b34

d16.Text= b44

End Sub


e1.Text= ""

e2.Text= ""

e3.Text= ""

e4.Text= ""

e5.Text= ""


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e6.Text= ""

e7.Text= ""

e8.Text= ""

e9.Text= ""

e10.Text= ""

e11.Text= ""

e12.Text= ""

e13.Text= ""

e14.Text= ""

e15.Text= ""

e16.Text= ""

d1.Text= ""

d2.Text= ""

d3.Text= ""

d4.Text= ""

d5.Text= ""

d6.Text= ""

d7.Text= ""

d8.Text= ""

d9.Text= ""

d10.Text= ""

d11.Text= ""

d12.Text= ""


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d13.Text= ""

d14.Text= ""

d15.Text= ""

d16.Text= ""

dA.Text= ""

End Sub


End

End Sub

Algorithm for 4 by 4 Matrix Inversion

10 Draw up a 4 by 4 matrix

20 Calculate the minor of each of the following elements ( i.e. a11,a12...a44)

by finding the determinant of the 3 by 3 matrix

30 Calculate the cofactor of the different elements of the rows andcolumns and apply the necessitated symbols in front of each of them.

40 Transpose the cofactor to obtain the adjoint

50 Calculate the determinant

60 Divide the adjoint by the determinant to obtain the inverse matrix.


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Highlights and Deficiencies of Method of solution

The method of solution employed in this program is the co-factor/adjointmethod. The method as we all know is easy to understand but it is very

long because of the step by step breakdown of the methodology employed.

The highlights of this method of solution include;

- Step by step understanding of the methodology involved

- Straightforwardness of the method of solution

Some of the deficiencies attached to this method of solution are;

- It is cumbersome to calculate.

- It is time-taking and could be really confusing if one is not careful.

Sample of the Input and Output of the Program

We are going to test run the program with a 4 by 4 matrix. The input is on

the left side of the program interface while the output is on the right side of

the program interface. A sample run of the program is displayed below;


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Before output is calculated

After the output has been displayed

BACKWARD COMPUTATION

Backward computation is a method used in solving traverse problems.

This problem is not as cumbersome as the 4 by 4 matrix inversion problem

although it involves the use of additional functions such as sine, cosine, etc.

As usual, we start off with the designing of the user interface which is

shown below:


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dx = x2 - x1

dist = Sqr(dy ^ 2 + dx ^ 2)

Distance.Text= dist

If(dx > 0 And dy > 0) Then

Bearing = (Atn(dx / dy)) * (180 / (4 * Atn(1)))

TrueBearing = Bearing

ElseIf(dx > 0 And dy < 0) Then


TrueBearing = 180 + Bearing

ElseIf(dx < 0 And dy < 0) Then



ElseIf(dx < 0 And dy > 0) Then



ElseIf(dx = 0 And dy > 0) Then


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TrueBearing = 0

ElseIf(dx = 0 And dy < 0) Then


TrueBearing = 180

ElseIf(dx > 0 And dy = 0) Then

TrueBearing = 90

ElseIf(dx < 0 And dy = 0) Then

TrueBearing = 270

End If

text6.Text= TrueBearing

latitude = dist * Cos(TrueBearing)

Text1.Text= latitude

departure = dist * Sin(TrueBearing)

Text2.Text= departure


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End Sub


End

End Sub


p1x.Text= ""

p2x.Text= ""

p1y.Text= ""

p2y.Text= ""

Distance.Text= ""

text6.Text= ""

Text1.Text = ""

Text2.Text = ""

End Sub

Algorithm for Backward Computation

10 Input coordinate of points A and B

20 Let E = EB EA

30 Let N = NB - NA


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40 Let = Tan -1(E/N)

50 Let {deg} = * (180/(atn(1)*4))

60 Let distance = sqr(E2 + N2)

70 If E > 0 and N > 0 then bearing AB = {deg}

80 If E > 0 and N < 0 then bearing AB = 180 - {deg}

90 If E < 0 and N > 0 then bearing AB = 360 - {deg}

100 If E < 0 and N < 0 then bearing AB = 180 + {deg}

110 If E = 0 and N > 0 then bearing AB = 0

120 If E = 0 and N < 0 then bearing AB = 180

130 If E = 0 and N > 0 then bearing AB = 90

140 If E = 0 and N = 0 then bearing AB = 360

150 Print distance and bearing AB

160 If AB < 180 then bearing BC = bearing AB + 180 +

170 If AB > 180 then bearing BC = bearing AB - 180 +

180 If AB > 360 then bearing BC = bearing BC 360

190 Print bearing BC

Highlights and Deficiencies of Method of Solution

The method of solution employed in this problem is very easy to use andeasily understandable. As regards the program itself, there are a couple of

deficiencies of which includes;

- Inadequate text boxes to enable the program compute results for more

coordinates.- Multi tasking is not enabled in the program.


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Some of the highlights to look out for include;

- The conversion of the bearings from radians to degrees

- The negative and positive signs in front of the coordinates or other

parameters.

Sample of input and output of the program

The above shows the program interface with the required inputs only. It

is only after the inputs must have been keyed in that we can then click on

the calculate button in order to get our output. It is shown below;


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4 by 4 Matrix Inversion

Documents

Transcript of 4 by 4 Matrix Inversion