Download Introduction to programming

Introduction to Programming
Lecture # 43
Math Library
 Complex number
 Matrix
 Quadratic equation and their solution
…………….…
Design Recipe

To design a program properly, we must :
– Analyze a problem statement, typically
expressed as a word problem
– Express its essence, abstractly and with
examples
– Formulate statements and comments in a
precise language i.e. code
– Evaluate and revise the activities in light
of checks and tests and
– PAY ATTENTION TO DETAIL
Matrix
• Matrix is nothing but a two
dimensional array of numbers
• Normally, represented in the
form of :
• Rows
• Columns
Example
A=
1
5
9
2
6
10
3
7
11
Three Rows
Four Columns
4
8
12
i & j are two Integers
i representing the Row number
j representing the Column number
Operations Performed with Matrix
• Addition of two matrices.
• Addition of a scalar and a matrix
• Subtraction of two matrices
• Subtraction of a scalar from a matrix
• Multiplication of two matrices
• Multiplication of a scalar with a matrix
• Division of a scalar with a matrix
• Transpose of a matrix
Interface
Addition of two Matrices
Aij+ Bij = Cij
Addition of two Matrices
Size of two matrices must be
same
Number of rows and columns
must be identical for the
matrices to be addable
Example
-2
-4
-5
-2
2
0
0
0
10
=
Cij
=
1
2
3
5
6
7
9
10
11
Aij
-
-
Bij
3
6
8
7
4
7
9
10
1
Adding a Scalar to
the Matrix
Ordinary number
added to every
element of the
matrix
Subtracting a Scalar
from a Matrix
Ordinary number
subtracted from
every element of the
matrix
Division of Matrix
by a Scalar
Divide every element
of Matrix by a scalar
number
Example
Let :
X be a Scalar number
A be a Matrix
C
ij
=
Aij
X
Multiplication of a scalar with a Matrix :
Example
Let :
X is a Scalar number
A is a Matrix
X*A
X
*
A ij
=
Cij
Multiply two
Matrices
1
5
2
6
*
2
1
4
2
=
(1)(2)+(2)(1)
(1)(4)+(2)(2)
(5)(2)+(6)(1)
(5)(4)+(6)(2)
Rules Regarding
Matrix Multiplication
Number of columns of the 1st Matrix
=
Number of rows of the 2nd Matrix
Rules regarding Matrix
Multiplication

First matrix has
– M rows
– N columns

Second matrix has
– N rows
– P columns

Resultant matrix will have
– M rows
– P columns
Transpose of a
Matrix
Interchange of rows
and columns
Transpose of a Matrix
Example
1
5
9
2
6
10
3
7
11
1
2
3
5
6
7
9
10
11
Transpose of a Non
Square Matrix
Size of matrix change after transpose
A
3 ( Rows ) * 4 ( Columns )
Before
T
A
4 ( Rows ) * 3 ( Columns )
After
Next Phase of
Analysis
• Determine the Constants
• Memory Allocation
• What is it’s user interface
Interface
Interface
Constructor : Parameters are
 Number of rows
 Number of columns
Display function
Plus operator : member operator of the class
Subtraction operator : member operator of the
class
Plus operator : friend of the class
Subtraction operator : friend of the class
Plus Operator
A+X
X+A
Subtraction Operator
A-X
X–A
Interface
Multiplication Operator : Member of the Class
Multiplication Operator : Friend of the Class
Division Operator : Member of the Class
Transpose Function : Member of the Class
Assignment Operator : Member of the Class
+= , -= : Members of the Class
Multiplication Operator
A*X
X*A
Assignment Operator
A=B
( Member Operator )
Interface
>> Extraction Operator : Friend Operator
<< Stream Insertion Operator : Friend Operator
Copy Constructor
Copy Constructor
 Assignment Operator
 Memory Allocation
 Memory Deallocation
