NUMERICAL METHODS WITH MATLAB PROGRAMMING

NUMERICAL METHODS WITH
MATLAB PROGRAMMING
By
A.DHARANI
ASSISTANT PROFFESSOR
PG DEPARTMENT OF MATHEMATICS
SRI SARADA NIKETAN COLLEGE FOR WOMEN

STATEMENT LEVEL CONTROL
STRUCTURES
 One way to think of computer programs is to consider how the
statements that compose the program are organized. Usually,
sections of computer code can be categorized into on of three
structures: sequences, selection structures and repetition
structures.
 Sequences: Sequences are lists of commands that are executed one
after another.
 Selection structure: A selection structure allows the programmer
to execute one command or group of commands if some criteria is
true and a second set of commands if the criteria is false. A selection
statement provides the means of choosing between these paths based
on a logical condition. The conditions that are evaluated often
contain relational and logical operators o r functions.
 Repetition structure: A repetition structure or loop, causes a
group of statements to be executed zero, one, or more times. The
number of times a loop is executed depends on either a counter or
the evaluation of a logical condition.

RELATIONAL OPERATORS
Relational Operators Interpretation
< Less than
<= Less than or equal to
> Greater than
>= Greater than or equal to
== Equal to
~= Not equal to

EXAMPLES
 MATLAB has six relational operators for comparing two
matrices of equal size, comparisons are either true or false
and most computer programs use the number 1 for true and
0 for false.
 x = [ 1 2 3 4 5 ];
 y = [-2 0 2 4 6];
 x<y
 returns
 ans=
 0 0 0 0 1
 which tells that the comparisons was false for the
first four elements but true for the last one.

MATLAB ALSO ALLOWS US TO COMPARE
COMPARISONS WITH LOGICAL OPERATORS:
AND, NOT, AND OR
Logical Operators interpretation
& and
~ not
| or

EXAMPLE FOR LOGICAL
OPERATORS
consider the following:
x = [ 1 2 3 4 5];
y = [ -2 0 2 4 6];
z = [ 8 8 8 8 8 ];
z>x & z>y
returns
ans=
1 1 1 1 1
Both z is greater than both x and y for every
element.

• Selection structures MATLAB offers two kinds of
selection structures: find and a family of if structures
• Find
The find command is unique to MATLAB, and can
often be used instead of both if and loop structures. The
usefulness of the find command is best described with
examples.
Assume that you have a list of temperatures
measured in a manufacturing process. If the
temperature is less than 95 degree F, them widgets
produced will be faulty:
temp = [ 100 98 94 101 93 ]
use the find function to determine which widgets are
family:
find(temp<95)
Returns a vector of element numbers;
ans=
3 5

Location of all elements greater than 9:
x = [ 1,2,3 10,5,1 3,12,2 8,3,1]
element = find(x>9)
[row, column] = find(x>9)
Returns
x =
1 2 3
10 5 1
3 12 2
8 3 1
Element =
2
7
row =
2
3
column =
1
2
The numbers 10 and 12 are the only two values greater than
9

IF , ELSE IF, ELSE:
EXAMPLE:
a = input (‘ enter a = ‘);
if a>0
disp (‘ a is positive’)
elseif a<0
disp (‘ a is negative’)
else
disp (‘ a is zero’)
end
Returns,
‘enter a = 5’
ans =
5 is positive
‘ enter a = -1’
ans =
-1 is negative
‘ enter a = 0’
ans =
zero

IF:
If the logical expression is true, the statement between if
and end are executed. If the logical expression is false, program
control jumps immediately to the statement following the end
statement.
ELSE IF:
It is a conditional statement performed after an if statement
that, if true, performs a function.
The elseif statement is only executed if the preceding if
expression evaluated to false, and the current elseif expression
evaluated to true.
ELSE:
Use else to specify a block of code to be executed, if the same
condition is false. Else doesn’t need a condition as it is the
default for everything where as else if is still an if so it needs a
condition.

. • Loops
A loop is a structure that allows you to repeat a set of statements.
In general, you should avoid loops in MATLAB because they are
seldom needed, and they can significantly increase the execution
time of a program.
For loops
In general, it Is possible to use either a for or a while loop in any
situation that requires a repetition structures. However, for loops
are the easier choice when you know how many times you want to
repeat a set of instructions.
The general format is
for index = expression
statements
end
Usually, the expression is a vector, and the statements are repeated
as many times as there are columns in the expression matrix. For
example, to find 5 raised to the 100th
power, first initialize a
running total:
total = 1;
for k = 1:100
total = total*5;
end

The first time through the loop, total = 1, so total ×5=5, the next line
through the loop, the value of total is updated to 5×5 equals 25,after 100
times through the loop, the final value is found, and corresponds to 5ˆ100.
Notice that the value of totalwas suppressed, so it won’t print out each
time through the loop. To recall the find value of total, type
total
which returns
total =
7.8886e+069
Another example of loop is,
for k = 1:4
k
end
returns
k =
1
k =
2
k=
3
k =
4

THE RULES FOR WRITING AND USING A FOR LOOP
ARE THE FOLLOWING:
• The index of a for loop must be a variable. Although k is often used
as the symbol for the index, any variable name can be used. The use
of k is strictly a style issue.
•If the expression matrix is the empty matrix, the loop will not be
executed. Control will pass to the statement following the end
statement.
• If the expression matrix is a scalar, the loop will be executed one
time, with the index containing the value of the scalar.
• If the expression is a row vector, each time through the loop the
index will contain the next column in the matrix.
• If the expression matrix, each time through the loop the index will
contain the next column in the matrix. This means that the index
will be a column vector.
• Upon completion of a for loop, the index contains the last value
used.
The colon operator can be used to define the expression matrix using
the following format:
for k = initial : increment : limit

• While loops:
The while loop is a structure used for repeating a set of
statements as long as specified condition is true. The general
format for this control structure is
while expression
Statements
end
The statements in the while loop are executed as long as the
real part of the expression has all nonzero elements. The
expression is usually a comparison using relational and logical
operators.
When the result of a comparison is true, the result is 1, and
therefore ‘nonzero’. The loop will continue repeating as long as
the comparison is still true. When the expression is evaluated
as false, control skips to the statement following the end
statement .
Consider the following example:
First initialize a:
a = 0;
Then find the smallest multiple of 3 that is less than 100:

while( a < 100 )
a = a+3;
end;
The last time through the loop a will start out as 99, then
will become 102 when 3 is added to 99. The smallest
multiple then becomes
a – 3
Which returns
ans =
99
The variable modified in the statements inside the loop
should include the variables in the expression, or else the
value of the expression will never change.
If the expression is always true, then the loop will execute
an infinite number of times.

COMMANDS AND FUNCTIONS
COMMAND MEANINGS
clock Determines the current time on the CPU clock
disp Displays matrix or test
else Defines the path if the result of an if statement is
false
elseif Defines the path if the result of an if statement is
false, and specifies a new logical test
end Identifies the end of a control structure
etime Finds elapsed time
find Determines which elements in a matrix meet the
input criteria
for Generates a loop structure
fprintf Prints formatted information
function Identifies an M-files as a function
if Tests a logical expression

COMMAND MEANING
input Prompts the user to enter a value
meshgrid Maps two input vectors onto two 2-D
matrices
nargin Determines the number of input
arguments in a function
nargout Determines the number of output
arguments from a function
num2string Converts an array into a string
ones Creates a matrix of ones
tic Starts a timing sequence
toc Stops a timing sequence
while Generates a loop structure
zeros Creates a matrix of zeros

NUMERICAL METHODS WITH MATLAB PROGRAMMING

Recommended

More Related Content

Similar to NUMERICAL METHODS WITH MATLAB PROGRAMMING (20)

Recently uploaded (20)

NUMERICAL METHODS WITH MATLAB PROGRAMMING