1.5 THE COLON SYMBOL (:)

1.5 THE COLON SYMBOL (:)

The colon symbol (:) is one of the most important operators in MATLAB. It

can be used (1) to create vectors and matrices, (2) to specify sub-matrices and

vectors, and (3) to perform iterations. The statement

t1 = 1:6

will generate a row vector containing the numbers from 1 to 6 with unit increment.

MATLAB produces the result

t1 =

1 2 3 4 5 6

Non-unity, positive or negative increments, may be specified. For example,

the statement

t2 = 3:-0.5:1

will result in

t2 =

3.0000 2.5000 2.0000 1.5000 1.0000

The statement

t3 = [(0:2:10);(5:-0.2:4)]

will result in a 2-by-4 matrix

t3 =

0 2.0000 4.0000 6.0000 8.0000 10.0000

5.0000 4.8000 4.6000 4.4000 4.2000 4.0000

Other MATLAB functions for generating vectors are linspace and logspace.

Linspace generates linearly evenly spaced vectors, while logspace generates

logarithmically evenly spaced vectors. The usage of these functions is of the

form:

linspace(i_value, f_value, np)

logspace(i_value, f_value, np)

where

i_value is the initial value

f_value is the final value

np is the total number of elements in the vector.

For example,

t4 = linspace(2, 6, 8)

will generate the vector

t4 =

Columns 1 through 7

2.0000 2.5714 3.1429 3.7143 4.2857 4.8571

5.4286

Column 8

6.0000

Individual elements in a matrix can be referenced with subscripts inside parentheses.

For example, t2(4) is the fourth element of vector t2. Also, for matrix

t3, t3(2,3) denotes the entry in the second row and third column. Using the colon

as one of the subscripts denotes all of the corresponding row or column.

For example, t3(:,4) is the fourth column of matrix t3. Thus, the statement

t5 = t3(:,4)

will give

t5 =

6.0000

4.4000

Also, the statement t3(2,:) is the second row of matrix t3. That is the statement

t6 = t3(2,:)

will result in

t6 =

5.0000 4.8000 4.6000 4.4000 4.2000 4.0000

If the colon exists as the only subscript, such as t3(:), the latter denotes the

elements of matrix t3 strung out in a long column vector. Thus, the statement

t7 = t3(:)

will result in

t7 =

0

5.0000

2.0000

4.8000

4.0000

4.6000

6.0000

4.4000

8.0000

4.2000

10.0000

4.0000

Example 1.1

The voltage, v, across a resistance is given as (Ohm’s Law), v = Ri , where

i is the current and R the resistance. The power dissipated in resistor R is

given by the expression

P = Ri2

If R = 10 Ohms and the current is increased from 0 to 10 A with increments

of 2A, write a MATLAB program to generate a table of current, voltage and

power dissipation.

Solution:

MATLAB Script

diary ex1_1.dat

% diary causes output to be written into file ex1_1.dat

% Voltage and power calculation

R=10; % Resistance value

i=(0:2:10); % Generate current values

v=i.*R; % array multiplication to obtain voltage

p=(i.^2)*R; % power calculation

sol=[i v p] % current, voltage and power values are printed

diary

% the last diary command turns off the diary state

MATLAB produces the following result:

sol =

Columns 1 through 6

0 2 4 6 8 10

Columns 7 through 12

0 20 40 60 80 100

Columns 13 through 18

0 40 160 360 640 1000

Columns 1 through 6 constitute the current values, columns 7 through 12 are

the voltages, and columns 13 through 18 are the power dissipation values