Vectors, Matrices, and Arrays: Basic Operations

Contents

Visualization

Assume we have

SampleArray = [1:5;2:6;3:7;4:8;5:9];

We can plot this data array by calling the function imagesc

imagesc(SampleArray)

Use the colorbar command to see what the colorcode refers to:

colorbar;

Basic Calculation

Simple math between two arrays with same size is straightforward. For example,

A = [1 2 3; 4 5 6];
B = [1 4 9; 16 25 36];

Try

A + B

ans =

     2     6    12
    20    30    42

and

A - B

ans =

     0    -2    -6
   -12   -20   -30

Dot-Operators

MATLAB uses the dot-operator (.) construction to distinguish between scalar-vectorized operations and matrix operations. Dot-operators are meant to repeat operations on the members of the array. For example,

A .* A

ans =

     1     4     9
    16    25    36

returns an array composed by square of each element in A.

(Note: This differs from A*A, which would fail in this case, since the matrix multiplication is only mathematically defined for arrays with the same number of rows and columns.)

Another example of dot-operator is the power (^) function:

B.^0.5

ans =

     1     2     3
     4     5     6

which applies the "raise to the 0.5 power" operation to each member of the array B.

The division between two arrays is also a dot-operator:

A ./ B

ans =

    1.0000    0.5000    0.3333
    0.2500    0.2000    0.1667

which allows us to divide elements in A by the corresponding elements in B.

Vectorized Functions

MATLAB is a vectorized language. That means it operates automatically over each member of an array without the need for an explicit loop (which would be necessary in C or FORTRAN). In fact, it is not only more compact, but more efficient and faster to avoid loops if possible.

Most (if not all) MATLAB functions are vectorized. For example:

B = [1 4 9; 16 25 36];
sqrt(B)

ans =

     1     2     3
     4     5     6

This uses the square root operator over each element of the array. Similarly, try:

log(B)

ans =

         0    1.3863    2.1972
    2.7726    3.2189    3.5835

sin(B)

ans =

    0.8415   -0.7568    0.4121
   -0.2879   -0.1324   -0.9918

Exercise

Consider the three arrays:

SampleA = [1:3;4:6;7:9];
SampleB = [ones(1,3);zeros(1,3)];
SampleC = [1:2:5;2:2:6];

For the following sets of two commands, point out which sets have identical commands, and explain why the commands in other sets are different:

1)

SampleA*SampleA;
SampleA.*SampleA;

2)

size(SampleB)./size(SampleC);
size(SampleB./SampleC);

3)

SampleC.*SampleC;
SampleC.^2;

Published with MATLAB® 7.8