All MATLAB variables are matrices. Vectors are special cases of a matrix with only one row or one column. Scalars are a matrix with one row and one column.
The linspace, ones, zeros functions and the transpose operator are used
to create vectors and matrices. The length and size functions are used
to inquire about the number of elements in vectors and matrices.
Refer to the on-line reference,
e.g. "doc linspace" or "help linspace", for more details on any of the commands
listed below.
Creating and manipulating vectors
linspace: create a row vector of linearly spaced elements
linspace(v1,v2) creates a row vector with 100 elements, equally spaced between v1 and v2
including the endpoints v1 and v2
linspace(v1,v2,n) creates a row vector with n elements, equally spaced between v1 and v2
including the endpoints v1 and v2
>> x = linspace(0,2*pi); % 100 elements in the interval 0 <= x <= 2*pi
>> x = linspace(-3,7,25); % 25 elements in the interval -3 <= x <= 7
If you want to create a column vector instead, append a transpose operator
to the closing parenthesis of the linspace command
>> x = linspace(0,25)' % x is a column vector
ones: create vectors and matrices with all elements equal to 1
ones(m,n) creates a matrix with rows and columns, and with all
elements equal to 1.
>> x = ones(1,5); % 5-element row vector with all elements = 1
>> x = ones(1,5)'; % 5-element column vector will all elements = 1
>> x = ones(5,1); % 5-element column vector will all elements = 1
>> A = ones(3,6); % 3-row, 6-column matrix with all elements = 1
zeros: create vectors and matrices with all elements equal to 0
zeros(m,n) creates a matrix with rows and columns, and with all
elements equal to 0. Analogous to ones.
zeros is often used to pre-allocate memory for a vector or matrix that will
then be used in a loop. pre-allocation is more efficient. Consider the following
code snippet
x = ... % x is a variable created by some statements,
% e.g. x = linspace(0,25)
z = zeros(size(x)) % z is a new variable with the same number of
% rows and columns as x
transpose with '
The transpose operator converts a row vector to a column vector, and vice versa.
>> x = [ 6 -2 8 ]; % x is a row vector
>> y = x'
y =
6
-2
8
>> z = y'
z =
6 -2
>> A = [ 7 5 -1; -2 9 4]
A =
7 5 -1
-2 9 4
>> B = A'
B =
7 -2
5 9
-1 4
Getting Information about Vectors and Matrices
length: determine the number of rows or columns in an existing vector
length is a convenience function that tells you the number of elements
in a vector. length is often used with a for loop, like this:
z = ... % z is a vector created by some other statements
for i = 1:length(z)
% body of loop processes each element of z as z(i)
end
Note: Do not use length to determine the number of elements in a
matrix. See size, below.
size: determine the number of rows and columns of an existing variable
If A is a vector or matrix, size(A) returns a two-element vector.
The first element is the number of rows in A. The second element is the
number of columns in A. size(x) also works when x is a vector.
>> A = [ 7 5 -1; -2 9 4]
A =
7 5 -1
-2 9 4
>> size(A)
ans =
2 3
>> x = linspace(0,10);
>> size(x)
ans =
1 100
size can accept an optional second argument to specify which of the
dimensions you wish to know. size(A,1) returns the
number of rows in A, and size(A,2) returns the number of columns
in A. The order of the dimensions is determined by the convention that
we speak of a matrix as being -by-, where is the
first dimension and is the number of rows, and is the second dimension
and is the number of columns.
>> A = [ 7 5 -1; -2 9 4];
>> size(A,1)
ans =
2
>> size(A,2)
ans =
3
size is often used with zeros to pre-allocate
variables to match the size (number of rows and/or columns) of another
existing variable.
x = ... % x is defined by some previous calculation
y = zeros(size(x)); % pre-allocate y for efficiency in the following loop
for i = 1:length(x)
y(i) = ... % some computation involving x(i)
end
Without the pre-allocation statement y = zeros(size(x)) the code in the
preceding loop is syntacticly correct MATLAB, and the code would run. However,
without pre-allocating y, MATLAB has to interrupt the computation to
resize y on each pass through the loop. For simple codes, or loops that
are run infrequently, the performance hit will be not be great. Nonetheless,
it is good practice to pre-allocate vectors and matrices before storing values
in those vectors or matrices one element at a time in a loop.