Matlab has many commands to create special matrices; the following command creates a row vector whose components increase arithmetically:
>> t = 1:5 t = 1 2 3 4 5The components can change by non-unit steps:
>> x = 0:.1:1 x = Columns 1 through 7 0 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 Columns 8 through 11 0.7000 0.8000 0.9000 1.0000A negative step is also allowed. The command linspace has similar results; it creates a vector with linearly spaced entries. Specifically, linspace(a,b,n) creates a vector of length n with entries :
>> linspace(0,1,11) ans = Columns 1 through 7 0 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 Columns 8 through 11 0.7000 0.8000 0.9000 1.0000There is a similar command logspace for creating vectors with logarithmically spaced entries:
>> logspace(0,1,11) ans = Columns 1 through 7 1.0000 1.2589 1.5849 1.9953 2.5119 3.1623 3.9811 Columns 8 through 11 5.0119 6.3096 7.9433 10.0000See help logspace for details.
A vector with linearly spaced entries can be regarded as defining a one-dimensional grid, which is useful for graphing functions. To create a graph of y = f(x) (or, to be precise, to graph points of the form (x,f(x)) and connect them with line segments), one can create a grid in the vector x and then create a vector y with the corresponding function values.
It is easy to create the needed vectors to graph a built-in function, since Matlab functions are vectorized. This means that if a built-in function such as sine is applied to a array, the effect is to create a new array of the same size whose entries are the function values of the entries of the original array. For example (see Figure 3):
>> x = (0:.1:2*pi); >> y = sin(x); >> plot(x,y)
Figure 3: Graph of y = sin(x)
Matlab also provides vectorized arithmetic operators, which are the same as the ordinary operators, preceded by ``.''. For example, to graph :
>> x = (-5:.1:5); >> y = x./(1+x.^2); >> plot(x,y)(the graph is not shown). Thus
x.^2squares each component of x, and
x./zdivides each component of x by the corresponding component of z. Addition and subtraction are performed component-wise by definition, so there are no ``.+'' or ``.-'' operators. Note the difference between
A.^2. The first is only defined if A is a square matrix, while the second is defined for any n-dimensional array A.