STEER Program Notes

__MATLAB__

MATLAB allows for easy manipulation of matrices. The following is an interesting take on inverses of matrices that I found in the MATLAB demo programs.

(In MATLAB programs, a “%” symbol indicates a comment.)

n =
100;

a =
rand(n); %Creates nxn matrix "a" containing random values from 0 to 1.

imagesc(a); %Scales the data in "a" and displays it
as an image.

%Each
element in "a" corresponds to a rectangular

%area in the image. The values of the elements of

%"a" are indices into the current colormap that

%determine the color
of each patch.

colormap(hot); %A colormap is an m x 3 matrix of real numbers

%between 0.0 and 1.0. Each row is an RGB vector

%that defines one color. "hot" is a colormap that

%varies
smoothly from black, through shades of red,

%orange, and yellow, to white.

axis square; %Makes the
current axis square. The x and y axis are

%equal lengths and the increments are equal.

b =
inv(a); %Creates the inverse matrix of "a".

imagesc(b); %See above.

axis square; %See above.

imagesc(a * b); %Creates
the image of the matrix of a * b.

axis square; %Creates a square plot. Since this should be the

%identity matrix, one should expect the graph
to be

%a white line down the
diagonal of the matrix,

%representing the ones down the diagonal.

%All else should be black (zeroes).

Plotting Graphs in MATLAB - One can also easily plot graphs and sets of graphs in MATLAB. This allows for simultaneous comparisons of functions.

%Create
a vector of values from 0 to 5, in steps of .5

t =
0:.5:5;

%Create
a 2x1 set of graphs. This is the first
of two graphs.

%Plot
t vs. sin(t).

subplot (2,1,1); plot(t,sin(t));

%Repeat
for cos(t). This is the second of 2 graphs.

subplot (2,1,2); plot(t,cos(t));