for i = 1:n, for j = 1:n, A(i,j) = 1/(i+j-1);
generates the Hilbert matrix.
for j = 2:n-1, for i = j:n-1, ...
A(i,j) = 0; end; A(j,j) = j; end; A
changes all but the ”outer edge” of the lower triangle and then prints the final matrix.
for h = 1.0: -0.1: -1.0, (<h, cos(pi*h)>)
prints a table of cosines.
<X,D> = EIG(A); for v = X, v, A*v
displays eigenvectors, one at a time.
The WHILE clause allows statements to be repeated an indefinite number of times. The general
form is
WHILE expr relop expr, statement,..., statement, END
where relop is =, ¡, ¿, ¡=, ¿=, or ¡¿ (not equal) . The statements are repeatedly executed as long
as the indicated comparison between the real parts of the first components of the two expressions
is true. Here are two examples. (Exercise for the reader: What do these segments do?)
eps = 1;
while 1 + eps > 1, eps = eps/2;
eps = 2*eps
E = 0*A; F = E + EYE; n = 1;
while NORM(E+F-E,1) > 0, E = E + F; F = A*F/n; n = n + 1;
E
The IF clause allows conditional execution of statements. The general form is
IF expr relop expr, statement, ..., statement,
ELSE statement, ..., statement
The first group of statements are executed if the relation is true and the second group are executed
if the relation is false. The ELSE and the statements following it may be omitted. For example,
if abs(i-j) = 2, A(i,j) = 0;
5 Commands, text, files and macros.
MATLAB has several commands which control the output format and the overall execution of the
system.
The HELP command allows on-line access to short portions of text describing various opera-
tions, functions and special characters. The entire HELP document is reproduced in an appendix.
11
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