Getting Started with MATLAB | Help Desk |
Flow Control
MATLAB has five flow control constructs:if
statement evaluates a logical expression and executes a group of statements when the expression is true. The optional elseif
and else
keywords provide for the execution of alternate groups of statements. An end
keyword, which matches the if
, terminates the last group of statements. The groups of statements are delineated by the four keywords - no braces or brackets are involved.
MATLAB's algorithm for generating a magic square of order n involves three different cases: when n is odd, when n is even but not divisible by 4, or when n is divisible by 4. This is described by
if rem(n,2) ~= 0 M = odd_magic(n) elseif rem(n,4) ~= 0 M = single_even_magic(n) else M = double_even_magic(n) endIn this example, the three cases are mutually exclusive, but if they weren't, the first true condition would be executed. It is important to understand how relational operators and
if
statements work with matrices. When you want to check for equality between two variables, you might use
if A == B, ...This is legal MATLAB code, and does what you expect when
A
and B
are scalars. But when A
and B
are matrices, A == B
does not test if they are equal, it tests where they are equal; the result is another matrix of 0's and 1's showing element-by-element equality. In fact, if A
and B
are not the same size, then A == B
is an error.
The proper way to check for equality between two variables is to use the isequal
function,
if isequal(A,B), ...Here is another example to emphasize this point. If
A
and B
are scalars, the following program will never reach the unexpected situation. But for most pairs of matrices, including our magic squares with interchanged columns, none of the matrix conditions A > B
, A < B
or A == B
is true for all elements and so the else
clause is executed.
if A > B 'greater' elseif A < B 'less' elseif A == B 'equal' else error('Unexpected situation') endSeveral functions are helpful for reducing the results of matrix comparisons to scalar conditions for use with
if
, including
isequal isempty all anyThe
switch
statement executes groups of statements based on the value of a variable or expression. The keywords case
and otherwise
delineate the groups. Only the first matching case is executed. There must always be an end
to match the switch
.
The logic of the magic squares algorithm can also be described by
switch (rem(n,4)==0) + (rem(n,2)==0) case 0 M = odd_magic(n) case 1 M = single_even_magic(n) case 2 M = double_even_magic(n) otherwise error('This is impossible') endNOTE FOR C PROGRAMMERS
for
loop repeats a group of statements a fixed, predetermined number of times. A matching end
delineates the statements.
for n = 3:32 r(n) = rank(magic(n)); end rThe semicolon terminating the inner statement suppresses repeated printing, and the
r
after the loop displays the final result.
It is a good idea to indent the loops for readability, especially when they are nested.
for i = 1:m for j = 1:n H(i,j) = 1/(i+j); end endThe
while
loop repeats a group of statements an indefinite number of times under control of a logical condition. A matching end
delineates the statements.
Here is a complete program, illustrating while
, if
, else
, and end
, that uses interval bisection to find a zero of a polynomial.
a = 0; fa = -inf; b = 3; fb = inf; while b-a > eps*b x = (a+b)/2; fx = x^3-2*x-5; if sign(fx) == sign(fa) a = x; fa = fx; else b = x; fb = fx; end end xThe result is a root of the polynomial x3 - 2x - 5, namely
x = 2.09455148154233The cautions involving matrix comparisons that are discussed in the section on the
if
statement also apply to the while
statement.
The break
statement lets you exit early from a for
or while
loop. In nested loops, break
exits from the innermost loop only.
Here is an improvement on the example from the previous section. Why is this use of break
a good idea?
a = 0; fa = -inf; b = 3; fb = inf; while b-a > eps*b x = (a+b)/2; fx = x^3-2*x-5; if fx == 0 break elseif sign(fx) == sign(fa) a = x; fa = fx; else b = x; fb = fx; end end x