Conditional Execution

When writing a program we may be faced with the need to use different equations, for instance, according to what the limiting conditions of validity are for each of them. This is achieved in MATLAB (and in many other programming languages) by using the IF statement.

An IF statement will execute equations subject to a logical condition

Logical Expressions

Statements within an IF Statement are executed subject to a logical condition being satisfied. For example the following logical expression would be TRUE if x was greater than 1, and FALSE if x was less than (or equal to) 1.

   x > 1

The list of relational operators and their meanings are:

Relational Operator              Meaning

        <                    less than
        <=                   less than or equal to
        ==                   equal to
        ~=                   not equal to
        >                    greater than
        >=                   greater than or equal to

Expressions can be combined using the logical operators AND, OR, and NOT. The MATLAB symbols for these are:

Logical Operator                 Meaning

        &                         AND
        :                         OR
        ~                         NOT

The AND operator returns the TRUE value if the expressions on both sides of the operator are true, otherwise it returns FALSE.
The OR operator returns TRUE if either or both of the expressions are true.
The NOT operator is applied to a single expression and returns TRUE if the expression is false, and vice versa.

Consider the following example; if we assume that x>y is true (i.e. x is greater than y) and that x < 10 is false, the following expressions return the values indicated:

  Expression                  
 
  x>y &  x<10                     FALSE
  x>y : x<10                      TRUE
  ~ x>y                           FALSE
  x>y & (~ x<10)                  TRUE

IF Statement

The IF statement is used to determine, when the program is running, whether a block of statements should be executed. It can also be used to execute alternative sequences of statements, depending on alternative conditions. An example of the simplest form of IF statement is shown below:

  ...
  if  x > y 
    'X is greater than Y and difference is '
    diff = x-y
  end 
  ...

The IF statement takes as its argument a logical expression, as described above. If that expression evaluates to TRUE, the statements that immediately follow the IF statement are executed. If the condition is not true (i.e. it is FALSE), execution proceeds with the statements after the END statement. In the example, if x were greater than y, a difference would be calculated and a message printed out. If x were less than or equal to y, execution would proceed immediately to the rest of the code indicated by the second set of ...'s.

A more general form of IF statement includes a second block of statements which are executed if the logical expression is false.

  ...
  if  x > y  
     'X is greater than Y. The difference is '
     diff = x - y
  else
     'In this case, X is less than Y. The difference is'
     diff = y - x
  end
  ...

This case differs from the previous example in that if x is not greater than y, a different method is used to calculate the difference and a slightly different message is printed out to the user. In general, if the argument to the IF statement is FALSE, execution proceeds to the statement immediately following the ELSE statement and continues until the END statement is reached.

A slight variation on this form of IF statement is one in which a series of conditions is tested. An example of this is shown below where the user is asked for the pressure (in atmospheres) of a vessel. This value is then checked against some criteria and if unsuitable, the user is asked to re-enter the data.

  ... 
  P = input('Please input the pressure of the vessel ');

  if P < 1.0  
    'Sub-atmospheric pressure not allowed.'
    P = input('Please re-enter the pressure of the vessel ');
  elseif P > 10.0
    'Pressure is too high!'
    P = input('Please re-enter the pressure of the vessel ');
  else
    'Pressure appears to be within valid range.';
  end
  ...

The tests of the logical expressions are made one after the other until one is true. The corresponding block of statements is then executed and the control is passed to the END statement ignoring any other tests that have not been done yet. If none of the conditions is true, the final ELSE clause (if such is present) is executed.

Finally we can have nested IF statements but each has to be fully contained in a block of the next outer IF statement. For example, to compare three quantities:

  if x > y 
      if  x > z 
          'X would appear to be the largest value.'
      else
          'Z is the largest value.'
      end 
  end

This example is not complete. What code do you need to write to cover all the cases? How can you rewrite this code using logical expressions to make it shorter (and hopefully easier to read!)?

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