### 4.6 Predicates for Numeric Objects

Since the type of a variable may change during the execution of a program, it can be necessary to type checking at run-time. Doing this also allows you to change the behaviour of a function depending on the type of the input. As an example, this naive implementation of `abs` returns the absolute value of the input if it is a real number, and the length of the input if it is a complex number.

         function a = abs (x)
           if (isreal (x))
             a = sign (x) .* x;
           elseif (iscomplex (x))
             a = sqrt (real(x).^2 + imag(x).^2);
           endif
         endfunction

The following functions are available for determining the type of a variable.

— Built-in Function: isnumeric (x)

> Return nonzero if x is a numeric object.

— Built-in Function: isreal (x)

> Return true if x is a real-valued numeric object.

— Built-in Function: iscomplex (x)

> Return true if x is a complex-valued numeric object.

— Built-in Function: ismatrix (a)

> Return 1 if a is a matrix. Otherwise, return 0.

— Function File: isvector (a)

> Return 1 if a is a vector. Otherwise, return 0.

> See also: size, rows, columns, length, isscalar, ismatrix.

— Function File: isscalar (a)

> Return 1 if a is a scalar. Otherwise, return 0.

> See also: size, rows, columns, length, isscalar, ismatrix.

— Function File: issquare (x)

> If x is a square matrix, then return the dimension of x. Otherwise, return 0.

> See also: size, rows, columns, length, ismatrix, isscalar, isvector.

— Function File: issymmetric (x, tol)

> If x is symmetric within the tolerance specified by tol, then return the dimension of x. Otherwise, return 0. If tol is omitted, use a tolerance equal to the machine precision. Matrix x is considered symmetric if `norm (`x`-` x`.', inf) / norm (`x`, inf) <` tol.

> See also: size, rows, columns, length, ishermitian, ismatrix, isscalar, issquare, isvector.

— Function File: isdefinite (x, tol)

> Return 1 if x is symmetric positive definite within the tolerance specified by tol or 0 if x is symmetric positive semidefinite. Otherwise, return -1. If tol is omitted, use a tolerance equal to 100 times the machine precision.

> See also: issymmetric.

— Built-in Function: islogical (x)

> Return true if x is a logical object.

— Function File: isprime (n)

> Return true if n is a prime number, false otherwise.

> Something like the following is much faster if you need to test a lot of small numbers:

>               t = ismember (n, primes (max (n (:))));

> If max(n) is very large, then you should be using special purpose factorization code.

> See also: primes, factor, gcd, lcm.