### 4.8 Predicates for Numeric Objects ¶

Since the type of a variable may change during the execution of a program, it can be necessary to do type checking at run-time. Doing this also allows you to change the behavior 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.

`tf =` isnumeric `(x)` ¶

  Return true if x is a numeric object, i.e., an integer, real, or complex array.

  Logical and character arrays are not considered to be numeric.

  See also: isinteger, isfloat, isreal, iscomplex, ischar, islogical, isstring, iscell, isstruct, isa.

`tf =` islogical `(x)` ¶
`tf =` isbool `(x)` ¶

  Return true if x is a logical object.

  Programming Note: `isbool` is an alias for `islogical` and can be used interchangeably.

  See also: ischar, isfloat, isinteger, isstring, isnumeric, isa.

`tf =` isfloat `(x)` ¶

  Return true if x is a floating-point numeric object.

  Objects of class double or single are floating-point objects.

  See also: isinteger, ischar, islogical, isnumeric, isstring, isa.

`tf =` isreal `(x)` ¶

  Return true if x is a non-complex matrix or scalar.

  For compatibility with MATLAB, this includes logical and character matrices.

  See also: iscomplex, isnumeric, isa.

`tf =` iscomplex `(x)` ¶

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

  See also: isreal, isnumeric, ischar, isfloat, islogical, isstring, isa.

`tf =` ismatrix `(x)` ¶

  Return true if x is a 2-D array.

  A matrix is an array of any type where `ndims (x) == 2` and for which `size (x)` returns `[M, N]` with non-negative M and N.

  See also: isscalar, isvector, iscell, isstruct, issparse, isa.

`tf =` isvector `(x)` ¶

  Return true if x is a vector.

  A vector is a 2-D array of any type where one of the dimensions is equal to 1 (either 1xN or Nx1). As a consequence of this definition, a 1x1 object (a scalar) is also a vector.

  See also: isscalar, ismatrix, iscolumn, isrow, size.

`tf =` isrow `(x)` ¶

  Return true if x is a row vector.

  A row vector is a 2-D array of any type for which `size (x)` returns `[1, N]` with non-negative N.

  See also: iscolumn, isscalar, isvector, ismatrix, size.

`tf =` iscolumn `(x)` ¶

  Return true if x is a column vector.

  A column vector is a 2-D array of any type for which `size (x)` returns `[N, 1]` with non-negative N.

  See also: isrow, isscalar, isvector, ismatrix, size.

`tf =` isscalar `(x)` ¶

  Return true if x is a scalar.

  A scalar is a single-element object of any type for which `size (x)` returns `[1, 1]`.

  See also: isvector, ismatrix, size.

`tf =` issquare `(x)` ¶

  Return true if x is a 2-D square array.

  A square array is a 2-D array of any type for which `size (x)` returns `[N, N]` where N is a non-negative integer.

  See also: isscalar, isvector, ismatrix, size.

`tf =` issymmetric `(A)` ¶
`tf =` issymmetric `(A, tol)` ¶
`tf =` issymmetric `(A, `"skew"`)` ¶
`tf =` issymmetric `(A, `"skew"`, tol)` ¶

  Return true if A is a symmetric or skew-symmetric numeric matrix within the tolerance specified by tol.

  The default tolerance is zero (uses faster code).

  The type of symmetry to check may be specified with the additional input `"nonskew"` (default) for regular symmetry or `"skew"` for skew-symmetry.

  Background: A matrix is symmetric if the transpose of the matrix is equal to the original matrix: `A == A.'`. If a tolerance is given then symmetry is determined by `norm (A - A.', Inf) / norm (A, Inf) < tol`.

  A matrix is skew-symmetric if the transpose of the matrix is equal to the negative of the original matrix: `A == -A.'`. If a tolerance is given then skew-symmetry is determined by `norm (A + A.', Inf) / norm (A, Inf) < tol`.

  See also: ishermitian, isdefinite.

`tf =` ishermitian `(A)` ¶
`tf =` ishermitian `(A, tol)` ¶
`tf =` ishermitian `(A, `"skew"`)` ¶
`tf =` ishermitian `(A, `"skew"`, tol)` ¶

  Return true if A is a Hermitian or skew-Hermitian numeric matrix within the tolerance specified by tol.

  The default tolerance is zero (uses faster code).

  The type of symmetry to check may be specified with the additional input `"nonskew"` (default) for regular Hermitian or `"skew"` for skew-Hermitian.

  Background: A matrix is Hermitian if the complex conjugate transpose of the matrix is equal to the original matrix: `A == A'`. If a tolerance is given then the calculation is `norm (A - A', Inf) / norm (A, Inf) < tol`.

  A matrix is skew-Hermitian if the complex conjugate transpose of the matrix is equal to the negative of the original matrix: `A == -A'`. If a tolerance is given then the calculation is `norm (A + A', Inf) / norm (A, Inf) < tol`.

  See also: issymmetric, isdefinite.

`tf =` isdefinite `(A)` ¶
`tf =` isdefinite `(A, tol)` ¶

  Return true if A is symmetric positive definite numeric matrix within the tolerance specified by tol.

  If tol is omitted, use a tolerance of `100 * eps * norm (A, "fro")`.

  Background: A positive definite matrix has eigenvalues which are all greater than zero. A positive semi-definite matrix has eigenvalues which are all greater than or equal to zero. The matrix A is very likely to be positive semi-definite if the following two conditions hold for a suitably small tolerance tol.

      isdefinite (A) ⇒  0
      isdefinite (A + 5*tol, tol) ⇒  1

  See also: issymmetric, ishermitian.

`tf =` isbanded `(A, lower, upper)` ¶

  Return true if A is a numeric matrix with entries confined between lower diagonals below the main diagonal and upper diagonals above the main diagonal.

  lower and upper must be non-negative integers.

  See also: isdiag, istril, istriu, bandwidth.

`tf =` isdiag `(A)` ¶

  Return true if A is a diagonal numeric matrix which is defined as a 2-D array where all elements above and below the main diagonal are zero.

  See also: isbanded, istril, istriu, diag, bandwidth.

`tf =` istril `(A)` ¶

  Return true if A is a lower triangular numeric matrix.

  A lower triangular matrix has nonzero entries only on the main diagonal and below.

  See also: istriu, isbanded, isdiag, tril, bandwidth.

`tf =` istriu `(A)` ¶

  Return true if A is an upper triangular numeric matrix.

  An upper triangular matrix has nonzero entries only on the main diagonal and above.

  See also: isdiag, isbanded, istril, triu, bandwidth.

`tf =` isprime `(x)` ¶

  Return a logical array which is true where the elements of x are prime numbers and false where they are not.

  A prime number is conventionally defined as a positive integer greater than 1 (e.g., 2, 3, …) which is divisible only by itself and 1. Octave extends this definition to include both negative integers and complex values. A negative integer is prime if its positive counterpart is prime. This is equivalent to `isprime (abs (x))`.

  If `class (x)` is complex, then primality is tested in the domain of Gaussian integers (https://en.wikipedia.org/wiki/Gaussian_integer). Some non-complex integers are prime in the ordinary sense, but not in the domain of Gaussian integers. For example, 5 = (1+2i)*(1-2i) shows that 5 is not prime because it has a factor other than itself and 1. Exercise caution when testing complex and real values together in the same matrix.

  Examples:

      isprime (1:6)
        ⇒   0  1  1  0  1  0

      isprime ([i, 2, 3, 5])
        ⇒   0  0  1  0

  Programming Note: `isprime` is suitable for all x in the range abs(x) < 2^64. Cast inputs larger than `flintmax` to `uint64`.

  For larger inputs, use ‘sym’ if you have the Symbolic package installed and loaded:

      isprime (sym ('58745389709258902525390450') + (0:4))
         ⇒   0  1  0  0  0

  Compatibility Note: MATLAB does not extend the definition of prime numbers and will produce an error if given negative or complex inputs.

  See also: primes, factor, gcd, lcm.

`tf =` isuniform `(v)` ¶
`[tf, delta] =` isuniform `(v)` ¶

  Return true if the real vector v is uniformly spaced and false otherwise.

  A vector is uniform if the mean difference (delta) between all elements is the same to within a tolerance of `4 * eps (max (abs (v)))`.

  The optional output delta is the uniform difference between elements. If the vector is not uniform then delta is `NaN`. delta is of the same class as v for floating point inputs and of class double for integer, logical, and character inputs.

  Programming Notes: The output is always false for the special cases of an empty input or a scalar input. If any element is `NaN` then the output is false. If delta is smaller than the calculated relative tolerance then an absolute tolerance of `eps` is used.

  See also: linspace, colon.

If instead of knowing properties of variables, you wish to know which variables are defined and to gather other information about the workspace itself, see Status of Variables.