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</div>
<hr>
<span id="Predicates-for-Numeric-Objects-1"></span><h3 class="section">4.8 Predicates for Numeric Objects</h3>
<p>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 <code>abs</code>
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.
</p>
<div class="example">
<pre class="example">function a = abs (x)
if (isreal (x))
a = sign (x) .* x;
elseif (iscomplex (x))
a = sqrt (real(x).^2 + imag(x).^2);
endif
endfunction
</pre></div>
<p>The following functions are available for determining the type of a
variable.
</p>
<span id="XREFisnumeric"></span><dl>
<dt id="index-isnumeric">: <em></em> <strong>isnumeric</strong> <em>(<var>x</var>)</em></dt>
<dd><p>Return true if <var>x</var> is a numeric object, i.e., an integer, real, or
complex array.
</p>
<p>Logical and character arrays are not considered to be numeric.
</p>
<p><strong>See also:</strong> <a href="Integer-Data-Types.html#XREFisinteger">isinteger</a>, <a href="#XREFisfloat">isfloat</a>, <a href="#XREFisreal">isreal</a>, <a href="#XREFiscomplex">iscomplex</a>, <a href="Character-Arrays.html#XREFischar">ischar</a>, <a href="#XREFislogical">islogical</a>, <a href="Character-Arrays.html#XREFisstring">isstring</a>, <a href="Basic-Usage-of-Cell-Arrays.html#XREFiscell">iscell</a>, <a href="Creating-Structures.html#XREFisstruct">isstruct</a>, <a href="Built_002din-Data-Types.html#XREFisa">isa</a>.
</p></dd></dl>
<span id="XREFislogical"></span><dl>
<dt id="index-islogical">: <em></em> <strong>islogical</strong> <em>(<var>x</var>)</em></dt>
<dt id="index-isbool">: <em></em> <strong>isbool</strong> <em>(<var>x</var>)</em></dt>
<dd><p>Return true if <var>x</var> is a logical object.
</p>
<p><strong>See also:</strong> <a href="Character-Arrays.html#XREFischar">ischar</a>, <a href="#XREFisfloat">isfloat</a>, <a href="Integer-Data-Types.html#XREFisinteger">isinteger</a>, <a href="Character-Arrays.html#XREFisstring">isstring</a>, <a href="#XREFisnumeric">isnumeric</a>, <a href="Built_002din-Data-Types.html#XREFisa">isa</a>.
</p></dd></dl>
<span id="XREFisfloat"></span><dl>
<dt id="index-isfloat">: <em></em> <strong>isfloat</strong> <em>(<var>x</var>)</em></dt>
<dd><p>Return true if <var>x</var> is a floating-point numeric object.
</p>
<p>Objects of class double or single are floating-point objects.
</p>
<p><strong>See also:</strong> <a href="Integer-Data-Types.html#XREFisinteger">isinteger</a>, <a href="Character-Arrays.html#XREFischar">ischar</a>, <a href="#XREFislogical">islogical</a>, <a href="#XREFisnumeric">isnumeric</a>, <a href="Character-Arrays.html#XREFisstring">isstring</a>, <a href="Built_002din-Data-Types.html#XREFisa">isa</a>.
</p></dd></dl>
<span id="XREFisreal"></span><dl>
<dt id="index-isreal">: <em></em> <strong>isreal</strong> <em>(<var>x</var>)</em></dt>
<dd><p>Return true if <var>x</var> is a non-complex matrix or scalar.
</p>
<p>For compatibility with <small>MATLAB</small>, this includes logical and character
matrices.
</p>
<p><strong>See also:</strong> <a href="#XREFiscomplex">iscomplex</a>, <a href="#XREFisnumeric">isnumeric</a>, <a href="Built_002din-Data-Types.html#XREFisa">isa</a>.
</p></dd></dl>
<span id="XREFiscomplex"></span><dl>
<dt id="index-iscomplex">: <em></em> <strong>iscomplex</strong> <em>(<var>x</var>)</em></dt>
<dd><p>Return true if <var>x</var> is a complex-valued numeric object.
</p>
<p><strong>See also:</strong> <a href="#XREFisreal">isreal</a>, <a href="#XREFisnumeric">isnumeric</a>, <a href="Character-Arrays.html#XREFischar">ischar</a>, <a href="#XREFisfloat">isfloat</a>, <a href="#XREFislogical">islogical</a>, <a href="Character-Arrays.html#XREFisstring">isstring</a>, <a href="Built_002din-Data-Types.html#XREFisa">isa</a>.
</p></dd></dl>
<span id="XREFismatrix"></span><dl>
<dt id="index-ismatrix">: <em></em> <strong>ismatrix</strong> <em>(<var>x</var>)</em></dt>
<dd><p>Return true if <var>x</var> is a 2-D array.
</p>
<p>A matrix is an object with two dimensions (<code>ndims (<var>x</var>) == 2</code>) for
which <code>size (<var>x</var>)</code> returns <code>[M, N]</code><!-- /@w --> with non-negative M and
N.
</p>
<p><strong>See also:</strong> <a href="#XREFisscalar">isscalar</a>, <a href="#XREFisvector">isvector</a>, <a href="Basic-Usage-of-Cell-Arrays.html#XREFiscell">iscell</a>, <a href="Creating-Structures.html#XREFisstruct">isstruct</a>, <a href="Information.html#XREFissparse">issparse</a>, <a href="Built_002din-Data-Types.html#XREFisa">isa</a>.
</p></dd></dl>
<span id="XREFisvector"></span><dl>
<dt id="index-isvector">: <em></em> <strong>isvector</strong> <em>(<var>x</var>)</em></dt>
<dd><p>Return true if <var>x</var> is a vector.
</p>
<p>A vector is a 2-D array where one of the dimensions is equal to 1 (either
1xN or Nx1). As a consequence of this definition, a 1x1
array (a scalar) is also a vector.
</p>
<p><strong>See also:</strong> <a href="#XREFisscalar">isscalar</a>, <a href="#XREFismatrix">ismatrix</a>, <a href="#XREFiscolumn">iscolumn</a>, <a href="#XREFisrow">isrow</a>, <a href="Object-Sizes.html#XREFsize">size</a>.
</p></dd></dl>
<span id="XREFisrow"></span><dl>
<dt id="index-isrow">: <em></em> <strong>isrow</strong> <em>(<var>x</var>)</em></dt>
<dd><p>Return true if <var>x</var> is a row vector.
</p>
<p>A row vector is a 2-D array for which <code>size (<var>x</var>)</code> returns
<code>[1, N]</code><!-- /@w --> with non-negative N.
</p>
<p><strong>See also:</strong> <a href="#XREFiscolumn">iscolumn</a>, <a href="#XREFisscalar">isscalar</a>, <a href="#XREFisvector">isvector</a>, <a href="#XREFismatrix">ismatrix</a>, <a href="Object-Sizes.html#XREFsize">size</a>.
</p></dd></dl>
<span id="XREFiscolumn"></span><dl>
<dt id="index-iscolumn">: <em></em> <strong>iscolumn</strong> <em>(<var>x</var>)</em></dt>
<dd><p>Return true if <var>x</var> is a column vector.
</p>
<p>A column vector is a 2-D array for which <code>size (<var>x</var>)</code> returns
<code>[N, 1]</code><!-- /@w --> with non-negative N.
</p>
<p><strong>See also:</strong> <a href="#XREFisrow">isrow</a>, <a href="#XREFisscalar">isscalar</a>, <a href="#XREFisvector">isvector</a>, <a href="#XREFismatrix">ismatrix</a>, <a href="Object-Sizes.html#XREFsize">size</a>.
</p></dd></dl>
<span id="XREFisscalar"></span><dl>
<dt id="index-isscalar">: <em></em> <strong>isscalar</strong> <em>(<var>x</var>)</em></dt>
<dd><p>Return true if <var>x</var> is a scalar.
</p>
<p>A scalar is an object with two dimensions for which <code>size (<var>x</var>)</code>
returns <code>[1, 1]</code><!-- /@w -->.
</p>
<p><strong>See also:</strong> <a href="#XREFisvector">isvector</a>, <a href="#XREFismatrix">ismatrix</a>, <a href="Object-Sizes.html#XREFsize">size</a>.
</p></dd></dl>
<span id="XREFissquare"></span><dl>
<dt id="index-issquare">: <em></em> <strong>issquare</strong> <em>(<var>x</var>)</em></dt>
<dd><p>Return true if <var>x</var> is a 2-D square array.
</p>
<p>A square array is a 2-D object for which <code>size (<var>x</var>)</code> returns
<code>[N, N]</code><!-- /@w --> where N is a non-negative integer.
</p>
<p><strong>See also:</strong> <a href="#XREFisscalar">isscalar</a>, <a href="#XREFisvector">isvector</a>, <a href="#XREFismatrix">ismatrix</a>, <a href="Object-Sizes.html#XREFsize">size</a>.
</p></dd></dl>
<span id="XREFissymmetric"></span><dl>
<dt id="index-issymmetric">: <em></em> <strong>issymmetric</strong> <em>(<var>A</var>)</em></dt>
<dt id="index-issymmetric-1">: <em></em> <strong>issymmetric</strong> <em>(<var>A</var>, <var>tol</var>)</em></dt>
<dt id="index-issymmetric-2">: <em></em> <strong>issymmetric</strong> <em>(<var>A</var>, <code>"skew"</code>)</em></dt>
<dt id="index-issymmetric-3">: <em></em> <strong>issymmetric</strong> <em>(<var>A</var>, <code>"skew"</code>, <var>tol</var>)</em></dt>
<dd><p>Return true if <var>A</var> is a symmetric or skew-symmetric matrix within the
tolerance specified by <var>tol</var>.
</p>
<p>The default tolerance is zero (uses faster code).
</p>
<p>The type of symmetry to check may be specified with the additional input
<code>"nonskew"</code> (default) for regular symmetry or <code>"skew"</code> for
skew-symmetry.
</p>
<p>Background: A matrix is symmetric if the transpose of the matrix is equal
to the original matrix: <code><var>A</var> == <var>A</var>.'</code><!-- /@w -->. If a tolerance
is given then symmetry is determined by
<code>norm (<var>A</var> - <var>A</var>.', Inf) / norm (<var>A</var>, Inf) < <var>tol</var></code>.
</p>
<p>A matrix is skew-symmetric if the transpose of the matrix is equal to the
negative of the original matrix: <code><var>A</var> == <span class="nolinebreak">-</span><var>A</var>.'</code><!-- /@w -->. If a
tolerance is given then skew-symmetry is determined by
<code>norm (<var>A</var> + <var>A</var>.', Inf) / norm (<var>A</var>, Inf) < <var>tol</var></code>.
</p>
<p><strong>See also:</strong> <a href="#XREFishermitian">ishermitian</a>, <a href="#XREFisdefinite">isdefinite</a>.
</p></dd></dl>
<span id="XREFishermitian"></span><dl>
<dt id="index-ishermitian">: <em></em> <strong>ishermitian</strong> <em>(<var>A</var>)</em></dt>
<dt id="index-ishermitian-1">: <em></em> <strong>ishermitian</strong> <em>(<var>A</var>, <var>tol</var>)</em></dt>
<dt id="index-ishermitian-2">: <em></em> <strong>ishermitian</strong> <em>(<var>A</var>, <code>"skew"</code>)</em></dt>
<dt id="index-ishermitian-3">: <em></em> <strong>ishermitian</strong> <em>(<var>A</var>, <code>"skew"</code>, <var>tol</var>)</em></dt>
<dd><p>Return true if <var>A</var> is a Hermitian or skew-Hermitian matrix within the
tolerance specified by <var>tol</var>.
</p>
<p>The default tolerance is zero (uses faster code).
</p>
<p>The type of symmetry to check may be specified with the additional input
<code>"nonskew"</code> (default) for regular Hermitian or <code>"skew"</code> for
skew-Hermitian.
</p>
<p>Background: A matrix is Hermitian if the complex conjugate transpose of the
matrix is equal to the original matrix: <code><var>A</var> == <var>A</var>'</code><!-- /@w -->. If
a tolerance is given then the calculation is
<code>norm (<var>A</var> - <var>A</var>', Inf) / norm (<var>A</var>, Inf) < <var>tol</var></code>.
</p>
<p>A matrix is skew-Hermitian if the complex conjugate transpose of the matrix
is equal to the negative of the original matrix:
<code><var>A</var> == <span class="nolinebreak">-</span><var>A</var>'</code><!-- /@w -->. If a
tolerance is given then the calculation is
<code>norm (<var>A</var> + <var>A</var>', Inf) / norm (<var>A</var>, Inf) < <var>tol</var></code>.
</p>
<p><strong>See also:</strong> <a href="#XREFissymmetric">issymmetric</a>, <a href="#XREFisdefinite">isdefinite</a>.
</p></dd></dl>
<span id="XREFisdefinite"></span><dl>
<dt id="index-isdefinite">: <em></em> <strong>isdefinite</strong> <em>(<var>A</var>)</em></dt>
<dt id="index-isdefinite-1">: <em></em> <strong>isdefinite</strong> <em>(<var>A</var>, <var>tol</var>)</em></dt>
<dd><p>Return true if <var>A</var> is symmetric positive definite matrix within the
tolerance specified by <var>tol</var>.
</p>
<p>If <var>tol</var> is omitted, use a tolerance of
<code>100 * eps * norm (<var>A</var>, "fro")</code>.
</p>
<p>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 <var>A</var> is very likely to
be positive semi-definite if the following two conditions hold for a
suitably small tolerance <var>tol</var>.
</p>
<div class="example">
<pre class="example">isdefinite (<var>A</var>) ⇒ 0
isdefinite (<var>A</var> + 5*<var>tol</var>, <var>tol</var>) ⇒ 1
</pre></div>
<p><strong>See also:</strong> <a href="#XREFissymmetric">issymmetric</a>, <a href="#XREFishermitian">ishermitian</a>.
</p></dd></dl>
<span id="XREFisbanded"></span><dl>
<dt id="index-isbanded">: <em></em> <strong>isbanded</strong> <em>(<var>A</var>, <var>lower</var>, <var>upper</var>)</em></dt>
<dd><p>Return true if <var>A</var> is a matrix with entries confined between
<var>lower</var> diagonals below the main diagonal and <var>upper</var> diagonals
above the main diagonal.
</p>
<p><var>lower</var> and <var>upper</var> must be non-negative integers.
</p>
<p><strong>See also:</strong> <a href="#XREFisdiag">isdiag</a>, <a href="#XREFistril">istril</a>, <a href="#XREFistriu">istriu</a>, <a href="Basic-Matrix-Functions.html#XREFbandwidth">bandwidth</a>.
</p></dd></dl>
<span id="XREFisdiag"></span><dl>
<dt id="index-isdiag">: <em></em> <strong>isdiag</strong> <em>(<var>A</var>)</em></dt>
<dd><p>Return true if <var>A</var> is a diagonal matrix.
</p>
<p><strong>See also:</strong> <a href="#XREFisbanded">isbanded</a>, <a href="#XREFistril">istril</a>, <a href="#XREFistriu">istriu</a>, <a href="Rearranging-Matrices.html#XREFdiag">diag</a>, <a href="Basic-Matrix-Functions.html#XREFbandwidth">bandwidth</a>.
</p></dd></dl>
<span id="XREFistril"></span><dl>
<dt id="index-istril">: <em></em> <strong>istril</strong> <em>(<var>A</var>)</em></dt>
<dd><p>Return true if <var>A</var> is a lower triangular matrix.
</p>
<p>A lower triangular matrix has nonzero entries only on the main diagonal and
below.
</p>
<p><strong>See also:</strong> <a href="#XREFistriu">istriu</a>, <a href="#XREFisbanded">isbanded</a>, <a href="#XREFisdiag">isdiag</a>, <a href="Rearranging-Matrices.html#XREFtril">tril</a>, <a href="Basic-Matrix-Functions.html#XREFbandwidth">bandwidth</a>.
</p></dd></dl>
<span id="XREFistriu"></span><dl>
<dt id="index-istriu">: <em></em> <strong>istriu</strong> <em>(<var>A</var>)</em></dt>
<dd><p>Return true if <var>A</var> is an upper triangular matrix.
</p>
<p>An upper triangular matrix has nonzero entries only on the main diagonal and
above.
</p>
<p><strong>See also:</strong> <a href="#XREFisdiag">isdiag</a>, <a href="#XREFisbanded">isbanded</a>, <a href="#XREFistril">istril</a>, <a href="Rearranging-Matrices.html#XREFtriu">triu</a>, <a href="Basic-Matrix-Functions.html#XREFbandwidth">bandwidth</a>.
</p></dd></dl>
<span id="XREFisprime"></span><dl>
<dt id="index-isprime">: <em></em> <strong>isprime</strong> <em>(<var>x</var>)</em></dt>
<dd><p>Return a logical array which is true where the elements of <var>x</var> are prime
numbers and false where they are not.
</p>
<p>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 <code>isprime (abs (x))</code>.
</p>
<p>If <code>class (<var>x</var>)</code> is complex, then primality is tested in the domain
of Gaussian integers (<a href="https://en.wikipedia.org/wiki/Gaussian_integer">https://en.wikipedia.org/wiki/Gaussian_integer</a>).
Some non-complex integers are prime in the ordinary sense, but not in the
domain of Gaussian integers. For example, <em>5 = (1+2i)*(1-2i)</em> 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.
</p>
<p>Examples:
</p>
<div class="example">
<pre class="example">isprime (1:6)
⇒ 0 1 1 0 1 0
</pre></div>
<div class="example">
<pre class="example">isprime ([i, 2, 3, 5])
⇒ 0 0 1 0
</pre></div>
<p>Programming Note: <code>isprime</code> is appropriate if the maximum value in
<var>x</var> is not too large (< 1e15). For larger values special purpose
factorization code should be used.
</p>
<p>Compatibility Note: <small>MATLAB</small> does not extend the definition of prime
numbers and will produce an error if given negative or complex inputs.
</p>
<p><strong>See also:</strong> <a href="Utility-Functions.html#XREFprimes">primes</a>, <a href="Utility-Functions.html#XREFfactor">factor</a>, <a href="Utility-Functions.html#XREFgcd">gcd</a>, <a href="Utility-Functions.html#XREFlcm">lcm</a>.
</p></dd></dl>
<p>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 <a href="Status-of-Variables.html">Status of Variables</a>.
</p>
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