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<h3 class="section">16.1 Finding Elements and Checking Conditions</h3>
<p>The functions <code>any</code> and <code>all</code> are useful for determining
whether any or all of the elements of a matrix satisfy some condition.
The <code>find</code> function is also useful in determining which elements of
a matrix meet a specified condition.
<!-- data.cc -->
<p><a name="doc_002dany"></a>
<div class="defun">
— Built-in Function: <b>any</b> (<var>x, dim</var>)<var><a name="index-any-1260"></a></var><br>
<blockquote><p>For a vector argument, return 1 if any element of the vector is
nonzero.
<p>For a matrix argument, return a row vector of ones and
zeros with each element indicating whether any of the elements of the
corresponding column of the matrix are nonzero. For example,
<pre class="example"> any (eye (2, 4))
⇒ [ 1, 1, 0, 0 ]
</pre>
<p>If the optional argument <var>dim</var> is supplied, work along dimension
<var>dim</var>. For example,
<pre class="example"> any (eye (2, 4), 2)
⇒ [ 1; 1 ]
</pre>
</blockquote></div>
<!-- data.cc -->
<p><a name="doc_002dall"></a>
<div class="defun">
— Built-in Function: <b>all</b> (<var>x, dim</var>)<var><a name="index-all-1261"></a></var><br>
<blockquote><p>The function <code>all</code> behaves like the function <code>any</code>, except
that it returns true only if all the elements of a vector, or all the
elements along dimension <var>dim</var> of a matrix, are nonzero.
</p></blockquote></div>
<p>Since the comparison operators (see <a href="Comparison-Ops.html#Comparison-Ops">Comparison Ops</a>) return matrices
of ones and zeros, it is easy to test a matrix for many things, not just
whether the elements are nonzero. For example,
<pre class="example"> all (all (rand (5) < 0.9))
⇒ 0
</pre>
<p class="noindent">tests a random 5 by 5 matrix to see if all of its elements are less
than 0.9.
<p>Note that in conditional contexts (like the test clause of <code>if</code> and
<code>while</code> statements) Octave treats the test as if you had typed
<code>all (all (condition))</code>.
<!-- ./miscellaneous/xor.m -->
<p><a name="doc_002dxor"></a>
<div class="defun">
— Mapping Function: <b>xor</b> (<var>x, y</var>)<var><a name="index-xor-1262"></a></var><br>
<blockquote><p>Return the `exclusive or' of the entries of <var>x</var> and <var>y</var>.
For boolean expressions <var>x</var> and <var>y</var>,
<code>xor (</code><var>x</var><code>, </code><var>y</var><code>)</code> is true if and only if <var>x</var> or <var>y</var>
is true, but not if both <var>x</var> and <var>y</var> are true.
</p></blockquote></div>
<!-- ./general/is_duplicate_entry.m -->
<p><a name="doc_002dis_005fduplicate_005fentry"></a>
<div class="defun">
— Function File: <b>is_duplicate_entry</b> (<var>x</var>)<var><a name="index-is_005fduplicate_005fentry-1263"></a></var><br>
<blockquote><p>Return non-zero if any entries in <var>x</var> are duplicates of one
another.
</p></blockquote></div>
<!-- ./general/diff.m -->
<p><a name="doc_002ddiff"></a>
<div class="defun">
— Function File: <b>diff</b> (<var>x, k, dim</var>)<var><a name="index-diff-1264"></a></var><br>
<blockquote><p>If <var>x</var> is a vector of length <var>n</var>, <code>diff (</code><var>x</var><code>)</code> is the
vector of first differences
<var>x</var>(2) - <var>x</var>(1), <small class="dots">...</small>, <var>x</var>(n) - <var>x</var>(n-1).
<p>If <var>x</var> is a matrix, <code>diff (</code><var>x</var><code>)</code> is the matrix of column
differences along the first non-singleton dimension.
<p>The second argument is optional. If supplied, <code>diff (</code><var>x</var><code>,
</code><var>k</var><code>)</code>, where <var>k</var> is a non-negative integer, returns the
<var>k</var>-th differences. It is possible that <var>k</var> is larger than
then first non-singleton dimension of the matrix. In this case,
<code>diff</code> continues to take the differences along the next
non-singleton dimension.
<p>The dimension along which to take the difference can be explicitly
stated with the optional variable <var>dim</var>. In this case the
<var>k</var>-th order differences are calculated along this dimension.
In the case where <var>k</var> exceeds <code>size (</code><var>x</var><code>, </code><var>dim</var><code>)</code>
then an empty matrix is returned.
</p></blockquote></div>
<!-- mappers.cc -->
<p><a name="doc_002disinf"></a>
<div class="defun">
— Mapping Function: <b>isinf</b> (<var>x</var>)<var><a name="index-isinf-1265"></a></var><br>
<blockquote><p>Return 1 for elements of <var>x</var> that are infinite and zero
otherwise. For example,
<pre class="example"> isinf ([13, Inf, NA, NaN])
⇒ [ 0, 1, 0, 0 ]
</pre>
</blockquote></div>
<!-- mappers.cc -->
<p><a name="doc_002disnan"></a>
<div class="defun">
— Mapping Function: <b>isnan</b> (<var>x</var>)<var><a name="index-isnan-1266"></a></var><br>
<blockquote><p>Return 1 for elements of <var>x</var> that are NaN values and zero
otherwise. NA values are also considered NaN values. For example,
<pre class="example"> isnan ([13, Inf, NA, NaN])
⇒ [ 0, 0, 1, 1 ]
</pre>
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<p class="noindent"><strong>See also:</strong> <a href="doc_002disna.html#doc_002disna">isna</a>.
</p></blockquote></div>
<!-- mappers.cc -->
<p><a name="doc_002dfinite"></a>
<div class="defun">
— Mapping Function: <b>finite</b> (<var>x</var>)<var><a name="index-finite-1267"></a></var><br>
<blockquote><p>Return 1 for elements of <var>x</var> that are finite values and zero
otherwise. For example,
<pre class="example"> finite ([13, Inf, NA, NaN])
⇒ [ 1, 0, 0, 0 ]
</pre>
</blockquote></div>
<!-- ./DLD-FUNCTIONS/find.cc -->
<p><a name="doc_002dfind"></a>
<div class="defun">
— Loadable Function: <b>find</b> (<var>x</var>)<var><a name="index-find-1268"></a></var><br>
— Loadable Function: <b>find</b> (<var>x, n</var>)<var><a name="index-find-1269"></a></var><br>
— Loadable Function: <b>find</b> (<var>x, n, direction</var>)<var><a name="index-find-1270"></a></var><br>
<blockquote><p>Return a vector of indices of nonzero elements of a matrix, as a row if
<var>x</var> is a row or as a column otherwise. To obtain a single index for
each matrix element, Octave pretends that the columns of a matrix form one
long vector (like Fortran arrays are stored). For example,
<pre class="example"> find (eye (2))
⇒ [ 1; 4 ]
</pre>
<p>If two outputs are requested, <code>find</code> returns the row and column
indices of nonzero elements of a matrix. For example,
<pre class="example"> [i, j] = find (2 * eye (2))
⇒ i = [ 1; 2 ]
⇒ j = [ 1; 2 ]
</pre>
<p>If three outputs are requested, <code>find</code> also returns a vector
containing the nonzero values. For example,
<pre class="example"> [i, j, v] = find (3 * eye (2))
⇒ i = [ 1; 2 ]
⇒ j = [ 1; 2 ]
⇒ v = [ 3; 3 ]
</pre>
<p>If two inputs are given, <var>n</var> indicates the maximum number of
elements to find from the beginning of the matrix or vector.
<p>If three inputs are given, <var>direction</var> should be one of "first" or
"last", requesting only the first or last <var>n</var> indices, respectively.
However, the indices are always returned in ascending order.
<p>Note that this function is particularly useful for sparse matrices, as
it extracts the non-zero elements as vectors, which can then be used to
create the original matrix. For example,
<pre class="example"> sz = size(a);
[i, j, v] = find (a);
b = sparse(i, j, v, sz(1), sz(2));
</pre>
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<p class="noindent"><strong>See also:</strong> <a href="doc_002dsparse.html#doc_002dsparse">sparse</a>.
</p></blockquote></div>
<!-- ./general/common_size.m -->
<p><a name="doc_002dcommon_005fsize"></a>
<div class="defun">
— Function File: [<var>err</var>, <var>y1</var>, <small class="dots">...</small>] = <b>common_size</b> (<var>x1, <small class="dots">...</small></var>)<var><a name="index-common_005fsize-1271"></a></var><br>
<blockquote><p>Determine if all input arguments are either scalar or of common
size. If so, <var>err</var> is zero, and <var>yi</var> is a matrix of the
common size with all entries equal to <var>xi</var> if this is a scalar or
<var>xi</var> otherwise. If the inputs cannot be brought to a common size,
errorcode is 1, and <var>yi</var> is <var>xi</var>. For example,
<pre class="example"> [errorcode, a, b] = common_size ([1 2; 3 4], 5)
⇒ errorcode = 0
⇒ a = [ 1, 2; 3, 4 ]
⇒ b = [ 5, 5; 5, 5 ]
</pre>
<p class="noindent">This is useful for implementing functions where arguments can either
be scalars or of common size.
</p></blockquote></div>
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