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Next: <a rel="next" accesskey="n" href="Rearranging-Matrices.html#Rearranging-Matrices">Rearranging Matrices</a>,
Up: <a rel="up" accesskey="u" href="Matrix-Manipulation.html#Matrix-Manipulation">Matrix Manipulation</a>
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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.
<!-- any src/data.cc -->
<p><a name="doc_002dany"></a>
<div class="defun">
— Built-in Function: <b>any</b> (<var>x</var>)<var><a name="index-any-1606"></a></var><br>
— Built-in Function: <b>any</b> (<var>x, dim</var>)<var><a name="index-any-1607"></a></var><br>
<blockquote><p>For a vector argument, return true (logical 1) if any element of the vector
is nonzero.
<p>For a matrix argument, return a row vector of logical 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>
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<p class="noindent"><strong>See also:</strong> <a href="doc_002dall.html#doc_002dall">all</a>.
</p></blockquote></div>
<!-- all src/data.cc -->
<p><a name="doc_002dall"></a>
<div class="defun">
— Built-in Function: <b>all</b> (<var>x</var>)<var><a name="index-all-1608"></a></var><br>
— Built-in Function: <b>all</b> (<var>x, dim</var>)<var><a name="index-all-1609"></a></var><br>
<blockquote><p>For a vector argument, return true (logical 1) if all elements of the vector
are nonzero.
<p>For a matrix argument, return a row vector of logical ones and
zeros with each element indicating whether all of the elements of the
corresponding column of the matrix are nonzero. For example:
<pre class="example"> all ([2, 3; 1, 0]))
⇒ [ 1, 0 ]
</pre>
<p>If the optional argument <var>dim</var> is supplied, work along dimension
<var>dim</var>.
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<p class="noindent"><strong>See also:</strong> <a href="doc_002dany.html#doc_002dany">any</a>.
</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>.
<!-- xor scripts/miscellaneous/xor.m -->
<p><a name="doc_002dxor"></a>
<div class="defun">
— Mapping Function: <var>z</var> = <b>xor</b> (<var>x, y</var>)<var><a name="index-xor-1610"></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 one of <var>x</var> or
<var>y</var> is true. Otherwise, for <var>x</var> and <var>y</var> both true or both
false, <code>xor</code> returns false.
<p>The truth table for the xor operation is
<p><table summary=""><tr align="left"><td valign="top" width="44%"></td><td valign="top" width="3%"><var>x</var> </td><td valign="top" width="5%"><var>y</var> </td><td valign="top" width="3%"><var>z</var> </td><td valign="top" width="44%">
<br></td></tr><tr align="left"><td valign="top" width="44%"></td><td valign="top" width="3%">0 </td><td valign="top" width="5%">0 </td><td valign="top" width="3%">0 </td><td valign="top" width="44%">
<br></td></tr><tr align="left"><td valign="top" width="44%"></td><td valign="top" width="3%">1 </td><td valign="top" width="5%">0 </td><td valign="top" width="3%">1 </td><td valign="top" width="44%">
<br></td></tr><tr align="left"><td valign="top" width="44%"></td><td valign="top" width="3%">0 </td><td valign="top" width="5%">1 </td><td valign="top" width="3%">1 </td><td valign="top" width="44%">
<br></td></tr><tr align="left"><td valign="top" width="44%"></td><td valign="top" width="3%">1 </td><td valign="top" width="5%">1 </td><td valign="top" width="3%">0 </td><td valign="top" width="44%">
<br></td></tr></table>
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<p class="noindent"><strong>See also:</strong> <a href="doc_002dand.html#doc_002dand">and</a>, <a href="doc_002dor.html#doc_002dor">or</a>, <a href="doc_002dnot.html#doc_002dnot">not</a>.
</p></blockquote></div>
<!-- diff src/data.cc -->
<p><a name="doc_002ddiff"></a>
<div class="defun">
— Built-in Function: <b>diff</b> (<var>x</var>)<var><a name="index-diff-1611"></a></var><br>
— Built-in Function: <b>diff</b> (<var>x, k</var>)<var><a name="index-diff-1612"></a></var><br>
— Built-in Function: <b>diff</b> (<var>x, k, dim</var>)<var><a name="index-diff-1613"></a></var><br>
<blockquote><p>If <var>x</var> is a vector of length n, <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
the 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>
an empty matrix is returned.
</p></blockquote></div>
<!-- isinf src/mappers.cc -->
<p><a name="doc_002disinf"></a>
<div class="defun">
— Mapping Function: <b>isinf</b> (<var>x</var>)<var><a name="index-isinf-1614"></a></var><br>
<blockquote><p>Return a logical array which is true where the elements of <var>x</var> are
are infinite and false where they are not.
For example:
<pre class="example"> isinf ([13, Inf, NA, NaN])
⇒ [ 0, 1, 0, 0 ]
</pre>
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<p class="noindent"><strong>See also:</strong> <a href="doc_002disfinite.html#doc_002disfinite">isfinite</a>, <a href="doc_002disnan.html#doc_002disnan">isnan</a>, <a href="doc_002disna.html#doc_002disna">isna</a>.
</p></blockquote></div>
<!-- isnan src/mappers.cc -->
<p><a name="doc_002disnan"></a>
<div class="defun">
— Mapping Function: <b>isnan</b> (<var>x</var>)<var><a name="index-isnan-1615"></a></var><br>
<blockquote><p>Return a logical array which is true where the elements of <var>x</var> are
NaN values and false where they are not.
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>, <a href="doc_002disinf.html#doc_002disinf">isinf</a>, <a href="doc_002disfinite.html#doc_002disfinite">isfinite</a>.
</p></blockquote></div>
<!-- isfinite src/mappers.cc -->
<p><a name="doc_002disfinite"></a>
<div class="defun">
— Mapping Function: <b>isfinite</b> (<var>x</var>)<var><a name="index-isfinite-1616"></a></var><br>
— Mapping Function: <b>finite</b> (<var>x</var>)<var><a name="index-finite-1617"></a></var><br>
<blockquote><p>Return a logical array which is true where the elements of <var>x</var> are
finite values and false where they are not.
For example:
<pre class="example"> finite ([13, Inf, NA, NaN])
⇒ [ 1, 0, 0, 0 ]
</pre>
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<p class="noindent"><strong>See also:</strong> <a href="doc_002disinf.html#doc_002disinf">isinf</a>, <a href="doc_002disnan.html#doc_002disnan">isnan</a>, <a href="doc_002disna.html#doc_002disna">isna</a>.
</p></blockquote></div>
<!-- common_size scripts/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-1618"></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,
<var>err</var> 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>
<!-- find src/DLD-FUNCTIONS/find.cc -->
<p><a name="doc_002dfind"></a>
<div class="defun">
— Loadable Function: <var>idx</var> = <b>find</b> (<var>x</var>)<var><a name="index-find-1619"></a></var><br>
— Loadable Function: <var>idx</var> = <b>find</b> (<var>x, n</var>)<var><a name="index-find-1620"></a></var><br>
— Loadable Function: <var>idx</var> = <b>find</b> (<var>x, n, direction</var>)<var><a name="index-find-1621"></a></var><br>
— Loadable Function: [i, j] = <b>find</b> (<var><small class="dots">...</small></var>)<var><a name="index-find-1622"></a></var><br>
— Loadable Function: [i, j, v] = <b>find</b> (<var><small class="dots">...</small></var>)<var><a name="index-find-1623"></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 vector 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_002dnonzeros.html#doc_002dnonzeros">nonzeros</a>.
</p></blockquote></div>
<!-- lookup src/DLD-FUNCTIONS/lookup.cc -->
<p><a name="doc_002dlookup"></a>
<div class="defun">
— Loadable Function: <var>idx</var> = <b>lookup</b> (<var>table, y</var>)<var><a name="index-lookup-1624"></a></var><br>
— Loadable Function: <var>idx</var> = <b>lookup</b> (<var>table, y, opt</var>)<var><a name="index-lookup-1625"></a></var><br>
<blockquote><p>Lookup values in a sorted table. Usually used as a prelude to
interpolation.
<p>If table is increasing and <code>idx = lookup (table, y)</code>, then
<code>table(idx(i)) <= y(i) < table(idx(i+1))</code> for all <code>y(i)</code>
within the table. If <code>y(i) < table(1)</code> then
<code>idx(i)</code> is 0. If <code>y(i) >= table(end)</code> or <code>isnan (y(i))</code> then
<code>idx(i)</code> is <code>n</code>.
<p>If the table is decreasing, then the tests are reversed.
For non-strictly monotonic tables, empty intervals are always skipped.
The result is undefined if <var>table</var> is not monotonic, or if
<var>table</var> contains a NaN.
<p>The complexity of the lookup is O(M*log(N)) where N is the size of
<var>table</var> and M is the size of <var>y</var>. In the special case when <var>y</var>
is also sorted, the complexity is O(min(M*log(N),M+N)).
<p><var>table</var> and <var>y</var> can also be cell arrays of strings
(or <var>y</var> can be a single string). In this case, string lookup
is performed using lexicographical comparison.
<p>If <var>opts</var> is specified, it must be a string with letters indicating
additional options.
<dl>
<dt><code>m</code><dd><code>table(idx(i)) == val(i)</code> if <code>val(i)</code>
occurs in table; otherwise, <code>idx(i)</code> is zero.
<br><dt><code>b</code><dd><code>idx(i)</code> is a logical 1 or 0, indicating whether
<code>val(i)</code> is contained in table or not.
<br><dt><code>l</code><dd>For numeric lookups
the leftmost subinterval shall be extended to infinity (i.e., all indices
at least 1)
<br><dt><code>r</code><dd>For numeric lookups
the rightmost subinterval shall be extended to infinity (i.e., all indices
at most n-1).
</dl>
</p></blockquote></div>
<p>If you wish to check if a variable exists at all, instead of properties
its elements may have, consult <a href="Status-of-Variables.html#Status-of-Variables">Status of Variables</a>.
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