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<h1>Module <code>pl.array2d</code></h1>
<p>Operations on two-dimensional arrays.</p>
<p> See <a href="../manual/02-arrays.md.html#Operations_on_two_dimensional_tables">The Guide</a></p>
<p> Dependencies: <a href="../libraries/pl.utils.html#">pl.utils</a>, <a href="../libraries/pl.tablex.html#">pl.tablex</a>, <a href="../libraries/pl.types.html#">pl.types</a></p>
<h2><a href="#Functions">Functions</a></h2>
<table class="function_list">
<tr>
<td class="name" nowrap><a href="#size">size (t)</a></td>
<td class="summary">return the row and column size.</td>
</tr>
<tr>
<td class="name" nowrap><a href="#column">column (a, key)</a></td>
<td class="summary">extract a column from the 2D array.</td>
</tr>
<tr>
<td class="name" nowrap><a href="#map">map (f, a, arg)</a></td>
<td class="summary">map a function over a 2D array</td>
</tr>
<tr>
<td class="name" nowrap><a href="#reduce_rows">reduce_rows (f, a)</a></td>
<td class="summary">reduce the rows using a function.</td>
</tr>
<tr>
<td class="name" nowrap><a href="#reduce_cols">reduce_cols (f, a)</a></td>
<td class="summary">reduce the columns using a function.</td>
</tr>
<tr>
<td class="name" nowrap><a href="#reduce2">reduce2 (opc, opr, a)</a></td>
<td class="summary">reduce a 2D array into a scalar, using two operations.</td>
</tr>
<tr>
<td class="name" nowrap><a href="#map2">map2 (f, ad, bd, a, b, arg)</a></td>
<td class="summary">map a function over two arrays.</td>
</tr>
<tr>
<td class="name" nowrap><a href="#product">product (f, t1, t2)</a></td>
<td class="summary">cartesian product of two 1d arrays.</td>
</tr>
<tr>
<td class="name" nowrap><a href="#flatten">flatten (t)</a></td>
<td class="summary">flatten a 2D array.</td>
</tr>
<tr>
<td class="name" nowrap><a href="#reshape">reshape (t, nrows, co)</a></td>
<td class="summary">reshape a 2D array.</td>
</tr>
<tr>
<td class="name" nowrap><a href="#swap_rows">swap_rows (t, i1, i2)</a></td>
<td class="summary">swap two rows of an array.</td>
</tr>
<tr>
<td class="name" nowrap><a href="#swap_cols">swap_cols (t, j1, j2)</a></td>
<td class="summary">swap two columns of an array.</td>
</tr>
<tr>
<td class="name" nowrap><a href="#extract_rows">extract_rows (t, ridx)</a></td>
<td class="summary">extract the specified rows.</td>
</tr>
<tr>
<td class="name" nowrap><a href="#extract_cols">extract_cols (t, cidx)</a></td>
<td class="summary">extract the specified columns.</td>
</tr>
<tr>
<td class="name" nowrap><a href="#remove_row">remove_row (t, i)</a></td>
<td class="summary">remove a row from an array.</td>
</tr>
<tr>
<td class="name" nowrap><a href="#remove_col">remove_col (t, j)</a></td>
<td class="summary">remove a column from an array.</td>
</tr>
<tr>
<td class="name" nowrap><a href="#parse_range">parse_range (s)</a></td>
<td class="summary">parse a spreadsheet range.</td>
</tr>
<tr>
<td class="name" nowrap><a href="#range">range (t, rstr)</a></td>
<td class="summary">get a slice of a 2D array using spreadsheet range notation.</td>
</tr>
<tr>
<td class="name" nowrap><a href="#slice">slice (t, i1, j1, i2, j2)</a></td>
<td class="summary">get a slice of a 2D array.</td>
</tr>
<tr>
<td class="name" nowrap><a href="#set">set (t, value, i1, j1, i2, j2)</a></td>
<td class="summary">set a specified range of an array to a value.</td>
</tr>
<tr>
<td class="name" nowrap><a href="#write">write (t, f, fmt, i1, j1, i2, j2)</a></td>
<td class="summary">write a 2D array to a file.</td>
</tr>
<tr>
<td class="name" nowrap><a href="#forall">forall (t, row_op, end_row_op, i1, j1, i2, j2)</a></td>
<td class="summary">perform an operation for all values in a 2D array.</td>
</tr>
<tr>
<td class="name" nowrap><a href="#move">move (dest, di, dj, src, i1, j1, i2, j2)</a></td>
<td class="summary">move a block from the destination to the source.</td>
</tr>
<tr>
<td class="name" nowrap><a href="#iter">iter (a, indices, i1, j1, i2, j2)</a></td>
<td class="summary">iterate over all elements in a 2D array, with optional indices.</td>
</tr>
<tr>
<td class="name" nowrap><a href="#columns">columns (a)</a></td>
<td class="summary">iterate over all columns.</td>
</tr>
<tr>
<td class="name" nowrap><a href="#new">new (rows, cols, val)</a></td>
<td class="summary">new array of specified dimensions</td>
</tr>
</table>
<br/>
<br/>
<h2><a name="Functions"></a>Functions</h2>
<dl class="function">
<dt>
<a name = "size"></a>
<strong>size (t)</strong>
</dt>
<dd>
return the row and column size.
<h3>Parameters:</h3>
<ul>
<li><span class="parameter">t</span>
<span class="types"><span class="type">array</span></span>
a 2d array
</li>
</ul>
<h3>Returns:</h3>
<ol>
<li>
<span class="types"><span class="type">int</span></span>
number of rows</li>
<li>
<span class="types"><span class="type">int</span></span>
number of cols</li>
</ol>
</dd>
<dt>
<a name = "column"></a>
<strong>column (a, key)</strong>
</dt>
<dd>
extract a column from the 2D array.
<h3>Parameters:</h3>
<ul>
<li><span class="parameter">a</span>
<span class="types"><span class="type">array</span></span>
2d array
</li>
<li><span class="parameter">key</span>
an index or key
</li>
</ul>
<h3>Returns:</h3>
<ol>
1d array
</ol>
</dd>
<dt>
<a name = "map"></a>
<strong>map (f, a, arg)</strong>
</dt>
<dd>
map a function over a 2D array
<h3>Parameters:</h3>
<ul>
<li><span class="parameter">f</span>
<span class="types"><span class="type">func</span></span>
a function of at least one argument
</li>
<li><span class="parameter">a</span>
<span class="types"><span class="type">array</span></span>
2d array
</li>
<li><span class="parameter">arg</span>
an optional extra argument to be passed to the function.
</li>
</ul>
<h3>Returns:</h3>
<ol>
2d array
</ol>
</dd>
<dt>
<a name = "reduce_rows"></a>
<strong>reduce_rows (f, a)</strong>
</dt>
<dd>
reduce the rows using a function.
<h3>Parameters:</h3>
<ul>
<li><span class="parameter">f</span>
<span class="types"><span class="type">func</span></span>
a binary function
</li>
<li><span class="parameter">a</span>
<span class="types"><span class="type">array</span></span>
2d array
</li>
</ul>
<h3>Returns:</h3>
<ol>
1d array
</ol>
<h3>See also:</h3>
<ul>
<a href="../libraries/pl.tablex.html#reduce">pl.tablex.reduce</a>
</ul>
</dd>
<dt>
<a name = "reduce_cols"></a>
<strong>reduce_cols (f, a)</strong>
</dt>
<dd>
reduce the columns using a function.
<h3>Parameters:</h3>
<ul>
<li><span class="parameter">f</span>
<span class="types"><span class="type">func</span></span>
a binary function
</li>
<li><span class="parameter">a</span>
<span class="types"><span class="type">array</span></span>
2d array
</li>
</ul>
<h3>Returns:</h3>
<ol>
1d array
</ol>
<h3>See also:</h3>
<ul>
<a href="../libraries/pl.tablex.html#reduce">pl.tablex.reduce</a>
</ul>
</dd>
<dt>
<a name = "reduce2"></a>
<strong>reduce2 (opc, opr, a)</strong>
</dt>
<dd>
reduce a 2D array into a scalar, using two operations.
<h3>Parameters:</h3>
<ul>
<li><span class="parameter">opc</span>
<span class="types"><span class="type">func</span></span>
operation to reduce the final result
</li>
<li><span class="parameter">opr</span>
<span class="types"><span class="type">func</span></span>
operation to reduce the rows
</li>
<li><span class="parameter">a</span>
2D array
</li>
</ul>
</dd>
<dt>
<a name = "map2"></a>
<strong>map2 (f, ad, bd, a, b, arg)</strong>
</dt>
<dd>
map a function over two arrays.
They can be both or either 2D arrays
<h3>Parameters:</h3>
<ul>
<li><span class="parameter">f</span>
<span class="types"><span class="type">func</span></span>
function of at least two arguments
</li>
<li><span class="parameter">ad</span>
<span class="types"><span class="type">int</span></span>
order of first array (1 or 2)
</li>
<li><span class="parameter">bd</span>
<span class="types"><span class="type">int</span></span>
order of second array (1 or 2)
</li>
<li><span class="parameter">a</span>
<span class="types"><span class="type">tab</span></span>
1d or 2d array
</li>
<li><span class="parameter">b</span>
<span class="types"><span class="type">tab</span></span>
1d or 2d array
</li>
<li><span class="parameter">arg</span>
optional extra argument to pass to function
</li>
</ul>
<h3>Returns:</h3>
<ol>
2D array, unless both arrays are 1D
</ol>
</dd>
<dt>
<a name = "product"></a>
<strong>product (f, t1, t2)</strong>
</dt>
<dd>
cartesian product of two 1d arrays.
<h3>Parameters:</h3>
<ul>
<li><span class="parameter">f</span>
<span class="types"><span class="type">func</span></span>
a function of 2 arguments
</li>
<li><span class="parameter">t1</span>
<span class="types"><span class="type">array</span></span>
a 1d table
</li>
<li><span class="parameter">t2</span>
<span class="types"><span class="type">array</span></span>
a 1d table
</li>
</ul>
<h3>Returns:</h3>
<ol>
2d table
</ol>
<h3>Usage:</h3>
<ul>
<pre class="example">product(<span class="string">'..'</span>,{<span class="number">1</span>,<span class="number">2</span>},{<span class="string">'a'</span>,<span class="string">'b'</span>}) == {{<span class="string">'1a'</span>,<span class="string">'2a'</span>},{<span class="string">'1b'</span>,<span class="string">'2b'</span>}}</pre>
</ul>
</dd>
<dt>
<a name = "flatten"></a>
<strong>flatten (t)</strong>
</dt>
<dd>
flatten a 2D array.
(this goes over columns first.)
<h3>Parameters:</h3>
<ul>
<li><span class="parameter">t</span>
<span class="types"><span class="type">array</span></span>
2d table
</li>
</ul>
<h3>Returns:</h3>
<ol>
a 1d table
</ol>
<h3>Usage:</h3>
<ul>
<pre class="example">flatten {{<span class="number">1</span>,<span class="number">2</span>},{<span class="number">3</span>,<span class="number">4</span>},{<span class="number">5</span>,<span class="number">6</span>}} == {<span class="number">1</span>,<span class="number">2</span>,<span class="number">3</span>,<span class="number">4</span>,<span class="number">5</span>,<span class="number">6</span>}</pre>
</ul>
</dd>
<dt>
<a name = "reshape"></a>
<strong>reshape (t, nrows, co)</strong>
</dt>
<dd>
reshape a 2D array.
<h3>Parameters:</h3>
<ul>
<li><span class="parameter">t</span>
<span class="types"><span class="type">array</span></span>
2d array
</li>
<li><span class="parameter">nrows</span>
<span class="types"><span class="type">int</span></span>
new number of rows
</li>
<li><span class="parameter">co</span>
<span class="types"><span class="type">bool</span></span>
column-order (Fortran-style) (default false)
</li>
</ul>
<h3>Returns:</h3>
<ol>
a new 2d array
</ol>
</dd>
<dt>
<a name = "swap_rows"></a>
<strong>swap_rows (t, i1, i2)</strong>
</dt>
<dd>
swap two rows of an array.
<h3>Parameters:</h3>
<ul>
<li><span class="parameter">t</span>
<span class="types"><span class="type">array</span></span>
a 2d array
</li>
<li><span class="parameter">i1</span>
<span class="types"><span class="type">int</span></span>
a row index
</li>
<li><span class="parameter">i2</span>
<span class="types"><span class="type">int</span></span>
a row index
</li>
</ul>
</dd>
<dt>
<a name = "swap_cols"></a>
<strong>swap_cols (t, j1, j2)</strong>
</dt>
<dd>
swap two columns of an array.
<h3>Parameters:</h3>
<ul>
<li><span class="parameter">t</span>
<span class="types"><span class="type">array</span></span>
a 2d array
</li>
<li><span class="parameter">j1</span>
<span class="types"><span class="type">int</span></span>
a column index
</li>
<li><span class="parameter">j2</span>
<span class="types"><span class="type">int</span></span>
a column index
</li>
</ul>
</dd>
<dt>
<a name = "extract_rows"></a>
<strong>extract_rows (t, ridx)</strong>
</dt>
<dd>
extract the specified rows.
<h3>Parameters:</h3>
<ul>
<li><span class="parameter">t</span>
<span class="types"><span class="type">array</span></span>
2d array
</li>
<li><span class="parameter">ridx</span>
<span class="types"><span class="type">{int}</span></span>
a table of row indices
</li>
</ul>
</dd>
<dt>
<a name = "extract_cols"></a>
<strong>extract_cols (t, cidx)</strong>
</dt>
<dd>
extract the specified columns.
<h3>Parameters:</h3>
<ul>
<li><span class="parameter">t</span>
<span class="types"><span class="type">array</span></span>
2d array
</li>
<li><span class="parameter">cidx</span>
<span class="types"><span class="type">{int}</span></span>
a table of column indices
</li>
</ul>
</dd>
<dt>
<a name = "remove_row"></a>
<strong>remove_row (t, i)</strong>
</dt>
<dd>
remove a row from an array.
<h3>Parameters:</h3>
<ul>
<li><span class="parameter">t</span>
<span class="types"><span class="type">array</span></span>
a 2d array
</li>
<li><span class="parameter">i</span>
<span class="types"><span class="type">int</span></span>
a row index
</li>
</ul>
</dd>
<dt>
<a name = "remove_col"></a>
<strong>remove_col (t, j)</strong>
</dt>
<dd>
remove a column from an array.
<h3>Parameters:</h3>
<ul>
<li><span class="parameter">t</span>
<span class="types"><span class="type">array</span></span>
a 2d array
</li>
<li><span class="parameter">j</span>
<span class="types"><span class="type">int</span></span>
a column index
</li>
</ul>
</dd>
<dt>
<a name = "parse_range"></a>
<strong>parse_range (s)</strong>
</dt>
<dd>
parse a spreadsheet range.
The range can be specified either as 'A1:B2' or 'R1C1:R2C2';
a special case is a single element (e.g 'A1' or 'R1C1')
<h3>Parameters:</h3>
<ul>
<li><span class="parameter">s</span>
<span class="types"><a class="type" href="http://www.lua.org/manual/5.2/manual.html#6.4">string</a></span>
a range.
</li>
</ul>
<h3>Returns:</h3>
<ol>
<li>
<span class="types"><span class="type">int</span></span>
start col</li>
<li>
<span class="types"><span class="type">int</span></span>
start row</li>
<li>
<span class="types"><span class="type">int</span></span>
end col</li>
<li>
<span class="types"><span class="type">int</span></span>
end row</li>
</ol>
</dd>
<dt>
<a name = "range"></a>
<strong>range (t, rstr)</strong>
</dt>
<dd>
get a slice of a 2D array using spreadsheet range notation. @see parse_range
<h3>Parameters:</h3>
<ul>
<li><span class="parameter">t</span>
<span class="types"><span class="type">array</span></span>
a 2D array
</li>
<li><span class="parameter">rstr</span>
<span class="types"><a class="type" href="http://www.lua.org/manual/5.2/manual.html#6.4">string</a></span>
range expression
</li>
</ul>
<h3>Returns:</h3>
<ol>
a slice
</ol>
<h3>See also:</h3>
<ul>
<li><a href="../libraries/pl.array2d.html#parse_range">array2d.parse_range</a></li>
<li><a href="../libraries/pl.array2d.html#slice">array2d.slice</a></li>
</ul>
</dd>
<dt>
<a name = "slice"></a>
<strong>slice (t, i1, j1, i2, j2)</strong>
</dt>
<dd>
get a slice of a 2D array. Note that if the specified range has
a 1D result, the rank of the result will be 1.
<h3>Parameters:</h3>
<ul>
<li><span class="parameter">t</span>
<span class="types"><span class="type">array</span></span>
a 2D array
</li>
<li><span class="parameter">i1</span>
<span class="types"><span class="type">int</span></span>
start row (default 1)
</li>
<li><span class="parameter">j1</span>
<span class="types"><span class="type">int</span></span>
start col (default 1)
</li>
<li><span class="parameter">i2</span>
<span class="types"><span class="type">int</span></span>
end row (default N)
</li>
<li><span class="parameter">j2</span>
<span class="types"><span class="type">int</span></span>
end col (default M)
</li>
</ul>
<h3>Returns:</h3>
<ol>
an array, 2D in general but 1D in special cases.
</ol>
</dd>
<dt>
<a name = "set"></a>
<strong>set (t, value, i1, j1, i2, j2)</strong>
</dt>
<dd>
set a specified range of an array to a value.
<h3>Parameters:</h3>
<ul>
<li><span class="parameter">t</span>
<span class="types"><span class="type">array</span></span>
a 2D array
</li>
<li><span class="parameter">value</span>
the value (may be a function)
</li>
<li><span class="parameter">i1</span>
<span class="types"><span class="type">int</span></span>
start row (default 1)
</li>
<li><span class="parameter">j1</span>
<span class="types"><span class="type">int</span></span>
start col (default 1)
</li>
<li><span class="parameter">i2</span>
<span class="types"><span class="type">int</span></span>
end row (default N)
</li>
<li><span class="parameter">j2</span>
<span class="types"><span class="type">int</span></span>
end col (default M)
</li>
</ul>
<h3>See also:</h3>
<ul>
<a href="../libraries/pl.tablex.html#set">tablex.set</a>
</ul>
</dd>
<dt>
<a name = "write"></a>
<strong>write (t, f, fmt, i1, j1, i2, j2)</strong>
</dt>
<dd>
write a 2D array to a file.
<h3>Parameters:</h3>
<ul>
<li><span class="parameter">t</span>
<span class="types"><span class="type">array</span></span>
a 2D array
</li>
<li><span class="parameter">f</span>
a file object (default stdout)
</li>
<li><span class="parameter">fmt</span>
<span class="types"><a class="type" href="http://www.lua.org/manual/5.2/manual.html#6.4">string</a></span>
a format string (default is just to use tostring)
</li>
<li><span class="parameter">i1</span>
<span class="types"><span class="type">int</span></span>
start row (default 1)
</li>
<li><span class="parameter">j1</span>
<span class="types"><span class="type">int</span></span>
start col (default 1)
</li>
<li><span class="parameter">i2</span>
<span class="types"><span class="type">int</span></span>
end row (default N)
</li>
<li><span class="parameter">j2</span>
<span class="types"><span class="type">int</span></span>
end col (default M)
</li>
</ul>
</dd>
<dt>
<a name = "forall"></a>
<strong>forall (t, row_op, end_row_op, i1, j1, i2, j2)</strong>
</dt>
<dd>
perform an operation for all values in a 2D array.
<h3>Parameters:</h3>
<ul>
<li><span class="parameter">t</span>
<span class="types"><span class="type">array</span></span>
2D array
</li>
<li><span class="parameter">row_op</span>
<span class="types"><span class="type">func</span></span>
function to call on each value
</li>
<li><span class="parameter">end_row_op</span>
<span class="types"><span class="type">func</span></span>
function to call at end of each row
</li>
<li><span class="parameter">i1</span>
<span class="types"><span class="type">int</span></span>
start row (default 1)
</li>
<li><span class="parameter">j1</span>
<span class="types"><span class="type">int</span></span>
start col (default 1)
</li>
<li><span class="parameter">i2</span>
<span class="types"><span class="type">int</span></span>
end row (default N)
</li>
<li><span class="parameter">j2</span>
<span class="types"><span class="type">int</span></span>
end col (default M)
</li>
</ul>
</dd>
<dt>
<a name = "move"></a>
<strong>move (dest, di, dj, src, i1, j1, i2, j2)</strong>
</dt>
<dd>
move a block from the destination to the source.
<h3>Parameters:</h3>
<ul>
<li><span class="parameter">dest</span>
<span class="types"><span class="type">array</span></span>
a 2D array
</li>
<li><span class="parameter">di</span>
<span class="types"><span class="type">int</span></span>
start row in dest
</li>
<li><span class="parameter">dj</span>
<span class="types"><span class="type">int</span></span>
start col in dest
</li>
<li><span class="parameter">src</span>
<span class="types"><span class="type">array</span></span>
a 2D array
</li>
<li><span class="parameter">i1</span>
<span class="types"><span class="type">int</span></span>
start row (default 1)
</li>
<li><span class="parameter">j1</span>
<span class="types"><span class="type">int</span></span>
start col (default 1)
</li>
<li><span class="parameter">i2</span>
<span class="types"><span class="type">int</span></span>
end row (default N)
</li>
<li><span class="parameter">j2</span>
<span class="types"><span class="type">int</span></span>
end col (default M)
</li>
</ul>
</dd>
<dt>
<a name = "iter"></a>
<strong>iter (a, indices, i1, j1, i2, j2)</strong>
</dt>
<dd>
iterate over all elements in a 2D array, with optional indices.
<h3>Parameters:</h3>
<ul>
<li><span class="parameter">a</span>
<span class="types"><span class="type">array</span></span>
2D array
</li>
<li><span class="parameter">indices</span>
<span class="types"><span class="type">{int}</span></span>
with indices (default false)
</li>
<li><span class="parameter">i1</span>
<span class="types"><span class="type">int</span></span>
start row (default 1)
</li>
<li><span class="parameter">j1</span>
<span class="types"><span class="type">int</span></span>
start col (default 1)
</li>
<li><span class="parameter">i2</span>
<span class="types"><span class="type">int</span></span>
end row (default N)
</li>
<li><span class="parameter">j2</span>
<span class="types"><span class="type">int</span></span>
end col (default M)
</li>
</ul>
<h3>Returns:</h3>
<ol>
either value or i,j,value depending on indices
</ol>
</dd>
<dt>
<a name = "columns"></a>
<strong>columns (a)</strong>
</dt>
<dd>
iterate over all columns.
<h3>Parameters:</h3>
<ul>
<li><span class="parameter">a</span>
<span class="types"><span class="type">array</span></span>
a 2D array
</li>
</ul>
<h3>Returns:</h3>
<ol>
each column in turn
</ol>
</dd>
<dt>
<a name = "new"></a>
<strong>new (rows, cols, val)</strong>
</dt>
<dd>
new array of specified dimensions
<h3>Parameters:</h3>
<ul>
<li><span class="parameter">rows</span>
<span class="types"><span class="type">int</span></span>
number of rows
</li>
<li><span class="parameter">cols</span>
<span class="types"><span class="type">int</span></span>
number of cols
</li>
<li><span class="parameter">val</span>
initial value; if it's a function then use <code>val(i,j)</code>
</li>
</ul>
<h3>Returns:</h3>
<ol>
new 2d array
</ol>
</dd>
</dl>
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