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<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
<html>
<head>
<meta content="text/html;charset=ISO-8859-1" http-equiv="Content-Type">
<title>Armadillo: API Reference</title>
<link rel="icon" href="armadillo_icon.png" type="image/png">
<style type="text/css">
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</head>
<body>
<a name="top"></a>
<a style="display:scroll; position:fixed; bottom:5px; right:5px;" href="#top"><font size=-1>[top]</font></a>
<center>
<table style="text-align: left; width: 80%; margin-left: auto; margin-right: auto;" border="0" cellpadding="0" cellspacing="0">
<tbody>
<tr>
<td style="vertical-align: top;">
<table style="text-align: left; width: 100%;" border="0" cellpadding="0" cellspacing="0">
<tbody>
<tr>
<td style="text-align: left; vertical-align: top;">
<font size=+2><b>Reference for Armadillo 4.300</b></font>
<br>
</td>
<td style="text-align: right; vertical-align: top;">
<b><a href="http://arma.sourceforge.net">to Armadillo home page</a></b>
<br>
<b><a href="http://nicta.com.au">to NICTA home page</a></b>
<br>
</td>
</tr>
</tbody>
</table>
<hr>
<br>
<br>
<!-- BEGIN CONTENT -->
<b>Preamble</b>
<br>
<br>
<table border="0" cellpadding="0" cellspacing="0">
<tbody>
<tr>
<td style="text-align: left; vertical-align: top; width: 50%;">
<ul>
<li>
To aid the conversion of Matlab/Octave programs,
see the <a href="#syntax">syntax conversion table</a>
</li>
<br>
<li>
First time users may want to have a look at a short <a href="#example_prog">example program</a>
</li>
<br>
<li>
If you discover any bugs or regressions, please <a href="http://arma.sourceforge.net/faq.html">report them</a>
</li>
<br>
<li>
Notes on <a href="#api_additions">API additions</a>
</li>
</ul>
</td>
<td>
</td>
<td class="line" style="vertical-align: top;">
<br>
</td>
<td style="text-align: left; vertical-align: top; width: 45%;">
<ul>
<li>
Please cite the following tech report if you use Armadillo in your research and/or software.
Citations are useful for the continued development and maintenance of the library.
<br>
<br>
<font size=-1>
Conrad Sanderson.
<br>
<i><a href="armadillo_nicta_2010.pdf">Armadillo: An Open Source C++ Linear Algebra Library for Fast Prototyping and Computationally Intensive Experiments</a></i>.
<br>
Technical Report, NICTA, 2010.
</font>
</li>
</ul>
</td>
</tr>
</tbody>
</table>
<br>
<br>
<b>Matrix, Vector, Cube and Field Classes</b>
<ul>
<a href="#Mat">Mat<<i>type</i>>, mat and cx_mat</a> ·
<a href="#Col">Col<<i>type</i>>, colvec and vec</a> ·
<a href="#Row">Row<<i>type</i>>, rowvec</a> ·
<a href="#Cube">Cube<<i>type</i>>, cube</a> ·
<a href="#field">field<<i>object type</i>></a> ·
<a href="#SpMat">SpMat<<i>type</i>>, sp_mat and sp_cx_mat</a>
</ul>
<br>
<b>Member Functions & Variables</b>
<ul>
<a href="#attributes">attributes</a> ·
<a href="#colptr">colptr</a> ·
<a href="#copy_size">copy_size</a> ·
<a href="#diag">diag</a> ·
<a href="#each_colrow">each_col/each_row</a> ·
<a href="#element_access">element access</a> ·
<a href="#element_initialisation">element initialisation</a> ·
<a href="#eval_member">eval</a> ·
<a href="#eye_member">eye</a> ·
<a href="#fill">fill</a> ·
<a href="#i_member">i (inverse)</a> ·
<a href="#imbue">imbue</a> ·
<a href="#insert">insert_rows/cols/slices</a> ·
<a href="#in_range">in_range</a> ·
<a href="#is_empty">is_empty</a> ·
<a href="#is_finite">is_finite</a> ·
<a href="#is_square">is_square</a> ·
<a href="#is_vec">is_vec</a> ·
<a href="#iterators_mat">iterators (matrices)</a> ·
<a href="#iterators_cube">iterators (cubes)</a> ·
<a href="#memptr">memptr</a> ·
<a href="#min_and_max_member">min/max</a> ·
<a href="#ones_member">ones</a> ·
<a href="#operators">operators</a> ·
<a href="#print">print</a> ·
<a href="#raw_print">raw_print</a> ·
<a href="#randi">randi</a> ·
<a href="#randu_randn_member">randu/randn</a> ·
<a href="#reset">reset</a> ·
<a href="#reshape_member">reshape</a> ·
<a href="#resize_member">resize</a> ·
<a href="#save_load_mat">save/load (matrices & cubes)</a> ·
<a href="#save_load_field">save/load (fields)</a> ·
<a href="#set_imag">set_imag/real</a> ·
<a href="#set_size">set_size</a> ·
<a href="#shed">shed_rows/cols/slices</a> ·
<a href="#stl_container_fns">STL container functions</a> ·
<a href="#submat">submatrix views</a> ·
<a href="#subcube">subcube views</a> ·
<a href="#subfield">subfield views</a> ·
<a href="#swap">swap</a> ·
<a href="#swap_rows">swap_rows/cols</a> ·
<a href="#t_st_members">t/st (transpose)</a> ·
<a href="#transform">transform</a> ·
<a href="#zeros_member">zeros</a>
</ul>
<br>
<b>Other Classes</b>
<ul>
<a href="#running_stat">running_stat<<i>type</i>></a> ·
<a href="#running_stat_vec">running_stat_vec<<i>vec_type</i>></a> ·
<a href="#wall_clock">wall_clock</a>
</ul>
<br>
<b>Generated Vectors/Matrices/Cubes</b>
<ul>
<a href="#eye_standalone">eye</a> ·
<a href="#linspace">linspace</a> ·
<a href="#ones_standalone">ones</a> ·
<a href="#randu_randn_standalone">randu/randn</a> ·
<a href="#repmat">repmat</a> ·
<a href="#speye">speye</a> ·
<a href="#spones">spones</a> ·
<a href="#sprandu_sprandn">sprandu/sprandn</a> ·
<a href="#toeplitz">toeplitz/circ_toeplitz</a> ·
<a href="#zeros_standalone">zeros</a>
</ul>
<br>
<b>Functions Individually Applied to Each Element of a Matrix/Cube</b>
<ul>
<a href="#abs">abs</a> ·
<a href="#conj">conj</a> ·
<a href="#conv_to">conv_to</a> ·
<a href="#eps">eps</a> ·
<a href="#imag_real">imag/real</a> ·
<a href="#misc_fns">misc functions (exp, log, pow, sqrt, round, sign, ...)</a> ·
<a href="#trig_fns">trigonometric functions (cos, sin, ...)</a>
</ul>
<br>
<b>Scalar Valued Functions of Vectors/Matrices/Cubes</b>
<ul>
<a href="#accu">accu</a> ·
<a href="#as_scalar">as_scalar</a> ·
<a href="#cond">cond</a> ·
<a href="#det">det</a> ·
<a href="#dot">dot/cdot/norm_dot</a> ·
<a href="#log_det">log_det</a> ·
<a href="#norm">norm</a> ·
<a href="#rank">rank</a> ·
<a href="#trace">trace</a>
</ul>
<br>
<b>Scalar/Vector Valued Functions of Vectors/Matrices</b>
<ul>
<a href="#all">all</a> ·
<a href="#any">any</a> ·
<a href="#diagvec">diagvec</a> ·
<a href="#min_and_max">min/max</a> ·
<a href="#prod">prod</a> ·
<a href="#sum">sum</a> ·
<a href="#stats_fns">statistics (mean, median, stddev, var)</a>
</ul>
<br>
<b>Vector/Matrix/Cube Valued Functions of Vectors/Matrices/Cubes</b>
<ul>
<a href="#conv">conv</a> ·
<a href="#cor">cor</a> ·
<a href="#cov">cov</a> ·
<a href="#cross">cross</a> ·
<a href="#cumsum">cumsum</a> ·
<a href="#diagmat">diagmat</a> ·
<a href="#find">find</a> ·
<a href="#find_finite">find_finite</a> ·
<a href="#find_nonfinite">find_nonfinite</a> ·
<a href="#flip">fliplr/flipud</a> ·
<a href="#hist">hist</a> ·
<a href="#histc">histc</a> ·
<a href="#inplace_strans">inplace_strans</a> ·
<a href="#inplace_trans">inplace_trans</a> ·
<a href="#join">join_rows/cols/slices</a> ·
<a href="#kron">kron</a> ·
<a href="#normalise">normalise</a> ·
<a href="#reshape">reshape</a> ·
<a href="#resize">resize</a> ·
<a href="#shuffle">shuffle</a> ·
<a href="#sort">sort</a> ·
<a href="#sort_index">sort_index</a> ·
<a href="#symmat">symmatu/symmatl</a> ·
<a href="#strans">strans</a> ·
<a href="#trans">trans</a> ·
<a href="#trimat">trimatu/trimatl</a> ·
<a href="#unique">unique</a> ·
<a href="#vectorise">vectorise</a>
</ul>
<br>
<b>Decompositions, Factorisations, Inverses and Equation Solvers</b>
<ul>
<a href="#chol">chol</a> ·
<a href="#eig_sym">eig_sym</a> ·
<a href="#eig_gen">eig_gen</a> ·
<a href="#eig_pair">eig_pair</a> ·
<a href="#eigs_sym">eigs_sym</a> ·
<a href="#eigs_gen">eigs_gen</a> ·
<a href="#fft">fft/ifft</a> ·
<a href="#fft2">fft2/ifft2</a> ·
<a href="#inv">inv</a> ·
<a href="#inv_sympd">inv_sympd</a> ·
<a href="#lu">lu</a> ·
<a href="#pinv">pinv</a> ·
<a href="#princomp">princomp</a> ·
<a href="#qr">qr</a> ·
<a href="#qr_econ">qr_econ</a> ·
<a href="#solve">solve</a> ·
<a href="#svd">svd</a> ·
<a href="#svd_econ">svd_econ</a> ·
<a href="#syl">syl</a>
</ul>
<br>
<b>Miscellaneous</b>
<ul>
<a href="#is_finite_standalone">is_finite()</a> ·
<a href="#logging">logging of errors/warnings</a> ·
<a href="#constants">pre-defined constants (pi, inf, speed of light, ...)</a> ·
<!--<a href="#log_add">log_add</a> ·-->
<a href="#uword">uword/sword</a> ·
<a href="#cx_double">cx_double/cx_float</a> ·
<a href="#syntax">Matlab/Armadillo syntax differences</a> ·
<a href="#example_prog">example program</a> ·
<!--<a href="#catching_exceptions">catching exceptions</a> ·-->
<a href="#config_hpp">config.hpp</a> ·
<a href="#api_additions">API additions</a>
</ul>
<br>
<br>
<br>
<hr class="greyline">
<hr class="greyline">
<br>
<br>
<font size=+1><b>Matrix, Vector, Cube and Field Classes</b></font>
<br>
<br>
<hr class="greyline">
<br>
<a name="Mat"></a><b>Mat<</b><i>type</i><b>></b>
<br><b>mat</b>
<br><b>cx_mat</b>
<ul>
<li>
The root matrix class is <b>Mat<</b><i>type</i><b>></b>, where <i>type</i> is one of:
<ul>
<li>
<i>float</i>, <i>double</i>, <i>std::complex<float></i>, <i>std::complex<double></i>,
<i>char</i>, <i>short</i>, <i>int</i>, <i>long</i> and unsigned versions of <i>char</i>, <i>short</i>, <i>int</i>, <i>long</i>
</li>
</ul>
</li>
<br>
<li>
For convenience the following typedefs have been defined:
<ul>
<table style="text-align: left;" border="0" cellpadding="2" cellspacing="2">
<tbody>
<tr>
<td style="vertical-align: top;">
mat
</td>
<td style="vertical-align: top;">
=
</td>
<td style="vertical-align: top;">
Mat<double>
</td>
</tr>
<tr>
<td style="vertical-align: top;">
fmat
</td>
<td style="vertical-align: top;">
=
</td>
<td style="vertical-align: top;">
Mat<float>
</td>
</tr>
<tr>
<td style="vertical-align: top;">
cx_mat
</td>
<td style="vertical-align: top;">
=
</td>
<td style="vertical-align: top;">
Mat<<a href="#cx_double">cx_double</a>>
</td>
</tr>
<tr>
<td style="vertical-align: top;">
cx_fmat
</td>
<td style="vertical-align: top;">
=
</td>
<td style="vertical-align: top;">
Mat<<a href="#cx_double">cx_float</a>>
</td>
</tr>
<tr>
<td style="vertical-align: top;">
umat
</td>
<td style="vertical-align: top;">
=
</td>
<td style="vertical-align: top;">
Mat<<a href="#uword">uword</a>>
</td>
</tr>
<tr>
<td style="vertical-align: top;">
imat
</td>
<td style="vertical-align: top;">
=
</td>
<td style="vertical-align: top;">
Mat<<a href="#uword">sword</a>>
</td>
</tr>
</tbody>
</table>
</ul>
</li>
<br>
<li>
In this documentation the <i>mat</i> type is used for convenience;
it is possible to use other types instead, eg. <i>fmat</i>
</li>
<br>
<li>
Functions which use LAPACK or ATLAS (generally matrix decompositions) are only valid for the following types:
<i>mat</i>, <i>fmat</i>, <i>cx_mat</i>, <i>cx_fmat</i>
</li>
<br>
<li>
Elements are stored with <a href="https://en.wikipedia.org/wiki/Column_major">column-major ordering</a> (ie. column by column)
</li>
<br>
<a name="constructors_mat"></a>
<li>
Constructors:
<ul>
<li>mat()</li>
<li>mat(n_rows, n_cols)</li>
<li>mat(n_rows, n_cols, fill_type)</li>
<li>mat(mat)</li>
<li>mat(vec)</li>
<li>mat(rowvec)</li>
<li>mat(string)</li>
<li>mat(std::vector) (treated as a column vector)</li>
<li>mat(initialiser_list) (C++11 only)</li>
<li>cx_mat(mat,mat) (for constructing a complex matrix out of two real matrices)</li>
</ul>
</li>
<br>
<li>
When specifying the size with <i>n_rows</i> and <i>n_cols</i>, by default the memory is uninitialised;
memory can be initialised by specifying the <i>fill_type</i>,
which is one of:
<i>fill::zeros</i>,
<i>fill::ones</i>,
<i>fill::eye</i>,
<i>fill::randu</i>,
<i>fill::randn</i>,
<i>fill::none</i>,
with the following meanings:
<ul>
<table>
<tbody>
<tr><td>fill::zeros</td><td> = </td><td>set all elements to 0</td></tr>
<tr><td>fill::ones</td><td> = </td><td>set all elements to 1</td></tr>
<tr><td>fill::eye</td><td> = </td><td>set the elements along the main diagonal to 1 and off-diagonal elements to 0</td></tr>
<tr><td>fill::randu</td><td> = </td><td>set each element to a random value from a uniform distribution in the [0,1] interval</td></tr>
<tr><td>fill::randn</td><td> = </td><td>set each element to a random value from a normal/Gaussian distribution with zero mean and unit variance</td></tr>
<tr><td>fill::none</td><td> = </td><td>do not modify the elements</td></tr>
</tbody>
</table>
</ul>
</li>
<br>
<li>
The string format for the constructor is elements separated by spaces, and rows denoted by semicolons.
For example, the 2x2 identity matrix can be created using the format string <code>"1 0; 0 1"</code>.
While string based initialisation is compact,
it is considerably faster to directly <a href="#element_access">set the elements</a>,
use <a href="#element_initialisation">element initialisation</a>,
or use C++11 initialiser lists.
</li>
<br>
<a name="adv_constructors_mat"></a>
<li>
Advanced constructors:
<br>
<br>
<ul>
<li>mat(aux_mem*, n_rows, n_cols, copy_aux_mem = true, strict = true)
<br>
<br>
<ul>
Create a matrix using data from writable auxiliary memory.
By default the matrix allocates its own memory and copies data from the auxiliary memory (for safety).
However, if <i>copy_aux_mem</i> is set to <i>false</i>,
the matrix will instead directly use the auxiliary memory (ie. no copying).
This is faster, but can be dangerous unless you know what you're doing!
<br>
<br>
The <i>strict</i> variable comes into effect only if <i>copy_aux_mem</i> is set to <i>false</i>
(ie. the matrix is directly using auxiliary memory).
If <i>strict</i> is set to <i>true</i>,
the matrix will be bound to the auxiliary memory for its lifetime;
the number of elements in the matrix can't be changed (directly or indirectly).
If <i>strict</i> is set to <i>false</i>, the matrix will not be bound to the auxiliary memory for its lifetime,
ie., the size of the matrix can be changed.
If the requested number of elements is different to the size of the auxiliary memory,
new memory will be allocated and the auxiliary memory will no longer be used.
</ul>
</li>
<br>
<li>mat(const aux_mem*, n_rows, n_cols)
<br>
<br>
<ul>
Create a matrix by copying data from read-only auxiliary memory.
</ul>
</li>
<a name="adv_constructors_mat_fixed"></a>
<br>
<li>mat::fixed<n_rows, n_cols>
<br>
<br>
<ul>
Create a fixed size matrix, with the size specified via template arguments.
Memory for the matrix is allocated at compile time.
This is generally faster than dynamic memory allocation, but the size of the matrix can't be changed afterwards (directly or indirectly).
<br>
<br>
For convenience, there are several pre-defined typedefs for each matrix type
(where the types are: <i>umat</i>, <i>imat</i>, <i>fmat</i>, <i>mat</i>, <i>cx_fmat</i>, <i>cx_mat</i>).
The typedefs specify a square matrix size, ranging from 2x2 to 9x9.
The typedefs were defined by simply appending a two digit form of the size to the matrix type
-- for example, <i>mat33</i> is equivalent to <i>mat::fixed<3,3></i>,
while <i>cx_mat44</i> is equivalent to <i>cx_mat::fixed<4,4></i>.
</ul>
</li>
<br>
<li>mat::fixed<n_rows, n_cols>(const aux_mem*)
<br>
<br>
<ul>
Create a fixed size matrix, with the size specified via template arguments,
and copying data from auxiliary memory.
</ul>
</li>
</ul>
</li>
<br>
<br>
<li>
Examples:
<ul>
<pre>
mat A = randu<mat>(5,5);
double x = A(1,2);
mat B = A + A;
mat C = A * B;
mat D = A % B;
cx_mat X(A,B);
B.zeros();
B.set_size(10,10);
B.ones(5,6);
mat E(4,5, fill::zeros);
//
// fixed size matrices:
mat::fixed<5,6> F;
F.ones();
mat44 G;
G.randn();
cout << mat22().randu() << endl;
//
// constructing matrices from
// auxiliary (external) memory:
double aux_mem[24];
mat H(aux_mem, 4, 6, false);
</pre>
</ul>
</li>
<br>
<li><b>Caveat:</b>
For mathematical correctness, scalars are treated as 1x1 matrices during initialisation.
As such, the code below <b>will not</b> generate a 5x5 matrix with every element equal to 123.0:
<ul>
<pre>
mat A(5,5); A = 123.0;
</pre>
</ul>
Use the following code instead:
<ul>
<pre>
mat A(5,5); A.fill(123.0);
</pre>
</ul>
<br>
<li>
See also:
<ul>
<li><a href="#attributes">matrix attributes</a></li>
<li><a href="#element_access">accessing elements</a></li>
<li><a href="#element_initialisation">initialising elements</a></li>
<li><a href="#operators">math & relational operators</a></li>
<li><a href="#submat">submatrix views</a></li>
<li><a href="#save_load_mat">saving & loading matrices</a></li>
<li><a href="#print">printing matrices</a></li>
<li><a href="#iterators_mat">STL-style element iterators</a></li>
<li><a href="#eval_member">.eval()</a></li>
<li><a href="#conv_to">conv_to()</a> (convert between matrix types)</li>
<li><a href="http://www.cplusplus.com/doc/tutorial/other_data_types/">explanation of <i>typedef</i></a> (cplusplus.com)
<li><a href="#Col">Col class</a></li>
<li><a href="#Row">Row class</a></li>
<li><a href="#Cube">Cube class</a></li>
<li><a href="#SpMat">SpMat class</a> (sparse matrix)</li>
<li><a href="#config_hpp">config.hpp</a></li>
</ul>
</li>
<br>
</ul>
<hr class="greyline">
<br>
<a name="Col"></a><b>Col<</b><i>type</i><b>></b>
<br><b>vec</b>
<br><b>cx_vec</b>
<ul>
<li>
Classes for column vectors (matrices with one column)
</li>
<br>
<li>The <b>Col<</b><i>type</i><b>></b> class is derived from the <b>Mat<</b><i>type</i><b>></b> class
and inherits most of the member functions
</li>
<br>
<li>
For convenience the following typedefs have been defined:
<ul>
<table style="text-align: left;" border="0" cellpadding="2" cellspacing="2">
<tbody>
<tr>
<td style="vertical-align: top;">
vec
</td>
<td style="vertical-align: top;">
=
</td>
<td style="vertical-align: top;">
colvec
</td>
<td style="vertical-align: top;">
=
</td>
<td style="vertical-align: top;">
Col<double>
</td>
</tr>
<tr>
<td style="vertical-align: top;">
fvec
</td>
<td style="vertical-align: top;">
=
</td>
<td style="vertical-align: top;">
fcolvec
</td>
<td style="vertical-align: top;">
=
</td>
<td style="vertical-align: top;">
Col<float>
</td>
</tr>
<tr>
<td style="vertical-align: top;">
cx_vec
</td>
<td style="vertical-align: top;">
=
</td>
<td style="vertical-align: top;">
cx_colvec
</td>
<td style="vertical-align: top;">
=
</td>
<td style="vertical-align: top;">
Col<<a href="#cx_double">cx_double</a>>
</td>
</tr>
<tr>
<td style="vertical-align: top;">
cx_fvec
</td>
<td style="vertical-align: top;">
=
</td>
<td style="vertical-align: top;">
cx_fcolvec
</td>
<td style="vertical-align: top;">
=
</td>
<td style="vertical-align: top;">
Col<<a href="#cx_double">cx_float</a>>
</td>
</tr>
<tr>
<td style="vertical-align: top;">
uvec
</td>
<td style="vertical-align: top;">
=
</td>
<td style="vertical-align: top;">
ucolvec
</td>
<td style="vertical-align: top;">
=
</td>
<td style="vertical-align: top;">
Col<<a href="#uword">uword</a>>
</td>
</tr>
<tr>
<td style="vertical-align: top;">
ivec
</td>
<td style="vertical-align: top;">
=
</td>
<td style="vertical-align: top;">
icolvec
</td>
<td style="vertical-align: top;">
=
</td>
<td style="vertical-align: top;">
Col<<a href="#uword">sword</a>>
</td>
</tr>
</tbody>
</table>
</ul>
</li>
<br>
<li>
In this documentation, the <b><i>vec</i></b> and <b><i>colvec</i></b> types have the <b>same meaning</b> and are used <b>interchangeably</b>
</li>
<br>
<li>
In this documentation, the types <i>vec</i> or <i>colvec</i> are used for convenience; it is possible to use other types instead, eg. <i>fvec</i>, <i>fcolvec</i>
</li>
<br>
<li>
Functions which take <i>Mat</i> as input can generally also take <i>Col</i> as input.
Main exceptions are functions which require square matrices
</li>
<br>
<li>
Constructors
<ul>
<li>vec()</li>
<li>vec(n_elem)</li>
<li>vec(n_elem, fill_type)</li>
<li>vec(vec)</li>
<li>vec(mat) (a <i>std::logic_error</i> exception is thrown if the given matrix has more than one column)</li>
<li>vec(string) (elements separated by spaces)</li>
<li>vec(std::vector)</li>
<li>vec(initialiser_list) (C++11 only)</li>
</ul>
</li>
<br>
<li>
When specifying the size with <i>n_elem</i>, by default the memory is uninitialised;
memory can be initialised by specifying the <i>fill_type</i>,
as per the <a href="#Mat">Mat class</a>
</li>
<br>
<a name="adv_constructors_col"></a>
<li>
Advanced constructors:
<br>
<br>
<ul>
<li>vec(aux_mem*, number_of_elements, copy_aux_mem = true, strict = true)
<br>
<br>
<ul>
Create a column vector using data from writable auxiliary memory.
By default the vector allocates its own memory and copies data from the auxiliary memory (for safety).
However, if <i>copy_aux_mem</i> is set to <i>false</i>,
the vector will instead directly use the auxiliary memory (ie. no copying).
This is faster, but can be dangerous unless you know what you're doing!
<br>
<br>
The <i>strict</i> variable comes into effect only if <i>copy_aux_mem</i> is set to <i>false</i>
(ie. the vector is directly using auxiliary memory).
If <i>strict</i> is set to <i>true</i>,
the vector will be bound to the auxiliary memory for its lifetime;
the number of elements in the vector can't be changed (directly or indirectly).
If <i>strict</i> is set to <i>false</i>, the vector will not be bound to the auxiliary memory for its lifetime,
ie., the vector's size can be changed.
If the requested number of elements is different to the size of the auxiliary memory,
new memory will be allocated and the auxiliary memory will no longer be used.
</ul>
</li>
<br>
<li>vec(const aux_mem*, number_of_elements)
<br>
<br>
<ul>
Create a column vector by copying data from read-only auxiliary memory.
</ul>
</li>
<a name="adv_constructors_col_fixed"></a>
<br>
<li>vec::fixed<number_of_elements>
<br>
<br>
<ul>
Create a fixed size column vector, with the size specified via the template argument.
Memory for the vector is allocated at compile time.
This is generally faster than dynamic memory allocation, but the size of the vector can't be changed afterwards (directly or indirectly).
<br>
<br>
For convenience, there are several pre-defined typedefs for each vector type
(where the types are: <i>uvec</i>, <i>ivec</i>, <i>fvec</i>, <i>vec</i>, <i>cx_fvec</i>, <i>cx_vec</i> as well as the corresponding <i>colvec</i> versions).
The pre-defined typedefs specify vector sizes ranging from 2 to 9.
The typedefs were defined by simply appending a single digit form of the size to the vector type
-- for example, <i>vec3</i> is equivalent to <i>vec::fixed<3></i>,
while <i>cx_vec4</i> is equivalent to <i>cx_vec::fixed<4></i>.
</ul>
</li>
<br>
<li>vec::fixed<number_of_elements>(const aux_mem*)
<br>
<br>
<ul>
Create a fixed size column vector, with the size specified via the template argument,
and copying data from auxiliary memory.
</ul>
</li>
</ul>
</li>
<br>
<br>
<li>
Examples:
<ul>
<pre>
vec x(10);
vec y = zeros<vec>(10);
mat A = randu<mat>(10,10);
vec z = A.col(5); // extract a column vector
</pre>
</ul>
</li>
<br>
<li><b>Caveat:</b>
For mathematical correctness, scalars are treated as 1x1 matrices during initialisation.
As such, the code below <b>will not</b> generate a column vector with every element equal to 123.0:
<ul>
<pre>
vec a(5); a = 123.0;
</pre>
</ul>
Use the following code instead:
<ul>
<pre>
vec a(5); a.fill(123.0);
</pre>
</ul>
</li>
<br>
<li>See also:
<ul>
<li><a href="#element_initialisation">element initialisation</a></li>
<li><a href="#Mat">Mat class</a></li>
<li><a href="#Row">Row class</a></li>
</ul>
</li>
<br>
</ul>
<hr class="greyline"><br>
<a name="Row"></a>
<b>Row<</b><i>type</i><b>></b>
<br><b>rowvec</b>
<br><b>cx_rowvec</b>
<ul>
<li>
Classes for row vectors (matrices with one row)
</li>
<br>
<li>The template <b>Row<</b><i>type</i><b>></b> class is derived from the <b>Mat<</b><i>type</i><b>></b> class
and inherits most of the member functions
</li>
<br>
<li>
For convenience the following typedefs have been defined:
<ul>
<table style="text-align: left;" border="0" cellpadding="2" cellspacing="2">
<tbody>
<tr>
<td style="vertical-align: top;">
rowvec
</td>
<td style="vertical-align: top;">
=
</td>
<td style="vertical-align: top;">
Row<double>
</td>
</tr>
<tr>
<td style="vertical-align: top;">
frowvec