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<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
<!--
Copyright 2008-2016 Conrad Sanderson (http://conradsanderson.id.au)
Copyright 2008-2016 National ICT Australia (NICTA)
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
-->
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<a class="noprint" style="display:scroll; position:fixed; bottom:5px; right:5px;" href="#top"><font size=-1>[top]</font></a>
<big><b>API Documentation for Armadillo 8.100</b></big>
<br>
<br>
<br>
<b>Preamble</b>
<br>
<br>
<table border="0" cellpadding="0" cellspacing="0">
<tbody>
<tr>
<td style="text-align: left; vertical-align: top; width: 45%;">
<ul>
<li>
For converting Matlab/Octave programs,
see the <a href="#syntax">syntax conversion table</a>
</li>
<br>
<li>
First time users: please see the 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>
History of <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: 50%;">
<ul>
<li>
Please cite the following article 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 and Ryan Curtin.
<br><i><a href="armadillo_joss_2016.pdf">Armadillo: a template-based C++ library for linear algebra</a></i>.
<br>Journal of Open Source Software, Vol. 1, pp. 26, 2016.
</font>
</li>
</ul>
</td>
</tr>
</tbody>
</table>
<br>
<br>
<b>Overview</b>
<ul>
<li><a href="#part_classes">matrix, vector, cube and field classes</a></li>
<li><a href="#part_membfns">member functions & variables</a></li>
<br>
<li><a href="#part_gen">generated vectors / matrices / cubes</a></li>
<li><a href="#part_fns">functions of vectors / matrices / cubes</a></li>
<br>
<li><a href="#part_decompdense">decompositions, factorisations, inverses and equation solvers (dense matrices)</a></li>
<li><a href="#part_decompsparse">decompositions, factorisations, and equation solvers (sparse matrices)</a></li>
<br>
<li><a href="#part_sigproc">signal & image processing</a></li>
<li><a href="#part_stats">statistics and clustering</a></li>
<li><a href="#part_misc">miscellaneous (constants, configuration)</a></li>
</ul>
<br>
<a name="part_classes"></a>
<b>Matrix, Vector, Cube and Field Classes</b>
<ul>
<table>
<tbody>
<tr><td><a href="#Mat">Mat<<i>type</i>>, mat, cx_mat</a></td><td> </td><td>dense matrix class</td></tr>
<tr><td><a href="#Col">Col<<i>type</i>>, colvec, vec</a></td><td> </td><td>dense column vector class</td></tr>
<tr><td><a href="#Row">Row<<i>type</i>>, rowvec</a></td><td> </td><td>dense row vector class</td></tr>
<tr><td> </td><td> </td><td> </td></tr>
<tr><td><a href="#Cube">Cube<<i>type</i>>, cube, cx_cube</a></td><td> </td><td>dense cube class ("3D matrix")</td></tr>
<tr><td><a href="#field">field<<i>object type</i>></a></td><td> </td><td>class for storing arbitrary objects in matrix-like or cube-like layouts</td></tr>
<tr><td><a href="#SpMat">SpMat<<i>type</i>>, sp_mat, sp_cx_mat</a></td><td> </td><td>sparse matrix class (compressed sparse column format)</td></tr>
<tr><td> </td><td> </td><td> </td></tr>
<tr><td><a href="#operators">operators</a></td><td> </td><td><code><big>+</big> <big>-</big> <big>*</big> / % == != <= >= < ></code></td></tr>
</tbody>
</table>
</ul>
<br>
<a name="part_membfns"></a>
<b>Member Functions & Variables</b>
<ul>
<table>
<tbody>
<tr><td><a href="#attributes">attributes</a></td><td> </td><td>.n_rows, .n_cols, .n_elem, .n_slices, ...</td></tr>
<tr><td><a href="#element_access">element access</a></td><td> </td><td>element/object access via (), [] and .at()</td></tr>
<tr><td><a href="#element_initialisation">element initialisation</a></td><td> </td><td>set elements via << operator or initialiser list</td></tr>
<tr><td><small><small> </small></small></td><td><small><small> </small></small></td><td><small><small> </small></small></td></tr>
<tr><td><a href="#zeros_member">.zeros</a></td><td> </td><td>set all elements to zero</td></tr>
<tr><td><a href="#ones_member">.ones</a></td><td> </td><td>set all elements to one</td></tr>
<tr><td><a href="#eye_member">.eye</a></td><td> </td><td>set elements along main diagonal to one and off-diagonal elements to zero</td></tr>
<tr><td><a href="#randu_randn_member">.randu / .randn</a></td><td> </td><td>set all elements to random values</td></tr>
<tr><td><small><small> </small></small></td><td><small><small> </small></small></td><td><small><small> </small></small></td></tr>
<tr><td><a href="#fill">.fill</a></td><td> </td><td>set all elements to specified value</td></tr>
<tr><td><a href="#imbue">.imbue</a></td><td> </td><td>imbue (fill) with values provided by functor or lambda function</td></tr>
<tr><td><small><small> </small></small></td><td><small><small> </small></small></td><td><small><small> </small></small></td></tr>
<tr><td><a href="#replace">.replace</a></td><td> </td><td>replace specific elements with a new value</td></tr>
<tr><td><a href="#transform">.transform</a></td><td> </td><td>transform each element via functor or lambda function</td></tr>
<tr><td><a href="#for_each">.for_each</a></td><td> </td><td>apply a functor or lambda function to each element</td></tr>
<tr><td><small><small> </small></small></td><td><small><small> </small></small></td><td><small><small> </small></small></td></tr>
<tr><td><a href="#set_size">.set_size</a></td><td> </td><td>change size without keeping elements (fast)</td></tr>
<tr><td><a href="#reshape_member">.reshape</a></td><td> </td><td>change size while keeping elements</td></tr>
<tr><td><a href="#resize_member">.resize</a></td><td> </td><td>change size while keeping elements and preserving layout</td></tr>
<tr><td><a href="#copy_size">.copy_size</a></td><td> </td><td>change size to be same as given object</td></tr>
<tr><td><a href="#reset">.reset</a></td><td> </td><td>change size to empty</td></tr>
<tr><td><small><small> </small></small></td><td><small><small> </small></small></td><td><small><small> </small></small></td></tr>
<tr><td><a href="#submat">submatrix views</a></td><td> </td><td>read/write access to contiguous and non-contiguous submatrices</td></tr>
<tr><td><a href="#subcube">subcube views</a></td><td> </td><td>read/write access to contiguous and non-contiguous subcubes</td></tr>
<tr><td><a href="#subfield">subfield views</a></td><td> </td><td>read/write access to contiguous subfields</td></tr>
<tr><td><small><small> </small></small></td><td><small><small> </small></small></td><td><small><small> </small></small></td></tr>
<tr><td><a href="#diag">.diag</a></td><td> </td><td>read/write access to matrix diagonals</td></tr>
<tr><td><a href="#each_colrow">.each_col / .each_row</a></td><td> </td><td>repeated operations on each column or row of matrix</td></tr>
<tr><td><a href="#each_slice">.each_slice</a></td><td> </td><td>repeated operations on each slice of cube</td></tr>
<tr><td><small><small> </small></small></td><td><small><small> </small></small></td><td><small><small> </small></small></td></tr>
<tr><td><a href="#set_imag">.set_imag / .set_real</a></td><td> </td><td>set imaginary/real part</td></tr>
<tr><td><a href="#insert">.insert_rows/cols/slices</a></td><td> </td><td>insert vector/matrix/cube at specified row/column/slice</td></tr>
<tr><td><a href="#shed">.shed_rows/cols/slices</a></td><td> </td><td>remove specified rows/columns/slices</td></tr>
<tr><td><a href="#swap_rows">.swap_rows/cols</a></td><td> </td><td>swap specified rows or columns</td></tr>
<tr><td><a href="#swap">.swap</a></td><td> </td><td>swap contents with given object</td></tr>
<tr><td><small><small> </small></small></td><td><small><small> </small></small></td><td><small><small> </small></small></td></tr>
<tr><td><a href="#memptr">.memptr</a></td><td> </td><td>raw pointer to memory</td></tr>
<tr><td><a href="#colptr">.colptr</a></td><td> </td><td>raw pointer to memory used by specified column</td></tr>
<tr><td><small><small> </small></small></td><td><small><small> </small></small></td><td><small><small> </small></small></td></tr>
<tr><td><a href="#iterators_mat">iterators (matrices)</a></td><td> </td><td>STL-style iterators and associated member functions for matrices and vectors</td></tr>
<tr><td><a href="#iterators_cube">iterators (cubes)</a></td><td> </td><td>STL-style iterators and associated member functions for cubes</td></tr>
<tr><td><a href="#stl_container_fns">STL container functions</a></td><td> </td><td>STL-style container functions</td></tr>
<tr><td><small><small> </small></small></td><td><small><small> </small></small></td><td><small><small> </small></small></td></tr>
<tr><td><a href="#t_st_members">.t / .st </a></td><td> </td><td>return matrix transpose</td></tr>
<tr><td><a href="#i_member">.i </a></td><td> </td><td>return inverse of square matrix</td></tr>
<tr><td><a href="#min_and_max_member">.min / .max</a></td><td> </td><td>return extremum value</td></tr>
<tr><td><a href="#index_min_and_index_max_member">.index_min / .index_max</a></td><td> </td><td>return index of extremum value</td></tr>
<tr><td><a href="#eval_member">.eval</a></td><td> </td><td>force evaluation of delayed expression</td></tr>
<tr><td><small><small> </small></small></td><td><small><small> </small></small></td><td><small><small> </small></small></td></tr>
<tr><td><a href="#in_range">.in_range</a></td><td> </td><td>check whether given location or span is valid</td></tr>
<tr><td><a href="#is_empty">.is_empty</a></td><td> </td><td>check whether object is empty</td></tr>
<tr><td><a href="#is_square">.is_square</a></td><td> </td><td>check whether matrix is square sized</td></tr>
<tr><td><a href="#is_vec">.is_vec</a></td><td> </td><td>check whether matrix is a vector</td></tr>
<tr><td><a href="#is_sorted">.is_sorted</a></td><td> </td><td>check whether vector or matrix is sorted</td></tr>
<tr><td><small><small> </small></small></td><td><small><small> </small></small></td><td><small><small> </small></small></td></tr>
<tr><td><a href="#is_finite_member">.is_finite</a></td><td> </td><td>check whether all elements are finite</td></tr>
<tr><td><a href="#has_inf">.has_inf</a></td><td> </td><td>check whether any element is +-Inf</td></tr>
<tr><td><a href="#has_nan">.has_nan</a></td><td> </td><td>check whether any element is NaN</td></tr>
<tr><td><small><small> </small></small></td><td><small><small> </small></small></td><td><small><small> </small></small></td></tr>
<tr><td><a href="#print">.print</a></td><td> </td><td>print object to <i>std::cout</i> or user specified stream</td></tr>
<tr><td><a href="#raw_print">.raw_print</a></td><td> </td><td>print object without formatting</td></tr>
<tr><td><small><small> </small></small></td><td><small><small> </small></small></td><td><small><small> </small></small></td></tr>
<tr><td><a href="#save_load_mat">.save/.load (matrices & cubes)</a></td><td> </td><td>save/load matrices and cubes in files or streams</td></tr>
<tr><td><a href="#save_load_field">.save/.load (fields)</a></td><td> </td><td>save/load fields in files or streams</td></tr>
</tbody>
</table>
</ul>
<br>
<a name="part_gen"></a>
<b>Generated Vectors/Matrices/Cubes</b>
<ul>
<table>
<tbody>
<tr style="background-color: #F5F5F5;"><td><a href="#eye_standalone">eye</a></td><td> </td><td>generate identity matrix</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#linspace">linspace</a></td><td> </td><td>generate vector with linearly spaced elements</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#logspace">logspace</a></td><td> </td><td>generate vector with logarithmically spaced elements</td></tr>
<tr><td><a href="#ones_standalone">ones</a></td><td> </td><td>generate object filled with ones</td></tr>
<tr><td><a href="#randi">randi</a></td><td> </td><td>generate object with random integer values in specified interval</td></tr>
<tr><td><a href="#randu_randn_standalone">randu / randn</a></td><td> </td><td>generate object with random values (uniform and normal distributions)</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#randg">randg</a></td><td> </td><td>generate object with random values (gamma distribution)</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#regspace">regspace</a></td><td> </td><td>generate vector with regularly spaced elements</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#speye">speye</a></td><td> </td><td>generate sparse identity matrix</td></tr>
<tr><td><a href="#spones">spones</a></td><td> </td><td>generate sparse matrix with non-zero elements set to one</td></tr>
<tr><td><a href="#sprandu_sprandn">sprandu / sprandn</a></td><td> </td><td>generate sparse matrix with non-zero elements set to random values</td></tr>
<tr><td><a href="#toeplitz">toeplitz</a></td><td> </td><td>generate Toeplitz matrix</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#zeros_standalone">zeros</a></td><td> </td><td>generate object filled with zeros</td></tr>
</tbody>
</table>
</ul>
<br>
<a name="part_fns"></a>
<b>Functions of Vectors/Matrices/Cubes</b>
<ul>
<table>
<tbody>
<tr style="background-color: #F5F5F5;"><td><a href="#abs">abs</a></td><td> </td><td>obtain magnitude of each element</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#accu">accu</a></td><td> </td><td>accumulate (sum) all elements</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#affmul">affmul</a></td><td> </td><td>affine matrix multiplication</td></tr>
<tr><td><a href="#all">all</a></td><td> </td><td>check whether all elements are non-zero, or satisfy a relational condition</td></tr>
<tr><td><a href="#any">any</a></td><td> </td><td>check whether any element is non-zero, or satisfies a relational condition</td></tr>
<tr><td><a href="#approx_equal">approx_equal</a></td><td> </td><td>approximate equality</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#arg">arg</a></td><td> </td><td>phase angle of each element</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#as_scalar">as_scalar</a></td><td> </td><td>convert 1x1 matrix to pure scalar</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#clamp">clamp</a></td><td> </td><td>obtain clamped elements according to given limits</td></tr>
<tr><td><a href="#cond">cond</a></td><td> </td><td>condition number of matrix</td></tr>
<tr><td><a href="#conj">conj</a></td><td> </td><td>obtain complex conjugate of each element</td></tr>
<tr><td><a href="#conv_to">conv_to</a></td><td> </td><td>convert between matrix types</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#cross">cross</a></td><td> </td><td>cross product</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#cumsum">cumsum</a></td><td> </td><td>cumulative sum</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#cumprod">cumprod</a></td><td> </td><td>cumulative product</td></tr>
<tr><td><a href="#det">det</a></td><td> </td><td>determinant</td></tr>
<tr><td><a href="#diagmat">diagmat</a></td><td> </td><td>generate diagonal matrix from given matrix or vector</td></tr>
<tr><td><a href="#diagvec">diagvec</a></td><td> </td><td>extract specified diagonal</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#diff">diff</a></td><td> </td><td>differences between adjacent elements</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#dot">dot / cdot / norm_dot</a></td><td> </td><td>dot product</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#eps">eps</a></td><td> </td><td>obtain distance of each element to next largest floating point representation</td></tr>
<tr><td><a href="#expmat">expmat</a></td><td> </td><td>matrix exponential</td></tr>
<tr><td><a href="#expmat_sym">expmat_sym</a></td><td> </td><td>matrix exponential (symmetric)</td></tr>
<tr><td><a href="#find">find</a></td><td> </td><td>find indices of non-zero elements, or elements satisfying a relational condition</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#find_finite">find_finite</a></td><td> </td><td>find indices of finite elements</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#find_nonfinite">find_nonfinite</a></td><td> </td><td>find indices of non-finite elements</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#find_unique">find_unique</a></td><td> </td><td>find indices of unique elements</td></tr>
<tr><td><a href="#flip">fliplr / flipud</a></td><td> </td><td>reverse order of columns or rows</td></tr>
<tr><td><a href="#imag_real">imag / real</a></td><td> </td><td>extract imaginary/real part</td></tr>
<tr><td><a href="#ind2sub">ind2sub</a></td><td> </td><td>convert linear index to subscripts</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#index_min_and_index_max_standalone">index_min / index_max</a></td><td> </td><td>indices of extremum values</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#inplace_trans">inplace_trans</a></td><td> </td><td>in-place transpose</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#is_finite">is_finite</a></td><td> </td><td>check whether all elements are finite</td></tr>
<tr><td><a href="#join">join_rows / join_cols</a></td><td> </td><td>concatenation of matrices</td></tr>
<tr><td><a href="#join_slices">join_slices</a></td><td> </td><td>concatenation of cubes</td></tr>
<tr><td><a href="#kron">kron</a></td><td> </td><td>Kronecker tensor product</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#log_det">log_det</a></td><td> </td><td>log determinant</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#logmat">logmat</a></td><td> </td><td>matrix logarithm</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#logmat_sympd">logmat_sympd</a></td><td> </td><td>matrix logarithm (symmetric)</td></tr>
<tr><td><a href="#min_and_max">min / max</a></td><td> </td><td>return extremum values</td></tr>
<tr><td><a href="#nonzeros">nonzeros</a></td><td> </td><td>return non-zero values</td></tr>
<tr><td><a href="#norm">norm</a></td><td> </td><td>various norms of vectors and matrices</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#normalise">normalise</a></td><td> </td><td>normalise vectors to unit <i>p</i>-norm</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#prod">prod</a></td><td> </td><td>product of elements</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#rank">rank</a></td><td> </td><td>rank of matrix</td></tr>
<tr><td><a href="#rcond">rcond</a></td><td> </td><td>reciprocal of condition number</td></tr>
<tr><td><a href="#repmat">repmat</a></td><td> </td><td>replicate matrix in block-like fashion</td></tr>
<tr><td><a href="#reshape">reshape</a></td><td> </td><td>change size while keeping elements</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#resize">resize</a></td><td> </td><td>change size while keeping elements and preserving layout</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#shift">shift</a></td><td> </td><td>shift elements</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#shuffle">shuffle</a></td><td> </td><td>randomly shuffle elements</td></tr>
<tr><td><a href="#size">size</a></td><td> </td><td>obtain dimensions of given object</td></tr>
<tr><td><a href="#sort">sort</a></td><td> </td><td>sort elements</td></tr>
<tr><td><a href="#sort_index">sort_index</a></td><td> </td><td>vector describing sorted order of elements</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#sqrtmat">sqrtmat</a></td><td> </td><td>square root of matrix</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#sqrtmat_sympd">sqrtmat_sympd</a></td><td> </td><td>square root of matrix (symmetric)</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#sum">sum</a></td><td> </td><td>sum of elements</td></tr>
<tr><td><a href="#sub2ind">sub2ind</a></td><td> </td><td>convert subscripts to linear index</td></tr>
<tr><td><a href="#symmat">symmatu / symmatl</a></td><td> </td><td>generate symmetric matrix from given matrix</td></tr>
<tr><td><a href="#trace">trace</a></td><td> </td><td>sum of diagonal elements</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#trans">trans</a></td><td> </td><td>transpose of matrix</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#trapz">trapz</a></td><td> </td><td>trapezoidal numerical integration</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#trimat">trimatu / trimatl</a></td><td> </td><td>copy upper/lower triangular part</td></tr>
<tr><td><a href="#unique">unique</a></td><td> </td><td>return unique elements</td></tr>
<tr><td><a href="#vectorise">vectorise</a></td><td> </td><td>convert matrix to vector</td></tr>
<tr><td><a href="#misc_fns">misc functions</a></td><td> </td><td>miscellaneous element-wise functions: exp, log, pow, sqrt, round, sign, ...</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#trig_fns">trig functions</a></td><td> </td><td>trigonometric element-wise functions: cos, sin, ...</td></tr>
</tbody>
</table>
</ul>
<br>
<a name="part_decompdense"></a>
<b>Decompositions, Factorisations, Inverses and Equation Solvers (Dense Matrices)</b>
<ul>
<table>
<tbody>
<tr style="background-color: #F5F5F5;"><td><a href="#chol">chol</a></td><td> </td><td>Cholesky decomposition</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#eig_sym">eig_sym</a></td><td> </td><td>eigen decomposition of dense symmetric/hermitian matrix</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#eig_gen">eig_gen</a></td><td> </td><td>eigen decomposition of dense general square matrix</td></tr>
<tr><td><a href="#eig_pair">eig_pair</a></td><td> </td><td>eigen decomposition for pair of general dense square matrices</td></tr>
<tr><td><a href="#inv">inv</a></td><td> </td><td>inverse of general square matrix</td></tr>
<tr><td><a href="#inv_sympd">inv_sympd</a></td><td> </td><td>inverse of symmetric positive definite matrix</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#lu">lu </a></td><td> </td><td>lower-upper decomposition</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#null">null</a></td><td> </td><td>orthonormal basis of null space</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#orth">orth</a></td><td> </td><td>orthonormal basis of range space</td></tr>
<tr><td><a href="#pinv">pinv</a></td><td> </td><td>pseudo-inverse</td></tr>
<tr><td><a href="#qr">qr </a></td><td> </td><td>QR decomposition</td></tr>
<tr><td><a href="#qr_econ">qr_econ</a></td><td> </td><td>economical QR decomposition</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#qz">qz </a></td><td> </td><td>generalised Schur decomposition</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#schur">schur</a></td><td> </td><td>Schur decomposition</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#solve">solve</a></td><td> </td><td>solve systems of linear equations</td></tr>
<tr><td><a href="#svd">svd</a></td><td> </td><td>singular value decomposition</td></tr>
<tr><td><a href="#svd_econ">svd_econ</a></td><td> </td><td>economical singular value decomposition</td></tr>
<tr><td><a href="#syl">syl</a></td><td> </td><td>Sylvester equation solver</td></tr>
</tbody>
</table>
</ul>
<br>
<a name="part_decompsparse"></a>
<b>Decompositions, Factorisations and Equation Solvers (Sparse Matrices)</b>
<ul>
<table>
<tbody>
<tr style="background-color: #F5F5F5;"><td><a href="#eigs_sym">eigs_sym</a></td><td> </td><td>limited number of eigenvalues & eigenvectors of sparse symmetric real matrix</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#eigs_gen">eigs_gen</a></td><td> </td><td>limited number of eigenvalues & eigenvectors of sparse general square matrix</td></tr>
<tr><td><a href="#spsolve">spsolve</a></td><td> </td><td>solve sparse systems of linear equations</td></tr>
<tr><td><a href="#svds">svds</a></td><td> </td><td>limited number of singular values & singular vectors of sparse matrix</td></tr>
</tbody>
</table>
</ul>
<br>
<a name="part_sigproc"></a>
<b>Signal & Image Processing</b>
<ul>
<table>
<tbody>
<tr style="background-color: #F5F5F5;"><td><a href="#conv">conv</a></td><td> </td><td>1D convolution</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#conv2">conv2</a></td><td> </td><td>2D convolution</td></tr>
<tr><td><a href="#fft">fft / ifft</a></td><td> </td><td>1D fast Fourier transform and its inverse</td></tr>
<tr><td><a href="#fft2">fft2 / ifft2</a></td><td> </td><td>2D fast Fourier transform and its inverse</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#interp1">interp1</a></td><td> </td><td>1D interpolation</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#polyfit">polyfit</a></td><td> </td><td>find polynomial coefficients for data fitting</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#polyval">polyval</a></td><td> </td><td>evaluate polynomial</td></tr>
</tbody>
</table>
</ul>
<br>
<a name="part_stats"></a>
<b>Statistics & Clustering</b>
<ul>
<table>
<tbody>
<tr style="background-color: #F5F5F5;"><td><a href="#stats_fns">stats functions</a></td><td> </td><td>mean, median, standard deviation, variance</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#cov">cov</a></td><td> </td><td>covariance</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#cor">cor</a></td><td> </td><td>correlation</td></tr>
<tr><td><a href="#hist">hist</a></td><td> </td><td>histogram of counts</td></tr>
<tr><td><a href="#histc">histc</a></td><td> </td><td>histogram of counts with user specified edges</td></tr>
<tr><td><a href="#princomp">princomp</a></td><td> </td><td>principal component analysis</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#running_stat">running_stat</a></td><td> </td><td>running statistics of one dimensional process/signal</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#running_stat_vec">running_stat_vec</a></td><td> </td><td>running statistics of multi-dimensional process/signal</td></tr>
<tr><td><a href="#kmeans">kmeans</a></td><td> </td><td>cluster data into disjoint sets</td></tr>
<tr><td><a href="#gmm_diag">gmm_diag/gmm_full</a></td><td> </td><td>model and evaluate data using Gaussian Mixture Models (GMMs)</td></tr>
</tbody>
</table>
</ul>
<br>
<a name="part_misc"></a>
<b>Miscellaneous</b>
<ul>
<table>
<tbody>
<tr style="background-color: #F5F5F5;"><td><a href="#constants">constants</a></td><td> </td><td>pi, inf, NaN, speed of light, ...</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#wall_clock">wall_clock</a></td><td> </td><td>timer for measuring number of elapsed seconds</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#logging">logging of errors/warnings</a></td><td> </td><td>how to change the streams for displaying warnings and errors</td></tr>
<tr><td><a href="#uword">uword / sword</a></td><td> </td><td>shorthand for unsigned and signed integers</td></tr>
<tr><td><a href="#cx_double">cx_double / cx_float</a></td><td> </td><td>shorthand for std::complex<double> and std::complex<float></td></tr>
<tr><td><a href="#syntax">Matlab/Armadillo syntax differences</a></td><td> </td><td>examples of Matlab syntax and conceptually corresponding Armadillo syntax</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#example_prog">example program</a></td><td> </td><td>short example program</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#config_hpp">config.hpp</a></td><td> </td><td>configuration options</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#api_additions">API additions</a></td><td> </td><td>API stability and list of API additions</td></tr>
<!--<tr><td><a href="#log_add">log_add</a></td><td> </td><td>TODO</td></tr>-->
<!--<tr><td><a href="#catching_exceptions">catching exceptions</a></td><td> </td><td>TODO</td></tr>-->
</tbody>
</table>
</ul>
<br>
<div class="pagebreak"></div>
<hr class="greyline">
<hr class="greyline">
<br>
<br>
<font size=+1><b>Matrix, Vector, Cube and Field Classes</b></font>
<br>
<br>
<div class="pagebreak"></div><div class="noprint"><hr class="greyline"><br></div>
<a name="Mat"></a><b>Mat<</b><i>type</i><b>></b>
<br><b>mat</b>
<br><b>cx_mat</b>
<ul>
<li>
Classes for dense matrices, with elements stored in <a href="https://en.wikipedia.org/wiki/Column_major">column-major ordering</a> (ie. column by column)
</li>
<br>
<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>short</i>, <i>int</i>, <i>long</i>, and unsigned versions of <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;">
<code>mat</code>
</td>
<td style="vertical-align: top;">
=
</td>
<td style="vertical-align: top;">
<code>Mat<double></code>
</td>
</tr>
<tr>
<td style="vertical-align: top;">
<code>fmat</code>
</td>
<td style="vertical-align: top;">
=
</td>
<td style="vertical-align: top;">
<code>Mat<float></code>
</td>
</tr>
<tr>
<td style="vertical-align: top;">
<code>cx_mat</code>
</td>
<td style="vertical-align: top;">
=
</td>
<td style="vertical-align: top;">
<code>Mat<<a href="#cx_double">cx_double</a>></code>
</td>
</tr>
<tr>
<td style="vertical-align: top;">
<code>cx_fmat</code>
</td>
<td style="vertical-align: top;">
=
</td>
<td style="vertical-align: top;">
<code>Mat<<a href="#cx_double">cx_float</a>></code>
</td>
</tr>
<tr>
<td style="vertical-align: top;">
<code>umat</code>
</td>
<td style="vertical-align: top;">
=
</td>
<td style="vertical-align: top;">
<code>Mat<<a href="#uword">uword</a>></code>
</td>
</tr>
<tr>
<td style="vertical-align: top;">
<code>imat</code>
</td>
<td style="vertical-align: top;">
=
</td>
<td style="vertical-align: top;">
<code>Mat<<a href="#uword">sword</a>></code>
</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>
<a name="constructors_mat"></a>
<li>
Constructors:
<ul>
<code>mat()</code>
<br><code>mat(<i>n_rows</i>, <i>n_cols</i>)</code>
<br><code>mat(<i>n_rows</i>, <i>n_cols</i>, <i>fill_type</i>)</code>
<br><code>mat(size(<i>X</i>))</code>
<br><code>mat(size(<i>X</i>), <i>fill_type</i>)</code>
<br><code>mat(mat)</code>
<br><code>mat(sp_mat)</code>
<br><code>mat(vec)</code>
<br><code>mat(rowvec)</code>
<br><code>mat(initializer_list)</code>
<br><code>mat(string)</code>
<br><code>mat(std::vector)</code> (treated as a column vector)
<br><code>cx_mat(mat,mat)</code> (for constructing a complex matrix out of two real matrices)
</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><code>fill::zeros</code></td><td> = </td><td>set all elements to 0</td></tr>
<tr><td><code>fill::ones</code></td><td> = </td><td>set all elements to 1</td></tr>
<tr><td><code>fill::eye</code></td><td> = </td><td>set the elements along the main diagonal to 1 and off-diagonal elements to 0</td></tr>
<tr><td><code>fill::randu</code></td><td> = </td><td>set each element to a random value from a uniform distribution in the [0,1] interval</td></tr>
<tr><td><code>fill::randn</code></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><code>fill::none</code></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 <code>"1 0; 0 1"</code>.
<br>
<b>Caveat:</b> string based initialisation is slower than directly <a href="#element_access">setting the elements</a> or using <a href="#element_initialisation">element initialisation</a>.
</li>
<br>
<a name="adv_constructors_mat"></a>
<li>
Advanced constructors:
<br>
<br>
<ul>
<code>mat(ptr_aux_mem, n_rows, n_cols, copy_aux_mem = true, strict = false)</code>
<br>
<br>
<ul>
Create a matrix using data from writable auxiliary (external) memory, where <i>ptr_aux_mem</i> is a pointer to the 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 are doing!
<br>
<br>
The <i>strict</i> parameter comes into effect only when <i>copy_aux_mem</i> is set to <i>false</i>
(ie. the matrix is directly using auxiliary memory)
<ul>
<li>
when <i>strict</i> is set to <i>false</i>, the matrix will use the auxiliary memory until a size change
</li>
<li>
when <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
</li>
<li>the default setting of <i>strict</i> in versions 6.000+ is <i>false</i></li>
<li>the default setting of <i>strict</i> in versions 5.600 and earlier is <i>true</i></li>
</ul>
</ul>
<br>
<code>mat(const ptr_aux_mem, n_rows, n_cols)</code>
<br>
<br>
<ul>
Create a matrix by copying data from read-only auxiliary memory,
where <i>ptr_aux_mem</i> is a pointer to the memory
</ul>
<a name="adv_constructors_mat_fixed"></a>
<br>
<code>mat::fixed<n_rows, n_cols></code>
<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>
<br>
<code>mat::fixed<n_rows, n_cols>(const ptr_aux_mem)</code>
<br>
<br>
<ul>
Create a fixed size matrix, with the size specified via template arguments;
data is copied from auxiliary memory, where <i>ptr_aux_mem</i> is a pointer to the memory
</ul>
</ul>
</li>
<br>
<br>
<li>
Examples:
<ul>
<pre>
mat A(5, 5, fill::randu);
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);
B.print("B:");
mat::fixed<5,6> F;
double aux_mem[24];
mat H(&aux_mem[0], 4, 6, false); // use auxiliary memory
</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 with compressed sparse column format)</li>
<li><a href="#config_hpp">config.hpp</a></li>
</ul>
</li>
<br>
</ul>
<div class="pagebreak"></div><div class="noprint"><hr class="greyline"><br></div>
<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 (dense 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;">
<code>vec</code>
</td>
<td style="vertical-align: top;">
=
</td>
<td style="vertical-align: top;">
<code>colvec</code>
</td>
<td style="vertical-align: top;">
=
</td>
<td style="vertical-align: top;">
<code>Col<double></code>
</td>
</tr>
<tr>
<td style="vertical-align: top;">
<code>fvec</code>
</td>
<td style="vertical-align: top;">
=
</td>
<td style="vertical-align: top;">
<code>fcolvec</code>
</td>
<td style="vertical-align: top;">
=
</td>
<td style="vertical-align: top;">
<code>Col<float></code>
</td>
</tr>
<tr>
<td style="vertical-align: top;">
<code>cx_vec</code>
</td>
<td style="vertical-align: top;">
=
</td>
<td style="vertical-align: top;">
<code>cx_colvec</code>
</td>
<td style="vertical-align: top;">
=
</td>
<td style="vertical-align: top;">
<code>Col<<a href="#cx_double">cx_double</a>></code>
</td>
</tr>
<tr>
<td style="vertical-align: top;">
<code>cx_fvec</code>
</td>
<td style="vertical-align: top;">
=
</td>
<td style="vertical-align: top;">
<code>cx_fcolvec</code>
</td>
<td style="vertical-align: top;">
=
</td>
<td style="vertical-align: top;">
<code>Col<<a href="#cx_double">cx_float</a>></code>
</td>
</tr>
<tr>
<td style="vertical-align: top;">
<code>uvec</code>
</td>
<td style="vertical-align: top;">
=
</td>
<td style="vertical-align: top;">
<code>ucolvec</code>
</td>
<td style="vertical-align: top;">
=
</td>
<td style="vertical-align: top;">
<code>Col<<a href="#uword">uword</a>></code>
</td>
</tr>
<tr>
<td style="vertical-align: top;">
<code>ivec</code>
</td>
<td style="vertical-align: top;">
=
</td>
<td style="vertical-align: top;">
<code>icolvec</code>
</td>
<td style="vertical-align: top;">
=
</td>
<td style="vertical-align: top;">
<code>Col<<a href="#uword">sword</a>></code>
</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>
<code>vec()</code>
<br><code>vec(<i>n_elem</i>)</code>
<br><code>vec(<i>n_elem</i>, <i>fill_type</i>)</code>
<br><code>vec(size(<i>X</i>))</code>
<br><code>vec(size(<i>X</i>), <i>fill_type</i>)</code>
<br><code>vec(vec)</code>
<br><code>vec(mat)</code> (a <i>std::logic_error</i> exception is thrown if the given matrix has more than one column)
<br><code>vec(initializer_list)</code>
<br><code>vec(string)</code> (elements separated by spaces)
<br><code>vec(std::vector)</code>
<br><code>cx_vec(vec,vec)</code> (for constructing a complex vector out of two real vectors)
</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>
<code>vec(ptr_aux_mem, number_of_elements, copy_aux_mem = true, strict = false)</code>
<br>
<br>
<ul>
Create a column vector using data from writable auxiliary (external) memory, where <i>ptr_aux_mem</i> is a pointer to the 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>,