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<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
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<title>Armadillo: API Documentation</title>
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<a name="top"></a>
<big><b>API Documentation for Armadillo 15.0</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="https://arma.sourceforge.net/faq.html">report them</a>
</li>
<br>
<li>
History of <a href="#changelog">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 papers if you use Armadillo in your research and/or software.
<br>
Citations are useful for the continued development and maintenance of the library.
<br>
<br>
Conrad Sanderson and Ryan Curtin.
<br><i><a href="armadillo_iccae_2025.pdf">Armadillo: An Efficient Framework for Numerical Linear Algebra</a></i>.
<br>International Conference on Computer and Automation Engineering, 2025.
<br>
<br>
<!--
Conrad Sanderson and Ryan Curtin.
<br><i><a href="armadillo_lncs_2018.pdf">A User-Friendly Hybrid Sparse Matrix Class in C++</a></i>.
<br>Lecture Notes in Computer Science (LNCS), Vol. 10931, pp. 422-430, 2018.
-->
Conrad Sanderson and Ryan Curtin.
<br><i><a href="armadillo_mca_2019.pdf">Practical Sparse Matrices in C++ with Hybrid Storage and Template-Based Expression Optimisation</a></i>.
<br>Mathematical and Computational Applications, Vol. 24, No. 3, 2019.
</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 options, ...)</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</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 initialiser lists</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="#clean">.clean</a></td><td> </td><td>replace elements below a threshold with zeros</td></tr>
<tr><td><a href="#replace_member">.replace</a></td><td> </td><td>replace specific elements with a new value</td></tr>
<tr><td><a href="#clamp_member">.clamp</a></td><td> </td><td>clamp values to lower and upper limits</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="#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>vector operations applied to each column/row of matrix (aka "broadcasting")</td></tr>
<tr><td><a href="#each_slice">.each_slice</a></td><td> </td><td>matrix operations applied to each slice of cube (aka "broadcasting")</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>iterators and associated member functions for dense matrices and vectors</td></tr>
<tr><td><a href="#iterators_cube">iterators (cubes)</a></td><td> </td><td>iterators and associated member functions for cubes</td></tr>
<tr><td><a href="#iterators_spmat">iterators (sparse matrices)</a></td><td> </td><td>iterators and associated member functions for sparse matrices</td></tr>
<tr><td><a href="#iterators_submat">iterators (submatrices)</a></td><td> </td><td>iterators and associated member functions for submatrices & subcubes</td></tr>
<tr><td><a href="#compat_container_fns">compat. container functions</a></td><td> </td><td>compatibility 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="#as_col_row">.as_col / .as_row</a></td><td> </td><td>return flattened matrix as column or row vector</td></tr>
<tr><td><a href="#col_row_as_mat">.col_as_mat / .row_as_mat</a></td><td> </td><td>return matrix representation of cube column or cube row</td></tr>
<tr><td><a href="#as_dense">.as_dense</a></td><td> </td><td>return dense vector/matrix representation of sparse matrix 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="#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_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_trimat">.is_trimatu / .is_trimatl</a></td><td> </td><td>check whether matrix is upper/lower triangular</td></tr>
<tr><td><a href="#is_diagmat">.is_diagmat</a></td><td> </td><td>check whether matrix is diagonal</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_symmetric">.is_symmetric</a></td><td> </td><td>check whether matrix is symmetric</td></tr>
<tr><td><a href="#is_hermitian">.is_hermitian</a></td><td> </td><td>check whether matrix is hermitian</td></tr>
<tr><td><a href="#is_sympd">.is_sympd</a></td><td> </td><td>check whether matrix is symmetric/hermitian positive definite</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_zero">.is_zero</a></td><td> </td><td>check whether all elements are zero</td></tr>
<tr><td><a href="#is_finite">.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 ±infinity</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><a href="#brief_print">.brief_print</a></td><td> </td><td>print object in shortened/abridged form</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="#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 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="#randperm">randperm</a></td><td> </td><td>generate vector with random permutation of a sequence of integers</td></tr>
<tr><td><a href="#eye_standalone">eye</a></td><td> </td><td>generate identity matrix</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="#zeros_standalone">zeros</a></td><td> </td><td>generate object filled with zeros</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#randu">randu</a></td><td> </td><td>generate object with random values (uniform distribution)</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#randn">randn</a></td><td> </td><td>generate object with random values (normal distribution)</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><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="#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 style="background-color: #F5F5F5;"><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 style="background-color: #F5F5F5;"><td><a href="#toeplitz">toeplitz</a></td><td> </td><td>generate Toeplitz matrix</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="#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><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="#balance">balance</a></td><td> </td><td>balance matrix</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/cast 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="#diags_spdiags">diags / spdiags</a></td><td> </td><td>generate band matrix from given set of vectors</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><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 of symmetric matrix</td></tr>
<tr style="background-color: #F5F5F5;"><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_nonfinite">find_finite / nonfinite</a></td><td> </td><td>find indices of finite / non-finite elements</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#find_nan_nonnan">find_nan / nonnan</a></td><td> </td><td>find indices of NaN / non-NaN elements</td></tr>
<tr><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>flip matrix left to right or upside down</td></tr>
<tr><td><a href="#imag_real">imag / real</a></td><td> </td><td>extract imaginary/real part</td></tr>
<tr style="background-color: #F5F5F5;"><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><td><a href="#intersect">intersect</a></td><td> </td><td>find common elements in two vectors/matrices</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 style="background-color: #F5F5F5;"><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="#log_det_sympd">log_det_sympd</a></td><td> </td><td>log determinant of symmetric positive definite matrix</td></tr>
<tr><td><a href="#logmat">logmat</a></td><td> </td><td>matrix logarithm</td></tr>
<tr><td><a href="#logmat_sympd">logmat_sympd</a></td><td> </td><td>matrix logarithm of symmetric matrix</td></tr>
<tr><td><a href="#min_and_max">min / max</a></td><td> </td><td>return extremum values</td></tr>
<tr style="background-color: #F5F5F5;"><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="#norm2est">norm2est</a></td><td> </td><td>fast estimate of the matrix 2-norm</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><td><a href="#nonzeros">nonzeros</a></td><td> </td><td>extract all non-zero elements</td></tr>
<tr><td><a href="#omit_nan_nonfinite">omit_nan / nonfinite</a></td><td> </td><td>extract all elements that are non-NaN / only finite</td></tr>
<tr><td><a href="#pow">pow</a></td><td> </td><td>element-wise power</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#powmat">powmat</a></td><td> </td><td>matrix power</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 condition number</td></tr>
<tr><td><a href="#repelem">repelem</a></td><td> </td><td>replicate elements</td></tr>
<tr><td><a href="#replace_standalone">replace</a></td><td> </td><td>replace specific elements with a new value</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#repmat">repmat</a></td><td> </td><td>replicate matrix in block-like fashion</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#repcube">repcube</a></td><td> </td><td>replicate cube in block-like fashion</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#reshape">reshape</a></td><td> </td><td>change size while keeping elements</td></tr>
<tr><td><a href="#resize">resize</a></td><td> </td><td>change size while keeping elements and preserving layout</td></tr>
<tr><td><a href="#reverse">reverse</a></td><td> </td><td>reverse order of elements</td></tr>
<tr><td><a href="#roots">roots</a></td><td> </td><td>roots of polynomial</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#shift">shift</a></td><td> </td><td>circular shift of elements</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#shuffle">shuffle</a></td><td> </td><td>randomly shuffle elements</td></tr>
<tr style="background-color: #F5F5F5;"><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><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 symmetric matrix</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#sum">sum</a></td><td> </td><td>sum of elements</td></tr>
<tr style="background-color: #F5F5F5;"><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><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 style="background-color: #F5F5F5;"><td><a href="#trimat_ind">trimatu_ind / trimatl_ind</a></td><td> </td><td>obtain indices of 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="#vecnorm">vecnorm</a></td><td> </td><td>obtain vector norm of each row or column of a matrix</td></tr>
<tr><td><a href="#vectorise">vectorise</a></td><td> </td><td>flatten matrix into vector</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#misc_fns">misc functions</a></td><td> </td><td>miscellaneous element-wise functions: exp, log, 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, tan, ...</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="#hess">hess</a></td><td> </td><td>upper Hessenberg decomposition</td></tr>
<tr><td><a href="#inv">inv</a></td><td> </td><td>inverse of general square matrix</td></tr>
<tr style="background-color: #F5F5F5;"><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><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 / generalised inverse</td></tr>
<tr><td><a href="#qr">qr </a></td><td> </td><td>QR decomposition</td></tr>
<tr style="background-color: #F5F5F5;"><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><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 style="background-color: #F5F5F5;"><td><a href="#sylvester">sylvester</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="#svds">svds</a></td><td> </td><td>truncated svd: limited number of singular values & singular vectors of sparse matrix</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#spsolve">spsolve</a></td><td> </td><td>solve sparse systems of linear equations</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#spsolve_factoriser">spsolve_factoriser</a></td><td> </td><td>factoriser for solving sparse systems of linear equations</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="#affmul">affmul</a></td><td> </td><td>affine matrix multiplication</td></tr>
<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="#interp2">interp2</a></td><td> </td><td>2D interpolation</td></tr>
<tr><td><a href="#polyfit">polyfit</a></td><td> </td><td>find polynomial coefficients for data fitting</td></tr>
<tr><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="#quantile">quantile</a></td><td> </td><td>quantiles of a dataset</td></tr>
<tr><td><a href="#princomp">princomp</a></td><td> </td><td>principal component analysis (PCA)</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#normpdf">normpdf</a></td><td> </td><td>probability density function of normal distribution</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#log_normpdf">log_normpdf</a></td><td> </td><td>logarithm version of probability density function of normal distribution</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#normcdf">normcdf</a></td><td> </td><td>cumulative distribution function of normal distribution</td></tr>
<tr><td><a href="#mvnrnd">mvnrnd</a></td><td> </td><td>random vectors from multivariate normal distribution</td></tr>
<tr><td><a href="#chi2rnd">chi2rnd</a></td><td> </td><td>random numbers from chi-squared distribution</td></tr>
<tr><td><a href="#wishrnd">wishrnd</a></td><td> </td><td>random matrix from Wishart distribution</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#iwishrnd">iwishrnd</a></td><td> </td><td>random matrix from inverse Wishart distribution</td></tr>
<tr style="background-color: #F5F5F5;"><td><a href="#running_stat">running_stat</a></td><td> </td><td>running statistics of scalars (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 vectors (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>probabilistic clustering and likelihood calculation via mixture of Gaussians</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, eps, 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="#rng_seed">RNG seed setting</a></td><td> </td><td>functions for changing RNG seeds</td></tr>
<tr><td><a href="#output_streams">output streams</a></td><td> </td><td>streams for printing 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 style="background-color: #F5F5F5;"><td><a href="#fp16_type">fp16 / cx_fp16</a></td><td> </td><td>shorthand for half-precision 16-bit floating point type</td></tr>
<tr style="background-color: #F5F5F5;"><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><td><a href="#config_hpp">config.hpp</a></td><td> </td><td>configuration options</td></tr>
<tr><td><a href="#changelog">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 matrix typedefs are defined:
<br>
<br>
<table style="text-align: left;" border="0" cellpadding="2" cellspacing="2">
<tbody>
<tr>
<td style="vertical-align: top; text-align: right;">
<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; text-align: right;">
<code>dmat</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; text-align: right;">
<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; text-align: right;">
<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; text-align: right;">
<code>cx_dmat</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; text-align: right;">
<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; text-align: right;">
<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; text-align: right;">
<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>
</li>
<br>
<li>
If supported by compiler and hardware, additional typedefs for matrices with half-precision element types are defined as:
<br>
<br>
<table style="text-align: left;" border="0" cellpadding="2" cellspacing="2">
<tbody>
<tr>
<td style="vertical-align: top; text-align: right;">
<code>hmat</code>
</td>
<td style="vertical-align: top;">
=
</td>
<td style="vertical-align: top;">
<code>Mat<<a href="#fp16_type">fp16</a>></code>
</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: right;">
<code>cx_hmat</code>
</td>
<td style="vertical-align: top;">
=
</td>
<td style="vertical-align: top;">
<code>Mat<<a href="#fp16_type">cx_fp16</a>></code>
</td>
</tr>
</tbody>
</table>
</li>
<br>
<li>
In this documentation the <i>mat</i> type is used for convenience;
it is possible to use other matrix types instead, eg. <i>fmat</i>
</li>
<br>
<li>
Matrix types with integer elements (such as <i>umat</i> and <i>imat</i>) cannot hold special values such as NaN and Inf
</li>
<br>
<li>
Functions which use LAPACK (generally matrix decompositions) are only valid for the following matrix types:
<i>mat</i>, <i>dmat</i>, <i>fmat</i>, <i>cx_mat</i>, <i>cx_dmat</i>, <i>cx_fmat</i>
</li>
<br>
<a name="constructors_mat"></a>
<li>
Constructors:
<ul>
<table>
<tbody>
<tr><td><code>mat()</code></td><td> </td><td> </td></tr>
<tr><td><code>mat(<i>n_rows</i>, <i>n_cols</i>)</code></td><td> </td><td> </td></tr>
<tr><td><code>mat(<i>n_rows</i>, <i>n_cols</i>, <i>fill_form</i>)</code></td><td> </td><td>(elements are initialised according to <i>fill_form</i>)</td></tr>
<tr><td><code>mat(size(<i>X</i>))</code></td><td> </td><td> </td></tr>
<tr><td><code>mat(size(<i>X</i>), <i>fill_form</i>)</code></td><td> </td><td>(elements are initialised according to <i>fill_form</i>)</td></tr>
<tr><td><code>mat(mat)</code></td><td> </td><td> </td></tr>
<tr><td><code>mat(vec)</code></td><td> </td><td> </td></tr>
<tr><td><code>mat(rowvec)</code></td><td> </td><td> </td></tr>
<tr><td><code>mat(initializer_list)</code></td><td> </td><td> </td></tr>
<tr><td><code>mat(string)</code></td><td> </td><td> </td></tr>
<tr><td><code>mat(std::vector)</code></td><td> </td><td>(treated as a column vector)</td></tr>
<tr><td><code>mat(sp_mat)</code></td><td> </td><td>(for converting a sparse matrix to a dense matrix)</td></tr>
<tr><td><code>cx_mat(mat,mat)</code></td><td> </td><td>(for constructing a complex matrix out of two real matrices)</td></tr>
</tbody>
</table>
</ul>
</li>
<br>
<li>
The elements can be explicitly initialised during construction by specifying <i>fill_form</i>,
which is one of:
<ul>
<table>
<tbody>
<tr><td><code>fill::zeros</code></td><td> ↦ </td><td>set all elements to 0 (default in Armadillo >= 10.5)</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 on the main diagonal to 1 and off-diagonal elements to 0</td></tr>
<tr><td><code>fill::randu</code></td><td> ↦ </td><td>set all elements to random values from a uniform distribution in the [0,1] interval</td></tr>
<tr><td><code>fill::randn</code></td><td> ↦ </td><td>set all elements to random values from a normal/Gaussian distribution with zero mean and unit variance</td></tr>
<tr><td><code>fill::value(scalar)</code></td><td> ↦ </td><td>set all elements to specified scalar</td></tr>
<tr><td><code>fill::none</code></td><td> ↦ </td><td>do not initialise the elements (matrix may have garbage values)</td></tr>
</tbody>
</table>
</ul>
</li>
<br>
<li>
<b>Caveat:</b>
<ul>
<li>in Armadillo >= 10.5, the default initialisation is <code>fill::zeros</code></li>
<li>in Armadillo <= 10.4, the default initialisation is <code>fill::none</code></li>
</ul>
</li>
<br>
<li>
For the <i>mat(string)</i> constructor, the format 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>;
note that 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>
<li>
Each instance of <i>mat</i> automatically allocates and releases internal memory.
All internally allocated memory used by an instance of <i>mat</i> is automatically released as soon as the instance goes out of scope.
For example, if an instance of <i>mat</i> is declared inside a function, it will be automatically destroyed at the end of the function.
To forcefully release memory at any point, use <a href="#reset">.reset()</a>; note that in normal use this is not required.
</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 or an aliasing event
</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>
</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 reserved 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 appending a two digit form of the size to the matrix type;
examples: <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>(<i>fill_form</i>)</code>
<br>
<br>
<ul>
Create a fixed size matrix, with the elements explicitly initialised according to <i>fill_form</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>
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">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="#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>
<li><a href="https://cplusplus.com/doc/tutorial/other_data_types/">explanation of <i>typedef</i></a> (cplusplus.com)
<li><a href="https://en.wikipedia.org/wiki/C_data_types">C data types</a> (Wikipedia)
</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 column vector typedefs are defined:
<br>
<br>
<table style="text-align: left;" border="0" cellpadding="2" cellspacing="2">
<tbody>
<tr>
<td style="vertical-align: top; text-align: right;">
<code>vec</code>
</td>
<td style="vertical-align: top;">
=
</td>
<td style="vertical-align: top; text-align: right;">
<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; text-align: right;">
<code>dvec</code>
</td>
<td style="vertical-align: top;">
=
</td>
<td style="vertical-align: top; text-align: right;">
<code>dcolvec</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; text-align: right;">
<code>fvec</code>
</td>
<td style="vertical-align: top;">