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<h1>utils.h File Reference</h1><code>#include <<a class="el" href="utils__defs_8h_source.html">mrpt/utils/utils_defs.h</a>></code><br/>
<code>#include <<a class="el" href="_c_matrix_template_numeric_8h_source.html">mrpt/math/CMatrixTemplateNumeric.h</a>></code><br/>
<code>#include <<a class="el" href="_c_matrix_fixed_numeric_8h_source.html">mrpt/math/CMatrixFixedNumeric.h</a>></code><br/>
<code>#include <<a class="el" href="_c_vector_template_8h_source.html">mrpt/math/CVectorTemplate.h</a>></code><br/>
<code>#include <<a class="el" href="_c_histogram_8h_source.html">mrpt/math/CHistogram.h</a>></code><br/>
<code>#include <<a class="el" href="ops__vectors_8h_source.html">mrpt/math/ops_vectors.h</a>></code><br/>
<code>#include <<a class="el" href="ops__matrices_8h_source.html">mrpt/math/ops_matrices.h</a>></code><br/>
<code>#include <numeric></code><br/>
<code>#include <cmath></code><br/>
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<table border="0" cellpadding="0" cellspacing="0">
<tr><td colspan="2"><h2>Namespaces</h2></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">namespace </td><td class="memItemRight" valign="bottom"><a class="el" href="namespacemrpt.html">mrpt</a></td></tr>
<p><tr><td class="mdescLeft"> </td><td class="mdescRight"><p>This is the global namespace for all Mobile Robot Programming Toolkit (MRPT) libraries. </p>
<br/></td></tr>
</p>
<tr><td class="memItemLeft" align="right" valign="top">namespace </td><td class="memItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math.html">mrpt::math</a></td></tr>
<p><tr><td class="mdescLeft"> </td><td class="mdescRight"><p>This base provides a set of functions for maths stuff. </p>
<br/></td></tr>
</p>
<tr><td colspan="2"><h2>Functions</h2></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">bool BASE_IMPEXP </td><td class="memItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math.html#a40e8e47dea9f504a28d2a70ea8ddb158">mrpt::math::loadVector</a> (utils::CFileStream &f, std::vector< int > &d)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Loads one row of a text file as a numerical std::vector. <a href="#a40e8e47dea9f504a28d2a70ea8ddb158"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">bool BASE_IMPEXP </td><td class="memItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math.html#a4b6641faf04526ff4cee645370007ae1">mrpt::math::loadVector</a> (utils::CFileStream &f, std::vector< double > &d)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Loads one row of a text file as a numerical std::vector. <a href="#a4b6641faf04526ff4cee645370007ae1"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">bool BASE_IMPEXP </td><td class="memItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math.html#a0789f5c3dde7a158cb9780f6061ddcc6">mrpt::math::isNaN</a> (float f) MRPT_NO_THROWS</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Returns true if the number is NaN. <a href="#a0789f5c3dde7a158cb9780f6061ddcc6"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">bool BASE_IMPEXP </td><td class="memItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math.html#af51d0919fb678849dd010440fc6c7e3d">mrpt::math::isNaN</a> (double f) MRPT_NO_THROWS</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Returns true if the number is NaN. <a href="#af51d0919fb678849dd010440fc6c7e3d"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">bool BASE_IMPEXP </td><td class="memItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math.html#af4a419952a205931911e0a5627a192fe">mrpt::math::isFinite</a> (float f) MRPT_NO_THROWS</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Returns true if the number is non infinity. <a href="#af4a419952a205931911e0a5627a192fe"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">bool BASE_IMPEXP </td><td class="memItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math.html#a2ebfac97f79a8835217cccf46b1e229f">mrpt::math::isFinite</a> (double f) MRPT_NO_THROWS</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Returns true if the number is non infinity. <a href="#a2ebfac97f79a8835217cccf46b1e229f"></a><br/></td></tr>
<tr><td class="memTemplParams" colspan="2">template<typename T , typename K > </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math.html#af2fe0cbaaea87f6cfe3754f09e85107b">mrpt::math::linspace</a> (T first, T last, size_t count, std::vector< K > &out_vector)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Generates an equidistant sequence of numbers given the first one, the last one and the desired number of points. <a href="#af2fe0cbaaea87f6cfe3754f09e85107b"></a><br/></td></tr>
<tr><td class="memTemplParams" colspan="2">template<class T > </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">std::vector< T > </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math.html#ac8f80d72dcbdee5d2e5f20be9463f0d4">mrpt::math::linspace</a> (T first, T last, size_t count)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Generates an equidistant sequence of numbers given the first one, the last one and the desired number of points. <a href="#ac8f80d72dcbdee5d2e5f20be9463f0d4"></a><br/></td></tr>
<tr><td class="memTemplParams" colspan="2">template<class T , T STEP> </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">std::vector< T > </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math.html#a2778a8538638098c0b8ac89ff8f77bfe">mrpt::math::sequence</a> (T first, size_t length)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Generates a sequence of values [first,first+STEP,first+2*STEP,. <a href="#a2778a8538638098c0b8ac89ff8f77bfe"></a><br/></td></tr>
<tr><td class="memTemplParams" colspan="2">template<class T > </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">std::vector< T > </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math.html#a9b252fa16014e886104f8065091f6b20">mrpt::math::ones</a> (size_t count)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Generates a vector of all ones of the given length. <a href="#a9b252fa16014e886104f8065091f6b20"></a><br/></td></tr>
<tr><td class="memTemplParams" colspan="2">template<class T > </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">std::vector< T > </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math.html#a4d194e83c716310064baac5cf375d5d3">mrpt::math::zeros</a> (size_t count)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Generates a vector of all zeros of the given length. <a href="#a4d194e83c716310064baac5cf375d5d3"></a><br/></td></tr>
<tr><td class="memTemplParams" colspan="2">template<class T > </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math.html#a63f0941328a709254c00147881525d62">mrpt::math::wrapTo2PiInPlace</a> (T &a)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Modifies the given angle to translate it into the [0,2pi[ range. <a href="#a63f0941328a709254c00147881525d62"></a><br/></td></tr>
<tr><td class="memTemplParams" colspan="2">template<class T > </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">T </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math.html#ae47d6345832411712f6f029c774b7acc">mrpt::math::wrapTo2Pi</a> (T a)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Modifies the given angle to translate it into the [0,2pi[ range. <a href="#ae47d6345832411712f6f029c774b7acc"></a><br/></td></tr>
<tr><td class="memTemplParams" colspan="2">template<class T > </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">T </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math.html#a28d2bd3941f3afd01f91ad31632fbe58">mrpt::math::wrapToPi</a> (T a)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Modifies the given angle to translate it into the ]-pi,pi] range. <a href="#a28d2bd3941f3afd01f91ad31632fbe58"></a><br/></td></tr>
<tr><td class="memTemplParams" colspan="2">template<class T > </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math.html#af3c7288572a603de6792159c491d36ea">mrpt::math::wrapToPiInPlace</a> (T &a)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Modifies the given angle to translate it into the ]-pi,pi] range. <a href="#af3c7288572a603de6792159c491d36ea"></a><br/></td></tr>
<tr><td class="memTemplParams" colspan="2">template<class T > </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math.html#a091f9b51386810a23689fda6360862dc">mrpt::math::normalize</a> (const std::vector< T > &v, std::vector< T > &out_v)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Normalize a vector, such as its norm is the unity. <a href="#a091f9b51386810a23689fda6360862dc"></a><br/></td></tr>
<tr><td class="memTemplParams" colspan="2">template<class VECTOR_OF_VECTOR , class VECTORLIKE , class MATRIXLIKE > </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math.html#ab7f55ad571c5d8bc95995dcf2f48adff">mrpt::math::meanAndCovVector</a> (const VECTOR_OF_VECTOR &v, VECTORLIKE &out_mean, MATRIXLIKE &out_cov)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Computes the mean vector and covariance from a list of values given as a vector of vectors, where each row is a sample. <a href="#ab7f55ad571c5d8bc95995dcf2f48adff"></a><br/></td></tr>
<tr><td class="memTemplParams" colspan="2">template<class VECTOR_OF_VECTOR > </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">CMatrixDouble </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math.html#a1e15137cfe79855f26e74f84fe9eb089">mrpt::math::covVector</a> (const VECTOR_OF_VECTOR &v)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Computes the covariance matrix from a list of values given as a vector of vectors, where each row is a sample. <a href="#a1e15137cfe79855f26e74f84fe9eb089"></a><br/></td></tr>
<tr><td class="memTemplParams" colspan="2">template<class VECTOR_OF_VECTORS , class MATRIXLIKE , class VECTORLIKE , class VECTORLIKE2 , class VECTORLIKE3 > </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math.html#a52234e08a658a81ded4a6fd932dd7e30">mrpt::math::covariancesAndMeanWeighted</a> (const VECTOR_OF_VECTORS &elements, MATRIXLIKE &covariances, VECTORLIKE &means, const VECTORLIKE2 *weights_mean, const VECTORLIKE3 *weights_cov, const bool *elem_do_wrap2pi=NULL)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Computes covariances and mean of any vector of containers, given optional weights for the different samples. <a href="#a52234e08a658a81ded4a6fd932dd7e30"></a><br/></td></tr>
<tr><td class="memTemplParams" colspan="2">template<class VECTOR_OF_VECTORS , class MATRIXLIKE , class VECTORLIKE > </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math.html#a9ed2005589fa01a91063e4008cf055ca">mrpt::math::covariancesAndMean</a> (const VECTOR_OF_VECTORS &elements, MATRIXLIKE &covariances, VECTORLIKE &means, const bool *elem_do_wrap2pi=NULL)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Computes covariances and mean of any vector of containers. <a href="#a9ed2005589fa01a91063e4008cf055ca"></a><br/></td></tr>
<tr><td class="memTemplParams" colspan="2">template<class VECTORLIKE1 , class VECTORLIKE2 > </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math.html#a9bf7414c05e0d04af0af80a619179991">mrpt::math::weightedHistogram</a> (const VECTORLIKE1 &values, const VECTORLIKE1 &weights, float binWidth, VECTORLIKE2 &out_binCenters, VECTORLIKE2 &out_binValues)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Computes the weighted histogram for a vector of values and their corresponding weights. <a href="#a9bf7414c05e0d04af0af80a619179991"></a><br/></td></tr>
<tr><td class="memTemplParams" colspan="2">template<class VECTORLIKE1 , class VECTORLIKE2 > </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math.html#ac085bbebb9dc4a6656c558b7db6236eb">mrpt::math::weightedHistogramLog</a> (const VECTORLIKE1 &values, const VECTORLIKE1 &log_weights, float binWidth, VECTORLIKE2 &out_binCenters, VECTORLIKE2 &out_binValues)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Computes the weighted histogram for a vector of values and their corresponding log-weights. <a href="#ac085bbebb9dc4a6656c558b7db6236eb"></a><br/></td></tr>
<tr><td class="memTemplParams" colspan="2">template<class VECTOR_OF_VECTORS , class VECTORLIKE > </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math.html#a772e54a8aacb068395f9823a90d8df50">mrpt::math::extractColumnFromVectorOfVectors</a> (const size_t colIndex, const VECTOR_OF_VECTORS &data, VECTORLIKE &out_column)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Extract a column from a vector of vectors, and store it in another vector. <a href="#a772e54a8aacb068395f9823a90d8df50"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">uint64_t BASE_IMPEXP </td><td class="memItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math.html#abde7e0c25e9bb6a0a962f8051fe8c19d">mrpt::math::factorial64</a> (unsigned int n)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Computes the factorial of an integer number and returns it as a 64-bit integer number. <a href="#abde7e0c25e9bb6a0a962f8051fe8c19d"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">double BASE_IMPEXP </td><td class="memItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math.html#a2fbe27097242531b344c8d5b9fe148c9">mrpt::math::factorial</a> (unsigned int n)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Computes the factorial of an integer number and returns it as a double value (internally it uses logarithms for avoiding overflow). <a href="#a2fbe27097242531b344c8d5b9fe148c9"></a><br/></td></tr>
<tr><td class="memTemplParams" colspan="2">template<class T > </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">T </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math.html#aafcf18a2df3abddbd5bfd8b0229961ee">mrpt::math::round2up</a> (T val)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Round up to the nearest power of two of a given number. <a href="#aafcf18a2df3abddbd5bfd8b0229961ee"></a><br/></td></tr>
<tr><td class="memTemplParams" colspan="2">template<class T > </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">T </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math.html#a251e4c9ee701b2c44198ffd4006ed4d9">mrpt::math::round_10power</a> (T val, int power10)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Round a decimal number up to the given 10'th power (eg, to 1000,100,10, and also fractions) power10 means round up to: 1 -> 10, 2 -> 100, 3 -> 1000, . <a href="#a251e4c9ee701b2c44198ffd4006ed4d9"></a><br/></td></tr>
<tr><td class="memTemplParams" colspan="2">template<class T > </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">double </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math.html#aae4ddf66a7d01007836ff2c8e3d7910d">mrpt::math::correlate_matrix</a> (const CMatrixTemplateNumeric< T > &a1, const CMatrixTemplateNumeric< T > &a2)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Calculate the correlation between two matrices (by AJOGD @ JAN-2007). <a href="#aae4ddf66a7d01007836ff2c8e3d7910d"></a><br/></td></tr>
<tr><td class="memTemplParams" colspan="2">template<class T > </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">void BASE_IMPEXP </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math.html#a004386d872f542d391f8a449bbd9ef1a">mrpt::math::qr_decomposition</a> (CMatrixTemplateNumeric< T > &A, CMatrixTemplateNumeric< T > &R, CMatrixTemplateNumeric< T > &Q, CVectorTemplate< T > &c, int &sing)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Matrix QR decomposition. <a href="#a004386d872f542d391f8a449bbd9ef1a"></a><br/></td></tr>
<tr><td class="memTemplParams" colspan="2">template<class T > </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">void BASE_IMPEXP </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math.html#a8b5f7e92f514f455254b3624da74256c">mrpt::math::UpdateCholesky</a> (CMatrixTemplateNumeric< T > &chol, CVectorTemplate< T > &r1Modification)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">If R = CHOL(A) is the original Cholesky factorization of A, then R1 = CHOLUPDATE(R,X) returns the upper triangular Cholesky factor of A + X*X', where X is a column vector of appropriate length. <a href="#a8b5f7e92f514f455254b3624da74256c"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">void BASE_IMPEXP </td><td class="memItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math.html#a6f3b83189d83180f5208b63ba5893100">mrpt::math::computeEigenValues2x2</a> (const CMatrixFloat &in_matrix, float &min_eigenvalue, float &max_eigenvalue)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Compute the two eigenvalues of a 2x2 matrix. <a href="#a6f3b83189d83180f5208b63ba5893100"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">double BASE_IMPEXP </td><td class="memItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math.html#a6cb458d9d6c45fae59084fc57e88666b">mrpt::math::averageLogLikelihood</a> (const vector_double &logLikelihoods)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">A numerically-stable method to compute average likelihood values with strongly different ranges (unweighted likelihoods: compute the arithmetic mean). <a href="#a6cb458d9d6c45fae59084fc57e88666b"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">double BASE_IMPEXP </td><td class="memItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math.html#a3bd9ff688b42b58bd8c2f5d6f420868f">mrpt::math::averageWrap2Pi</a> (const vector_double &angles)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Computes the average of a sequence of angles in radians taking into account the correct wrapping in the range <img class="formulaInl" alt="$ ]-\pi,\pi [ $" src="form_51.png"/>, for example, the mean of (2,-2) is <img class="formulaInl" alt="$ \pi $" src="form_52.png"/>, not 0. <a href="#a3bd9ff688b42b58bd8c2f5d6f420868f"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">double BASE_IMPEXP </td><td class="memItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math.html#aecd0c40688b7bd9e4554e8180f05f07a">mrpt::math::averageLogLikelihood</a> (const vector_double &logWeights, const vector_double &logLikelihoods)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">A numerically-stable method to average likelihood values with strongly different ranges (weighted likelihoods). <a href="#aecd0c40688b7bd9e4554e8180f05f07a"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">std::string BASE_IMPEXP </td><td class="memItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math.html#a96a2265441098c93f3388951c7e5339c">mrpt::math::MATLAB_plotCovariance2D</a> (const CMatrixFloat &cov22, const CVectorFloat &mean, const float &stdCount, const std::string &style=std::string("b"), const size_t &nEllipsePoints=30)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Generates a string with the MATLAB commands required to plot an confidence interval (ellipse) for a 2D Gaussian ('float' version). <a href="#a96a2265441098c93f3388951c7e5339c"></a><br/></td></tr>
<tr><td class="memTemplParams" colspan="2">template<class MATRIXLIKE1 , class MATRIXLIKE2 > </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top"> </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math.html#ada8c6a6c8b66ca4e7b0cd30a1673cabb">mrpt::math::RET_VOID_ASSERT_MRPTMATRICES</a> (MATRIXLIKE1, MATRIXLIKE2) homogeneousMatrixInverse(const MATRIXLIKE1 &M</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Efficiently compute the inverse of a 4x4 homogeneous matrix by only transposing the rotation 3x3 part and solving the translation with dot products. <a href="#ada8c6a6c8b66ca4e7b0cd30a1673cabb"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">class VECTORLIKE3 class <br class="typebreak"/>
MATRIXLIKE class USERPARAM <br class="typebreak"/>
void </td><td class="memItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math.html#a470380f4563a26d6fe05e8456afebeda">mrpt::math::estimateJacobian</a> (const VECTORLIKE &x, void(*functor)(const VECTORLIKE &x, const USERPARAM &y, VECTORLIKE3 &out), const VECTORLIKE2 &increments, const USERPARAM &userParam, MATRIXLIKE &out_Jacobian)</td></tr>
<tr><td class="memTemplParams" colspan="2">template<typename T , typename At , size_t N> </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">std::vector< T > & </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math.html#a5ef59eb64a2bdf451a4e7e2a457045a0">mrpt::math::loadVector</a> (std::vector< T > &v, At(&theArray)[N])</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Assignment operator for initializing a std::vector from a C array (The vector will be automatically set to the correct size). <a href="#a5ef59eb64a2bdf451a4e7e2a457045a0"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math.html#a6b94c41c7406e0d606111a7b771b72e0">mrpt::math::unwrap2PiSequence</a> (vector_double &x)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Modify a sequence of angle values such as no consecutive values have a jump larger than PI in absolute value. <a href="#a6b94c41c7406e0d606111a7b771b72e0"></a><br/></td></tr>
<tr><td class="memTemplParams" colspan="2">template<size_t N, typename T > </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">std::vector< T > </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math.html#a816638baf88338f71838c60b6a392707">mrpt::math::make_vector</a> (const T val1,...)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">A versatile template to build vectors on-the-fly in a style close to MATLAB's v=[a b c d . <a href="#a816638baf88338f71838c60b6a392707"></a><br/></td></tr>
<tr><td colspan="2"><div class="groupHeader">Interpolation functions</div></td></tr>
<tr><td colspan="2"><div class="groupText"><p><a class="anchor" id="amgrpa5104052c708f848ff96176af3bae8a2"></a> </p>
</div></td></tr>
<tr><td class="memTemplParams" colspan="2">template<class T > </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">T </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math.html#aa94b40599b9bca0808afe97bf8cb84c8">mrpt::math::interpolate</a> (const T &x, const std::vector< T > &ys, const T &x0, const T &x1)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Interpolate a data sequence "ys" ranging from "x0" to "x1" (equally spaced), to obtain the approximation of the sequence at the point "x". <a href="#aa94b40599b9bca0808afe97bf8cb84c8"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">double BASE_IMPEXP </td><td class="memItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math.html#a199ae09bf97644048fe53590964abd1b">mrpt::math::interpolate2points</a> (const double x, const double x0, const double y0, const double x1, const double y1, bool wrap2pi=false)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Linear interpolation/extrapolation: evaluates at "x" the line (x0,y0)-(x1,y1). <a href="#a199ae09bf97644048fe53590964abd1b"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">double BASE_IMPEXP </td><td class="memItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math.html#a43125e4a8a9b7f33c66a55645fe5f0cf">mrpt::math::spline</a> (const double t, const std::vector< double > &x, const std::vector< double > &y, bool wrap2pi=false)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Interpolates the value of a function in a point "t" given 4 SORTED points where "t" is between the two middle points If wrap2pi is true, output "y" values are wrapped to ]-pi,pi] (It is assumed that input "y" values already are in the correct range). <a href="#a43125e4a8a9b7f33c66a55645fe5f0cf"></a><br/></td></tr>
<tr><td class="memTemplParams" colspan="2">template<typename NUMTYPE , class VECTORLIKE > </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">NUMTYPE </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math.html#a25fa2d8b0c20370e79b17eb6bf4c7024">mrpt::math::leastSquareLinearFit</a> (const NUMTYPE t, const VECTORLIKE &x, const VECTORLIKE &y, bool wrap2pi=false)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Interpolates or extrapolates using a least-square linear fit of the set of values "x" and "y", evaluated at a single point "t". <a href="#a25fa2d8b0c20370e79b17eb6bf4c7024"></a><br/></td></tr>
<tr><td class="memTemplParams" colspan="2">template<class VECTORLIKE1 , class VECTORLIKE2 , class VECTORLIKE3 > </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math.html#aeb6b0124cceebe60a0bbd02fbb68b38a">mrpt::math::leastSquareLinearFit</a> (const VECTORLIKE1 &ts, VECTORLIKE2 &outs, const VECTORLIKE3 &x, const VECTORLIKE3 &y, bool wrap2pi=false)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Interpolates or extrapolates using a least-square linear fit of the set of values "x" and "y", evaluated at a sequence of points "ts" and returned at "outs". <a href="#aeb6b0124cceebe60a0bbd02fbb68b38a"></a><br/></td></tr>
<tr><td colspan="2"><div class="groupHeader">Probability density distributions (pdf) distance metrics</div></td></tr>
<tr><td colspan="2"><div class="groupText"><p><a class="anchor" id="amgrpdb2daf45b16b18c4afdb9c6e8421ce62"></a> </p>
</div></td></tr>
<tr><td class="memTemplParams" colspan="2">template<class VECTORLIKE1 , class VECTORLIKE2 , class MAT > </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">VECTORLIKE1::value_type </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math.html#a53f4c3a4bf3e33ed4c7d3a2fb0e88940">mrpt::math::mahalanobisDistance2</a> (const VECTORLIKE1 &X, const VECTORLIKE2 &MU, const MAT &COV)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Computes the squared mahalanobis distance of a vector X given the mean MU and the covariance *inverse* COV_inv </p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ d^2 = (X-MU)^\top \Sigma^{-1} (X-MU) \]" src="form_54.png"/>
</p>
<p>. <a href="#a53f4c3a4bf3e33ed4c7d3a2fb0e88940"></a><br/></td></tr>
<tr><td class="memTemplParams" colspan="2">template<class VECTORLIKE1 , class VECTORLIKE2 , class MAT > </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">VECTORLIKE1::value_type </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math.html#a4cd811ce384b89dcde154df501ea75ba">mrpt::math::mahalanobisDistance</a> (const VECTORLIKE1 &X, const VECTORLIKE2 &MU, const MAT &COV)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Computes the mahalanobis distance of a vector X given the mean MU and the covariance *inverse* COV_inv </p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ d = \sqrt{ (X-MU)^\top \Sigma^{-1} (X-MU) } \]" src="form_55.png"/>
</p>
<p>. <a href="#a4cd811ce384b89dcde154df501ea75ba"></a><br/></td></tr>
<tr><td class="memTemplParams" colspan="2">template<class VECTORLIKE , class MAT1 , class MAT2 , class MAT3 > </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">VECTORLIKE::value_type </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math.html#ab21830875035b515702e4c682c9da806">mrpt::math::mahalanobisDistance2</a> (const VECTORLIKE &mean_diffs, const MAT1 &COV1, const MAT2 &COV2, const MAT3 &CROSS_COV12)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Computes the squared mahalanobis distance between two *non-independent* Gaussians, given the two covariance matrices and the vector with the difference of their means. <a href="#ab21830875035b515702e4c682c9da806"></a><br/></td></tr>
<tr><td class="memTemplParams" colspan="2">template<class VECTORLIKE , class MAT1 , class MAT2 , class MAT3 > </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">VECTORLIKE::value_type </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math.html#adeaba1cf641db3280a1505f8e8ed2e1e">mrpt::math::mahalanobisDistance</a> (const VECTORLIKE &mean_diffs, const MAT1 &COV1, const MAT2 &COV2, const MAT3 &CROSS_COV12)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Computes the mahalanobis distance between two *non-independent* Gaussians (or independent if CROSS_COV12=NULL), given the two covariance matrices and the vector with the difference of their means. <a href="#adeaba1cf641db3280a1505f8e8ed2e1e"></a><br/></td></tr>
<tr><td class="memTemplParams" colspan="2">template<class VECTORLIKE , class MATRIXLIKE > </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">MATRIXLIKE::value_type </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math.html#abee66a02cce54891990d9e6070003c86">mrpt::math::mahalanobisDistance2</a> (const VECTORLIKE &delta_mu, const MATRIXLIKE &cov)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Computes the squared mahalanobis distance between a point and a Gaussian, given the covariance matrix and the vector with the difference between the mean and the point. <a href="#abee66a02cce54891990d9e6070003c86"></a><br/></td></tr>
<tr><td class="memTemplParams" colspan="2">template<class VECTORLIKE , class MATRIXLIKE > </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">MATRIXLIKE::value_type </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math.html#a6606b022b617b31c015638abe5b7cf7a">mrpt::math::mahalanobisDistance</a> (const VECTORLIKE &delta_mu, const MATRIXLIKE &cov)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Computes the mahalanobis distance between a point and a Gaussian, given the covariance matrix and the vector with the difference between the mean and the point. <a href="#a6606b022b617b31c015638abe5b7cf7a"></a><br/></td></tr>
<tr><td class="memTemplParams" colspan="2">template<typename T > </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">T </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math.html#a6394e8aa0763af3ee3e58f4d1a57b07b">mrpt::math::productIntegralTwoGaussians</a> (const std::vector< T > &mean_diffs, const CMatrixTemplateNumeric< T > &COV1, const CMatrixTemplateNumeric< T > &COV2)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Computes the integral of the product of two Gaussians, with means separated by "mean_diffs" and covariances "COV1" and "COV2". <a href="#a6394e8aa0763af3ee3e58f4d1a57b07b"></a><br/></td></tr>
<tr><td class="memTemplParams" colspan="2">template<typename T , size_t DIM> </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">T </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math.html#a5969b4519634e57c2b31a99ec5f576db">mrpt::math::productIntegralTwoGaussians</a> (const std::vector< T > &mean_diffs, const CMatrixFixedNumeric< T, DIM, DIM > &COV1, const CMatrixFixedNumeric< T, DIM, DIM > &COV2)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Computes the integral of the product of two Gaussians, with means separated by "mean_diffs" and covariances "COV1" and "COV2". <a href="#a5969b4519634e57c2b31a99ec5f576db"></a><br/></td></tr>
<tr><td class="memTemplParams" colspan="2">template<typename T , class VECLIKE , class MATLIKE1 , class MATLIKE2 > </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math.html#ab1134acbd0e3851e111d7003d88b0984">mrpt::math::productIntegralAndMahalanobisTwoGaussians</a> (const VECLIKE &mean_diffs, const MATLIKE1 &COV1, const MATLIKE2 &COV2, T &maha2_out, T &intprod_out, const MATLIKE1 *CROSS_COV12=NULL)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Computes both, the integral of the product of two Gaussians and their square Mahalanobis distance. <a href="#ab1134acbd0e3851e111d7003d88b0984"></a><br/></td></tr>
<tr><td class="memTemplParams" colspan="2">template<typename T , class VECLIKE , class MATRIXLIKE > </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math.html#a6fcc3623c84f0b50ba868882606a18e5">mrpt::math::mahalanobisDistance2AndLogPDF</a> (const VECLIKE &diff_mean, const MATRIXLIKE &cov, T &maha2_out, T &log_pdf_out)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Computes both, the logarithm of the PDF and the square Mahalanobis distance between a point (given by its difference wrt the mean) and a Gaussian. <a href="#a6fcc3623c84f0b50ba868882606a18e5"></a><br/></td></tr>
<tr><td class="memTemplParams" colspan="2">template<typename T , class VECLIKE , class MATRIXLIKE > </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math.html#ada235c3a883ebebac5ba4b6e1c5d8b04">mrpt::math::mahalanobisDistance2AndPDF</a> (const VECLIKE &diff_mean, const MATRIXLIKE &cov, T &maha2_out, T &pdf_out)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Computes both, the PDF and the square Mahalanobis distance between a point (given by its difference wrt the mean) and a Gaussian. <a href="#ada235c3a883ebebac5ba4b6e1c5d8b04"></a><br/></td></tr>
</table>
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