#include <mrpt/math/CMatrixFixed.h>#include <mrpt/math/CVectorDynamic.h>#include <mrpt/math/ops_matrices.h>#include <mrpt/math/wrap2pi.h>
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Namespaces | |
| mrpt | |
| This is the global namespace for all Mobile Robot Programming Toolkit (MRPT) libraries. | |
| mrpt::math | |
| This base provides a set of functions for maths stuff. | |
Functions | |
Probability density distributions (pdf) distance metrics | |
| template<class VECTORLIKE1 , class VECTORLIKE2 , class MAT > | |
| MAT::Scalar | mrpt::math::mahalanobisDistance2 (const VECTORLIKE1 &X, const VECTORLIKE2 &MU, const MAT &COV) |
| Computes the squared mahalanobis distance of a vector X given the mean MU and the covariance inverse COV_inv
. More... | |
| template<class VECTORLIKE1 , class VECTORLIKE2 , class MAT > | |
| VECTORLIKE1::Scalar | mrpt::math::mahalanobisDistance (const VECTORLIKE1 &X, const VECTORLIKE2 &MU, const MAT &COV) |
| Computes the mahalanobis distance of a vector X given the mean MU and the covariance inverse COV_inv
. More... | |
| template<class VECTORLIKE , class MAT1 , class MAT2 , class MAT3 > | |
| MAT1::Scalar | mrpt::math::mahalanobisDistance2 (const VECTORLIKE &mean_diffs, const MAT1 &COV1, const MAT2 &COV2, const MAT3 &CROSS_COV12) |
| Computes the squared mahalanobis distance between two non-independent Gaussians, given the two covariance matrices and the vector with the difference of their means. More... | |
| template<class VECTORLIKE , class MAT1 , class MAT2 , class MAT3 > | |
| VECTORLIKE::Scalar | mrpt::math::mahalanobisDistance (const VECTORLIKE &mean_diffs, const MAT1 &COV1, const MAT2 &COV2, const MAT3 &CROSS_COV12) |
| Computes the mahalanobis distance between two non-independent Gaussians (or independent if CROSS_COV12=nullptr), given the two covariance matrices and the vector with the difference of their means. More... | |
| template<class VECTORLIKE , class MATRIXLIKE > | |
| MATRIXLIKE::Scalar | mrpt::math::mahalanobisDistance2 (const VECTORLIKE &delta_mu, const MATRIXLIKE &cov) |
| 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. More... | |
| template<class VECTORLIKE , class MATRIXLIKE > | |
| MATRIXLIKE::Scalar | mrpt::math::mahalanobisDistance (const VECTORLIKE &delta_mu, const MATRIXLIKE &cov) |
| 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. More... | |
| template<typename T > | |
| T | mrpt::math::productIntegralTwoGaussians (const std::vector< T > &mean_diffs, const CMatrixDynamic< T > &COV1, const CMatrixDynamic< T > &COV2) |
| Computes the integral of the product of two Gaussians, with means separated by "mean_diffs" and covariances "COV1" and "COV2". More... | |
| template<typename T , size_t DIM> | |
| T | mrpt::math::productIntegralTwoGaussians (const std::vector< T > &mean_diffs, const CMatrixFixed< T, DIM, DIM > &COV1, const CMatrixFixed< T, DIM, DIM > &COV2) |
| Computes the integral of the product of two Gaussians, with means separated by "mean_diffs" and covariances "COV1" and "COV2". More... | |
| template<typename T , class VECLIKE , class MATLIKE1 , class MATLIKE2 > | |
| void | mrpt::math::productIntegralAndMahalanobisTwoGaussians (const VECLIKE &mean_diffs, const MATLIKE1 &COV1, const MATLIKE2 &COV2, T &maha2_out, T &intprod_out, const MATLIKE1 *CROSS_COV12=nullptr) |
| Computes both, the integral of the product of two Gaussians and their square Mahalanobis distance. More... | |
| template<typename T , class VECLIKE , class MATRIXLIKE > | |
| void | mrpt::math::mahalanobisDistance2AndLogPDF (const VECLIKE &diff_mean, const MATRIXLIKE &cov, T &maha2_out, T &log_pdf_out) |
| 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. More... | |
| template<typename T , class VECLIKE , class MATRIXLIKE > | |
| void | mrpt::math::mahalanobisDistance2AndPDF (const VECLIKE &diff_mean, const MATRIXLIKE &cov, T &maha2_out, T &pdf_out) |
| Computes both, the PDF and the square Mahalanobis distance between a point (given by its difference wrt the mean) and a Gaussian. More... | |
| template<class VECTOR_OF_VECTORS , class MATRIXLIKE , class VECTORLIKE , class VECTORLIKE2 , class VECTORLIKE3 > | |
| void | mrpt::math::covariancesAndMeanWeighted (const VECTOR_OF_VECTORS &elements, MATRIXLIKE &covariances, VECTORLIKE &means, const VECTORLIKE2 *weights_mean, const VECTORLIKE3 *weights_cov, const bool *elem_do_wrap2pi=nullptr) |
| Computes covariances and mean of any vector of containers, given optional weights for the different samples. More... | |
| template<class VECTOR_OF_VECTORS , class MATRIXLIKE , class VECTORLIKE > | |
| void | mrpt::math::covariancesAndMean (const VECTOR_OF_VECTORS &elements, MATRIXLIKE &covariances, VECTORLIKE &means, const bool *elem_do_wrap2pi=nullptr) |
| Computes covariances and mean of any vector of containers. More... | |
| template<class VECTORLIKE1 , class VECTORLIKE2 > | |
| void | mrpt::math::weightedHistogram (const VECTORLIKE1 &values, const VECTORLIKE1 &weights, float binWidth, VECTORLIKE2 &out_binCenters, VECTORLIKE2 &out_binValues) |
| Computes the weighted histogram for a vector of values and their corresponding weights. More... | |
| template<class VECTORLIKE1 , class VECTORLIKE2 > | |
| void | mrpt::math::weightedHistogramLog (const VECTORLIKE1 &values, const VECTORLIKE1 &log_weights, float binWidth, VECTORLIKE2 &out_binCenters, VECTORLIKE2 &out_binValues) |
| Computes the weighted histogram for a vector of values and their corresponding log-weights. More... | |
| double | mrpt::math::averageLogLikelihood (const CVectorDouble &logLikelihoods) |
| A numerically-stable method to compute average likelihood values with strongly different ranges (unweighted likelihoods: compute the arithmetic mean). More... | |
| double | mrpt::math::averageWrap2Pi (const CVectorDouble &angles) |
Computes the average of a sequence of angles in radians taking into account the correct wrapping in the range ![$ ]-\pi,\pi [ $](form_51.png) , for example, the mean of (2,-2) is  , not 0. More... | |
| double | mrpt::math::averageLogLikelihood (const CVectorDouble &logWeights, const CVectorDouble &logLikelihoods) |
| A numerically-stable method to average likelihood values with strongly different ranges (weighted likelihoods). More... | |
![\[ d^2 = (X-MU)^\top \Sigma^{-1} (X-MU) \]](form_42.png)
![\[ d = \sqrt{ (X-MU)^\top \Sigma^{-1} (X-MU) } \]](form_43.png)