--- name: "mlpack_math" section: "3" platform: "linux" package: "mlpack-doc" version: "1.0.10-1" release: "Debian 8 (Jessie)" platforms: ["linux"] url: "https://new.carta.tech/mlpack_math" --- # mlpack\_math(3) Miscellaneous math routines. ## NAME mlpack::math - Miscellaneous math routines. ## SYNOPSIS ### Classes class **Range**\ *Simple real-valued range.* ### Functions void **Center** (const arma::mat &x, arma::mat &xCentered)\ *Creates a centered matrix, where centering is done by subtracting the sum over the columns (a column vector) from each column of the matrix.* double **ClampNonNegative** (const double d)\ *Forces a number to be non-negative, turning negative numbers into zero.* double **ClampNonPositive** (const double d)\ *Forces a number to be non-positive, turning positive numbers into zero.* double **ClampRange** (double value, const double rangeMin, const double rangeMax)\ *Clamp a number between a particular range.* void **Orthogonalize** (const arma::mat &x, arma::mat &W)\ *Orthogonalize x and return the result in W, using eigendecomposition.* void **Orthogonalize** (arma::mat &x)\ *Orthogonalize x in-place.* int **RandInt** (const int hiExclusive)\ *Generates a uniform random integer.* int **RandInt** (const int lo, const int hiExclusive)\ *Generates a uniform random integer.* double **RandNormal** ()\ *Generates a normally distributed random number with mean 0 and variance 1.* double **RandNormal** (const double mean, const double variance)\ *Generates a normally distributed random number with specified mean and variance.* double **Random** ()\ *Generates a uniform random number between 0 and 1.* double **Random** (const double lo, const double hi)\ *Generates a uniform random number in the specified range.* void **RandomSeed** (const size\_t seed)\ *Set the random seed used by the random functions (***Random()** *and* **RandInt()***).* void **RandVector** (arma::vec &v)\ *Overwrites a dimension-N vector to a random vector on the unit sphere in R^N.* void **RemoveRows** (const arma::mat &input, const std::vector\< size\_t \> &rowsToRemove, arma::mat &output)\ *Remove a certain set of rows in a matrix while copying to a second matrix.* void **VectorPower** (arma::vec &vec, const double power)\ *Auxiliary function to raise vector elements to a specific power.* void **WhitenUsingEig** (const arma::mat &x, arma::mat &xWhitened, arma::mat &whiteningMatrix)\ *Whitens a matrix using the eigendecomposition of the covariance matrix.* void **WhitenUsingSVD** (const arma::mat &x, arma::mat &xWhitened, arma::mat &whiteningMatrix)\ *Whitens a matrix using the singular value decomposition of the covariance matrix.* ### Variables boost::mt19937 **randGen**\ boost::normal\_distribution **randNormalDist**\ boost::uniform\_01\ \< boost::mt19937, double \> **randUniformDist**"\ ## Detailed Description Miscellaneous math routines. ## Function Documentation ### void mlpack::math::Center (const arma::mat &x, arma::mat &xCentered) Creates a centered matrix, where centering is done by subtracting the sum over the columns (a column vector) from each column of the matrix. **Parameters:** *x* Input matrix \ *xCentered* Matrix to write centered output into ### double mlpack::math::ClampNonNegative (const doubled)` [inline]` Forces a number to be non-negative, turning negative numbers into zero. Avoids branching costs (this is a measurable improvement). **Parameters:** *d* Double to clamp. **Returns:** 0 if d \< 0, d otherwise. Definition at line 38 of file clamp.hpp. Referenced by ClampRange(). ### double mlpack::math::ClampNonPositive (const doubled)` [inline]` Forces a number to be non-positive, turning positive numbers into zero. Avoids branching costs (this is a measurable improvement). **Parameters:** *d* Double to clamp. \ *0* if d \> 0, d otherwise. Definition at line 50 of file clamp.hpp. Referenced by ClampRange(). ### double mlpack::math::ClampRange (doublevalue, const doublerangeMin, const doublerangeMax)` [inline]` Clamp a number between a particular range. **Parameters:** *value* The number to clamp. \ *rangeMin* The first of the range. \ *rangeMax* The last of the range. **Returns:** max(rangeMin, min(rangeMax, d)). Definition at line 63 of file clamp.hpp. References ClampNonNegative(), and ClampNonPositive(). ### void mlpack::math::Orthogonalize (const arma::mat &x, arma::mat &W) Orthogonalize x and return the result in W, using eigendecomposition. We will be using the formula $ W = x (x^T x)^{-0.5} $. ### void mlpack::math::Orthogonalize (arma::mat &x) Orthogonalize x in-place. This could be sped up by a custom implementation. ### int mlpack::math::RandInt (const inthiExclusive)` [inline]` Generates a uniform random integer. Definition at line 100 of file random.hpp. References randGen, and randUniformDist. Referenced by mlpack::sparse\_coding::DataDependentRandomInitializer::Initialize(), mlpack::amf::RandomAcolInitialization\< p \>::Initialize(), and mlpack::kernel::RandomSelection::Select(). ### int mlpack::math::RandInt (const intlo, const inthiExclusive)` [inline]` Generates a uniform random integer. Definition at line 114 of file random.hpp. References randGen, and randUniformDist. ### double mlpack::math::RandNormal ()` [inline]` Generates a normally distributed random number with mean 0 and variance 1. Definition at line 131 of file random.hpp. References randGen, and randNormalDist. ### double mlpack::math::RandNormal (const doublemean, const doublevariance)` [inline]` Generates a normally distributed random number with specified mean and variance. **Parameters:** *mean* Mean of distribution. \ *variance* Variance of distribution. Definition at line 143 of file random.hpp. References randGen, and randNormalDist. ### double mlpack::math::Random ()` [inline]` Generates a uniform random number between 0 and 1. Definition at line 72 of file random.hpp. References randGen, and randUniformDist. ### double mlpack::math::Random (const doublelo, const doublehi)` [inline]` Generates a uniform random number in the specified range. Definition at line 86 of file random.hpp. References randGen, and randUniformDist. ### void mlpack::math::RandomSeed (const size\_tseed)` [inline]` Set the random seed used by the random functions (**Random()** and **RandInt()**). The seed is casted to a 32-bit integer before being given to the random number generator, but a size\_t is taken as a parameter for API consistency. **Parameters:** *seed* Seed for the random number generator. Definition at line 63 of file random.hpp. References randGen. ### void mlpack::math::RandVector (arma::vec &v) Overwrites a dimension-N vector to a random vector on the unit sphere in R^N. ### void mlpack::math::RemoveRows (const arma::mat &input, const std::vector\< size\_t \> &rowsToRemove, arma::mat &output) Remove a certain set of rows in a matrix while copying to a second matrix. **Parameters:** *input* Input matrix to copy. \ *rowsToRemove* Vector containing indices of rows to be removed. \ *output* Matrix to copy non-removed rows into. ### void mlpack::math::VectorPower (arma::vec &vec, const doublepower) Auxiliary function to raise vector elements to a specific power. The sign is ignored in the power operation and then re-added. Useful for eigenvalues. ### void mlpack::math::WhitenUsingEig (const arma::mat &x, arma::mat &xWhitened, arma::mat &whiteningMatrix) Whitens a matrix using the eigendecomposition of the covariance matrix. Whitening means the covariance matrix of the result is the identity matrix. ### void mlpack::math::WhitenUsingSVD (const arma::mat &x, arma::mat &xWhitened, arma::mat &whiteningMatrix) Whitens a matrix using the singular value decomposition of the covariance matrix. Whitening means the covariance matrix of the result is the identity matrix. ## Variable Documentation ### boost::mt19937 mlpack::math::randGen Referenced by RandInt(), RandNormal(), Random(), and RandomSeed(). ### boost::normal\_distribution mlpack::math::randNormalDist Referenced by RandNormal(). ### boost::uniform\_01\ mlpack::math::randUniformDist Referenced by RandInt(), and Random(). ## Author Generated automatically by Doxygen for MLPACK from the source code.