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| | OSDE1D (const AbsClassicalOrthoPoly1D &poly1d, double xmin, double xmax) |
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| OSDE1D (const OSDE1D &) |
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OSDE1D & | operator= (const OSDE1D &) |
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| const AbsClassicalOrthoPoly1D & | clpoly () const |
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double | xmin () const |
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double | xmax () const |
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double | weight (double x) const |
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| double | poly (const unsigned deg, const double x) const |
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| std::pair< double, double > | twopoly (unsigned deg1, unsigned deg2, double x) const |
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| double | series (const double *coeffs, unsigned maxdeg, double x) const |
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| double | integrateSeries (const double *coeffs, const unsigned maxdeg) const |
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| double | integratePoly (const unsigned degree, const unsigned power) const |
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| double | jointIntegral (const unsigned *degrees, unsigned nDegrees) const |
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| Matrix< double > | tMatrix (unsigned maxdeg) const |
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| template<class Functor , class Quadrature > |
| void | calculateCoeffs (const Functor &fcn, const Quadrature &quad, double *coeffs, unsigned maxdeg) const |
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| void | densityCoeffs (const AbsDistribution1D &distro, unsigned nIntegrationPoints, double *coeffs, unsigned maxdeg) const |
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| void | densityCoeffsVariance (const AbsDistribution1D &distro, unsigned nIntegrationPoints, const double *coeffs, unsigned maxdeg, double expectedSampleSize, double *variances) const |
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| npstat::Matrix< double > | densityCoeffsCovariance (const AbsDistribution1D &distro, unsigned nIntegrationPoints, const double *coeffs, unsigned maxdeg, double expectedSampleSize) const |
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| template<class Numeric > |
| void | sampleCoeffs (const Numeric *coords, unsigned long lenCoords, double *coeffs, unsigned maxdeg) const |
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| template<class Numeric > |
| void | sampleCoeffsVariance (const Numeric *coords, unsigned long lenCoords, const double *coeffs, unsigned maxdeg, double *variances) const |
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| template<class Numeric > |
| npstat::Matrix< double > | sampleCoeffsCovariance (const Numeric *coords, unsigned long lenCoords, const double *coeffs, unsigned maxdeg) const |
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| template<class Pair > |
| void | weightedSampleCoeffs (const Pair *points, unsigned long numPoints, double *coeffs, unsigned maxdeg) const |
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| template<class Pair > |
| void | weightedSampleCoeffsVariance (const Pair *points, unsigned long nPoints, const double *coeffs, unsigned maxdeg, double *variances) const |
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| template<class Pair > |
| npstat::Matrix< double > | weightedSampleCoeffsCovariance (const Pair *points, unsigned long nPoints, const double *coeffs, unsigned maxdeg) const |
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| template<class Functor , class Quadrature > |
| double | integratedSquaredError (const Functor &fcn, const Quadrature &quad, const double *coeffs, unsigned maxdeg) const |
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| template<class Functor , class Quadrature > |
| double | integratedSquaredError (const Functor &fcn, const Quadrature &quad, const double *coeffs, unsigned maxdeg, double xmin, double xmax) const |
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| static std::pair< double, double > | supportRegion (const AbsClassicalOrthoPoly1D &poly1d, double leftLimit, bool leftIsFromSample, double rightLimit, bool rightIsFromSample, unsigned long nPoints) |
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| static unsigned | optimalDegreeHart (const double *coeffs, const double *variances, unsigned maxdeg, double k=2.0) |
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◆ OSDE1D()
Main constructor. The arguments are as follows:
poly1d – classical orthogonal polynomial system to use
xmin – lower bound of the density support region
xmax – upper bound of the density support region
Note that the density estimate will be automatically normalized for Legendre polynomials only.
◆ calculateCoeffs()
template<class Functor , class Quadrature >
| void npstat::OSDE1D::calculateCoeffs |
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const Functor & |
fcn, |
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const Quadrature & |
quad, |
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double * |
coeffs, |
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unsigned |
maxdeg |
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Build the coefficients of the orthogonal polynomial series for the given function. The length of the array "coeffs" should be at least maxdeg + 1. Note that the coefficients are returned in the order of increasing degree (same order is used by the "series" function).
◆ clpoly()
Basic inspection of object properties
◆ densityCoeffs()
| void npstat::OSDE1D::densityCoeffs |
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const AbsDistribution1D & |
distro, |
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unsigned |
nIntegrationPoints, |
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double * |
coeffs, |
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unsigned |
maxdeg |
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Build the coefficients of the orthogonal polynomial series for the given density using Gauss-Legendre quadratures. The length of the array "coeffs" should be at least maxdeg + 1.
◆ densityCoeffsCovariance()
| npstat::Matrix<double> npstat::OSDE1D::densityCoeffsCovariance |
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const AbsDistribution1D & |
distro, |
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unsigned |
nIntegrationPoints, |
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const double * |
coeffs, |
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unsigned |
maxdeg, |
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double |
expectedSampleSize |
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Expected covariances of the coefficients obtained previously with the "densityCoeffs" method.
◆ densityCoeffsVariance()
| void npstat::OSDE1D::densityCoeffsVariance |
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const AbsDistribution1D & |
distro, |
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unsigned |
nIntegrationPoints, |
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const double * |
coeffs, |
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unsigned |
maxdeg, |
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double |
expectedSampleSize, |
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double * |
variances |
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Expected variances of the coefficients obtained previously with the "densityCoeffs" method. The length of the array "variances" should be at least maxdeg + 1.
◆ integratedSquaredError() [1/2]
template<class Functor , class Quadrature >
| double npstat::OSDE1D::integratedSquaredError |
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const Functor & |
fcn, |
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const Quadrature & |
quad, |
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const double * |
coeffs, |
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unsigned |
maxdeg |
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Integrated squared error between the given function and the polynomial series
◆ integratedSquaredError() [2/2]
template<class Functor , class Quadrature >
| double npstat::OSDE1D::integratedSquaredError |
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const Functor & |
fcn, |
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const Quadrature & |
quad, |
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const double * |
coeffs, |
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unsigned |
maxdeg, |
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double |
xmin, |
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double |
xmax |
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Integrated squared error between the given function and the polynomial series on an arbitrary interval. If the given interval has regions beyond xmin() and xmax(), the integration will assume that on those regions the value of the series is 0, and the quadrature will be carried out there separately.
◆ integratePoly()
| double npstat::OSDE1D::integratePoly |
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const unsigned |
degree, |
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const unsigned |
power |
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inline |
Unweighted polynomial integral
◆ integrateSeries()
| double npstat::OSDE1D::integrateSeries |
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const double * |
coeffs, |
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const unsigned |
maxdeg |
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◆ jointIntegral()
| double npstat::OSDE1D::jointIntegral |
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const unsigned * |
degrees, |
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unsigned |
nDegrees |
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Unweighted integral of a product of multiple polynomials
◆ optimalDegreeHart()
| static unsigned npstat::OSDE1D::optimalDegreeHart |
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const double * |
coeffs, |
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const double * |
variances, |
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unsigned |
maxdeg, |
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double |
k = 2.0 |
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Optimal OSDE truncation degree according to the Hart scheme. Minimizes Sum_{i=0}^M (k*variances[i] - coeffs[i]^2) over M. The default value of k = 2 corresponds to the original scheme. Argument arrays "coeffs" and "variances" should have at least maxdeg + 1 elements and should be calculated in advance with "sampleCoeffs"/"sampleCoeffsVariance" or with "weightedSampleCoeffs"/"weightedSampleCoeffsVariance" methods.
◆ poly()
| double npstat::OSDE1D::poly |
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const unsigned |
deg, |
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const double |
x |
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◆ sampleCoeffs()
template<class Numeric >
| void npstat::OSDE1D::sampleCoeffs |
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const Numeric * |
coords, |
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unsigned long |
lenCoords, |
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double * |
coeffs, |
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unsigned |
maxdeg |
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Build the coefficients of the orthogonal polynomial series for the given sample of points (empirical density function). The length of the array "coeffs" should be at least maxdeg + 1. Note that the coefficients are returned in the order of increasing degree (same order is used by the "series" function).
◆ sampleCoeffsCovariance()
template<class Numeric >
| npstat::Matrix<double> npstat::OSDE1D::sampleCoeffsCovariance |
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const Numeric * |
coords, |
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unsigned long |
lenCoords, |
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const double * |
coeffs, |
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unsigned |
maxdeg |
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Estimate covariances of the coefficients obtained previously with the "sampleCoeffs" method.
◆ sampleCoeffsVariance()
template<class Numeric >
| void npstat::OSDE1D::sampleCoeffsVariance |
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const Numeric * |
coords, |
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unsigned long |
lenCoords, |
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const double * |
coeffs, |
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unsigned |
maxdeg, |
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double * |
variances |
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Estimate variances of the coefficients obtained previously with the "sampleCoeffs" method.
◆ series()
| double npstat::OSDE1D::series |
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const double * |
coeffs, |
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unsigned |
maxdeg, |
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double |
x |
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Polynomial series representing the fitted density
◆ supportRegion()
| static std::pair<double,double> npstat::OSDE1D::supportRegion |
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const AbsClassicalOrthoPoly1D & |
poly1d, |
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double |
leftLimit, |
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bool |
leftIsFromSample, |
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double |
rightLimit, |
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bool |
rightIsFromSample, |
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unsigned long |
nPoints |
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A helper function for choosing the density support interval if it is unknown and has to be estimated from the sample. If the limit is not from the sample (as indicated by the corresponding boolean argument), it is left unchanged. The first element of the returned pair will correspond to the lower limit of the interval and the second element to the upper.
◆ tMatrix()
| Matrix<double> npstat::OSDE1D::tMatrix |
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unsigned |
maxdeg | ) |
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Matrix of unweighted pairwise integrals. The returned matrix will be dimensioned (maxdeg + 1) x (maxdeg + 1).
◆ twopoly()
| std::pair<double,double> npstat::OSDE1D::twopoly |
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unsigned |
deg1, |
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unsigned |
deg2, |
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double |
x |
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A pair of polynomial values. Faster than calling "poly" two times.
◆ weightedSampleCoeffs()
template<class Pair >
| void npstat::OSDE1D::weightedSampleCoeffs |
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const Pair * |
points, |
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unsigned long |
numPoints, |
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double * |
coeffs, |
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unsigned |
maxdeg |
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Build the coefficients of the orthogonal polynomial series for the given sample of weighted points (empirical density function). The first element of the pair will be treated as the coordinate and the second element will be treated as weight. Weights must not be negative. The length of the array "coeffs" should be at least maxdeg + 1. Note that the coefficients are returned in the order of increasing degree (same order is used by the "series" function).
◆ weightedSampleCoeffsCovariance()
template<class Pair >
| npstat::Matrix<double> npstat::OSDE1D::weightedSampleCoeffsCovariance |
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const Pair * |
points, |
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unsigned long |
nPoints, |
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const double * |
coeffs, |
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unsigned |
maxdeg |
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Estimate covariances of the coefficients obtained previously with the "weightedSampleCoeffs" method. This code assumes that weights and coordinates are statistically independent from each other.
◆ weightedSampleCoeffsVariance()
template<class Pair >
| void npstat::OSDE1D::weightedSampleCoeffsVariance |
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const Pair * |
points, |
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unsigned long |
nPoints, |
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const double * |
coeffs, |
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unsigned |
maxdeg, |
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double * |
variances |
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Estimate variances of the coefficients obtained previously with the "weightedSampleCoeffs" method. This code assumes that weights and coordinates are statistically independent from each other.
The documentation for this class was generated from the following file:
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1.9.1