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MercuryDPM
Beta
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MercuryDPM
Beta
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This class is used to define polynomial axisymmetric coarse-graining functions. More...
#include <NormalisedPolynomial.h>
Public Member Functions | |
| NORMALIZED_POLYNOMIAL () | |
| Basic constructor; note that this does not determine the particular polynomial; one needs to call set_polynomial to define the coefficients. More... | |
| void | set_polynomial (std::vector< Mdouble > new_coefficients, unsigned int new_dim) |
| Use this function to set the polynomial coefficients \(c_i\). This function calls finish_set_polynomial to normalize the coefficients. More... | |
| void | set_polynomial (Mdouble *new_coefficients, unsigned int num_coeff, unsigned int new_dim) |
| Some as set_polynomial, but avoids the use of a vector. More... | |
| void | setName (const char *new_name) |
| Use this function to change the name of the polynomial. More... | |
| std::string | getName () |
| Returns name of the polynomial. More... | |
| Mdouble | evaluate (Mdouble r) |
| Returns the value of the polynomial, \(p(r)=\sum_{i=0}^N c_i r^{N-i}\). More... | |
| Mdouble | evaluateGradient (Mdouble r) |
| Returns the gradient of the polynomial, \(\partial_\alpha p(x,y,z)=\sum_{i=0}^N c_{i,\alpha} r^{N-i},\ \alpha=x,y,z\). More... | |
| Mdouble | evaluateIntegral (Mdouble a, Mdouble b, Mdouble t) |
| Returns the value of the line integral along the normal P1P2 "from a to b" over the axisymmetric function. More... | |
| int | getOrder (void) |
| Returns the order of the polynomial. More... | |
Private Member Functions | |
| void | finish_set_polynomial () |
| Normalizes the polynomial coefficients \(c_i\) such that the integral over the unit sphere of the axisymmetric function \(p(r)\) is unity. More... | |
| Mdouble | get_volume () |
| Returns the integral over the unit sphere of the axisymmetric function \(p(r)\). More... | |
| Mdouble | evaluate_1D (Mdouble r) |
| Returns the value of the polynomial averaged over 2 dimensions. For StatType=X, \(r=|x|\). See also set_average_1D. More... | |
| Mdouble | evaluate_2D (Mdouble r) |
| Returns the value of the polynomial averaged over 1 dimension. For StatType=XY, \(r=\sqrt{x^2+y^2}\). More... | |
| void | set_average () |
| Sets averaged_coefficients. More... | |
| void | set_average_1D () |
| Sets averaged_coefficients \(\bar{c}_i\) for StatType=X,Y,Z such that \(\sum_{i=0}^N \bar{c}_i x^{N-i} = \int\int_{|\vec{x}|\leq 1} p(|\vec{x}|) dy dz\). See evaluate_1D. More... | |
| void | set_average_2D () |
| For StatType=XY,XZ,XZ, averaged_coefficients is not used since \(\bar{p}(r)\) can be evaluated as a function of \(c_i\). See evaluate_2D. More... | |
| Mdouble | evaluateGradient_1D (Mdouble r) |
| Returns the value of the gradient averaged over 2 dimensions. More... | |
| Mdouble | evaluateGradient_2D (Mdouble r) |
| Returns the value of the gradient averaged over 1 dimensions. More... | |
| Mdouble | evaluateIntegral_1D (Mdouble a, Mdouble b, Mdouble t) |
| Returns the value of the line integral along the normal P1P2 "from a to b" over the axisymmetric function averaged over 2 dimensions. More... | |
| Mdouble | evaluateIntegral_2D (Mdouble a, Mdouble b, Mdouble t) |
| Returns the value of the line integral along the normal P1P2 "from a to b" over the axisymmetric function averaged over 1 dimensions. More... | |
| Mdouble | operator[] (int i) const |
| Access to the coefficients. More... | |
Private Attributes | |
| std::string | name |
| Contains the name of the polynomial which will be displayed as CGtype by the statistical code. More... | |
| unsigned int | dim |
| The system dimension. More... | |
| std::vector< Mdouble > | coefficients |
| Stores the coefficients \(c_i\). More... | |
| std::vector< Mdouble > | averaged_coefficients |
| Stores some coefficients used in evaluate and evaluateIntegral for StatTypes different from XYZ. More... | |
Friends | |
| std::ostream & | operator<< (std::ostream &os, const NORMALIZED_POLYNOMIAL &P) |
| Returns a text description of the polynomial. More... | |
This class is used to define polynomial axisymmetric coarse-graining functions.
This class stores a polynomial, \(p(r)=\sum_{i=0}^N c_i r^{N-i}\), which is normalized such that the integral over the unit sphere of the axisymmetric function \(p(|\vec{x}|)\) is unity.
Use set_polynomial to define the polynomial. Use evaluate to evaluate the polynomial. Use evaluateGradient to evaluate the polynomial's gradient.
Calculations can be found in src/docs/Polynomials.nb
This is used to define polynomial axisymmetric coarse-graining functions (see StatisticsVector).
Note: not everything is implemented yet: only dim=3 is working, no gradients are computed.
Definition at line 51 of file NormalisedPolynomial.h.
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Basic constructor; note that this does not determine the particular polynomial; one needs to call set_polynomial to define the coefficients.
Definition at line 85 of file NormalisedPolynomial.h.
References NORMALIZED_POLYNOMIAL< T >::coefficients, NORMALIZED_POLYNOMIAL< T >::dim, and NORMALIZED_POLYNOMIAL< T >::setName().
| Mdouble NORMALIZED_POLYNOMIAL< T >::evaluate | ( | Mdouble | r | ) |
Returns the value of the polynomial, \(p(r)=\sum_{i=0}^N c_i r^{N-i}\).
For averaged StatType this function is templated. If averaging statistics are used, then an averaged function is stored as well; for averaging a over certain dimensions is stored as well.
For averaging over two dimensions, \((y_{max}-y_{min})\cdot (z_{max}-z_{min})\cdot \bar{p}(x)=\int_{\vec{x}\leq1} p(|\vec{x}|) dy\,dz = \sum_{i=0}^N \bar{c}_i r^{N-i}\).
For averaging over one dimensions, \((z_{max}-z_{min})\cdot \bar{p}(x,y)=\int_{\vec{x}\leq1} p(|\vec{x}|) dz = \sum_{i=0}^N \bar{c}_i r^{N-i}\).
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Returns the value of the polynomial averaged over 2 dimensions. For StatType=X, \(r=|x|\). See also set_average_1D.
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Returns the value of the polynomial averaged over 1 dimension. For StatType=XY, \(r=\sqrt{x^2+y^2}\).
| Mdouble NORMALIZED_POLYNOMIAL< T >::evaluateGradient | ( | Mdouble | r | ) |
Returns the gradient of the polynomial, \(\partial_\alpha p(x,y,z)=\sum_{i=0}^N c_{i,\alpha} r^{N-i},\ \alpha=x,y,z\).
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Returns the value of the gradient averaged over 2 dimensions.
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Returns the value of the gradient averaged over 1 dimensions.
| Mdouble NORMALIZED_POLYNOMIAL< T >::evaluateIntegral | ( | Mdouble | a, |
| Mdouble | b, | ||
| Mdouble | t | ||
| ) |
Returns the value of the line integral along the normal P1P2 "from a to b" over the axisymmetric function.
For averaged StatType this function is templated.
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Returns the value of the line integral along the normal P1P2 "from a to b" over the axisymmetric function averaged over 2 dimensions.
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Returns the value of the line integral along the normal P1P2 "from a to b" over the axisymmetric function averaged over 1 dimensions.
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Normalizes the polynomial coefficients \(c_i\) such that the integral over the unit sphere of the axisymmetric function \(p(r)\) is unity.
\(\int_0^1 f(r) p(r) dr = 1\), with \(f(r)=4\pi r^2\) for 3D, \(f(r)=2\pi r\) for 2D, \(f(r)=2\) for 1D systems.
Also sets averaged_coefficients
Assumes that dim and coefficients are already set.
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Returns the integral over the unit sphere of the axisymmetric function \(p(r)\).
\(\int_{|\vec{x}|\leq1} p(|\vec{x}|) d\vec{x} = \int_0^1 f(r) p(r) dr = 1\), with \(f(r)=4\pi r^2\) for 3D, \(f(r)=2\pi r\) for 2D, \(f(r)=2\) for 1D systems.
For \(p(r)=\sum_{i=0}^{N-1} c_i r^{N-1-i}\), we obtain \(V = \sum_{i=0}^{N-1} 4\pi c_i/(2+N-i)\) for 3D, \(V = \sum_{i=0}^{N-1} 2\pi c_i/(1+N-i)\) for 2D, \(V = \sum_{i=0}^{N-1} 2 c_i/(N-i)\) for 1D systems.
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Returns name of the polynomial.
Definition at line 113 of file NormalisedPolynomial.h.
References NORMALIZED_POLYNOMIAL< T >::name.
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Returns the order of the polynomial.
Definition at line 148 of file NormalisedPolynomial.h.
References NORMALIZED_POLYNOMIAL< T >::coefficients.
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Access to the coefficients.
Definition at line 247 of file NormalisedPolynomial.h.
References NORMALIZED_POLYNOMIAL< T >::coefficients.
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Sets averaged_coefficients.
This function is templated, with the default used only for StatType=XYZ, so it does nothing.
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Sets averaged_coefficients \(\bar{c}_i\) for StatType=X,Y,Z such that \(\sum_{i=0}^N \bar{c}_i x^{N-i} = \int\int_{|\vec{x}|\leq 1} p(|\vec{x}|) dy dz\). See evaluate_1D.
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For StatType=XY,XZ,XZ, averaged_coefficients is not used since \(\bar{p}(r)\) can be evaluated as a function of \(c_i\). See evaluate_2D.
| void NORMALIZED_POLYNOMIAL< T >::set_polynomial | ( | std::vector< Mdouble > | new_coefficients, |
| unsigned int | new_dim | ||
| ) |
Use this function to set the polynomial coefficients \(c_i\). This function calls finish_set_polynomial to normalize the coefficients.
| void NORMALIZED_POLYNOMIAL< T >::set_polynomial | ( | Mdouble * | new_coefficients, |
| unsigned int | num_coeff, | ||
| unsigned int | new_dim | ||
| ) |
Some as set_polynomial, but avoids the use of a vector.
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Use this function to change the name of the polynomial.
Definition at line 105 of file NormalisedPolynomial.h.
References NORMALIZED_POLYNOMIAL< T >::name.
Referenced by NORMALIZED_POLYNOMIAL< T >::NORMALIZED_POLYNOMIAL().
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Returns a text description of the polynomial.
Definition at line 156 of file NormalisedPolynomial.h.
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Stores some coefficients used in evaluate and evaluateIntegral for StatTypes different from XYZ.
Definition at line 76 of file NormalisedPolynomial.h.
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Stores the coefficients \(c_i\).
Definition at line 71 of file NormalisedPolynomial.h.
Referenced by NORMALIZED_POLYNOMIAL< T >::getOrder(), NORMALIZED_POLYNOMIAL< T >::NORMALIZED_POLYNOMIAL(), and NORMALIZED_POLYNOMIAL< T >::operator[]().
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The system dimension.
Definition at line 66 of file NormalisedPolynomial.h.
Referenced by NORMALIZED_POLYNOMIAL< T >::NORMALIZED_POLYNOMIAL().
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Contains the name of the polynomial which will be displayed as CGtype by the statistical code.
Definition at line 61 of file NormalisedPolynomial.h.
Referenced by NORMALIZED_POLYNOMIAL< T >::getName(), and NORMALIZED_POLYNOMIAL< T >::setName().
1.8.7 
