numeric::interpolation Namespace Reference

Namespaces
	periodic_range
	spline

Classes
class	Histogram
	A histogram with fixed-width bins. More...
struct	HistogramAP
struct	HistogramCAP
struct	HistogramCOP
struct	HistogramOP
class	InterpolatedPotential
struct	TempStruct
struct	TempStruct< T, 1 >

Enumerations
enum	CatmullRomSplineBoundaryType { PERIODIC, FLAT, LINEAR }

Functions
template<Size N>
void	polycubic_interpolation (numeric::interpolation::InterpolatedPotential< N > const &interpolated_potential, utility::fixedsizearray1< Real, N > const &values, Real &score, utility::fixedsizearray1< Real, N > &dscoreddof)
template<typename X , typename F >
F	interpolated (X const &x, X const &x1, X const &x2, F const &f1, F const &f2)
	Linearly interpolated value: f( x ) More...
template<typename X , typename F >
F	interpolated (X const &a, F const &f1, F const &f2)
	Linearly interpolated value: f( x ) More...
template<typename X , typename F >
F	interpolated_delta (X const &a, F const &f1, F const &f2)
	Linearly interpolated delta value: f( x ) - f1. More...
template<typename X , typename Y , typename F >
F	bilinearly_interpolated (X const &x, X const &x1, X const &x2, Y const &y, Y const &y1, Y const &y2, F const &f11, F const &f12, F const &f21, F const &f22)
	Bilinearly interpolated value: f( x, y ) More...
template<typename X , typename Y , typename F >
F	bilinearly_interpolated (X const &ax, Y const &ay, F const &f11, F const &f12, F const &f21, F const &f22)
	Bilinearly interpolated value. More...
template<typename X , typename Y , typename F >
F	bilinearly_interpolated (X const &ax, Y const &ay, X const &bx, Y const &by, F const &f11, F const &f12, F const &f21, F const &f22)
	Bilinearly interpolated value. More...
template<typename T , numeric::Size N>
Real	multilinear_interpolation (MathNTensor< T, N > const &tensor, utility::fixedsizearray1< Real, N > const &minval, utility::fixedsizearray1< Real, N > const &binwidth, utility::fixedsizearray1< Real, N > const &xs, utility::fixedsizearray1< Real, N > &deriv, bool const &compute_deriv=true)
	Perform multilinear interpolation over an N-dimensional tensor, with derivatives. More...
template<typename T , numeric::Size N>
numeric::Real	multilinear_interpolation (numeric::MathNTensor< T, N > const &tensor, utility::fixedsizearray1< numeric::Real, N > const &minval, utility::fixedsizearray1< numeric::Real, N > const &binwidth, utility::fixedsizearray1< numeric::Real, N > const &xs)
	Perform multilinear interpolation over an N-dimensional tensor (without derivative computation) More...
template<Size N>
void	polycubic_interpolation (utility::fixedsizearray1< utility::fixedsizearray1< Real,(1<< N) >,(1<< N) > n_derivs, utility::fixedsizearray1< Real, N > dbbp, utility::fixedsizearray1< Real, N > binwbb, Real &val, utility::fixedsizearray1< Real, N > &dvaldbb)
	Perform cubic interpolation over each of N axes, using the 2^N derivatives at 2^N gridpoints. More...
std::string	to_string (CatmullRomSplineBoundaryType const &type)
template<typename T >
T	catmull_rom_interpolate_basic (utility::fixedsizearray1< T, 4 > const &p, Real const &x, Real &dval_dx, utility::fixedsizearray1< T, 4 > &dval_dp, bool const compute_deriv=true)
template<typename T >
T	catmull_rom_interpolate_basic (utility::fixedsizearray1< T, 4 > const &p, T const &x, T &dval_dx, bool const compute_deriv=true)
template<typename T >
T	catmull_rom_interpolate_basic (utility::fixedsizearray1< T, 4 > const &p, T const &x)
template<typename T , numeric::Size N>
T	catmull_rom_interpolate (utility::fixedsizearray1< T, 1<< (2 *N) > const &F_patch, utility::fixedsizearray1< T, N > const &d, utility::fixedsizearray1< T, N > &deriv, bool const compute_deriv)
template<typename T , numeric::Size N>
T	get_val (MathNTensor< T, N > const &F, utility::fixedsizearray1< int, N > &idx, utility::fixedsizearray1< CatmullRomSplineBoundaryType, N > const &boundary, Size const which_dim)
template<typename T , numeric::Size N>
void	get_patch (utility::fixedsizearray1< T, 1<< (2 *N) > &F_patch, utility::fixedsizearray1< Real, N > &d, MathNTensor< T, N > const &F, utility::fixedsizearray1< Real, N > const &minval, utility::fixedsizearray1< Real, N > const &binwidth, utility::fixedsizearray1< Real, N > const &xs, utility::fixedsizearray1< CatmullRomSplineBoundaryType, N > const &boundary)
template<typename T , numeric::Size N>
T	polycubic_interpolate_catmull_rom (MathNTensor< T, N > const &F, utility::fixedsizearray1< Real, N > const &minval, utility::fixedsizearray1< Real, N > const &binwidth, utility::fixedsizearray1< Real, N > const &xs, utility::fixedsizearray1< CatmullRomSplineBoundaryType, N > const &boundary, utility::fixedsizearray1< Real, N > &deriv, bool const &compute_deriv=true)
	Catmull-Rom spline interpolation of an N-dimensional tensor defined on a equispaced grid. More...
template<typename T , numeric::Size N>
T	polycubic_interpolate_catmull_rom (MathNTensor< T, N > const &F, utility::fixedsizearray1< Real, N > const &minval, utility::fixedsizearray1< Real, N > const &binwidth, utility::fixedsizearray1< Real, N > const &xs, utility::fixedsizearray1< CatmullRomSplineBoundaryType, N > const &boundary)
	Catmull-Rom spline interpolation of an N-dimensional tensor defined on a equispaced grid, without derivative computation. More...
spline::SplineGenerator	spline_from_file (std::string const &filename, platform::Real const &bin_size)
	given a file, return a 2D spline More...

Enumeration Type Documentation

enum numeric::interpolation::CatmullRomSplineBoundaryType

Enumerator
PERIODIC
FLAT
LINEAR

Function Documentation

template<typename X , typename Y , typename F >

F numeric::interpolation::bilinearly_interpolated ( X const &  x, X const &  x1, X const &  x2, Y const &  y, Y const &  y1, Y const &  y2, F const &  f11, F const &  f12, F const &  f21, F const &  f22  )

inline

Bilinearly interpolated value: f( x, y )

References ObjexxFCL::format::X().

template<typename X , typename Y , typename F >

F numeric::interpolation::bilinearly_interpolated ( X const &  ax, Y const &  ay, F const &  f11, F const &  f12, F const &  f21, F const &  f22  )

inline

Bilinearly interpolated value.

References ObjexxFCL::format::X().

template<typename X , typename Y , typename F >

F numeric::interpolation::bilinearly_interpolated ( X const &  ax, Y const &  ay, X const &  bx, Y const &  by, F const &  f11, F const &  f12, F const &  f21, F const &  f22  )

inline

Bilinearly interpolated value.

References numeric::eq_tol(), and ObjexxFCL::format::X().

template<typename T , numeric::Size N>

T numeric::interpolation::catmull_rom_interpolate ( )

inline

Referenced by polycubic_interpolate_catmull_rom().

template<typename T >

T numeric::interpolation::catmull_rom_interpolate_basic ( utility::fixedsizearray1< T, 4 > const &  p, Real const &  x, Real &  dval_dx, utility::fixedsizearray1< T, 4 > &  dval_dp, bool const  compute_deriv = true  )

inline

References numeric::crick_equations::x().

Referenced by catmull_rom_interpolate_basic(), numeric::interpolation::TempStruct< T, N >::operator()(), and numeric::interpolation::TempStruct< T, 1 >::operator()().

template<typename T >

T numeric::interpolation::catmull_rom_interpolate_basic ( utility::fixedsizearray1< T, 4 > const &  p, T const &  x, T &  dval_dx, bool const  compute_deriv = true  )

inline

References catmull_rom_interpolate_basic().

template<typename T >

T numeric::interpolation::catmull_rom_interpolate_basic ( utility::fixedsizearray1< T, 4 > const &  p, T const &  x  )

inline

References catmull_rom_interpolate_basic().

template<typename T , numeric::Size N>

void numeric::interpolation::get_patch ( )

inline

References get_val(), ObjexxFCL::pow(), and runtime_assert.

Referenced by polycubic_interpolate_catmull_rom().

template<typename T , numeric::Size N>

T numeric::interpolation::get_val ( MathNTensor< T, N > const &  F, utility::fixedsizearray1< int, N > &  idx, utility::fixedsizearray1< CatmullRomSplineBoundaryType, N > const &  boundary, Size const  which_dim  )

inline

References ObjexxFCL::format::F(), FLAT, numeric::MathNTensor< T, N >::is_valid_position(), LINEAR, utility::modulo(), numeric::MathNTensor< T, N >::n_bins(), PERIODIC, runtime_assert, and utility_exit_with_message.

Referenced by get_patch().

template<typename X , typename F >

F numeric::interpolation::interpolated ( X const &  x, X const &  x1, X const &  x2, F const &  f1, F const &  f2  )

inline

Linearly interpolated value: f( x )

Note

Extrapolates if x not in [ x1, x2 ]

References ObjexxFCL::format::X().

Referenced by numeric::interpolation::Histogram< typename, typename >::interpolate_linear(), numeric::interpolation::periodic_range::half::interpolated(), and numeric::interpolation::periodic_range::full::interpolated().

template<typename X , typename F >

F numeric::interpolation::interpolated ( X const &  a, F const &  f1, F const &  f2  )

inline

Linearly interpolated value: f( x )

Note

Extrapolates if a not in [ 0, 1 ]

template<typename X , typename F >

F numeric::interpolation::interpolated_delta ( X const &  a, F const &  f1, F const &  f2  )

inline

Linearly interpolated delta value: f( x ) - f1.

Note

Extrapolates if a not in [ 0, 1 ]

template<typename T , numeric::Size N>

Real numeric::interpolation::multilinear_interpolation	(	MathNTensor< T, N > const &	tensor,
		utility::fixedsizearray1< Real, N > const &	minval,
		utility::fixedsizearray1< Real, N > const &	binwidth,
		utility::fixedsizearray1< Real, N > const &	xs,
		utility::fixedsizearray1< Real, N > &	deriv,
		bool const &	compute_deriv = true
	)

Perform multilinear interpolation over an N-dimensional tensor, with derivatives.

Straightforward generalization of bilinear interpolation. Currently extrapolates linearly when asked for point outside tensor range TODO: allow periodic; allow different extrapolation behavior (e.g., constant).

Parameters

[in]	tensor	is the data array, using MathNTensor
[in]	minval	is the tensor's minimum value in each direction.
[in]	binwidth	is the bin width in each direction
[in]	xs	is the position
[out]	deriv	is the interpolated derivative
[in]	compute_deriv	– set to false to reduce computation

Author

rhiju

References basic::options::OptionKeys::score::fiber_diffraction::a, numeric::interpolation::periodic_range::half::bin(), test.T110_Numeric::m, max(), min(), numeric::MathNTensor< T, N >::n_bins(), and basic::options::OptionKeys::rna::denovo::offset.

Referenced by multilinear_interpolation().

template<typename T , numeric::Size N>

numeric::Real numeric::interpolation::multilinear_interpolation ( numeric::MathNTensor< T, N > const &  tensor, utility::fixedsizearray1< numeric::Real, N > const &  minval, utility::fixedsizearray1< numeric::Real, N > const &  binwidth, utility::fixedsizearray1< numeric::Real, N > const &  xs  )

inline

Perform multilinear interpolation over an N-dimensional tensor (without derivative computation)

Straightforward generalization of bilinear interpolation. Currently extrapolates linearly when asked for point outside tensor range TODO: allow periodic; allow different extrapolation behavior (e.g., constant).

Parameters

[in]	tensor	is the data array, using MathNTensor
[in]	minval	is the tensor's minimum value in each direction.
[in]	xs	is the position at which to evaluate spline
[in]	binwidth	is the bin width in each direction

Author

rhiju

References multilinear_interpolation().

template<typename T , numeric::Size N>

T numeric::interpolation::polycubic_interpolate_catmull_rom ( MathNTensor< T, N > const &  F, utility::fixedsizearray1< Real, N > const &  minval, utility::fixedsizearray1< Real, N > const &  binwidth, utility::fixedsizearray1< Real, N > const &  xs, utility::fixedsizearray1< CatmullRomSplineBoundaryType, N > const &  boundary, utility::fixedsizearray1< Real, N > &  deriv, bool const &  compute_deriv = true  )

inline

Catmull-Rom spline interpolation of an N-dimensional tensor defined on a equispaced grid.

References catmull_rom_interpolate(), and get_patch().

Referenced by polycubic_interpolate_catmull_rom().

template<typename T , numeric::Size N>

T numeric::interpolation::polycubic_interpolate_catmull_rom ( MathNTensor< T, N > const &  F, utility::fixedsizearray1< Real, N > const &  minval, utility::fixedsizearray1< Real, N > const &  binwidth, utility::fixedsizearray1< Real, N > const &  xs, utility::fixedsizearray1< CatmullRomSplineBoundaryType, N > const &  boundary  )

inline

Catmull-Rom spline interpolation of an N-dimensional tensor defined on a equispaced grid, without derivative computation.

References polycubic_interpolate_catmull_rom().

template<Size N>

void numeric::interpolation::polycubic_interpolation	(	numeric::interpolation::InterpolatedPotential< N > const &	interpolated_potential,
		utility::fixedsizearray1< Real, N > const &	values,
		Real &	score,
		utility::fixedsizearray1< Real, N > &	dscoreddof
	)

References numeric::interpolation::InterpolatedPotential< N >::axis_range(), numeric::interpolation::InterpolatedPotential< N >::bin_width(), numeric::interpolation::InterpolatedPotential< N >::get_indices(), numeric::interpolation::InterpolatedPotential< N >::grid_size(), test.T200_Scoring::ii, and erraser_single_res_analysis::score.

template<Size N>

void numeric::interpolation::polycubic_interpolation	(	utility::fixedsizearray1< utility::fixedsizearray1< Real,(1<< N) >,(1<< N) >	n_derivs,
		utility::fixedsizearray1< Real, N >	dbbp,
		utility::fixedsizearray1< Real, N >	binwbb,
		Real &	val,
		utility::fixedsizearray1< Real, N > &	dvaldbb
	)

Perform cubic interpolation over each of N axes, using the 2^N derivatives at 2^N gridpoints.

The way encoding gridpoints and derivatives into a linear structure like this is actually pretty simple. Imagine the "right or left" part of a cube, or the "derivative taken or not" on a particular variable, as zero or one. Then "just the actual function value" maps to 000, the z derivative (for example) maps to 001, d2/dydz maps to 011, etc.

Parameters

[in]	n_derivs	is a 2^N x 2^N matrix: 2^N derivatives at 2^N gridpoints
[in]	dbbp	is how far along the bin our target point is, in each direction
[in]	binwbb	is the bin width in each direction
[out]	val	is the interpolated value
[out]	dvaldbb	are the interpolated derivatives

References test.T200_Scoring::ii.

spline::SplineGenerator numeric::interpolation::spline_from_file	(	std::string const &	filename,
		platform::Real const &	bin_size
	)

given a file, return a 2D spline

read in a file, read out a spline. The file should be tab separated, and have two lines The first field of one line should be "x_axis", the next fields should be the x values of the points for the spline The first field of the other line should be "y_axis", the next fields should be the y values for the points on the spline For an example, see "scoring/constraints/epr_distance_potential.histogram"

References numeric::interpolation::spline::SplineGenerator::add_boundary_function(), numeric::interpolation::spline::SplineGenerator::add_known_value(), utility::io::izstream::close(), clean_pdb_keep_ligand::count, basic::options::OptionKeys::cp::cutoff, utility::from_string(), ObjexxFCL::getline(), ObjexxFCL::index(), line, utility::io::izstream::open(), utility::string_split(), tag, ObjexxFCL::trim(), and utility_exit_with_message.

std::string numeric::interpolation::to_string ( CatmullRomSplineBoundaryType const &  type )

inline

References FLAT, LINEAR, and PERIODIC.

Referenced by binder::bind_member_functions_for_call_back(), binder::function_arguments_for_lambda(), binder::function_arguments_for_py_overload(), binder::Context::generate(), utility::DenseBoolMap< NUM_ELEMS, BASE_INDEX >::get(), binder::Context::global_insertion_operator(), binder::line_number(), main(), retag(), utility::DenseBoolMap< NUM_ELEMS, BASE_INDEX >::set(), and binder::Context::trace_line().