polyfunc.h File Reference

Bunch of 1-D polynomial related functionality similar to numpy.polyfit, etc. More...

#include <cmath>
#include <tuple>
#include <Eigen/Dense>
#include <isce3/core/Poly1d.h>
#include <isce3/except/Error.h>

Go to the source code of this file.

Namespaces
namespace	isce3
	base interpolator is an abstract base class

Functions
std::tuple< Eigen::ArrayXd, double, double >	isce3::math::polyfit (const Eigen::Ref< const Eigen::ArrayXd > &x, const Eigen::Ref< const Eigen::ArrayXd > &y, int deg, bool center_scale=false)
	Perform 1-D polyfitting for overdertmined problem via LSE using full-pivot House holder QR decomposition.
double	isce3::math::polyval (const Eigen::Ref< const Eigen::ArrayXd > &coef, double x, double mean=0.0, double std=1.0)
	Perform 1-D polynomial evaluation via Horner's method
Eigen::ArrayXd	isce3::math::polyval (const Eigen::Ref< const Eigen::ArrayXd > &coef, const Eigen::Ref< const Eigen::ArrayXd > &x, double mean=0.0, double std=1.0)
	Perform 1-D polynomial evaluation.
Eigen::ArrayXd	isce3::math::polyder (const Eigen::Ref< const Eigen::ArrayXd > &coef, double std=1.0)
	Perform first-derivative of 1-D polynomial coeff in ascending order.
isce3::core::Poly1d	isce3::math::polyfitObj (const Eigen::Ref< const Eigen::ArrayXd > &x, const Eigen::Ref< const Eigen::ArrayXd > &y, int deg, bool center_scale=false)
	Function to encapsulate polyfitted outputs in isce3 Poly1d object format.

Detailed Description

Bunch of 1-D polynomial related functionality similar to numpy.polyfit, etc.

Function Documentation

polyder()

Eigen::ArrayXd isce3::math::polyder	(	const Eigen::Ref< const Eigen::ArrayXd > &	coef,
		double	std = 1.0 )

Perform first-derivative of 1-D polynomial coeff in ascending order.

Parameters

[in]	coef	a vector of polynomial coeff in ascending order.
[in]	std	(optional) std value or divider for scaling input. Default is 1.0 which implies no scaling.

Returns

derivative of input coeff in ascending order

Exceptions

LengthError,InvalidArgument

polyfit()

std::tuple< Eigen::ArrayXd, double, double > isce3::math::polyfit	(	const Eigen::Ref< const Eigen::ArrayXd > &	x,
		const Eigen::Ref< const Eigen::ArrayXd > &	y,
		int	deg,
		bool	center_scale = false )

Perform 1-D polyfitting for overdertmined problem via LSE using full-pivot House holder QR decomposition.

See Eigen QR Solver To improve performance and stability, centering and scaling of the input vector will be performed per request. See centering and scaling in Matlab polyfit

Parameters

[in]	x	eigen vector of input values
[in]	y	eigen vector of "f(x)" and shall have the same size as "x"
[in]	deg	order of polynomial.
[in]	center_scale	if true will centerize and rescale "x" by its mean and std, respectively, prior to solving for coeffs.

Returns

tuple of three values, a vector of coeff in ascending order, mean of "x", and std of "x". If "center_scale" is false, no centering and scaling is done and thus mean of "x" is set to 0 and std of "x" is set to 1.

Exceptions

LengthError,InvalidArgument

polyfitObj()

isce3::core::Poly1d isce3::math::polyfitObj	(	const Eigen::Ref< const Eigen::ArrayXd > &	x,
		const Eigen::Ref< const Eigen::ArrayXd > &	y,
		int	deg,
		bool	center_scale = false )

Function to encapsulate polyfitted outputs in isce3 Poly1d object format.

Parameters

[in]	x	eigen vector of inputs
[in]	y	eigen vector of "f(x)" and shall have the same size as "x"
[in]	deg	order of polynomial.
[in]	center_scale	if true will centerize and rescale "x" by its mean and std, respectively, prior to solving for coeffs.

Returns

isce3 Poly1d object

Exceptions

LengthError,InvalidArgument

See also

polyfit()

polyval() [1/2]

Eigen::ArrayXd isce3::math::polyval	(	const Eigen::Ref< const Eigen::ArrayXd > &	coef,
		const Eigen::Ref< const Eigen::ArrayXd > &	x,
		double	mean = 0.0,
		double	std = 1.0 )

Perform 1-D polynomial evaluation.

Parameters

[in]	coef	a vector of polynomial coeff in ascending order.
[in]	x	array of x values to be evaluated.
[in]	mean	(optional) mean value or offset for centralizing input. Default is 0.0 which implies no centralization.
[in]	std	(optional) std value or divider for scaling input. Default is 1.0 which implies no scaling.

Returns

array of evaluated values of x.

Exceptions

LengthError,InvalidArgument

polyval() [2/2]

double isce3::math::polyval	(	const Eigen::Ref< const Eigen::ArrayXd > &	coef,
		double	x,
		double	mean = 0.0,
		double	std = 1.0 )

Perform 1-D polynomial evaluation via Horner's method

Parameters

[in]	coef	a vector of polynomial coeff in ascending order.
[in]	x	desired x value to be evaluated.
[in]	mean	(optional) mean value or offset for centralizing input. Default is 0.0 which implies no centralization.
[in]	std	(optional) std value or divider for scaling input. Default is 1.0 which implies no scaling.

Returns

evaluated scalar value at "x".

Exceptions

LengthError,InvalidArgument