Data Structures
struct	_polynomial

Functions
cpl_matrix *	xsh_matrix_product_normal_create (const cpl_matrix *self)

cpl_matrix *	xsh_matrix_solve_normal (const cpl_matrix coeff, const cpl_matrix rhs)

polynomial *	xsh_polynomial_new (const cpl_polynomial *pol)
	Create a polynomial.

polynomial *	xsh_polynomial_new_zero (int dim)
	Create a zero polynomial.

void	xsh_polynomial_delete (polynomial **p)
	Delete a polynomial.

void	xsh_polynomial_delete_const (const polynomial **p)
	Delete a const polynomial.

int	xsh_polynomial_get_degree (const polynomial *p)
	Get degree.

polynomial *	xsh_polynomial_duplicate (const polynomial *p)
	Copy a polynomial.

cpl_table *	xsh_polynomial_convert_to_table (const polynomial *p)
	Convert a polynomial to a table.

polynomial *	xsh_polynomial_convert_from_table (cpl_table *t)
	Convert a table to a polynomial.

int	xsh_polynomial_get_dimension (const polynomial *p)
	Get the dimension of a polynomial.

void	xsh_polynomial_dump (const polynomial p, FILE stream)
	Print a polynomial.

cpl_error_code	xsh_polynomial_rescale (polynomial *p, int varno, double scale)
	Rescale a polynomial.

cpl_error_code	xsh_polynomial_shift (polynomial *p, int varno, double shift)
	Shift a polynomial.

double	xsh_polynomial_evaluate_1d (const polynomial *p, double x)
	Evaluate a 1d polynomial.

double	xsh_polynomial_evaluate_2d (const polynomial *p, double x1, double x2)
	Evaluate a 2d polynomial.

double	xsh_polynomial_solve_1d (const polynomial *p, double value, double guess, int multiplicity)
	Solve p(x) = value.

double	xsh_polynomial_solve_2d (const polynomial *p, double value, double guess, int multiplicity, int varno, double x_value)
	Solve p(x1, x2) = value.

double	xsh_polynomial_derivative_2d (const polynomial *p, double x1, double x2, int varno)
	Evaluate the partial derivative of a 2d polynomial.

double	xsh_polynomial_derivative_1d (const polynomial *p, double x)
	Evaluate the derivative of a 1d polynomial.

polynomial *	xsh_polynomial_add_2d (const polynomial p1, const polynomial p2)
	Add two polynomials.

static cpl_error_code	derivative_cpl_polynomial (cpl_polynomial *p, int varno)
	Calculate the partial derivative of a CPL-polynomial.

cpl_error_code	xsh_polynomial_derivative (polynomial *p, int varno)
	Calculate the partial derivative of a polynomial.

double	xsh_polynomial_get_coeff_2d (const polynomial *p, int degree1, int degree2)
	Get a coefficient of a 2D polynomial.

double	xsh_polynomial_get_coeff_1d (const polynomial *p, int degree)
	Get a coefficient of a 1D polynomial.

polynomial *	xsh_polynomial_collapse (const polynomial *p, int varno, double value)
	Collapse a polynomial by fixing one variable to a constant.

polynomial *	xsh_polynomial_fit_1d (const cpl_vector x_pos, const cpl_vector values, const cpl_vector sigmas, int poly_deg, double mse)
	Fit a 1d function with a polynomial.

polynomial *	xsh_polynomial_fit_2d (const cpl_bivector xy_pos, const cpl_vector values, const cpl_vector sigmas, int poly_deg1, int poly_deg2, double mse, double red_chisq, polynomial *variance)
	Fit a 2d surface with a polynomial in x and y.

Detailed Description

This module provides N dimensional polynomials.

This class is a wrapper of CPL's polynomial class, but it improves the accuracy of the fitting routine (related to DFS ticket: DFS02237), and it allows fitting with a 2d polynomial with different degree of the independent variables (which CPL does not support), and also allows propagation of the uncertainty of the fit.

Also, the module adds simple functionalities like shifting a 2d polynomial, collapsing a 2d polynomial to a 1d polynomial, and conversion of a polynomial to/from a CPL table (which can be used for I/O).

The functionality in this module has been implemented only as needed. Therefore, 1) some functionality which "should" to be there (like collapsing a polynomial of any dimension) is missing, but 2) all the functionality present has been tested.

Function Documentation

◆ derivative_cpl_polynomial()

static cpl_error_code derivative_cpl_polynomial	(	cpl_polynomial *	p,
		int	varno
	)

static

Calculate the partial derivative of a CPL-polynomial.

Parameters

p	The input polynomial
varno	Differentiate with respect to this variable number (counting from 1 to dimension)

Returns: CPL_ERROR_NONE iff okay.

The polynomial is transformed from p to dp/dx_varno.

1D and 2D polynomials are supported.

Definition at line 993 of file xsh_utils_polynomial.c.

References assure, degree, and dimension.

Referenced by xsh_polynomial_derivative().

◆ xsh_matrix_product_normal_create()

cpl_matrix * xsh_matrix_product_normal_create ( const cpl_matrix * self )

Definition at line 106 of file xsh_utils_polynomial.c.

References m, and n.

Referenced by xsh_matrix_solve_normal().

◆ xsh_matrix_solve_normal()

cpl_matrix * xsh_matrix_solve_normal	(	const cpl_matrix *	coeff,
		const cpl_matrix *	rhs
	)

Definition at line 152 of file xsh_utils_polynomial.c.

References xsh_matrix_product_normal_create().

Referenced by xsh_polynomial_fit_1d(), and xsh_polynomial_fit_2d().

◆ xsh_polynomial_add_2d()

polynomial * xsh_polynomial_add_2d	(	const polynomial *	p1,
		const polynomial *	p2
	)

Add two polynomials.

Parameters

p1	left
p2	right

Returns: p1 + p2

Definition at line 928 of file xsh_utils_polynomial.c.

References assure, degree, xsh_free_polynomial(), xsh_max_int(), xsh_polynomial_get_coeff_2d(), xsh_polynomial_get_degree(), xsh_polynomial_get_dimension(), and xsh_polynomial_new().

◆ xsh_polynomial_collapse()

polynomial * xsh_polynomial_collapse	(	const polynomial *	p,
		int	varno,
		double	value
	)

Collapse a polynomial by fixing one variable to a constant.

Parameters

p	The polynomial to collapse
varno	Variable number to fix
value	Fix variable number varno to this value

Returns: A newly allocated, collapsed polynomial which must be deallocated with xsh_polynomial_delete(), or NULL on error.

This function fixes one variable of a polynomial to a constant value, thereby producing a polynomial, p(x1, ..., x_varno = value, ..., xn), with dimension n - 1.

Currently, only n=2 is supported.

Definition at line 1213 of file xsh_utils_polynomial.c.

References assure, assure_mem, degree, dimension, _polynomial::pol, _polynomial::scale, _polynomial::shift, xsh_free_polynomial(), xsh_polynomial_delete(), xsh_polynomial_get_dimension(), and xsh_polynomial_new().

Referenced by xsh_polynomial_solve_2d().

◆ xsh_polynomial_convert_from_table()

polynomial * xsh_polynomial_convert_from_table ( cpl_table * t )

Convert a table to a polynomial.

Parameters

t	Table to convert

Returns: The polynomial stored in the table, which must be deallocated with xsh_polynomial_delete(), or NULL on error.

Currently, only 2d polynomials are supported. See also xsh_polynomial_convert_to_table() .

Definition at line 456 of file xsh_utils_polynomial.c.

References assure, check_msg, COLUMN_COEFF, COLUMN_ORDER1, COLUMN_ORDER2, xsh_free_polynomial(), xsh_msg_debug, xsh_polynomial_delete(), xsh_polynomial_new(), xsh_polynomial_rescale(), xsh_polynomial_shift(), and xsh_tostring_cpl_type().

◆ xsh_polynomial_convert_to_table()

cpl_table * xsh_polynomial_convert_to_table ( const polynomial * p )

Convert a polynomial to a table.

Parameters

p	polynomial to convert

Returns: A table representation of the polynomial, or NULL on error.

Currently, only 2d polynomials are supported. The polynomial is written to the table in an internal format ; Therefore the table should not be read or edited manually, but only read using the function xsh_polynomial_convert_from_table() .

Definition at line 376 of file xsh_utils_polynomial.c.

References assure, COLUMN_COEFF, COLUMN_ORDER1, COLUMN_ORDER2, degree, _polynomial::pol, _polynomial::scale, _polynomial::shift, and xsh_polynomial_get_dimension().

◆ xsh_polynomial_delete()

void xsh_polynomial_delete ( polynomial ** p )

Delete a polynomial.

Parameters

p	polynomial to delete

p is deleted and set to NULL.

Definition at line 282 of file xsh_utils_polynomial.c.

References xsh_polynomial_delete_const().

Referenced by xsh_background_poly(), xsh_polynomial_collapse(), xsh_polynomial_convert_from_table(), xsh_polynomial_duplicate(), xsh_polynomial_get_coeff_1d(), xsh_polynomial_get_coeff_2d(), xsh_polynomial_new(), xsh_polynomial_regression_2d(), and xsh_polynomial_solve_2d().

◆ xsh_polynomial_delete_const()

void xsh_polynomial_delete_const ( const polynomial ** p )

Delete a const polynomial.

Parameters

p	polynomial to delete

p is deleted and set to NULL.

Definition at line 296 of file xsh_utils_polynomial.c.

References xsh_free().

Referenced by xsh_polynomial_delete().

◆ xsh_polynomial_derivative()

cpl_error_code xsh_polynomial_derivative	(	polynomial *	p,
		int	varno
	)

Calculate the partial derivative of a polynomial.

Parameters

p	The input polynomial
varno	Differentiate with respect to this variable number (counting from 1 to dimension)

Returns: CPL_ERROR_NONE iff okay.

The polynomial is transformed from p to dp/dx_varno.

Definition at line 1059 of file xsh_utils_polynomial.c.

References assure, check_msg, derivative_cpl_polynomial(), dimension, _polynomial::pol, _polynomial::scale, _polynomial::shift, and xsh_polynomial_get_dimension().

Referenced by xsh_polynomial_get_coeff_1d(), and xsh_polynomial_get_coeff_2d().

◆ xsh_polynomial_derivative_1d()

double xsh_polynomial_derivative_1d	(	const polynomial *	p,
		double	x
	)

Evaluate the derivative of a 1d polynomial.

Parameters

p	The input polynomial
x	Where to evaluate the derivative

Returns: dp/dx evaluated at x, or undefined on error.

Definition at line 904 of file xsh_utils_polynomial.c.

References assure, check_msg, _polynomial::pol, _polynomial::scale, _polynomial::shift, x, and xsh_polynomial_get_dimension().

◆ xsh_polynomial_derivative_2d()

double xsh_polynomial_derivative_2d	(	const polynomial *	p,
		double	x1,
		double	x2,
		int	varno
	)

Evaluate the partial derivative of a 2d polynomial.

Parameters

p	The input polynomial
x1	Where to evaluate the derivative
x2	Where to evaluate the derivative
varno	Evaluate partial derivative with respect to this variable (1 or 2)

Returns: dp/dx_varno evaluated at (x1, x2), or undefined on error.

Definition at line 815 of file xsh_utils_polynomial.c.

References assure, degree, _polynomial::pol, _polynomial::scale, _polynomial::shift, and xsh_polynomial_get_dimension().

◆ xsh_polynomial_dump()

void xsh_polynomial_dump	(	const polynomial *	p,
		FILE *	stream
	)

Print a polynomial.

Parameters

p	The polynomial to print
stream	Where to dump the polynomial (e.g. "stdout")

This function does not use CPL's messaging system and should be used only for debugging.

Definition at line 555 of file xsh_utils_polynomial.c.

References _polynomial::pol, _polynomial::scale, _polynomial::shift, and xsh_polynomial_get_dimension().

◆ xsh_polynomial_duplicate()

polynomial * xsh_polynomial_duplicate ( const polynomial * p )

Copy a polynomial.

Parameters

p	polynomial to copy

Returns: A clone of the input polynomial or NULL on error.

Definition at line 334 of file xsh_utils_polynomial.c.

References assure, check_msg, dimension, _polynomial::pol, _polynomial::scale, _polynomial::shift, xsh_polynomial_delete(), xsh_polynomial_get_dimension(), and xsh_polynomial_new().

Referenced by xsh_polynomial_get_coeff_1d(), and xsh_polynomial_get_coeff_2d().

◆ xsh_polynomial_evaluate_1d()

double xsh_polynomial_evaluate_1d	(	const polynomial *	p,
		double	x
	)

Evaluate a 1d polynomial.

Parameters

p	The polynomial to evaluate
x	Where to evaluate the polynomial

Returns: p ( x ), or undefined on error.

The polynomial must be 1d. See also xsh_polynomial_evaluate_2d() .

Definition at line 661 of file xsh_utils_polynomial.c.

References assure, check_msg, _polynomial::pol, _polynomial::scale, _polynomial::shift, x, and xsh_polynomial_get_dimension().

Referenced by xsh_polynomial_get_coeff_1d().

◆ xsh_polynomial_evaluate_2d()

double xsh_polynomial_evaluate_2d	(	const polynomial *	p,
		double	x1,
		double	x2
	)

Evaluate a 2d polynomial.

Parameters

p	The polynomial to evaluate
x1	Where to evaluate the polynomial
x2	Where to evaluate the polynomial

Returns: p ( x1 ,x2 ), or undefined on error.

The polynomial must be 2d. See also xsh_polynomial_evaluate_1d() .

Definition at line 692 of file xsh_utils_polynomial.c.

References assure, _polynomial::dimension, _polynomial::pol, _polynomial::scale, _polynomial::shift, _polynomial::vec, and _polynomial::vec_data.

Referenced by xsh_image_generate_background(), xsh_polynomial_fit_2d(), xsh_polynomial_get_coeff_2d(), and xsh_polynomial_regression_2d().

◆ xsh_polynomial_fit_1d()

polynomial * xsh_polynomial_fit_1d	(	const cpl_vector *	x_pos,
		const cpl_vector *	values,
		const cpl_vector *	sigmas,
		int	poly_deg,
		double *	mse
	)

Fit a 1d function with a polynomial.

Parameters

x_pos	List of positions of the signal to fit.
values	List of values of the signal to fit.
sigmas	List of uncertainties of the surface points. If NULL, constant uncertainties are used.
poly_deg	Polynomial degree.
mse	Output mean squared error.

Returns: The fitted polynomial or NULL in error case

This function is a straightforward adaption of CPL's cpl_polynomial_fit_1d_create() . But before performing the fit, all values are shifted, so that they are centered around zero. This improves the accuracy of the fit.

Also, there's support for taking into account the uncertainties of the dependent variable.

See also cpl_polynomial_fit_1d_create() and xsh_polynomial_regression_1d() .

Definition at line 1319 of file xsh_utils_polynomial.c.

References assure, assure_nomsg, check_msg, xsh_free_matrix(), xsh_free_polynomial(), xsh_free_vector(), xsh_matrix_solve_normal(), xsh_polynomial_new(), xsh_polynomial_shift(), and xsh_pow_int().

◆ xsh_polynomial_fit_2d()

polynomial * xsh_polynomial_fit_2d	(	const cpl_bivector *	xy_pos,
		const cpl_vector *	values,
		const cpl_vector *	sigmas,
		int	poly_deg1,
		int	poly_deg2,
		double *	mse,
		double *	red_chisq,
		polynomial **	variance
	)

Fit a 2d surface with a polynomial in x and y.

Parameters

xy_pos	List of positions of the surface to fit.
values	List of values of the surface points.
sigmas	List of uncertainties of the surface points.
poly_deg1	Polynomial degree of 1st variable (x)
poly_deg2	Polynomial degree of 2nd variable (y)
mse	Output mean squared error
red_chisq	Output reduced chi square
variance	Variance polynomial (see below)

Returns: The fitted polynomial or NULL in error case.

This function fits a 2d polynomial to a surface. The input grid is given in xy_pos and values. xy_pos and values of course must contain the same number of points. If sigmas is NULL, constant sigma (equal to 1) is used.

This function is an adaption of CPL's cpl_polynomial_fit_2d_create() . But the fit is made with a general rectangular coefficient matrix (the size of which is indicated by the polynomial degrees, poly_deg1 and poly_deg2) instead of the upper-left triangular matrix used by cpl_polynomial_fit_2d_create().

And before performing the fit, all values are shifted, so that they are centered around zero, which improves the accuracy of the fit. Rescaling with stdev makes the fit worse (empirically) so this is not done.

If mse is non-NULL, the mean squared error of the fit is returned through this variable. If red_chisq is non-NULL, the reduced chi square of the fit is returned through this variable.

If variance is non-NULL the variance polynomial defined as (using the error propagation formula for correlated coefficients {coeff_i}) variance(x,y) = sum_{ij} d(p_fit)/d(coeff_i) * cov_{ij} * d(p_fit)/d(coeff_j) = sum_{ij} x^degx[i]*y^degy[i] * cov_{ij} * x^degx[j]*y^degy[j] = sum_{ij} cov_{ij} * x^(degx[i]+degx[j]) * y^(degy[i]+degy[j]) will be returned through this variable (i.e. the parameter must be the address of a (polynomial*) variable. The variance polynomial gives the associated uncertainty when evaluating the fitted polynomial, i.e. the variance of p_fit(x, y) = sum_{ij} (a_{ij} * x^i * y^j)

See also cpl_polynomial_fit_2d_create() and xsh_polynomial_regression_2d() .

Definition at line 1499 of file xsh_utils_polynomial.c.

References assure, assure_mem, passure, xsh_free_matrix(), xsh_free_polynomial(), xsh_matrix_solve_normal(), xsh_polynomial_evaluate_2d(), xsh_polynomial_new(), and xsh_polynomial_shift().

Referenced by xsh_polynomial_regression_2d().

◆ xsh_polynomial_get_coeff_1d()

double xsh_polynomial_get_coeff_1d	(	const polynomial *	p,
		int	degree
	)

Get a coefficient of a 1D polynomial.

Parameters

p	The input polynomial
degree	Coefficient degree

Returns: The coefficient of the degree'th term, or undefined on error.

If the required degree is greater than the polynomial's degree, the function does not fail but returns 0 as it should.

Definition at line 1158 of file xsh_utils_polynomial.c.

References assure, check_msg, degree, dimension, xsh_polynomial_delete(), xsh_polynomial_derivative(), xsh_polynomial_duplicate(), xsh_polynomial_evaluate_1d(), and xsh_polynomial_get_dimension().

◆ xsh_polynomial_get_coeff_2d()

double xsh_polynomial_get_coeff_2d	(	const polynomial *	p,
		int	degree1,
		int	degree2
	)

Get a coefficient of a 2D polynomial.

Parameters

p	The input polynomial
degree1	The coefficient degree
degree2	The coefficient degree

Returns: The coefficient of the term (degree1, degree2), or undefined on error.

Definition at line 1102 of file xsh_utils_polynomial.c.

References assure, check_msg, dimension, xsh_polynomial_delete(), xsh_polynomial_derivative(), xsh_polynomial_duplicate(), xsh_polynomial_evaluate_2d(), and xsh_polynomial_get_dimension().

Referenced by xsh_polynomial_add_2d().

◆ xsh_polynomial_get_degree()

int xsh_polynomial_get_degree ( const polynomial * p )

Get degree.

Parameters

p	polynomial

Returns: degree

Definition at line 315 of file xsh_utils_polynomial.c.

References assure, and _polynomial::pol.

Referenced by xsh_polynomial_add_2d().

◆ xsh_polynomial_get_dimension()

int xsh_polynomial_get_dimension ( const polynomial * p )

Get the dimension of a polynomial.

Parameters

p	The input polynomial

Returns: The dimension of p, undefined in case of error.

Definition at line 534 of file xsh_utils_polynomial.c.

References assure, and _polynomial::dimension.

Referenced by xsh_polynomial_add_2d(), xsh_polynomial_collapse(), xsh_polynomial_convert_to_table(), xsh_polynomial_derivative(), xsh_polynomial_derivative_1d(), xsh_polynomial_derivative_2d(), xsh_polynomial_dump(), xsh_polynomial_duplicate(), xsh_polynomial_evaluate_1d(), xsh_polynomial_get_coeff_1d(), xsh_polynomial_get_coeff_2d(), xsh_polynomial_rescale(), xsh_polynomial_shift(), and xsh_polynomial_solve_1d().

◆ xsh_polynomial_new()

polynomial * xsh_polynomial_new ( const cpl_polynomial * pol )

Create a polynomial.

Parameters

pol	The CPL polynomial to wrap

Returns: A new polynomial, which must be deallocated with xsh_polynomial_delete(), or NULL on error.

Note: The provided CPL polynomial is duplicated and must still be deallocated independently from the polynomial returned from this function.

Definition at line 207 of file xsh_utils_polynomial.c.

References assure, assure_mem, check_msg, _polynomial::dimension, _polynomial::pol, _polynomial::scale, _polynomial::shift, _polynomial::vec, _polynomial::vec_data, and xsh_polynomial_delete().

Referenced by xsh_polynomial_add_2d(), xsh_polynomial_collapse(), xsh_polynomial_convert_from_table(), xsh_polynomial_duplicate(), xsh_polynomial_fit_1d(), xsh_polynomial_fit_2d(), and xsh_polynomial_new_zero().

◆ xsh_polynomial_new_zero()

polynomial * xsh_polynomial_new_zero ( int dim )

Create a zero polynomial.

Parameters

dim	Dimension of polynomial

Returns: A new polynomial, which must be deallocated with xsh_polynomial_delete(), or NULL on error.

Definition at line 254 of file xsh_utils_polynomial.c.

References assure, assure_mem, xsh_free_polynomial(), and xsh_polynomial_new().

◆ xsh_polynomial_rescale()

cpl_error_code xsh_polynomial_rescale	(	polynomial *	p,
		int	varno,
		double	scale
	)

Rescale a polynomial.

Parameters

p	The polynomial to rescale
varno	Rescale with respect to this variable (number)
scale	The rescaling factor

Returns: CPL_ERROR_NONE iff OK

The variable specified by varno is rescaled: p (x_1, ..., x_varno, ..., x_n) :=p (x_1, ..., x_varno / scale, ..., x_n).

If varno is zero, a the polynomial itself is rescaled: p(x) := p(x) * scale . Negative values of varno are illegal.

Definition at line 588 of file xsh_utils_polynomial.c.

References assure, _polynomial::scale, _polynomial::shift, and xsh_polynomial_get_dimension().

Referenced by xsh_polynomial_convert_from_table().

◆ xsh_polynomial_shift()

cpl_error_code xsh_polynomial_shift	(	polynomial *	p,
		int	varno,
		double	shift
	)

Shift a polynomial.

Parameters

p	The polynomial to shift
varno	Shift with respect to this variable (number)
shift	The amount to shift

Returns: CPL_ERROR_NONE iff OK

The polynomial is shifted: p (x_1, ..., x_varno, ..., x_n) :=p (x_1, ..., x_varno - shift, ..., x_n).

If varno is zero, a constant is added to the polynomial: p(x) := p(x) + shift . Negative values of varno are illegal.

Definition at line 629 of file xsh_utils_polynomial.c.

References assure, _polynomial::shift, and xsh_polynomial_get_dimension().

Referenced by xsh_polynomial_convert_from_table(), xsh_polynomial_fit_1d(), and xsh_polynomial_fit_2d().

◆ xsh_polynomial_solve_1d()

double xsh_polynomial_solve_1d	(	const polynomial *	p,
		double	value,
		double	guess,
		int	multiplicity
	)

Solve p(x) = value.

Parameters

p	The input polynomial
value	The requested value of the polynomial
guess	A guess solution
multiplicity	The multiplycity of the root (or 1 if unknown)

Returns: x satisfying the equation p (x) = value, or undefined on error.

This function uses cpl_polynomial_solve_1d() to solve the equation p (x) = value . See cpl_polynomial_solve_1d() for a description of the algorithm.

Definition at line 730 of file xsh_utils_polynomial.c.

References assure, check_msg, _polynomial::pol, _polynomial::scale, _polynomial::shift, and xsh_polynomial_get_dimension().

Referenced by xsh_polynomial_solve_2d().

◆ xsh_polynomial_solve_2d()

double xsh_polynomial_solve_2d	(	const polynomial *	p,
		double	value,
		double	guess,
		int	multiplicity,
		int	varno,
		double	x_value
	)

Solve p(x1, x2) = value.

Parameters

p	The input polynomial
value	The requested value of the polynomial
guess	A guess solution
multiplicity	The multiplycity of the root (or 1 if unknown)
varno	The variable number to fix (1 or 2)
x_value	Variable number varno is fixed to this value

Returns: The solution of the equation, or undefined on error.

This function solves the equation p (x1, x2) = value, where either x1 or x2 is already fixed to x_value.

For example, to solve the equation p (37, x) = 500 for x, call xsh_polynomial_solve_2d(p, 500, x_guess, 1, 1, 37) .

Definition at line 784 of file xsh_utils_polynomial.c.

References assure, check_msg, xsh_polynomial_collapse(), xsh_polynomial_delete(), and xsh_polynomial_solve_1d().

Data Structures

Functions

Detailed Description

Function Documentation

◆ derivative_cpl_polynomial()

◆ xsh_matrix_product_normal_create()

◆ xsh_matrix_solve_normal()

◆ xsh_polynomial_add_2d()

◆ xsh_polynomial_collapse()

◆ xsh_polynomial_convert_from_table()

◆ xsh_polynomial_convert_to_table()

◆ xsh_polynomial_delete()

◆ xsh_polynomial_delete_const()

◆ xsh_polynomial_derivative()

◆ xsh_polynomial_derivative_1d()

◆ xsh_polynomial_derivative_2d()

◆ xsh_polynomial_dump()

◆ xsh_polynomial_duplicate()

◆ xsh_polynomial_evaluate_1d()

◆ xsh_polynomial_evaluate_2d()

◆ xsh_polynomial_fit_1d()

◆ xsh_polynomial_fit_2d()

◆ xsh_polynomial_get_coeff_1d()

◆ xsh_polynomial_get_coeff_2d()

◆ xsh_polynomial_get_degree()

◆ xsh_polynomial_get_dimension()

◆ xsh_polynomial_new()

◆ xsh_polynomial_new_zero()

◆ xsh_polynomial_rescale()

◆ xsh_polynomial_shift()

◆ xsh_polynomial_solve_1d()

◆ xsh_polynomial_solve_2d()