`IMLCV.tools._rbfinterp_pythran`#

Module Contents#

`linear`(r)
`thin_plate_spline`(r)
`cubic`(r)
`quintic`(r)
`multiquadric`(r)
`inverse_multiquadric`(r)
`inverse_quadratic`(r)
`gaussian`(r)
`scale`(val, metric)
`cv_norm`(x, y, metric, eps)
`cv_vals`(x, powers, metric)
`kernel_vector`(x, y, metric, epsilon, kernel_func)	Evaluate RBFs, with centers at y, at the point x.
`polynomial_vector`(x, powers, metric)	Evaluate monomials, with exponents from powers, at the point x.
`kernel_matrix`(x, metric, eps, kernel_func)	Evaluate RBFs, with centers at x, at x.
`polynomial_matrix`(x, metric, powers)	Evaluate monomials, with exponents from powers, at x.
`_polynomial_matrix`(x, powers, metric)	Return monomials, with exponents from powers, evaluated at x.
`_build_system`(y, metric, d, smoothing, kernel, ...)	Build the system used to solve for the RBF interpolant coefficients.
`_build_evaluation_coefficients`(x, y, metric, kernel, ...)	Construct the coefficients needed to evaluate

IMLCV.tools._rbfinterp_pythran.cv_norm(x: IMLCV.base.CV.CV, y: IMLCV.base.CV.CV, metric: IMLCV.base.CV.CvMetric, eps)[source]#

IMLCV.tools._rbfinterp_pythran.cv_vals(x: IMLCV.base.CV.CV, powers, metric: IMLCV.base.CV.CvMetric)[source]#

IMLCV.tools._rbfinterp_pythran.kernel_vector(x: IMLCV.base.CV.CV, y: IMLCV.base.CV.CV, metric: IMLCV.base.CV.CvMetric, epsilon, kernel_func)[source]#: Evaluate RBFs, with centers at y, at the point x.

IMLCV.tools._rbfinterp_pythran.polynomial_vector(x: IMLCV.base.CV.CV, powers, metric: IMLCV.base.CV.CvMetric)[source]#: Evaluate monomials, with exponents from powers, at the point x.

IMLCV.tools._rbfinterp_pythran.kernel_matrix(x: IMLCV.base.CV.CV, metric: IMLCV.base.CV.CvMetric, eps, kernel_func)[source]#: Evaluate RBFs, with centers at x, at x.

IMLCV.tools._rbfinterp_pythran.polynomial_matrix(x: IMLCV.base.CV.CV, metric: IMLCV.base.CV.CvMetric, powers)[source]#: Evaluate monomials, with exponents from powers, at x.

IMLCV.tools._rbfinterp_pythran._polynomial_matrix(x: IMLCV.base.CV.CV, powers, metric)[source]#: Return monomials, with exponents from powers, evaluated at x.

IMLCV.tools._rbfinterp_pythran._build_system(y: IMLCV.base.CV.CV, metric: IMLCV.base.CV.CvMetric, d, smoothing, kernel, epsilon, powers)[source]#

Build the system used to solve for the RBF interpolant coefficients.

Parameters:

y ((P, N) float ndarray) – Data point coordinates.
d ((P, S) float ndarray) – Data values at y.
smoothing ((P,) float ndarray) – Smoothing parameter for each data point.
kernel (str) – Name of the RBF.
epsilon (float) – Shape parameter.
powers ((R, N) int ndarray) – The exponents for each monomial in the polynomial.

Returns:

lhs ((P + R, P + R) float ndarray) – Left-hand side matrix.
rhs ((P + R, S) float ndarray) – Right-hand side matrix.
shift ((N,) float ndarray) – Domain shift used to create the polynomial matrix.
scale ((N,) float ndarray) – Domain scaling used to create the polynomial matrix.

IMLCV.tools._rbfinterp_pythran._build_evaluation_coefficients(x: IMLCV.base.CV.CV, y: IMLCV.base.CV.CV, metric: IMLCV.base.CV.CvMetric, kernel, epsilon, powers)[source]#

Construct the coefficients needed to evaluate the RBF.

Parameters:

x ((Q, N) float ndarray) – Evaluation point coordinates.
y ((P, N) float ndarray) – Data point coordinates.
kernel (str) – Name of the RBF.
epsilon (float) – Shape parameter.
powers ((R, N) int ndarray) – The exponents for each monomial in the polynomial.
shift ((N,) float ndarray) – Shifts the polynomial domain for numerical stability.
scale ((N,) float ndarray) – Scales the polynomial domain for numerical stability.

Return type:

(Q, P + R) float ndarray