leniax.kernel_functions package

leniax.kernel_functions.poly_quad(params, X)[source]

Quadratic polynomial

\[y = (q * X * (1 - X))^q\]

(Source code, png, hires.png, pdf)

_images/leniax-kernel_functions-1.png
Parameters

  • params (jax._src.numpy.ndarray.ndarray) – Kernel function parameters

  • X (jax._src.numpy.ndarray.ndarray) – Raw kernel

leniax.kernel_functions.gauss_bump(params, X)[source]

Gaussian bump function

\[y = e^{q * [q - \frac{1}{X * (1 - X)}]}\]

(Source code, png, hires.png, pdf)

_images/leniax-kernel_functions-2.png
Parameters

  • params (jax._src.numpy.ndarray.ndarray) – Kernel function parameters

  • X (jax._src.numpy.ndarray.ndarray) – Raw kernel

leniax.kernel_functions.gauss(params, X)[source]

Gauss function

\[y = e^{-\frac{1}{2} \left(\frac{X - q}{0.3 * q}\right)^2}\]

(Source code, png, hires.png, pdf)

_images/leniax-kernel_functions-3.png
Parameters

  • params (jax._src.numpy.ndarray.ndarray) – Kernel function parameters

  • X (jax._src.numpy.ndarray.ndarray) – Raw kernel

leniax.kernel_functions.step(params, X)[source]

Step function

\[\begin{split}y = \begin{cases} 1 ,& \text{if } X \geq q \text{ and } X \leq 1 - q\\ 0 ,& \text{otherwise} \end{cases}\end{split}\]

(Source code, png, hires.png, pdf)

_images/leniax-kernel_functions-4.png
Parameters

  • params (jax._src.numpy.ndarray.ndarray) – Kernel function parameters

  • X (jax._src.numpy.ndarray.ndarray) – Raw kernel

leniax.kernel_functions.staircase(params, X)[source]

Staircase function

\[\begin{split}y = \begin{cases} 0.5 ,& \text{if } X \geq m - s \text{ and } X < m - \frac{s}{2}\\ 1 ,& \text{if } X \geq m - \frac{s}{2} \text{ and } X \leq m + \frac{s}{2}\\ 0.5 ,& \text{if } X > m + \frac{s}{2} \text{ and } X \leq m + s\\ 0 ,& \text{otherwise} \end{cases}\end{split}\]

(Source code, png, hires.png, pdf)

_images/leniax-kernel_functions-5.png
Parameters

  • params (jax._src.numpy.ndarray.ndarray) – Kernel function parameters

  • X (jax._src.numpy.ndarray.ndarray) – Raw kernel

leniax.kernel_functions.triangle(params, X)[source]

Gauss function

\[\begin{split}y = \begin{cases} \frac{X - (m - s)}{m - (m - s)} ,& \text{if } X \geq m - s \text{ and } X < m\\ \frac{X - (m + s)}{m - (m + s)} ,& \text{if } X \geq m \text{ and } X \leq m + s\\ 0 ,& \text{otherwise} \end{cases}\end{split}\]

(Source code, png, hires.png, pdf)

_images/leniax-kernel_functions-6.png
Parameters

  • params (jax._src.numpy.ndarray.ndarray) – Kernel function parameters

  • X (jax._src.numpy.ndarray.ndarray) – Raw kernel