pisces.math_utils.sampling.sample_from_pdf#
- pisces.math_utils.sampling.sample_from_pdf(x: ndarray, y: ndarray, num_particles: int) ndarray[source]#
Sample particle positions from a probability density function (PDF) defined at discrete positions.
This function first constructs a normalized cumulative distribution function (CDF) from the input PDF using the trapezoidal rule, and then uses inverse transform sampling to generate samples.
- Parameters:
x (
np.ndarray) – A strictly increasing 1D array representing the domain of the PDF.y (
np.ndarray) – A 1D array of the same length as x, containing the PDF values at each position. Values must be non-negative.num_particles (
int) – The number of samples to draw from the distribution.
- Returns:
A 1D array of shape (num_particles,) containing particle positions sampled from the input distribution.
- Return type:
np.ndarray- Raises:
ValueError – If inputs are not 1D arrays of the same length, if x is not strictly increasing, or if y contains negative values.
Notes
This function uses inverse transform sampling: it constructs a CDF via cumulative trapezoidal integration, normalizes it to [0, 1], and maps uniform random values through the inverse CDF (using linear interpolation).