dcegm.numerical_integration

Functions

quadrature_hermite(→ Tuple[numpy.ndarray, numpy.ndarray])

Return the Hermite quadrature points and weights.

quadrature_legendre(→ Tuple[jax.numpy.ndarray, ...)

Return the Gauss-Legendre quadrature points and weights.

Module Contents

dcegm.numerical_integration.quadrature_hermite(n_quad_points: int, income_shock_std: float) → Tuple[numpy.ndarray, numpy.ndarray]

Return the Hermite quadrature points and weights.

It is the specific quadrature rule for the normal distribution. As it produces different numeric results than in the original dcegm paper, we leave it out for now.

Parameters:

  • n_quad_points (int) – Number of quadrature points.

  • income_shock_std (float) – Standard deviation of the normal distribution.

Returns:

  • quad_points_scaled (np.ndarray): 1d array of shape (n_quad_points,)

    containing the Hermite quadrature points.

  • quad_weights (np.ndarray): 1d array of shape (n_quad_points,)

    containing the associated Hermite quadrature weights.

Return type:

tuple

dcegm.numerical_integration.quadrature_legendre(n_quad_points: int) → Tuple[jax.numpy.ndarray, jax.numpy.ndarray]

Return the Gauss-Legendre quadrature points and weights.

The stochastic Gauss-Legendre quadrature points are shifted points drawn from the [0, 1] interval.

Parameters:

  • n_quad_points (int) – Number of quadrature points.

  • income_shock_std (float) – Standard deviation of the normal distribution.

Returns:

  • quad_points_normal (np.ndarray): 1d array of shape (n_quad_points,)

    containing the Hermite quadrature points.

  • quad_weights (np.ndarray): 1d array of shape (n_quad_points,)

    containing the associated stochastic quadrature weights.

Return type:

tuple