dcegm.interpolation.interp1d

Functions

linear_interpolation_formula(y_high, y_low, x_high, ...)

Linear interpolation formula.

get_index_high_and_low(x, x_new)

Get index of the highest value in x that is smaller than x_new.

interp1d_policy_and_value_on_wealth(→ Tuple[float, float])

Interpolate policy and value function given a single wealth grid point.

interp_value_on_wealth(→ jax.numpy.ndarray | float)

Interpolate value function on a single wealth point.

interp_policy_on_wealth(→ float)

Interpolate policy function on a single wealth point.

interp_value_and_check_creditconstraint(...)

Calculate the interpolated value with accounting for a possible credit

Module Contents

dcegm.interpolation.interp1d.linear_interpolation_formula(y_high: float | jax.numpy.ndarray, y_low: float | jax.numpy.ndarray, x_high: float | jax.numpy.ndarray, x_low: float | jax.numpy.ndarray, x_new: float | jax.numpy.ndarray)

Linear interpolation formula.

dcegm.interpolation.interp1d.get_index_high_and_low(x, x_new)

Get index of the highest value in x that is smaller than x_new.

Parameters:

  • x (np.ndarray) – 1d array of shape (n,) containing the x-values.

  • x_new (float) – The new x-value at which to evaluate the interpolation function.

Returns:

Index of the value in the wealth grid which is higher than x_new. Or in

case of extrapolation last or first index of not nan element.

Return type:

int

dcegm.interpolation.interp1d.interp1d_policy_and_value_on_wealth(wealth: float | jax.numpy.ndarray, wealth_grid: jax.numpy.ndarray, policy_grid: jax.numpy.ndarray, value_grid: jax.numpy.ndarray, compute_utility: Callable, state_choice_vec: Dict[str, int], params: Dict[str, float], discount_factor) → Tuple[float, float]

Interpolate policy and value function given a single wealth grid point.

Parameters:

  • wealth (float | jnp.ndarray) – New wealth point(s) to interpolate.

  • wealth_grid (jnp.ndarray) – Solved endogenous wealth grid.

  • policy_grid (jnp.ndarray) – Solved policy function.

  • value_grid (jnp.ndarray) – Solved value function.

  • state_choice_vec (Dict) – Dictionary containing a single state and choice.

  • params (Dict) – Dictionary containing the model parameters.

Returns:

  • policy_interp (float): Interpolated optimal policy for wealth.

  • value_interp (float): Interpolated value for wealth.

Return type:

tuple

dcegm.interpolation.interp1d.interp_value_on_wealth(wealth: float | jax.numpy.ndarray, wealth_grid: jax.numpy.ndarray, value: jax.numpy.ndarray, compute_utility: Callable, state_choice_vec: Dict[str, int], params: Dict[str, float], discount_factor: float) → jax.numpy.ndarray | float

Interpolate value function on a single wealth point.

Parameters:

  • wealth (float) – New wealth point to interpolate.

  • wealth_grid (jnp.ndarray) – Solved endogenous wealth grid.

  • value (jnp.ndarray) – Solved value function.

  • state_choice_vec (Dict) – Dictionary containing a single state and choice.

  • params (Dict) – Dictionary containing the model parameters.

Returns:

Interpolated value for wealth.

Return type:

jnp.ndarray | float

dcegm.interpolation.interp1d.interp_policy_on_wealth(wealth: float | jax.numpy.ndarray, endog_grid: jax.numpy.ndarray, policy: jax.numpy.ndarray) → float

Interpolate policy function on a single wealth point.

Parameters:

  • wealth (float) – New wealth point to interpolate.

  • endog_grid (jnp.ndarray) – Solved endogenous wealth grid.

  • value (jnp.ndarray) – Solved value function.

  • state_choice_vec (Dict) – Dictionary containing a single state and choice.

  • params (Dict) – Dictionary containing the model parameters.

Returns:

Interpolated value for wealth.

Return type:

float

dcegm.interpolation.interp1d.interp_value_and_check_creditconstraint(value_high: float | jax.numpy.ndarray, wealth_high: float | jax.numpy.ndarray, value_low: float | jax.numpy.ndarray, wealth_low: float | jax.numpy.ndarray, new_wealth: float | jax.numpy.ndarray, compute_utility: Callable, endog_grid_min: float | jax.numpy.ndarray, value_at_zero_wealth: float | jax.numpy.ndarray, state_choice_vec: Dict[str, int], params: Dict[str, float], discount_factor: float) → float | jax.numpy.ndarray

Calculate the interpolated value with accounting for a possible credit constrained solution.

This function first calculates the interpolated value and then checks if we are in the credit constrained region, i.e. below endog_grid_min. If so, it returns the value as the sum of the utility when consumed all wealth and the discounted value at zero savings. Creditconstrained means it is optimal to consume all!

Parameters:

  • value_high (float) – Value function value at the higher end of the interpolation interval.

  • wealth_high (float) – Endogenous wealth grid value at the higher end of the interpolation interval.

  • value_low (float) – Value function value at the lower end of the interpolation interval.

  • wealth_low (float) – Endogenous wealth grid value at the lower end of the interpolation interval.

  • new_wealth (float) – New endogenous wealth grid value.

  • endog_grid_min (float) – Minimum endogenous wealth grid value.

  • value_at_zero_wealth (float) – The value at zero wealth.

  • state_choice_vec (Dict) – Dictionary containing a single state and choice.

  • params (dict) – Dictionary containing the model parameters.

Returns:

  • value_interp (float): Interpolated value function.

Return type:

tuple