Project: s41467-024-45514-6 | Function: stationary_distribution (python)

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**DESCRIPTION:** Estimate the stationary distribution using Dynamic Galerkin Approximation with memory terms for molecular dynamics simulations

**KEY TERMS:** {
  "basis": "basis functions for estimating the distribution",
  "weights": "weight of each frame",
  "lag": "maximum lag time",
  "mem": "number of memory terms",
  "coef": "projection coefficients",
  "mem_coef": "memory-correction coefficients"
}

**CONTEXT CODE:** """Estimate statistics from trajectories using DGA with memory."""

import numpy as np
import scipy as sp

from dgamem.stop import backward_stop, forward_stop

__all__ = [
    "stationary_distribution",
    "stationary_distribution_matrices",
    "stationary_distribution_projection",
    "stationary_distribution_solution",
    "forecast",
    "forecast_matrices",
    "forecast_projection",
    "forecast_solution",
    "aftcast",
    "aftcast_matrices",
    "aftcast_projection",
    "aftcast_solution",
    "solve",
]


def stationary_distribution(
    basis,
    weights,
    lag,
    mem,
    test_basis=None,
    *,
    return_projection=False,
    return_solution=True,
    return_coef=False,
    return_mem_coef=False,
):
    """
    Estimate the stationary distribution using DGA with memory.

    Parameters
    ----------
    basis : Sequence[NDArray[float] | SparseArray[float]], \
            shape=(n_trajs, n_frames[traj], n_basis)
        Basis for estimating the stationary distribution. Each basis
        function must have zero mean with respect to `weights`.
    weights : Sequence[NDArray[float]], shape=(n_trajs, n_frames[traj])
        Weight of each frame. The last `lag` frames of each trajectory
        must be zero.
    lag : int
        Maximum lag time in units of frames.
    mem : int
        Number of memory terms to use. These are evaluated at equally
        spaced times between time 0 and time `lag`, so `mem+1` must
        evenly divide `lag`. For example, with a `lag=32`, `mem=3` and
        `mem=7` are fine since 7+1=8 and 3+1=4 evenly divide 32. Setting
        `mem=0` corresponds to not using memory.
    test_basis : Sequence[NDArray[float] | SparseArray[float]], \
            shape=(n_trajs, n_frames[traj], n_basis), optional
        Test basis against which to minimize the error. Must have the
        same shape as `basis`. If `None`, use `basis`.
    return_projection : bool, optional
        If True, return the estimated projection.
    return_solution : bool, optional
        If True (default), return the estimated solution.
    return_coef : bool, optional
        If True, return the projection coefficients.
    return_mem_coef : bool, optional
        If True, return the memory-correction coefficients.

    Returns
    -------
    projection : Sequence[NDArray[float]], shape=(n_trajs, n_frames[traj])
        Estimate of the projected stationary distribution.
    solution : Sequence[NDArray[float]], shape=(n_trajs, n_frames[traj])
        Estimate of the stationary distribution.
    coef : NDArray[float], shape=(n_basis,)
        Projection coefficients.
    mem_coef : NDArray[float], shape=(mem, n_basis)
        Memory-correction coefficients.

    """
    # MASKED: Estimate the stationary distribution using Dynamic Galerkin Approximation with memory terms for molecular dynamics simulations implementation
    raise NotImplementedError("This function is masked for testing purposes.")


def stationary_distribution_matrices(
    basis, weights, lag, mem, test_basis=None
):
    """
    Compute matrices for estimating the stationary distribution using
    DGA with memory.

    Parameters
    ----------
    basis : Sequence[NDArray[float] | SparseArray[float]], \
            shape=(n_trajs, n_frames[traj], n_basis)
        Basis for estimating the stationary distribution. Each basis
        function must have zero mean with respect to `weights`.
    weights : Sequence[NDArray[float]], shape=(n_trajs, n_frames[traj])
        Weight of each frame. The last `lag` frames of each trajectory
        must be zero.
    lag : int
        Maximum lag time in units of frames.
    mem : int
        Number of memory terms to use. These are evaluated at equally
        spaced times between time 0 and time `lag`, so `mem+1` must
        evenly divide `lag`. For example, with a `lag=32`, `mem=3` and
        `mem=7` are fine since 7+1=8 and 3+1=4 evenly divide 32. Setting
        `mem=0` corresponds to not using memory.
    test_basis : Sequence[NDArray[float] | SparseArray[float]], \
            shape=(n_trajs, n_frames[traj], n_basis), optional
        Test basis against which to minimize the error. Must have the
        same shape as `basis`. If `None`, use `basis`.

    Returns
    -------
    a : NDArray[float], shape=(mem+1, n_basis, n_basis)
        Matrices for the homogeneous term.
    b : NDArray[float], shape=(mem+1, n_basis)
        Matrices for the nonhomogeneous term.
    c0 : NDArray[float], shape=(n_basis, n_basis)
        Matrix of inner products of basis functions.

    """


Complete the function implementation replacing "raise NotImplementedError".