Module molgri.analysis

Functions

def count_points_within_alpha(grid, central_vec: numpy.ndarray, alpha: float)

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def count_points_within_alpha(grid, central_vec: np.ndarray, alpha: float):
    grid_points = grid.get_grid()
    num_points = 0
    for point in grid_points:
        if vector_within_alpha(central_vec, point, alpha):
            num_points += 1
    return num_points

def random_axes_count_points(grid, alpha: float, num_random_points: int = 1000)

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def random_axes_count_points(grid, alpha: float, num_random_points: int = 1000):
    central_vectors = random_sphere_points(num_random_points)
    all_ratios = np.zeros(num_random_points)

    for i, central_vector in enumerate(central_vectors):
        num_within = count_points_within_alpha(grid, central_vector, alpha)
        all_ratios[i] = num_within/grid.N
    return all_ratios

def random_sphere_points(n: int = 1000) ‑> numpy.ndarray

Create n points that are truly randomly distributed across the sphere. Eg. to test the uniformity of your grid.

Args

n

number of points

Returns

an array of grid points, shape (n, 3)

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def random_sphere_points(n: int = 1000) -> np.ndarray:
    """
    Create n points that are truly randomly distributed across the sphere. Eg. to test the uniformity of your grid.

    Args:
        n: number of points

    Returns:
        an array of grid points, shape (n, 3)
    """
    phi = np.random.uniform(0, 2*pi, (n, 1))
    costheta = np.random.uniform(-1, 1, (n, 1))
    theta = np.arccos(costheta)

    x = np.sin(theta) * np.cos(phi)
    y = np.sin(theta) * np.sin(phi)
    z = np.cos(theta)
    return np.concatenate((x, y, z), axis=1)

def unit_dist_on_sphere(vector1: numpy.ndarray, vector2: numpy.ndarray) ‑> numpy.ndarray

Same as dist_on_sphere, but accepts and returns arrays and should only be used for already unitary vectors.

Args

vector1

vector shape (n1, d)

vector2

vector shape (n2, d)

Returns

an array the shape (n1, n2) containing distances between both sets of points on sphere

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def unit_dist_on_sphere(vector1: np.ndarray, vector2: np.ndarray) -> np.ndarray:
    """
    Same as dist_on_sphere, but accepts and returns arrays and should only be used for already unitary vectors.

    Args:
        vector1: vector shape (n1, d)
        vector2: vector shape (n2, d)

    Returns:
        an array the shape (n1, n2) containing distances between both sets of points on sphere
    """
    angle = np.arccos(np.clip(np.dot(vector1, vector2.T), -1.0, 1.0))  # in radians
    return angle

def unit_vector(vector)

Returns the unit vector of the vector.

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def unit_vector(vector):
    """ Returns the unit vector of the vector.  """
    return vector / np.linalg.norm(vector)

def vector_within_alpha(central_vec: numpy.ndarray, side_vector: numpy.ndarray, alpha: float)

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def vector_within_alpha(central_vec: np.ndarray, side_vector: np.ndarray, alpha: float):
    v1_u = unit_vector(central_vec)
    v2_u = unit_vector(side_vector)
    angle_vectors = np.arccos(np.clip(np.dot(v1_u, v2_u), -1.0, 1.0))
    return angle_vectors < alpha