Quadtree

Classes for all astroQTpy quadtree types.

class astroqtpy.quadtree.Chi2QuadTree(x_min: float, x_max: float, y_min: float, y_max: float, data: ndarray, model_func: callable, weights: ndarray = None, max_chi2: float = 10, split_threshold: float = 0.2, node_statistic: str = 'mean', N_points: int = 20, min_depth: int = 3, max_depth: int = 6, N_proc: int = 1, verbose: bool = False, filename_points: str = 'points.txt', filename_nodes: str = 'nodes.txt', overwrite: bool = False)

Chi2 quadtree.

A quadtree class for mapping 2-parameter reduced \(\chi^2\) values.

\[\chi^2_r = \frac{\chi^2}{\nu}\]

where \(\nu\) is the number of degrees of freedom and

\[\chi^2 = \sum_{i=0}^{N-1} \frac{\Big(y_i - f(x_i | a, b)\Big)^2}{\sigma_i^2}\]

Note

The model_func argument must be callable and take two arguments: x_data and parameters (a, b). It must return a single float value y. For example:

def my_model(x, parameters):
    a, b = parameters  # unpack parameters

    # ... do something ...
    y = a * x + b

    return y

See tutorials for more examples.

Parameters:

  • x_min (float) – Minimum x value (param a) for this quadtree.

  • x_max (float) – Maximum x value (param a)for this quadtree.

  • y_min (float) – Minimum y value (param b)for this quadtree.

  • y_max (float) – Maximum y value (param b)for this quadtree.

  • data (np.ndarray) – Data array. Must have shape (2, N).

  • model_func (callable) – Function \(f(x | a, b)\) to calculate a model to compare to data.

  • weights (np.ndarray, optional) – Data weights, typically expressed as \(1/\sigma^2\). Defaults to None.

  • max_chi2 (float, optional) – Largest permitted reduced \(\chi^2\). Defaults to 10.

  • split_threshold (float, optional) – Threshold discrepancy in order to split nodes. Defaults to 0.2.

  • node_statistic (str, optional) – Statistic to compute node values [‘count’, ‘mean’, ‘std’, or ‘median’]. Defaults to ‘mean’.

  • N_points (int, optional) – Maximum number of points per node. Defaults to 20.

  • min_depth (int, optional) – Minimum quadtree depth. Defaults to 3.

  • max_depth (int, optional) – Maximum quadtree depth. Defaults to 6.

  • N_proc (int, optional) – Number of cores for multiprocessing. Defaults to 1.

  • verbose (bool, optional) – Option to print node values in real time. Defaults to False.

  • filename_points (str, optional) – Name of output file to save points. Defaults to ‘points.txt’.

  • filename_nodes (str, optional) – Name of output file to save nodes. Defaults to ‘nodes.txt’.

  • overwrite (bool, optional) – Option to automatically overwrite previously saved results. Defaults to False.

draw_tree(ax: Axes, cmap: str = 'RdYlGn_r', vmin: float = None, vmax: float = None, show_colors: bool = True, show_lines: bool = True, show_points: bool = False, show_values: bool = False) → ScalarMappable

Draw quadtree.

Plot the entire quadtree on a given axis.

Parameters:

  • ax (matplotlib.axes.Axes) – Matplotlib axis for plotting.

  • cmap (str, optional) – Matplotlib colormap. Defaults to ‘RdYlGn_r’.

  • vmin (float, optional) – Minimum value for colorbar. Defaults to None.

  • vmax (float, optional) – Maximum value for colorbar. Defaults to None.

  • show_colors (bool, optional) – Option to show node colors. Defaults to True.

  • show_lines (bool, optional) – Option to plot node boundary lines. Defaults to True.

  • show_points (bool, optional) – Option to plot node points. Defaults to False.

  • show_values (bool, optional) – Option to print node values on plot. Defaults to False.

Returns:

Matplotlib ScalarMappable.

Return type:

matplotlib.cm.ScalarMappable

evaluate_multiple_points(node: QuadNode, N_points: int) → None

Evaulate multiple points.

Evaluate multiple points contained within a given node in parallel.

Parameters:

  • node (QuadNode) – Node in which to evaulate points.

  • N_points (int) – Maximum number of points to evaulate within this node.

evaluate_point(node: QuadNode, rng_seed: int = 123456) → QuadPoint

Evaluate point.

Calculate the value of one point within a given node.

Parameters:

  • node (QuadNode) – Quadtree node in which to evaulate point.

  • rng_seed (int, optional) – Random number generator seed. Defaults to 123456.

Returns:

A QuadPoint object.

Return type:

QuadPoint

fill(node: QuadNode, N_points: int) → None

Fill.

Fill a given node with points.

Parameters:

  • node (QuadNode) – The quadtree node to be filled.

  • N_points (int) – Number of points to put inside this node.

get_chi2_min() → QuadPoint

Get chi^2 min.

Get the point with the smallest reduced chi^2 value.

Returns:

Quadtree point with least chi^2.

Return type:

QuadPoint

load_points() → None

Load points.

Load all points from a previously saved quadtree.

print_all_nodes() → None

Print all nodes.

Print all current quadtree node values to a file (‘filename_nodes’).

print_all_points() → None

Print all points.

Print all current quadtree points to a file (‘filename_points’).

run_quadtree() → None

Run quadtree.

Run the quadtree from a previously saved run, or start a new run.

squeeze_node(node: QuadNode) → None

Squeeze node.

Distribute quadtree points from parent to children.

class astroqtpy.quadtree.Hist2dQuadTree(x_min: float, x_max: float, y_min: float, y_max: float, node_statistic: str = 'count', N_points: int = 20, min_depth: int = 3, max_depth: int = 6)

2D histogram quadtree.

A class for creating a 2D histogram quadtree given some data.

Parameters:

  • x_min (float) – Minimum x value for this quadtree.

  • x_max (float) – Maximum x value for this quadtree.

  • y_min (float) – Minimum y value for this quadtree.

  • y_max (float) – Maximum y value for this quadtree.

  • node_statistic (str, optional) – Statistic to compute node values [‘count’, ‘mean’, ‘std’, or ‘median’]. Defaults to ‘count’.

  • N_points (int, optional) – Maximum number of points per node. Defaults to 20.

  • min_depth (int, optional) – Minimum quadtree depth. Defaults to 3.

  • max_depth (int, optional) – Maximum quadtree depth. Defaults to 6.

add_data(x: ndarray, y: ndarray, z: ndarray = None)

Add data.

Add x, y, and z (optional) data to this quadtree object to create a histogram.

Parameters:

  • x (np.ndarray) – x data array.

  • y (np.ndarray) – y data array. Must have same length as x.

  • z (np.ndarray, optional) – z data array. Must have same length as x. Defaults to None.

draw_tree(ax: Axes, cmap: str = 'RdYlGn_r', vmin: float = None, vmax: float = None, show_colors: bool = True, show_lines: bool = True, show_points: bool = False, show_values: bool = False) → ScalarMappable

Draw quadtree.

Plot the entire quadtree on a given axis.

Parameters:

  • ax (matplotlib.axes.Axes) – Matplotlib axis for plotting.

  • cmap (str, optional) – Matplotlib colormap. Defaults to ‘RdYlGn_r’.

  • vmin (float, optional) – Minimum value for colorbar. Defaults to None.

  • vmax (float, optional) – Maximum value for colorbar. Defaults to None.

  • show_colors (bool, optional) – Option to show node colors. Defaults to True.

  • show_lines (bool, optional) – Option to plot node boundary lines. Defaults to True.

  • show_points (bool, optional) – Option to plot node points. Defaults to False.

  • show_values (bool, optional) – Option to print node values on plot. Defaults to False.

Returns:

Matplotlib ScalarMappable.

Return type:

matplotlib.cm.ScalarMappable

evaluate_multiple_points(node: QuadNode, N_points: int) → None

Evaulate multiple points.

Evaluate multiple points contained within a given node in parallel.

Parameters:

  • node (QuadNode) – Node in which to evaulate points.

  • N_points (int) – Maximum number of points to evaulate within this node.

evaluate_point(node: QuadNode, rng_seed: int = 123456) → QuadPoint

Evaluate point.

Method not needed here.

fill(node: QuadNode, N_points: int) → None

Fill.

Fill a given node with points.

Parameters:

  • node (QuadNode) – The quadtree node to be filled.

  • N_points (int) – Number of points to put inside this node.

load_points() → None

Load points.

Load all points from a previously saved quadtree.

print_all_nodes() → None

Print all nodes.

Print all current quadtree node values to a file (‘filename_nodes’).

print_all_points() → None

Print all points.

Print all current quadtree points to a file (‘filename_points’).

run_quadtree() → None

Run quadtree.

Run the quadtree from a previously saved run, or start a new run.

squeeze_node(node: QuadNode) → None

Squeeze node.

Distribute quadtree points from parent to children.

class astroqtpy.quadtree.NbodyQuadTree(x_min: float, x_max: float, y_min: float, y_max: float, simulation_func: callable, split_threshold: float = 0.2, node_statistic: str = 'mean', N_points: int = 20, min_depth: int = 3, max_depth: int = 6, N_proc: int = 1, verbose: bool = False, filename_points: str = 'points.txt', filename_nodes: str = 'nodes.txt', overwrite: bool = False)

Nbody quadtree.

A class for creating a quadtree for running N-body simulations.

Note

The simulation_func argument must be callable and take a single argument (x, y). It must return a single float value. For example:

def my_function(parameters):
    x, y = parameters  # unpack parameters

    # ... do something ...
    number = float(1)

    return number

See tutorials for more examples.

Parameters:

  • x_min (float) – Minimum x value for this quadtree.

  • x_max (float) – Maximum x value for this quadtree.

  • y_min (float) – Minimum y value for this quadtree.

  • y_max (float) – Maximum y value for this quadtree.

  • simulation_func (callable) – Function to calculate the outcome of an Nbody simulation.

  • split_threshold (float, optional) – Threshold discrepancy in order to split nodes. Defaults to 0.2.

  • node_statistic (str, optional) – Statistic to compute node values [‘count’, ‘mean’, ‘std’, or ‘median’]. Defaults to ‘mean’.

  • N_points (int, optional) – Maximum number of points per node. Defaults to 20.

  • min_depth (int, optional) – Minimum quadtree depth. Defaults to 3.

  • max_depth (int, optional) – Maximum quadtree depth. Defaults to 6.

  • N_proc (int, optional) – Number of cores for multiprocessing. Defaults to 1.

  • verbose (bool, optional) – Option to print node values in real time. Defaults to False.

  • filename_points (str, optional) – Name of output file to save points. Defaults to ‘points.txt’.

  • filename_nodes (str, optional) – Name of output file to save nodes. Defaults to ‘nodes.txt’.

  • overwrite (bool, optional) – Option to automatically overwrite previously saved results. Defaults to False.

draw_tree(ax: Axes, cmap: str = 'RdYlGn_r', vmin: float = None, vmax: float = None, show_colors: bool = True, show_lines: bool = True, show_points: bool = False, show_values: bool = False) → ScalarMappable

Draw quadtree.

Plot the entire quadtree on a given axis.

Parameters:

  • ax (matplotlib.axes.Axes) – Matplotlib axis for plotting.

  • cmap (str, optional) – Matplotlib colormap. Defaults to ‘RdYlGn_r’.

  • vmin (float, optional) – Minimum value for colorbar. Defaults to None.

  • vmax (float, optional) – Maximum value for colorbar. Defaults to None.

  • show_colors (bool, optional) – Option to show node colors. Defaults to True.

  • show_lines (bool, optional) – Option to plot node boundary lines. Defaults to True.

  • show_points (bool, optional) – Option to plot node points. Defaults to False.

  • show_values (bool, optional) – Option to print node values on plot. Defaults to False.

Returns:

Matplotlib ScalarMappable.

Return type:

matplotlib.cm.ScalarMappable

evaluate_multiple_points(node: QuadNode, N_points: int) → None

Evaulate multiple points.

Evaluate multiple points contained within a given node in parallel.

Parameters:

  • node (QuadNode) – Node in which to evaulate points.

  • N_points (int) – Maximum number of points to evaulate within this node.

evaluate_point(node: QuadNode, rng_seed: int = 123456) → QuadPoint

Evaluate point.

Calculate the value of one point within a given node from an N-body simulation.

Parameters:

  • node (QuadNode) – Quadtree node in which to evaulate point.

  • rng_seed (int, optional) – Random number generator seed. Defaults to 123456.

Returns:

A QuadPoint object.

Return type:

QuadPoint

fill(node: QuadNode, N_points: int) → None

Fill.

Fill a given node with points.

Parameters:

  • node (QuadNode) – The quadtree node to be filled.

  • N_points (int) – Number of points to put inside this node.

load_points() → None

Load points.

Load all points from a previously saved quadtree.

print_all_nodes() → None

Print all nodes.

Print all current quadtree node values to a file (‘filename_nodes’).

print_all_points() → None

Print all points.

Print all current quadtree points to a file (‘filename_points’).

run_quadtree() → None

Run quadtree.

Run the quadtree from a previously saved run, or start a new run.

squeeze_node(node: QuadNode) → None

Squeeze node.

Distribute quadtree points from parent to children.

class astroqtpy.quadtree.RandomQuadTree(x_min: float, x_max: float, y_min: float, y_max: float, split_threshold: float = 0.2, node_statistic: str = 'mean', N_points: int = 20, min_depth: int = 3, max_depth: int = 6, N_proc: int = 1, verbose: bool = False, filename_points: str = 'points.txt', filename_nodes: str = 'nodes.txt', overwrite: bool = False)

Random quadtree.

A class for creating a quadtree with randomly sampled points.

Parameters:

  • x_min (float) – Minimum x value for this quadtree.

  • x_max (float) – Maximum x value for this quadtree.

  • y_min (float) – Minimum y value for this quadtree.

  • y_max (float) – Maximum y value for this quadtree.

  • split_threshold (float, optional) – Threshold discrepancy in order to split nodes. Defaults to 0.2.

  • node_statistic (str, optional) – Statistic to compute node values [‘count’, ‘mean’, ‘std’, or ‘median’]. Defaults to ‘mean’.

  • N_points (int, optional) – Maximum number of points per node. Defaults to 20.

  • min_depth (int, optional) – Minimum quadtree depth. Defaults to 3.

  • max_depth (int, optional) – Maximum quadtree depth. Defaults to 6.

  • N_proc (int, optional) – Number of cores for multiprocessing. Defaults to 1.

  • verbose (bool, optional) – Option to print node values in real time. Defaults to False.

  • filename_points (str, optional) – Name of output file to save points. Defaults to ‘points.txt’.

  • filename_nodes (str, optional) – Name of output file to save nodes. Defaults to ‘nodes.txt’.

  • overwrite (bool, optional) – Option to automatically overwrite previously saved results. Defaults to False.

draw_tree(ax: Axes, cmap: str = 'RdYlGn_r', vmin: float = None, vmax: float = None, show_colors: bool = True, show_lines: bool = True, show_points: bool = False, show_values: bool = False) → ScalarMappable

Draw quadtree.

Plot the entire quadtree on a given axis.

Parameters:

  • ax (matplotlib.axes.Axes) – Matplotlib axis for plotting.

  • cmap (str, optional) – Matplotlib colormap. Defaults to ‘RdYlGn_r’.

  • vmin (float, optional) – Minimum value for colorbar. Defaults to None.

  • vmax (float, optional) – Maximum value for colorbar. Defaults to None.

  • show_colors (bool, optional) – Option to show node colors. Defaults to True.

  • show_lines (bool, optional) – Option to plot node boundary lines. Defaults to True.

  • show_points (bool, optional) – Option to plot node points. Defaults to False.

  • show_values (bool, optional) – Option to print node values on plot. Defaults to False.

Returns:

Matplotlib ScalarMappable.

Return type:

matplotlib.cm.ScalarMappable

evaluate_multiple_points(node: QuadNode, N_points: int) → None

Evaulate multiple points.

Evaluate multiple points contained within a given node in parallel.

Parameters:

  • node (QuadNode) – Node in which to evaulate points.

  • N_points (int) – Maximum number of points to evaulate within this node.

evaluate_point(node: QuadNode, rng_seed: int = 123456) → QuadPoint

Evaluate point.

Calculate the value of one point within a given node as either 1 or 0.

Parameters:

  • node (QuadNode) – Quadtree node in which to evaulate point.

  • rng_seed (int, optional) – Random number generator seed. Defaults to 123456.

Returns:

A QuadPoint object.

Return type:

QuadPoint

fill(node: QuadNode, N_points: int) → None

Fill.

Fill a given node with points.

Parameters:

  • node (QuadNode) – The quadtree node to be filled.

  • N_points (int) – Number of points to put inside this node.

load_points() → None

Load points.

Load all points from a previously saved quadtree.

print_all_nodes() → None

Print all nodes.

Print all current quadtree node values to a file (‘filename_nodes’).

print_all_points() → None

Print all points.

Print all current quadtree points to a file (‘filename_points’).

run_quadtree() → None

Run quadtree.

Run the quadtree from a previously saved run, or start a new run.

squeeze_node(node: QuadNode) → None

Squeeze node.

Distribute quadtree points from parent to children.