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__init__.py
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__init__.py
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# Squarified Treemap Layout
# Implements algorithm from Bruls, Huizing, van Wijk, "Squarified Treemaps"
# (but not using their pseudocode)
# INTERNAL FUNCTIONS not meant to be used by the user
def pad_rectangle(rect):
if rect["dx"] > 2:
rect["x"] += 1
rect["dx"] -= 2
if rect["dy"] > 2:
rect["y"] += 1
rect["dy"] -= 2
def layoutrow(sizes, x, y, dx, dy):
# generate rects for each size in sizes
# dx >= dy
# they will fill up height dy, and width will be determined by their area
# sizes should be pre-normalized wrt dx * dy (i.e., they should be same units)
covered_area = sum(sizes)
width = covered_area / dy
rects = []
for size in sizes:
rects.append({"x": x, "y": y, "dx": width, "dy": size / width})
y += size / width
return rects
def layoutcol(sizes, x, y, dx, dy):
# generate rects for each size in sizes
# dx < dy
# they will fill up width dx, and height will be determined by their area
# sizes should be pre-normalized wrt dx * dy (i.e., they should be same units)
covered_area = sum(sizes)
height = covered_area / dx
rects = []
for size in sizes:
rects.append({"x": x, "y": y, "dx": size / height, "dy": height})
x += size / height
return rects
def layout(sizes, x, y, dx, dy):
return (
layoutrow(sizes, x, y, dx, dy) if dx >= dy else layoutcol(sizes, x, y, dx, dy)
)
def leftoverrow(sizes, x, y, dx, dy):
# compute remaining area when dx >= dy
covered_area = sum(sizes)
width = covered_area / dy
leftover_x = x + width
leftover_y = y
leftover_dx = dx - width
leftover_dy = dy
return (leftover_x, leftover_y, leftover_dx, leftover_dy)
def leftovercol(sizes, x, y, dx, dy):
# compute remaining area when dx >= dy
covered_area = sum(sizes)
height = covered_area / dx
leftover_x = x
leftover_y = y + height
leftover_dx = dx
leftover_dy = dy - height
return (leftover_x, leftover_y, leftover_dx, leftover_dy)
def leftover(sizes, x, y, dx, dy):
return (
leftoverrow(sizes, x, y, dx, dy)
if dx >= dy
else leftovercol(sizes, x, y, dx, dy)
)
def worst_ratio(sizes, x, y, dx, dy):
return max(
[
max(rect["dx"] / rect["dy"], rect["dy"] / rect["dx"])
for rect in layout(sizes, x, y, dx, dy)
]
)
# PUBLIC API
def squarify(sizes, x, y, dx, dy):
"""Compute treemap rectangles.
Given a set of values, computes a treemap layout in the specified geometry
using an algorithm based on Bruls, Huizing, van Wijk, "Squarified Treemaps".
See README for example usage.
Parameters
----------
sizes : list-like of numeric values
The set of values to compute a treemap for. `sizes` must be positive
values sorted in descending order and they should be normalized to the
total area (i.e., `dx * dy == sum(sizes)`)
x, y : numeric
The coordinates of the "origin".
dx, dy : numeric
The full width (`dx`) and height (`dy`) of the treemap.
Returns
-------
list[dict]
Each dict in the returned list represents a single rectangle in the
treemap. The order corresponds to the input order.
"""
sizes = list(map(float, sizes))
if len(sizes) == 0:
return []
if len(sizes) == 1:
return layout(sizes, x, y, dx, dy)
# figure out where 'split' should be
i = 1
while i < len(sizes) and worst_ratio(sizes[:i], x, y, dx, dy) >= worst_ratio(
sizes[: (i + 1)], x, y, dx, dy
):
i += 1
current = sizes[:i]
remaining = sizes[i:]
(leftover_x, leftover_y, leftover_dx, leftover_dy) = leftover(current, x, y, dx, dy)
return layout(current, x, y, dx, dy) + squarify(
remaining, leftover_x, leftover_y, leftover_dx, leftover_dy
)
def padded_squarify(sizes, x, y, dx, dy):
"""Compute padded treemap rectangles.
See `squarify` docstring for details. The only difference is that the
returned rectangles have been "padded" to allow for a visible border.
"""
rects = squarify(sizes, x, y, dx, dy)
for rect in rects:
pad_rectangle(rect)
return rects
def normalize_sizes(sizes, dx, dy):
"""Normalize list of values.
Normalizes a list of numeric values so that `sum(sizes) == dx * dy`.
Parameters
----------
sizes : list-like of numeric values
Input list of numeric values to normalize.
dx, dy : numeric
The dimensions of the full rectangle to normalize total values to.
Returns
-------
list[numeric]
The normalized values.
"""
total_size = sum(sizes)
total_area = dx * dy
sizes = map(float, sizes)
sizes = map(lambda size: size * total_area / total_size, sizes)
return list(sizes)
def plot(
sizes,
norm_x=100,
norm_y=100,
color=None,
label=None,
value=None,
ax=None,
pad=False,
bar_kwargs=None,
text_kwargs=None,
**kwargs
):
"""Plotting with Matplotlib.
Parameters
----------
sizes
input for squarify
norm_x, norm_y
x and y values for normalization
color
color string or list-like (see Matplotlib documentation for details)
label
list-like used as label text
value
list-like used as value text (in most cases identical with sizes argument)
ax
Matplotlib Axes instance
pad
draw rectangles with a small gap between them
bar_kwargs : dict
keyword arguments passed to matplotlib.Axes.bar
text_kwargs : dict
keyword arguments passed to matplotlib.Axes.text
**kwargs
Any additional kwargs are merged into `bar_kwargs`. Explicitly provided
kwargs here will take precedence.
Returns
-------
matplotlib.axes.Axes
Matplotlib Axes
"""
import matplotlib.pyplot as plt
if ax is None:
ax = plt.gca()
if color is None:
import matplotlib.cm
import random
cmap = matplotlib.cm.get_cmap()
color = [cmap(random.random()) for i in range(len(sizes))]
if bar_kwargs is None:
bar_kwargs = {}
if text_kwargs is None:
text_kwargs = {}
if len(kwargs) > 0:
bar_kwargs.update(kwargs)
normed = normalize_sizes(sizes, norm_x, norm_y)
if pad:
rects = padded_squarify(normed, 0, 0, norm_x, norm_y)
else:
rects = squarify(normed, 0, 0, norm_x, norm_y)
x = [rect["x"] for rect in rects]
y = [rect["y"] for rect in rects]
dx = [rect["dx"] for rect in rects]
dy = [rect["dy"] for rect in rects]
ax.bar(
x, dy, width=dx, bottom=y, color=color, label=label, align="edge", **bar_kwargs
)
if value is not None:
va = "center" if label is None else "top"
for v, r in zip(value, rects):
x, y, dx, dy = r["x"], r["y"], r["dx"], r["dy"]
ax.text(x + dx / 2, y + dy / 2, v, va=va, ha="center", **text_kwargs)
if label is not None:
va = "center" if value is None else "bottom"
for l, r in zip(label, rects):
x, y, dx, dy = r["x"], r["y"], r["dx"], r["dy"]
ax.text(x + dx / 2, y + dy / 2, l, va=va, ha="center", **text_kwargs)
ax.set_xlim(0, norm_x)
ax.set_ylim(0, norm_y)
return ax