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from __future__ import annotations
from abc import abstractmethod
from enum import Enum
import io
from typing import TYPE_CHECKING, Any, Literal, cast
import matplotlib.pyplot as plt
import numpy as np
from contourpy import FillType, LineType, contour_generator
if TYPE_CHECKING:
from collections.abc import Sequence
from matplotlib.axes import Axes
from matplotlib.figure import Figure
from contourpy._contourpy import (
CoordinateArray,
FillReturn_OuterCode,
LineReturn_SeparateCode,
MaskArray,
)
class PointType(Enum):
CORNER = 0
LOWER = 1
UPPER = 2
class Corner(Enum):
NW = 1
NE = 0
SW = 3
SE = 2
class Config:
corner_mask: bool
name: str
quad_as_tri: bool
show_text: bool
arrowsize: float
axes: Sequence[Axes] # Set in derived classes.
axes_index: int
fill_alpha: float
fig: Figure | None # Set in derived classes.
fontsize: float
gap: float
grid_kwargs: dict[str, Any]
mask: MaskArray | Literal[False]
marker_size: float
text_gap: float
title_fontsize: float
x: CoordinateArray
y: CoordinateArray
def __init__(
self, name: str, corner_mask: bool, quad_as_tri: bool, show_text: bool,
) -> None:
self.name = name
self.corner_mask = corner_mask
self.quad_as_tri = quad_as_tri
self.show_text = show_text
self.arrowsize = 0.1
self.fontsize = 8
self.title_fontsize = 8
self.marker_size = 3.5
self.gap = 0.1
self.text_gap = self.gap/2
self.grid_kwargs = {"color": "gray", "linewidth": 0.35}
self.fill_alpha = 0.2
self.x, self.y = np.meshgrid([0.0, 1.0], [0.0, 1.0])
self.mask = False
import matplotlib as mpl
mpl.use("Agg")
def __del__(self) -> None:
self.clear()
def _arrow(
self, ax: Axes, line_start: CoordinateArray, line_end: CoordinateArray, color: str,
) -> None:
mid = 0.5*(line_start + line_end)
along = line_end - line_start
along /= np.sqrt(np.dot(along, along)) # Unit vector.
right = np.asarray((along[1], -along[0]))
arrow = np.stack((
mid - (along*0.5 - right)*self.arrowsize,
mid + along*0.5*self.arrowsize,
mid - (along*0.5 + right)*self.arrowsize))
ax.plot(arrow[:, 0], arrow[:, 1], "-", c=color)
@abstractmethod
def _decode_config(self, config: int, corner: Corner | None = None) -> tuple[int | None, ...]:
pass
@abstractmethod
def _quad_lines(
self,
ax: Axes,
z: np.ma.MaskedArray[Any, Any],
zlower: float,
zupper: float,
corner: Corner | None,
) -> None:
pass
def _next_quad(
self,
config: int,
corner: Corner | None = None,
suffix: str = "",
set_0: float = 0,
set_1: float = 1,
set_2: float = 2,
) -> None:
zlower = 0.5
zupper = 1.5
ax = self.axes[self.axes_index]
nw, ne, sw, se = self._decode_config(config, corner)
# Quad edge.
ax.axis("off")
if corner is None:
ax.plot([0, 1, 1, 0, 0], [0, 0, 1, 1, 0], **self.grid_kwargs)
if self.quad_as_tri and not nw == ne == sw == se:
ax.plot([0, 1], [0, 1], [0, 1], [1, 0], **self.grid_kwargs)
title = f"{nw}{ne}{sw}{se}={config}{suffix}"
elif corner == Corner.NW:
ax.plot([0, 1, 0, 0], [0, 1, 1, 0], **self.grid_kwargs)
title = f"{nw}{ne}{sw}={config}{suffix}"
elif corner == Corner.NE:
ax.plot([1, 1, 0, 1], [0, 1, 1, 0], **self.grid_kwargs)
title = f"{nw}{ne}{se}={config}{suffix}"
elif corner == Corner.SW:
ax.plot([0, 1, 0, 0], [0, 0, 1, 0], **self.grid_kwargs)
title = f"{nw}{sw}{se}={config}{suffix}"
elif corner == Corner.SE:
ax.plot([0, 1, 1, 0], [0, 0, 1, 0], **self.grid_kwargs)
title = f"{ne}{sw}{se}={config}{suffix}"
else:
raise RuntimeError("Invalid corner")
if self.show_text:
ax.set_title(title, size=self.title_fontsize)
# Axes bounds include gap for arrows and corner points.
ax.set_xlim(-self.gap, 1.0+self.gap)
ax.set_ylim(-self.gap, 1.0+self.gap)
if self.show_text:
# Text for corner and optional middle z-levels.
fontsize = self.fontsize
if corner != Corner.NW:
ax.text(1+self.text_gap, 0, str(se), va="center", size=fontsize, ha="left")
if corner != Corner.SW:
ax.text(1+self.text_gap, 1, str(ne), va="center", size=fontsize, ha="left")
if corner != Corner.NE:
ax.text(-self.text_gap, 0, str(sw), va="center", size=fontsize, ha="right")
if corner != Corner.SE:
ax.text(-self.text_gap, 1, str(nw), va="center", size=fontsize, ha="right")
if suffix: # Suffix (without brackets) is the z-level of quad middle.
ax.text(0.5, 0.5, suffix[1:-1], va="center", size=fontsize, ha="center")
lookup = {0: set_0, 1: set_1, 2: set_2, None: None}
z_nw = lookup[nw]
z_ne = lookup[ne]
z_sw = lookup[sw]
z_se = lookup[se]
z = np.asarray([[z_sw, z_se], [z_nw, z_ne]], dtype=np.float64)
z_masked = np.ma.array(z, mask=self.mask) # type: ignore[no-untyped-call]
if suffix:
zmean = z.mean()
if suffix == "(0)":
if zmean > zlower:
raise RuntimeError(
f"Inconsistent zlower {zlower} for config {config}{suffix} with middle_z "
f"{zmean}")
elif suffix in ["(1)", "(>0)", "(<2)"]:
if zmean < zlower:
raise RuntimeError(
f"Inconsistent zlower {zlower} for config {config}{suffix} with middle_z "
f"{zmean}")
elif zmean > zupper:
raise RuntimeError(
f"Inconsistent zupper {zupper} for config {config}{suffix} with middle_z "
f"{zmean}")
elif suffix == "(2)":
if zmean < zupper:
raise RuntimeError(
f"Inconsistent zupper {zupper} for config {config}{suffix} with middle_z "
f"{zmean}")
else:
raise RuntimeError(f"Unexpected suffix {suffix} for config {config}")
self._quad_lines(ax, z_masked, zlower, zupper, corner)
self.axes_index += 1
def _set_mask(self, corner: Corner | None) -> None:
if corner is None:
self.mask = False
else:
self.mask = np.zeros(4, dtype=bool)
self.mask[corner.value] = True
self.mask.reshape((2, 2))
def clear(self) -> None:
if self.fig:
self.axes = []
plt.close(self.fig)
self.fig = None
def save_to_buffer(self) -> io.BytesIO:
if not self.fig:
raise RuntimeError("self.fig not set")
buf = io.BytesIO()
self.fig.savefig(buf, format="png")
buf.seek(0)
return buf
def save_to_file(self, filename: str) -> None:
if not self.fig:
raise RuntimeError("self.fig not set")
self.fig.savefig(filename)
class ConfigFilledCommon(Config):
def __init__(self, name: str, corner_mask: bool, quad_as_tri: bool, show_text: bool) -> None:
super().__init__(name, corner_mask, quad_as_tri, show_text)
def _decode_config(self, config: int, corner: Corner | None = None) -> tuple[int | None, ...]:
if corner is None:
nw = (config >> 6) & 0x3
ne = (config >> 4) & 0x3
sw = (config >> 2) & 0x3
se = config & 0x3
else:
a = (config >> 4) & 0x3
b = (config >> 2) & 0x3
c = config & 0x3
if corner == Corner.NW:
[nw, ne, sw, se] = [a, b, c, None]
elif corner == Corner.NE:
[nw, ne, sw, se] = [a, b, None, c]
elif corner == Corner.SW:
[nw, ne, sw, se] = [a, None, b, c]
else: # Corner.SE
[nw, ne, sw, se] = [None, a, b, c]
if nw == 3 or ne == 3 or sw == 3 or se == 3:
raise ValueError(f"Invalid config {config}")
return nw, ne, sw, se
def _quad_lines(
self,
ax: Axes,
z: np.ma.MaskedArray[Any, Any],
zlower: float,
zupper: float,
corner: Corner | None,
) -> None:
cont_gen = contour_generator(
self.x, self.y, z, name=self.name, corner_mask=self.corner_mask,
quad_as_tri=self.quad_as_tri, fill_type=FillType.OuterCode)
filled = cont_gen.filled(zlower, zupper)
assert cont_gen.fill_type == FillType.OuterCode
if TYPE_CHECKING:
filled = cast(FillReturn_OuterCode, filled)
lines = filled[0]
# May be 0..2 polygons, and there cannot be any holes.
for points in lines:
n = len(points)
ax.fill(points[:, 0], points[:, 1], c="C2", alpha=self.fill_alpha, ec=None)
# Classify points, either corner, lower level or upper level.
point_types = np.empty(n, dtype=PointType)
for i in range(n-1):
xy = points[i]
x_on_quad_edge = (xy[0] in (0.0, 1.0))
y_on_quad_edge = (xy[1] in (0.0, 1.0))
if x_on_quad_edge and y_on_quad_edge:
point_types[i] = PointType.CORNER
elif corner is not None or x_on_quad_edge or y_on_quad_edge:
if (self._interp(z, xy[0], xy[1], corner) < 0.5*(zlower + zupper)):
point_types[i] = PointType.LOWER
else:
point_types[i] = PointType.UPPER
else:
# Point on quad diagonal from middle point, so same type as previous point.
point_types[i] = point_types[i-1]
# End point is the same as the start point.
point_types[-1] = point_types[0]
# Draw lines.
for i in range(n-1):
s = points[i]
e = points[i+1]
c = "C2"
if point_types[i] == point_types[i+1] and point_types[i] != PointType.CORNER:
c = "C3" if point_types[i] == PointType.LOWER else "C0"
ax.plot([s[0], e[0]], [s[1], e[1]], "-", c=c)
# Arrows on boundary and contour levels (the latter only if not quad_as_tri).
if point_types[i] == point_types[i+1] and (
point_types[i] == PointType.CORNER or not self.quad_as_tri):
self._arrow(ax, s, e, c)
# Arrows on contour levels (lower and upper) for quad_as_tri. Only want a single
# arrow on each line strip, so find and use the longest line segment. Care needed
# identifying the longest due to rounding error, so find all segments within a small
# length of the longest and take the max index of these.
if self.quad_as_tri:
for point_type in [PointType.LOWER, PointType.UPPER]:
mask = np.equal(point_types, point_type) # type: ignore[call-overload]
start_indices = np.nonzero(np.logical_and(mask[1:], ~mask[:-1]))[0]
for start_index in start_indices:
start_index = (start_index + 1) % (n-1)
# Roll point_types array so start segment of line strip is at front.
rolled = np.roll(point_types[:-1], -start_index)
end_offset = np.nonzero(rolled != point_type)[0][0]
pts = points[start_index:start_index+end_offset] # Line strip points.
diff = np.diff(pts, axis=0)
lengths = np.sum(np.square(diff), axis=1) # Segment lengths.
offset = np.nonzero(lengths > lengths.max() - 1e-6)[0].max()
i = (start_index + offset) % (n-1)
c = "C3" if point_type == PointType.LOWER else "C0"
self._arrow(ax, points[i], points[i+1], c)
# Draw markers.
for i in range(n-1):
if point_types[i] != PointType.CORNER:
c = "C3" if point_types[i] == PointType.LOWER else "C0"
ax.plot(points[i][0], points[i][1], "o", c=c, ms=self.marker_size)
def _interp(
self,
zquad: CoordinateArray,
x: CoordinateArray,
y: CoordinateArray,
corner: Corner | None = None,
) -> float:
# Interpolate zquad to determine value of z at (x, y). Could use
# scipy.interp2d for this, but do not want scipy as a dependency just
# for this.
# (x, y) must lie on one of the edges of the quad.
# zquad[0,0] = sw, zquad[0,1] = se, zquad[1,0] = nw, zquad[1,1] = ne
ret: float
if x == 0.0:
ret = zquad[0, 0]*(1.0-y) + zquad[1, 0]*y
elif x == 1.0:
ret = zquad[0, 1]*(1.0-y) + zquad[1, 1]*y
elif y == 0.0:
ret = zquad[0, 0]*(1.0-x) + zquad[0, 1]*x
elif y == 1.0:
ret = zquad[1, 0]*(1.0-x) + zquad[1, 1]*x
else:
# corner is not None
if corner in (Corner.NW, Corner.SE):
ret = zquad[0, 0]*(1.0-y) + zquad[1, 1]*y
else:
ret = zquad[0, 1]*(1.0-y) + zquad[1, 0]*y
return ret
class ConfigFilled(ConfigFilledCommon):
def __init__(self, name: str, quad_as_tri: bool = False, show_text: bool = True) -> None:
super().__init__(name, False, quad_as_tri, show_text)
subplot_kw = {"aspect": "equal"}
if self.quad_as_tri:
self.fig, axes = plt.subplots(18, 12, figsize=(10.4, 17.1), subplot_kw=subplot_kw)
else:
self.fig, axes = plt.subplots(9, 11, figsize=(9.4, 8.4), subplot_kw=subplot_kw)
self.axes = axes.flatten()
self.axes_index = 0
for config in range(171):
try:
(nw, ne, sw, se) = self._decode_config(config)
except ValueError:
continue
assert nw is not None and ne is not None and sw is not None and se is not None
all = np.asarray((nw, ne, sw, se))
# A quad is degenerate if all 4 quad edges include either the lower
# or upper contour levels.
degenerate_lower = (se == nw == 0 and sw > 0 and ne > 0) or \
(sw == ne == 0 and se > 0 and nw > 0)
degenerate_upper = (se == nw == 2 and sw < 2 and ne < 2) or \
(sw == ne == 2 and se < 2 and nw < 2)
if self.quad_as_tri:
if not nw == ne == sw == se:
zmax = all.max()
zmin = all.min()
zsum = all.sum()
if zmin == 0 and zmax == 1:
lookup_0 = {1: 0, 2: -1, 3: -1.8}
self._next_quad(config, suffix="(0)", set_0=lookup_0[zsum])
lookup_1 = {1: 0.4, 2: 0.35, 3: 0}
self._next_quad(config, suffix="(1)", set_0=lookup_1[zsum])
elif zmin == 0 and zmax == 2:
count_1 = np.count_nonzero(all == 1)
lookup_0 = {2: -0.3, 3: -1, 4: -2-count_1/2, 5: -5, 6: -6} # type: ignore[dict-item]
self._next_quad(config, suffix="(0)", set_0=lookup_0[zsum])
if zsum <= 3:
self._next_quad(config, suffix="(1)", set_2=3.01)
elif zsum <= 5:
self._next_quad(config, suffix="(1)")
elif zsum == 6:
self._next_quad(config, suffix="(1)", set_0=-1)
lookup_2 = {2: 8.01, 3: 7.01, 4: 4+count_1/2, 5: 3.5, 6: 2.5}
self._next_quad(config, suffix="(2)", set_2=lookup_2[zsum]) # type: ignore[arg-type]
elif zmin == 1 and zmax == 2:
lookup_1 = {5: 2, 6: 1.65, 7: 1.6}
self._next_quad(config, suffix="(1)", set_2=lookup_1[zsum])
lookup_2 = {5: 4, 6: 3, 7: 2}
self._next_quad(config, suffix="(2)", set_2=lookup_2[zsum]) # type: ignore[arg-type]
else:
raise RuntimeError(f"Invalid combination of zmin {zmin} and zmax {zmax}")
else:
self._next_quad(config)
else: # !quad_as_tri
if degenerate_lower and degenerate_upper:
# middle needs to be 0, 1 and 2.
self._next_quad(config, suffix="(0)", set_0=-1.01)
self._next_quad(config, suffix="(1)")
self._next_quad(config, suffix="(2)", set_2=3.01)
elif degenerate_lower:
# middle needs to be 0 and >0.
self._next_quad(config, suffix="(0)", set_0=-0.01 if all.max() == 1 else -0.51)
self._next_quad(config, suffix="(>0)", set_1=1.01)
elif degenerate_upper:
# middle needs to be <2 and 2.
self._next_quad(config, suffix="(<2)")
self._next_quad(config, suffix="(2)", set_2=2.01 if all.min() == 1 else 2.51)
else:
# Not degenerate.
self._next_quad(config)
# Hide unwanted axes.
for i in range(self.axes_index, len(self.axes)):
self.axes[i].axis("off")
self.fig.tight_layout()
class ConfigFilledCorner(ConfigFilledCommon):
def __init__(self, name: str, show_text: bool = True) -> None:
super().__init__(name, corner_mask=True, quad_as_tri=False, show_text=show_text)
self.fig, axes = plt.subplots(8, 14, figsize=(12.1, 7.6), subplot_kw={"aspect": "equal"})
self.axes = axes.flatten()
corners = [Corner.NW, Corner.NE, Corner.SW, Corner.SE]
self.axes_index = 0
for icorner in range(4):
corner = corners[icorner]
self._set_mask(corner)
for config in range(43):
try:
_ = self._decode_config(config, corner)
except ValueError:
continue
self._next_quad(config, corner=corner)
self.axes[self.axes_index].axis("off")
self.axes_index += 1
self.fig.tight_layout()
class ConfigLinesCommon(Config):
def __init__(self, name: str, corner_mask: bool, quad_as_tri: bool, show_text: bool) -> None:
super().__init__(name, corner_mask, quad_as_tri, show_text)
def _decode_config(self, config: int, corner: Corner | None = None) -> tuple[int | None, ...]:
if corner is None:
nw = (config >> 3) & 0x1
ne = (config >> 2) & 0x1
sw = (config >> 1) & 0x1
se = config & 0x1
else:
a = (config >> 2) & 0x1
b = (config >> 1) & 0x1
c = config & 0x1
if corner == Corner.NW:
[nw, ne, sw, se] = [a, b, c, None]
elif corner == Corner.NE:
[nw, ne, sw, se] = [a, b, None, c]
elif corner == Corner.SW:
[nw, ne, sw, se] = [a, None, b, c]
else: # Corner.SE
[nw, ne, sw, se] = [None, a, b, c]
return nw, ne, sw, se
def _quad_lines(
self,
ax: Axes,
z: np.ma.MaskedArray[Any, Any],
zlower: float,
zupper: float,
corner: Corner | None,
) -> None:
cont_gen = contour_generator(
self.x, self.y, z, name=self.name, corner_mask=self.corner_mask,
quad_as_tri=self.quad_as_tri, line_type=LineType.SeparateCode)
lines_and_codes = cont_gen.lines(zlower)
assert cont_gen.line_type == LineType.SeparateCode
if TYPE_CHECKING:
lines_and_codes = cast(LineReturn_SeparateCode, lines_and_codes)
lines = lines_and_codes[0]
for points in lines:
ax.plot(points[:, 0], points[:, 1], "o-", c="C3", ms=self.marker_size)
# Single arrow in middle segment (if even number of points) or the following
# segment (if odd number of points).
n = len(points)
i = (n-1) // 2
self._arrow(ax, points[i], points[i+1], "C3")
class ConfigLines(ConfigLinesCommon):
def __init__(self, name: str, quad_as_tri: bool = False, show_text: bool = True) -> None:
super().__init__(name, False, quad_as_tri, show_text)
subplot_kw = {"aspect": "equal"}
if self.quad_as_tri:
self.fig, axes = plt.subplots(5, 6, figsize=(5.2, 4.75), subplot_kw=subplot_kw)
else:
self.fig, axes = plt.subplots(3, 6, figsize=(5.2, 2.85), subplot_kw=subplot_kw)
self.axes = axes.flatten()
self.axes_index = 0
for config in range(16):
(nw, ne, sw, se) = self._decode_config(config)
assert nw is not None and ne is not None and sw is not None and se is not None
# A quad is degenerate if all 4 quad edges include the z level.
degenerate = (se == nw == 0 and sw > 0 and ne > 0) or \
(sw == ne == 0 and se > 0 and nw > 0)
if degenerate or (self.quad_as_tri and not nw == ne == sw == se):
if self.quad_as_tri:
count_1 = np.count_nonzero((nw, ne, sw, se))
count_0 = 4 - count_1
self._next_quad(config, suffix="(0)", set_0=1.01 - count_1)
self._next_quad(config, suffix="(1)", set_1=0.01 + count_0)
else:
self._next_quad(config, suffix="(0)", set_1=0.99)
self._next_quad(config, suffix="(1)", set_1=1.01)
else:
self._next_quad(config)
self.fig.tight_layout()
class ConfigLinesCorner(ConfigLinesCommon):
# All 4 corners plotted together.
def __init__(self, name: str, show_text: bool = True) -> None:
super().__init__(name, corner_mask=True, quad_as_tri=False, show_text=show_text)
self.fig, axes = plt.subplots(4, 8, figsize=(6.93, 3.8), subplot_kw={"aspect": "equal"})
self.axes = axes.flatten()
self.axes_index = 0
corners = [Corner.NW, Corner.NE, Corner.SW, Corner.SE]
for icorner in range(4):
corner = corners[icorner]
self._set_mask(corner)
for config in range(8):
self._next_quad(config, corner)
self.fig.tight_layout()
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