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Copy pathgrid.py
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234 lines (199 loc) · 8.46 KB
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import numpy as np
from numpy import cos, sin, sqrt, pi, exp
import matplotlib.pyplot as plt
from mpl_toolkits.axisartist import SubplotHost
from mpl_toolkits.axisartist.grid_helper_curvelinear \
import GridHelperCurveLinear
import mpl_toolkits.axisartist.angle_helper as angle_helper
from matplotlib.projections import PolarAxes
from matplotlib.transforms import Affine2D
class FormatterDMS(object):
'''Transforms angle ticks to damping ratios'''
def __call__(self, direction, factor, values):
angles_deg = np.asarray(values)/factor
damping_ratios = np.cos((180-angles_deg) * np.pi/180)
ret = ["%.2f" % val for val in damping_ratios]
return ret
class ModifiedExtremeFinderCycle(angle_helper.ExtremeFinderCycle):
# Changed to allow only left hand-side polar grid
# https://matplotlib.org/_modules/mpl_toolkits/axisartist/angle_helper.html#ExtremeFinderCycle.__call__
def __call__(self, transform_xy, x1, y1, x2, y2):
x, y = np.meshgrid(
np.linspace(x1, x2, self.nx), np.linspace(y1, y2, self.ny))
lon, lat = transform_xy(np.ravel(x), np.ravel(y))
with np.errstate(invalid='ignore'):
if self.lon_cycle is not None:
lon0 = np.nanmin(lon)
# Changed from 180 to 360 to be able to span only
# 90-270 (left hand side)
lon -= 360. * ((lon - lon0) > 360.)
if self.lat_cycle is not None: # pragma: no cover
lat0 = np.nanmin(lat)
lat -= 360. * ((lat - lat0) > 180.)
lon_min, lon_max = np.nanmin(lon), np.nanmax(lon)
lat_min, lat_max = np.nanmin(lat), np.nanmax(lat)
lon_min, lon_max, lat_min, lat_max = \
self._add_pad(lon_min, lon_max, lat_min, lat_max)
# check cycle
if self.lon_cycle:
lon_max = min(lon_max, lon_min + self.lon_cycle)
if self.lat_cycle: # pragma: no cover
lat_max = min(lat_max, lat_min + self.lat_cycle)
if self.lon_minmax is not None:
min0 = self.lon_minmax[0]
lon_min = max(min0, lon_min)
max0 = self.lon_minmax[1]
lon_max = min(max0, lon_max)
if self.lat_minmax is not None:
min0 = self.lat_minmax[0]
lat_min = max(min0, lat_min)
max0 = self.lat_minmax[1]
lat_max = min(max0, lat_max)
return lon_min, lon_max, lat_min, lat_max
def sgrid(fig=None, position=None):
"""Creates a plot axis with an s-plane (continuous-time) grid
of constant damping factors and natural frequencies.
"""
# From matplotlib demos:
# https://matplotlib.org/gallery/axisartist/demo_curvelinear_grid.html
# https://matplotlib.org/gallery/axisartist/demo_floating_axis.html
if fig is None:
fig = plt.gcf()
if position is None:
position = (1, 1, 1)
# PolarAxes.PolarTransform takes radian. However, we want our coordinate
# system in degree
tr = Affine2D().scale(np.pi/180., 1.) + PolarAxes.PolarTransform()
# polar projection, which involves cycle, and also has limits in
# its coordinates, needs a special method to find the extremes
# (min, max of the coordinate within the view).
# 20, 20 : number of sampling points along x, y direction
n_points = 20
extreme_finder = ModifiedExtremeFinderCycle(n_points, n_points,
lon_cycle=360,
lat_cycle=None,
lon_minmax=(90,270),
lat_minmax=(0, np.inf))
grid_locator1 = angle_helper.LocatorDMS(15)
tick_formatter1 = FormatterDMS()
grid_helper = GridHelperCurveLinear(tr,
extreme_finder=extreme_finder,
grid_locator1=grid_locator1,
tick_formatter1=tick_formatter1
)
# TODO: Allow positions of type '211', '212' etc.
ax = SubplotHost(fig, position[0], position[1], position[2],
grid_helper=grid_helper)
# make ticklabels of right invisible, and top axis visible.
visible = True
ax.axis[:].major_ticklabels.set_visible(visible)
ax.axis[:].major_ticks.set_visible(False)
ax.axis[:].invert_ticklabel_direction()
ax.axis["wnxneg"] = axis = ax.new_floating_axis(0, 180)
axis.set_ticklabel_direction("-")
axis.label.set_visible(False)
ax.axis["wnxpos"] = axis = ax.new_floating_axis(0, 0)
axis.label.set_visible(False)
ax.axis["wnypos"] = axis = ax.new_floating_axis(0, 90)
axis.label.set_visible(False)
axis.set_axis_direction("left")
ax.axis["wnyneg"] = axis = ax.new_floating_axis(0, 270)
axis.label.set_visible(False)
axis.set_axis_direction("left")
axis.invert_ticklabel_direction()
axis.set_ticklabel_direction("-")
# let left axis shows ticklabels for 1st coordinate (angle)
ax.axis["left"].get_helper().nth_coord_ticks = 0
ax.axis["right"].get_helper().nth_coord_ticks = 0
ax.axis["left"].get_helper().nth_coord_ticks = 0
ax.axis["bottom"].get_helper().nth_coord_ticks = 0
fig.add_subplot(ax)
### RECTANGULAR X Y AXES WITH SCALE
#par2 = ax.twiny()
#par2.axis["top"].toggle(all=False)
#par2.axis["right"].toggle(all=False)
#new_fixed_axis = par2.get_grid_helper().new_fixed_axis
#par2.axis["left"] = new_fixed_axis(loc="left",
# axes=par2,
# offset=(0, 0))
#par2.axis["bottom"] = new_fixed_axis(loc="bottom",
# axes=par2,
# offset=(0, 0))
### FINISH RECTANGULAR
ax.grid(True, zorder=0,linestyle='dotted')
_final_setup(ax)
return ax, fig
def _final_setup(ax, axcolor='black', axlinestyle='-',
axlinewidth=1, equal=True):
# Add axes labels and lines through the origin
ax.set_xlabel('Real')
ax.set_ylabel('Imaginary')
ax.axhline(y=0, linestyle=axlinestyle, color=axcolor, lw=axlinewidth,
zorder=-20)
ax.axvline(x=0, linestyle=axlinestyle, color=axcolor, lw=axlinewidth,
zorder=-20)
if equal:
ax.axis('equal')
def nogrid(ax=None, axlinestyle='-', axlinewidth=1):
if ax is None:
ax = plt.gca()
fig = ax.figure
_final_setup(ax, axlinestyle=axlinestyle, axlinewidth=axlinewidth)
return ax, fig
def zgrid(zetas=None, wns=None, fig=None, ax=None, position=None):
"""Creates a plot axis with a z-plane (discrete-time) grid of
constant damping factors and natural frequencies.
"""
if fig is None:
if ax is None:
ax = plt.gca()
fig = ax.figure
else:
# Create the axis if only figure is provided
if position is None:
position = (1, 1, 1)
ax = fig.add_subplot(position[0], position[1], position[2])
# Constant damping lines
if zetas is None:
zetas = np.linspace(0, 0.9, 10)
for zeta in zetas:
# Calculate in polar coordinates
factor = zeta/sqrt(1-zeta**2)
x = np.linspace(0, sqrt(1-zeta**2), 200)
ang = pi*x
mag = exp(-pi*factor*x)
# Draw upper part in retangular coordinates
xret = mag*cos(ang)
yret = mag*sin(ang)
ax.plot(xret, yret, ':', color='grey', lw=0.75)
# Draw lower part in retangular coordinates
xret = mag*cos(-ang)
yret = mag*sin(-ang)
ax.plot(xret, yret, ':', color='grey', lw=0.75)
# Annotation
an_i = int(len(xret)/2.5)
an_x = xret[an_i]
an_y = yret[an_i]
ax.annotate(str(round(zeta, 2)), xy=(an_x, an_y),
xytext=(an_x, an_y), size=7)
# Constant natural frequency lines
if wns is None:
wns = np.linspace(0, 1, 10)
for a in wns:
# Calculate in polar coordinates
x = np.linspace(-pi/2, pi/2, 200)
ang = pi*a*sin(x)
mag = exp(-pi*a*cos(x))
# Draw in retangular coordinates
xret = mag*cos(ang)
yret = mag*sin(ang)
ax.plot(xret, yret, ':', color='grey', lw=0.75)
# Annotation
an_i = -1
an_x = xret[an_i]
an_y = yret[an_i]
num = '{:1.1f}'.format(a)
ax.annotate(r"$\frac{"+num+r"\pi}{T}$", xy=(an_x, an_y),
xytext=(an_x, an_y), size=9)
_final_setup(ax)
return ax, fig