python: How to add p values signifance to barplot - python

Below i have a code for the barplot, I would also like to show the Pvalue significane for these plots. Is there any easy way to indicate the statistical significance for these bars
import matplotlib.pyplot as plt
X= [-0.9384815619939103, 1.0755888058123153, 0.061274066731665564, 0.65064830688728]
x_labels = ['A' ,'B', 'C', 'D']
error = [0.23722952107696088, 0.25505883348061764, 0.26038015798295744, 0.26073839861422]
pvalue = [0.000076, 0.000025, 0.813956, 0.012581]
fig, ax = plt.subplots()
ax.bar(x_labels, X, width=0.4, align='center', yerr=error)
plt.show()

It can be done like the way shown here with slight modification
import matplotlib.pyplot as plt
X= [-0.9384815619939103, 1.0755888058123153, 0.061274066731665564,0.65064830688728]
x_labels = ['A' ,'B', 'C', 'D']
error = [0.23722952107696088, 0.25505883348061764, 0.26038015798295744, 0.26073839861422]
pvalue = [0.000076, 0.000025, 0.813956, 0.012581]
fig, ax = plt.subplots()
rects = ax.bar(x_labels, X, width=0.4, align = 'center', yerr=error)
def autolabel(rects, pvalue, xpos='center',):
"""
Attach a text label above each bar in *rects*, displaying its height.
*xpos* indicates which side to place the text w.r.t. the center of
the bar. It can be one of the following {'center', 'right', 'left'}.
"""
xpos = xpos.lower() # normalize the case of the parameter
ha = {'center': 'center', 'right': 'left', 'left': 'right'}
offset = {'center': 0.5, 'right': 0.57, 'left': 0.43} # x_txt = x + w*off
for i, rect in enumerate(rects):
height = rect.get_height()
ax.text(rect.get_x() + rect.get_width()*offset[xpos], 1.01*height,
'p = {}'.format(pvalue[i]), ha=ha[xpos], va='bottom')
autolabel(rects, pvalue, "left")
plt.show()
which results in

Here is another solution which puts the p-values to the plot's legend. For my eyes, this is more pleasant compared to plotting the p-values over the bars.
import matplotlib.pyplot as plt
X= [-0.9384815619939103, 1.0755888058123153, 0.061274066731665564, 0.65064830688728]
x_labels = ['A' ,'B', 'C', 'D']
error = [0.23722952107696088, 0.25505883348061764, 0.26038015798295744, 0.26073839861422]
pvalue = [0.000076, 0.000025, 0.813956, 0.012581]
fig, ax = plt.subplots()
cont = ax.bar(x_labels, X, width=0.4, align='center', yerr=error)
for i, art in enumerate(cont):
art.set_color('C{}'.format(i))
ax.legend(cont.patches, [r'$p={:.6f}$'.format(pv) for pv in pvalue])

Related

Line chart to surface chart

[UPDATE: Sorry for not providing the piece where the author of the codes create example data. I have updated the codes]
I found an example of a 3D mesh line chart that satisfied what I need (colouring change with level on z dimension). However, instead of line, I want surface plot. How can I change the codes to have the 3d surface plot?
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from matplotlib import animation, rc
from matplotlib.cm import get_cmap
from mpl_toolkits.mplot3d import Axes3D
from matplotlib.font_manager import FontProperties
from matplotlib.collections import LineCollection
from matplotlib.colors import ListedColormap
from mpl_toolkits.mplot3d.art3d import Line3DCollection
index_returns = np.random.normal(loc=1e-4, scale=5e-3, size=(783, 9))
index_returns = np.vstack((np.zeros(shape=(1, 9)) + 100, index_returns))
index_prices = np.cumprod(1 + index_returns, axis=0)
window = 261
df = np.zeros(shape=(index_prices.shape[0]-window, 9))
for i in range(window, index_prices.shape[0], 1):
df[i-window] = (index_prices[i]/index_prices[i-window]) - 1
index = pd.date_range('2019-01-01', periods=index_prices.shape[0]-window, freq='B')
columns = ['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I']
df = pd.DataFrame(df, index=index, columns=columns)
# create the figure
fig = plt.figure(figsize=(14.4, 9))
ax = fig.add_subplot(111, projection='3d')
fig.patch.set_alpha(1)
# get the cmap to use
cmap = get_cmap('RdYlGn')
# get the slice based on data frame
current_slice = df.values[:261, :]
index_names = df.columns
index_dates = df.index
# list holding the lines
lines = []
# for each index...
for i in range(current_slice.shape[1]):
# get the coordinates
x = np.array(np.arange(current_slice.shape[0]))
y = np.tile(i, current_slice.shape[0])
z = np.array(current_slice[:, i])
# crete points and segments to color
points = np.array([x, y, z]).T.reshape(-1, 1, 3)
segments = np.concatenate([points[:-1], points[1:]], axis=1)
# Create a continuous norm to map from data points to colors
norm = plt.Normalize(-0.19, 0.19)
lc = Line3DCollection(segments, cmap=cmap, norm=norm, zorder=current_slice.shape[1]-i)
# Set the values used for colormapping
lc.set_array(z)
lc.set_linewidth(2)
lc.set_color(cmap(z[-1] * 2.5 + 0.5))
lc.set_label(index_names[i])
lines.append(ax.add_collection(lc))
# add the grids
ax.legend(loc='center right', bbox_to_anchor=(1.1, 0.46), fancybox=True, facecolor=(.95,.95,.95,1), framealpha=1, shadow=False, frameon=True, ncol=1, columnspacing=0, prop={'family': 'DejaVu Sans Mono'})
ax.set_zlabel('Rolling Equity 1Y', labelpad=10)
ax.set_zlim(-0.39, 0.39)
ax.set_zticklabels([' '* 3 + '{:.0%}'.format(val) for val in ax.get_zticks()], fontdict={'verticalalignment': 'center', 'horizontalalignment': 'center'})
ax.set_xlabel('Date', labelpad=30)
ax.set_xlim(0, current_slice.shape[0]-1)
ax.set_xticklabels([index_dates[int(val)].strftime('%m/%y') for val in ax.get_xticks()[:-1]] + [''], rotation=0, fontdict={'verticalalignment': 'top', 'horizontalalignment': 'center'})
ax.set_yticks(np.arange(current_slice.shape[1]))
ax.set_yticklabels([index_names[i] for i in range(current_slice.shape[1])], rotation=-15, fontdict={'verticalalignment': 'center', 'horizontalalignment': 'left'})
# show the plot
plt.show()

How to create a 3D graph with filled-below curves and position the y-ticks?

I am making my first 3D graph in Python on an Anaconda Jupyter Notebook. The idea is to obtain a graph with a format similar to the following:
The code I made is as follows:
import numpy as np
import matplotlib
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from mpl_toolkits.mplot3d.art3d import Poly3DCollection
fig = plt.figure()
ax = Axes3D(fig)
def func(x, pos): # formatter function takes tick label and tick position
s = str(x)
ind = s.index('.')
return s[:ind] + ',' + s[ind+1:] # change dot to comma
x_format = tkr.FuncFormatter(func)
ax.xaxis.set_major_formatter(x_format)
ax.yaxis.set_major_formatter(x_format)
df = pd.read_excel('EDS 7.xlsx', header=None, usecols=[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15], names=['A', 'B', 'C', 'D','E','F','G','H', 'I', 'J', 'K', 'L', 'M', 'N', 'O', 'P'])
plt.rcParams["figure.figsize"] = [14.5,10]
nomes = ['Triângulo de MoSe$_2$','Losango branco','Losango cinzento','Fundo']
ax.set_yticks(range(0,4))
ax.set_yticklabels(nomes)
ax.tick_params(axis='z', pad=10)
ax.tick_params(axis='y', pad=20)
# put 0s on the y-axis, and put the y axis on the z-axis
ax.plot(xs=df['A'], ys=df['B'], zs=df['C'], zdir='z', label='ys=0, zdir=z', color='blue', linewidth=3)
ax.plot(xs=df['D'], ys=df['E'], zs=df['F'], zdir='z', label='ys=0, zdir=z', color='red', linewidth=3)
ax.plot(xs=df['G'], ys=df['H'], zs=df['I'], zdir='z', label='ys=0, zdir=z', color='green', linewidth=3)
ax.plot(xs=df['J'], ys=df['K'], zs=df['L'], zdir='z', label='ys=0, zdir=z', color='orange', linewidth=3)
y=df['M'];
plt.xlim([0.0, 4.0])
#plt.ylim([0.0, 4.0])
ax.set_zlim(0,1400)
plt.rc('xtick', labelsize=16)
plt.rc('ytick', labelsize=16)
#plt.xticks(np.arange(0.0,1.4,0.1).round(decimals=1))
#plt.yticks(np.arange(-0.8,1.3,0.2).round(decimals=1))
ax.w_xaxis.set_pane_color((1.0, 1.0, 1.0, 1.0))
ax.w_yaxis.set_pane_color((1.0, 1.0, 1.0, 1.0))
ax.w_zaxis.set_pane_color((1.0, 1.0, 1.0, 1.0))
ax.xaxis._axinfo["grid"]['linestyle'] = '--'
ax.xaxis._axinfo["grid"]['color'] = 'silver'
ax.yaxis._axinfo["grid"]['linestyle'] = '--'
ax.yaxis._axinfo["grid"]['color'] = 'silver'
ax.zaxis._axinfo["grid"]['linestyle'] = '--'
ax.zaxis._axinfo["grid"]['color'] = 'silver'
ax.set_xlabel('Energia (keV)', fontsize=20, labelpad=18)
ax.set_zlabel('Contagens', fontsize=20, labelpad=18)
#plt.show()
plt.savefig('output.png', dpi=500, bbox_inches='tight')
Excel file:
The graphic I got is this:
I am having two problems that I am unable to solve:
The underside of the lines is not filled with color and I would like them to be opaque.
In the yy axis, the strings are too far to the left and for example the string "Triângulo de MoSe2" of the yy axis is to the left of the number 4.0 of the xx axis. I would like the y-axis strings to be more centered.
How can I adjust the code for the graph to have these two characteristics that I lack?
Here is an example to create something similar to the desired plot. Some toy data are used to create 4 curves.
To fill the area below the curves, the approach from this tutorial is used. For the y tick labels, it seems ax.set_yticklabels(..., ha='left') together with ax.tick_params(axis='y', pad=0) get quite close to the desired result.
To make the polygons fully opaque, set the opaqueness alpha in PolyCollection(...) to a value closer to 1. Usually a small bit of transparency gives a better feeling of being a 3D plot. You can leave out the call to ax.plot(...) if the thicker "border" isn't needed.
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from matplotlib.collections import PolyCollection
def polygon_under_graph(xlist, ylist):
return [(xlist[0], 0.), *zip(xlist, ylist), (xlist[-1], 0.)]
x_cols = {col: np.linspace(0, 4, 50) for col in [*'ADGJ']}
z_cols = {col: 1400 ** np.random.rand(50) for col in [*'CFIL']}
df = pd.DataFrame({**x_cols, **z_cols})
fig = plt.figure()
ax = Axes3D(fig)
plt.rcParams["figure.figsize"] = [14.5, 10]
nomes = ['Triângulo de MoSe$_2$', 'Losango branco', 'Losango cinzento', 'Fundo']
ax.set_yticks(range(0, 4))
ax.set_yticklabels(nomes, ha='left')
ax.tick_params(axis='z', pad=10)
ax.tick_params(axis='y', pad=0)
color_list = ['cornflowerblue', 'crimson', 'limegreen', 'orange']
verts = []
ys = [3, 2, 1, 0]
for x_col, z_col, y, color in zip(['A', 'D', 'G', 'J'], ['C', 'F', 'I', 'L'], ys, color_list):
xs = df[x_col].to_numpy()
zs = df[z_col].to_numpy()
ax.plot(xs=xs, ys=np.repeat(y, len(xs)), zs=zs, zdir='z', color=color, linewidth=3)
verts.append(polygon_under_graph(xs, zs))
poly = PolyCollection(verts, facecolors=color_list, alpha=.8)
ax.add_collection3d(poly, zs=ys, zdir='y')
plt.show()
About having the outlines of the 3 panes in black, some experimenting with 3D figures from Matplotlib visibility of pane edge leads to the following. It is unclear to me why that hack works (an other approaches don't).
def lims(mplotlims):
scale = 1.021
offset = (mplotlims[1] - mplotlims[0]) * scale
return mplotlims[1] - offset, mplotlims[0] + offset
xlims, ylims, zlims = lims(ax.get_xlim()), lims(ax.get_ylim()), lims(ax.get_zlim())
i = np.array([xlims[0], ylims[0], zlims[0]])
f = np.array([xlims[0], ylims[0], zlims[1]])
p = art3d.Poly3DCollection(np.array([[i, f]]))
p.set_color('black')
ax.add_collection3d(p)
ax.xaxis.pane.set_edgecolor('#000000FF')
ax.yaxis.pane.set_edgecolor('#000000FF')
ax.zaxis.pane.set_edgecolor('#000000FF')

How to plot matplotlib errorbars

I tried to plot error bar with Matplotlib like graphic attached, I can't made it, any suggestion?
import numpy as np
import matplotlib.pyplot as plt
Media = data["Media"]
Periodo = data["Periodo"]
P10th = data["P10th"]
P90th = data["P90th"]
ind = np.arange(N) # the x locations for the groups
width = 0.35 # the width of the bars: can also be len(x) sequence
fig, ax = plt.subplots()
ax.errorbar(Media, P90th, P10th, color='red', ls='--', marker='o', capsize=5, capthick=1, ecolor='black')
plt.xticks(ind, ('1910-1940', '1950-1990', '1990-2000', '2001-2010') )
ax.set_ylim(ylims)
, please can you help me.
This is my output
Here's the plot for your data:
p_10 = [.19,.62, .77, 1]
p_90 = [7.19, 6.67, 7.36, 8.25]
M = [1.16, 2.06, 2.17, 2.52]
fig = plt.figure()
x = [1, 2, 3, 4]
y = M
yerr = [p_10, # 'down' error
p_90] # 'up' error
plt.errorbar(x, y, yerr=yerr, capsize=3, fmt="r--o", ecolor = "black")

How to label Y ticklabels as group/category in seaborn clustermap?

I want to make a clustermap/heatmap of gene presence-absence data from patients where the genes will be grouped into categories (e.g chemotaxis, endotoxin etc) and labelled appropriately. I haven't found any such option in seaborn documentation. I know how to generate the heatmap, I just don't know how to label yticks as categories. Here is a sample (unrelated to my work) of what I want to achieve:
Here , yticklabels January, February and March are given group label winter and other yticklabels are also similarly labelled.
I've reproduced the example you gave in seaborn, adapting #Stein's answer from here.
import pandas as pd
import numpy as np
from matplotlib import pyplot as plt
from itertools import groupby
import datetime
import seaborn as sns
def test_table():
months = [datetime.date(2008, i+1, 1).strftime('%B') for i in range(12)]
seasons = ['Winter',]*3 + ['Spring',]*2 + ['Summer']*3 + ['Pre-Winter',]*4
tuples = list(zip(months, seasons))
index = pd.MultiIndex.from_tuples(tuples, names=['first', 'second'])
d = {i: [np.random.randint(0,50) for _ in range(12)] for i in range(1950, 1960)}
df = pd.DataFrame(d, index=index)
return df
def add_line(ax, xpos, ypos):
line = plt.Line2D([ypos, ypos+ .2], [xpos, xpos], color='black', transform=ax.transAxes)
line.set_clip_on(False)
ax.add_line(line)
def label_len(my_index,level):
labels = my_index.get_level_values(level)
return [(k, sum(1 for i in g)) for k,g in groupby(labels)]
def label_group_bar_table(ax, df):
xpos = -.2
scale = 1./df.index.size
for level in range(df.index.nlevels):
pos = df.index.size
for label, rpos in label_len(df.index,level):
add_line(ax, pos*scale, xpos)
pos -= rpos
lypos = (pos + .5 * rpos)*scale
ax.text(xpos+.1, lypos, label, ha='center', transform=ax.transAxes)
add_line(ax, pos*scale , xpos)
xpos -= .2
df = test_table()
fig = plt.figure(figsize = (10, 10))
ax = fig.add_subplot(111)
sns.heatmap(df)
#Below 3 lines remove default labels
labels = ['' for item in ax.get_yticklabels()]
ax.set_yticklabels(labels)
ax.set_ylabel('')
label_group_bar_table(ax, df)
fig.subplots_adjust(bottom=.1*df.index.nlevels)
plt.show()
Gives:
Hope that helps.
I haven't tested this with seaborn yet, but the following works with vanilla matplotlib.
#!/usr/bin/env python
"""
Annotate a group of y-tick labels as such.
"""
import matplotlib.pyplot as plt
from matplotlib.transforms import TransformedBbox
def annotate_yranges(groups, ax=None):
"""
Annotate a group of consecutive yticklabels with a group name.
Arguments:
----------
groups : dict
Mapping from group label to an ordered list of group members.
ax : matplotlib.axes object (default None)
The axis instance to annotate.
"""
if ax is None:
ax = plt.gca()
label2obj = {ticklabel.get_text() : ticklabel for ticklabel in ax.get_yticklabels()}
for ii, (group, members) in enumerate(groups.items()):
first = members[0]
last = members[-1]
bbox0 = _get_text_object_bbox(label2obj[first], ax)
bbox1 = _get_text_object_bbox(label2obj[last], ax)
set_yrange_label(group, bbox0.y0 + bbox0.height/2,
bbox1.y0 + bbox1.height/2,
min(bbox0.x0, bbox1.x0),
-2,
ax=ax)
def set_yrange_label(label, ymin, ymax, x, dx=-0.5, ax=None, *args, **kwargs):
"""
Annotate a y-range.
Arguments:
----------
label : string
The label.
ymin, ymax : float, float
The y-range in data coordinates.
x : float
The x position of the annotation arrow endpoints in data coordinates.
dx : float (default -0.5)
The offset from x at which the label is placed.
ax : matplotlib.axes object (default None)
The axis instance to annotate.
"""
if not ax:
ax = plt.gca()
dy = ymax - ymin
props = dict(connectionstyle='angle, angleA=90, angleB=180, rad=0',
arrowstyle='-',
shrinkA=10,
shrinkB=10,
lw=1)
ax.annotate(label,
xy=(x, ymin),
xytext=(x + dx, ymin + dy/2),
annotation_clip=False,
arrowprops=props,
*args, **kwargs,
)
ax.annotate(label,
xy=(x, ymax),
xytext=(x + dx, ymin + dy/2),
annotation_clip=False,
arrowprops=props,
*args, **kwargs,
)
def _get_text_object_bbox(text_obj, ax):
# https://stackoverflow.com/a/35419796/2912349
transform = ax.transData.inverted()
# the figure needs to have been drawn once, otherwise there is no renderer?
plt.ion(); plt.show(); plt.pause(0.001)
bb = text_obj.get_window_extent(renderer = ax.get_figure().canvas.renderer)
# handle canvas resizing
return TransformedBbox(bb, transform)
if __name__ == '__main__':
import numpy as np
fig, ax = plt.subplots(1,1)
# so we have some extra space for the annotations
fig.subplots_adjust(left=0.3)
data = np.random.rand(10,10)
ax.imshow(data)
ticklabels = 'abcdefghij'
ax.set_yticks(np.arange(len(ticklabels)))
ax.set_yticklabels(ticklabels)
groups = {
'abc' : ('a', 'b', 'c'),
'def' : ('d', 'e', 'f'),
'ghij' : ('g', 'h', 'i', 'j')
}
annotate_yranges(groups)
plt.show()

How to show Cartesian system in polar plot in python?

Here I tried to add the polar plot on top of the Cartesian grid,but what I got instead was 2 separate figures(one polar another Cartesian),I want this polar figure to be embedded in the Cartesian plot. Also I have used some of the code previously available as I am new to matplotlib.
from pylab import *
import matplotlib.pyplot as plt
x = [0,10,-3,-10]
y = [0,10,1,-10]
color=['w','w','w','w']
fig = plt.figure()
ax1 = fig.add_subplot(111)
scatter(x,y, s=100 ,marker='.', c=color,edgecolor='w')
circle1=plt.Circle((0,0),5,color='r',fill=False)
circle_min=plt.Circle((0,0),4.5,color='g',fill=False)
circle_max=plt.Circle((0,0),5.445,color='b',fill=False)
fig = plt.gcf()
fig.gca().add_artist(circle1)
fig.gca().add_artist(circle_min)
fig.gca().add_artist(circle_max)
left,right = ax1.get_xlim()
low,high = ax1.get_ylim()
arrow( left, 0, right -left, 0, length_includes_head = True, head_width = 0.15 )
arrow( 0, low, 0, high-low, length_includes_head = True, head_width = 0.15 )
grid()
fig = plt.figure()
ax2 = fig.add_subplot(111)
scatter(x,y, s=100 ,marker='.', c=color,edgecolor='w')
circle2=plt.Circle((0,0),5,color='r',fill=False)
circle_min=plt.Circle((0,0),4.5,color='g',fill=False)
circle_max=plt.Circle((0,0),5.445,color='b',fill=False)
fig = plt.gcf()
fig.gca().add_artist(circle2)
fig.gca().add_artist(circle_min)
fig.gca().add_artist(circle_max)
left,right = ax2.get_xlim()
low,high = ax2.get_ylim()
arrow( left, 0, right -left, 0, length_includes_head = True, head_width = 0.15 )
arrow( 0, low, 0, high-low, length_includes_head = True, head_width = 0.15 )
import numpy as np
import matplotlib.pyplot as plt
theta = np.linspace(-np.pi, np.pi, 100)
r1 = 1 - np.sin(3*theta)
r2 = 1 + np.cos(theta)
ax = plt.subplot(111, polar=True, # add subplot in polar coordinates
axisbg='Azure') # background colour
ax.set_rmax(2.2) # r maximum value
ax.grid(True) # add the grid
ax.plot(theta, r1,
color='Tomato', # line colour
ls='--', # line style
lw=3, # line width
label='a 3-fold curve') # label
ax.plot(theta, r2,
color='purple',
linewidth=3,
ls = '-',
label = 'a cardioid')
ax.legend(loc="lower right") # legend location
titlefont = {
'family' : 'serif',
'color' : 'black',
'weight' : 'bold',
'size' : 16,
}
ax.set_title("A plot in polar coordinates", # title
va='bottom', # some space below the title
fontdict = titlefont # set the font properties
)
grid()
show()
#I am getting a separate Cartesian image + a polar image while what I need is both the things in a single image
import matplotlib.pyplot as plt
import numpy as np
#########################################
color=['w','w','w','w']
theta = np.linspace(-np.pi, np.pi, 100)
fig = plt.figure()# initializing the figure
rect = [0.1, 0.1, 0.8, 0.8]# setting the axis limits in [left, bottom, width, height]
ax_carthesian = fig.add_axes(rect)# the carthesian axis:
ax_polar = fig.add_axes(rect, polar=True, frameon=False)# the polar axis:
#########################################
ax_carthesian.add_artist(plt.Circle((0.5,0.5),5/15,color='r',fill=False))
ax_carthesian.add_artist(plt.Circle((0.5,0.5),4.5/15,color='g',fill=False))
ax_carthesian.add_artist(plt.Circle((0.5,0.5),5.445/15,color='b',fill=False))
ax_polar.plot(theta, 1 - np.sin(3*theta), color='Tomato',ls='--',lw=1, label='a 3-fold curve')
ax_polar.plot(theta, 1 + np.cos(theta), color='purple',linewidth=1,ls = '-',label = 'a cardioid')
plt.show()
I am not used to matplotlib but I reduced your code to his minimum to better understand it and make it look less redudant. look at what I get:
import pylab
import matplotlib.pyplot as plt
import numpy as np
#########################################
x = [0,10,-3,-10]
y = [0,10,1,-10]
color=['w','w','w','w']
theta = np.linspace(-np.pi, np.pi, 100)
#########################################
pylab.scatter(x,y, s=100 ,marker='.', c=color,edgecolor='w')
plt.gcf().gca().add_artist(plt.Circle((0,0),5,color='r',fill=False))
plt.gcf().gca().add_artist(plt.Circle((0,0),4.5,color='g',fill=False))
plt.gcf().gca().add_artist(plt.Circle((0,0),5.445,color='b',fill=False))
plt.figure().add_subplot(111)
ax = plt.subplot(111, polar=True,axisbg='Azure')
ax.plot(theta, 1 - np.sin(3*theta),color='Tomato',ls='--',lw=3,label='a 3-fold curve')
ax.plot(theta, 1 + np.cos(theta),color='purple',linewidth=3,ls = '-',label = 'a cardioid')
pylab.show()
it is nearly the same result...

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