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How to plot the Fourier transform of I(x) that includes the Dirac function (defined in the code)?
import matplotlib.pyplot as plt
from sympy import DiracDelta
import numpy as np
a1 = 1.6
a2 = 0.6
x1 = 1
x2 = 5
x_start = 0
x_end = 6
x = np.linspace(x_start, x_end, 1000)
I = a1 * DiracDelta(x-x1) + a2 * DiracDelta(x-x2)
FurI = ???????
fig, ax = plt.subplots(figsize=(10,5))
plt.xlim(x_start, x_end)
y1 = 0
plt.ylim(y1,1.2)
plt.plot(x, FurI, c='navy')
ax.set_xlabel(r'$x$')
ax.set_ylabel(r'$I$')
plt.show()
The desired result is a period function.
I have some x and y data, with which I would like to generate a 3D histogram, with a color gradient (bwr or whatever).
I have written a script which plot the interesting values, in between -2 and 2 for both x and y abscesses:
import numpy as np
import numpy.random
import matplotlib.pyplot as plt
# To generate some test data
x = np.random.randn(500)
y = np.random.randn(500)
XY = np.stack((x,y),axis=-1)
def selection(XY, limitXY=[[-2,+2],[-2,+2]]):
XY_select = []
for elt in XY:
if elt[0] > limitXY[0][0] and elt[0] < limitXY[0][1] and elt[1] > limitXY[1][0] and elt[1] < limitXY[1][1]:
XY_select.append(elt)
return np.array(XY_select)
XY_select = selection(XY, limitXY=[[-2,+2],[-2,+2]])
heatmap, xedges, yedges = np.histogram2d(XY_select[:,0], XY_select[:,1], bins = 7, range = [[-2,2],[-2,2]])
extent = [xedges[0], xedges[-1], yedges[0], yedges[-1]]
plt.figure("Histogram")
#plt.clf()
plt.imshow(heatmap.T, extent=extent, origin='lower')
plt.show()
And give this correct result:
Now, I would like to turn this into a 3D histogram. Unfortunatly I don't success to plot it correctly with bar3d because it takes by default the length of x and y for abscisse.
I am quite sure that there is a very easy way to plot this in 3D with imshow. Like an unknow option...
I finaly succeded in doing it. I am almost sure there is a better way to do it, but at leat it works:
import numpy as np
import numpy.random
import matplotlib.pyplot as plt
# To generate some test data
x = np.random.randn(500)
y = np.random.randn(500)
XY = np.stack((x,y),axis=-1)
def selection(XY, limitXY=[[-2,+2],[-2,+2]]):
XY_select = []
for elt in XY:
if elt[0] > limitXY[0][0] and elt[0] < limitXY[0][1] and elt[1] > limitXY[1][0] and elt[1] < limitXY[1][1]:
XY_select.append(elt)
return np.array(XY_select)
XY_select = selection(XY, limitXY=[[-2,+2],[-2,+2]])
xAmplitudes = np.array(XY_select)[:,0]#your data here
yAmplitudes = np.array(XY_select)[:,1]#your other data here
fig = plt.figure() #create a canvas, tell matplotlib it's 3d
ax = fig.add_subplot(111, projection='3d')
hist, xedges, yedges = np.histogram2d(x, y, bins=(7,7), range = [[-2,+2],[-2,+2]]) # you can change your bins, and the range on which to take data
# hist is a 7X7 matrix, with the populations for each of the subspace parts.
xpos, ypos = np.meshgrid(xedges[:-1]+xedges[1:], yedges[:-1]+yedges[1:]) -(xedges[1]-xedges[0])
xpos = xpos.flatten()*1./2
ypos = ypos.flatten()*1./2
zpos = np.zeros_like (xpos)
dx = xedges [1] - xedges [0]
dy = yedges [1] - yedges [0]
dz = hist.flatten()
cmap = cm.get_cmap('jet') # Get desired colormap - you can change this!
max_height = np.max(dz) # get range of colorbars so we can normalize
min_height = np.min(dz)
# scale each z to [0,1], and get their rgb values
rgba = [cmap((k-min_height)/max_height) for k in dz]
ax.bar3d(xpos, ypos, zpos, dx, dy, dz, color=rgba, zsort='average')
plt.title("X vs. Y Amplitudes for ____ Data")
plt.xlabel("My X data source")
plt.ylabel("My Y data source")
plt.savefig("Your_title_goes_here")
plt.show()
I use this example, but I modified it, because it introduced an offset. The result is this:
You can generate the same result using something as simple as the following:
import numpy as np
import matplotlib.pyplot as plt
x = np.linspace(-2, 2, 7)
y = np.linspace(-2, 2, 7)
xx, yy = np.meshgrid(x, y)
z = xx*0+yy*0+ np.random.random(size=[7,7])
plt.imshow(z, interpolation='nearest', cmap=plt.cm.viridis, extent=[-2,2,2,2])
plt.show()
from mpl_toolkits.mplot3d import Axes3D
ax = Axes3D(plt.figure())
ax.plot_surface(xx, yy, z, cmap=plt.cm.viridis, cstride=1, rstride=1)
plt.show()
The results are given below:
Hi I a have a data set which I project onto a sphere such that the magnitude of the data, as a function of theta and phi, is shown using a colour spectrum (which uses "ax.plot_surface", "plt.colorbar" and "facecolors"). My query is that at this stage I am limited to "cm.hot" and "cm.jet". Does anyone know of any other colour schemes which are available for this purpose. Please see my code and the figures below
Code:
from numpy import*
import math
import matplotlib.pyplot as plt
from matplotlib import cm
from mpl_toolkits.mplot3d import Axes3D
import numpy as np
import matplotlib.cm as cm
#theta inclination angle
#phi azimuthal angle
n_theta = 100 #number of values for theta
n_phi = 100 #number of values for phi
r = 1 #radius of sphere
theta, phi = np.mgrid[0: pi:n_theta*1j,-pi:pi:n_phi*1j ]
x = r*np.sin(theta)*np.cos(phi)
y = r*np.sin(theta)*np.sin(phi)
z = r*np.cos(theta)
inp = []
f = open("data.dat","r")
for line in f:
i = float(line.split()[0])
j = float(line.split()[1])
val = float(line.split()[2])
inp.append([i, j, val])
inp = np.array(inp)
#reshape the input array to the shape of the x,y,z arrays.
c = inp[:,2].reshape((n_phi,n_theta))
#Set colours and render
fig = plt.figure(figsize=(10, 8))
ax = fig.add_subplot(111, projection='3d')
#use facecolors argument, provide array of same shape as z
# cm.<cmapname>() allows to get rgba color from array.
# array must be normalized between 0 and 1
surf = ax.plot_surface(
x,y,z, rstride=1, cstride=1, facecolors=cm.jet(c), alpha=0.9, linewidth=1, shade=False)
ax.set_xlim([-2.0,2.0])
ax.set_ylim([-2.0,2.0])
ax.set_zlim([-2,2])
ax.set_aspect("equal")
plt.title('Plot with cm.jet')
#Label axis.
ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_zlabel('Z')
#Creates array for colorbar from 0 to 1.
a = array( [1.0, 0.5, 0.0])
#Creates colorbar
m = cm.ScalarMappable(cmap=cm.jet)
m.set_array(a)
plt.colorbar(m)
plt.savefig('facecolor plots')
f.close()
plt.show()
The following is a list of colormaps provided directly by matplotlib. It's taken from the Colormap reference example.
cmaps = [('Perceptually Uniform Sequential', [
'viridis', 'plasma', 'inferno', 'magma', 'cividis']),
('Sequential', [
'Greys', 'Purples', 'Blues', 'Greens', 'Oranges', 'Reds',
'YlOrBr', 'YlOrRd', 'OrRd', 'PuRd', 'RdPu', 'BuPu',
'GnBu', 'PuBu', 'YlGnBu', 'PuBuGn', 'BuGn', 'YlGn']),
('Sequential (2)', [
'binary', 'gist_yarg', 'gist_gray', 'gray', 'bone', 'pink',
'spring', 'summer', 'autumn', 'winter', 'cool', 'Wistia',
'hot', 'afmhot', 'gist_heat', 'copper']),
('Diverging', [
'PiYG', 'PRGn', 'BrBG', 'PuOr', 'RdGy', 'RdBu',
'RdYlBu', 'RdYlGn', 'Spectral', 'coolwarm', 'bwr', 'seismic']),
('Qualitative', [
'Pastel1', 'Pastel2', 'Paired', 'Accent',
'Dark2', 'Set1', 'Set2', 'Set3',
'tab10', 'tab20', 'tab20b', 'tab20c']),
('Miscellaneous', [
'flag', 'prism', 'ocean', 'gist_earth', 'terrain', 'gist_stern',
'gnuplot', 'gnuplot2', 'CMRmap', 'cubehelix', 'brg', 'hsv',
'gist_rainbow', 'rainbow', 'jet', 'nipy_spectral', 'gist_ncar'])]
To easily view them all you may e.g. use the following 3D colormap viewer (written in PyQt5).
import numpy as np
from mpl_toolkits.mplot3d import Axes3D
from PyQt5 import QtGui, QtCore, QtWidgets
from matplotlib.backends.backend_qt5agg import FigureCanvasQTAgg as FigureCanvas
from matplotlib.figure import Figure
import sys
class MainWindow(QtWidgets.QMainWindow):
def __init__(self):
QtWidgets.QMainWindow.__init__(self)
self.main_widget = QtWidgets.QWidget(self)
self.fig = Figure()
self.canvas = FigureCanvas(self.fig)
self.ax = self.fig.add_subplot(111, projection=Axes3D.name)
u = np.linspace(0, 2 * np.pi, 100)
v = np.linspace(0, np.pi, 100)
x = 10 * np.outer(np.cos(u), np.sin(v))
y = 10 * np.outer(np.sin(u), np.sin(v))
z = 10 * np.outer(np.ones(np.size(u)), np.cos(v))
# Plot the surface
self.surf = self.ax.plot_surface(x, y, z, cmap="YlGnBu")
self.cb = self.fig.colorbar(self.surf)
self.canvas.setSizePolicy(QtWidgets.QSizePolicy.Expanding,
QtWidgets.QSizePolicy.Expanding)
self.canvas.updateGeometry()
self.dropdown1 = QtWidgets.QComboBox()
items = []
for cats in cmaps:
items.extend(cats[1])
self.dropdown1.addItems(items)
self.dropdown1.currentIndexChanged.connect(self.update)
self.label = QtWidgets.QLabel("A plot:")
self.layout = QtWidgets.QGridLayout(self.main_widget)
self.layout.addWidget(QtWidgets.QLabel("Select Colormap"))
self.layout.addWidget(self.dropdown1)
self.layout.addWidget(self.canvas)
self.setCentralWidget(self.main_widget)
self.show()
self.update()
def update(self):
self.surf.set_cmap(self.dropdown1.currentText())
self.fig.canvas.draw_idle()
if __name__ == '__main__':
app = QtWidgets.QApplication(sys.argv)
win = MainWindow()
sys.exit(app.exec_())
i plotted a density map with histograme2d and pcolomesh using a csv file containning lat/lon.
Now i want to turn the histogram2d output into contours matplotlib.
my code is as shown below:
import csv
import numpy as np
from mpl_toolkits.basemap import Basemap
import matplotlib.pyplot as plt
from matplotlib.colors import LinearSegmentedColormap
lats, lons = [], []
with open('fou.csv') as f:
reader = csv.reader(f)
next(reader) # Ignore the header row.
lonMin, lonMax, dLon = -20.0, 5.0, 5
latMin, latMax, dLat = 18.0, 40.0, 5
for row in reader:
lat = float(row[2])
lon = float(row[3])
# filter lat,lons to (approximate) map view:
if lonMin <= lon <= lonMax and latMin <= lat <= latMax:
lats.append( lat )
lons.append( lon )
m = Basemap(llcrnrlon=lonMin, llcrnrlat=latMin, urcrnrlon=lonMax, urcrnrlat=latMax, projection='merc', resolution='f')
m.drawcoastlines()
m.drawcountries()
m.drawstates()
db = 1 # bin padding
lon_bins = np.linspace(min(lons)-db, max(lons)+db, 100) # 10 bins
lat_bins = np.linspace(min(lats)-db, max(lats)+db, 100) # 13 bins
density, xbins, ybins =(np.histogram2d(lats, lons, [lat_bins, lon_bins]))
plt.contourf(density.transpose(),extent=[xbins[0],xbins[-1],ybins[0],ybins[-1]],levels = [1,5,10,25,50,70,80,100])
cbar = plt.colorbar(orientation='horizontal', shrink=0.625, aspect=20, fraction=0.2,pad=0.02)
cbar.set_label('the keraunic level density',size=18)
plt.gcf().set_size_inches(15,15)
plt.show()
what am I missing ?
I have an elliptic curve plotted. I want to draw a line along a P,Q,R (where P and Q will be determined independent of this question). The main problem with the P is that sympy solve() returns another equation and it needs to instead return a value so it can be used to plot the x-value for P. As I understood it, solve() should return a value, so I'm clearly doing something wrong here that I'm just totally not seeing. For reference, here's how P+Q=R should look:
I've been going over the docs and other material and this is as far as I've been able to get myself into trouble:
from mpl_toolkits.axes_grid.axislines import SubplotZero
from pylab import *
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.path import Path
import matplotlib.patches as patches
from matplotlib import rc
import random
from sympy.solvers import solve
from sympy import *
def plotGraph():
fig = plt.figure(1)
#ax = SubplotZero(fig, 111)
#fig.add_subplot(ax)
#for direction in ["xzero", "yzero"]:
#ax.axis[direction].set_axisline_style("-|>")
#ax.axis[direction].set_visible(True)
#ax.axis([-10,10,-10,10])
a = -2; b = 1
y, x = np.ogrid[-10:10:100j, -10:10:100j]
xlist = x.ravel(); ylist = y.ravel()
elliptic_curve = pow(y, 2) - pow(x, 3) - x * a - b
plt.contour(xlist, ylist, elliptic_curve, [0])
#rand = random.uniform(-5,5)
randmid = random.randint(30,70)
#y = ylist[randmid]; x = xlist[randmid]
xsym, ysym = symbols('x ylist[randmid]')
x_result = solve(pow(ysym, 2) - pow(xsym, 3) - xsym * a - b, xsym) # 11/5/13 needs to return a value
plt.plot([-1.5,5], [-1,8], color = "c", linewidth=1) # plot([x1,x2,x3,...],[y1,y2,y3,...])
plt.plot([xlist[randmid],5], [ylist[randmid],8], color = "m", linewidth=1)
#rc('text', usetex=True)
text(-9,6,' size of xlist: %s \n size of ylist: %s \n x_coord: %s \n random_y: %s'
%(len(xlist),len(ylist),x_result,ylist[randmid]),
fontsize=10, color = 'blue',bbox=dict(facecolor='tan', alpha=0.5))
plt.annotate('$P+Q=R$', xy=(2, 1), xytext=(3, 1.5),arrowprops=dict(facecolor='black', shrink=0.05))
## verts = [(-5, -10),(5, 10)] # [(x,y)startpoint,(x,y)endpoint] #,(0, 0)]
## codes = [Path.MOVETO,Path.LINETO] # related to verts[] #,Path.STOP]
## path = Path(verts, codes)
## patch = patches.PathPatch(path, facecolor='none', lw=2)
## ax.add_patch(patch)
plt.grid(True)
plt.show()
def main():
plotGraph()
if __name__ == '__main__':
main()
Ultimately, I'd like to draw a line to show P+Q=R, so if someone also has something to add on how to code to get the Q that would be greatly appreciated. I'm teaching myself about Python and elliptic curves so I'm sure that any entry-level programmer can figure out in 2 minutes what I've been on for some time already.
I don't know what are you calculating, but here is the code that can plot the graph:
import numpy as np
import pylab as pl
Y, X = np.mgrid[-10:10:100j, -10:10:100j]
def f(x):
return x**3 -3*x + 5
px = -2.0
py = -np.sqrt(f(px))
qx = 0.5
qy = np.sqrt(f(qx))
k = (qy - py)/(qx - px)
b = -px*k + py
poly = np.poly1d([-1, k**2, 2*k*b+3, b**2-5])
x = np.roots(poly)
y = np.sqrt(f(x))
pl.contour(X, Y, Y**2 - f(X), levels=[0])
pl.plot(x, y, "o")
pl.plot(x, -y, "o")
x = np.linspace(-5, 5)
pl.plot(x, k*x+b)
graph:
based on HYRY's answer, I just update some details to make it better:
import numpy as np
import pylab as pl
Y, X = np.mgrid[-10:10:100j, -10:10:100j]
def f(x, a, b):
return x**3 + a*x + b
a = -2
b = 4
# the 1st point: 0, -2
x1 = 0
y1 = -np.sqrt(f(x1, a, b))
print(x1, y1)
# the second point
x2 = 3
y2 = np.sqrt(f(x2, a, b))
print(x2, y2)
# line: y=kl*x+bl
kl = (y2 - y1)/(x2 - x1)
bl = -x1*kl + y1 # bl = -x2*kl + y2
# y^2=x^3+ax+b , y=kl*x+bl => [-1, kl^2, 2*kl*bl, bl^2-b]
poly = np.poly1d([-1, kl**2, 2*kl*bl-a, bl**2-b])
# the roots of the poly
x = np.roots(poly)
y = np.sqrt(f(x, a, b))
print(x, y)
pl.contour(X, Y, Y**2 - f(X, a, b), levels=[0])
pl.plot(x, y, "o")
pl.plot(x, -y, "o")
x = np.linspace(-5, 5)
pl.plot(x, kl*x+bl)
And we got the roots of this poly:
[3. 2.44444444 0. ] [5. 3.7037037 2. ]