I'm trying to demonstrate a cost function right now and wondering if there's a way to traverse the parabola by adding plot in the same subplot and figure.
def costfuntion(b, a):
# b Value
x = np.linspace(b*(-b), b*(b), 100)
y = (x - a)**2
return y
My Plot Attempt:
plt.plot(costfuntion(20,5))
plt.ylabel("Cost Value");
#b = 'some b value'
plt.plot(b, marker='o', color='b')
What I'm trying to mimic
(Around: 1:13)
Since the y values depend on the a values you need to specify an a for the y lookup. Consider the following:
def costfunction(b, a):
# b Value
x = np.linspace(b*(-b), b*(b), 100)
y = (x - a)**2
return x, y
a = 5
c = costfunction(20, a)
plt.plot(c[0], c[1], linestyle='-', linewidth=1)
plt.ylabel("Cost Value");
b = 100
yb = (b - a)**2 # Find the corresponding y-value
plt.plot(b, yb, marker='o', color='b')
plt.show()
This will give you
You might also note that I modified the costfunction definition to return the x values, otherwise matplotlib will just use whatever values it pleases.
def costfuntion(b, a):
# b Value
x = np.linspace(b*(-b), b*(b), 100)
y = (x - a)**2
return x, y
x, y = costfuntion(20,5)
plt.plot(x, y)
for i in range(0, len(x), 2):
plt.plot(x[i], y[i], marker='o', color='b')
Change the cost function to return both x and y of the function you are plotting and use this information to plot points on the function.
Related
I would like to rotate a curve to a pass through a point on a 2D plot but l cant find a way of doing it .
Say l want to rotate
y=np.exp(x)+2 #pass through (x=5,y=6) point
You can subtract value of y(x_0) from y and add desired y.
For example
x = np.arange(10)
y = np.exp(x) + 2
x_ind = 5 #This is not value of x, this is index of desired x
y_desired = 6
y -= y[x[x_ind]] + y_desired
plt.plot(x, y, color='b')
plt.scatter([x[x_ind]], [y_desired], color='r')
plt.show()
I am not sure how to phrase my question in any way better. Basically, I have three lists of the same length x, y and z and I want to fill a 2D numpy array in the z/y plane with the average of the associated z values.
Here is how I can achieve what I wan to do:
import numpy as np
import matplotlib.pyplot as plt
x = [37.59390426045407, 38.00530354847739, 38.28412244348653, 38.74871247986305, 38.73175910429809, 38.869008864244016, 39.188234404976555, 39.92835838352555, 40.881394113153334, 41.686136269465884]
y = [0.1305391767832006, 0.13764519613447768, 0.14573326951792354, 0.15090729309032114, 0.16355823707239897, 0.17327106424274763, 0.17749746339532224, 0.17310384614773594, 0.16545780437882962, 0.1604752704890856]
z = [0.05738534353865021, 0.012572155256903583, -0.021709582561809437, -0.11191337750722108, -0.07931921785775153, -0.06241610118871843, 0.014216349927058225, 0.042002641153291886, -0.029354425271534645, 0.061894011359833856]
n = 5
image = np.zeros(shape=(n,n))
# Fill the 2D array
x0 = min(x)
y0 = min(y)
dx = (max(x) - min(x))/n
dy = (max(y) - min(y))/n
# Loop over each 2D cell
for index_x in range(n):
for index_y in range(n):
# find the limits of the cell
x1 = x0 + index_x * dx
x2 = x0 + (index_x+1) * dx
y1 = y0 + index_y * dy
y2 = y0 + (index_y+1) * dy
# find the points of z that lie within the range of the cell
vec_z = [z[idx] for idx in range(len(z)) if x[idx]>=x1 and x[idx]<x2 and y[idx]>=y1 and y[idx]<y2]
if vec_z:
image[index_x, index_y] = np.mean(vec_z)
# In the end, used to create a surface plot
fig, ax = plt.subplots()
ax.imshow(image, cmap=plt.cm.gray, interpolation='nearest')
plt.show()
Is there a more easy way to achieve this? I can imagine there is a numpy method for that.
If I understand correctly what you want to do, maybe a 2D interpolation from scipy.interpolate.interp2d is what you are looking for.
You define the interpolation function of your points:
f = interp2d(x = x, y = y, z = z)
Then you define the X and Y meshgrid:
N = 50
x_axis = np.linspace(np.min(x), np.max(x), N)
y_axis = np.linspace(np.min(y), np.max(y), N)
X, Y = np.meshgrid(x_axis, y_axis)
Finally you can compute Z interpolated values on the meshgrid:
Z = np.zeros((N, N))
for i in range(N):
for j in range(N):
Z[i, j] = f(X[i, j], Y[i, j])
If you plot in 3D the interpolated surface, you get:
fig = plt.figure()
ax = fig.add_subplot(projection = '3d')
ax.plot_surface(X, Y, Z, cmap = 'jet', shade = False)
ax.set_xlabel('x')
ax.set_ylabel('y')
ax.set_zlabel('z')
plt.show()
Interpolated surface compared to interpolation data points:
ax.scatter(x, y, z, color = 'black', s = 100, alpha = 1)
I have a function that is split in 3. (0 < x < L1) (L1 < x < a) (a < x L2).
I need to add a notation on the plot for the max value no matter where x is on the (0 < x < L2).
I have:
c1 = np.arange(0,L1+0.1, 0.1)
c2 = np.arange(L1,a+0.1, 0.1)
c3 = np.arange(a,L+0.1, 0.1)
y1 = -q*c1
y2 = -q*c2 + RAV
y3 = -q*c3 + RAV - P
fig, (ax1, ax2) = plt.subplots(2, 1, sharex=True)
ax1.fill_between(c1, y1)
ax1.fill_between(c2, y2)
ax1.fill_between(c3, y3)
ax1.set_title('S curve')
Mmax1=np.max(y1)
Mmax2=np.max(y2)
Mmax3=np.max(y3)
Mmax= round(max(Mmax1,Mmax2,Mmax3), 2)
Now I want to take find the x coordinate of the y value Mmax, but I don't know how to use something like x[np.argmax(Mmax)] where x = a.any(c1, c2, c3).
I need the x coordinate so that I can plot it in, where the value occurs
ax2.annotate(text2,
xy=(max_x, Mmax), xycoords='data',
xytext=(0, 30), textcoords='offset points',
arrowprops=dict(arrowstyle="->"))
How can I fix it? Thank you!
Here I would illustrate what may be useful for you,As I don't have you complete code to create your desire function I have defined 3 simple function with following description:
by out_arr=np.maximum.reduce([y1,y2,y3]) we would have maximum in ever x and by result = np.where(out_arr == np.amax(out_arr)) we find out which index have maximum value. then maximum pint would be point=[Max_X,out_arr[Max_X]]
import matplotlib.pyplot as plt
import numpy as np
x= np.arange(0., 6., 1)
y1=x
y2=x**2
y3=x**3
out_arr=np.maximum.reduce([y1,y2,y3])
result = np.where(out_arr == np.amax(out_arr))
Max_X=result[0]
print(Max_X)
point=[Max_X,out_arr[Max_X]]
plt.plot(Max_X,out_arr[Max_X],'ro')
# red dashes, blue squares and green triangles
plt.plot(x, y1, 'r--', x, y2, 'bs', x, y3, 'g^')
plt.show()
I'm trying to plot a cdf with matplotlib. However, cdfs begin in the origin, thus I prepended zeros to the x and y arrays. The problem is now that the origin now is marked as a data point. I'd like to remove that single marker in the point (0,0).
Code and picture below.
#Part of the myplot (my own) class
def cdf(self):
markers = ["x","v","o","^","8","s","p","+","D","*"]
for index,item in enumerate(np.asarray(self.data).transpose()):
x = np.sort(item)
y = np.arange(1,len(x)+1) / len(x)
x = np.insert(x,0,0)
y = np.insert(y,0,0)
self.plot = plt.plot(x,
y,
marker=markers[index],
label=self.legend[index])
self.setLabels( xlabel=self.xlabel,
ylabel="cumulative density",
title=self.title)
self.ax.set_ylim(ymax=1)
You cannot remove a marker. What you may do is to plot all the markers first, then append the origin and then plot a line.
x = np.sort(item)
y = np.arange(1,len(x)+1) / len(x)
self.plot, = plt.plot(x, y, marker=markers[index], ls="", label=self.legend[index])
x = np.insert(x,0,0)
y = np.insert(y,0,0)
self.plot2, = plt.plot(x, y, marker="", color=self.plot.get_color())
Alternative: Use the markevery argument.
x = np.sort(item)
y = np.arange(1,len(x)+1) / len(x)
x = np.insert(x,0,0)
y = np.insert(y,0,0)
markevery = range(1, len(x))
self.plot, = plt.plot(x, y, marker=markers[index], markevery=markevery,
ls="", label=self.legend[index])
Given a function g(x), I want to find a fixed point to this function using
fixed point iteration. Except for finding the point itself, I want to plot the graph to the function using matplotlib.pyplot, and include the vertical and horizontal bars that show how the iteration closes in on the fixed point (if one exists). Example picture
All help appreciated!
/programming newbie
EDIT: Since I'm no too comfortable with generator objects yet, I've written the following code. It doesn't quite work though: what's wrong with it?
from matlibplot.axes import vlines, hlines
def fixpt(f, x, epsilon=1.0E-4, N=500, store=False):
y = f(x)
n = 0
if store: Values = [(x, y)]
while abs(y-x) >= epsilon and n < N:
x = f(x)
n += 1
y = f(x)
if store: Values.append((x, y))
vlines(x, min(x, y), max(x, y), color='b')
hlines(y, min(y, x), max(y, x), color='b')
if store:
return y, Values
else:
if n >= N:
return "No fixed point for given start value"
else:
return x, n, y
def fixedpoint(f,x):
while x != f(x):
yield x
x = f(x)
yield x
Usage: fixedpoint(g,some_starting_value).
Vertical and horizontal bars depend on plotting library. Specify which one you use.
Your function looks fine. I am not familiar with vlines and hlines. I used your store arg to get the points, and plot them outside the function (it is generally better to separate problems like this).
I used only the plot function from matplotlib.pyplot, and the show function to display the graph.
from matplotlib import pyplot as plt
import numpy as np
def fixpt(f, x, epsilon=1.0E-4, N=500, store=False):
y = f(x)
n = 0
if store: Values = [(x, y)]
while abs(y-x) >= epsilon and n < N:
x = f(x)
n += 1
y = f(x)
if store: Values.append((x, y))
if store:
return y, Values
else:
if n >= N:
return "No fixed point for given start value"
else:
return x, n, y
# define f
def f(x):
return 0.2*x*x
# find fixed point
res, points = fixpt(f, 3, store = True)
# create mesh for plots
xx = np.arange(0, 6, 0.1)
#plot function and identity
plt.plot(xx, f(xx), 'b')
plt.plot(xx, xx, 'r')
# plot lines
for x, y in points:
plt.plot([x, x], [x, y], 'g')
plt.plot([x, y], [y, y], 'g')
# show result
plt.show()
Here is how I thought it through :
from pylab import *
def f(x):
return 8*x/(1 + 2*x)
def cobweb(x0, n, ax):
xs = [x0]
ys = [0]
for i in range(1,n):
if i % 2 == 0:
xs.append(ys[-1])
ys.append(ys[-1])
else:
xs.append(xs[-1])
ys.append(f(xs[-1]))
ax.plot(xs, ys, 'k--', lw=2.0)
x = linspace(0, 4, 100)
fig = figure()
ax = fig.add_subplot(111)
ax.plot(x, x, 'k', lw=2.0)
ax.plot(x, f(x), 'r', lw=2.0)
cobweb(0.5, 50, ax)
ax.set_xlabel(r'$x$')
ax.set_ylabel(r'$f(x)$')
grid()
show()