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Generating a random float below and above a line created by numpy arrays python

I would like to generate a random float point above and below a line created by numpy arrays.
For example I have these line equations:
x_values = np.linspace(-1, 1, 100)
y1 = 2 * x_values -5
y2= -3 * x_values +2
plt.plot(x_values,y1, '-k')
plt.plot(x_values,y2, '-g')
I have tried this method from Generate random points above and below a line in Python and it works if np.arrange is used like so:
lower, upper = -25, 25
num_points = 1
x1 = [random.randrange(start=1, stop=9) for i in range(num_points)]
x2 = [random.randrange(start=1, stop=9) for i in range(num_points)]
y1 = [random.randrange(start=lower, stop=(2 * x -5) )for x in x1]
y2 = [random.randrange(start=(2 * x -5), stop=upper) for x in x2]
plt.plot(np.arange(10), 2 * np.arange(10) -5)
plt.scatter(x1, y1, c='blue')
plt.scatter(x2, y2, c='red')
However, I wanted to find a way to generate a random point if np.linspace(-1, 1, 100) was used to create the line graph. The difference is involving/allowing float coordinates to be picked to. But unsure how.
Any ideas will be appreciated.

Here is an approach, using functions for the y-values. Random x positions are chosen uniformly over the x-range. For each random x, a value is randomly chosen between its y-ranges.
import numpy as np
import matplotlib.pyplot as plt
x_values = np.linspace(-1, 1, 100)
f1 = lambda x: 2 * x - 5
f2 = lambda x: -3 * x + 2
y1 = f1(x_values)
y2 = f2(x_values)
plt.plot(x_values, y1, '-k')
plt.plot(x_values, y2, '-g')
plt.fill_between (x_values, y1, y2, color='gold', alpha=0.2)
num_points = 20
xs = np.random.uniform(x_values[0], x_values[-1], num_points)
ys = np.random.uniform(f1(xs), f2(xs))
plt.scatter(xs, ys, color='crimson')
plt.show()
PS: Note that the simplicity of the approach chooses x uniform over its length. If you need an even distribution over the area of the trapezium, you need the x less probable at the right, and more at the left. You can visualize this with many more points and using transparency. With the simplistic approach, the right will look denser than the left.
The following code first generates x,y points in a parallelogram, and remaps the points on the wrong side back to its mirror position. The code looks like:
import numpy as np
import matplotlib.pyplot as plt
x0, x1 = -1, 1
x_values = np.linspace(x0, x1, 100)
f1 = lambda x: 2 * x - 5
f2 = lambda x: -3 * x + 2
y1 = f1(x_values)
y2 = f2(x_values)
plt.plot(x_values, y1, '-k')
plt.plot(x_values, y2, '-g')
plt.fill_between(x_values, y1, y2, color='gold', alpha=0.2)
num_points = 100_000
h0 = f2(x0) - f1(x0)
h1 = f2(x1) - f1(x1)
xs1 = np.random.uniform(x0, x1, num_points)
ys1 = np.random.uniform(0, h0 + h1, num_points) + f1(xs1)
xs = np.where(ys1 <= f2(xs1), xs1, x0 + x1 - xs1)
ys = np.where(ys1 <= f2(xs1), ys1, f1(xs) + h0 + h1 + f1(xs1) - ys1)
plt.scatter(xs, ys, color='crimson', alpha=0.2, ec='none', s=1)
plt.show()
Plot comparing the two approaches:

First of all, if you have 2 intersecting lines, there will most likely be a triangle in which you can pick random points. This is dangerously close to Bertrand's paradox, so make sure that your RNG suits its purpose.
If you don't really care about how "skewed" your randomness is, try this:
import numpy as np
left, right = -1, 1
# x_values = np.linspace(left, right, 100)
k1, k2 = 2, -3
b1, b2 = -5, 2
y1 = lambda x: k1*x + b1
y2 = lambda x: k2*x + b2
# If you need a point above the 1st equation, but below the second one.
# Check the limits where you can pick the points under this condition.
nosol = False
if k1==k2:
if b1>=b2:
inters = -100
nosol = True
else:
rand_x = np.random.uniform(left,right)
rand_y = np.random.uniform(y1(rand_x),y2(rand_x))
print(f'Random point is ({round(rand_x,2)}, {round(rand_y,2)})')
else:
inters = (b2-b1)/(k1-k2)
if inters<=left:
if k1>=k2:
nosol=True
elif inters>=right:
if k1<=k2:
nosol=True
if nosol:
print('No solution')
else:
if k1>k2:
right = inters
else:
left = inters
# Pick random X between "left" and "right"
# Pick whatever distribution you like or need
rand_x = np.random.uniform(left,right)
rand_y = np.random.uniform(y1(rand_x),y2(rand_x))
print(f'Random point is ({round(rand_x,2)}, {round(rand_y,2)})')
If your random X needs to belong to a specific number sequence, use some other np.random function: randint, choice...

Is it possible to create multiple axis plot side by side and have them connected?

I have data with 5 parameters, which I want to plot on multiple y axes and have them connected. Please see the example picture.
Currently I tried with normalizing all the values and create dictionary to do a scatter plot where on x axis would be values 1, 2, 3, 4, 5 and on y axis 5 parameter values for each data point. But this way I will need to add axis lines and values later on in Photoshop.
Is there a better way to create such graph using matplotlib and python?

One idea is to create 4 extra y axes, and set explicit limits for them. All the y-values can be rescaled to be compatible with the host axis.
(The code can still be optimized to make better use of numpy.)
import matplotlib.pyplot as plt
import numpy as np
fig, host = plt.subplots()
N = 20
y1 = np.random.uniform(10, 50, N)
y2 = np.sin(np.random.uniform(0, np.pi, N))
y3 = np.random.binomial(300, 0.9, N)
y4 = np.random.pareto(10, N)
y5 = np.random.uniform(0, 800, N)
ys = [y1, y2, y3, y4, y5]
y0min = ys[0].min()
dy = ys[0].max() - y0min
zs = [ys[0]] + [(y - y.min()) / (y.max() - y.min()) * dy + y0min for y in ys[1:]]
ynames = ['P1', 'P2', 'P3', 'P4', 'P5']
axes = [host] + [host.twinx() for i in range(len(ys) - 1)]
for i, (ax, y) in enumerate(zip(axes, ys)):
ax.set_ylim(y.min(), y.max())
ax.spines['top'].set_visible(False)
ax.spines['bottom'].set_visible(False)
if ax != host:
ax.spines['left'].set_visible(False)
ax.yaxis.set_ticks_position('right')
ax.spines["right"].set_position(("axes", i / (len(ys) - 1)))
host.set_xlim(0, len(ys) - 1)
host.set_xticks(range(len(ys)))
host.set_xticklabels(ynames)
host.tick_params(axis='x', which='major', pad=7)
host.spines['right'].set_visible(False)
colors = plt.cm.tab20.colors
for j in range(len(ys[0])):
host.plot(range(len(ys)), [z[j] for z in zs], c=colors[j % len(colors)])
plt.show()

Generate random points above and below a line in Python

I would like to generate random points on an x,y scatter plot that are either above or below a given line. For example, if the line is y=x I would like to generate a list of points in the top left of the plot (above the line) and a list of points in the bottom right of the plot (below the line). Here's is an example where the points are above or below y=5:
import random
import matplotlib.pyplot as plt
num_points = 10
x1 = [random.randrange(start=1, stop=9) for i in range(num_points)]
x2 = [random.randrange(start=1, stop=9) for i in range(num_points)]
y1 = [random.randrange(start=1, stop=5) for i in range(num_points)]
y2 = [random.randrange(start=6, stop=9) for i in range(num_points)]
plt.scatter(x1, y1, c='blue')
plt.scatter(x2, y2, c='red')
plt.show()
However, I generated the x and y points independently, which limits me to equations where y = c (where c is a constant). How can I expand this to any y=mx+b?

You can change the stop and start limits for y1 and y2 to be the line you want. You will need to decide where the plane ends (set lower and upper).
Note this only works for integers. You can use truncated multivariate distributions if you want something more sophisticated.
m, b = 1, 0
lower, upper = -25, 25
x1 = [random.randrange(start=1, stop=9) for i in range(num_points)]
x2 = [random.randrange(start=1, stop=9) for i in range(num_points)]
y1 = [random.randrange(start=lower, stop=m*x+b) for x in x1]
y2 = [random.randrange(start=m*x+b, stop=upper) for x in x2]
plt.plot(np.arange(10), m*np.arange(10)+b)
plt.scatter(x1, y1, c='blue')
plt.scatter(x2, y2, c='red')

You may as well have my answer too.
This way puts Gaussian noise above the line, and below. I have deliberately set the mean of the noise to 20 so that it would stand out from the line, which is y = 10*x + 5. You would probably make the mean zero.
>>> import random
>>> def y(x, m, b):
... return m*x + b
...
>>> import numpy as np
>>> X = np.linspace(0, 10, 100)
>>> y_above = [y(x, 10, 5) + abs(random.gauss(20,5)) for x in X]
>>> y_below = [y(x, 10, 5) - abs(random.gauss(20,5)) for x in X]
>>> import matplotlib.pyplot as plt
>>> plt.scatter(X, y_below, c='g')
>>> plt.scatter(X, y_above, c='r')
>>> plt.show()
Here's the plot.

There are many approaches possible, but if your only requirement is that they are above and below the y = mx + b line, then you can simply plug the random x values into the equation and then add or subtract a random y value.
import random
import matplotlib.pyplot as plt
slope = 1
intercept = 0
def ymxb(slope, intercept, x):
return slope * x + intercept
num_points = 10
x1 = [random.randrange(start=1, stop=9) for i in range(num_points)]
x2 = [random.randrange(start=1, stop=9) for i in range(num_points)]
y1 = [ymxb(slope, intercept, x) - random.randrange(start=1, stop=9) for x in x1]
y2 = [ymxb(slope, intercept, x) + random.randrange(start=1, stop=9) for x in x2]
plt.scatter(x1, y1, c='blue')
plt.scatter(x2, y2, c='red')
plt.show()
That looks like this:

Side of (x, y) is defined by the sign of y - mx - b. You can read it here, for example.
import random
import matplotlib.pyplot as plt
num_points = 50
x = [random.randrange(start=1, stop=9) for i in range(num_points)]
y = [random.randrange(start=1, stop=9) for i in range(num_points)]
m = 5
b = -3
colors = ['blue' if y[i] - m * x[i] - b > 0 else 'red' for i in range(num_points) ]
plt.plot([0, 10], [b, 10 * m + b], c='green')
plt.xlim((0, 10))
plt.ylim((0, 10))
plt.scatter(x, y, c=colors)
plt.show()

matplotlib, how to plot 3d 2 variable function under given conditions

Plotting the function:
(x1 - 3)^2 + (x2 - 2)^2
With constraints:
x1^2 - x2 - 3 <= 0
x2 - 1 <= 0
-x1 <= 0
The equation can also be found here.
I am trying to solve this graphically using matplotlib
but ended up with the above graph using the code below (the question i found that helped me with the code) which is missing the first condition.
import matplotlib.pyplot as plt
from numpy import arange
from pylab import meshgrid
# function to be plotted
def z_func(a, b):
return (a - 3) * (a - 3) + (b - 2) * (b - 2)
x1 = arange(15.0, 0, -0.1) # x1 >= 0 according to given conditions
x2 = arange(-15.0, 1, 0.1) # x2 <= 1 according to given conditions
X1,X2 = meshgrid(x1, x2)
Z = z_func(X1, X2)
fig = plt.figure()
ax = fig.gca(projection='3d')
surf = ax.plot_surface(X1, X2, Z, rstride=1, cstride=1, cmap=cm.RdBu,linewidth=0, antialiased=False)
ax.zaxis.set_major_locator(LinearLocator(10))
ax.zaxis.set_major_formatter(FormatStrFormatter('%.02f'))
ax.set_xlabel('x-axis')
ax.set_ylabel('y-axis')
ax.set_zlabel('z-axis')
ax.view_init(elev=25, azim=-120)
fig.colorbar(surf, shrink=0.5, aspect=5)
plt.show()
in which way shall the above code be altered in order to also take the first condition into account?
thanks

You can filter the array to plot and set all values outside the condition to nan:
Z[X1**2 - X2 - 3 > 0] = np.nan
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d.axes3d import Axes3D
import numpy as np
from pylab import meshgrid
# function to be plotted
def z_func(a, b):
return (a - 3) * (a - 3) + (b - 2) * (b - 2)
x1 = np.arange(15.0, 0, -0.1) # x1 >= 0 according to given conditions
x2 = np.arange(-15.0, 1, 0.1) # x2 <= 1 according to given conditions
X1,X2 = meshgrid(x1, x2)
Z = z_func(X1, X2)
# set all values outside condition to nan
Z[X1**2 - X2 - 3 > 0] = np.nan
fig = plt.figure()
ax = fig.gca(projection='3d')
surf = ax.plot_surface(X1, X2, Z, rstride=1, cstride=1,vmin=0, vmax=np.nanmax(Z),
cmap=plt.cm.RdBu,linewidth=0, antialiased=False)
ax.set_xlabel('x-axis')
ax.set_ylabel('y-axis')
ax.set_zlabel('z-axis')
ax.view_init(elev=25, azim=-120)
ax.set_ylim(0,4)
fig.colorbar(surf, shrink=0.5, aspect=5)
plt.show()

Draw a curve connecting two points instead of a straight line

I want to do something like this:
I have the points but don't know how to plot the curves instead of straight lines.
Thank you.

For people interested in this question, I followed Matthew's suggestion and came up with this implementation:
def hanging_line(point1, point2):
import numpy as np
a = (point2[1] - point1[1])/(np.cosh(point2[0]) - np.cosh(point1[0]))
b = point1[1] - a*np.cosh(point1[0])
x = np.linspace(point1[0], point2[0], 100)
y = a*np.cosh(x) + b
return (x,y)
Here is what the result looks like:
import matplotlib.pyplot as plt
point1 = [0,1]
point2 = [1,2]
x,y = hanging_line(point1, point2)
plt.plot(point1[0], point1[1], 'o')
plt.plot(point2[0], point2[1], 'o')
plt.plot(x,y)

You are going to need some expression for the curve you want to plot, then you can make the curve out of many line segments.
Here's a parabola:
x = np.linspace(-1, 1, 100)
y = x*x
plt.plot(x, y)
Here's a sin curve:
x = np.linspace(-2*np.pi, 2*np.pi, 100)
y = np.sin(x)
plt.plot(x, y)
Each of these looks smooth, but is actually made up of many small line segments.
To get a collection of curves like you showed, you are going to need some expression for a curve you want to plot in terms of its two endpoints. The ones in your picture look like catenarys which are (approximately) the shape a hanging chain assumes under the force of gravity:
x = np.linspace(-2*np.pi, 2*np.pi, 100)
y = 2*np.cosh(x/2)
plt.plot(x, y)
You will have to find a way of parameterizing this curve in terms of its two endpoints, which will require you substituting your values of y and x into:
y = a*cosh(x/a) + b
and solving the resulting pair of equations for a and b.

There is a cool (at least for me) way to draw curve lines between two points, using Bezier curves. Just with some simple code you can create lists with dots connecting points and chart them with matplotlib, for example:
def recta(x1, y1, x2, y2):
a = (y1 - y2) / (x1 - x2)
b = y1 - a * x1
return (a, b)
def curva_b(xa, ya, xb, yb, xc, yc):
(x1, y1, x2, y2) = (xa, ya, xb, yb)
(a1, b1) = recta(xa, ya, xb, yb)
(a2, b2) = recta(xb, yb, xc, yc)
puntos = []
for i in range(0, 1000):
if x1 == x2:
continue
else:
(a, b) = recta(x1, y1, x2, y2)
x = i*(x2 - x1)/1000 + x1
y = a*x + b
puntos.append((x,y))
x1 += (xb - xa)/1000
y1 = a1*x1 + b1
x2 += (xc - xb)/1000
y2 = a2*x2 + b2
return puntos
Then, just run the function for some starting, mid and ending points, and use matplotlib:
lista1 = curva_b(1, 2, 2, 1, 3, 2.5)
lista2 = curva_b(1, 2, 2.5, 1.5, 3, 2.5)
lista3 = curva_b(1, 2, 2.5, 2, 3, 2.5)
lista4 = curva_b(1, 2, 1.5, 3, 3, 2.5)
fig, ax = plt.subplots()
ax.scatter(*zip(*lista1), s=1, c='b')
ax.scatter(*zip(*lista2), s=1, c='r')
ax.scatter(*zip(*lista3), s=1, c='g')
ax.scatter(*zip(*lista4), s=1, c='k')
This should be the results:
several Bezier quadratic curves
By extending the code a little more, you can get forms like this:
Bezier quartic curve