Define a trend up or down a trend

Question

I am trying to read data and plot it on a graph using python (standard line graph). Can someone please advise how I can classify whether certain points on the chart are upward or downward trends programmatically? What would be the best way to achieve this? Of course, this is a solvable problem and is there a mathematical equation to identify this?

Here are some examples of data with some trends and downtrends.

x = [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30]
y = [2,5,7,9,10,13,16,18,21,22,21,20,19,18,17,14,10,9,7,5,7,9,10,12,13,15,16,17,22,27]

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Answer 1

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import numpy as np
import matplotlib.pyplot as plt
from scipy.interpolate import interp1d
from scipy.misc import derivative

x = np.array([1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,\
              16,17,18,19,20,21,22,23,24,25,26,27,28,29,30])
y = np.array([2,5,7,9,10,13,16,18,21,22,21,20,19,18,\
              17,14,10,9,7,5,7,9,10,12,13,15,16,17,22,27])

# Simple interpolation of x and y    
f = interp1d(x, y)
x_fake = np.arange(1.1, 30, 0.1)

# derivative of y with respect to x
df_dx = derivative(f, x_fake, dx=1e-6)

# Plot
fig = plt.figure()
ax1 = fig.add_subplot(211)
ax2 = fig.add_subplot(212)

ax1.errorbar(x, y, fmt="o", color="blue", label='Input data')
ax1.errorbar(x_fake, f(x_fake), label="Interpolated data", lw=2)
ax1.set_xlabel("x")
ax1.set_ylabel("y")

ax2.errorbar(x_fake, df_dx, lw=2)
ax2.errorbar(x_fake, np.array([0 for i in x_fake]), ls="--", lw=2)
ax2.set_xlabel("x")
ax2.set_ylabel("dy/dx")

leg = ax1.legend(loc=2, numpoints=1,scatterpoints=1)
leg.draw_frame(False)

, " " ( ) " " ( ), (dy/dx) . dy/dx = 0, . scipy- :

http://docs.scipy.org/doc/scipy/reference/generated/scipy.misc.derivative.html

http://docs.scipy.org/doc/scipy/reference/tutorial/interpolate.html

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