Added function visualization toolbox(sorry I'm still an amateur compared to Andre)

Author: OceanNuclear

FunctionVisualization/sin(arccos(x)).png

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+#!/home/ocean/anaconda3/bin/python3
+#^change the line above to point to your python environment
+#This function visualize a function as a bunch of arrows instead of a 2D graph. See https://www.youtube.com/watch?v=CfW845LNObM for details
+#The evenly spaced points on the original number line are connected to where they will land in the transformed number line (below and parallel to the original number line.)
+#Author: Ocean Wong, May 2018, University of Birmingham.
+from numpy import *; from numpy import array as ary; import numpy as np; tau = 2*pi
+import matplotlib.pyplot as plt; import matplotlib as mpl
+
+#<Change-able parameters>
+Range = ary([-1,1])
+def f(x):
+	return sin(arccos(x))
+#Must keep the function on line 12, because of some hack-y function below
+#</Change-able parameters>
+
+#Get the function name
+Line = open(__file__).readlines()
+function = Line[11][8:-1]
+functionFileName = function.replace("/", "_over_")#change the forbidden characters to something else.
+
+#plotting
+x = np.linspace(Range[0],Range[1], 100)
+y = f(x)
+z = np.diff( f(x) )/np.diff(x)
+Color = np.transpose(
+	ary([np.linspace(1,1,len(x)), #Make the color vary
+	np.linspace(0,1,len(x)),
+	np.linspace(0,0,len(x)),
+	np.linspace(0.8,0.8,len(x))])
+	)	#transposed such that I can give a list of len(Color[n])==4 when plotting.
+
+fig = plt.figure(facecolor='black')
+#fig.patch.set_facecolor('black')
+ax = fig.add_subplot(111,facecolor='black')
+#ax.set_faceolor
+
+ax.set_aspect(1)	#fix aspect ratio
+ax.set_xlim(Range)	#cut off the excess of the graph
+#ax.set_ylim([-1.1,1.1])
+ax.set_yticks([])	#vertical case shouldn't have any coordinates.
+plt.tight_layout() #same as adding #fig = plt.figure(); fig.set_tight_layout(True)#These two lines needs to be added before ax declaration
+
+option = str(input("Do you want to differentiate (diff) or integrate the function (int)? \n (enter nothing if you want neither)"))
+
+if option == "diff":
+	z = np.diff( f(x) )/np.diff(x)
+	for n in range (len(z)):
+		ax.plot( [y[n],z[n]], [1,0], color = Color[n])
+	plt.title("differentiate "+function)
+	#plt.show()
+	plt.savefig("differentiate_"+functionFileName+".png")
+
+elif option == "int":
+	dx = np.diff(x)[0]
+	def Y(y):
+		Y = np.zeros(len(y))
+		for n in range (len(y)):
+			Y[n] = sum(y[0:n])*dx
+		return Y
+	z = Y(y)
+	for n in range (len(z)):
+		ax.plot( [y[n],z[n]], [1,0], color = Color[n])
+	plt.title("integrate "+function)
+	#plt.show()
+	plt.savefig("integrate_"+functionFileName+".png")
+
+else:
+	for n in range (len(x)):
+		ax.plot( [x[n],y[n]] , [1,0], color = Color[n])
+		plt.title(function)
+		plt.tight_layout() #same as adding #fig = plt.figure(); fig.set_tight_layout(True)#These two lines needs to be added before 
+	plt.savefig(functionFileName+".png")