Terminal Cruise

Generating the Weierstrass Monster with #Python

This is pathology of calculus that is continuous everywhere but differentiable nowhere. Henri Poincaré condemned it as “an outrage against common sense.” Charles Hermite called it a “deplorable evil.” Muahahahaha!

#!/usr/bin/env python3
import numpy as n,matplotlib.pyplot as p
a=.5;b=11;n_terms=50
x=n.linspace(-2,2,20000)
f=sum(a**k*n.cos(b**k*n.pi*x) for k in range(n_terms))
p.plot(x,f,'b',lw=.1)
p.title('Weierstrass Function')
p.grid()
p.show()

Calculate parallel resistance (or series capacitance) with Python

#!/usr/bin/env python3
import sys,numpy as n
print(sys.argv[1:],'->',1/(1/n.array(sys.argv[1:],float)).sum())

Solve for the intersection of two lines from four points with Python

#!/usr/bin/env python3
import sys,numpy as n
p,q,r,s=map(n.array,((float(sys.argv[i]),float(sys.argv[i+1])) for i in (1,3,5,7)))
M=n.c_[q-p,s-r]
d=n.linalg.det(M)
if abs(d)<1e-10:
    print("Coincident" if abs(n.cross(q-p,r-p))<1e-10 else "Parallel")
else:
    t,_=n.linalg.solve(M,r-p)
    print(p+t*(q-p))

Closing in on a square wave with the Fourier series under Python

#!/usr/bin/env python3
import numpy as n,matplotlib.pyplot as p
x=n.linspace(0,2*n.pi,1000)
def s(x,t):
    k=n.arange(1,2*t,2)
    return 4/n.pi*(n.sin(k[:,None]*x)/k[:,None]).sum(0)
N=12
colors=p.cm.rainbow(n.linspace(0,1,N))
for i,t in enumerate(range(1,N+1)):
    p.plot(x,s(x,t),color=colors[i],label=f'{2*t-1} harmonics')
p.title('Fourier Series Approximation of a Square Wave')
p.grid()
p.legend()
p.show()

Plotting a trig function and its derivative with Python

#!/usr/bin/env python3
import numpy as n,matplotlib.pyplot as p
x=n.linspace(-4,4,400)
f=n.arctan(x**2);df=2*x/(x**4+1)
p.plot(x,f,'b',label='f(x)=arctan(x²)')
p.plot(x,df,'r',label="f'(x)=2x/(x⁴+1)")
p.axhline(0,c='k',lw=.5);p.axvline(0,c='k',lw=.5)
p.ylim(-2,2);p.xlabel('x');p.ylabel('y')
p.title("f(x) and f'(x)")
p.grid(ls=':',alpha=.7);p.legend();p.show()

The gamma function with Python

#!/usr/bin/env python3
from scipy.special import gamma
a,b=.1,2
n=25
p=(5**.5-1)/2
c=b-p*(b-a)
d=a+p*(b-a)
fc,fd=gamma(c),gamma(d)
print(f'{"Iter":>4} {"x":>12} {"gamma(x)":>12}')
for i in range(1,n+1):
    if fc<fd:
        b,d,fd=d,c,fc
        c=b-p*(b-a)
        fc=gamma(c)
        x,f=c,fc
    else:
        a,c,fc=c,d,fd
        d=a+p*(b-a)
        fd=gamma(d)
        x,f=d,fd
    print(f"{i:4d} {x:12.8f} {f:12.8f}")
print(f"\nLocal minimum approx: x = {x:.10f}, gamma(x) = {f:.10f}")\

#!/usr/bin/env python3
import numpy as n,matplotlib.pyplot as p
from scipy.special import gamma
x=n.linspace(.1,2,500)
y=gamma(x)
m=1.461632
p.plot(x,y,label='gamma(x)')
p.axvline(m,color='r',ls='--',label=f'min near x={m:.6f}')
p.scatter(m,gamma(m),color='r')
p.title('Gamma function near its first local minimum')
p.xlabel('x')
p.ylabel('gamma(x)')
p.grid()
p.legend()
p.tight_layout()
p.show()

Python for all your linear algebra homework:

#!/usr/bin/env python3
import sys,ast,numpy as np
a=np.array(ast.literal_eval(sys.argv[1]))
print("Matrix:")
print(np.matrix(a))
print("\nTranspose:")
print(np.matrix(a.T))
print("\nTrace:",a.trace())
print("\nRank:",np.linalg.matrix_rank(a))
if a.shape[0]==a.shape[1]:
    print("\nDeterminant:",round(np.linalg.det(a),6))
    d,e=np.linalg.eig(a)
    print("\nEigenvalues:",np.round(d,6))
    print("\nEigenvectors:")
    print(np.round(e,6))
print("\nPseudo-inverse:")
print(np.matrix(np.linalg.pinv(a)))

Convert text to italics with Python

#!/usr/bin/env python3
import sys
a="ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz"
b="𝘈𝘉𝘊𝘋𝘌𝘍𝘎𝘏𝘐𝘑𝘒𝘓𝘔𝘕𝘖𝘗𝘘𝘙𝘚𝘛𝘜𝘝𝘞𝘟𝘠𝘡𝘢𝘣𝘤𝘥𝘦𝘧𝘨𝘩𝘪𝘫𝘬𝘭𝘮𝘯𝘰𝘱𝘲𝘳𝘴𝘵𝘶𝘷𝘸𝘹𝘺𝘻"
print(" ".join(sys.argv[1:]).translate(str.maketrans(a,b)))

#!/usr/bin/env python3
import sys
c="ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789"
b="𝗔𝗕𝗖𝗗𝗘𝗙𝗚𝗛𝗜𝗝𝗞𝗟𝗠𝗡𝗢𝗣𝗤𝗥𝗦𝗧𝗨𝗩𝗪𝗫𝗬𝗭𝗮𝗯𝗰𝗱𝗲𝗳𝗴𝗵𝗶𝗷𝗸𝗹𝗺𝗻𝗼𝗽𝗾𝗿𝘀𝘁𝘂𝘃𝘄𝘅𝘆𝘇𝟬𝟭𝟮𝟯𝟰𝟱𝟲𝟳𝟴𝟵"
print("".join(b[c.find(x)] if x in c else x for x in " ".join(sys.argv[1:])))

Find anagrams with Python

#!/usr/bin/env python3
from collections import Counter
import sys,os
s=sys.argv[1]
def anagrams(word,words):
    cw=Counter(word)
    return [w for w in words if Counter(w)==cw]
base=os.path.dirname(os.path.abspath(__file__))
path=os.path.join(base,"words.txt")
with open(path) as f:
    lines=f.read().splitlines()
print(anagrams(s,lines))