crclayton | routh-hurwitz

Routh-Hurwitz Criterion Calculator

Input

Output

Instructions

Enter coefficients in descending order of s, specify the significant figures, and specify with which mode to do the calculations.

As you modify the input code, the output will be continuously updated.

Approximate Mode

This program approximates ^±1⁄ ₀= ±10 ¹⁰⁰, ⁰⁄ ₀= 1, and 0 = 10 ⁻¹⁰⁰. To see why approximate mode is important, compare modes True and False with the program's default coefficients of [1,3,2,0,0].

About

This program uses Skulpt and CodeMirror. Skulpt is a pretty cool in-browser Python interpretter, so feel free to play around with the input and try to crash your browser. Unfortunately Python's' eval function has not been implemented yet, so this application only does numerical Routh-Hurwitz calculations. Feel free to contribute on GitHub.

Also, if you don't have adblock on, you may notice and ad below. If you wanted to click it, that'd be a big help. No pressure.

coefficients = [float(i) for i in coefficients]
n = len(coefficients) - 1
r = []

# this program will do the routh-hurwitz of any 
# order polynomial if you add more padding. 
# We give enough for order 40 which should 
padding = [0]*20

# show the user the polynomial
s = [str(a) + "s<sup>" + str(i) + "</sup>" for i, a in enumerate(coefficients[::-1])]
print "characteristic equation: \n   " + " + ".join(s[::-1]) + "\n"

# create the top two rows
r.append(coefficients[::2] + padding)
r.append(coefficients[1::2] + padding)

# implement the algorithm here: http://en.wikipedia.org/wiki/Routh%E2%80%93Hurwitz_stability_criterion#Higher-order_example
for j in range(2, len(coefficients)):
    row = []
    for i in range(n):
        numerator = (r[j-1][0]*r[j-2][i+1])-(r[j-2][0]*r[j-1][i+1])
        denominator = r[j-1][0]
        if denominator == 0:
            if numerator > 0:   result = 10**100
            elif numerator < 0: result = -(10**100)
            else:               result = 1
        else:
            result = numerator/denominator
            if result == 0 and approximate_mode == True: 
				result = 10**(-100)
                
        row.append(result)
    r.append(row + padding)

# print the created routh-hurwitz table
table = "<table>"
for row in r:
	table += "<tr>"
	for i in range(n):
		result = "%s" % float( ("%." + str(significant_figures) + "g") % row[i])
		if i == 0: result = "<b>" + result + "</b>"
		table += "<td>" + result + "</td>" 
	table += "</tr>"
print table + "</table>"