From 14e9e99b0be854c207a8069a3f14f87691f33f23 Mon Sep 17 00:00:00 2001
From: nandard <nanda.r.d@mail.ugm.ac.id>
Date: Thu, 8 Sep 2022 03:24:34 +0700
Subject: [PATCH] Add documentation

---
 README.md | 43 ++++++++++++++++++++++++++++++++++++++++++-
 1 file changed, 42 insertions(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 40b9120..7ef422a 100644
--- a/README.md
+++ b/README.md
@@ -6,4 +6,45 @@ Libraries that used in this program is ```numpy``` and ```pandas```. ```numpy```
 ```
 import numpy as np
 import pandas as pd
-```
\ No newline at end of file
+```
+
+## RouthStability Class
+This class contains lots of procedures to simplify our Routh Stability Table Generator process. 
+```
+def __init__(self, den):
+    self.den = np.array([float(item) for item in den.split()])
+    self.deg = len(self.den)
+```
+The constructor ```__init__``` takes string of coefficiens from polynomial, extract the number, and load into class variable. It also define ```self.deg``` variable to save array's length, reducing number of calling ```len()``` function
+
+```
+def set_k(self, k):
+    self.den = np.append(self.den, float(k))
+    self.deg += 1
+```
+This function only takes one number from user and append it to ```self.den``` which defined as gain (constant). Also ```self.deg``` will increase by one
+
+```
+def calc_routh(self):
+    height = (self.deg+1)//2
+    arr = np.zeros((height + 2,height))
+    for index in range(self.deg):
+        if index % 2 == 0:
+        arr[0][index//2] = self.den[index]
+        else:
+        arr[1][(index-1)//2] = self.den[index]
+
+    for i in range(2, height+2):
+        for j in range(height-1):
+        arr[i][j] = (arr[i-1][0]*arr[i-2][j+1] - arr[i-2][0]*arr[i-1][j+1])//2
+        arr[i][j] += 0
+
+    self.df = pd.DataFrame(arr)
+    self.show_tab()
+    if self.is_stable() == True:
+        print("SYSTEM IS STABLE")
+    else:
+        print("SYSTEM IS UNSTABLE")
+```
+```calc_routh(self)``` as the core process of this class contains initialization and process about Routh Stability Process. Firstly, it define an empty zero (basically it filled with zeros) and iteratively being inserted by ```self.den``` (refering to Routh Table principle). After that, each cell will be updated by calculating Routh Table formula 
+$$  arr_{i,j} = \frac{arr_{i-1][0]*arr[i-2][j+1] - arr[i-2][0]*arr[i-1][j+1]}{arr_{i-1][0]} $$