Create bisection_method.py

Author: sudipto3331

bisection_method.py

@@ -0,0 +1,123 @@
+# -*- coding: utf-8 -*-
+"""
+@author: sudipto3331
+"""
+
+#Import libraries as necessary
+import math
+import numpy as np
+#import xlwt
+from xlwt import Workbook
+
+#Take necessary input
+#For bisection, two input is required to bracket the root
+xl=np.float(input ('Enter 1st initial value: '))   #1st input
+xu=float(input ('Enter 2nd initial value: '))   #2nd input
+
+#computing function values corresponding to initial values
+
+fxl=(667.38/xl)*(1-math.exp(-0.146843*xl))-40
+fxu=(667.38/xu)*(1-math.exp(-0.146843*xu))-40
+
+#checking initial input values
+if fxl*fxu>0:
+        print('Wrong initial input')
+#if the initial input is correct        
+elif fxl*fxu<0:
+    #taking input
+    err=float(input('Enter desired percentage relative error: '))
+    ite=int(input('Enter number of iterations: '))
+    #initialization
+    x_l=np.zeros([ite])
+    x_u=np.zeros([ite])
+    x_c=np.zeros([ite])
+    
+    f_xl=np.zeros([ite])
+    f_xu=np.zeros([ite])
+    f_xc=np.zeros([ite])
+    
+    rel_err=np.zeros([ite])
+    itern=np.zeros([ite])
+    #storing initial computed values into array
+    x_l[0]=xl
+    x_u[0]=xu
+    
+    f_xl[0]=fxl
+    f_xu[0]=fxu 
+    #begin iteration   
+    for i in range(ite):
+        #storing the values of iteration
+        itern[i]=i+1
+        #Bisection Formula
+        x_c[i]=(x_l[i]+x_u[i])/2
+        
+        f_xl[i]=(667.38/x_l[i])*(1-math.exp(-0.146843*x_l[i]))-40
+        f_xu[i]=(667.38/x_u[i])*(1-math.exp(-0.146843*x_u[i]))-40
+        f_xc[i]=(667.38/x_c[i])*(1-math.exp(-0.146843*x_c[i]))-40
+        #calculating error    
+        if i>0:
+            rel_err[i]=((x_c[i]-x_c[i-1])/x_c[i])*100
+        #terminate if error criteria meets
+        if all ([i>0, abs(rel_err[i])<err]):
+            break 
+        elif f_xc[i]==0:
+            break
+   
+        if i==ite-1:
+            break
+        #replacement of the new estimate
+        if all ([f_xc[i]>0, f_xl[i]>0]):
+            x_l[i+1]=x_c[i]
+            x_u[i+1]=x_u[i]
+        elif all ([f_xc[i]>0, f_xu[i]>0]):
+            x_u[i+1]=x_c[i]
+            x_l[i+1]=x_l[i]
+        elif all ([f_xc[i]<0, f_xl[i]<0]):
+            x_l[i+1]=x_c[i]
+            x_u[i+1]=x_u[i]
+        elif all ([f_xc[i]<0, f_xu[i]<0]):
+            x_u[i+1]=x_c[i]
+            x_l[i+1]=x_l[i]
+    
+    #Writing the results on an excel sheet    
+    #Workbook is created
+    wb = Workbook()
+      
+    # add_sheet is used to create sheet.
+    sheet1 = wb.add_sheet('Sheet 1')
+    num_of_iter=i
+    
+    #writing on excel
+    #sheet1.write(0,2,'The')
+    sheet1.write(0,3,'Bisection')
+    sheet1.write(0,4,'Method')
+    #sheet1.write(0,5,x_c[i])
+    
+    sheet1.write(1,0,'Number of iteration')
+    sheet1.write(1,1,'x_l')
+    sheet1.write(1,2,'x_u')
+    sheet1.write(1,3,'f(x_l)')
+    sheet1.write(1,4,'f(x_u)')
+    sheet1.write(1,5,'x_c')
+    sheet1.write(1,6,'f(x_c)')
+    sheet1.write(1,7,'Relative error')
+    
+    #writing values on excel    
+    for n in range(num_of_iter+1):
+        
+        sheet1.write(n+2,0,itern[n])
+        sheet1.write(n+2,1,x_l[n])
+        sheet1.write(n+2,2,x_u[n])
+        sheet1.write(n+2,3,f_xl[n])
+        sheet1.write(n+2,4,f_xu[n])
+        sheet1.write(n+2,5,x_c[n])
+        sheet1.write(n+2,6,f_xc[n])
+        sheet1.write(n+2,7,rel_err[n])
+    
+    sheet1.write(n+4,2,'The')
+    sheet1.write(n+4,3,'root')
+    sheet1.write(n+4,4,'is')
+    sheet1.write(n+4,5,x_c[i])
+    
+    #save the excel file
+    wb.save('LAB1.xls')