Create gauss_seidel_elimination.py

Author: sudipto3331

gauss_seidel_elimination.py

@@ -0,0 +1,130 @@
+# -*- coding: utf-8 -*-
+"""
+
+@author: Sudipto3331
+"""
+
+##Import libraries as necessary
+import numpy as np
+import xlrd
+from xlwt import Workbook
+def brcond_Seidel(E,err,n):
+    
+    a=0
+    for i in range(n):  
+        if E[i]<err:
+            a=a+1
+    return a/n
+
+#taking necessary input values from keyboard
+err=float(input('Enter desired percentage relative error: '))
+ite=int(input('Enter number of iterations: '))
+relaxation=float(input('Enter relaxation factor: '))
+
+#Reading data from excel file
+loc = ('data.xls')
+
+wb = xlrd.open_workbook(loc)
+sheet = wb.sheet_by_index(3)
+
+n=sheet.nrows   #number of unknown variables
+#Initialize variables
+a=np.zeros([n,n+1])
+E=np.zeros([n])
+rel_err=np.zeros([ite,n])
+X=np.zeros([n])
+x=np.zeros([ite,n])
+x_new=np.zeros([ite,n])
+itern=np.zeros([ite])
+p=np.zeros([n])
+
+for i in range(sheet.ncols):
+    for j in range(sheet.nrows):
+        a[j,i]=sheet.cell_value(j, i)
+
+#Iteration for Gauss Seidel begins here.
+for j in range(ite):
+    #storing the values of iteration
+    itern[j]=j+1
+             
+    for i in range(n):
+        summation=0
+        
+        for k in range(n):
+            
+            if k>i or k<i:
+                summation=summation+a[i,k]*x[j,k]
+        
+        x_new[j,i]=(a[i,n]-summation)/a[i,i]   #Determining the values of unknown variables
+        if j>0:
+            x[j,i]=x_new[j,i]*relaxation+(1-relaxation)*x[j-1,i]   #Determining the values of unknown variables
+        if j==0:
+            x[j,i]=x_new[j,i]
+            
+        #Error calculation
+        if j>0:
+            rel_err[j,i]=((x[j,i]-x[j-1,i])/x[j,i])*100
+            E[i]=rel_err[j,i]
+    
+    if j>0:
+        Q=brcond_Seidel(E,err,n)
+        
+        if Q==1:
+            break
+    
+    if j==ite-1:
+        break
+     
+    x[j+1,:]=x[j,:]
+
+num_of_iter=j
+X=x[j,:]
+
+print('The values of the unknown variables are respectively:')
+print(X)
+
+wb = Workbook()
+  
+# add_sheet is used to create sheet.
+sheet1 = wb.add_sheet('Sheet 1')
+
+#writing on excel
+sheet1.write(0,n,'Gauss')
+sheet1.write(0,n+1,'Seidel')
+sheet1.write(1,0,'Number of iteration')
+
+for i in range(1,n+1):
+    sheet1.write(1,i,'x_'+str(i))
+    
+for i in range(n+1,2*n+1):
+    sheet1.write(1,i,'Relative error of x_'+str(i-n))
+
+for i in range(num_of_iter+1):
+    
+    sheet1.write(i+2,0,itern[i])
+    for j in range(n):
+        sheet1.write(i+2,1+j,x[i,j])
+        sheet1.write(i+2,n+1+j,rel_err[i,j])
+   
+sheet1.write(i+4,0,'The')
+sheet1.write(i+4,1,'unknown')
+sheet1.write(i+4,2,'values')
+sheet1.write(i+4,3,'are:')
+for k in range(n):
+    sheet1.write(i+4,k+4,X[k])
+
+#save the excel file
+wb.save('xlwt example.xls')
+
+#Result Verification    
+for i in range(n):
+    summation=0
+    for j in range(n):
+        summation=summation+a[i,j]*X[j]
+    
+    p[i]=summation-a[i,j+1]
+    
+#The implementation is corrct if verification results are all zero
+print('The verification results are:')
+print(p)
+print('The implementation is corrct if verification results are all zero')