New linear algebra algorithm

linear_algebra/src/python-polynom-for-points.py

@@ -0,0 +1,103 @@
+
+from decimal import *
+getcontext().prec=28
+
+
+def points_to_polynomial(coordinates):
+    #the list (coordinates) is two dimensional: [[x, y],[x, y],...]
+
+    if __name__ == "__main__" :
+        #number of points you want to use
+        try:
+            more_check=0
+            d=coordinates[0][0]
+            for j in range(len(coordinates)):
+                if j==0:
+                    continue
+                if d==coordinates[j][0]:
+                    more_check+=1
+                    solved="x="+str(coordinates[j][0])
+                    if more_check == len(coordinates)-1:
+                        check=2
+                        break
+                    elif more_check > 0 and more_check != len(coordinates)-1:
+                        check=3
+                    else:
+                        check=1
+
+            if len(coordinates)==1 and coordinates[0][0]==0:
+                check=2
+                solved="x=0"
+        except:
+            check=3
+
+
+        x=len(coordinates)
+
+        if check==1:
+            count_of_line=0
+            matrix=[]
+            #put the x and x to the power values in a matrix
+            while count_of_line < x:
+                count_in_line=0
+                a=coordinates[count_of_line][0]
+                count_line=[]
+                while count_in_line < x:
+                    count_line.append(a**(x-(count_in_line+1)))
+                    count_in_line+=1
+                matrix.append(count_line)
+                count_of_line+=1
+
+            count_of_line=0
+            #put the y values into a vector
+            vector=[]
+            while count_of_line < x:
+                count_in_line=0
+                vector.append(coordinates[count_of_line][1])
+                count_of_line+=1
+
+            count=0
+
+            while count < x:
+                zahlen=0
+                while zahlen < x:
+                    if count==zahlen:
+                        zahlen+=1
+                    if zahlen==x:
+                        break
+                    bruch=(matrix[zahlen][count])/(matrix[count][count])
+                    counting_columns=0
+                    for i in range(len(matrix[count])):
+                        #manipulating all the values in the matrix
+                        matrix[zahlen][counting_columns]-=(matrix[count][i])*bruch
+                        counting_columns+=1
+                    #manipulating the values in the vector
+                    vector[zahlen]-=vector[count]*bruch
+                    zahlen+=1
+                count+=1
+
+            count=0
+            #make solutions
+            solution=[]
+            while count < x:
+                solution.append(vector[count]/matrix[count][count])
+                count+=1
+
+            count=0
+            solved="f(x)="
+
+            while count < x:
+                remove_e=str(solution[count]).split("E")
+                if len(remove_e) > 1:
+                    solution[count]=remove_e[0]+"*10^"+remove_e[1]
+                solved+="x^"+ str(x-(count+1))+ "*" +str(solution[count])
+                if count+1 != x:
+                    solved+="+"
+                count+=1
+
+            return solved
+
+        elif check==2:
+            return solved
+        else:
+            return "The program cannot work out a fitting polynomial."