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leastSquareMethod.py
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leastSquareMethod.py
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#welcome screen
print("-"*72)
print("""+ Least Square Method +
+ The least square method is the process of finding the best-fitting +
+ curve or line of best fit for a set of data points by reducing the +
+ sum of the squares of the offsets (residual part) of the points +
+ from the curve. +""")
print("-"*72)
#########################################################################
#animation
import time
import sys
print("Wait a sec")
animation = "|/-\\"
for i in range(60):
time.sleep(0.1)
sys.stdout.write("\r" + animation[i % len(animation)])
sys.stdout.flush()
print ("\nProgram Loaded Succesfully!")
########################################################################
import numpy as np
import math
from tabulate import tabulate
#clearscreen
def clear_screen():
import os
os.system("clear") # Linux - OSX
os.system("cls") # Windows
#welcometext
welcometext="""
{+}-----------------------{+}---------------------------{+}
# #
# 1) Straight line: y=ax+b #
# 2) Parabola: y=ax^2+bx+c or y=a+bx+cx^2 #
# 3) Exponential curve: y=ae^bx #
# 4) Curve: y=ax^b and #
# 5) Another curve: y=ab^x #
# {99} Exit #
# #
{+}-----------------------{+}---------------------------{+}
"""
print("\nFollowing are the available option for Curve fitting:")
print(welcometext)
print("To Use any of the curve input corresponding number:")
#######################################################################
while True:
try:
curve=input("\nSelect a Curve= ")
clear_screen()
#straight line
if curve=='1':
welcome="""
#*#*#*#*#*#*#*#*#**#*#*#*#**#*#*#*#**#*#*#*#*#*#**#*#*#*#**#*#*#*#**#*#
#* #*
#* Curve Fitting #*
#* By #*
#* Least Square Method #*
#* Find the Straight Line that BEST fits for your data #*
#* Credit- Monirul Shawon #*
#* #*
#*#*#*#*#*#*#*#*#**#*#*#*#**#*#*#*#**#*#*#*#*#*#**#*#*#*#**#*#*#*#**#*#
"""
print(welcome)
x=[]
y=[]
try:
n=int(input("How many number of sets you've got there? \n n= "))
print("Let, Y=mX+c")
#taking x values
print("\nInput values of x: ")
for i in range(1,n+1):
xnum=float(input(f" x{i} = "))
x.append(xnum)
#taking y values
print("\nInput values of y:")
for j in range(1,n+1):
ynum=float(input(f" y{j} = "))
y.append(ynum)
#making x square row
squarex=[a*a for a in x]
#making x*y row
multi=[a*b for a,b in zip(x,y)]
#table
table=[(p,q,r,s) for p,q,r,s in zip(x,y,squarex,multi)]
headers=['x','y','x^2','xy']
print(tabulate(table,headers,tablefmt="pretty"))
#table summation
sumx=sum(x)
sumy=sum(y)
sumsquarex=sum(squarex)
sumxy=sum(multi)
#table2
table2=[(sumx,sumy,sumsquarex,sumxy)]
headers2=['∑x','∑y','∑x^2','∑xy']
print(tabulate(table2,headers2,tablefmt="pretty"))
#print equation
print(f"\nEquation 1 is: {sumx} a + {n} b = {sumy}")
print(f"Equation 2 is: {sumsquarex} a + {sumx} b = {sumxy}")
#calculation
p=float(((sumy*sumx)-(sumxy*n)))
q=float(((sumxy*sumx)-(sumy*sumsquarex)))
r=float(((sumx*sumx)-(n*sumsquarex)))
a=float(p/r)
b=float(q/r)
if b>0:
print("\nThe Best fitted Straight Line for your data is Y = {} X + {}".format(a,b))
else:
print("\nThe Best fitted Straight Line for your data is Y = {} X {}".format(a,b))
except:
print("\nNo.. input is not a number. It's a string.")
print("Please input number to continue your calculation")
#Parabola
elif curve=='2':
welcome="""
#*#*#*#*#*#*#*#*#**#*#*#*#**#*#*#*#**#*#*#*#*#*#**#*#*#*#**#*#*#*#**#*#
#* #*
#* Curve Fitting #*
#* By #*
#* Least Square Method #*
#* Find the Parabola that BEST fits for your data #*
#* Credit- Monirul Shawon #*
#* #*
#*#*#*#*#*#*#*#*#**#*#*#*#**#*#*#*#**#*#*#*#*#*#**#*#*#*#**#*#*#*#**#*#
"""
print(welcome)
curve="""
{1} Y = aX^2 + bX + c
{2} Y = a + bX + cX^2
"""
print(curve)
choice=input("1 or 2 ? : ")
def Parabola1():
try:
x=[]
y=[]
n=int(input("How many number of sets you've got there? \n n= "))
#taking x values
print("\nInput values of x: ")
for i in range(1,n+1):
xnum=float(input(f" x{i} = "))
x.append(xnum)
#taking y values
print("\nInput values of y:")
for j in range(1,n+1):
ynum=float(input(f" y{j} = "))
y.append(ynum)
#x^2
squarex=[a*a for a in x]
#x^3
cubex=[a*a*a for a in x]
#x^4
quadx=[a*a*a*a for a in x]
#making x*y row
multi=[a*b for a,b in zip(x,y)]
#x*x*y
xsquarey=[a*b for a,b in zip(x,multi)]
#table
table=[(p,q,r,s,t,u,v) for p,q,r,s,t,u,v in zip(x,y,squarex,cubex,quadx,multi,xsquarey)]
headers=['x','y','x^2','x^3','x^4','xy','x^2*y']
print(tabulate(table,headers,tablefmt="pretty"))
#table summation
sumx=sum(x)
sumy=sum(y)
sumsquarex=sum(squarex)
sumcubex=sum(cubex)
sumquadx=sum(quadx)
sumxy=sum(multi)
sumxsquarey=sum(xsquarey)
#table2
table2=[(sumx,sumy,sumsquarex,sumcubex,sumquadx,sumxy,sumxsquarey)]
headers2=['∑x','∑y','∑x^2','∑x^3','∑x^4','∑xy','∑x^2*y']
print(tabulate(table2,headers2,tablefmt="pretty"))
#print equation
print(f"\nEquation 1 is: {sumy} = {sumsquarex} a + {sumx} b + {n} c")
print(f"Equation 2 is: {sumxy} = {sumcubex} a + {sumsquarex} b + {sumx} c")
print(f"Equation 3 is: {sumxsquarey} = {sumquadx} a + {sumcubex} b + {sumsquarex} c")
#calculation
A=np.array([[sumsquarex,sumx,n],[sumcubex,sumsquarex,sumx],[sumquadx,sumcubex,sumsquarex]])
B=np.array([sumy,sumxy,sumxsquarey])
X=np.linalg.solve(A,B)
print("So, the best fitted Parabola for your data is:")
if X[2]<0:
print(f" Y = {X[0]} X^2 + {X[1]} X {X[2]}")
elif X[1]<0:
print(f" Y = {X[0]} X^2 {X[1]} X + {X[2]}")
else:
print(f" Y = {X[0]} X^2 + {X[1]} X + {X[2]}")
except:
print("\nPlease input number to continue your calculation")
def Parabola2():
try:
x=[]
y=[]
n=int(input("How many number of sets you've got there? \n n= "))
#taking x values
print("\nInput values of x: ")
for i in range(1,n+1):
xnum=float(input(f" x{i} = "))
x.append(xnum)
#taking y values
print("\nInput values of y:")
for j in range(1,n+1):
ynum=float(input(f" y{j} = "))
y.append(ynum)
#x^2
squarex=[a*a for a in x]
#x^3
cubex=[a*a*a for a in x]
#x^4
quadx=[a*a*a*a for a in x]
#making x*y row
multi=[a*b for a,b in zip(x,y)]
#x*x*y
xsquarey=[a*b for a,b in zip(x,multi)]
#table
table=[(p,q,r,s,t,u,v) for p,q,r,s,t,u,v in zip(x,y,squarex,cubex,quadx,multi,xsquarey)]
headers=['x','y','x^2','x^3','x^4','xy','x^2*y']
print(tabulate(table,headers,tablefmt="pretty"))
#table summation
sumx=sum(x)
sumy=sum(y)
sumsquarex=sum(squarex)
sumcubex=sum(cubex)
sumquadx=sum(quadx)
sumxy=sum(multi)
sumxsquarey=sum(xsquarey)
#table2
table2=[(sumx,sumy,sumsquarex,sumcubex,sumquadx,sumxy,sumxsquarey)]
headers2=['∑x','∑y','∑x^2','∑x^3','∑x^4','∑xy','∑x^2*y']
print(tabulate(table2,headers2,tablefmt="pretty"))
#print equation
print(f"\nEquation 1 is: {sumy} = {n} a + {sumx} b + {sumsquarex} c")
print(f"Equation 2 is: {sumxy} = {sumx} a + {sumsquarex} b + {sumcubex} c")
print(f"Equation 3 is: {sumxsquarey} = {sumsquarex} a + {sumcubex} b + {sumquadx} c")
#calculation
A=np.array([[sumsquarex,sumx,n],[sumcubex,sumsquarex,sumx],[sumquadx,sumcubex,sumsquarex]])
B=np.array([sumy,sumxy,sumxsquarey])
X=np.linalg.solve(A,B)
print("So, the best fitted Parabola for your data is:")
if X[0]<0:
print(f" Y = {X[2]} + {X[1]} X {X[0]} X^2")
elif X[1]<0:
print(f" Y = {X[2]} {X[1]} X + {X[0]} X^2")
else:
print(f" Y = {X[2]} + {X[1]} X + {X[0]} X^2")
except:
print("\nPlease input number to continue your calculation")
#choice a curve
if choice=='1':
Parabola1()
elif choice=='2':
Parabola2()
else:
print("You didn't choose a valid number")
#exponential curve
elif curve=='3':
welcome="""
#*#*#*#*#*#*#*#*#**#*#*#*#**#*#*#*#**#*#*#*#*#*#**#*#*#*#**#*#*#*#**#*#
#* #*
#* Curve Fitting #*
#* By #*
#* Least Square Method #*
#* Find the Exponential Curve that BEST fits for your data #*
#* Credit- Monirul Shawon #*
#* #*
#*#*#*#*#*#*#*#*#**#*#*#*#**#*#*#*#**#*#*#*#*#*#**#*#*#*#**#*#*#*#**#*#
"""
print(welcome)
x=[]
y=[]
try:
n=int(input("How many number of sets you've got there? \n n= "))
print('-'*70)
print("Let, y=ae^(bx) or Y=A+Bx where Y=log10(y) , A=log10(a) and B=blog10(e) ")
print('-'*70)
#taking x values
print("\nInput values of x: ")
for i in range(1,n+1):
xnum=float(input(f" x{i} = "))
x.append(xnum)
#taking y values
print("\nInput values of y:")
for j in range(1,n+1):
ynum=float(input(f" y{j} = "))
y.append(ynum)
#making x square row
squarex=[a*a for a in x]
#making Y=log10(y) row
Y=[math.log10(b) for b in y]
#making x*y row
multi=[a*b for a,b in zip(x,Y)]
#table
table=[(p,q,r,s,t) for p,q,r,s,t in zip(x,y,Y,squarex,multi)]
headers=['x','y','Y=log10(y)','x^2','xY']
print(tabulate(table,headers,tablefmt="pretty"))
#table summation
sumx=sum(x)
sumy=sum(y)
sumY=sum(Y)
sumsquarex=sum(squarex)
sumxY=sum(multi)
#table2
table2=[(sumx,sumy,sumY,sumsquarex,sumxY)]
headers2=['∑x','∑y','∑Y','∑x^2','∑xY']
print(tabulate(table2,headers2,tablefmt="pretty"))
#print equation
print(f"\nEquation 1 is: {sumY} = {n} A + {sumx} B")
print(f"Equation 2 is: {sumxY} = {sumx} A + {sumsquarex} B")
#solve liner equations
M=np.array([[n,sumx],[sumx,sumsquarex]])
N=np.array([sumY,sumxY])
X=np.linalg.solve(M,N)
#solve a and b
a=math.pow(10,X[0])
b=X[1]/(math.log10(math.e))
print(f"Hence, the required curve is: y={a} e^({b} x)")
except:
print("\nNo.. input is not a number. It's a string.")
print("Please input number to continue your calculation")
#curve4
elif curve=='4':
welcome="""
#*#*#*#*#*#*#*#*#**#*#*#*#**#*#*#*#**#*#*#*#*#*#**#*#*#*#**#*#*#*#**#*#
#* #*
#* Curve Fitting #*
#* By #*
#* Least Square Method #*
#* Find the y=ax^b Curve that BEST fits for your data #*
#* Credit- Monirul Shawon #*
#* #*
#*#*#*#*#*#*#*#*#**#*#*#*#**#*#*#*#**#*#*#*#*#*#**#*#*#*#**#*#*#*#**#*#
"""
print(welcome)
x=[]
y=[]
try:
n=int(input("How many number of sets you've got there? \n n= "))
print("-"*70)
print("Let, y=ax^b or Y=A+bX where Y=log10(y) , A=log10(a) and X=log10(x)")
print("-"*70)
#taking x values
print("\nInput values of x: ")
for i in range(1,n+1):
xnum=float(input(f" x{i} = "))
x.append(xnum)
#taking y values
print("\nInput values of y:")
for j in range(1,n+1):
ynum=float(input(f" y{j} = "))
y.append(ynum)
#making X=log10(x)
X=[math.log10(a) for a in x]
#making x square row
squareX=[a*a for a in X]
#making Y=log10(y) row
Y=[math.log10(b) for b in y]
#making x*y row
multi=[a*b for a,b in zip(X,Y)]
#table
table=[(p,q,r,s,t,u) for p,q,r,s,t,u in zip(x,y,X,Y,squareX,multi)]
headers=['x','y','X=log10(x)','Y=log10(y)','x^2','XY']
print(tabulate(table,headers,tablefmt="pretty"))
#table summation
sumx=sum(x)
sumy=sum(y)
sumX=sum(X)
sumY=sum(Y)
sumsquareX=sum(squareX)
sumXY=sum(multi)
#table2
table2=[(sumx,sumy,sumX,sumY,sumsquareX,sumXY)]
headers2=['∑x','∑y','∑X','∑Y','∑x^2','∑XY']
print(tabulate(table2,headers2,tablefmt="pretty"))
#print equation
print(f"\nEquation 1 is: {sumY} = {n} A + {sumX} b")
print(f"Equation 2 is: {sumXY} = {sumX} A + {sumsquareX} b")
#solve liner equations
M=np.array([[n,sumX],[sumX,sumsquareX]])
N=np.array([sumY,sumXY])
soln=np.linalg.solve(M,N)
#solve a and b
a=math.pow(10,soln[0])
b=soln[1]
print(f"Hence, the required curve is: y={a}(x)^{b}")
except:
print("\nNo.. input is not a number. It's a string.")
print("Please input number to continue your calculation")
#final curve
elif curve=='5':
welcome="""
#*#*#*#*#*#*#*#*#**#*#*#*#**#*#*#*#**#*#*#*#*#*#**#*#*#*#**#*#*#*#**#*#
#* #*
#* Curve Fitting #*
#* By #*
#* Least Square Method #*
#* Find the y=ab^x Curve that BEST fits for your data #*
#* Credit- Monirul Shawon #*
#* #*
#*#*#*#*#*#*#*#*#**#*#*#*#**#*#*#*#**#*#*#*#*#*#**#*#*#*#**#*#*#*#**#*#
"""
print(welcome)
x=[]
y=[]
try:
n=int(input("How many number of sets you've got there? \n n= "))
print("-"*70)
print("Let, y=ab^x or Y=A+Bx where Y=log10(y) , A=log10(a) and B=log10(b)")
print("-"*70)
#taking x values
print("\nInput values of x: ")
for i in range(1,n+1):
xnum=float(input(f" x{i} = "))
x.append(xnum)
#taking y values
print("\nInput values of y:")
for j in range(1,n+1):
ynum=float(input(f" y{j} = "))
y.append(ynum)
#making x square row
squarex=[a*a for a in x]
#making Y=log10(y) row
Y=[math.log10(b) for b in y]
#making x*y row
multi=[a*b for a,b in zip(x,Y)]
#table
table=[(p,q,r,s,t) for p,q,r,s,t in zip(x,y,Y,squarex,multi)]
headers=['x','y','Y=log10(y)','x^2','xY']
print(tabulate(table,headers,tablefmt="pretty"))
#table summation
sumx=sum(x)
sumy=sum(y)
sumY=sum(Y)
sumsquarex=sum(squarex)
sumxY=sum(multi)
#table2
table2=[(sumx,sumy,sumY,sumsquarex,sumxY)]
headers2=['∑x','∑y','∑Y','∑x^2','∑xY']
print(tabulate(table2,headers2,tablefmt="pretty"))
#print equation
print(f"\nEquation 1 is: {sumY} = {n} A + {sumx} B")
print(f"Equation 2 is: {sumxY} = {sumx} A + {sumsquarex} B")
#solve liner equations
M=np.array([[n,sumx],[sumx,sumsquarex]])
N=np.array([sumY,sumxY])
soln=np.linalg.solve(M,N)
#solve a and b
a=math.pow(10,soln[0])
b=math.pow(10,soln[1])
print(f"Hence, the required curve is: y={a}({b})^x")
except:
print("\nNo.. input is not a number. It's a string.")
print("Please input number to continue your calculation")
#condition close
elif curve=='99':
exit()
else:
print("Your Input isn't valid")
print(welcometext)
print("\nSelect curve number, i.e, to use straight line input 1")
#yes or no
again=str(input("\nWant to calculate again? Yes or No : ")).lower()
if 'y' in again:
clear_screen()
print("Welcome again!")
print("\nFollowing are the available option for Curve fitting:")
print(welcometext)
print("To Use any of the curve input corresponding number:")
continue
else:
exit()
except:
print("\nGoodbye!")
exit()