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mathsclass.py
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mathsclass.py
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#Methods 1 and 2 designed for 3 linear equations in 3 variables
def GaussJacobi():
a1 = int(input("a1:"))
a2 = int(input("a2:"))
a3 = int(input("a3:"))
b1 = int(input("b1:"))
b2 = int(input("b2:"))
b3 = int(input("b3:"))
c1 = int(input("c1:"))
c2 = int(input("c2:"))
c3 = int(input("c3:"))
d1 = int(input("d1:"))
d2 = int(input("d2:"))
d3 = int(input("d3:"))
prevx = 0
prevy = 0
prevz = 0
cx = 1
cy = 1
cz = 1
counter=0
while True:
counter+=1
cx = (d1-b1*prevy-c1*prevz)/a1
cy = (d2-a2*prevx-c2*prevz)/b2
cz = (d3-a3*prevx-b3*prevy)/c3
if round(cx,2)==round(prevx,2):
print(cx,cy,cz,counter)
break
else:
prevx=cx
prevy=cy
prevz=cz
print(cx,cy,cz,counter)
def GaussSeidle():
a1 = int(input("a1:"))
a2 = int(input("a2:"))
a3 = int(input("a3:"))
b1 = int(input("b1:"))
b2 = int(input("b2:"))
b3 = int(input("b3:"))
c1 = int(input("c1:"))
c2 = int(input("c2:"))
c3 = int(input("c3:"))
d1 = int(input("d1:"))
d2 = int(input("d2:"))
d3 = int(input("d3:"))
prevx = 0
prevy = 0
prevz = 0
cx = 1
cy = 1
cz = 1
counter=0
while True:
counter+=1
cx = (d1-b1*prevy-c1*prevz)/a1
cy = (d2-a2*cx-c2*prevz)/b2
cz = (d3-a3*cx-b3*cy)/c3
if round(cx,2)==round(prevx,2):
print(cx,cy,cz,counter)
break
else:
prevx=cx
prevy=cy
prevz=cz
print(cx,cy,cz,counter)
def eigstuff():
import numpy as np
a = int(input("Dimension of Square Matrix:"))
M = np.zeros((a,a))
for i in range(a):
for j in range(a):
inpstr = "x"+str(i+1)+str(j+1)+":"
M[i,j] = float(input(inpstr))
print("The Matrix is\n",M)
vals = np.linalg.eigvals(M)
print("The eigenvalues are\n",vals)
print(np.linalg.eig(M))
def EchelonMatrix():
import sympy as sp
a = int(input("Dimension of Square Matrix:"))
M = sp.zeros(a,a)
for i in range(a):
for j in range(a):
inpstr = "x"+str(i+1)+str(j+1)+":"
M[i,j] = float(input(inpstr))
print("The echelon form is\n",M.rref())
print("The rank is",M.rank())
def lineqnsolve():
import numpy as np
a = int(input("Dimension of Square Matrix:"))
M = np.zeros((a,a))
N = np.zeros((a,1))
for i in range(a):
for j in range(a):
inpstr = "x"+str(i+1)+str(j+1)+":"
M[i,j] = float(input(inpstr))
print("The Matrix is\n",M)
for i in range(a):
str2 = "d"+str(i+1)+":"
N[i,0]= float(input(str2))
Minv = np.linalg.inv(M)
X = np.matmul(Minv,N)
print("The values of variables are\n",X)
def LUMatrix():
from scipy.linalg import lu
import numpy as np
a = int(input("Dimension of Square Matrix:"))
M = np.zeros((a,a))
for i in range(a):
for j in range(a):
inpstr = "x"+str(i+1)+str(j+1)+":"
M[i,j] = float(input(inpstr))
print("The Matrix is\n",M)
p,l,u = lu(M)
print("L is \n",l)
print("u is \n",u)
def powermethod():
import numpy as np
a = int(input("Dimension of Square Matrix:"))
iternum = int(input("Number of iterations:"))
vect = np.zeros((a,1))
M = np.zeros((a,a))
for i in range(a):
for j in range(a):
inpstr = "x"+str(i+1)+str(j+1)+":"
M[i,j] = float(input(inpstr))
print("The Matrix is\n",M)
for i in range(a):
inpstr = "x"+str(i+1)+"1"+":"
vect[i,0] = float(input(inpstr))
for i in range(iternum):
prodvect = np.matmul(M,vect)
eigval = prodvect.max()
vect = prodvect/eigval
print("iter",i+1,"is",eigval)
print("iter",i+1,"vector is\n",vect)
#if round(eigval,2) in eigvals(M):
# break
def isSimilar():
import numpy as np
similar = True
a = int(input("Number of rows in Matrix:"))
b = int(input("Number of columns in Matrix:"))
M = np.zeros((a,b))
for i in range(a):
for j in range(b):
inpstr = "x"+str(i+1)+str(j+1)+":"
M[i,j] = float(input(inpstr))
N = np.zeros((a,b))
for i in range(a):
for j in range(b):
inpstr = "x"+str(i+1)+str(j+1)+":"
N[i,j] = float(input(inpstr))
if np.linalg.det(M) != np.linalg.det(N):
similar=False
valsM = np.linalg.eigvals(M)
valsN = np.linalg.eigvals(N)
for i in valsM:
if i not in valsN:
similar=False
break
if similar:
print("They are similar")
else:
print("Not similar")