def ConjugatedGradient(m,A,a,epsilon,p):
'''
The following 5 lines are not part of the algorithm per se. They are helpers.
'''
VECTOR = 1 # See above. Here, it is 1 because we use math notation
nOptim = 0
xOptim = Matrix(m,m)
mathP = p+1 #We use mathP (p+1) because the algorithm is written in mathematical notation (k = 1,p). By employing the matrix API, we can directly use the mathematical notation
mathM = m+1 #We use mathM for the same reason we use mathP. It is used only for iterations, not defining sizes
X = Matrix(m,VECTOR)
Y = Matrix(m,VECTOR)
r = Matrix(m,VECTOR)
aux = Matrix(m,VECTOR)
v = Matrix(m,VECTOR)
for i in range(1,mathM):
X.mathInsert(i,VECTOR,1)
aux = copy.deepcopy(A.multiplyMatrix(X))
r = copy.deepcopy(a.substractMatrix(aux))
v = copy.deepcopy(r)
for i in range(1,mathM):
sum1 = 0
for j in range(1,mathM):
sum1 = sum1 + r.mathAt(j,1)**2
av = Matrix(m,VECTOR)
av = copy.deepcopy(A.multiplyMatrix(v))
sum2 = 0
for j in range(1,mathM):
sum2 = sum2 + av.mathAt(j,1) * v.mathAt(j,1)
ai = 0
ai = sum1 / sum2+(10**(-10))
aux = copy.deepcopy(v.scalarMultiplication(ai))
aux = copy.deepcopy(aux.addMatrix(X))
Y = copy.deepcopy(aux)
aux = copy.deepcopy(A.multiplyMatrix(Y))
r = copy.deepcopy(a.substractMatrix(aux))
sum3 = 0
ci = 0
for j in range(1,mathM):
sum3 = sum3 + r.mathAt(j,1)**2
ci = sum3 / sum1
aux = copy.deepcopy(v.scalarMultiplication(ci))
aux = copy.deepcopy(r.addMatrix(aux))
v = copy.deepcopy(aux)
X = copy.deepcopy(Y)
print("===== Conjugated Gradient =====")
print("Optim solution (x):")
X.display()
print("Test:")
result = A.multiplyMatrix(X)
result.display()
print("====================")
def otherJacobi(m,A,a,epsilon,p):
VECTOR = 1
X = Matrix(m,VECTOR)
oldX = Matrix(m,VECTOR)
r = Matrix(m,VECTOR)
D = copy.deepcopy(A.diagonalMatrix())
E = copy.deepcopy((A.negativeElements()).lowerTriangularMatrix())
F = copy.deepcopy((A.negativeElements()).upperTriangularMatrix())
P = copy.deepcopy(D)
N = copy.deepcopy(D.substractMatrix(A))
inverseD = copy.deepcopy(D.inverse())
Bj = copy.deepcopy(inverseD.multiplyMatrix(copy.deepcopy(E.addMatrix(F))))
for iteration in range(0,100):
Bjp = copy.deepcopy((Bj.scalarMultiplication(p)).addMatrix((matrix.newIdentiryMatrix(m,m)).scalarMultiplication(1-p)))
condition = True
iterationNumber = 0
while condition:
r = copy.deepcopy(a.substractMatrix(A.multiplyMatrix(X)))
oldX = copy.deepcopy(X)
X = copy.deepcopy(oldX.addMatrix( copy.deepcopy( inverseD.scalarMultiplication(p) ).multiplyMatrix(r) ))
condition = not r.isAlmostZero()
if iterationNumber%100 == 0:
print("-----")
print("Situation at iteration:",iterationNumber)
print("Condition:",condition)
print("oldX:")
oldX.display()
print("X:")
X.display()
print("The r vector:")
r.display()
print("-----")
iterationNumber += 1
print("===== Other Jacobi =====")
print("X:")
X.display()
print("Test:")
r.display()
print("====================")