def seidel(a, b, coeff=1.0, eps=1e-10, limit=1000):
if not checkSize(a, b):
raise Exception("Invalid operands")
a = deepcopy(a)
b = deepcopy(b)
n = shape(a)[0]
for i in range(n):
if a[i, i] == 0:
raise Exception("Powerless method")
b[i] /= a[i, i]
a[i] /= a[i, i]
x = zeroTerm(n)
iters = 0
maxNorm = 1e100 * n
while norm(a * x - b) > eps:
nextX = deepcopy(x)
for i in range(n):
nextX[i] -= a[i] * nextX - b[i]
x += coeff * (nextX - x)
iters += 1
curNorm = norm(a * x - b)
if iters >= limit or curNorm > maxNorm:
return None
it.append(iters)
norms.append(curNorm)
return x
def seidel(a, b, coeff=1., eps=1e-10, limit=1000):
if not checkSize(a, b):
raise Exception("Invalid operands")
a = deepcopy(a)
b = deepcopy(b)
n = shape(a)[0]
for i in range(n):
if a[i, i] == 0:
raise Exception("Powerless method")
b[i] /= a[i, i]
a[i] /= a[i, i]
x = zeroTerm(n)
iters = 0
maxNorm = 1e100 * n
while norm(a * x - b) > eps:
nextX = deepcopy(x)
for i in range(n):
nextX[i] -= a[i] * nextX - b[i]
x += coeff * (nextX - x)
iters += 1
curNorm = norm(a * x - b)
if iters >= limit or curNorm > maxNorm:
return None
it.append(iters)
norms.append(curNorm)
return x
def gradient(a, b, eps = 1e-10, limit = 1000):
a = deepcopy(a)
b = deepcopy(b)
if not checkSize(a, b):
raise Exception("Invalid operands")
n = shape(a)[0]
x = zeroTerm(n)
r1 = b - a * x
r2 = b - a.transpose() * x
p1 = r1
p2 = r2
x0 = matrix([[inf]] * n)
iters = 0
maxNorm = 1e100 * n
while norm(r1) > eps:
koef = (r2.transpose() * r1).item(0) / (p2.transpose() * (a * p1)).item(0)
x0 = x
x = x0 + koef * p1
r1_new = r1 - koef * a * p1
r2_new = r2 - koef * a.transpose() * p2
beta = (r2_new.transpose() * r1_new).item(0) / (r2.transpose() * r1).item(0)
r1 = r1_new
r2 = r2_new
p1 = r1 + beta * p1
p2 = r2 + beta * p2
iters += 1
curNorm = norm(r1)
if iters >= limit or curNorm > maxNorm:
return None
it.append(iters)
norms.append(curNorm)
return x