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Week3: Rewrote Solvers to include a max_iter parameter

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Eric Teunis de Boone 2 years ago
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4b90ae8898
  1. 126
      week3/solvers.py

126
week3/solvers.py

@ -1,113 +1,99 @@
#!/usr/bin/env python3
import numpy as np
from itertools import count as count
def diff(a, b):
return np.amax(np.abs(a-b))
def jacobi(A, b, eps):
def jacobi(A, b, eps, max_iter = None):
""" Use the Jacobi Method to solve a Linear System. """
A = np.array(A, dtype=np.float64)
b = np.array(b, dtype=np.float64)
# Determine Diagonal and Upper and Lower matrices
D = np.diag(A)
L = -np.tril(A, -1)
U = -np.triu(A, 1)
D_inv = np.diagflat(np.reciprocal(D))
# initially x_f = x_(i-1)
# this changes when in the loop
x_i = np.dot(D_inv, b)
x_f = np.zeros(len(A))
k = 1
while diff(x_i, x_f) >= eps:
k += 1
x_0 = D_inv @ b
for i in count():
x_1 = D_inv @ ( L + U) @ x_0
# Save the previous solution vector as x_f
x_f = x_i
# Are we close enough?
if diff(x_0, x_1) < eps:
return x_1, i
# Create new solution vector
x_i = np.dot(np.dot(D_inv, ( L + U )), x_f ) + np.dot(D_inv, b)
# Running out of iterations
if max_iter is not None and max_iter >= i:
raise RuntimeError("Did not converge in {} steps".format(max_iter))
return x_i, k
# Set values for next loop
x_0 = x_1
def steepest_descent(A, b, eps):
def steepest_descent(A, b, eps, max_iter = None):
""" Use Steepest Descent to solve a Linear System. """
A = np.array(A, dtype=np.float64)
b = np.array(b, dtype=np.float64)
# initially x_f = x_(i-1)
# this changes when in the loop
x_f = np.zeros(len(A), dtype=np.float64)
k = 1
v_f = b
t = np.dot(v_f, v_f) / np.dot(v_f, np.dot(A, v_f))
x_i = x_f + t*v_f
x_0 = np.zeros(len(A), dtype=np.float64)
while diff(x_i, x_f) >= eps:
k += 1
for i in count():
Ax = A @ x_0
v = b - Ax
t = np.dot(v,v) / np.dot(v, A @ v )
# Pre calculate v_f and t
v_f = b - np.dot(A, x_i)
t = np.dot(v_f, v_f) / np.dot(v_f, np.dot(A, v_f))
x_1 = x_0 + t*v
# Save the previous solution vector as x_f
x_f = x_i
# Are we close enough?
if diff(x_0, x_1) < eps:
return x_1, i
# Create new solution vector
x_i = x_f + t * v_f
# Running out of iterations
if max_iter is not None and max_iter >= i:
raise RuntimeError("Did not converge in {} steps".format(max_iter))
return x_i, k
# Set values for next loop
x_0 = x_1
def conjugate_gradient(A, b, eps):
def conjugate_gradient(A, b, eps, max_iter = None):
""" Use the Conjugate Gradient Method to solve a Linear System. """
A = np.array(A, dtype=np.float64)
b = np.array(b, dtype=np.float64)
# initially x_f = x_(i-1)
# this changes when in the loop
x_f = np.zeros(len(A), dtype=np.float64)
r_f = b - np.dot(A, x_f)
v_f = r_f
k = 1
# Calculate first iteration
t = np.dot(r_f, r_f) / np.dot(v_f, np.dot(A, v_f))
x_i = x_f + t*v_f
# Setup vectors
x_0 = np.zeros(len(A), dtype=np.float64)
r_0 = b - A @ x_0
v = r_0.copy()
r_i = r_f - t * np.dot(A, v_f)
s = np.dot(r_i, r_i) / np.dot(r_f, r_f)
v_i = r_i + s*v_f
# Set r and v vectors for next loop
r_f = r_i
v_f = v_i
while diff(x_i, x_f) >= eps:
k += 1
for i in count():
Ax = A @ x_0
Av = A @ v
t = np.dot(r_f, r_f) / np.dot(v_f, np.dot(A, v_f))
# Save the previous solution vector as x_f
x_f = x_i
r_0_square = np.dot(r_0, r_0)
# Create new solution vector
x_i = x_f + t*v_f
t = r_0_square / np.dot(v, Av )
x_1 = x_0 + t*v
# Calculate r and v vectors
r_1 = r_0 - t * Av
r_i = r_f - t * np.dot(A, v_f)
s = np.dot(r_i, r_i) / np.dot(r_f, r_f)
v_i = r_i + s*v_f
# Save r and v vectors for next loop
r_f = r_i
v_f = v_i
s = np.dot(r_1, r_1) / r_0_square
v = r_1 + s*v
return x_i, k
# Are we close enough?
if diff(x_0, x_1) < eps:
return x_1, i
# Running out of iterations
if max_iter is not None and max_iter >= i:
raise RuntimeError("Did not converge in {} steps".format(max_iter))
# Set values for next loop
x_0 = x_1
r_0 = r_1