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utils.py
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utils.py
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import numpy as np
from scipy.sparse import tril
from scipy.sparse.linalg import spsolve_triangular
def relative_error(x, xk1):
return np.linalg.norm(np.subtract(xk1, x))/np.linalg.norm(x)
def jacobi(A, b, x, tol):
charts = {
"residual_chart": [],
"errrel_chart": [],
}
niter = 0
new_vector = np.asarray([0]*len(x))
inverted_p_matrix = 1/A.diagonal()
residual = b - A.dot(new_vector)
charts["residual_chart"].append(
np.linalg.norm(residual)/np.linalg.norm(b))
charts["errrel_chart"].append(relative_error(x, new_vector))
while np.linalg.norm(residual)/np.linalg.norm(b) >= tol and niter <= 20000:
new_vector = new_vector + (inverted_p_matrix * (residual))
residual = b - A.dot(new_vector)
charts["residual_chart"].append(
np.linalg.norm(residual)/np.linalg.norm(b))
charts["errrel_chart"].append(relative_error(x, new_vector))
niter = niter + 1
# return {"iter": niter, "err_rel": relative_error(x, new_vector)}
if niter > 20000:
if np.linalg.norm(residual)/np.linalg.norm(b) >= tol:
print("superato il numero massimo di iterazioni")
# Risultato
return charts
def gauss_seidel(mtxA, vectB, vectX, tol):
# Variabili
charts = {
"residual_chart": [],
"errrel_chart": [],
}
maxIter = 20000
mtxP = tril(mtxA, format="csr")
k = 0
vectX1 = np.zeros(mtxA.shape[0])
residual = vectB - mtxA.dot(vectX1)
charts["residual_chart"].append(
np.linalg.norm(residual)/np.linalg.norm(vectB))
charts["errrel_chart"].append(relative_error(vectX, vectX1))
# Funzione
while np.linalg.norm(residual)/np.linalg.norm(vectB) >= tol and k <= maxIter:
k += 1
vectX1 = vectX1 + spsolve_triangular(mtxP, residual, lower=True)
residual = vectB - mtxA.dot(vectX1)
charts["residual_chart"].append(
np.linalg.norm(residual)/np.linalg.norm(vectB))
charts["errrel_chart"].append(relative_error(vectX, vectX1))
if k > 20000:
if np.linalg.norm(residual)/np.linalg.norm(vectB) > tol:
print("superato il numero massimo di iterazioni")
# Risultato
return charts
def gradiente(mtxA, vectB, vectX, tol):
charts = {
"residual_chart": [],
"errrel_chart": [],
}
# Variabili
k = 0
vectX1 = np.zeros(mtxA.shape[0])
residual = vectB - mtxA.dot(vectX1)
charts["residual_chart"].append(
np.linalg.norm(residual)/np.linalg.norm(vectB))
charts["errrel_chart"].append(relative_error(vectX, vectX1))
# Funzione
while np.linalg.norm(residual)/np.linalg.norm(vectB) >= tol and k <= 20000:
k += 1
y = mtxA.dot(residual)
a = residual.T.dot(residual)
b = residual.T.dot(y)
alpha = a/b
vectX1 = vectX1 + alpha * residual
residual = vectB - mtxA.dot(vectX1)
charts["residual_chart"].append(
np.linalg.norm(residual)/np.linalg.norm(vectB))
charts["errrel_chart"].append(relative_error(vectX, vectX1))
if k > 20000:
if np.linalg.norm(residual)/np.linalg.norm(vectB) >= tol:
print("superato il numero massimo di iterazioni")
# Risultato
return charts
def gradiente_coniugato(A, b, x, tol):
charts = {
"residual_chart": [],
"errrel_chart": [],
}
niter = 0
new_vector = np.asarray([0]*len(x))
residual = b - A.dot(new_vector)
dir = residual.copy()
charts["residual_chart"].append(
np.linalg.norm(residual)/np.linalg.norm(b))
charts["errrel_chart"].append(relative_error(x, new_vector))
while np.linalg.norm(residual)/np.linalg.norm(b) >= tol and niter <= 20000:
y = A.dot(dir)
z = A.dot(residual)
ak = (np.dot(dir, residual)) / (np.dot(dir, y))
new_vector = new_vector + (ak * dir)
residual = b - A.dot(new_vector)
w = A.dot(residual)
bk = (np.dot(dir, w)) / (np.dot(dir, y))
dir = residual - (bk*dir)
residual = b - A.dot(new_vector)
charts["residual_chart"].append(
np.linalg.norm(residual)/np.linalg.norm(b))
charts["errrel_chart"].append(relative_error(x, new_vector))
niter = niter + 1
if niter > 20000:
if np.linalg.norm(residual)/np.linalg.norm(b) >= tol:
print("superato il numero massimo di iterazioni")
# Risultato
return charts
def printTime(time):
tmp = []
tmp.append(time) # microsecondi - tmp[0]
tmp.append((int)(tmp[0]/1000)) # millisecondi - tmp[1]
tmp.append((int)(tmp[1]/1000)) # secondi - tmp[2]
tmp.append((int)(tmp[2]/60)) # minuti - tmp[3]
tmp[0] = tmp[0] - (tmp[1] * 1000)
tmp[1] = tmp[1] - (tmp[2] * 1000)
tmp[2] = tmp[2] - (tmp[3] * 60)
mu = "\u03BC"
if tmp[3] != 0:
res = str(tmp[3]) + "m " + str(tmp[2]) + "s"
elif tmp[2] != 0:
res = str(tmp[2]) + "." + str(round(tmp[1]/100)) + "s"
elif tmp[1] != 0:
res = str(tmp[1]) + "." + str(round(tmp[0]/100)) + "ms"
else:
res = str(tmp[0]) + "\u03BCs"
# print(str(tmp[3]) + " : " + str(tmp[2]) + " : " + str(tmp[1]) + " : " + str(tmp[0]))
# print(res)
return (res)