def plot_accuracy(ref=1, save=False):
name = 'accuracy'
params = ((0, 0), (0, 50), (50, 0), (50, 50))
regimes = ['Statique', 'Stationnaire', 'Harmonique', 'Dynamique']
solvers = ['LU', 'QR', 'Numpy']
plots_id = []
plt.Figure(figsize=(20, 20))
plt.title('Précision')
plt.xlabel('Régime')
# plt.yscale('log')
plt.ylabel('Précision')
plt.ylim(bottom=10e-16, top=2.8 * 10e-15)
for s in range(len(solvers)):
acc = []
for param in params:
setVariables(ref=ref, vel=param[0], freq=param[1])
setSolver(solvers[s])
ndt.main(show=False, test=False, solver=True)
b = ndt.b
A = np.array(ndt.A)
num = np.linalg.norm(A @ ndt.x - b)
den = np.linalg.norm(b)
acc.append((num / den))
print("\n\nWOUHOU : %s : %.15f\n\n" % (solvers[s],
(num / den) * 10e13))
p = plt.scatter(regimes, acc, color=COLORS[s])
plots_id.append(p)
plt.legend(plots_id, solvers)
if save: plt.savefig('res/plots/%s.png' % (name))
plt.show()
return
def plot_ilu(ref=1, save=False):
name = 'conditionnementILU'
params = ((0, 0), (0, 50), (50, 0), (50, 50))
regimes = ['Statique', 'Stationnaire', 'Harmonique', 'Dynamique']
func = [ILU, getA]
plots_names = ['M$^{{{}}}$A'.format(-1), 'A']
plots_id = []
plt.Figure(figsize=(20, 20))
plt.xlabel('Régime')
plt.yscale('log')
plt.ylabel('Nombre de conditionnement')
for s in range(len(func)):
k = []
for param in params:
setVariables(ref=ref, vel=param[0], freq=param[1])
ndt.main(show=False, test=False, solver=False)
A = func[s](ndt.A)
[min, max] = my.get_min_max_singular_values(A)
k.append(max / min)
p = plt.scatter(regimes, k, color=COLORS[s])
plots_id.append(p)
plt.legend(plots_id, plots_names)
if save: plt.savefig('res/plots/%s.png' % (name))
plt.show()
return
def spectrum(save=False, name='spectrum'):
ndt.vel = 0
ndt.freq = 0
ndt.ref = 1
ndt.main(solver=False, show=False, test=False)
ndt.A = np.array(ndt.A)
ndt.b = np.array(ndt.b)
marksize = 4
fig = plt.Figure()
plt.subplot(211)
plt.title(
'Spectre de la matrice initiale et de la matrice préconditionnée')
plt.xlabel('$\Re(z)$')
plt.ticklabel_format(style='sci', axis='x', scilimits=(0, 0))
plt.ylabel('$\Im(z)$')
plt.ticklabel_format(style='sci', axis='y', scilimits=(0, 0))
eigen, _ = lin.eig(ndt.A)
plt.plot(np.real(eigen),
np.imag(eigen),
'o',
markersize=marksize,
color=orange,
label='Spectre de la matrice initiale ($A$)')
sM, iM, jM = csrILU0(*CSRformat(ndt.A))
ILU = invCSRformat(sM, iM, jM)
L = np.tril(ILU, -1) + np.eye(len(ILU))
U = np.triu(ILU)
M_1 = lin.inv(np.dot(L, U)) @ ndt.A
eigen, _ = lin.eig(M_1)
plt.plot(np.real(eigen),
np.imag(eigen),
'o',
markersize=marksize + 2,
color=purple,
label='Spectre de la matrice préconditionnée (M$^{-1}A$)')
plt.legend()
plt.subplot(212)
plt.title('Spectre de la matrice préconditionnée')
plt.xlabel('$\Re(z)$')
plt.ticklabel_format(style='sci', axis='x', scilimits=(0, 0))
plt.ylabel('$\Im(z)$')
plt.ticklabel_format(style='sci', axis='y', scilimits=(0, 0))
plt.plot(np.real(eigen),
np.imag(eigen),
'o',
markersize=marksize + 2,
color=purple,
label='Spectre de la matrice préconditionnée (M$^{-1}A$)')
plt.legend()
if save: plt.savefig('res/plots/%s.png' % (name))
else: plt.show()
return
def complexitylog(precision, save=False, name='complexitylog'):
ndt.vel = 1
ndt.freq = 50
selfColors = [orange, purple, purple]
selfChar = ['o', 'o', 'x']
plus = [0.5, 0.25, 0]
names = ['LUsolve', 'LUcsrsolve', 'LUcsrsolve avec RCMK']
selfSolver = [LUsolve, LUcsrsolve, LUcsrsolve]
selfRMCK = [False, False, True]
plt.Figure()
plt.tick_params(
labelleft=False, # ticks along the top edge are off
labelbottom=False)
plt.title('Logarithme des complexités temporelles des différents solvers')
plt.xlabel('Nombre de noeuds [log$_{10}$]')
plt.ticklabel_format(style='sci', axis='x', scilimits=(0, 0))
plt.ylabel('Temps d\'exécution [log$_{10}$ sec]')
plt.ticklabel_format(style='sci', axis='y', scilimits=(0, 0))
plotID = []
for i in range(len(selfSolver)):
times = []
sizes = []
for ndt.ref in precision:
ndt.main()
A = np.array(ndt.A)
b = np.array(ndt.b)
if (selfRMCK[i]):
r = RCMK(*CSRformat(A)[1:3])
A = (A[:, r])[r, :]
b = b[r]
sizes.append(len(A))
tic = timer()
selfSolver[i](A, b)
tac = timer()
times.append(tac - tic)
logx = np.log10(sizes)
logy = np.log10(times) + plus[i]
ranger = np.linspace(logx[0], logx[-1], 100)
fit = np.polyfit(logx, logy, 1)
plt.plot(logx, logy, selfChar[i], color=selfColors[i])
plt.plot(ranger, np.poly1d(fit)(ranger), '--', color=selfColors[i])
plotID.append(fit)
plt.legend([
names[0],
'Polyfit LUsolve : %.2fx+...' % plotID[0][0], names[1],
'Polyfit LUcsrsolve sans RCMK: %.2fx+...' % plotID[1][0], names[2],
'Polyfit LUcsrsolve avec RCMK: %.2fx+...' % plotID[2][0]
])
if save: plt.savefig('res/plots/%s.png' % (name))
else: plt.show()
return
def denseA(precision, save=False, name='DensityA'):
Standard_densities = []
sizes = []
for ref in precision:
ndt.ref = ref
ndt.main()
A = np.array(ndt.A)
Standard_densities.append(density(A))
sizes.append(len(A))
plt.Figure()
plt.title('Densité de la matrice initiale')
plt.xlabel('Nombre de noeuds')
plt.ticklabel_format(style='sci', axis='x', scilimits=(0, 0))
plt.ylabel('Densité')
plt.scatter(sizes, Standard_densities, color=purple)
if save: plt.savefig('res/plots/%s.png' % (name))
else: plt.show()
return
def band(precision, save=False, name='bandRCMK'):
Standard_width = []
RCMK_width = []
sizes = []
for ndt.ref in precision:
ndt.main()
A = np.array(ndt.A)
size = len(A)
sizes.append(size)
sA, iA, jA = CSRformat(A)
r = RCMK(iA, jA)
ARCMK = (A[:, r])[r, :]
sARCMK, iARCMK, jARCMK = CSRformat(ARCMK)
Standard_width.append(bandwidth(iA, jA)[2])
RCMK_width.append(bandwidth(iARCMK, jARCMK)[2])
plt.Figure()
plt.title('Largeur de bande des matrices selon RCMK')
plt.xlabel('Nombre de noeuds')
plt.ticklabel_format(style='sci', axis='x', scilimits=(0, 0))
plt.ylabel('Largeur de la bande')
plt.ticklabel_format(style='sci', axis='y', scilimits=(0, 0))
ps = plt.plot(sizes, Standard_width, 'o', color=purple)
pr = plt.plot(sizes, RCMK_width, 'o', color=orange)
ranger = np.linspace(sizes[0], sizes[-1], 100)
spoly = np.polyfit(sizes, Standard_width, 1)
rpoly = np.polyfit(sizes, RCMK_width, 1)
pps = plt.plot(ranger, np.poly1d(spoly)(ranger), '--', color=purple)
ppr = plt.plot(ranger, np.poly1d(rpoly)(ranger), '--', color=orange)
plt.legend([
'Sans RCMK', 'Avec RCMK',
'Polyfit sans RCMK : %.2fx+...' % (spoly[0]),
'Polyfit avec RCMK : %.2fx+...' % (rpoly[0])
])
if save: plt.savefig('res/plots/%s.png' % (name))
else: plt.show()
return
def regimes(refs, iterations=1000, save=False, name='regimes'):
vels = [0, 50]
freqs = [0, 50]
linestyle = [[10, 0], [10, 10]]
lwidth = [1.5, 3.0]
names = ['statique', 'harmonique', 'stationnaire', 'dynamique']
xranger = np.arange(iterations)
fig = plt.Figure()
ax = fig.add_subplot(111)
plt.title(
'Convergence de la norme du résidu en fonction du nombre d\'itérations et des différents régimes'
)
plt.xlabel('Nombre d\'itérations')
plt.ticklabel_format(style='sci', axis='x', scilimits=(0, 0))
plt.ylabel('Norme du résidu (||b-Ax$_n$||$_2$)')
plt.ticklabel_format(style='sci', axis='y', scilimits=(0, 0))
for (i, ndt.ref) in zip(range(len(refs)), refs):
for (j, ndt.freq) in zip(range(len(freqs)), freqs):
for (k, ndt.vel) in zip(range(len(vels)), vels):
ndt.main()
A = np.array(ndt.A)
b = np.array(ndt.b)
_, res = csrGMRES(*CSRformat(A),
b,
rtol=1e-30,
prec=False,
max_iterations=iterations,
res_history=[])
plt.loglog(xranger,
res,
dashes=linestyle[j],
color=COLORS[len(freqs) * j + k],
label='Régime %s (%d noeuds)' %
(names[len(freqs) * j + k], ndt.Nodes),
linewidth=lwidth[i])
plt.legend()
if save: plt.savefig('res/plots/%s.png' % (name))
else: plt.show()
return
def complexity(precision, save=False, name='complexity'):
ndt.vel = 0
ndt.freq = 50
selfColors = [orange, purple, purple]
selfChar = ['--o', '--o', '--x']
names = ['LUsolve', 'LUcsrsolve', 'LUcsrsolve avec RCMK']
selfSolver = [LUsolve, LUcsrsolve, LUcsrsolve]
selfRMCK = [False, False, True]
plt.Figure()
plt.title('Complexité temporelle selon matrice creuse et RCMK')
plt.xlabel('Nombre de noeuds')
plt.ticklabel_format(style='sci', axis='x', scilimits=(0, 0))
plt.ylabel('Temps d\'exécution [sec]')
plt.ticklabel_format(style='sci', axis='y', scilimits=(0, 0))
plotID = []
for i in range(len(selfSolver)):
times = []
sizes = []
for ndt.ref in precision:
ndt.main()
A = np.array(ndt.A)
b = np.array(ndt.b)
if (selfRMCK[i]):
r = RCMK(*CSRformat(A)[1:3])
A = (A[:, r])[r, :]
b = b[r]
sizes.append(len(A))
tic = timer()
selfSolver[i](A, b)
tac = timer()
times.append(tac - tic)
id = plt.scatter(sizes, times, marker=selfChar[i], color=selfColors[i])
plotID.append(id)
plt.legend(plotID, names)
if save: plt.savefig('res/plots/%s.png' % (name))
else: plt.show()
return
def CSR(precision, save=False, name='CSR'):
times = []
sizes = []
for ndt.ref in precision:
ndt.main()
A = np.array(ndt.A)
size = len(A)
sizes.append(size)
mean = []
for m in range(4):
tic = timer()
sA, iA, jA = CSRformat(A)
tac = timer()
mean.append(tac - tic)
times.append(sum(mean) / len(mean))
plt.Figure()
plt.title('Complexité temporelle de CSRformat')
plt.xlabel('Nombre de noeuds [log$_{10}$]')
plt.ticklabel_format(style='sci', axis='x', scilimits=(0, 0))
plt.ylabel('Temps d\'exécution [log$_{10}$ sec]')
plt.ticklabel_format(style='sci', axis='y', scilimits=(0, 0))
logx = np.log10(sizes)
logy = np.log10(times)
ps = plt.scatter(logx, logy, color=purple)
fitab = np.polyfit(logx, logy, 1)
fit = np.poly1d(fitab)
ranger = np.linspace(logx[0], logx[-1], 100)
pfit = plt.plot(ranger, fit(ranger), '--', color=orange)
plt.legend([
'Polyfit : (%.2fx-%.2f)' % (fitab[0], abs(fitab[1])),
'Complexités temporelles'
])
if save: plt.savefig('res/plots/%s.png' % (name))
else: plt.show()
return
def precond(refs, iterations=1000, save=False, name='precond'):
ndt.vel = 0
ndt.freq = 0
linestyle = ['--', '-']
precs = [True, False]
names = ['Avec préconditionnement', 'Sans préconditionnement']
xranger = np.arange(iterations)
fig = plt.Figure(figsize=(15, 22))
ax = fig.add_subplot(111)
plt.title(
'Convergence de la norme du résidu en fonction du nombre d\'itéartions et du préconditionnement'
)
plt.xlabel('Nombre d\'itérations')
plt.ticklabel_format(style='sci', axis='x', scilimits=(0, 0))
plt.ylabel('Norme du résidu')
plt.ticklabel_format(style='sci', axis='y', scilimits=(0, 0))
for (i, ndt.ref) in zip(range(len(refs)), refs):
for j in range(len(precs)):
ndt.main()
A = np.array(ndt.A)
b = np.array(ndt.b)
_, res = csrGMRES(*CSRformat(A),
b,
rtol=1e-30,
prec=precs[j],
max_iterations=iterations,
res_history=[])
print('res 0 : ', res[0])
plt.loglog(xranger,
res,
linestyle[i],
color=COLORS[i + j],
label='%s (%d noeuds)' % (names[i + j], ndt.Nodes))
plt.legend()
if save: plt.savefig('res/plots/%s.png' % (name))
else: plt.show()
return
def all_RCMK():
ndt.main()
A = ndt.A
L = LU.LU(A)[0]
sA, iA, jA = CSRformat(A)
r = RCMK(iA, jA)
a_rcmk = (A[:, r])[r, :]
sA, iA, jA = CSRformat(A)
sA, iA, jA = CSRformat(a_rcmk)
LRMCK = LU.LU(a_rcmk)[0]
sA, iA, jA = CSRformat(LRMCK)
plt.subplot(221)
plt.title('Initial A')
plt.spy(A)
plt.subplot(222)
plt.title('LU with initial A')
plt.spy(L)
plt.subplot(223)
plt.title('A reordered')
plt.spy((a_rcmk))
plt.subplot(224)
plt.title('LU with A reordered')
plt.spy(LRMCK)
plt.show()
firstIndex = iA[i]
length = iA[i + 1] - firstIndex
for j in range(length):
curIndex = firstIndex + j
A[i, jA[curIndex]] = sA[curIndex]
return A
def csr_arnoldi(sA, iA, jA, v0, k: int, *M):
n = len(v0)
H = np.zeros((k + 1, k))
Q = np.zeros((n, k + 1))
q = v0 / np.linalg.norm(v0)
Q[:, 0] = q
for j in range(k):
v = csr_dot(sA, iA, jA, Q[:, j])
for i in range(j + 1):
H[i, j] = np.dot(Q[:, i], v)
v -= H[i, j] * Q[:, i]
H[j + 1, j] = np.linalg.norm(v)
if H[j + 1, j] != 0 and j != n - 1:
q = v / H[j + 1, j]
Q[:, j + 1] = q
else:
return Q, H
return Q, H
if __name__ == '__main__':
ndt.main(show=True, solver=True)
def timer(SOLVER, **kwargs):
start = time.time()
setSolver(SOLVER)
ndt.main(**kwargs)
return time.time() - start
#!/usr/bin/env python
# coding=utf-8
# Stan 2012-04-14
from pyramid.paster import setup_logging, get_appsettings
from wsgiref.simple_server import make_server
from ndt import main
if __name__ == '__main__':
config_uri = '../development.ini'
settings = get_appsettings(config_uri)
app = main(global_config=None, **settings)
server = make_server('0.0.0.0', 8080, app)
server.serve_forever()