def figure_CJDR_6(debug_print=False):
data = []
M_inv_x0 = M_inv.dot(x0 - center) + center
steps = np.hstack((M_inv_x0, center))
text = [py_text_sub('x', '(0)'), py_text_sub('x', '(*)')]
textposition = ['top right', 'top left']
d = Scatter_R3(steps[0],
steps[1],
steps[2],
mode='text, markers',
color='rgb(0,0,140)',
width=3.,
text=text,
textposition=textposition,
hoverinfo='x+y+z+text')
data.append(d)
d, axes_max = get_plotly_data_for_level_k_and_its_dilated_ball(
debug_print=debug_print)
data.extend(d)
pt.plot_it_R3(data,
axes_max,
title='CJDR.Fig.6',
filename="Fig_CJDR_6.html")
return
def figure_CJDR_7(debug_print=False):
data = []
steps = orthogonal_directions_with_standard_basis()
text = [
py_text_sub('x', '(0)'),
py_text_sub('x', '(1)'),
py_text_sub('x', '(2)'),
py_text_sub('x', '(*)')
]
textposition = ['top right', 'top right', 'top right', 'top left']
d = Scatter_R3(steps[0],
steps[1],
steps[2],
mode='lines, text, markers',
color='rgb(0,0,140)',
width=3.,
text=text,
textposition=textposition,
hoverinfo='x+y+z+text')
data.append(d)
d, axes_max = get_plotly_data_for_level_k_and_its_dilated_ball(
debug_print=debug_print)
data.extend(d)
pt.plot_it_R3(data,
axes_max,
title='CJDR.Fig.7',
filename="Fig_CJDR_7.html")
return
def figure_PLE_7(debug_print=False):
data = []
ams = []
d, axes_max, E = qfc.level_k_ellipsoid(A,
b,
c,
alpha,
beta,
k=k,
debug_print=debug_print)
data.extend(d)
phi_k = compute_phi_k(k, alpha, beta, b, c, evals, evecs)
sqrtkq = sqrt(phi_k / phi_1)
name = 'f(x)={}'.format(rnd(k, 3))
dkq, amkq, Ekq = qfc.ellipsoid_from_ellipsoid_and_map(E,
name=name,
M=M_inv,
center=center)
data.append(dkq)
for j in range(Ekq.shape[1]):
w = norm(Ekq[:, j] - center.flatten())
assert np.abs(
w - sqrtkq
) < 1e-9, "norm of Ekq = {} for col={} is wrong. S/b = {}".format(
w, j, sqrtkq)
pt.plot_it_R3(data, axes_max, title='PLE.Fig.7', filename="Fig_PLE_7.html")
return
def figure_CJDR_8(debug_print=False):
data = []
steps = orthogonal_directions_with_standard_basis()
for i in range(3):
steps[:, i] = (M.dot(steps[:, i].reshape(3, 1) - center) +
center).reshape(3, )
for i in range(3):
u = steps[:, i + 1] - steps[:, i]
for j in range(i + 1, 3):
v = steps[:, j + 1] - steps[:, j]
assert_A_orthogonal(A, u, v)
text = [
py_text_sub('x', '(0)'),
py_text_sub('x', '(1)'),
py_text_sub('x', '(2)'),
py_text_sub('x', '(*)')
]
textposition = ['top right', 'top right', 'top right', 'top left']
d = Scatter_R3(steps[0],
steps[1],
steps[2],
mode='lines, text, markers',
color='rgb(0,0,140)',
width=3.,
text=text,
textposition=textposition,
hoverinfo='x+y+z+text')
data.append(d)
d, axes_max, _ = qfc.level_k_ellipsoid(A,
b,
c,
alpha,
beta,
k=k,
debug_print=debug_print)
data.extend(d)
pt.plot_it_R3(data,
axes_max,
title='CJDR.Fig.8',
filename="Fig_CJDR_8.html")
return
def test_axes_max(debug_print=False):
data, axes_max, _ = qfc.level_k_ellipsoid(A,
b,
c,
alpha,
beta,
k,
display_ellipsoid=False,
show_standard_basis=True,
rotate_eigenvectors=True,
rotate_standard_basis=True,
debug_print=debug_print)
if debug_print: print("Test.AxesMax.1 axes_max={}".format(axes_max))
assert np.abs(
axes_max - 2.9193548387
) < 1e-4, "incorrect axes_max={}. it should be 2.9193548387".format(
axes_max)
pt.plot_it_R3(data,
axes_max,
title='Test.AxesMax.1',
filename="test_axes_max_01.html")
data, axes_max, _ = qfc.level_k_ellipsoid(A,
b,
c,
alpha,
beta,
k,
show_standard_basis=True,
rotate_eigenvectors=True,
rotate_standard_basis=True,
debug_print=debug_print)
if debug_print: print("Test.AxesMax.2 axes_max={}".format(axes_max))
assert np.abs(
axes_max - 4.3164557013
) < 1e-4, "incorrect axes_max={}. it should be 4.3164557013".format(
axes_max)
pt.plot_it_R3(data,
axes_max,
title='Test.AxesMax.2',
filename="test_axes_max_02.html")
return
def test1(debug_print=False):
data = []
ams = []
k = 2. * pi
d1, am1, E1 = qfc.level_k_ellipsoid(A,
b,
c,
alpha,
beta,
k=k,
show_standard_basis=True,
debug_print=debug_print)
data.extend(d1)
ams.append(am1)
axes_max = np.max(np.abs(ams))
pt.plot_it_R3(data,
axes_max,
title='Fig.Test.1.R3',
filename="Fig_Test_1_R3.html")
return
def figure_CJDR_2(debug_print=False):
data = []
ams = []
k = 1.
r0 = b - A.dot(x0)
alpha0 = innprd(r0, r0) / innprd(r0, A.dot(r0))
x1 = x0 + alpha0 * r0
steps = np.hstack((x0, x1, center))
text = [
py_text_sub('x', '(0)'),
py_text_sub('x', '(1)'),
py_text_sub('x', '(*)')
]
textposition = ['top right', 'top right', 'top right']
d = Scatter_R3(steps[0],
steps[1],
steps[2],
mode='text, markers',
color='rgb(0,0,140)',
width=3.,
text=text,
textposition=textposition,
hoverinfo='x+y+z+text')
data.append(d)
r0_normalized = r0.flatten() / norm(r0)
d, _ = qfc.prep_vector_data(r0_normalized,
center=x0,
M=None,
color='rgb(0,140,0)',
name=py_text_sub('r', '(0)'))
data.extend(d)
Ar0 = A.dot(r0_normalized)
d, _ = qfc.prep_vector_data(Ar0,
center=x0,
M=None,
color='rgb(170,0,0)',
name=py_text_sub('Ar', '(0)'))
data.extend(d)
e1 = x1 - center
d, _ = qfc.prep_vector_data(e1,
center=center,
M=None,
color='rgb(0,140,0)',
name=py_text_sub('e', '(1)'),
textposition='top right')
data.extend(d)
e1_normalized = e1.flatten() / norm(e1)
assert_orthogonal(Ar0, e1_normalized)
d, _ = qfc.prep_vector_data(e1_normalized,
center=x0,
M=None,
color='rgb(170,0,0)',
name=py_text_sub('e', '(1)'))
data.extend(d)
assert_A_orthogonal(A, r0, -e1)
d, _ = qfc.prep_vector_data(-e1_normalized,
center=x0,
M=None,
color='rgb(170,0,0)',
name=py_text_sub('-e', '(1)'))
data.extend(d)
for i in range(1, 8):
if i == 4: continue
R = make_general_rotation_matrix_R3(angle=(i / 4) * np.pi,
axis=A.dot(r0))
oi = R.dot(e1)
oi_normalized = oi / norm(oi)
Ar0n = Ar0 / norm(Ar0)
assert_orthogonal(Ar0n, oi_normalized, atol=1e-1)
d, _ = qfc.prep_vector_data(oi_normalized,
center=x0,
M=None,
color='rgb(170,0,0)',
name=py_text_sub('o', '({})'.format(i)))
data.extend(d)
d, am, _ = qfc.level_k_ellipsoid(A,
b,
c,
alpha,
beta,
k=k,
debug_print=debug_print)
data.extend(d)
ams.append(am)
axes_max = np.max(np.abs(ams))
pt.plot_it_R3(data,
axes_max,
title='CJDR.Fig.2',
filename="Fig_CJDR_2.html")
return
def figures_PLE():
wr = 1.5
data, axes_max, _ = qfc.level_k_ellipsoid(A,
b,
c,
alpha,
beta,
k,
RTDR_variation='I',
centered_at_origin=True,
show_standard_basis=True,
debug_print=True)
pt.plot_it_R3(data, wr, title='PLE.Fig.1', filename="fig_PLE_01.html")
data, axes_max, _ = qfc.level_k_ellipsoid(A,
b,
c,
alpha,
beta,
k,
display_ellipsoid=False,
RTDR_variation='I',
centered_at_origin=True,
show_standard_basis=True,
debug_print=True)
pt.plot_it_R3(data, wr, title='PLE.Fig.2', filename="fig_PLE_02.html")
data, axes_max, _ = qfc.level_k_ellipsoid(A,
b,
c,
alpha,
beta,
k,
RTDR_variation='R',
centered_at_origin=True,
show_standard_basis=True,
rotate_eigenvectors=True,
rotate_standard_basis=True,
debug_print=True)
pt.plot_it_R3(data, wr, title='PLE.Fig.3', filename="fig_PLE_03.html")
data, axes_max, _ = qfc.level_k_ellipsoid(A,
b,
c,
alpha,
beta,
k,
RTDR_variation='DR',
centered_at_origin=True,
show_standard_basis=True,
rotate_eigenvectors=True,
rotate_standard_basis=True,
debug_print=True)
pt.plot_it_R3(data, wr, title='PLE.Fig.4', filename="fig_PLE_04.html")
data, axes_max, _ = qfc.level_k_ellipsoid(A,
b,
c,
alpha,
beta,
k,
centered_at_origin=True,
show_standard_basis=True,
rotate_eigenvectors=True,
rotate_standard_basis=True,
debug_print=True)
pt.plot_it_R3(data, wr, title='PLE.Fig.5', filename="fig_PLE_05.html")
data, axes_max, _ = qfc.level_k_ellipsoid(A,
b,
c,
alpha,
beta,
k,
show_standard_basis=True,
rotate_eigenvectors=True,
rotate_standard_basis=True,
debug_print=True)
pt.plot_it_R3(data,
axes_max,
title='PLE.Fig.6',
filename="fig_PLE_06.html")
figure_PLE_7(debug_print=True)
return
def figure_ISD_2(debug_print=False):
data = []
ams = []
steps = steepest_descent(A, b, x0)
if debug_print:
print("Number of steps in Steepest Descent: {}".format(steps.shape[1]))
assert np.allclose(steps[:, -1], center.flatten()
), "steepest_descent didn't find the minimum point of f"
for i in range(steps.shape[1] - 1):
x_i = steps[:, i]
r_i = b.flatten() - A.dot(x_i)
x_ip1 = steps[:, i + 1]
e_ip1 = x_ip1 - center.flatten()
assert_A_orthogonal(A, r_i, e_ip1)
trajectories = []
for s in steps.T:
r = b.flatten() - A.dot(s)
rn = r / norm(r)
if len(trajectories) == 0:
trajectories.append((rn, 1))
continue
w = True
for j, (t, cnt) in enumerate(trajectories):
if np.allclose(rn, t, rtol=0., atol=1e-7):
cnt += 1
del trajectories[j]
trajectories.insert(0, (t, cnt))
w = False
break
if w: trajectories.append((rn, 1))
if debug_print:
print("Num steps = {} Num trajectories = {} Num dup = {}".format(
steps.shape[1], len(trajectories),
steps.shape[1] - len(trajectories)))
text = [
py_text_sub('x', '(0)'),
py_text_sub('x', '(1)'),
py_text_sub('x', '(2)')
]
t2 = [''] * (steps.shape[1] - 4)
text.extend(t2)
text.append(py_text_sub('x', '(*)'))
textposition = ['top right', 'top right', 'top right']
tp2 = ['top center'] * len(t2)
textposition.extend(tp2)
textposition.append('top left')
d = Scatter_R3(steps[0],
steps[1],
steps[2],
mode='lines, text, markers',
color='rgb(0,0,140)',
width=3.,
text=text,
textposition=textposition,
hoverinfo='x+y+z+text')
data.append(d)
r0 = b - A.dot(x0)
alpha0 = innprd(r0, r0) / innprd(r0, A.dot(r0))
x1 = x0 + alpha0 * r0
assert np.allclose(x1.flatten(),
steps[:, 1]), "x1={} doesn't equal step[:,1]={}".format(
x1.flatten(), steps[:, 1])
r0_normalized = r0.flatten() / norm(r0)
d, _ = qfc.prep_vector_data(r0_normalized,
center=x0,
M=None,
color='rgb(0,140,0)',
name=py_text_sub('r', '(0)'))
data.extend(d)
e1 = x1 - center
d, _ = qfc.prep_vector_data(e1,
center=center,
M=None,
color='rgb(0,140,0)',
name=py_text_sub('e', '(1)'),
textposition='top right')
data.extend(d)
d1, am1, E1 = qfc.level_k_ellipsoid(A,
b,
c,
alpha,
beta,
k=k,
debug_print=debug_print)
data.extend(d1)
ams.append(am1)
axes_max = np.max(np.abs(ams))
pt.plot_it_R3(data, axes_max, title='ISD.Fig.2', filename="Fig_ISD_2.html")
return