def figure_GSC_1(debug_print=False):
A = np_array([4., 1, 1, 15]).reshape(2, 2)
data1, data2, data3 = [], [], []
u = np_array([1., 1])
v = np_array([-0.5, 2])
w0, w1 = gram_schmidt_conjugation(A, [u, v])
assert_A_orthogonal(A, w0, w1)
c = 2.3
u0 = w0
u1 = w1 + c * w0
du0, m1 = draw_vector_R2(u0, color='blue', name=py_text_sub('u', 0))
du1, m2 = draw_vector_R2(u1, color='blue', name=py_text_sub('u', 1))
data1.extend(du0)
data1.extend(du1)
dw0, m1 = draw_vector_R2(u1, t=w1, color='red')
dw1, m2 = draw_vector_R2(w1, color='green')
Au0 = A.dot(u0)
Au0n = Au0 / norm(Au0)
dAu0, m1 = draw_vector_R2(3.5 * Au0n,
color='grey',
name=py_text_sub('Au', 0))
data2.extend(dw0)
data2.extend(dw1)
data2.extend(du0)
data2.extend(du1)
data2.extend(dAu0)
d0, d1 = gram_schmidt_conjugation(A, [u0, u1])
assert_A_orthogonal(A, d0, d1)
dd0, m1 = draw_vector_R2(d0, color='blue', name=py_text_sub('d', '(0)'))
dd1, m2 = draw_vector_R2(d1, color='blue', name=py_text_sub('d', '(1)'))
data3.extend(dd0)
data3.extend(dd1)
m = np_max([m1, m2])
plot_it_R2_short_3in1(data1,
data2,
data3,
axes_max1=m,
axes_max2=m,
axes_max3=m,
title='GSC.Fig.1',
filename='Fig_GSC_1.html')
return
def figure_ISD_1(debug_print=False):
steps = steepest_descent(A, b, x0)
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)
text = [py_text_sub('x', '(0)'), py_text_sub('x', '(1)')]
t2 = [''] * (steps.shape[1] - 3)
text.extend(t2)
text.append(py_text_sub('x', '(*)'))
textposition = ['middle left', 'top right']
tp2 = ['top center'] * len(t2)
textposition.extend(tp2)
textposition.append('bottom center')
plotly_data = []
r0 = b - A.dot(x0)
alpha0 = innprd(r0, r0) / innprd(r0, A.dot(r0))
x1 = x0 + alpha0 * r0
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)'))
plotly_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='bottom left')
plotly_data.extend(d)
draw_concentric_contours(steps,
text,
textposition,
plotly_data=plotly_data,
title='ISD.Fig.1',
filename='Fig_ISD_1.html',
debug_print=debug_print)
return
def figure_CJDR_1(debug_print=False):
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 = ['middle left', 'middle left', 'bottom center']
plotly_data = []
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)'))
plotly_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)'))
plotly_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')
plotly_data.extend(d)
e1_normalized = e1.flatten() / norm(e1)
d, _ = qfc.prep_vector_data(e1_normalized,
center=x0,
M=None,
color='rgb(170,0,0)',
name=py_text_sub('e', '(1)'))
plotly_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)'))
plotly_data.extend(d)
draw_concentric_contours(steps,
text,
textposition,
plotly_data=plotly_data,
title='CJDR.Fig.1',
filename='Fig_CJDR_1.html',
steps_mode='text, markers',
debug_print=debug_print)
return
def draw_concentric_balls(steps,
text,
textposition,
title,
filename,
steps_mode='lines, text, markers',
debug_print=False):
ply_data = []
ams = []
if debug_print:
print("{}: steepest-descent: start at x0={}".format(title, x0))
print("number of steps for Steepest Descent={}".format(steps.shape[1]))
for k, ec in zip(ks, ecs):
expected_radius = compute_radius_after_dilating_ellipse_to_ball(
alpha, beta, b, c, evals, evecs, k=k, phi_q=phi_1)
_, am, E = qfc.level_k_ellipsoid(A,
b,
c,
alpha,
beta,
k=k,
ellipsoid_color=ec,
show_eigenvectors=False,
debug_print=debug_print)
ams.append(am)
d, am, E = qfc.ellipsoid_from_ellipsoid_and_map(
E,
name='radius={}'.format(rnd(expected_radius, 1)),
color=ec,
M=M_inv,
center=center)
for x in E.T:
computed_radius = norm(x - center.flatten())
assert np_abs( computed_radius - expected_radius ) < 1e-9, \
"computed radius={} doesn't equal expected radius={}".format( computed_radius, expected_radius )
ply_data.append(d)
ams.append(am)
steps_ply_data = Scatter_R2(steps[0],
steps[1],
color='rgb(0,0,140)',
width=1.,
mode=steps_mode,
text=text,
textposition=textposition,
textfontsize=18,
hoverinfo='x+y')
ply_data.append(steps_ply_data)
axes_max = np_max(np_abs(ams))
lds = qfc.prep_line_data_for_vectors(evecs, axes_max, center=center)
ply_data.extend(lds)
for i in range(2):
d, _ = qfc.prep_vector_data(evecs[:, i],
center=center,
M=None,
name=py_text_sub('v', i + 1))
ply_data.extend(d)
plot_it_R2(ply_data,
axes_max,
title=title,
filename=filename,
buffer_scale=1.,
buffer_fixed=.1)
return