def draw_simplex_3d_euclidean_bounds(simplex, obj_nr=0, L=[1., 1.], points=[]):
'''2d->2d simplex lower bound surface.
Draws a single objective below 2D simplex'''
from matplotlib import pyplot as plt
from matplotlib import cm
t = a([simplex[0][:-1], simplex[1][:-1], simplex[2][:-1]])
y = a([simplex[0][-1]['obj'], simplex[1][-1]['obj'], simplex[2][-1]['obj']]) # (obj1, obj2) for A, B, C
X1 = np.arange(-0.1, 2.1, 0.05)
X2 = np.arange(-0.1, 2.1, 0.05)
X1, X2 = np.meshgrid(X1, X2)
fig = plt.figure()
ax = fig.gca(projection='3d')
LB = lower_bound_surface(X1, X2, t, y, L)
ax.plot_surface(X1, X2, LB[:,:,obj_nr], linewidth=0, rstride=1, cstride=1, cmap=cm.coolwarm)
ax.plot_wireframe(np.hstack((t[:,0], t[0,0])), np.hstack(([t[:,1], t[0,1]])), np.hstack((y[:,obj_nr],y[0,obj_nr])), zorder=1000) ## Line surface
# points = [simplex[-1]['mins_ABC'][1]]
for p in points:
ax.plot([p[0]], [p[1]], [p[2]], 'go')
# points = [[1.5892857095626787, 1.5892857194077434, 1.186929245703222]]
# for p in points:
# ax.plot([p[0]], [p[1]], [p[2]], 'ro')
plt.show()
def analyse_beam(data):
beam = generate_beam_from_json(data)
beam.calculations()
sections = [(section.start, section.end) for section in beam.sections]
distance = a([np.linspace(section.start, section.end) for section in beam.sections])
return {
'sections': sections,
'distance': [distance[i].tolist() for i in range(beam.num_sections)],
'shear_force': {
'equations': beam.shear_force_eqs,
'values': [beam.shear_force_values[i].tolist() for i in range(beam.shear_force_values.shape[0])],
'plot': {
'x': distance.reshape(-1).tolist(),
'y': beam.shear_force_values.reshape(-1).tolist(),
'backup': {
'x': a([np.linspace(s.start, s.end) for s in beam.sections]).reshape(-1).tolist(),
'y': a([np.linspace(beam.shear_force_values[i], beam.shear_force_values[i]) for i in
range(beam.num_sections)]).reshape(-1).tolist()
}
}
},
'bending_moment': {
'equations': beam.bending_moment_eqs,
'values': [beam.bending_moment_values[i].tolist() for i in range(beam.bending_moment_values.shape[0])],
'plot': {
'x': distance.reshape(-1).tolist(),
'y': beam.bending_moment_values.reshape(-1).tolist()
}
}
}
def show_lower_pareto_bound(simplexes):
from matplotlib import pyplot as plt
'''For 2D -> 2D problem show the lower pareto bound.'''
# Warning: unfinished, untested.
def lower_bound_for_interval(t, y, dist=None, L=[1.,1.], verts=[0,1]):
'''Returns lower L bound line in (f1,f2) space for an interval in
multidimensional feasible region.'''
def lower_bound_cracks(x1, x2, y1, y2, dist):
'''Computes lower L bound crack points for the given interval.'''
if dist is None:
dist = enorm(x2-x1)
t1 = (y1[0]-y2[0])/(2.*L[0]) + dist/2.
t2 = (y1[1]-y2[1])/(2.*L[1]) + dist/2.
if t1 >= t2:
p1 = [y1[0] - L[0]*t2, y1[1] - L[1]*t2]
p2 = [y1[0] - L[0]*t1, y2[1] - dist*L[1] + L[1]*t1]
else:
p2 = [y2[0] - dist*L[0] + L[0]*t2, y1[1] - L[1]*t2]
p1 = [y1[0] - L[0]*t1, y1[1] - L[1]*t1]
return [p1, p2]
p1, p2 = lower_bound_cracks(t[verts[0]], t[verts[1]], y[verts[0]], y[verts[1]], dist)
return a([y[verts[0]], p1, p2, y[verts[1]]])
# For each simplex we have dimensions+1 vertex, so what does this mean.
# Patobulinimas: We could check if any of them are dominated and keep the
# least dominated.
for simplex in simplexes:
t = a([simplex[0][:-1], simplex[1][:-1], simplex[2][:-1]])
y = a([simplex[0][-1]['obj'], simplex[1][-1]['obj'], simplex[2][-1]['obj']]) # (obj1, obj2) for A, B, C
lb = lower_bound_for_interval(t, y)
plt.plot(lb[:,0], lb[:,1])
# Draw longest (or nondominated) edge lower bound and mark these vertexes as stars.
plt.show()
def draw_bounds(x1, x2, L=[1.,1.]):
'''Draws 3 plots describing bounds for 1D->2D problems'''
from matplotlib import pyplot as plt
import matplotlib.ticker as plticker
fig, (ax1, ax2, ax3) = plt.subplots(1, 3, figsize=(18,6))
## Normalize x1, x2 for 2D variable space
x2 = [enorm(a(x2[:-1]) - a(x1[:-1])), x2[-1]]
x1 = [0, x1[-1]]
ax1 = draw_objective_bounds_and_hat_epsilon(x1, x2, ax=ax1, L=L)
ax2 = draw_tolerance_change(x1, x2, ax=ax2, L=L)
ax3 = draw_objective_bounds(x1, x2, ax=ax3, L=L)
ax1.xaxis.set_major_locator(plticker.MultipleLocator(base=0.2))
ax1.yaxis.set_major_locator(plticker.MultipleLocator(base=0.1))
# ax1.axis([0,1.,0,1.2])
ax2.xaxis.set_major_locator(plticker.MultipleLocator(base=0.2))
ax2.yaxis.set_major_locator(plticker.MultipleLocator(base=0.1))
ax3.xaxis.set_major_locator(plticker.MultipleLocator(base=0.2))
ax3.yaxis.set_major_locator(plticker.MultipleLocator(base=0.1))
# ax3.axis([0,1.2,0,1.2])
plt.show()
def test_select_point_to_explore_in_two_dimensions(self):
'''
This test case just runs code on a multi-dimensional input dataset.
It doesn't test any conditions, but could presumably do so in the future.
'''
acquire(
x=a([
[-0.5, -0.5],
[-0.5, 0.5],
]),
# Fake fmap and Cmap values from another set of x's
fmap=a([
[0.03254087],
[-0.03254087],
]),
Cmap=a([
[0.07894662, -0.07894662],
[-0.07894662, 0.07894662],
]),
bounds=a([
[-1.0, 1.0],
[-1.0, 1.0],
]),
kernelfunc=default_kernel
)
def test_run_optimization(self):
f, _ = newton_rhapson(
x=a([
[0.0, 1.0],
[1.0, 1.0],
[-1.0, 0.0],
[2.0, 2.0],
[1.5, -1.0]
]),
f0=a([
[0.0],
[0.0],
[0.0],
[0.0],
[0.0],
]),
comparisons=a([
[3, 1],
[0, 1],
[2, 1],
[4, 0],
[2, 4],
]),
kernelfunc=default_kernel,
Hfunc=compute_H,
gfunc=compute_g,
sigma=2,
maxiter=20,
)
self.assertTrue(f[3][0] > f[1][0])
self.assertTrue(f[0][0] > f[1][0])
self.assertTrue(f[2][0] > f[1][0])
self.assertTrue(f[4][0] > f[0][0])
self.assertTrue(f[2][0] > f[4][0])
def test_get_distinct_x_from_comparisons(self):
comp = a([
[[0.0], [1.0]],
[[2.0], [3.0]]
])
x = get_distinct_x(comp)
self.assertAlmostEqual(x, a([[0.0], [1.0], [2.0], [3.0]]))
def test_compute_expectation(self):
'''
Intermediate results expected
Kernel matrix:
1.0 .135335283
.135335283 1.0
K^-1:
1.018657360 -0.137860282
-0.137860282 1.018657360
Kernel vector:
.324652467
.882496903
k' * Kinv:
0.209048353 0.854205285
'''
expected = predict_f(x=a([
[-1.0, 1.0],
[1.0, 1.0],
]),
fmap=a([
[1.0],
[3.0],
]),
xnew=a([0.5, 1.0]),
kernelfunc=default_kernel)
self.assertAlmostEqual(expected, 2.771664208)
def getColor(self, u, v):
if self.tex is None:
return a([1.,1.,1.])
else:
u, v = map(int,(u*(self.tex.size[0]-1),v*(self.tex.size[1]-1)))
c = a(self.tex.getpixel((u,v)), float)
return c/255
def test_select_point_to_exploit(self):
# We attempt to force exploitation by covering most of the input
# space and expecting that the maximization algorithm will choose
# the point between the highest outputs, given a symmetric output function.
next_point = acquire(
x=a([
[-0.75],
[-0.25],
[0.25],
[0.75],
]),
# I got these fmap and Cmap values from running our optimizer
# on the input data with comparisons [1, 0], [1, 3], [2, 0], [2, 3].
fmap=a([
[0.08950024],
[0.21423927],
[0.21423927],
[0.08950024],
]),
Cmap=a([
[0.15672336, -0.07836168, -0.07836168, 0.0],
[-0.07836168, 0.15672336, 0.0, -0.07836168],
[-0.07836168, 0.0, 0.15672336, -0.07836168],
[0.0, -0.07836168, -0.07836168, 0.15672336],
]),
bounds=a([
[-1.0, 1.0],
]),
kernelfunc=default_kernel)
self.assertTrue(next_point[0] > -.25)
self.assertTrue(next_point[0] < .25)
def getNormal(self, u, v):
if self.bump is None:
return a([0,0,0])
else:
u, v = map(int,(u*(self.bump.size[0]-1),v*(self.bump.size[1]-1)))
n = 2*a(self.bump.getpixel((u,v)), float)/255 - a([1.,1.,1])
return Vec3(*n).normalized()
def test_run_optimization(self):
f, _ = newton_rhapson(
x=a([[0.0, 1.0], [1.0, 1.0], [-1.0, 0.0], [2.0, 2.0], [1.5,
-1.0]]),
f0=a([
[0.0],
[0.0],
[0.0],
[0.0],
[0.0],
]),
comparisons=a([
[3, 1],
[0, 1],
[2, 1],
[4, 0],
[2, 4],
]),
kernelfunc=default_kernel,
Hfunc=compute_H,
gfunc=compute_g,
sigma=2,
maxiter=20,
)
self.assertTrue(f[3][0] > f[1][0])
self.assertTrue(f[0][0] > f[1][0])
self.assertTrue(f[2][0] > f[1][0])
self.assertTrue(f[4][0] > f[0][0])
self.assertTrue(f[2][0] > f[4][0])
def test_select_point_to_exploit(self):
# We attempt to force exploitation by covering most of the input
# space and expecting that the maximization algorithm will choose
# the point between the highest outputs, given a symmetric output function.
next_point = acquire(
x=a([
[-0.75],
[-0.25],
[0.25],
[0.75],
]),
# I got these fmap and Cmap values from running our optimizer
# on the input data with comparisons [1, 0], [1, 3], [2, 0], [2, 3].
fmap=a([
[0.08950024],
[0.21423927],
[0.21423927],
[0.08950024],
]),
Cmap=a([
[0.15672336, -0.07836168, -0.07836168, 0.0],
[-0.07836168, 0.15672336, 0.0, -0.07836168],
[-0.07836168, 0.0, 0.15672336, -0.07836168],
[0.0, -0.07836168, -0.07836168, 0.15672336],
]),
bounds=a([
[-1.0, 1.0],
]),
kernelfunc=default_kernel
)
self.assertTrue(next_point[0] > -.25)
self.assertTrue(next_point[0] < .25)
def test_skip_repetitions_within_comparison(self):
comp = a([
[[0.0], [1.0]],
[[2.0], [2.0]]
])
x = get_distinct_x(comp)
self.assertAlmostEqual(x, a([[0.0], [1.0], [2.0]]))
def test_skip_repetitions_across_comparisons(self):
comp = a([
[[1.0], [2.0]],
[[2.0], [3.0]]
])
x = get_distinct_x(comp)
self.assertAlmostEqual(x, a([[1.0], [2.0], [3.0]]))
def test_compute_expectation(self):
'''
Intermediate results expected
Kernel matrix:
1.0 .135335283
.135335283 1.0
K^-1:
1.018657360 -0.137860282
-0.137860282 1.018657360
Kernel vector:
.324652467
.882496903
k' * Kinv:
0.209048353 0.854205285
'''
expected = predict_f(
x=a([
[-1.0, 1.0],
[1.0, 1.0],
]),
fmap=a([
[1.0],
[3.0],
]),
xnew=a([0.5, 1.0]),
kernelfunc=default_kernel
)
self.assertAlmostEqual(expected, 2.771664208)
def test_get_distinct_x_from_2_dimensional_input_data(self):
comp = a([
[[1.0, 2.0], [2.0, 2.0]],
[[2.0, 2.0], [3.0, 3.0]]
])
x = get_distinct_x(comp)
self.assertAlmostEqual(x, a([[1.0, 2.0], [2.0, 2.0], [3.0, 3.0]]))
def optimal_myopic(domain, domain_mu_prior, domain_cm_prior, xObs, yObs,\
xres, yres, ysdbounds, lenscale, sigvar, noisevar2):
out = {}
bounds = [domain[0], domain[-1]]
xcandidates = linspace(bounds[0], bounds[1], xres)
out['x'] = xcandidates
out['ev'] = zeros_like(xcandidates)
ysdcandidates = linspace(ysdbounds[0], ysdbounds[1], yres)
pysdcandidates = norm.pdf(ysdcandidates)
for ix0, x0 in enumerate(xcandidates):
x0 = a([x0])
xObsPlusX0 = append(xObs, x0)
xcmpri0 = jbgp.K_se(x0, x0, lenscale, sigvar)
ymu0 = jbgp.conditioned_mu(x0, xObs, yObs, lenscale, sigvar, noisevar2)
ycm0 = jbgp.conditioned_covmat(x0, atleast_2d(xcmpri0), xObs, lenscale, sigvar, noisevar2)
ysd0 = diag(ycm0)
ycands = a([ymu0 + (ysd0 * n) for n in ysdcandidates])
for iy0, y0 in enumerate(ycands):
yObsPlusY0 = append(yObs, y0)
py0 = pysdcandidates[iy0]
mu0 = jbgp.conditioned_mu(domain, xobsPlusX0, yObsPlusY0, lenscale, sigvar, noisevar2)
evmax = mu0.max()
out['ev'][ix0] += evmax * py0
return out
def emep(domainbounds, xObs, yObs, lenscale, sigvar, noisevar2, xres, yres, ysdbounds):
"""expected value of the max expected value of the posterior"""
out = {}
xcandidates = linspace(domainbounds[0], domainbounds[1], xres)
out['x'] = xcandidates
out['emep'] = zeros_like(xcandidates)
ySDcandidates = linspace(ysdbounds[0], ysdbounds[1], yres)
pdfySDcandidates = norm.pdf(ySDcandidates)
cdfySDcandidates = norm.cdf(ySDcandidates)
for ix0, xx0 in enumerate(xcandidates):
# print 'x: ' + str(ix0)
x0 = a([xx0])
# get ymu and ysd for x0 so know what points to consider for generating prob-weighted ev of max of posterior
ymu0 = jbgp.conditioned_mu(x0, xObs, yObs, lenscale, sigvar, noisevar2)
xcmpri0 = jbgp.K_se(x0, x0, lenscale, sigvar) # get covmat for xSam
ycm0 = jbgp.conditioned_covmat(x0, atleast_2d(xcmpri0), xObs, lenscale, sigvar, noisevar2)
ysd0 = diag(ycm0)
# y-vals to consider with probs pysdcandidates
ycands = a([ymu0 + (ysd0 * d) for d in ySDcandidates])
xObsPlusX0 = append(xObs, x0) # add considered point to xObs locations
# run simulations of what happens with certain y-vals
mep = zeros_like(cdfySDcandidates)
for iy0, y0 in enumerate(ycands):
# print 'y: ' + str(iy0)
yObsPlusY0 = append(yObs, y0)
py0 = pdfySDcandidates[iy0]
mu0 = jbgp.conditioned_mu(domain, xObsPlusX0, yObsPlusY0, lenscale, sigvar, noisevar2)
mep[iy0] = mu0.max()
out['emep'][ix0] = trapz(maxevpost, cdfySDcandidates)
return out
def setUp(self):
self.default_f = a([
[6.0],
[1.0],
[2.0],
])
self.default_comparison = a([0, 2], dtype=np.int)
self.default_sigma = 2.0
def testBlockSub2CenterCarWithoutBand(self):
'''test BlockSub2CenterCarWithoutBand'''
example = ( ( 0, a([-1.9,-1.9,-1.9])),
( 1, a([-1.7,-1.9,-1.9])) )
for ind,right in example:
sub = self.bnd.BlockInd2SubWithoutBand(ind)
rslt = self.bnd.BlockSub2CenterCarWithoutBand(sub)
npt.assert_array_equal(rslt, right)
def test_compute_kernel_vector(self):
x = a([
[0.0, 1.0],
[1.0, 1.0]
])
xnew = a([0.0, 0.0])
k = kernel_vector(default_kernel, x, xnew)
self.assertAlmostEqual(k, a([[.60653066], [.367879441]]))
def testNorm1(self):
'''test Norm1.'''
example = ( ( a( [1,1,1] ), 1 ) ,
( a( [[1,3,4],[2,-2,1]] ), a( [4,2] ))
)
for x,y in example:
rslt = Band.norm1(x)
npt.assert_allclose(rslt, y)
def setUp(self):
self.default_f = a([
[6.0],
[1.0],
[2.0],
])
self.default_comparison = a([0, 2], dtype=np.int)
self.default_sigma = 2.0
def testBlockSub2CenterCarWithoutBand(self):
'''test BlockSub2CenterCarWithoutBand'''
if 1 == 1: return
example = ( ( 0, a([-1.9,-1.9,-1.9])),
( 1, a([-1.7,-1.9,-1.9])) )
for ind,right in example:
sub = self.bnd.BlockInd2SubWithoutBand(ind)
rslt = self.bnd.BlockSub2CenterCarWithoutBand(sub)
npt.assert_array_equal(rslt, right)
def sort_vertexes_longest_edge_first(simplex):
'''Motves longest edge vertexes to the simplex vertex list beggining.'''
edge_lengths = []
for i in xrange(len(simplex)):
edge_lengths.append(enorm(a(simplex[i-1][:-1]) - a(simplex[i][:-1])))
max_len_index = edge_lengths.index(max(edge_lengths))
top_vertex = simplex.pop(max_len_index - 2)
simplex.append(top_vertex)
return simplex
def get_simplex_lower_bound_minimum(X, simp, L, verts=3): # How to set current simplex for one argument function?
'''Uses 3 vertex information'''
if not is_in_simplex(simp[:,:-1], X):
return float('inf')
lb_values = []
for i, v in enumerate(simp):
if i < verts:
lb_values.append(v[-1] - L*enorm(a(v[:-1]) - a(X)))
return max(lb_values)
def test_get_indices_for_comparisons(self):
comp = a([[[1.0, 2.5], [3.0, 2.0]], [[1.0, 2.5], [1.0, 2.5]],
[[2.0, 3.0], [3.0, 2.0]]])
x = a([[1.0, 2.5], [3.0, 2.0], [2.0, 3.0]])
indices = get_comparison_indices(x, comp)
self.assertEqual(indices, a([
[0, 1],
[0, 0],
[2, 1],
]))
def test_one_iteration_yields_expected_result(self):
'''
Taking our results from the computation of H in the last test,
H^-1:
[
-1.066045352 -0.661325899 -0.301834093
-0.661325899 -1.045461463 -0.027289758
-0.301834093 -0.027289758 -1.066045352
]
b (computed fresh):
[
[-.603424068]
[0.0]
[.603424068]
]
g:
[
[-9.616613948]
[4.388339650]
[1.558974488]
]
Then, we compute that H^-1 * g:
[
[6.879072286]
[1.729331837]
[1.120927715]
]
'''
f1, _ = newton_rhapson(
x=a([
[0.0, 1.0],
[1.0, 1.0],
[-1.0, 0.0],
]),
f0=a([
[6.0],
[1.0],
[2.0],
]),
comparisons=a([
[0, 2],
[2, 0],
]),
kernelfunc=default_kernel,
Hfunc=compute_H,
gfunc=compute_g,
sigma=2.0,
maxiter=1,
)
self.assertAlmostEqual(
f1, a([
[-.879072286],
[-.729331837],
[.879072285],
]))
def testBlockInd2SubWithoutBand(self):
'''test BlockInd2SubWithoutBand'''
example = ( (5, a([5,0,0]) ),
(21,a([1,1,0]) ),
(a([401,402]),a([[1,2],[0,0],[1,1]])) )
for ind,sub in example:
result = self.bnd.BlockInd2SubWithoutBand(ind)
npt.assert_array_equal(result,sub)
ExceptionExample = (10000,8000)
for i in ExceptionExample:
self.assertRaises(exceptions.IndexError, self.bnd.BlockInd2SubWithoutBand,i)
def test_one_iteration_yields_expected_result(self):
'''
Taking our results from the computation of H in the last test,
H^-1:
[
-1.066045352 -0.661325899 -0.301834093
-0.661325899 -1.045461463 -0.027289758
-0.301834093 -0.027289758 -1.066045352
]
b (computed fresh):
[
[-.603424068]
[0.0]
[.603424068]
]
g:
[
[-9.616613948]
[4.388339650]
[1.558974488]
]
Then, we compute that H^-1 * g:
[
[6.879072286]
[1.729331837]
[1.120927715]
]
'''
f1, _ = newton_rhapson(
x=a([
[0.0, 1.0],
[1.0, 1.0],
[-1.0, 0.0],
]),
f0=a([
[6.0],
[1.0],
[2.0],
]),
comparisons=a([
[0, 2],
[2, 0],
]),
kernelfunc=default_kernel,
Hfunc=compute_H,
gfunc=compute_g,
sigma=2.0,
maxiter=1,
)
self.assertAlmostEqual(f1, a([
[-.879072286],
[-.729331837],
[.879072285],
]))
def test_compute_kernel_matrix(self):
x = a([
[0.0, 1.0],
[1.0, 1.0],
[-1.0, 0.0],
])
K = kernel_matrix(default_kernel, x)
self.assertAlmostEqual(K, a([
[1.0, .60653066, .367879441],
[.60653066, 1.0, .082084999],
[.367879441, .082084999, 1.0],
]))
def testBlockInd2SubWithoutBand(self):
'''test BlockInd2SubWithoutBand'''
if 1 == 1:return
example = ( (5, a([5,0,0]) ),
(21,a([1,1,0]) ),
(a([401,402]),a([[1,0,1],[2,0,1]])) )
for ind,sub in example:
result = self.bnd.BlockInd2SubWithoutBand(ind)
npt.assert_array_equal(result,sub,'{0} is wrong '.format(ind))
ExceptionExample = (10000,8000)
for i in ExceptionExample:
self.assertRaises(exceptions.IndexError, self.bnd.BlockInd2SubWithoutBand,i)
def is_in_region(t, p):
'''Checks if point is in the triangle region using Barycentric coordinates:
www.farinhansford.com/dianne/teaching/cse470/materials/BarycentricCoords.pdf'''
A = det(a([[t[0][0], t[1][0], t[2][0]], [t[0][1], t[1][1], t[2][1]], [1., 1., 1.]]))
A1 = det(a([[p[0], t[1][0], t[2][0]], [p[1], t[1][1], t[2][1]], [1, 1, 1]]))
A2 = det(a([[t[0][0], p[0], t[2][0]], [t[0][1], p[1], t[2][1]], [1, 1, 1]]))
A3 = det(a([[t[0][0], t[1][0], p[0]], [t[0][1], t[1][1], p[1]], [1, 1, 1]]))
u = A1 / A
v = A2 / A
w = A3 / A
if u >= 0 and v >= 0 and w >= 0:
return True
return False
def test_get_indices_for_comparisons(self):
comp = a([
[[1.0, 2.5], [3.0, 2.0]],
[[1.0, 2.5], [1.0, 2.5]],
[[2.0, 3.0], [3.0, 2.0]]
])
x = a([[1.0, 2.5], [3.0, 2.0], [2.0, 3.0]])
indices = get_comparison_indices(x, comp)
self.assertEqual(indices, a([
[0, 1],
[0, 0],
[2, 1],
]))
def test_compute_b_with_j_for_each_point(self):
b = compute_b(
f=self.default_f,
comparisons=a([
[0, 2],
[2, 1],
]),
sigma=self.default_sigma,
)
self.assertAlmostEqual(b, a([
[.056317811],
[-.207629909],
[.151312099],
]))
def test_compose_c_matrix(self):
C = compute_C(
f=self.default_f,
comparisons=a([
[0, 2],
[2, 0],
]),
sigma=self.default_sigma,
)
self.assertAlmostEqual(C, a([
[.136719008, 0.0, -.136719008],
[0.0, 0.0, 0.0],
[-.136719008, 0.0, .136719008],
]))
def test_compute_kernel_matrix(self):
x = a([
[0.0, 1.0],
[1.0, 1.0],
[-1.0, 0.0],
])
K = kernel_matrix(default_kernel, x)
self.assertAlmostEqual(
K,
a([
[1.0, .60653066, .367879441],
[.60653066, 1.0, .082084999],
[.367879441, .082084999, 1.0],
]))
def hartman3(X):
'''http://www.sfu.ca/~ssurjano/hart3.html'''
alpha = (1.0, 1.2, 3.0, 3.2)
A = a([[3.0, 10, 30], [0.1, 10, 35], [3.0, 10, 30], [0.1, 10, 35]])
P = a([[0.3689, 0.1170, 0.2673],
[0.4699, 0.4387, 0.7470],
[0.1091, 0.8732, 0.5547],
[0.0381, 0.5743, 0.8828]])
sum1 = 0
for i in range(4):
sum2 = 0
for j in range(3):
sum2 += A[i][j] * (X[j] - P[i][j])**2
sum1 += alpha[i] * np.exp(-sum2)
return -sum1
def test_compute_b_with_j_for_each_point(self):
b = compute_b(
f=self.default_f,
comparisons=a([
[0, 2],
[2, 1],
]),
sigma=self.default_sigma,
)
self.assertAlmostEqual(
b, a([
[.056317811],
[-.207629909],
[.151312099],
]))
def test_compose_c_matrix(self):
C = compute_C(
f=self.default_f,
comparisons=a([
[0, 2],
[2, 0],
]),
sigma=self.default_sigma,
)
self.assertAlmostEqual(
C,
a([
[.136719008, 0.0, -.136719008],
[0.0, 0.0, 0.0],
[-.136719008, 0.0, .136719008],
]))
def celluloid(self, array, nb_shade):
minr = amin(array[:, :, 0])
maxr = amax(array[:, :, 0])
minv = amin(array[:, :, 1])
maxv = amax(array[:, :, 1])
minb = amin(array[:, :, 2])
maxb = amax(array[:, :, 2])
seqr = a(linspace(minr, maxr, nb_shade))
seqv = a(linspace(minv, maxv, nb_shade))
seqb = a(linspace(minb, maxb, nb_shade))
shade_tab = stack((seqr, seqv, seqb), axis=0).T
cp = copy(array)
for line in range(cp.shape[0]):
for color in range(cp.shape[1]):
cp[line][color] = self.find_shade(cp[line][color], shade_tab)
return cp
def pico(curvaNivel=False):
aumento = 0.1
rango = 6
aumentoX = 0.4
h = 2.6
p = 1
if curvaNivel:
aumento = 0.025
rango = 18
aumentoX = 0.1
b = 0.6
x = 0
for i in range(0, rango):
points_set_1 = a([[-b, -1, h], [-1, -p - x, h], [1, -p - x, h],
[b, -1, h]])
t_points = np.arange(0, 1, 0.01)
curve_set_1 = Bezier.Curve(t_points, points_set_1)
ax.plot(curve_set_1[:, 0],
curve_set_1[:, 1],
curve_set_1[:, 2],
color="green")
h = h + aumento
x = x + aumentoX
def test_compute_gradient(self):
'''
About this computation:
Recall from the above test case that the kernel will be:
[
[1.0, .60653066, .367879441],
[.60653066, 1.0, .082084999],
[.367879441, .082084999, 1.0],
]
It follows that the inverted kernel is:
[
[ 1.88589785, -1.09427888, -0.60395917],
[-1.09427888, 1.64173123, 0.2678012 ],
[-0.60395917, 0.2678012 , 1.2002017 ]
]
From the above example for computing b, we know that b is:
[
[.056317811],
[-.207629909],
[.151312099],
]
Therefore, the expected calculation of -K^-1 * f + b is:
-9.013189880 .056317811 -8.956872069
4.388339650 + -.207629909 = 4.180709741
0.955550420 .151312099 1.106862519
'''
g = compute_g(kernelfunc=default_kernel,
x=a([
[0.0, 1.0],
[1.0, 1.0],
[-1.0, 0.0],
]),
f=self.default_f,
comparisons=a([
[0, 2],
[2, 1],
]),
sigma=self.default_sigma)
self.assertAlmostEqual(
g, a([
[-8.956872069],
[4.180709741],
[1.106862519],
]))
def test_compute_H(self):
'''
This test reuse intermediate test results that can be seen in tests
for computing the kernel, computing the gradient, and computing C.
From these previous test cases, we know that:
K^-1 is:
[
[ 1.88589785, -1.09427888, -0.60395917],
[-1.09427888, 1.64173123, 0.2678012 ],
[-0.60395917, 0.2678012 , 1.2002017 ]
]
and C is:
[
[.136719008, 0.0, -.136719008],
[0.0, 0.0, 0.0],
[-.136719008, 0.0, .136719008],
]
We add these two matrices to compute the second derivative H.
'''
H = compute_H(
kernelfunc=default_kernel,
x=a([
[0.0, 1.0],
[1.0, 1.0],
[-1.0, 0.0],
]),
f=a([
[6.0],
[1.0],
[2.0],
]),
comparisons=a([
[0, 2],
[2, 0],
]),
sigma=2.0,
)
self.assertAlmostEqual(
H,
a([
[-1.749178842, 1.094278880, 0.467240162],
[1.094278880, -1.641731230, -0.267801200],
[0.467240162, -0.267801200, -1.063482692],
]))
def g_get_points(n):
z = a([[0], [1]])
for k in range(n):
m = g1(z)
n = g2(z)
z = np.concatenate((m,n), axis=1)
x = z.real
y = z.imag
return x, y
def test_b_j_composed_of_one_summand_if_only_one_relevant_pair(self):
res = b_j(
f=self.default_f,
j=2,
comparisons=a([
[0, 2],
]),
sigma=self.default_sigma,
)
self.assertAlmostEqual(res, -.056317811)
def test_b_j_made_up_of_multiple_terms_if_j_in_multiple_comparisons(self):
res = b_j(
f=self.default_f,
j=2,
comparisons=a([
[0, 2],
[2, 1],
]),
sigma=self.default_sigma,
)
self.assertAlmostEqual(res, .151312099)
def test_b_j_is_zero_when_no_comparisons_contain_j(self):
res = b_j(
f=self.default_f,
j=1,
comparisons=a([
[0, 2],
[2, 0],
]),
sigma=self.default_sigma,
)
self.assertAlmostEqual(res, 0.0)
def test_c_entry_with_two_constrasting_comparisons(self):
res = c_m_n(
f=self.default_f,
m=0,
n=2,
comparisons=a([
[0, 2],
[2, 0],
]),
sigma=self.default_sigma,
)
self.assertAlmostEqual(res, -.136719008)
def test_select_point_to_explore(self):
next_point = acquire(
x=a([
[-0.75],
[-0.4],
]),
# I got these fmap and Cmap values from running our optimizer
# on the input data with comparisons [0, 1]
fmap=a([
[0.03254087],
[-0.03254087],
]),
Cmap=a([
[0.07894662, -0.07894662],
[-0.07894662, 0.07894662],
]),
bounds=a([
[-1.0, 1.0],
]),
kernelfunc=default_kernel)
self.assertTrue(next_point[0] > -.4)
def calculate_framerate(self):
"""Calculate the image acquisition frequency in Hz and store it
in the member variable 'framerate'"""
# The "StatFrameRate" attribute always reads 0.0.
# Called preiodically from "resume".
from numpy import argsort, array as a, nan
if len(self.Frames) < 2: return nan
# Find the last two image based on their frame count.
counts = a([
self.Frames[i].frame.FrameCount
for i in range(0, len(self.Frames))
])
times = a(
[self.frame_timestamp(i) for i in range(0, len(self.Frames))])
order = argsort(counts)
count1, count2 = counts[order][-2:]
time1, time2 = times[order][-2:]
if count1 == 0 or count2 == 0: return nan # not enough valid images.
# Calculate the frame rate based on the last two images.
if time2 == time1: return nan
self.framerate = (count2 - count1) / (time2 - time1)
def test_c_entry_is_summand_over_doubled_squared_sigma_when_only_one_relevant_comparison(
self):
res = c_m_n(
f=self.default_f,
m=0,
n=2,
comparisons=a([
[0, 2],
]),
sigma=self.default_sigma,
)
self.assertAlmostEqual(res, -.250644809 / 8.0)
class agent:
c = a([0, 0]) # Row,Col
E = [] # Sensing Matrix
env = '' # Environment Generator
f = 0 # Fitness Score
G = [] # Gene Matrix
P = [] # Next Step Policy
cfg = ''
def __init__(self, env, cfg):
self.c = [int(g(0, 10)), int(g(0, 10))]
self.env = env
self.E = env.getSensingMatrix(self.c)
self.G = gene(cfg)
self.cfg = cfg
def step(self):
if np.linalg.norm(self.c) < self.cfg.B + 10:
self.E = self.env.getSensingMatrix(self.c)
self.P = self.G.A @ self.E @ self.G.B
for i in range(len(self.P)):
if self.P[i] == np.array(self.P).max():
break
# Up
if i == 0:
self.c += a([1, 0])
# Down
elif i == 1:
self.c += a([-1, 0])
# Left
elif i == 2:
self.c += a([0, -1])
# Right
elif i == 3:
self.c += a([0, 1])
# Up Right
elif i == 4:
self.c += a([1, 1])
# Down Right
elif i == 5:
self.c += a([-1, 1])
# Down Left
elif i == 6:
self.c += a([-1, -1])
# Up Left
elif i == 7:
self.c += a([1, -1])
self.f += self.env.consume(self.c)
def geometry_to_points(geo):
points = dict()
# Bottom bracket
points['bottom bracket'] = a([0., 0.])
# Seat tube
points['seat tube bottom'] = points['bottom bracket']
points['seat tube top'] = a([
-cos(radians(geo['seat angle'])) * geo['seat tube'],
sin(radians(geo['seat angle'])) * geo['seat tube'],
])
# Axles
points['rear axle'] = a([
-sqrt(geo['chain stay']**2 - geo['bottom bracket drop']),
geo['bottom bracket drop'],
])
points['front axle'] = a([
points['rear axle'][0] + geo['wheelbase'],
points['rear axle'][1],
])
# Head tube
points['head tube top'] = a([
geo['reach'],
geo['stack'],
])
points['head tube bottom'] = a([
cos(radians(geo['head angle'])) * geo['head tube'] + geo['reach'],
-sin(radians(geo['head angle'])) * geo['head tube'] + geo['stack'],
])
return points
def closestPointToCartesian(self, xx, verbose=0):
""" brue force search over all triangles """
x, y, z = xx
(dd, cpx, cpy, cpz) = FindClosestPointToTriSet(x, y, z, self.F, self.V)
cp = a([cpx, cpy, cpz])
dist = norm(xx - cp, 2)
bdy = 0 # TODO: I guess!
#others = dict(whichFace=tmin)
others = {}
if (verbose >= 0):
print "found cp: x,cp,dist=", xx, cp, dist
return cp, dist, bdy, others
def f_get_points(n):
z = a([[0, 1], [0, 0]])
for k in range(n):
z1 = f1real(z)
z2 = f2real(z)
z = np.concatenate((z1,z2), axis=1)
x = np.zeros([2, 2**n])
y = np.zeros([2, 2**n])
for k in range(2**n):
x[:, k] = z[0, k:k+2]
y[:, k] = z[1, k:k+2]
return x, y