def _get_fpt_ell_collection(dm, fpts, T_data, alpha, edgecolor):
ell_patches = []
for (x, y, a, c, d) in fpts: # Manually Calculated sqrtm(inv(A))
with catch_warnings():
simplefilter("ignore")
aIS = 1 / sqrt(a)
cIS = (c / sqrt(a) - c / sqrt(d)) / (a - d + eps(1))
dIS = 1 / sqrt(d)
transEll = Affine2D([(aIS, 0, x), (cIS, dIS, y), (0, 0, 1)])
unitCirc1 = Circle((0, 0), 1, transform=transEll)
ell_patches = [unitCirc1] + ell_patches
ellipse_collection = PatchCollection(ell_patches)
ellipse_collection.set_facecolor("none")
ellipse_collection.set_transform(T_data)
ellipse_collection.set_alpha(alpha)
ellipse_collection.set_edgecolor(edgecolor)
return ellipse_collection
def _get_fpt_ell_collection(dm, fpts, T_data, alpha, edgecolor):
ell_patches = []
for (x,y,a,c,d) in fpts: # Manually Calculated sqrtm(inv(A))
with catch_warnings():
simplefilter("ignore")
aIS = 1/sqrt(a)
cIS = (c/sqrt(a) - c/sqrt(d))/(a - d + eps(1))
dIS = 1/sqrt(d)
transEll = Affine2D([\
( aIS, 0, x),\
( cIS, dIS, y),\
( 0, 0, 1)])
unitCirc1 = Circle((0,0),1,transform=transEll)
ell_patches = [unitCirc1] + ell_patches
ellipse_collection = PatchCollection(ell_patches)
ellipse_collection.set_facecolor('none')
ellipse_collection.set_transform(T_data)
ellipse_collection.set_alpha(alpha)
ellipse_collection.set_edgecolor(edgecolor)
return ellipse_collection
def build_model(vm, force_recomp=False):
''' Builds the model, if needed. Tries to reload if it can '''
logmsg('\n\nRequested: Build Model')
if not force_recomp and not vm.isDirty:
logmsg('The model is clean and is not forced to recompute')
return True
cm = vm.hs.cm
# Delete old index and resample chips to index
vm.delete_model()
vm.sample_train_set()
# Try to load the correct model
if not force_recomp and vm.load_model():
logmsg('Loaded saved model from disk')
return
logmsg('Building the model. This may take some time.')
# Could not load old model. Do full rebuild
# -----
# STEP 1 - Loading
logdbg('Step 1: Aggregate the model support (Load feature vectors) ---')
tx2_cx = vm.get_train_cx()
tx2_cid = vm.get_train_cid()
assert len(tx2_cx) > 0, 'Training set cannot be np.empty'
logdbg('Building model with %d sample chips' % (vm.num_train()))
cm.load_features(tx2_cx)
tx2_nfpts = cm.cx2_nfpts(tx2_cx)
num_train_keypoints = sum(tx2_nfpts)
# -----
# STEP 2 - Aggregating
logdbg('Step 2: Build the model Words')
isTFIDF = False
if vm.hs.am.algo_prefs.model.quantizer == 'naive_bayes':
logdbg('No Quantization. Aggregating all fdscriptors for nearest neighbor search.')
vm.wx2_fdsc = np.empty((num_train_keypoints,128),dtype=np.uint8)
_p = 0
for cx in tx2_cx:
nfdsc = cm.cx2_nfpts(cx)
vm.wx2_fdsc[_p:_p+nfdsc,:] = cm.cx2_fdsc[cx]
_p += nfdsc
ax2_wx = np.array(range(0,num_train_keypoints),dtype=np.uint32)
if vm.hs.am.algo_prefs.model.quantizer == 'akmeans':
raise NotImplementedError(':)')
# -----
# STEP 3 - Inverted Indexing
logdbg('Step 3: Point the parts of the model back to their source')
vm.wx2_axs = np.empty(vm.wx2_fdsc.shape[0], dtype=object)
for ax in xrange(0,num_train_keypoints):
if vm.wx2_axs[ax] is None:
vm.wx2_axs[ax] = []
wx = ax2_wx[ax]
vm.wx2_axs[wx].append(ax)
vm.ax2_cid = -np.ones(num_train_keypoints,dtype=np.int32)
vm.ax2_fx = -np.ones(num_train_keypoints,dtype=np.int32)
ax2_tx = -np.ones(num_train_keypoints,dtype=np.int32)
curr_fx = 0; next_fx = 0
for tx in xrange(vm.num_train()):
nfpts = tx2_nfpts[tx]
next_fx = next_fx + nfpts
ax_range = range(curr_fx,next_fx)
ax2_tx[ax_range] = tx
vm.ax2_cid[ax_range] = tx2_cid[tx] # Point to Inst
vm.ax2_fx[ax_range] = range(nfpts) # Point to Kpts
curr_fx = curr_fx + nfpts
if isTFIDF: # Compute info for TF-IDF
logdbg('Computing TF-IDF metadata')
max_tx = len(tx2_cx)
tx2_wtf_denom = np.float32(cm.cx2_nfpts(tx2_cx))
vm.wx2_maxtf = map(lambda ax_of_wx:\
max( np.float32(bincount(ax2_tx[ax_of_wx], minlength=max_tx)) / tx2_wtf_denom ), vm.wx2_axs)
vm.wx2_idf = np.log2(map(lambda ax_of_wx:\
vm.num_train()/len(pylab.unique(ax2_tx[ax_of_wx])),\
vm.wx2_axs)+eps(1))
logdbg('Built Model using %d feature vectors. Preparing to index.' % len(vm.ax2_cid))
# -----
# STEP 4 - Indexing
logdbg('Step 4: Building FLANN Index: over '+str(len(vm.wx2_fdsc))+' words')
assert vm.flann is None, 'Flann already exists'
vm.flann = FLANN()
flann_param_dict = vm.hs.am.algo_prefs.model.indexer.to_dict()
flann_params = vm.flann.build_index(vm.wx2_fdsc, **flann_param_dict)
vm.isDirty = False
vm.save_model()
logmsg('The model was built.')
def compute_hulls(S, fS, domain):
"""
(Re-)compute upper and lower hull given
the segment points `S` with function values
`fS` and the `domain` of the logpdf.
Parameters
----------
S : np.ndarray (N, 1)
Straight-line segment points accumulated thus far.
fS : tuple
Value of the `logpdf` under sampling for each
of the given segment points in `S`.
domain : Tuple[float, float]
Domain of `logpdf`.
May be unbounded on either or both sides,
in which case `(float("-inf"), float("inf"))`
would be passed.
If this domain is unbounded to the left,
the derivative of the logpdf
for x<= a must be positive.
If this domain is unbounded to the right the derivative of the logpdf for x>=b
must be negative.
Returns
----------
lower_hull: List[arspy.hull.HullNode]
upper_hull: List[arspy.hull.HullNode]
"""
assert (len(S) == len(fS))
assert (len(domain) == 2)
lower_hull = []
for li in range(len(S) - 1):
m = (fS[li + 1] - fS[li]) / (S[li + 1] - S[li])
b = fS[li] - m * S[li]
left = S[li]
right = S[li + 1]
lower_hull.append(HullNode(m=m, b=b, left=left, right=right))
# compute upper piecewise-linear hull
# expected final length of upper hull after full computation
n_upper_segments = 2 * (len(S) - 2) + isinf(domain[0]) + isinf(domain[1])
upper_hull = []
if isinf(domain[0]):
# first line (from -infinity)
m = (fS[1] - fS[0]) / (S[1] - S[0])
b = fS[0] - m * S[0]
pr = compute_segment_log_prob(float("-inf"), S[0], m, b)
upper_hull.append(
HullNode(m=m, b=b, pr=pr, left=float("-inf"), right=S[0]))
# second line
m = (fS[2] - fS[1]) / (S[2] - S[1])
b = fS[1] - m * S[1]
pr = compute_segment_log_prob(S[0], S[1], m, b)
upper_hull.append(HullNode(m=m, b=b, pr=pr, left=S[0], right=S[1]))
# interior lines
# there are two lines between each abscissa
for li in range(1, len(S) - 2):
m1 = (fS[li] - fS[li - 1]) / (S[li] - S[li - 1])
b1 = fS[li] - m1 * S[li]
m2 = (fS[li + 2] - fS[li + 1]) / (S[li + 2] - S[li + 1])
b2 = fS[li + 1] - m2 * S[li + 1]
if isinf(m1) and isinf(m2):
raise ValueError("both hull slopes are infinite")
dx1 = S[li] - S[li - 1]
df1 = fS[li] - fS[li - 1]
dx2 = S[li + 2] - S[li + 1]
df2 = fS[li + 2] - fS[li + 1]
f1 = fS[li]
f2 = fS[li + 1]
x1 = S[li]
x2 = S[li + 1]
# more numerically stable than above
ix = ((f1 * dx1 - df1 * x1) * dx2 -
(f2 * dx2 - df2 * x2) * dx1) / (df2 * dx1 - df1 * dx2)
if isinf(m1) or abs(m1 - m2) < 10.0**8 * eps(m1):
ix = S[li]
pr1 = float("-inf")
pr2 = compute_segment_log_prob(ix, S[li + 1], m2, b2)
elif isinf(m2):
ix = S[li + 1]
pr1 = compute_segment_log_prob(S[li], ix, m1, b1)
pr2 = float("-inf")
else:
if isinf(ix):
raise ValueError("Non finite intersection")
if abs(ix - S[li]) < 10.0**12 * eps(S[li]):
ix = S[li]
elif abs(ix - S[li + 1]) < 10.0**12 * eps(S[li + 1]):
ix = S[li + 1]
if ix < S[li] or ix > S[li + 1]:
raise ValueError(
"Intersection out of bounds -- logpdf is not concave")
pr1 = compute_segment_log_prob(S[li], ix, m1, b1)
pr2 = compute_segment_log_prob(ix, S[li + 1], m2, b2)
upper_hull.append(
HullNode(m=m1, b=b1, pr=pr1, left=S[li], right=ix))
upper_hull.append(
HullNode(m=m2, b=b2, pr=pr2, left=ix, right=S[li + 1]))
# second last line
m = (fS[-2] - fS[-3]) / float(S[-2] - S[-3])
b = fS[-2] - m * S[-2]
pr = compute_segment_log_prob(S[-2], S[-1], m, b)
upper_hull.append(HullNode(m=m, b=b, pr=pr, left=S[-2], right=S[-1]))
if isinf(domain[1]):
# last line (to infinity)
m = (fS[-1] - fS[-2]) / (S[-1] - S[-2])
b = fS[-1] - m * S[-1]
pr = compute_segment_log_prob(S[-1], float("inf"), m, b)
upper_hull.append(
HullNode(m=m, b=b, pr=pr, left=S[-1], right=float("inf")))
# normalize probabilities
normalized_probabilities = exp_normalize(
asarray([node.pr for node in upper_hull]))
for node, probability in zip(upper_hull, normalized_probabilities):
node.pr = probability
assert (len(lower_hull) == len(S) - 1)
assert (len(upper_hull) == n_upper_segments)
return lower_hull, upper_hull
def elu(param, x):
return param * (np.eps(x) - 1.) if x < 0 else x
