def testFewPoints(self):
# check sanity of paths with less than 3 points
path1=[[4.3,0.8]]
path2=numpy.array([[1,2],[2,4]])
m=4
d=2
s=iisignature.prepare(d,m,"cosx")
s_a=iisignature.prepare(d,2,"cosx")
length=iisignature.siglength(d,m)
loglength=iisignature.logsiglength(d,m)
loglength_a=iisignature.logsiglength(d,2)
blankLogSig=numpy.zeros(loglength)
blankLogSig_a=numpy.zeros(loglength_a)
blankSig=numpy.zeros(length)
self.assertLess(diff(iisignature.sig(path1,m),blankSig),0.000000001)
self.assertTrue(numpy.array_equal(iisignature.sig(path1,m,2),numpy.zeros([0,length])))
self.assertLess(diff(iisignature.logsig(path1,s,"C"),blankLogSig),0.000000001)
self.assertLess(diff(iisignature.logsig(path1,s,"O"),blankLogSig),0.000000001)
self.assertLess(diff(iisignature.logsig(path1,s,"S"),blankLogSig),0.000000001)
self.assertLess(diff(iisignature.logsig(path1,s,"X"),blankSig),0.000000001)
self.assertLess(diff(iisignature.logsig(path1,s_a,"A"),blankLogSig_a),0.000000001)
blankLogSig[:d]=path2[1]-path2[0]
blankLogSig_a[:d]=path2[1]-path2[0]
blankSig[:d]=path2[1]-path2[0]
self.assertLess(diff(iisignature.logsig(path2,s,"C"),blankLogSig),0.000001)
self.assertLess(diff(iisignature.logsig(path2,s,"O"),blankLogSig),0.000001)
self.assertLess(diff(iisignature.logsig(path2,s,"S"),blankLogSig),0.000001)
self.assertLess(diff(iisignature.logsig(path2,s,"X"),blankSig),0.000001)
self.assertLess(diff(iisignature.logsig(path2,s_a,"A"),blankLogSig_a),0.000001)
def testFewPoints(self):
# check sanity of paths with less than 3 points
path1=[[4.3,0.8]]
path2=numpy.array([[1,2],[2,4]])
m=4
d=2
s=iisignature.prepare(d,m,"cosx")
s_a=iisignature.prepare(d,2,"cosx")
length=iisignature.siglength(d,m)
loglength=iisignature.logsiglength(d,m)
loglength_a=iisignature.logsiglength(d,2)
blankLogSig=numpy.zeros(loglength)
blankLogSig_a=numpy.zeros(loglength_a)
blankSig=numpy.zeros(length)
self.assertLess(diff(iisignature.sig(path1,m),blankSig),0.000000001)
self.assertTrue(numpy.array_equal(iisignature.sig(path1,m,2),numpy.zeros([0,length])))
self.assertLess(diff(iisignature.logsig(path1,s,"C"),blankLogSig),0.000000001)
self.assertLess(diff(iisignature.logsig(path1,s,"O"),blankLogSig),0.000000001)
self.assertLess(diff(iisignature.logsig(path1,s,"S"),blankLogSig),0.000000001)
self.assertLess(diff(iisignature.logsig(path1,s,"X"),blankSig),0.000000001)
self.assertLess(diff(iisignature.logsig(path1,s_a,"A"),blankLogSig_a),0.000000001)
blankLogSig[:d]=path2[1]-path2[0]
blankLogSig_a[:d]=path2[1]-path2[0]
blankSig[:d]=path2[1]-path2[0]
self.assertLess(diff(iisignature.logsig(path2,s,"C"),blankLogSig),0.000001)
self.assertLess(diff(iisignature.logsig(path2,s,"O"),blankLogSig),0.000001)
self.assertLess(diff(iisignature.logsig(path2,s,"S"),blankLogSig),0.000001)
self.assertLess(diff(iisignature.logsig(path2,s,"X"),blankSig),0.000001)
self.assertLess(diff(iisignature.logsig(path2,s_a,"A"),blankLogSig_a),0.000001)
def doplot(n_samples=100, m=5, d=3, nplot=None):
x = vanilla_data(n_samples=n_samples, d=d)
# do something to make it interesting: if last coord ever hist 1, then zero out the rest
hitting_event = np.maximum.accumulate(np.abs(x[:, -1])) > 3
x[hitting_event, :-1] = 3
# x[:,:-1] = np.where(cumulative_maximum > 1, 0, x[:,:-1])
# x = x - x.mean(axis=0)
# x = x / x.std(axis=0)
# x = np.exp(x)
# x = x / x.sum(axis=0)
s = iis.prepare(d, m)
if nplot is None:
nplot = n_samples
ii = n_samples // nplot
figure(1)
clf()
ax = subplot(2, 1, 1)
plot(x, alpha=0.5)
ylabel('path')
t = list()
data = list()
for i in range(ii, n_samples, ii):
t.append(i)
temp = iis.logsig(x[:i], s)
data.append(temp)
data = np.array(data)
assert data.shape[1] == iis.logsiglength(d, m), 'not match!'
t = np.array(t)
ax = subplot(2, 1, 2)
plot(t, (data.T / (t**0)).T, alpha=0.5)
# plot(t, (data[:,-1].T / (t ** 0)).T, alpha=0.5)
ylabel('logsig')
xlabel('t')
show()
return locals()
def CLF_grad_Imp(g, path, deg_of_logsig, number_of_segment):
"""
The implementation of computing the derivatives of gradient from backpropagation.
g: the flown gradient from backpropagation
path: dimension (sample_size,n, d)
number_of_segment: the number of segments
deg_of_logsig: the degree of the log-signature
"""
nT = int(np.shape(path)[1])
dim_path = int(np.shape(path)[-1])
t_vec = np.linspace(1,nT,number_of_segment+1)
t_vec = [int(round(x)) for x in t_vec]
s = iisignature.prepare(dim_path, deg_of_logsig)
MultiLevelBP = []
for k in range(int(np.shape(path)[0])):
tmpMultiLevelBP = np.zeros([1,np.shape(path)[-1]])
for i in range(number_of_segment):
temp_path = path[k][t_vec[i]-1:t_vec[i+1], :]
tempBP = iisignature.logsigbackprop(g[k][i], temp_path , s, None)
tmpMultiLevelBP[-1] += tempBP[0]
tempBP = np.delete(tempBP, 0, axis=0)
tmpMultiLevelBP = np.concatenate((tmpMultiLevelBP, tempBP), axis=0)
MultiLevelBP.append(tmpMultiLevelBP)
return np.float32(np.array(MultiLevelBP))
def prepare(self, dimension, depth):
if (dimension, depth) in self._log_sig_prepare_cache:
return self._log_sig_prepare_cache[(dimension, depth)]
s = iisignature.prepare(dimension, depth)
self._log_sig_prepare_cache[(dimension, depth)] = s
return s
def testLevel1(self):
m = 1
d = 2
path = numpy.random.uniform(size=(10, d))
rightSig = path[-1, :] - path[0, :]
s = iisignature.prepare(d, m, "cosx2")
self.assertLess(diff(iisignature.sig(path, m), rightSig), 0.0000001)
for type_ in ("C", "O", "S", "X", "A"):
self.assertLess(diff(iisignature.logsig(path, s, type_), rightSig),
0.0000001, type_)
self.assertLess(diff(rightSig, iisignature.logsigtosig(rightSig, s)),
0.000001)
derivs = numpy.array([2.1, 3.2])
pathderivs = numpy.zeros_like(path)
pathderivs[-1] = derivs
pathderivs[0] = -derivs
self.assertLess(
diff(iisignature.logsigbackprop(derivs, path, s), pathderivs),
0.00001)
self.assertLess(
diff(iisignature.logsigbackprop(derivs, path, s, "X"), pathderivs),
0.00001)
self.assertLess(
diff(iisignature.sigbackprop(derivs, path, m), pathderivs),
0.00001)
def ComputeLogsigFeatures(path, number_of_segment, deg_of_logsig):
"""
The implementation of computing the log-signature of segments of path.
path: dimension (sample_size,n, d)
number_of_segment: the number of segments
deg_of_logsig: the degree of the log-signature
"""
nT = int(np.shape(path)[1])
dim_path = int(np.shape(path)[-1])
t_vec = np.linspace(1, nT, number_of_segment + 1)
t_vec = [int(round(x)) for x in t_vec]
s = iisignature.prepare(dim_path, deg_of_logsig)
MultiLevelLogSig = []
for k in range(int(np.shape(path)[0])):
tmpMultiLevelLogSig = np.zeros(
(number_of_segment,
iisignature.logsiglength(dim_path, deg_of_logsig)))
for i in range(number_of_segment):
temp_path = path[k][t_vec[i] - 1:t_vec[i + 1], :]
temp_start = temp_path[0]
tmpMultiLevelLogSig[i, :] = iisignature.logsig(temp_path, s)
MultiLevelLogSig.append(tmpMultiLevelLogSig)
return np.float32(np.array(MultiLevelLogSig))
def doplot(n_samples=100, m=5, d=3, nplot=None):
x = vanilla_data(n_samples=n_samples, d=d)
# do something to make it interesting: if last coord ever hist 1, then zero out the rest
hitting_event = np.maximum.accumulate(np.abs(x[:,-1])) > 3
x[hitting_event,:-1] = 3
# x[:,:-1] = np.where(cumulative_maximum > 1, 0, x[:,:-1])
# x = x - x.mean(axis=0)
# x = x / x.std(axis=0)
# x = np.exp(x)
# x = x / x.sum(axis=0)
s = iis.prepare(d, m)
if nplot is None:
nplot = n_samples
ii = n_samples // nplot
figure(1)
clf()
ax = subplot(2,1,1)
plot(x, alpha=0.5)
ylabel('path')
t = list()
data = list()
for i in range(ii, n_samples, ii):
t.append(i)
temp = iis.logsig(x[:i], s)
data.append(temp)
data = np.array(data)
assert data.shape[1] == iis.logsiglength(d, m), 'not match!'
t = np.array(t)
ax = subplot(2,1,2)
plot(t, (data.T / (t ** 0)).T, alpha=0.5)
# plot(t, (data[:,-1].T / (t ** 0)).T, alpha=0.5)
ylabel('logsig')
xlabel('t')
show()
return locals()
def ComputeMultiLevelLogsig1dBM(BM_paths, number_of_segment, depth_of_tensors, T):
"""
Compute the log-signature of all samples
"""
no_of_samples = np.shape(BM_paths)[0]
if depth_of_tensors == 1:
MultiLevelLogSigs = np.zeros(
[no_of_samples, 2 * number_of_segment], dtype=float)
else:
MultiLevelLogSigs = np.zeros([no_of_samples, iisignature.logsiglength(
2, depth_of_tensors) * number_of_segment], dtype=float)
MultiStart = np.zeros([no_of_samples, number_of_segment], dtype=float)
s = iisignature.prepare(2, depth_of_tensors)
print('start computing the logsigs of degree %d:' % depth_of_tensors)
for j in tqdm(range(0, no_of_samples, 1), total=no_of_samples):
BM = TimeJointPath(BM_paths[j, :], T)
result2 = ComputeMultiLevelSig(
BM, number_of_segment, depth_of_tensors, s)
#MultiLevelSigs[j] = result2['MultiLevelSig']
# print(result2)
MultiLevelLogSigs[j] = result2['MultiLevelLogSig']
MultiStart[j] = result2['MultiStart']
n_input = int(np.shape(MultiLevelLogSigs)[1] / number_of_segment)
X_logsig_start = MultiLevelLogSigs.reshape(
(np.shape(MultiLevelLogSigs)[0], number_of_segment, n_input))
batch_x0 = MultiStart.reshape(
(np.shape(MultiLevelLogSigs)[0], number_of_segment, 1))
X_logsig_start = np.concatenate((X_logsig_start, batch_x0), axis=2)
return X_logsig_start
def iisignature_prepare(channels, depth, method='d'):
"""Like iisignature.prepare, but caches every result."""
try:
return _iisignature_prepare_cache[(channels, depth, method)]
except KeyError:
prepared = iisignature.prepare(channels, depth, method)
_iisignature_prepare_cache[(channels, depth, method)] = prepared
return prepared
def _getPrep(d, m, lyndon=False):
hash2use = _prepLyndon if lyndon else _prep
key = (d, m)
if key in hash2use:
return hash2use[key]
ans = iisignature.prepare(d, m, "D" if lyndon else "DH")
hash2use[key] = ans
return ans
def _getPrep(d,m, lyndon=False):
hash2use = _prepLyndon if lyndon else _prep
key = (d,m)
if key in hash2use:
return hash2use[key]
ans = iisignature.prepare(d,m, "D" if lyndon else "DH")
hash2use[key]=ans
return ans
def consistency(self, coropa, dim, level):
#numpy.random.seed(21)
s = iisignature.prepare(dim,level,"coshx" if coropa else "cosx")
myinfo = {"level":level, "dimension":dim,
"methods": ("COSAX" if level <= 2 else "COSX"),
"basis":("Standard Hall" if coropa else "Lyndon")}
self.assertEqual(iisignature.info(s),myinfo)
path = numpy.random.uniform(size=(10,dim))
basis = iisignature.basis(s)
logsig = iisignature.logsig(path,s)
sig = iisignature.sig(path,level)
#check lengths
self.assertEqual(len(basis),iisignature.logsiglength(dim,level))
self.assertEqual((len(basis),),logsig.shape)
self.assertEqual(sig.shape,(iisignature.siglength(dim,level),))
#calculate a signature from logsig
expanded_logsig = [numpy.zeros(dim ** m) for m in range(1,level + 1)]
for coeff, expression in zip(logsig,basis):
values, depth = valueOfBracket(expression,dim)
expanded_logsig[depth - 1]+=values * coeff
calculated_sig = numpy.concatenate(exponentiateTensor(expanded_logsig))
self.assertLess(diff(sig,calculated_sig),0.00001)
#calculate a log signature from sig
fullLogSig = numpy.concatenate(logTensor(splitConcatenatedTensor(sig,dim,level)))
fullLogSigLib = iisignature.logsig(path,s,"x")
diff1 = numpy.max(numpy.abs(fullLogSigLib - fullLogSig))
#print
#(numpy.vstack([fullLogSig,fullLogSigLib,numpy.abs(fullLogSigLib-fullLogSig)]).transpose())
self.assertLess(diff1,0.00001)
basisMatrix = []
zeros = [numpy.zeros(dim ** m) for m in range(1,level + 1)]
for expression in basis:
values, depth = valueOfBracket(expression, dim)
temp = zeros[depth - 1]
zeros[depth - 1] = values
basisMatrix.append(numpy.concatenate(zeros))
zeros[depth - 1] = temp
calculatedLogSig = lstsq(numpy.transpose(basisMatrix),fullLogSig)[0]
diff2 = numpy.max(numpy.abs(logsig - calculatedLogSig))
self.assertLess(diff2,0.00001)
#check consistency of methods
slowLogSig = iisignature.logsig(path,s,"o")
diffs = numpy.max(numpy.abs(slowLogSig - calculatedLogSig))
self.assertLess(diffs,0.00001)
sigLogSig = iisignature.logsig(path,s,"s")
diffs = numpy.max(numpy.abs(sigLogSig - calculatedLogSig))
self.assertLess(diffs,0.00001)
if level < 3:
areaLogSig = iisignature.logsig(path,s,"a")
diffs = numpy.max(numpy.abs(areaLogSig - calculatedLogSig))
self.assertLess(diffs,0.00001)
def consistency(self, coropa, dim, level):
#numpy.random.seed(21)
s = iisignature.prepare(dim,level,"coshx" if coropa else "cosx")
myinfo = {"level":level, "dimension":dim,
"methods": ("COSAX" if level <= 2 else "COSX"),
"basis":("Standard Hall" if coropa else "Lyndon")}
self.assertEqual(iisignature.info(s),myinfo)
path = numpy.random.uniform(size=(10,dim))
basis = iisignature.basis(s)
logsig = iisignature.logsig(path,s)
sig = iisignature.sig(path,level)
#check lengths
self.assertEqual(len(basis),iisignature.logsiglength(dim,level))
self.assertEqual((len(basis),),logsig.shape)
self.assertEqual(sig.shape,(iisignature.siglength(dim,level),))
#calculate a signature from logsig
expanded_logsig = [numpy.zeros(dim ** m) for m in range(1,level + 1)]
for coeff, expression in zip(logsig,basis):
values, depth = valueOfBracket(expression,dim)
expanded_logsig[depth - 1]+=values * coeff
calculated_sig = numpy.concatenate(exponentiateTensor(expanded_logsig))
self.assertLess(diff(sig,calculated_sig),0.00001)
#calculate a log signature from sig
fullLogSig = numpy.concatenate(logTensor(splitConcatenatedTensor(sig,dim,level)))
fullLogSigLib = iisignature.logsig(path,s,"x")
diff1 = numpy.max(numpy.abs(fullLogSigLib - fullLogSig))
#print
#(numpy.vstack([fullLogSig,fullLogSigLib,numpy.abs(fullLogSigLib-fullLogSig)]).transpose())
self.assertLess(diff1,0.00001)
basisMatrix = []
zeros = [numpy.zeros(dim ** m) for m in range(1,level + 1)]
for expression in basis:
values, depth = valueOfBracket(expression, dim)
temp = zeros[depth - 1]
zeros[depth - 1] = values
basisMatrix.append(numpy.concatenate(zeros))
zeros[depth - 1] = temp
calculatedLogSig = lstsq(numpy.transpose(basisMatrix),fullLogSig)[0]
diff2 = numpy.max(numpy.abs(logsig - calculatedLogSig))
self.assertLess(diff2,0.00001)
#check consistency of methods
slowLogSig = iisignature.logsig(path,s,"o")
diffs = numpy.max(numpy.abs(slowLogSig - calculatedLogSig))
self.assertLess(diffs,0.00001)
sigLogSig = iisignature.logsig(path,s,"s")
diffs = numpy.max(numpy.abs(sigLogSig - calculatedLogSig))
self.assertLess(diffs,0.00001)
if level < 3:
areaLogSig = iisignature.logsig(path,s,"a")
diffs = numpy.max(numpy.abs(areaLogSig - calculatedLogSig))
self.assertLess(diffs,0.00001)
def testLyndon(self):
d=2
m=5
s=iisignature.prepare(d,m,"O")
for expression in iisignature.basis(s):
word = ''.join(c for c in expression if c not in '[,]')
if len(word) > 1:
for prefixLength in range(1,len(word)):
self.assertLess(word[:prefixLength],word[prefixLength:])
def testLyndon(self):
d=2
m=5
s=iisignature.prepare(d,m,"O")
for expression in iisignature.basis(s):
word = ''.join(c for c in expression if c not in '[,]')
if len(word) > 1:
for prefixLength in range(1,len(word)):
self.assertLess(word[:prefixLength],word[prefixLength:])
def __init__(self,
model,
dim,
level=2,
transform=lambda x: x,
**model_args):
self.prepared = prepare(dim,
level) # iisignature prepare log signature
super().__init__(model, level, transform, **model_args)
def tryLogSig():
s=iisignature.prepare(2,2)
for expanded in (False, True):
inp = Variable(torch.randn(8, 2), requires_grad=True)
if expanded:
result = LogSig(inp,s,"x")
else:
result = LogSig(inp, s)
print(result.data.numpy())
result.backward(torch.randn(result.size()))
print(inp.grad.data)
def tryLogSig():
for expanded in (False, True):
sess=tf.Session()
path=[[2,3],[3,5],[4,5]]
m=2
s=iisignature.prepare(2,m)
a = tf.placeholder(tf.float32)
out= LogSig(a,s,"x") if expanded else LogSig(a,s)
grad = tf.gradients(tf.reduce_sum(out),a)[0]
#grad = tf.gradients(out,a)[0]
out_vals=(sess.run([out,grad], {a: path}))
print (out_vals[0])
print(out_vals[1])
def test_logsigbackwards_can_augment_s(self):
numpy.random.seed(291)
d=2
m=7
pathLength=3
path = numpy.random.uniform(size=(pathLength,d))
increment = 0.1*numpy.random.uniform(size=(pathLength,d))
dFdlogSig = numpy.ones(iisignature.logsiglength(d,m))
for types in (("x","o","s"),("xh","oh","sh")):
ss=[iisignature.prepare(d,m,t) for t in types]
backs=[iisignature.logsigbackprop(dFdlogSig,path,s) for s in ss]
self.assertTrue(numpy.allclose(backs[0],backs[2]),types[0])
self.assertTrue(numpy.allclose(backs[1],backs[2]),types[1])
fwds=[iisignature.logsig(path,s,"s") for s in ss]
self.assertTrue(numpy.allclose(fwds[0],fwds[2]),types[0])
self.assertTrue(numpy.allclose(fwds[1],fwds[2]),types[1])
def testLevel1(self):
m=1
d=2
path=numpy.random.uniform(size=(10,d))
rightSig = path[-1,:]-path[0,:]
s=iisignature.prepare(d,m,"cosx")
self.assertLess(diff(iisignature.sig(path,m),rightSig),0.0000001)
for type_ in ("C","O","S","X","A"):
self.assertLess(diff(iisignature.logsig(path,s,type_),rightSig),0.0000001,type_)
derivs=numpy.array([2.1,3.2])
pathderivs=numpy.zeros_like(path)
pathderivs[-1]=derivs
pathderivs[0]=-derivs
self.assertLess(diff(iisignature.logsigbackprop(derivs,path,s),pathderivs),0.00001)
self.assertLess(diff(iisignature.logsigbackprop(derivs,path,s,"X"),pathderivs),0.00001)
self.assertLess(diff(iisignature.sigbackprop(derivs,path,m),pathderivs),0.00001)
def test_logsigbackwards_can_augment_s(self):
numpy.random.seed(291)
d=2
m=7
pathLength=3
path = numpy.random.uniform(size=(pathLength,d))
increment = 0.1*numpy.random.uniform(size=(pathLength,d))
dFdlogSig = numpy.ones(iisignature.logsiglength(d,m))
for types in (("x","o","s"),("xh","oh","sh")):
ss=[iisignature.prepare(d,m,t) for t in types]
backs=[iisignature.logsigbackprop(dFdlogSig,path,s) for s in ss]
self.assertTrue(numpy.allclose(backs[0],backs[2]),types[0])
self.assertTrue(numpy.allclose(backs[1],backs[2]),types[1])
fwds=[iisignature.logsig(path,s,"s") for s in ss]
self.assertTrue(numpy.allclose(fwds[0],fwds[2]),types[0])
self.assertTrue(numpy.allclose(fwds[1],fwds[2]),types[1])
def logSig(self, type, m=5):
numpy.random.seed(291)
d=2
pathLength=10
s=iisignature.prepare(d,m,type)
path = numpy.random.uniform(size=(pathLength,d))
path = numpy.cumsum(2 * (path - 0.5),0)#makes it more random-walk-ish, less like a scribble
increment = 0.01*path
increment = 0.1*numpy.random.uniform(size=(pathLength,d))
manualChange = fdDeriv(lambda x:iisignature.logsig(x,s,type),path,increment,4)
dFdlogSig = numpy.ones(iisignature.siglength(d,m) if "X"==type else iisignature.logsiglength(d,m))
calculatedChange = numpy.sum(increment*iisignature.logsigbackprop(dFdlogSig,path,s,type))
#print(manualChange, calculatedChange)
self.assertLess(numpy.abs(manualChange-calculatedChange),0.0001)
def logSig(self, type, m=5):
numpy.random.seed(291)
d=2
pathLength=10
s=iisignature.prepare(d,m,type)
path = numpy.random.uniform(size=(pathLength,d))
path = numpy.cumsum(2 * (path - 0.5),0)#makes it more random-walk-ish, less like a scribble
increment = 0.01*path
increment = 0.1*numpy.random.uniform(size=(pathLength,d))
manualChange = fdDeriv(lambda x:iisignature.logsig(x,s,type),path,increment,4)
dFdlogSig = numpy.ones(iisignature.siglength(d,m) if "X"==type else iisignature.logsiglength(d,m))
calculatedChange = numpy.sum(increment*iisignature.logsigbackprop(dFdlogSig,path,s,type))
#print(manualChange, calculatedChange)
self.assertLess(numpy.abs(manualChange-calculatedChange),0.0001)
def doL2S(self, coropa):
numpy.random.seed(212)
d = 3
m = 6
path = numpy.random.uniform(size=(12, d))
sig = iisignature.sig(path, m)
s = iisignature.prepare(d, m, "S2H" if coropa else "S2")
self.assertTrue(iisignature.info(s)["logsigtosig_supported"])
logsig = iisignature.logsig(path, s)
sig_ = iisignature.logsigtosig(logsig, s)
self.assertEqual(sig.shape, sig_.shape)
self.assertTrue(numpy.allclose(sig, sig_))
#Like the other iisig functions, we check that derivatives
#of logsigtosig allow sum(logsigtosig) to be backproped correctly
#This is a boring thing to calculate, because after the first level
#each of the log signature elements is a lie bracket and so
#contributes a net total of 0 to the signature
derivsOfSum = numpy.ones((sig.shape[0], ), dtype="float64")
bumpedLogSig = 1.01 * logsig
calculated = iisignature.logsigtosigbackprop(derivsOfSum, logsig, s)
#wantedbackprop = allSensitivities(logsig, lambda l: iisignature.logsigtosig(l,s).sum())
manualChange = fdDeriv(lambda x: iisignature.logsigtosig(x, s), logsig,
bumpedLogSig - logsig, 6)
calculatedChange = numpy.sum((bumpedLogSig - logsig) * calculated)
self.assertLess(numpy.abs(manualChange - calculatedChange), 0.00001)
#beyond the first level, all zero
if m > 1:
self.assertLess(numpy.max(numpy.abs(calculated[d:])), 0.00001)
self.assertEqual(calculated.shape, logsig.shape)
#Now for a better test, we backprop sum(random*logsigtosig)
#specifically calculate the change in it caused by bump two ways
random = numpy.random.uniform(size=sig.shape[0], )
derivsOfSum = random
calculated = iisignature.logsigtosigbackprop(derivsOfSum, logsig, s)
manualChange = fdDeriv(
lambda x: iisignature.logsigtosig(x, s) * random, logsig,
bumpedLogSig - logsig, 4)
calculatedChange = numpy.sum((bumpedLogSig - logsig) * calculated)
self.assertLess(numpy.abs(manualChange - calculatedChange), 0.00001)
self.assertEqual(calculated.shape, logsig.shape)
def ComputeMultiLevelSig1dBM(BM_paths, number_of_segment, depth_of_tensors, T):
"""
Compute the signature of all samples
"""
s = iisignature.prepare(2, depth_of_tensors)
no_of_samples = np.shape(BM_paths)[0]
MultiLevelSigs = np.zeros([no_of_samples, iisignature.siglength(
2, depth_of_tensors) * number_of_segment - 1], dtype=float)
print('start computing the sigs of degree %d:' % depth_of_tensors)
for j in tqdm(range(0, no_of_samples, 1), total=no_of_samples):
BM = TimeJointPath(BM_paths[j, :], T)
result2 = ComputeMultiLevelSig(
BM, number_of_segment, depth_of_tensors, s, sig='True')
MultiLevelSigs[j] = result2['MultiLevelLogSig']
if number_of_segment > 1:
n_input = int(np.shape(MultiLevelSigs)[1] / number_of_segment)
X_sig = MultiLevelSigs.reshape(
(np.shape(MultiLevelSigs)[0], number_of_segment, n_input))
else:
X_sig = MultiLevelSigs
return X_sig
def demo():
#1. generate some dummy data
d=3
m=6
path1=np.random.uniform(size=(20,d))
path2=np.random.uniform(size=(20,d))
paths = (path1,path2)
s=iisignature.prepare(d,m)
#2. print the dot product of the log signatures in tensor space
#(The "x" means that the log signature is returned in tensor space.)
expandedLogSig1,expandedLogSig2=(iisignature.logsig(i,s,"x") for i in paths)
target = np.inner(expandedLogSig1,expandedLogSig2)
print_ ("Target:", float(target))
#3. use getMatrices to act on the log signatures expressed in a basis
# and get the same answer.
matrices=getMatrices(s)
logsig1,logsig2=(iisignature.logsig(i,s) for i in paths)
adjustment=scipy.linalg.block_diag(*matrices)
#print(np.dot(adjustment,logsig2).shape)
print_ ("We get:", float(np.inner(logsig1,np.dot(adjustment,logsig2))))
def save_plot_sig_logsig_handwritten_data():
for truncation_order in range(1, 16):
fig_sig, axs_sig = plt.subplots(10)
fig_sig.suptitle(
f"Sig of handwritten digits (0 top and 9 bottom); k={truncation_order}"
)
fig_logsig, axs_logsig = plt.subplots(10)
fig_logsig.suptitle(
f"Log_sig of handwritten digits (0 top and 9 bottom); k={truncation_order}"
)
for i in range(10):
# 1. logsig
s = iisignature.prepare(2, truncation_order)
log_sig = iisignature.logsig(handwritting_ds.training_X_ordered[i],
s)
log_sig_df = pd.DataFrame(log_sig) # signatures are rows
log_sig_df = log_sig_df.transpose(
) # ; we move them into columns so that time series format
axs_logsig[i].plot(log_sig_df.values)
fig_logsig.savefig(
f"/home/raymess-lin/git/auto-sig-encoder/plots/handwritten_log_sig_k_{truncation_order}.png"
)
# 2. sig
sig = iisignature.sig(handwritting_ds.training_X_ordered[i],
truncation_order)
sig_df = pd.DataFrame(sig) # signatures are rows
sig_df = sig_df.transpose(
) # ; we move them into columns so that time series format
axs_sig[i].plot(sig_df.values)
fig_sig.savefig(
f"/home/raymess-lin/git/auto-sig-encoder/plots/handwritten_sig_k_{truncation_order}.png"
)
'PROTEINS/': 59
}
batch_size = bs[dataset_name]
test_size = data_len // 10
train_batches = np.ceil((data_len - test_size) / batch_size).astype(int)
print('number of batches = ', train_batches, ' batch size = ', batch_size)
torch.manual_seed(0)
rng_state = torch.get_rng_state(
) #seed init to ensure same initial conditions for each training
### eigenvalue path signature ####
if xtra_feat:
pslevel = 4
sig_prep = iisignature.prepare(2, pslevel)
#xtra_feat_length = iisignature.logsiglength(2, pslevel)
siglength = iisignature.logsiglength(2, pslevel)
xtra_feat_length = siglength
if xxtra: xtra_feat_length += 7
else:
xtra_feat_length = 0
###### preprocess #####
data = []
label = []
mx, mn = -np.inf, np.inf
Alist = None
Aker = None
def testHighDim(self):
for m in [1]:
d=1000
path = numpy.random.rand(10,d)
s=iisignature.prepare(d,m)
iisignature.logsig(path,s,"A")
def test_batch(self):
numpy.random.seed(734)
d=2
m=2
n=15
paths = [numpy.random.uniform(-1,1,size=(6,d)) for i in range(n)]
pathArray15=stack(paths)
pathArray1315=numpy.reshape(pathArray15,(1,3,1,5,6,d))
sigs = [iisignature.sig(i,m) for i in paths]
sigArray=stack(sigs)
sigArray15=iisignature.sig(pathArray15,m)
sigArray1315=iisignature.sig(pathArray1315,m)
siglength=iisignature.siglength(d,m)
self.assertEqual(sigArray1315.shape,(1,3,1,5,siglength))
self.assertTrue(numpy.allclose(sigArray1315.reshape(n,siglength),sigs))
self.assertEqual(sigArray15.shape,(15,siglength))
self.assertTrue(numpy.allclose(sigArray15,sigs))
backsigs=[iisignature.sigbackprop(i,j,m) for i,j in zip(sigs,paths)]
backsigArray = stack(backsigs)
backsigs1315=iisignature.sigbackprop(sigArray1315,pathArray1315,m)
self.assertEqual(backsigs1315.shape,(1,3,1,5,6,d))
self.assertTrue(numpy.allclose(backsigs1315.reshape(n,6,2),backsigArray))
data=[numpy.random.uniform(size=(d,)) for i in range(n)]
dataArray1315=stack(data).reshape((1,3,1,5,d))
joined=[iisignature.sigjoin(i,j,m) for i,j in zip(sigs,data)]
joined1315=iisignature.sigjoin(sigArray1315,dataArray1315,m)
self.assertEqual(joined1315.shape,(1,3,1,5,siglength))
self.assertTrue(numpy.allclose(joined1315.reshape(n,-1),stack(joined)))
backjoined=[iisignature.sigjoinbackprop(i,j,k,m) for i,j,k in zip(joined,sigs,data)]
backjoinedArrays=[stack([i[j] for i in backjoined]) for j in range(2)]
backjoined1315=iisignature.sigjoinbackprop(joined1315,sigArray1315,dataArray1315,m)
self.assertEqual(backjoined1315[0].shape,sigArray1315.shape)
self.assertEqual(backjoined1315[1].shape,dataArray1315.shape)
self.assertTrue(numpy.allclose(backjoined1315[0].reshape(n,-1),backjoinedArrays[0]))
self.assertTrue(numpy.allclose(backjoined1315[1].reshape(n,-1),backjoinedArrays[1]))
dataAsSigs=[iisignature.sig(numpy.row_stack([numpy.zeros((d,)),i]),m) for i in data]
dataArray13151=dataArray1315[:,:,:,:,None,:]
dataArray13151=numpy.repeat(dataArray13151,2,4)*[[0.0],[1.0]]
dataArrayAsSigs1315=iisignature.sig(dataArray13151,m)
combined1315=iisignature.sigcombine(sigArray1315,dataArrayAsSigs1315,d,m)
self.assertEqual(joined1315.shape,combined1315.shape)
self.assertTrue(numpy.allclose(joined1315,combined1315))
backcombined1315=iisignature.sigcombinebackprop(joined1315,sigArray1315,dataArrayAsSigs1315,d,m)
backcombined=[iisignature.sigcombinebackprop(i,j,k,d,m) for i,j,k in zip(joined,sigs,dataAsSigs)]
backcombinedArrays=[stack([i[j] for i in backcombined]) for j in range(2)]
self.assertEqual(backcombined1315[0].shape,sigArray1315.shape)
self.assertEqual(backcombined1315[1].shape,sigArray1315.shape)
self.assertTrue(numpy.allclose(backjoined1315[0],backcombined1315[0]))
self.assertTrue(numpy.allclose(backcombined1315[0].reshape(n,-1),backcombinedArrays[0]))
self.assertTrue(numpy.allclose(backcombined1315[1].reshape(n,-1),backcombinedArrays[1]))
scaled=[iisignature.sigscale(i,j,m) for i,j in zip(sigs,data)]
scaled1315=iisignature.sigscale(sigArray1315,dataArray1315,m)
self.assertEqual(scaled1315.shape,(1,3,1,5,siglength))
self.assertTrue(numpy.allclose(scaled1315.reshape(n,-1),stack(scaled)))
backscaled=[iisignature.sigscalebackprop(i,j,k,m) for i,j,k in zip(scaled,sigs,data)]
backscaledArrays=[stack([i[j] for i in backscaled]) for j in range(2)]
backscaled1315=iisignature.sigscalebackprop(scaled1315,sigArray1315,dataArray1315,m)
self.assertEqual(backscaled1315[0].shape,sigArray1315.shape)
self.assertEqual(backscaled1315[1].shape,dataArray1315.shape)
self.assertTrue(numpy.allclose(backscaled1315[0].reshape(n,-1),backscaledArrays[0]))
self.assertTrue(numpy.allclose(backscaled1315[1].reshape(n,-1),backscaledArrays[1]))
s_s=(iisignature.prepare(d,m,"cosax"),iisignature.prepare(d,m,"cosahx"))
for type in ("c","o","s","x","a","ch","oh","sh","ah"):
s=s_s[1 if "h" in type else 0]
logsigs = [iisignature.logsig(i,s,type) for i in paths]
logsigArray=stack(logsigs)
logsigArray1315=iisignature.logsig(pathArray1315,s,type)
self.assertEqual(logsigArray1315.shape,(1,3,1,5,logsigs[0].shape[0]),type)
self.assertTrue(numpy.allclose(logsigArray1315.reshape(n,-1),logsigArray),type)
if type in ("s","x","sh"):
backlogs = stack(iisignature.logsigbackprop(i,j,s,type) for i,j in zip(logsigs,paths))
backlogs1315 = iisignature.logsigbackprop(logsigArray1315,pathArray1315,s,type)
self.assertEqual(backlogs1315.shape,backsigs1315.shape)
self.assertTrue(numpy.allclose(backlogs1315.reshape(n,6,d),backlogs),type)
a=iisignature.rotinv2dprepare(m,"a")
rots=stack([iisignature.rotinv2d(i,a) for i in paths])
rots1315=iisignature.rotinv2d(pathArray1315,a)
self.assertEqual(rots1315.shape,(1,3,1,5,rots.shape[1]))
self.assertTrue(numpy.allclose(rots1315.reshape(n,-1),rots))
def test_batch(self):
numpy.random.seed(734)
d=2
m=2
n=15
paths = [numpy.random.uniform(-1,1,size=(6,d)) for i in range(n)]
pathArray15=stack(paths)
pathArray1315=numpy.reshape(pathArray15,(1,3,1,5,6,d))
sigs = [iisignature.sig(i,m) for i in paths]
sigArray=stack(sigs)
sigArray15=iisignature.sig(pathArray15,m)
sigArray1315=iisignature.sig(pathArray1315,m)
siglength=iisignature.siglength(d,m)
self.assertEqual(sigArray1315.shape,(1,3,1,5,siglength))
self.assertTrue(numpy.allclose(sigArray1315.reshape(n,siglength),sigs))
self.assertEqual(sigArray15.shape,(15,siglength))
self.assertTrue(numpy.allclose(sigArray15,sigs))
backsigs=[iisignature.sigbackprop(i,j,m) for i,j in zip(sigs,paths)]
backsigArray = stack(backsigs)
backsigs1315=iisignature.sigbackprop(sigArray1315,pathArray1315,m)
self.assertEqual(backsigs1315.shape,(1,3,1,5,6,d))
self.assertTrue(numpy.allclose(backsigs1315.reshape(n,6,2),backsigArray))
data=[numpy.random.uniform(size=(d,)) for i in range(n)]
dataArray1315=stack(data).reshape((1,3,1,5,d))
joined=[iisignature.sigjoin(i,j,m) for i,j in zip(sigs,data)]
joined1315=iisignature.sigjoin(sigArray1315,dataArray1315,m)
self.assertEqual(joined1315.shape,(1,3,1,5,siglength))
self.assertTrue(numpy.allclose(joined1315.reshape(n,-1),stack(joined)))
backjoined=[iisignature.sigjoinbackprop(i,j,k,m) for i,j,k in zip(joined,sigs,data)]
backjoinedArrays=[stack([i[j] for i in backjoined]) for j in range(2)]
backjoined1315=iisignature.sigjoinbackprop(joined1315,sigArray1315,dataArray1315,m)
self.assertEqual(backjoined1315[0].shape,sigArray1315.shape)
self.assertEqual(backjoined1315[1].shape,dataArray1315.shape)
self.assertTrue(numpy.allclose(backjoined1315[0].reshape(n,-1),backjoinedArrays[0]))
self.assertTrue(numpy.allclose(backjoined1315[1].reshape(n,-1),backjoinedArrays[1]))
scaled=[iisignature.sigscale(i,j,m) for i,j in zip(sigs,data)]
scaled1315=iisignature.sigscale(sigArray1315,dataArray1315,m)
self.assertEqual(scaled1315.shape,(1,3,1,5,siglength))
self.assertTrue(numpy.allclose(scaled1315.reshape(n,-1),stack(scaled)))
backscaled=[iisignature.sigscalebackprop(i,j,k,m) for i,j,k in zip(scaled,sigs,data)]
backscaledArrays=[stack([i[j] for i in backscaled]) for j in range(2)]
backscaled1315=iisignature.sigscalebackprop(scaled1315,sigArray1315,dataArray1315,m)
self.assertEqual(backscaled1315[0].shape,sigArray1315.shape)
self.assertEqual(backscaled1315[1].shape,dataArray1315.shape)
self.assertTrue(numpy.allclose(backscaled1315[0].reshape(n,-1),backscaledArrays[0]))
self.assertTrue(numpy.allclose(backscaled1315[1].reshape(n,-1),backscaledArrays[1]))
s_s=(iisignature.prepare(d,m,"cosax"),iisignature.prepare(d,m,"cosahx"))
for type in ("c","o","s","x","a","ch","oh","sh","ah"):
s=s_s[1 if "h" in type else 0]
logsigs = [iisignature.logsig(i,s,type) for i in paths]
logsigArray=stack(logsigs)
logsigArray1315=iisignature.logsig(pathArray1315,s,type)
self.assertEqual(logsigArray1315.shape,(1,3,1,5,logsigs[0].shape[0]),type)
self.assertTrue(numpy.allclose(logsigArray1315.reshape(n,-1),logsigArray),type)
if type in ("s","x","sh"):
backlogs = stack(iisignature.logsigbackprop(i,j,s,type) for i,j in zip(logsigs,paths))
backlogs1315 = iisignature.logsigbackprop(logsigArray1315,pathArray1315,s,type)
self.assertEqual(backlogs1315.shape,backsigs1315.shape)
self.assertTrue(numpy.allclose(backlogs1315.reshape(n,6,d),backlogs),type)
a=iisignature.rotinv2dprepare(m,"a")
rots=stack([iisignature.rotinv2d(i,a) for i in paths])
rots1315=iisignature.rotinv2d(pathArray1315,a)
self.assertEqual(rots1315.shape,(1,3,1,5,rots.shape[1]))
self.assertTrue(numpy.allclose(rots1315.reshape(n,-1),rots))
def testHighDim(self):
for m in [1,2]:
d=1000
path = numpy.random.rand(10,d)
s=iisignature.prepare(d,m)
iisignature.logsig(path,s,"A")
import numpy as np
import time
start_time = time.time()
max_frames = 420
min_frames = 130
processes = 12
id_set = get_id_set()
size = len(id_set)
explored = {}
k = 3
d = 69
words, word_index = signature.get_words(d, k)
s = prepare(d, k)
def similarity(a, b):
return log_signature.concatenate_metric(a, b, s)
return log_signature.linear_metric(a, b)
return signature.inverse_tensor_metric(a, b, words, word_index, k, d)
return signature.linear_metric(a, b)
return signature.concatenate_group_metric(a, b, words, word_index, k, d)
return signature.concatenate_algebra_metric(a, b, words, word_index, k, d)
return log_signature.concatenate_group_metric(a, b, s)
def explore(id):
subject, animation, description = unpack(
fetch_animations(1, animation_id=id))
def setup(obj):
obj.path = torch.rand(obj.size, dtype=torch.float).numpy()
shape = obj.size[-3], iisignature.logsiglength(obj.size[-1], obj.depth)
obj.grad = torch.rand(shape).numpy()
obj.prepare = iisignature.prepare(obj.path.shape[-1], obj.depth)
import six.moves
#add the parent directory, so we find our iisignature build if it was built --inplace
sys.path.append(os.path.dirname(os.path.abspath(os.path.dirname(__file__))))
import iisignature
from iisignature_theano import LogSig, Sig
#1: SETUP VARIABLES
dim=2
level=3
pathlength=4
timedim=False
useLogSig = True
s=iisignature.prepare(dim,level)
numpy.random.seed(51)
target = numpy.random.uniform(size=(pathlength,dim)).astype("float32")
#target = numpy.cumsum(2*(target-0.5),0)#makes it more random-walk-ish, less like a scribble
targetSig = iisignature.logsig(target,s) if useLogSig else iisignature.sig(target,level)
start = numpy.random.uniform(size=(pathlength,dim)).astype("float32")
start[0,:] = target[0,:]
learnable_mask = numpy.ones((pathlength,dim)).astype("float32")
learnable_mask[0,:]=0 #to stop the starting point being modified
if timedim:
for i in six.moves.xrange(pathlength):
target[i,0]=start[i,0]=i*0.2
learnable_mask[i,0]=0
learning_rate_decay = 1.003
def transform(self, X):
prepared = prepare(self.dim, self.level)
return np.array([logsig(x, prepared) for x in X])
#see their log signatures printed on the console.
#based on https://kivy.org/docs/tutorials/firstwidget.html
from kivy.app import App
from kivy.uix.widget import Widget
from kivy.graphics import Color, Ellipse, Line
import numpy as np, os, sys
#add the parent directory, so we find our iisignature build if it was built --inplace
sys.path.append(os.path.dirname(os.path.abspath(os.path.dirname(__file__))))
import iisignature
np.set_printoptions(suppress=True)
m=2
s=iisignature.prepare(2,m)
class MyPaintWidget(Widget):
def on_touch_down(self, touch):
with self.canvas:
Color(1, 1, 0)
touch.ud['line'] = Line(points=(touch.x, touch.y))
def on_touch_move(self, touch):
touch.ud['line'].points += [touch.x, touch.y]
def on_touch_up(self, touch):
path=np.reshape(touch.ud['line'].points,(-1,2))
print(iisignature.logsig(path,s))
def testIssue16(self):
# github-reported crash, issue #16
iisignature.prepare(3, 3, '2')
def setup(obj):
obj.path = torch.rand(obj.size, dtype=torch.float).numpy()
obj.prepare = iisignature.prepare(obj.path.shape[-1], obj.depth)
import theano, numpy, sys
import six.moves
#add the parent directory, so we find our iisignature build if it was built --inplace
sys.path.append(os.path.dirname(os.path.abspath(os.path.dirname(__file__))))
import iisignature
from iisignature_theano import LogSig, Sig
#1: SETUP VARIABLES
dim = 2
level = 3
pathlength = 4
timedim = False
useLogSig = True
s = iisignature.prepare(dim, level)
numpy.random.seed(51)
target = numpy.random.uniform(size=(pathlength, dim)).astype("float32")
#target = numpy.cumsum(2*(target-0.5),0)#makes it more random-walk-ish, less like a scribble
targetSig = iisignature.logsig(target, s) if useLogSig else iisignature.sig(
target, level)
start = numpy.random.uniform(size=(pathlength, dim)).astype("float32")
start[0, :] = target[0, :]
learnable_mask = numpy.ones((pathlength, dim)).astype("float32")
learnable_mask[0, :] = 0 #to stop the starting point being modified
if timedim:
for i in six.moves.xrange(pathlength):
target[i, 0] = start[i, 0] = i * 0.2
learnable_mask[i, 0] = 0
#This program just continually runs some of the important functionality in
#iisignature on small data, so that you can check that memory usage
#does not grow. Even a tiny memory leak becomes very visible e.g. in htop.
#add the parent directory, so we find our iisignature build if it was built --inplace
sys.path.append(os.path.dirname(os.path.abspath(os.path.dirname(__file__))))
import iisignature
length = 20
dim=3
level=2
npaths=3
paths_ = np.random.uniform(size=(npaths,length,dim))
scale_ = np.random.uniform(size=(npaths,dim))
initialsigs_ = np.random.uniform(size=(npaths,iisignature.siglength(dim,level)))
p=iisignature.prepare(dim,level,"cosx")
while 0:
iisignature.sig(paths[0],level)
for i in range(10**10):
#copy major parts of the input data, in case we are leaking references to it
paths=paths_[:]
increment=scale=scale_[:]
initialsigs=initialsigs_[:]
iisignature.sigjoin(initialsigs,scale,level)
iisignature.sigscale(initialsigs,scale,level)
iisignature.sigjoinbackprop(initialsigs,initialsigs,scale,level)
iisignature.sigscalebackprop(initialsigs,initialsigs,scale,level)
iisignature.sig(paths[0,:,:],level)
iisignature.sigbackprop(initialsigs[0,:],paths[0,:,:],level)
#iisignature.sigjacobian(paths[0,:,:],level)
#iisignature.prepare(dim,level,"cosx")#much slower than other functions
