def infer_shape(self,node,shapes):
#d=shapes[0][-1]
s,method=_prepared_obeject_store[node.inputs[1].get_value()]
m=iisignature.info(s)["level"]
d=iisignature.info(s)["dimension"]
if "x" in method or "X" in method:
length=iisignature.siglength(d,m)
else:
length=iisignature.logsiglength(d,m)
return [shapes[0][:-2]+(length,)]
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 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 getMatrices(s):
info=iisignature.info(s)
m=info["level"]
d=info["dimension"]
values=[[] for i in range(m)]
for exp in iisignature.basis(s):
vec,level = valueOfBracket(exp,d)
values[level-1].append(vec)
out=[]
for v in values:
def f(x,y): return numpy.inner(v[x],v[y])
out.append(numpy.fromfunction(
numpy.vectorize(f),(len(v),len(v)),dtype=int))
# store=[]
# for x1 in v:
# store.append([])
# for x2 in v:
# store[-1].append(numpy.inner(x1,x2))
# out.append(numpy.array(store))
return out