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 test_lyndon_brackets():
"""Tests the lyndon_brackets function"""
for channels in range(2, 11): # iisignature supports channels with unique symbols in the range 2 to 10 inclusive
for depth in range(1, 6):
iisignature_brackets = iisignature.basis(h.iisignature_prepare(channels, depth))
signatory_brackets = signatory.lyndon_brackets(channels, depth)
for ii_elem, sig_elem in zip(iisignature_brackets, signatory_brackets):
print('channels=' + str(channels))
print('depth=' + str(depth))
assert sig_elem == eval(_iisignature_convert(ii_elem))
def test_lyndon_words():
"""Tests the lyndon_words function"""
for channels in range(2, 11): # iisignature supports channels with unique symbols in the range 2 to 10 inclusive
for depth in range(1, 6):
iisignature_brackets = iisignature.basis(h.iisignature_prepare(channels, depth))
signatory_words = signatory.lyndon_words(channels, depth)
for ii_elem, sig_elem in zip(iisignature_brackets, signatory_words):
ii_elem_new = ii_elem.replace('[', '').replace(']', '').replace(',', '')
ii_elem_new = _iisignature_convert(ii_elem_new)
sig_elem_new = ''.join(str(i) for i in sig_elem)
print('channels=' + str(channels))
print('depth=' + str(depth))
print('ii_elem' + str(ii_elem))
print('sig_elem' + str(sig_elem))
assert sig_elem_new == ii_elem_new
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
def log_sig_keys(self, dimension, depth):
s = self.prepare(dimension, depth)
return iisignature.basis(dimension, depth)
def logsigkeys(d, m):
s = _getPrep(d, m)
return " " + " ".join(iisignature.basis(s))
def logsigkeys(d,m):
s=_getPrep(d,m)
return " "+" ".join(iisignature.basis(s))