def __init__(
self,
n_units,
sig_level=2,
train_time_lapse=False,
initial_time_lapse=0.1,
output_signatures=False, #whether the output includes the signatures
use_signatures=True, #whether each new state can depend on the signature
kernel_initializer='glorot_uniform',
recurrent_initializer='he_normal', #could be good to use 'orthogonal' if not use_signatures
activation='tanh', #not applied to signature elements
**kwargs):
self.sig_level = sig_level
self.sigsize = iisignature.siglength(2, sig_level)
self.n_units = n_units #like output_dim
self.units = n_units * (self.sigsize +
1) if output_signatures else n_units
self.train_time_lapse = train_time_lapse
self.initial_time_lapse = initial_time_lapse
self.output_signatures = output_signatures
self.use_signatures = use_signatures
self.kernel_initializer = initializers.get(kernel_initializer)
self.recurrent_initializer = initializers.get(recurrent_initializer)
self.activation = activations.get(activation)
super(RecurrentSig, self).__init__(**kwargs)
def __init__(self, ef_num_hlayers, ef_num_hu, ef_num_filters, pslevel,
num_slices, dropout):
'''
for each diagram, we have different slices
Across different functions, we have the same parameters for #h0slices, #h0siglevel, #h1slices, #h1siglevel
'''
super(dgmslice_ps2, self).__init__()
self.filters = ef_num_filters
self.pslevel = pslevel #list [pslevel for h0, pslevel for h1]
self.slices = num_slices #list [#slices for h0, #slices for pslevel for h1]
#self.siglength = [iisignature.siglength(num_slices+1, m) for m in pslevel]
self.siglength = [
iisignature.siglength(num_slices[i], pslevel[i]) for i in range(2)
] #
self.eigfs = nn.ModuleList()
self.projections0 = nn.ModuleList()
self.projections1 = nn.ModuleList()
self.final_vec_length = self.filters * sum(self.siglength)
for i in range(self.filters):
self.eigfs.append(eigf(ef_num_hlayers, ef_num_hu))
for i in range(self.filters):
self.projections0.append(nn.Conv1d(1, self.slices[0], 2, 2))
for i in range(self.filters):
self.projections1.append(nn.Conv1d(1, self.slices[1], 2, 2))
self.final_layer = nn.Sequential(nn.Dropout(dropout),
nn.Linear(self.final_vec_length, 1),
nn.BatchNorm1d(1))
def testcombining(self):
dim = 2
level = 2
siglength = iisignature.siglength(dim,level)
pathLength = 20
halfPathLength=10
numberToDo=4
path = numpy.random.uniform(size=(numberToDo,pathLength,dim))
sig = iisignature.sig(path,level)
sig1 = iisignature.sig(path[:,:halfPathLength],level)
sig2 = iisignature.sig(path[:,(halfPathLength-1):],level)
combined = iisignature.sigcombine(sig1,sig2,dim,level)
self.assertLess(diff(sig,combined),0.0001)
extra = numpy.random.uniform(size=(siglength,))
bumpedsig1 = 1.001 * sig1
bumpedsig2 = 1.001 * sig2
base = numpy.sum(iisignature.sigcombine(sig1,sig2,dim,level))
bump1 = numpy.sum(iisignature.sigcombine(bumpedsig1,sig2,dim,level))
bump2 = numpy.sum(iisignature.sigcombine(sig1,bumpedsig2,dim,level))
derivsOfSum = numpy.ones((numberToDo,siglength))
calculated = iisignature.sigcombinebackprop(derivsOfSum,sig1,sig2,dim,level)
self.assertEqual(len(calculated), 2)
diff1 = (bump1 - base) - numpy.sum(calculated[0] * (bumpedsig1 - sig1))
diff2 = (bump2 - base) - numpy.sum(calculated[1] * (bumpedsig2 - sig2))
#print ("\n",bump1,bump2,base,diff1,diff2)
self.assertLess(numpy.abs(diff1),0.000001)
self.assertLess(numpy.abs(diff2),0.00001)
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 __init__(self,
input_size,
n_units,
sig_level=2,
train_time_lapse=True,
initial_time_lapse=0.1,
output_signatures=False,
use_signatures=True):
super(RecurrentSig, self).__init__()
self.sig_level = sig_level
self.sigsize = iisignature.siglength(2, sig_level)
self.n_units = n_units
self.units = n_units * (self.sigsize +
1) if output_signatures else n_units
self.train_time_lapse = train_time_lapse
#self.initial_time_lapse = initial_time_lapse
self.output_signatures = output_signatures
self.use_signatures = use_signatures
saved_data_length = self.n_units * (1 + self.sigsize
if self.use_signatures else 1)
self.W = nn.Linear(input_size, self.n_units)
self.U = nn.Linear(saved_data_length, self.n_units)
if self.train_time_lapse:
self.log_timelapse = nn.parameter.Parameter(
torch.FloatTensor([math.log(initial_time_lapse)]))
else:
self.time_lapse = Variable(torch.FloatTensor([initial_time_lapse]))
def get_penalization(self, n, k, Kpen):
"""Returns the penalization function used in the estimator of the truncation order, that is,
pen_n(k)=Kpen*sqrt((d^(k+1)-1)/(d-1))/n^rho.
Parameters
----------
n: int
Number of samples.
k: int
Truncation order of the signature.
Kpen: float, default=1
Constant in front of the penalization, it has to be strictly positive.
Returns
-------
pen_n(k):float
The penalization pen_n(k)
"""
if k == 0:
size_sig = 1
else:
size_sig = isig.siglength(self.d, k) + 1
return Kpen * n**(-self.rho) * math.sqrt(size_sig)
def get_sigX(X, k):
"""Returns a matrix containing signatures truncated at k of n samples
given in the input tensor X.
Parameters
----------
X: array, shape (n, npoints, d)
A 3-dimensional array, containing the coordinates in R^d of n
piecewise linear paths, each composed of n_points.
k: int
Truncation order of the signature
Returns
-------
sigX: array, shape (n,p)
A matrix containing in each row the signature truncated at k of a sample.
"""
if k == 0:
return np.full((np.shape(X)[0], 1), 1)
else:
d = X.shape[2]
sigX = np.zeros((np.shape(X)[0], isig.siglength(d, k) + 1))
sigX[:, 0] = 1
for i in range(np.shape(X)[0]):
sigX[i, 1:] = isig.sig(X[i, :, :], k)
return sigX
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 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 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 get_sig_dimension(self):
""" Returns the dimension of the signature vector truncated at
self.order and with the embedding chosen by self.path
Returns
-------
siglength: int
The dimension of the signature vector.
"""
return (isig.siglength(self.get_embedding_dimension(), self.order))
def delayedBM_limit(BM_1d, depth, time):
"""Returns limiting rough path in p-var top for the delayed BM problem (with iisignature and BnB)"""
N = len(BM_1d)
X_inf = np.zeros((N, iisignature.siglength(2, depth)))
for k, t in enumerate(time):
X_inf[k, 0] = BM_1d[k]
X_inf[k, 1] = BM_1d[k]
X_inf[k, 2] = 0.
X_inf[k, 3] = t / 2.
X_inf[k, 4] = -t / 2.
X_inf[k, 5] = 0.
return X_inf
def testSig(self):
#test that sigjacobian and sigbackprop compatible with sig
numpy.random.seed(291)
d = 3
m = 5
pathLength = 10
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 * numpy.random.uniform(size=(pathLength,d))
base_sig = iisignature.sig(path,m)
target = fdDeriv(lambda x:iisignature.sig(x,m),path,increment,2, nosum=True)
gradient = iisignature.sigjacobian(path,m)
calculated = numpy.tensordot(increment,gradient)
diffs = numpy.max(numpy.abs(calculated - target))
niceOnes = numpy.abs(calculated) > 1.e-4
niceOnes2 = numpy.abs(calculated) < numpy.abs(base_sig)
diffs1 = numpy.max(numpy.abs((calculated[niceOnes2] - target[niceOnes2]) / base_sig[niceOnes2]))
diffs2 = numpy.max(numpy.abs(calculated[1 - niceOnes2] - target[1 - niceOnes2]))
ratioDiffs = numpy.max(numpy.abs(calculated[niceOnes] / target[niceOnes] - 1))
#numpy.set_printoptions(suppress=True,linewidth=os.popen('stty size',
#'r').read().split()[1] #LINUX
#numpy.set_printoptions(suppress=True,linewidth=150)
#print ("")
#print (path)
#print
#(numpy.vstack([range(len(base_sig)),base_sig,calculated,target,(calculated-target)/base_sig,calculated/target-1]).transpose())
#print (diffs, ratioDiffs, diffs1, diffs2)
#print(numpy.argmax(numpy.abs(calculated[niceOnes]/target[niceOnes]-1)),numpy.argmax(numpy.abs((calculated-target)/base_sig)))
self.assertLess(diffs,0.00001)
self.assertLess(ratioDiffs,0.01)
self.assertLess(diffs1,0.001)
self.assertLess(diffs2,0.00001)
#compatibility between sigbackprop and sigjacobian is strong
dFdSig = numpy.random.uniform(size=(iisignature.siglength(d,m),))
backProp = iisignature.sigbackprop(dFdSig,path,m)
manualCalcBackProp = numpy.dot(gradient,dFdSig)
backDiffs = numpy.max(numpy.abs(backProp - manualCalcBackProp))
if 0: # to investigate the compile logic problem I used this and
# (d,m,pathLength)=(1,2,2)
print("")
print(dFdSig)
print(path)
print(backProp)
print(manualCalcBackProp)
self.assertLess(backDiffs,0.000001)
def testSig(self):
#test that sigjacobian and sigbackprop compatible with sig
numpy.random.seed(291)
d = 3
m = 5
pathLength = 10
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 * numpy.random.uniform(size=(pathLength,d))
base_sig = iisignature.sig(path,m)
target = fdDeriv(lambda x:iisignature.sig(x,m),path,increment,2, nosum=True)
gradient = iisignature.sigjacobian(path,m)
calculated = numpy.tensordot(increment,gradient)
diffs = numpy.max(numpy.abs(calculated - target))
niceOnes = numpy.abs(calculated) > 1.e-4
niceOnes2 = numpy.abs(calculated) < numpy.abs(base_sig)
diffs1 = numpy.max(numpy.abs((calculated[niceOnes2] - target[niceOnes2]) / base_sig[niceOnes2]))
diffs2 = numpy.max(numpy.abs(calculated[1 - niceOnes2] - target[1 - niceOnes2]))
ratioDiffs = numpy.max(numpy.abs(calculated[niceOnes] / target[niceOnes] - 1))
#numpy.set_printoptions(suppress=True,linewidth=os.popen('stty size',
#'r').read().split()[1] #LINUX
#numpy.set_printoptions(suppress=True,linewidth=150)
#print ("")
#print (path)
#print
#(numpy.vstack([range(len(base_sig)),base_sig,calculated,target,(calculated-target)/base_sig,calculated/target-1]).transpose())
#print (diffs, ratioDiffs, diffs1, diffs2)
#print(numpy.argmax(numpy.abs(calculated[niceOnes]/target[niceOnes]-1)),numpy.argmax(numpy.abs((calculated-target)/base_sig)))
self.assertLess(diffs,0.00001)
self.assertLess(ratioDiffs,0.01)
self.assertLess(diffs1,0.001)
self.assertLess(diffs2,0.00001)
#compatibility between sigbackprop and sigjacobian is strong
dFdSig = numpy.random.uniform(size=(iisignature.siglength(d,m),))
backProp = iisignature.sigbackprop(dFdSig,path,m)
manualCalcBackProp = numpy.dot(gradient,dFdSig)
backDiffs = numpy.max(numpy.abs(backProp - manualCalcBackProp))
if 0: # to investigate the compile logic problem I used this and
# (d,m,pathLength)=(1,2,2)
print("")
print(dFdSig)
print(path)
print(backProp)
print(manualCalcBackProp)
self.assertLess(backDiffs,0.000001)
def __init__(self, trend, init_money=10000, window_size=20): #这里把df改为trend
self.n_actions = 3 # 动作数量
self.n_features = window_size + iisignature.siglength(2, 3) # 特征数量
#self.trend = df['close'].values # 收盘数据
#self.df = df #数据的DataFrame
self.trend = trend # 收盘数据
self.init_money = init_money # 初始化资金
self.n_lagged_time_steps = 20 #用于计算signature的p-lag value 200
self.window_size = window_size #滑动窗口大小
self.half_window = window_size // 2
#self.signature = np.empty(shape=[len(self.trend),iisignature.siglength(2,3)])
self.signature = self.signature_normalisation(self.trend)
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 delayed_roughBM(BM, BM_del, delay, depth, time):
if delay == 0:
return delayedBM_limit(BM, depth, time)
BM = np.concatenate((BM, np.array(delay * [BM[-1]])), 0)
N = len(BM)
roughBM = np.zeros((N, iisignature.siglength(2, depth)))
DeltaBM = np.append(0., np.diff(BM, 0))
for k in range(N):
roughBM[k, 0] = BM[k]
roughBM[k, 1] = BM_del[k]
roughBM[k, 2] = 0.
levy_area = (BM_del[:k] * DeltaBM[:k]).sum() - 0.5 * BM[k] * BM_del[k]
roughBM[k, 3] = levy_area
roughBM[k, 4] = -levy_area
roughBM[k, 5] = 0.
return roughBM
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 testjoining(self):
numberToDo = 1
dim = 2
level = 2
siglength = iisignature.siglength(dim,level)
for fixedPoint, inputDim, fixed in [(float('nan'),dim,False),(0.1,dim - 1,True)]:
pathLength = 10
def makePath():
p = numpy.random.uniform(size=(pathLength,dim))
if fixed:
p[:,-1] = fixedPoint * numpy.arange(pathLength)
return p
paths = [makePath() for i in range(numberToDo)]
sig = numpy.vstack([iisignature.sig(path,level) for path in paths])
joinee = numpy.zeros((numberToDo,siglength))
for i in range(1,pathLength):
displacements = [path[i:(i + 1),:] - path[(i - 1):i,:] for path in paths]
displacement = numpy.vstack(displacements)
if fixed:
displacement = displacement[:,:-1]
joinee = iisignature.sigjoin(joinee,displacement,level,fixedPoint)
self.assertLess(diff(sig,joinee),0.0001,"fullSig matches sig" + (" with fixed Dim" if fixed else ""))
extra = numpy.random.uniform(size=(numberToDo,inputDim))
bumpedExtra = 1.001 * extra
bumpedJoinee = 1.001 * joinee
base = numpy.sum(iisignature.sigjoin(joinee,extra,level,fixedPoint))
bump1 = numpy.sum(iisignature.sigjoin(bumpedJoinee,extra,level,fixedPoint))
bump2 = numpy.sum(iisignature.sigjoin(joinee,bumpedExtra,level,fixedPoint))
derivsOfSum = numpy.ones((numberToDo,siglength))
calculated = iisignature.sigjoinbackprop(derivsOfSum,joinee,extra,
level,fixedPoint)
self.assertEqual(len(calculated),3 if fixed else 2)
diff1 = (bump1 - base) - numpy.sum(calculated[0] * (bumpedJoinee - joinee))
diff2 = (bump2 - base) - numpy.sum(calculated[1] * (bumpedExtra - extra))
#print ("\n",bump1,bump2,base,diff1,diff2)
self.assertLess(numpy.abs(diff1),0.000001,"diff1 as expected " + (" with fixed Dim" if fixed else ""))
self.assertLess(numpy.abs(diff2),0.00001,"diff2 as expected " + (" with fixed Dim" if fixed else ""))
if fixed:
bumpedFixedPoint = fixedPoint * 1.01
bump3 = numpy.sum(iisignature.sigjoin(joinee,extra, level, bumpedFixedPoint))
diff3 = (bump3-base - numpy.sum(calculated[2] * (bumpedFixedPoint-fixedPoint)))
#print("\n",bump3,base, fixedPoint, bumpedFixedPoint, calculated[2])
self.assertLess(numpy.abs(diff3),0.00001, "diff3")
def testjoining(self):
numberToDo = 1
dim = 2
level = 2
siglength = iisignature.siglength(dim,level)
for fixedPoint, inputDim, fixed in [(float('nan'),dim,False),(0.1,dim - 1,True)]:
pathLength = 10
def makePath():
p = numpy.random.uniform(size=(pathLength,dim))
if fixed:
p[:,-1] = fixedPoint * numpy.arange(pathLength)
return p
paths = [makePath() for i in range(numberToDo)]
sig = numpy.vstack([iisignature.sig(path,level) for path in paths])
joinee = numpy.zeros((numberToDo,siglength))
for i in range(1,pathLength):
displacements = [path[i:(i + 1),:] - path[(i - 1):i,:] for path in paths]
displacement = numpy.vstack(displacements)
if fixed:
displacement = displacement[:,:-1]
joinee = iisignature.sigjoin(joinee,displacement,level,fixedPoint)
self.assertLess(diff(sig,joinee),0.0001,"fullSig matches sig" + (" with fixed Dim" if fixed else ""))
extra = numpy.random.uniform(size=(numberToDo,inputDim))
bumpedExtra = 1.001 * extra
bumpedJoinee = 1.001 * joinee
base = numpy.sum(iisignature.sigjoin(joinee,extra,level,fixedPoint))
bump1 = numpy.sum(iisignature.sigjoin(bumpedJoinee,extra,level,fixedPoint))
bump2 = numpy.sum(iisignature.sigjoin(joinee,bumpedExtra,level,fixedPoint))
derivsOfSum = numpy.ones((numberToDo,siglength))
calculated = iisignature.sigjoinbackprop(derivsOfSum,joinee,extra,
level,fixedPoint)
self.assertEqual(len(calculated),3 if fixed else 2)
diff1 = (bump1 - base) - numpy.sum(calculated[0] * (bumpedJoinee - joinee))
diff2 = (bump2 - base) - numpy.sum(calculated[1] * (bumpedExtra - extra))
#print ("\n",bump1,bump2,base,diff1,diff2)
self.assertLess(numpy.abs(diff1),0.000001,"diff1 as expected " + (" with fixed Dim" if fixed else ""))
self.assertLess(numpy.abs(diff2),0.00001,"diff2 as expected " + (" with fixed Dim" if fixed else ""))
if fixed:
bumpedFixedPoint = fixedPoint * 1.01
bump3 = numpy.sum(iisignature.sigjoin(joinee,extra, level, bumpedFixedPoint))
diff3 = (bump3-base - numpy.sum(calculated[2] * (bumpedFixedPoint-fixedPoint)))
#print("\n",bump3,base, fixedPoint, bumpedFixedPoint, calculated[2])
self.assertLess(numpy.abs(diff3),0.00001, "diff3")
def __init__(
self,
n_hidden,
sig_dimension,
sig_level=2,
kernel_initializer='glorot_uniform',
#inner_init='he_normal',#could be good to use 'orthogonal' - not used
activation='tanh', #not applied to signature elements
**kwargs):
self.n_hidden = n_hidden
self.units = n_hidden
self.sig_dimension = sig_dimension
self.sig_level = sig_level
self.sigsize = iisignature.siglength(sig_dimension, sig_level)
self.kernel_initializer = initializers.get(kernel_initializer)
self.activation = activations.get(activation)
self.states = [None, None]
super(LSTMSig, self).__init__(**kwargs)
def get_Y_sig(self, X, mast, noise_std=100, plot=False):
"""Compute the target values Y as scalar products of the truncated signatures of rows of X with a certain
parameter beta plus a gaussian noise. Y follows therefore the signature linear model.
Parameters
----------
X: array, shape (n, self.npoints, self.d)
Array of paths. It is a 3-dimensional array, containing the coordinates in R^d of n piecewise linear paths,
each composed of npoints.
mast: int
True value of the truncation order of the signature.
noise_std: float, default=100
Amount of noise of Y, Y is equal to the scalar product of the signature of X against beta plus a uniform
noise on [-noise_std,noise_std].
plot: boolean, default=False
If True, output two plots: one plot with the signature coefficients of one sample and the regression vector
beta, one scatter plot with Y against Y+noise to check the calibration of the noise variance.
Returns
-------
Y: array, shape (n)
Target values
"""
n = X.shape[0]
if mast == 0:
size_sig = 1
else:
size_sig = isig.siglength(self.d, mast) + 1
beta = np.random.random(size=size_sig) / 1000
noise = 2 * noise_std * np.random.random(size=n) - noise_std
SigX = get_sigX(X, mast)
beta_repeated = np.repeat(beta.reshape(1, size_sig), n, axis=0)
Y = np.sum(beta_repeated * SigX, axis=1)
if plot:
plt.scatter(Y, Y + noise)
plt.title("Y against Y+noise")
plt.show()
return Y + noise
def __init__(self, ef_num_hlayers, ef_num_hu, ef_num_filters, pslevel,
num_slices, dropout):
super(dgmslice_ps, self).__init__()
self.filters = ef_num_filters
self.pslevel = pslevel
self.siglength = [
iisignature.siglength(num_slices + 1, m) for m in pslevel
]
self.eigfs = nn.ModuleList()
self.final_vec_length = self.filters * sum(self.siglength)
self.slices = num_slices
for i in range(self.filters):
self.eigfs.append(eigf(ef_num_hlayers, ef_num_hu))
self.projections = nn.Conv1d(1, self.slices, 2, 2)
self.final_layer = nn.Sequential(nn.Dropout(dropout),
nn.Linear(self.final_vec_length, 1),
nn.BatchNorm1d(1))
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 __init__(self, n_units,
sig_level=2,
train_time_lapse =False,
initial_time_lapse=0.1,
output_signatures = False,#whether the output includes the signatures
use_signatures = True, #whether each new state can depend on the signature
kernel_initializer='glorot_uniform',
recurrent_initializer='he_normal',#could be good to use 'orthogonal' if not use_signatures
activation='tanh',#not applied to signature elements
**kwargs):
self.sig_level = sig_level
self.sigsize = iisignature.siglength(2,sig_level)
self.n_units = n_units #like output_dim
self.units = n_units*(self.sigsize+1) if output_signatures else n_units
self.train_time_lapse = train_time_lapse
self.initial_time_lapse = initial_time_lapse
self.output_signatures = output_signatures
self.use_signatures = use_signatures
self.kernel_initializer = initializers.get(kernel_initializer)
self.recurrent_initializer = initializers.get(recurrent_initializer)
self.activation = activations.get(activation)
super(RecurrentSig, self).__init__(**kwargs)
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 dotest(self,type):
m = 8
nPaths = 95
nAngles = 348
numpy.random.seed(775)
s = iisignature.rotinv2dprepare(m,type)
coeffs = iisignature.rotinv2dcoeffs(s)
angles = numpy.random.uniform(0,math.pi * 2,size=nAngles + 1)
angles[0] = 0
rotationMatrices = [numpy.array([[math.cos(i),math.sin(i)],[-math.sin(i),math.cos(i)]]) for i in angles]
paths = [numpy.random.uniform(-1,1,size=(32,2)) for i in range(nPaths)]
samePathRotInvs = [iisignature.rotinv2d(numpy.dot(paths[0],mtx),s) for mtx in rotationMatrices]
#check the length matches
(length,) = samePathRotInvs[0].shape
self.assertEqual(length,sum(i.shape[0] for i in coeffs))
self.assertEqual(length,iisignature.rotinv2dlength(s))
if type == "a":
self.assertEqual(length,sumCentralBinomialCoefficient(m // 2))
self.assertLess(length,nAngles)#sanity check on the test itself
#check that the invariants are invariant
if 0:
print("\n",numpy.column_stack(samePathRotInvs[0:7]))
for i in range(nAngles):
if 0 and diff(samePathRotInvs[0],samePathRotInvs[1 + i]) > 0.01:
print(i)
print(samePathRotInvs[0] - samePathRotInvs[1 + i])
print(diff(samePathRotInvs[0],samePathRotInvs[1 + i]))
self.assertLess(diff(samePathRotInvs[0],samePathRotInvs[1 + i]),0.01)
#check that the invariants match the coefficients
if 1:
sigLevel=iisignature.sig(paths[0],m)[iisignature.siglength(2,m-1):]
lowerRotinvs = 0 if 2==m else iisignature.rotinv2dlength(iisignature.rotinv2dprepare(m-2,type))
#print("\n",numpy.dot(coeffs[-1],sigLevel),"\n",samePathRotInvs[0][lowerRotinvs:])
#print(numpy.dot(coeffs[-1],sigLevel)-samePathRotInvs[0][lowerRotinvs:])
self.assertTrue(numpy.allclose(numpy.dot(coeffs[-1],sigLevel),samePathRotInvs[0][lowerRotinvs:],atol=0.000001))
#check that we are not missing invariants
if type == "a":
#print("\nrotinvlength=",length,"
#siglength=",iisignature.siglength(2,m))
sigOffsets = []
for path in paths:
samePathSigs = [iisignature.sig(numpy.dot(path,mtx),m) for mtx in rotationMatrices[1:70]]
samePathSigsOffsets = [i - samePathSigs[0] for i in samePathSigs[1:]]
sigOffsets.extend(samePathSigsOffsets)
#print(numpy.linalg.svd(numpy.row_stack(sigOffsets))[1])
def split(a, dim, level):
start = 0
out = []
for m in range(1,level + 1):
levelLength = dim ** m
out.append(a[:,start:(start + levelLength)])
start = start + levelLength
assert(start == a.shape[1])
return out
allOffsets = numpy.row_stack(sigOffsets)
#print (allOffsets.shape)
splits = split(allOffsets,2,m)
#print()
rank_tolerance = 0.01 # this is hackish
#print
#([numpy.linalg.matrix_rank(i.astype("float64"),rank_tolerance)
#for
#i in splits])
#print ([i.shape for i in splits])
#print(numpy.linalg.svd(splits[-1])[1])
#sanity check on the test
self.assertLess(splits[-1].shape[1],splits[0].shape[0])
totalUnspannedDimensions = sum(i.shape[1] - numpy.linalg.matrix_rank(i,rank_tolerance) for i in splits)
self.assertEqual(totalUnspannedDimensions,length)
if 0: #This doesn't work - the rank of the whole thing is less than
#sigLength-totalUnspannedDimensions, which suggests that there are
#inter-level dependencies,
#even though the shuffle product dependencies aren't linear.
#I don't know why this is.
sigLength = iisignature.siglength(2,m)
numNonInvariant = numpy.linalg.matrix_rank(numpy.row_stack(sigOffsets))
predictedNumberInvariant = sigLength - numNonInvariant
print(sigLength,length,numNonInvariant)
self.assertLess(sigLength,nAngles)
self.assertEqual(predictedNumberInvariant,length)
def sigdim(d,m):
return 1 + iisignature.siglength(d,m)
def perform(self,node,inp,out):
#do I really need to create an array here?
out[0][0]=np.array(iisignature.siglength(inp[0],inp[1]),dtype="int32")
fixed = 0.1
numpy.random.seed(51)
start = numpy.random.uniform(size=(pathlength, dim)).astype("float32")
#2: DEFINE THEANO STUFF
path = theano.shared(start, "path")
if not numpy.isnan(fixed):
fixedT = theano.shared(fixed, "fixedT")
path = theano.tensor.horizontal_stack(
path[:, :-1], fixedT * T.shape_padright(T.arange(pathlength)))
cost1 = theano.tensor.mean(theano.tensor.sqr(Sig(path, level)))
grad1 = theano.grad(cost1, path)
signature = numpy.zeros((1, iisignature.siglength(dim,
level))).astype("float32")
for i in six.moves.xrange(1, pathlength):
if not numpy.isnan(fixed):
displacement = path[i:(i + 1), :-1] - path[(i - 1):i, :-1]
signature = SigJoin(signature, displacement, level, fixedT)
else:
displacement = path[i:(i + 1), :] - path[(i - 1):i, :]
signature = SigJoin(signature, displacement, level)
cost2 = theano.tensor.mean(theano.tensor.sqr(signature))
grad2 = theano.grad(cost2, path)
#theano.printing.pydotprint(grad2,outfile="a.png")
ff = theano.function([], [grad1, grad2])
#theano.printing.pydotprint(ff,outfile="b.png")
def setup(obj):
obj.path = torch.rand(obj.size, dtype=torch.float).numpy()
shape = obj.size[-3], iisignature.siglength(obj.size[-1], obj.depth)
obj.grad = torch.rand(shape).numpy()
#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)
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 iisignature_sig(x, d):
if len(x) <= 1:
return np.zeros(iisignature.siglength(x.shape[1], d))
else:
return iisignature.sig(x, d)
import os, sys
#os.environ["KERAS_BACKEND"]="tensorflow"
#os.environ["THEANO_FLAGS"]="mode=DebugMode,device=cpu,optimizer_excluding=local_shape_to_shape_i"
import numpy as np, keras
import keras.models, keras.layers.recurrent, keras.layers.core
import keras.backend as K
sys.path.append(os.path.dirname(os.path.abspath(os.path.dirname(__file__))))
if K.backend() == "theano":
from iisignature_theano import Sig
if K.backend() == "tensorflow":
from iisignature_tensorflow import Sig
import iisignature
sig_level = 2
siglen = iisignature.siglength(2, sig_level)
nSamples = 21
xDim = 55
X = np.zeros((nSamples, xDim), dtype="float32")
Y = np.ones((nSamples, ), dtype="float32")
m = keras.models.Sequential()
m.add(keras.layers.core.Dense(106, input_shape=(xDim, )))
m.add(keras.layers.core.Reshape((53, 2)))
m.add(keras.layers.core.Lambda(lambda x: Sig(x, 2), output_shape=(siglen, )))
m.add(keras.layers.core.Reshape((siglen, 1)))
m.add(keras.layers.pooling.AveragePooling1D(siglen))
m.add(keras.layers.core.Flatten())
m.compile(loss='mse', optimizer="sgd")
import os, sys
#os.environ["KERAS_BACKEND"]="tensorflow"
#os.environ["THEANO_FLAGS"]="mode=DebugMode,device=cpu,optimizer_excluding=local_shape_to_shape_i"
import numpy as np, keras
import keras.models, keras.layers.recurrent, keras.layers.core
import keras.backend as K
sys.path.append(os.path.dirname(os.path.abspath(os.path.dirname(__file__))))
if K.backend() == "theano":
from iisignature_theano import Sig
if K.backend() == "tensorflow":
from iisignature_tensorflow import Sig
import iisignature
sig_level=2
siglen = iisignature.siglength(2,sig_level)
nSamples=21
xDim=55
X=np.zeros((nSamples,xDim),dtype="float32")
Y=np.ones((nSamples,),dtype="float32")
m=keras.models.Sequential()
m.add(keras.layers.core.Dense(106, input_shape=(xDim,)))
m.add(keras.layers.core.Reshape((53,2)))
m.add(keras.layers.core.Lambda(lambda x:Sig(x,2),output_shape=(siglen,)))
m.add(keras.layers.core.Reshape((siglen,1)))
m.add(keras.layers.pooling.AveragePooling1D(siglen))
m.add(keras.layers.core.Flatten())
m.compile(loss='mse',optimizer="sgd")
#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)
def perform(self,node,inp,out):
#do I really need to create an array here?
out[0][0]=numpy.array(iisignature.siglength(inp[0],inp[1]),dtype="int32")
def sigdim(d, m):
return 1 + iisignature.siglength(d, m)
def dotest(self,type):
m = 8
nPaths = 95
nAngles = 348
numpy.random.seed(775)
s = iisignature.rotinv2dprepare(m,type)
coeffs = iisignature.rotinv2dcoeffs(s)
angles = numpy.random.uniform(0,math.pi * 2,size=nAngles + 1)
angles[0] = 0
rotationMatrices = [numpy.array([[math.cos(i),math.sin(i)],[-math.sin(i),math.cos(i)]]) for i in angles]
paths = [numpy.random.uniform(-1,1,size=(32,2)) for i in range(nPaths)]
samePathRotInvs = [iisignature.rotinv2d(numpy.dot(paths[0],mtx),s) for mtx in rotationMatrices]
#check the length matches
(length,) = samePathRotInvs[0].shape
self.assertEqual(length,sum(i.shape[0] for i in coeffs))
self.assertEqual(length,iisignature.rotinv2dlength(s))
if type == "a":
self.assertEqual(length,sumCentralBinomialCoefficient(m // 2))
self.assertLess(length,nAngles)#sanity check on the test itself
#check that the invariants are invariant
if 0:
print("\n",numpy.column_stack(samePathRotInvs[0:7]))
for i in range(nAngles):
if 0 and diff(samePathRotInvs[0],samePathRotInvs[1 + i]) > 0.01:
print(i)
print(samePathRotInvs[0] - samePathRotInvs[1 + i])
print(diff(samePathRotInvs[0],samePathRotInvs[1 + i]))
self.assertLess(diff(samePathRotInvs[0],samePathRotInvs[1 + i]),0.01)
#check that the invariants match the coefficients
if 1:
sigLevel=iisignature.sig(paths[0],m)[iisignature.siglength(2,m-1):]
lowerRotinvs = 0 if 2==m else iisignature.rotinv2dlength(iisignature.rotinv2dprepare(m-2,type))
#print("\n",numpy.dot(coeffs[-1],sigLevel),"\n",samePathRotInvs[0][lowerRotinvs:])
#print(numpy.dot(coeffs[-1],sigLevel)-samePathRotInvs[0][lowerRotinvs:])
self.assertTrue(numpy.allclose(numpy.dot(coeffs[-1],sigLevel),samePathRotInvs[0][lowerRotinvs:],atol=0.000001))
#check that we are not missing invariants
if type == "a":
#print("\nrotinvlength=",length,"
#siglength=",iisignature.siglength(2,m))
sigOffsets = []
for path in paths:
samePathSigs = [iisignature.sig(numpy.dot(path,mtx),m) for mtx in rotationMatrices[1:70]]
samePathSigsOffsets = [i - samePathSigs[0] for i in samePathSigs[1:]]
sigOffsets.extend(samePathSigsOffsets)
#print(numpy.linalg.svd(numpy.row_stack(sigOffsets))[1])
def split(a, dim, level):
start = 0
out = []
for m in range(1,level + 1):
levelLength = dim ** m
out.append(a[:,start:(start + levelLength)])
start = start + levelLength
assert(start == a.shape[1])
return out
allOffsets = numpy.row_stack(sigOffsets)
#print (allOffsets.shape)
splits = split(allOffsets,2,m)
#print()
rank_tolerance = 0.01 # this is hackish
#print
#([numpy.linalg.matrix_rank(i.astype("float64"),rank_tolerance)
#for
#i in splits])
#print ([i.shape for i in splits])
#print(numpy.linalg.svd(splits[-1])[1])
#sanity check on the test
self.assertLess(splits[-1].shape[1],splits[0].shape[0])
totalUnspannedDimensions = sum(i.shape[1] - numpy.linalg.matrix_rank(i,rank_tolerance) for i in splits)
self.assertEqual(totalUnspannedDimensions,length)
if 0: #This doesn't work - the rank of the whole thing is less than
#sigLength-totalUnspannedDimensions, which suggests that there are
#inter-level dependencies,
#even though the shuffle product dependencies aren't linear.
#I don't know why this is.
sigLength = iisignature.siglength(2,m)
numNonInvariant = numpy.linalg.matrix_rank(numpy.row_stack(sigOffsets))
predictedNumberInvariant = sigLength - numNonInvariant
print(sigLength,length,numNonInvariant)
self.assertLess(sigLength,nAngles)
self.assertEqual(predictedNumberInvariant,length)
fixed = float("nan")
fixed = 0.1
numpy.random.seed(51)
start = numpy.random.uniform(size=(pathlength,dim)).astype("float32")
#2: DEFINE THEANO STUFF
path = theano.shared(start, "path")
if not numpy.isnan(fixed):
fixedT = theano.shared(fixed, "fixedT")
path=theano.tensor.horizontal_stack(path[:,:-1],fixedT*T.shape_padright(T.arange(pathlength)))
cost1 = theano.tensor.mean(theano.tensor.sqr(Sig(path,level)))
grad1 = theano.grad(cost1,path)
signature = numpy.zeros((1,iisignature.siglength(dim,level))).astype("float32")
for i in six.moves.xrange(1,pathlength):
if not numpy.isnan(fixed):
displacement = path[i:(i+1),:-1]-path[(i-1):i,:-1]
signature = SigJoin(signature,displacement,level,fixedT)
else:
displacement = path[i:(i+1),:]-path[(i-1):i,:]
signature = SigJoin(signature,displacement,level)
cost2 = theano.tensor.mean(theano.tensor.sqr(signature))
grad2 = theano.grad(cost2,path)
#theano.printing.pydotprint(grad2,outfile="a.png")
ff = theano.function([],[grad1,grad2])
#theano.printing.pydotprint(ff,outfile="b.png")
