def backward(ctx, grad_output):
X, Y = ctx.saved_tensors
m = ctx.m
result = iisignature.sigjoinbackprop(grad_output.numpy(),
X.detach().numpy(),
Y.detach().numpy(), m)
return torch.FloatTensor(result[0]), torch.FloatTensor(result[1]), None
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 perform(self,node,inputs_storage,out):
s=inputs_storage[0]
x=inputs_storage[1]
y=inputs_storage[2]
m=inputs_storage[3]
fixed=inputs_storage[4]
if report_contig:
contig_check([s,x,y])
o=iisignature.sigjoinbackprop(s,x,y,m,fixed)
if(nancheck):
if contains_nan(s):
raise RuntimeError("nan in s")
if contains_nan(x):
raise RuntimeError("nan in x")
if contains_nan(y):
raise RuntimeError("nan in y")
if contains_nan(o[0]) or contains_nan(o[1]):
raise RuntimeError("nan in output")
out[0][0]=o[0]
out[1][0]=o[1]
def perform(self,node,inputs_storage,out):
s=inputs_storage[0]
x=inputs_storage[1]
y=inputs_storage[2]
m=inputs_storage[3]
fixed=inputs_storage[4]
if report_contig:
contig_check([s,x,y])
o=iisignature.sigjoinbackprop(s,x,y,m,fixed)
if(nancheck):
if contains_nan(s):
raise RuntimeError("nan in s")
if contains_nan(x):
raise RuntimeError("nan in x")
if contains_nan(y):
raise RuntimeError("nan in y")
if contains_nan(o[0]) or contains_nan(o[1]):
raise RuntimeError("nan in output")
out[0][0]=o[0]
out[1][0]=o[1]
out[2][0]=np.array(0.0 if np.isnan(fixed) else o[2], dtype="float64")
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))
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
iisignature.logsig(paths[0,:,:],p,"c")
iisignature.logsig(paths[0,:,:],p,"o")
iisignature.logsig(paths[0,:,:],p,"s")
if i%10000==0:
print (i)
def backward(self, grad_output):
X, Y, fixed = self.saved_tensors
result = iisignature.sigjoinbackprop(grad_output.numpy(), X.numpy(),
Y.numpy(), self.m, fixed.numpy())
return torch.FloatTensor(result[0]), torch.FloatTensor(
result[1]), torch.FloatTensor([result[2]])
def backward(self, grad_output):
X,Y,fixed = self.saved_tensors
result = iisignature.sigjoinbackprop(grad_output.numpy(),X.numpy(),Y.numpy(),self.m, fixed.numpy())
return torch.FloatTensor(result[0]),torch.FloatTensor(result[1]),torch.FloatTensor([result[2]])
def _sigJoinGradFixedImp(g,x,y,m,fixedlast):
o= iisignature.sigjoinbackprop(g,x,y,m,fixedlast)
return o[0],o[1],_zero,np.array(o[2],dtype="float32")
def _sigJoinGradImp(g,x,y,m):
o= iisignature.sigjoinbackprop(g,x,y,m)
return o[0],o[1],_zero
def _sigJoinGradFixedImp(g, x, y, m, fixedlast):
o = iisignature.sigjoinbackprop(g, x, y, m, fixedlast)
return o[0], o[1], _zero, np.array(o[2], dtype="float32")
def _sigJoinGradImp(g, x, y, m):
o = iisignature.sigjoinbackprop(g, x, y, m)
return o[0], o[1], _zero
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))
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
iisignature.logsig(paths[0, :, :], p, "c")
iisignature.logsig(paths[0, :, :], p, "o")
iisignature.logsig(paths[0, :, :], p, "s")
if i % 10000 == 0:
print(i)
