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 backward(ctx, grad_output):
device = grad_output.device
backprop = iisignature.sigbackprop(grad_output.cpu().numpy(), ctx.path,
ctx.depth)
# transpose again to go back to the PyTorch convention of channels first
out = torch.tensor(backprop, dtype=torch.float, device=device).t()
# better safe than sorry
# https://discuss.pytorch.org/t/when-should-you-save-for-backward-vs-storing-in-ctx/6522/9
# not sure this is actually necessary though
del ctx.path
del ctx.depth
return out, None
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 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 backward(self, grad_output):
(X,) = self.saved_tensors
result = iisignature.sigbackprop(grad_output.numpy(),X.numpy(),self.m)
return torch.FloatTensor(result)
def perform(self,node,inputs_storage,out):
s=inputs_storage[0]
x=inputs_storage[1]
m=inputs_storage[2]
out[0][0]=iisignature.sigbackprop(s,x,m)
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, ) = self.saved_tensors
result = iisignature.sigbackprop(grad_output.numpy(), X.numpy(),
self.m)
return torch.FloatTensor(result)
def backward(ctx, grad):
return torch.tensor(iisignature.sigbackprop(grad.cpu(), ctx.path,
ctx.depth),
device=ctx.device,
dtype=ctx.dtype), None
def backward(ctx, grad_output):
X, m, = ctx.saved_tensors
result = iisignature.sigbackprop(grad_output.detach().numpy(), X.detach().numpy(), int(m))
return torch.tensor(result).float(), None
def backward(ctx, grad_output):
(X, ) = ctx.saved_tensors
m = ctx.m
result = iisignature.sigbackprop(grad_output.numpy(),
X.detach().numpy(), m)
return torch.FloatTensor(result), None
def run(obj):
return iisignature.sigbackprop(obj.grad, obj.path, obj.depth)
def _sigGradImp(g,x,m):
o=iisignature.sigbackprop(g,x,m)
return o, _zero
def perform(self,node,inputs_storage,out):
s=inputs_storage[0]
x=inputs_storage[1]
m=inputs_storage[2]
out[0][0]=iisignature.sigbackprop(s,x,m)
def _sigGradImp(g, x, m):
o = iisignature.sigbackprop(g, x, m)
return o, _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))
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)
