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 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 _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)