variational_models.py 5.54 KB
Newer Older
 Jakob Knollmüller committed Feb 26, 2021 1 2 ``````import numpy as np from ..operators.multifield_flattener import MultifieldFlattener `````` Jakob Knollmüller committed Mar 01, 2021 3 ``````from ..operators.simple_linear_operators import FieldAdapter, PartialExtractor `````` Jakob Knollmüller committed Feb 26, 2021 4 5 ``````from ..operators.energy_operators import EnergyOperator from ..operators.sandwich_operator import SandwichOperator `````` Jakob Knollmüller committed Mar 01, 2021 6 7 8 ``````from ..operators.linear_operator import LinearOperator from ..operators.einsum import MultiLinearEinsum from ..sugar import full, from_random, makeField, domain_union `````` Jakob Knollmüller committed Feb 26, 2021 9 10 11 ``````from ..linearization import Linearization from ..field import Field from ..multi_field import MultiField `````` Jakob Knollmüller committed Mar 01, 2021 12 13 ``````from ..domain_tuple import DomainTuple from ..domains.unstructured_domain import UnstructuredDomain `````` Jakob Knollmüller committed Feb 26, 2021 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 `````` class MeanfieldModel(): def __init__(self, domain): self.domain = domain self.Flat = MultifieldFlattener(self.domain) self.std = FieldAdapter(self.Flat.target,'var').absolute() self.latent = FieldAdapter(self.Flat.target,'latent') self.mean = FieldAdapter(self.Flat.target,'mean') self.generator = self.Flat.adjoint(self.mean + self.std * self.latent) self.entropy = GaussianEntropy(self.std.target) @ self.std def get_initial_pos(self, initial_mean=None): initial_pos = from_random(self.generator.domain).to_dict() initial_pos['latent'] = full(self.generator.domain['latent'], 0.) initial_pos['var'] = full(self.generator.domain['var'], 1.) if initial_mean is None: initial_mean = 0.1*from_random(self.generator.target) initial_pos['mean'] = self.Flat(initial_mean) return MultiField.from_dict(initial_pos) `````` Jakob Knollmüller committed Mar 01, 2021 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 ``````class FullCovarianceModel(): def __init__(self, domain): self.domain = domain self.Flat = MultifieldFlattener(self.domain) one_space = UnstructuredDomain(1) self.latent_domain = self.Flat.target[0] N_tri = self.latent_domain.shape[0]*(self.latent_domain.shape[0]+1)//2 triangular_space = DomainTuple.make(UnstructuredDomain(N_tri)) tri = FieldAdapter(triangular_space, 'cov') mat_space = DomainTuple.make((self.latent_domain,self.latent_domain)) lat_mat_space = DomainTuple.make((one_space,self.latent_domain)) lat = FieldAdapter(lat_mat_space,'latent') LT = LowerTriangularProjector(triangular_space,mat_space) mean = FieldAdapter(self.latent_domain,'mean') cov = LT @ tri co = FieldAdapter(cov.target, 'co') matmul_setup_dom = domain_union((co.domain,lat.domain)) co_part = PartialExtractor(matmul_setup_dom, co.domain) lat_part = PartialExtractor(matmul_setup_dom, lat.domain) matmul_setup = lat_part.adjoint @ lat.adjoint @ lat + co_part.adjoint @ co.adjoint @ cov `````` Jakob Knollmüller committed Mar 01, 2021 58 `````` breakpoint() `````` Jakob Knollmüller committed Mar 01, 2021 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 `````` MatMult = MultiLinearEinsum(matmul_setup.domain,'ij,ki->jk', key_order=('co','latent')) Resp = Respacer(MatMult.target, mean.target) self.generator = self.Flat.adjoint @ (mean + Resp @ MatMult @ matmul_setup) Diag = DiagonalSelector(cov.target, self.Flat.target) diag_cov = Diag(cov).absolute() self.entropy = GaussianEntropy(diag_cov.target) @ diag_cov def get_initial_pos(self, initial_mean = None): initial_pos = from_random(self.generator.domain).to_dict() initial_pos['latent'] = full(self.latent_domain.domain['latent'], 0.) diag_tri = np.diag(np.ones(self.latent_domain.shape[0]))[np.tril_indices(self.latent_domain.shape[0])] initial_pos['cov'] = makeField(self.generator.domain['cov'], diag_tri) if initial_mean is None: initial_mean = 0.1*from_random(self.generator.target) initial_pos['mean'] = self.Flat(initial_mean) return MultiField.from_dict(initial_pos) `````` Jakob Knollmüller committed Feb 26, 2021 79 80 81 82 83 84 85 86 87 88 89 90 `````` class GaussianEntropy(EnergyOperator): def __init__(self, domain): self._domain = domain def apply(self, x): self._check_input(x) res = -0.5* (2*np.pi*np.e*x**2).log().sum() if not isinstance(x, Linearization): return Field.scalar(res) if not x.want_metric: return res `````` Jakob Knollmüller committed Mar 01, 2021 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 `````` return res.add_metric(SandwichOperator.make(res.jac)) #FIXME not sure about metric class LowerTriangularProjector(LinearOperator): def __init__(self, domain, target): self._domain = domain self._target = target self._indices=np.tril_indices(target.shape[1]) self._capability = self.TIMES | self.ADJOINT_TIMES def apply(self, x, mode): self._check_mode(mode) if mode == self.TIMES: mat = np.zeros(self._target.shape[1:]) mat[self._indices] = x.val return makeField(self._target,mat.reshape((1,)+mat.shape)) return makeField(self._domain, x.val[0][self._indices].reshape(self._domain.shape)) class DiagonalSelector(LinearOperator): def __init__(self, domain, target): self._domain = domain self._target = target self._capability = self.TIMES | self.ADJOINT_TIMES def apply(self, x, mode): self._check_mode(mode) if mode == self.TIMES: result = np.diag(x.val[0]) return makeField(self._target,result) return makeField(self._domain,np.diag(x.val).reshape(self._domain.shape)) class Respacer(LinearOperator): def __init__(self, domain, target): self._domain = domain self._target = target self._capability = self.TIMES | self.ADJOINT_TIMES def apply(self,x,mode): self._check_mode(mode) if mode == self.TIMES: return makeField(self._target,x.val.reshape(self._target.shape)) return makeField(self._domain,x.val.reshape(self._domain.shape))``````