我们从Python开源项目中，提取了以下50个代码示例，用于说明如何使用numpy.einsum()。
def total_length_selected(ed='empty', coords='empty', ob='empty'): '''Returns the total length of all edge segments''' if ob == 'empty': ob = bpy.context.object if coords == 'empty': coords = get_coords(ob) if ed == 'empty': ed = get_edge_idx(ob) edc = coords[ed] e1 = edc[:, 0] e2 = edc[:, 1] ee1 = e1 - e2 sel = get_selected_edges(ob) ee = ee1[sel] leng = np.einsum('ij,ij->i', ee, ee) return np.sum(np.sqrt(leng))
def transitions_old(width, height, configs=None, one_per_state=False): digit = width * height if configs is None: configs = generate_configs(digit) if one_per_state: def pickone(thing): index = np.random.randint(0,len(thing)) return thing[index] transitions = np.array([ generate( [c1,pickone(successors(c1,width,height))],width,height) for c1 in configs ]) else: transitions = np.array([ generate([c1,c2],width,height) for c1 in configs for c2 in successors(c1,width,height) ]) return np.einsum('ab...->ba...',transitions)
def puzzle_plot(p): p.setup() def name(template): return template.format(p.__name__) from itertools import islice configs = list(islice(p.generate_configs(9), 1000)) # be careful, islice is not immutable!!! import numpy.random as random random.shuffle(configs) configs = configs[:10] puzzles = p.generate(configs, 3, 3) print(puzzles.shape, "mean", puzzles.mean(), "stdev", np.std(puzzles)) plot_image(puzzles[-1], name("{}.png")) plot_image(np.clip(puzzles[-1]+np.random.normal(0,0.1,puzzles[-1].shape),0,1),name("{}+noise.png")) plot_image(np.round(np.clip(puzzles[-1]+np.random.normal(0,0.1,puzzles[-1].shape),0,1)),name("{}+noise+round.png")) plot_grid(puzzles, name("{}s.png")) _transitions = p.transitions(3,3,configs=configs) print(_transitions.shape) transitions_for_show = \ np.einsum('ba...->ab...',_transitions) \ .reshape((-1,)+_transitions.shape[2:]) print(transitions_for_show.shape) plot_grid(transitions_for_show, name("{}_transitions.png"))
def run(ae,xs): zs = ae.encode_binary(xs) ys = ae.decode_binary(zs) mod_ys = [] correlations = [] print(ys.shape) print("corrlations:") print("bit \ image {}".format(range(len(xs)))) for i in range(ae.N): mod_zs = np.copy(zs) # increase the latent value from 0 to 1 and check the difference for j in range(11): mod_zs[:,i] = j / 10.0 mod_ys.append(ae.decode_binary(mod_zs)) zero_zs,one_zs = np.copy(zs),np.copy(zs) zero_zs[:,i] = 0. one_zs[:,i] = 1. correlation = np.mean(np.square(ae.decode_binary(zero_zs) - ae.decode_binary(one_zs)), axis=(1,2)) correlations.append(correlation) print("{:>5} {}".format(i,correlation)) plot_grid2(np.einsum("ib...->bi...",np.array(mod_ys)).reshape((-1,)+ys.shape[1:]), w=11,path=ae.local("dump_significance.png")) return np.einsum("ib->bi",correlations)
def buildFock(self): """Routine to build the AO basis Fock matrix""" if self.direct: if self.incFockRst: # restart incremental fock build? self.G = formPT(self.P,np.zeros_like(self.P),self.bfs, self.nbasis,self.screen,self.scrTol) self.G = 0.5*(self.G + self.G.T) self.F = self.Core.astype('complex') + self.G else: self.G = formPT(self.P,self.P_old,self.bfs,self.nbasis, self.screen,self.scrTol) self.G = 0.5*(self.G + self.G.T) self.F = self.F_old + self.G else: self.J = np.einsum('pqrs,sr->pq', self.TwoE.astype('complex'),self.P) self.K = np.einsum('psqr,sr->pq', self.TwoE.astype('complex'),self.P) self.G = 2.*self.J - self.K self.F = self.Core.astype('complex') + self.G
def pointsInRegion(regNum, vor, p, overlap=0.0): """ returns the subset of points p that are inside the regNum region of the voronoi object vor. The boundaries of the region are extended by an amount given by 'overlap'. """ reg = vor.regions[vor.point_region[regNum]] # region associated with the point if -1 in reg: raise Exception('Open region associated with generator') nVerts = len(reg) # number of verticies in the region p0 = vor.points[regNum] for i in range(len(reg)): vert1, vert2 = vor.vertices[reg[i]], vor.vertices[reg[(i + 1) % len(reg)]] dr = vert1 - vert2 # edge dr = dr / numpy.linalg.norm(dr) # normalize dn = numpy.array([dr[1], -dr[0]]) # normal to edge dn = dn if numpy.dot(dn, vert2 - p0[:2]) > 0 else -dn # orient so that the normal is outwards d1 = numpy.einsum('i,ji', dn, vert2 + dn * overlap - p[:, :2]) p = p[d1 * numpy.dot(dn, vert2 - p0[:2]) > 0] return p
def test_einsum_misc(self): # This call used to crash because of a bug in # PyArray_AssignZero a = np.ones((1, 2)) b = np.ones((2, 2, 1)) assert_equal(np.einsum('ij...,j...->i...', a, b), [[[2], [2]]]) # The iterator had an issue with buffering this reduction a = np.ones((5, 12, 4, 2, 3), np.int64) b = np.ones((5, 12, 11), np.int64) assert_equal(np.einsum('ijklm,ijn,ijn->', a, b, b), np.einsum('ijklm,ijn->', a, b)) # Issue #2027, was a problem in the contiguous 3-argument # inner loop implementation a = np.arange(1, 3) b = np.arange(1, 5).reshape(2, 2) c = np.arange(1, 9).reshape(4, 2) assert_equal(np.einsum('x,yx,zx->xzy', a, b, c), [[[1, 3], [3, 9], [5, 15], [7, 21]], [[8, 16], [16, 32], [24, 48], [32, 64]]])
def test_einsum_all_contig_non_contig_output(self): # Issue gh-5907, tests that the all contiguous special case # actually checks the contiguity of the output x = np.ones((5, 5)) out = np.ones(10)[::2] correct_base = np.ones(10) correct_base[::2] = 5 # Always worked (inner iteration is done with 0-stride): np.einsum('mi,mi,mi->m', x, x, x, out=out) assert_array_equal(out.base, correct_base) # Example 1: out = np.ones(10)[::2] np.einsum('im,im,im->m', x, x, x, out=out) assert_array_equal(out.base, correct_base) # Example 2, buffering causes x to be contiguous but # special cases do not catch the operation before: out = np.ones((2, 2, 2))[..., 0] correct_base = np.ones((2, 2, 2)) correct_base[..., 0] = 2 x = np.ones((2, 2), np.float32) np.einsum('ij,jk->ik', x, x, out=out) assert_array_equal(out.base, correct_base)
def dihedral_transform_batch(x): g = np.random.randint(low=0, high=8, size=x.shape[0]) h, w = x.shape[-2:] hh = (h - 1) / 2. hw = (w - 1) / 2. I, J = np.meshgrid(np.linspace(-hh, hh, x.shape[-2]), np.linspace(-hw, hw, x.shape[-1])) C = np.r_[[I, J]] D4C = np.einsum('...ij,jkl->...ikl', D4, C) D4C[:, 0] += hh D4C[:, 1] += hw D4C = D4C.astype(int) x_out = np.empty_like(x) for i in range(x.shape[0]): I, J = D4C[g[i]] x_out[i, :] = x[i][:, J, I] return x_out
def get_vol(simplex): # Compute the volume via the Cayley-Menger determinant # <http://mathworld.wolfram.com/Cayley-MengerDeterminant.html>. One # advantage is that it can compute the volume of the simplex indenpendent # of the dimension of the space where it's embedded. # compute all edge lengths edges = numpy.subtract(simplex[:, None], simplex[None, :]) ei_dot_ej = numpy.einsum('...k,...k->...', edges, edges) j = simplex.shape[0] - 1 a = numpy.empty((j+2, j+2) + ei_dot_ej.shape[2:]) a[1:, 1:] = ei_dot_ej a[0, 1:] = 1.0 a[1:, 0] = 1.0 a[0, 0] = 0.0 a = numpy.moveaxis(a, (0, 1), (-2, -1)) det = numpy.linalg.det(a) vol = numpy.sqrt((-1.0)**(j+1) / 2**j / math.factorial(j)**2 * det) return vol
def scalar_product_interval(anchors, indizes_1, indizes_2): q = (anchors[1][0]-anchors[0][0]) vector_1 = np.vstack([ anchors[0][1][indizes_1], # a_1 anchors[0][2][indizes_1] * q, # b_1 anchors[1][1][indizes_1], # c_1 anchors[1][2][indizes_1] * q, # d_1 ]) vector_2 = np.vstack([ anchors[0][1][indizes_2], # a_2 anchors[0][2][indizes_2] * q, # b_2 anchors[1][1][indizes_2], # c_2 anchors[1][2][indizes_2] * q, # d_2 ]) return np.einsum( vector_1, [0,2], sp_matrix, [0,1], vector_2, [1,2] )*q
def scalar_product_partial(anchors, indizes_1, indizes_2, start): q = (anchors[1][0]-anchors[0][0]) z = (start-anchors[1][0]) / q vector_1 = np.vstack([ anchors[0][1][indizes_1], # a_1 anchors[0][2][indizes_1] * q, # b_1 anchors[1][1][indizes_1], # c_1 anchors[1][2][indizes_1] * q, # d_1 ]) vector_2 = np.vstack([ anchors[0][1][indizes_2], # a_2 anchors[0][2][indizes_2] * q, # b_2 anchors[1][1][indizes_2], # c_2 anchors[1][2][indizes_2] * q, # d_2 ]) return np.einsum( vector_1, [0,2], partial_sp_matrix(z), [0,1], vector_2, [1,2] )*q
def mvl(pha, amp, optimize): """Mean Vector Length (Canolty, 2006). Parameters ---------- pha : array_like Array of phases of shapes (npha, ..., npts) amp : array_like Array of amplitudes of shapes (namp, ..., npts) Returns ------- pac : array_like PAC of shape (npha, namp, ...) """ # Number of time points : npts = pha.shape[-1] return np.abs(np.einsum('i...j, k...j->ik...', amp, np.exp(1j * pha), optimize=optimize)) / npts
def ps(pha, amp, optimize): """Phase Synchrony (Penny, 2008; Cohen, 2008). Parameters ---------- pha : array_like Array of phases of shapes (npha, ..., npts) amp : array_like Array of amplitudes of shapes (namp, ..., npts) Returns ------- pac : array_like PAC of shape (npha, namp, ...) """ # Number of time points : npts = pha.shape[-1] pac = np.einsum('i...j, k...j->ik...', np.exp(-1j * amp), np.exp(1j * pha), optimize=optimize) return np.abs(pac) / npts
def half_space(self): """Return the half space polytope respresentation of the infinite beam.""" # add half beam width along the normal direction to each of the points half = self.normal * self.size / 2 edges = [Line(self.p1 + half, self.p2 + half), Line(self.p1 - half, self.p2 - half)] A = np.ndarray((len(edges), self.dim)) B = np.ndarray(len(edges)) for i in range(0, 2): A[i, :], B[i] = edges[i].standard # test for positive or negative side of line if np.einsum('i, i', self.p1._x, A[i, :]) > B[i]: A[i, :] = -A[i, :] B[i] = -B[i] p = pt.Polytope(A, B) return p
def forward_prop_random_thru_post_mm(self, model, mx, vx, mu, Su): Kuu_noiseless = compute_kernel( 2 * model.ls, 2 * model.sf, model.zu, model.zu) Kuu = Kuu_noiseless + np.diag(jitter * np.ones((self.M, ))) # TODO: remove inv Kuuinv = np.linalg.inv(Kuu) A = np.dot(Kuuinv, mu) Smm = Su + np.outer(mu, mu) B_sto = np.dot(Kuuinv, np.dot(Smm, Kuuinv)) - Kuuinv psi0 = np.exp(2.0 * model.sf) psi1, psi2 = compute_psi_weave( 2 * model.ls, 2 * model.sf, mx, vx, model.zu) mout = np.einsum('nm,md->nd', psi1, A) Bpsi2 = np.einsum('ab,nab->n', B_sto, psi2)[:, np.newaxis] vout = psi0 + Bpsi2 - mout**2 return mout, vout
def _forward_prop_deterministic_thru_post(self, x, return_info=False): """Propagate deterministic inputs thru posterior Args: x (float): input values, size K x Din return_info (bool, optional): Description Returns: float, size K x Dout: output means float, size K x Dout: output variances """ psi0 = np.exp(2 * self.sf) psi1 = compute_kernel(2 * self.ls, 2 * self.sf, x, self.zu) mout = np.einsum('nm,dm->nd', psi1, self.A) Bpsi2 = np.einsum('dab,na,nb->nd', self.B_det, psi1, psi1) vout = psi0 + Bpsi2 if return_info: return mout, vout, psi1 else: return mout, vout
def _forward_prop_random_thru_post_mm(self, mx, vx, return_info=False): """Propagate uncertain inputs thru posterior, using Moment Matching Args: mx (float): input means, size K x Din vx (TYPE): input variances, size K x Din return_info (bool, optional): Description Returns: float, size K x Dout: output means float, size K x Dout: output variances """ psi0 = np.exp(2.0 * self.sf) psi1, psi2 = compute_psi_weave( 2 * self.ls, 2 * self.sf, mx, vx, self.zu) mout = np.einsum('nm,dm->nd', psi1, self.A) Bpsi2 = np.einsum('dab,nab->nd', self.B_sto, psi2) vout = psi0 + Bpsi2 - mout**2 if return_info: return mout, vout, psi1, psi2 else: return mout, vout
def sample(self, x): """Summary Args: x (TYPE): Description Returns: TYPE: Description """ Su = self.Su mu = self.mu Lu = np.linalg.cholesky(Su) epsilon = np.random.randn(self.Dout, self.M) u_sample = mu + np.einsum('dab,db->da', Lu, epsilon) kff = compute_kernel(2 * self.ls, 2 * self.sf, x, x) kff += np.diag(JITTER * np.ones(x.shape[0])) kfu = compute_kernel(2 * self.ls, 2 * self.sf, x, self.zu) qfu = np.dot(kfu, self.Kuuinv) mf = np.einsum('nm,dm->nd', qfu, u_sample) vf = kff - np.dot(qfu, kfu.T) Lf = np.linalg.cholesky(vf) epsilon = np.random.randn(x.shape[0], self.Dout) f_sample = mf + np.einsum('ab,bd->ad', Lf, epsilon) return f_sample
def _forward_prop_deterministic_thru_cav(self, x): """Propagate deterministic inputs thru cavity Args: x (float): input values, size K x Din Returns: float, size K x Dout: output means float, size K x Dout: output variances float, size K x M: cross covariance matrix """ kff = np.exp(2 * self.sf) kfu = compute_kernel(2 * self.ls, 2 * self.sf, x, self.zu) mout = np.einsum('nm,dm->nd', kfu, self.Ahat) Bkfukuf = np.einsum('dab,na,nb->nd', self.Bhat_det, kfu, kfu) vout = kff + Bkfukuf return mout, vout, kfu
def _forward_prop_random_thru_cav_mm(self, mx, vx): """Propagate uncertain inputs thru cavity, using simple Moment Matching Args: mx (float): input means, size K x Din vx (TYPE): input variances, size K x Din Returns: output means and variances, and intermediate info for backprop """ psi0 = np.exp(2 * self.sf) psi1, psi2 = compute_psi_weave( 2 * self.ls, 2 * self.sf, mx, vx, self.zu) mout = np.einsum('nm,dm->nd', psi1, self.Ahat) Bhatpsi2 = np.einsum('dab,nab->nd', self.Bhat_sto, psi2) vout = psi0 + Bhatpsi2 - mout**2 return mout, vout, psi1, psi2
def psi1compDer(dL_dpsi1, _psi1, variance, lengthscale, Z, mu, S): # here are the "statistics" for psi1 # Produced intermediate results: dL_dparams w.r.t. psi1 # _dL_dvariance 1 # _dL_dlengthscale Q # _dL_dZ MxQ # _dL_dgamma NxQ # _dL_dmu NxQ # _dL_dS NxQ lengthscale2 = np.square(lengthscale) Lpsi1 = dL_dpsi1 * _psi1 Zmu = Z[None, :, :] - mu[:, None, :] # NxMxQ denom = 1. / (S + lengthscale2) Zmu2_denom = np.square(Zmu) * denom[:, None, :] # NxMxQ _dL_dvar = Lpsi1.sum() / variance _dL_dmu = np.einsum('nm,nmq,nq->nq', Lpsi1, Zmu, denom) _dL_dS = np.einsum('nm,nmq,nq->nq', Lpsi1, (Zmu2_denom - 1.), denom) / 2. _dL_dZ = -np.einsum('nm,nmq,nq->mq', Lpsi1, Zmu, denom) _dL_dl = np.einsum('nm,nmq,nq->q', Lpsi1, (Zmu2_denom + (S / lengthscale2)[:, None, :]), denom * lengthscale) return _dL_dvar, _dL_dl, _dL_dZ, _dL_dmu, _dL_dS
def kfucompDer(dL_dkfu, kfu, variance, lengthscale, Z, mu, grad_x): # here are the "statistics" for psi1 # Produced intermediate results: dL_dparams w.r.t. psi1 # _dL_dvariance 1 # _dL_dlengthscale Q # _dL_dZ MxQ lengthscale2 = np.square(lengthscale) Lpsi1 = dL_dkfu * kfu Zmu = Z[None, :, :] - mu[:, None, :] # NxMxQ _dL_dvar = Lpsi1.sum() / variance _dL_dZ = -np.einsum('nm,nmq->mq', Lpsi1, Zmu / lengthscale2) _dL_dl = np.einsum('nm,nmq->q', Lpsi1, np.square(Zmu) / lengthscale**3) if grad_x: _dL_dx = np.einsum('nm,nmq->nq', Lpsi1, Zmu / lengthscale2) return _dL_dvar, _dL_dl, _dL_dZ, _dL_dx else: return _dL_dvar, _dL_dl, _dL_dZ
def _forward_prop_deterministic_thru_cav(self, n, x, alpha): """Summary Args: n (TYPE): Description x (TYPE): Description alpha (TYPE): Description Returns: TYPE: Description """ muhat, Suhat, SuinvMuhat, Suinvhat = self.compute_cavity(n, alpha) Kuuinv = self.Kuuinv Ahat = np.einsum('ab,ndb->nda', Kuuinv, muhat) Bhat = np.einsum( 'ab,ndbc->ndac', Kuuinv, np.einsum('ndab,bc->ndac', Suhat, Kuuinv)) - Kuuinv kff = np.exp(2 * self.sf) kfu = compute_kernel(2 * self.ls, 2 * self.sf, x, self.zu) mout = np.einsum('nm,ndm->nd', kfu, Ahat) Bkfukuf = np.einsum('ndab,na,nb->nd', Bhat, kfu, kfu) vout = kff + Bkfukuf extra_res = [muhat, Suhat, SuinvMuhat, Suinvhat, kfu, Ahat, Bhat] return mout, vout, extra_res
def _forward_prop_deterministic_thru_post(self, x): """Summary Args: x (TYPE): Description Returns: TYPE: Description """ Kuuinv = self.Kuuinv A = np.einsum('ab,db->da', Kuuinv, self.mu) B = np.einsum( 'ab,dbc->dac', Kuuinv, np.einsum('dab,bc->dac', self.Su, Kuuinv)) - Kuuinv kff = np.exp(2 * self.sf) kfu = compute_kernel(2 * self.ls, 2 * self.sf, x, self.zu) mout = np.einsum('nm,dm->nd', kfu, A) Bpsi2 = np.einsum('dab,na,nb->nd', B, kfu, kfu) vout = kff + Bpsi2 return mout, vout # TODO
def _forward_prop_random_thru_post_mm(self, mx, vx): """Summary Args: mx (TYPE): Description vx (TYPE): Description Returns: TYPE: Description """ Kuuinv = self.Kuuinv A = np.einsum('ab,db->da', Kuuinv, self.mu) Smm = self.Su + np.einsum('da,db->dab', self.mu, self.mu) B = np.einsum( 'ab,dbc->dac', Kuuinv, np.einsum('dab,bc->dac', Smm, Kuuinv)) - Kuuinv psi0 = np.exp(2.0 * self.sf) psi1, psi2 = compute_psi_weave( 2 * self.ls, 2 * self.sf, mx, vx, self.zu) mout = np.einsum('nm,dm->nd', psi1, A) Bpsi2 = np.einsum('dab,nab->nd', B, psi2) vout = psi0 + Bpsi2 - mout**2 return mout, vout
def compute_cavity(self, n, alpha=1.0): """Summary Args: n (TYPE): Description alpha (float, optional): Description Returns: TYPE: Description """ # compute the leave one out moments t1n = self.t1[n, :, :] t2n = self.t2[n, :, :, :] Suinvhat = self.Suinv - alpha * t2n SuinvMuhat = self.SuinvMu - alpha * t1n Suhat = np.linalg.inv(Suinvhat) muhat = np.einsum('ndab,ndb->nda', Suhat, SuinvMuhat) return muhat, Suhat, SuinvMuhat, Suinvhat
def forward_prop_thru_post(self, x): """Summary Args: x (TYPE): Description Returns: TYPE: Description """ Kuuinv = self.Kuuinv A = np.einsum('ab,db->da', Kuuinv, self.mu) B = np.einsum( 'ab,dbc->dac', Kuuinv, np.einsum('dab,bc->dac', self.Su, Kuuinv)) - Kuuinv kff = np.exp(2 * self.sf) kfu = compute_kernel(2 * self.ls, 2 * self.sf, x, self.zu) mout = np.einsum('nm,dm->nd', kfu, A) Bpsi2 = np.einsum('dab,na,nb->nd', B, kfu, kfu) vout = kff + Bpsi2 return mout, vout
def update_posterior(self, x_train=None, new_hypers=False): """Summary Returns: TYPE: Description """ # compute the posterior approximation if new_hypers and x_train is not None: Kfu = compute_kernel(2*self.ls, 2*self.sf, x_train, self.zu) KuuinvKuf = np.dot(self.Kuuinv, Kfu.T) self.Kfu = Kfu self.KuuinvKuf = KuuinvKuf self.Kff_diag = compute_kernel_diag(2*self.ls, 2*self.sf, x_train) KuuinvKuf_div_var = np.einsum('an,nd->dan', self.KuuinvKuf, 1.0 / self.variances) T2u = np.einsum('dan,bn->dab', KuuinvKuf_div_var, self.KuuinvKuf) T1u = np.einsum('bn,nd->db', self.KuuinvKuf, self.means / self.variances) Vinv = self.Kuuinv + T2u self.Suinv = Vinv self.Su = np.linalg.inv(Vinv) self.mu = np.einsum('dab,db->da', self.Su, T1u) self.gamma = np.einsum('ab,db->da', self.Kuuinv, self.mu) self.beta = self.Kuuinv - np.einsum('ab,dbc->dac', self.Kuuinv, np.einsum('dab,bc->dac', self.Su, self.Kuuinv))
def compute_cavity(self, idxs, alpha): # deletion p_i = self.KuuinvKuf[:, idxs].T[:, np.newaxis, :] k_i = self.Kfu[idxs, :] k_ii = self.Kff_diag[idxs][:, np.newaxis] gamma = self.gamma beta = self.beta h_si = p_i - np.einsum('dab,nb->nda', beta, k_i) variance_i = self.variances[idxs, :] mean_i = self.means[idxs, :] dlogZd_dmi2 = 1.0 / (variance_i/alpha - np.sum(k_i[:, np.newaxis, :] * h_si, axis=2)) dlogZd_dmi = -dlogZd_dmi2 * (mean_i - np.sum(k_i[:, np.newaxis, :] * gamma, axis=2)) hd1 = h_si * dlogZd_dmi[:, :, np.newaxis] hd2h = np.einsum('nda,ndb->ndab', h_si, h_si) * dlogZd_dmi2[:, :, np.newaxis, np.newaxis] gamma_si = gamma + hd1 beta_si = beta - hd2h # projection h = p_i - np.einsum('ndab,nb->nda', beta_si, k_i) m_si_i = np.einsum('na,nda->nd', k_i, gamma_si) v_si_ii = k_ii - np.einsum('na,ndab,nb->nd', k_i, beta_si, k_i) return m_si_i, v_si_ii, [h, beta_si, gamma_si]
def project3Dto2D(self, Li, idxs): """ Project 3D point to 2D :param Li: joints in normalized 3D :param idxs: frames specified by subset :return: 2D points, in normalized 2D coordinates """ if not isinstance(idxs, numpy.ndarray): idxs = numpy.asarray([idxs]) # 3D -> 2D projection also shift by M to cropped window Li_glob3D = (numpy.reshape(Li, (len(idxs), self.numJoints, 3))*self.Di_scale[idxs][:, None, None]+self.Di_off3D[idxs][:, None, :]).reshape((len(idxs)*self.numJoints, 3)) Li_glob3D_hom = numpy.concatenate([Li_glob3D, numpy.ones((len(idxs)*self.numJoints, 1), dtype='float32')], axis=1) Li_glob2D_hom = numpy.dot(Li_glob3D_hom, self.cam_proj.T) Li_glob2D = (Li_glob2D_hom[:, 0:3] / Li_glob2D_hom[:, 3][:, None]).reshape((len(idxs), self.numJoints, 3)) Li_img2D_hom = numpy.einsum('ijk,ikl->ijl', Li_glob2D, self.Di_trans2D[idxs]) Li_img2D = (Li_img2D_hom[:, :, 0:2] / Li_img2D_hom[:, :, 2][:, :, None]).reshape((len(idxs), self.numJoints*2)) Li_img2Dcrop = (Li_img2D - (self.Di.shape[3]/2.)) / (self.Di.shape[3]/2.) return Li_img2Dcrop
def compute_dr_wrt(self, wrt): if wrt is not self.v: return None v = self.v.r.reshape(-1, 3) blocks = -np.einsum('ij,ik->ijk', v, v) * (self.ss**(-3./2.)).reshape((-1, 1, 1)) for i in range(3): blocks[:, i, i] += self.s_inv if True: # pylint: disable=using-constant-test data = blocks.ravel() indptr = np.arange(0, (self.v.r.size+1)*3, 3) indices = col(np.arange(0, self.v.r.size)) indices = np.hstack([indices, indices, indices]) indices = indices.reshape((-1, 3, 3)) indices = indices.transpose((0, 2, 1)).ravel() result = sp.csc_matrix((data, indices, indptr), shape=(self.v.r.size, self.v.r.size)) return result else: matvec = lambda x: np.einsum('ijk,ik->ij', blocks, x.reshape((blocks.shape[0], 3))).ravel() return sp.linalg.LinearOperator((self.v.r.size, self.v.r.size), matvec=matvec)
def test_exKxz_pairwise(self): covall = np.array([self.Xcov, self.Xcovc]) for k in self.kernels: with self.test_context(): if isinstance(k, ekernels.Linear): continue k.compile() exKxz = k.compute_exKxz_pairwise(self.Z, self.Xmu, covall) Kxz = k.compute_K(self.Xmu[:-1, :], self.Z) # NxM xKxz = np.einsum('nm,nd->nmd', Kxz, self.Xmu[1:, :]) self.assertTrue(np.allclose(xKxz, exKxz)) # def test_exKxz(self): # for k in self.kernels: # with self.test_session(): # if isinstance(k, ekernels.Linear): # continue # k.compile() # exKxz = k.compute_exKxz(self.Z, self.Xmu, self.Xcov) # Kxz = k.compute_K(self.Xmu, self.Z) # NxM # xKxz = np.einsum('nm,nd->nmd', Kxz, self.Xmu) # self.assertTrue(np.allclose(xKxz, exKxz))
def _accumulate_sufficient_statistics(self, stats, obs, framelogprob, posteriors, fwdlattice, bwdlattice): super(GaussianHMM, self)._accumulate_sufficient_statistics( stats, obs, framelogprob, posteriors, fwdlattice, bwdlattice) if 'm' in self.params or 'c' in self.params: stats['post'] += posteriors.sum(axis=0) stats['obs'] += np.dot(posteriors.T, obs) if 'c' in self.params: if self.covariance_type in ('spherical', 'diag'): stats['obs**2'] += np.dot(posteriors.T, obs ** 2) elif self.covariance_type in ('tied', 'full'): # posteriors: (nt, nc); obs: (nt, nf); obs: (nt, nf) # -> (nc, nf, nf) stats['obs*obs.T'] += np.einsum( 'ij,ik,il->jkl', posteriors, obs, obs)
def __init__(self, matrix, w): W = np.sum(w) self.w = w self.X = matrix self.left = None self.right = None self.mu = np.einsum('ij,i->j', self.X, w)/W diff = self.X - np.tile(self.mu, [np.shape(self.X)[0], 1]) t = np.einsum('ij,i->ij', diff, np.sqrt(w)) self.cov = (t.T @ t)/W + 1e-5*np.eye(3) self.N = self.X.shape[0] V, D = np.linalg.eig(self.cov) self.lmbda = np.max(np.abs(V)) self.e = D[np.argmax(np.abs(V))] # S is measurements vector - dim nxd # w is weights vector - dim n
def _solve_2D2(self, X, Z): """Solves :math:`Z^T N^{-1}X`, where :math:`X` and :math:`Z` are 2-d arrays. """ ZNX = np.dot(Z.T / self._nvec, X) for slc, jv in zip(self._slices, self._jvec): if slc.stop - slc.start > 1: Zblock = Z[slc, :] Xblock = X[slc, :] niblock = 1 / self._nvec[slc] beta = 1.0 / (np.einsum('i->', niblock)+1.0/jv) zn = np.dot(niblock, Zblock) xn = np.dot(niblock, Xblock) ZNX -= beta * np.outer(zn.T, xn) return ZNX
def ss_framerotate(mjd, planet, x, y, z, dz, offset=None, equatorial=False): """ Rotate planet trajectory given as (n,3) tensor, by ecliptic Euler angles x, y, z, and by z rate dz. The rate has units of rad/year, and is referred to offset 2010/1/1. dates must be given in MJD. """ if equatorial: planet = eq2ecl_vec(planet) E = euler_vec(z + dz * (mjd - t_offset) / 365.25, y, x, planet.shape[0]) planet = np.einsum('ijk,ik->ij', E, planet) if offset is not None: planet = np.array(offset) + planet if equatorial: planet = ecl2eq_vec(planet) return planet
def _log_prod_students_t(self, i, mu, log_prod_var, inv_var, v): """ Return the value of the log of the product of the univariate Student's t PDFs at `X[i]`. """ delta = self.X[i, :] - mu return ( self.D * ( self._cached_gammaln_by_2[v + 1] - self._cached_gammaln_by_2[v] - 0.5*self._cached_log_v[v] - 0.5*self._cached_log_pi ) - 0.5*log_prod_var - (v + 1.)/2. * (np.log(1. + 1./v * np.square(delta) * inv_var)).sum() ) #-----------------------------------------------------------------------------# # UTILITY FUNCTIONS # #-----------------------------------------------------------------------------# # Below is slightly faster than np.sum, see http://stackoverflow.com/questions/ # 18365073/why-is-numpys-einsum-faster-than-numpys-built-in-functions
def setUp(self): self.f = links.Bilinear( self.in_shape[0], self.in_shape[1], self.out_size) self.f.W.data[...] = _uniform(*self.f.W.data.shape) self.f.V1.data[...] = _uniform(*self.f.V1.data.shape) self.f.V2.data[...] = _uniform(*self.f.V2.data.shape) self.f.b.data[...] = _uniform(*self.f.b.data.shape) self.f.zerograds() self.W = self.f.W.data.copy() self.V1 = self.f.V1.data.copy() self.V2 = self.f.V2.data.copy() self.b = self.f.b.data.copy() self.e1 = _uniform(self.batch_size, self.in_shape[0]) self.e2 = _uniform(self.batch_size, self.in_shape[1]) self.gy = _uniform(self.batch_size, self.out_size) self.y = ( numpy.einsum('ij,ik,jkl->il', self.e1, self.e2, self.W) + self.e1.dot(self.V1) + self.e2.dot(self.V2) + self.b)
def inside_triangle(point,triangles): v0 = triangles[:,2]-triangles[:,0] v1 = triangles[:,1]-triangles[:,0] v2 = point-triangles[:,0] dot00 = np.einsum('ij,ij->i',v0,v0) dot01 = np.einsum('ij,ij->i',v0,v1) dot02 = np.einsum('ij,ij->i',v0,v2) dot11 = np.einsum('ij,ij->i',v1,v1) dot12 = np.einsum('ij,ij->i',v1,v2) invDenom = 1./(dot00 * dot11-dot01*dot01) u = np.float16((dot11 * dot02 - dot01 * dot12)*invDenom) v = np.float16((dot00 * dot12 - dot01 * dot02)*invDenom) return (u>=0) & (v>=0) & (u+v<=1)
def omgp_model_bound(omgp): ''' Calculate the part of the omgp bound which does not depend on the response variable. ''' GP_bound = 0.0 LBs = [] # Precalculate the bound minus data fit, # and LB matrices used for data fit term. for i, kern in enumerate(omgp.kern): K = kern.K(omgp.X) B_inv = np.diag(1. / ((omgp.phi[:, i] + 1e-6) / omgp.variance)) Bi, LB, LBi, Blogdet = pdinv(K + B_inv) LBs.append(LB) # Penalty GP_bound -= 0.5 * Blogdet # Constant GP_bound -= 0.5 * omgp.D * np.einsum('j,j->', omgp.phi[:, i], np.log(2 * np.pi * omgp.variance)) model_bound = GP_bound + omgp.mixing_prop_bound() + omgp.H return model_bound, LBs
def _predict_output_derivatives(self, x): n = x.shape[0] nt = self.nt ny = self.training_points[None][0][1].shape[1] num = self.num dy_dstates = np.empty(n * num['dof']) self.rbfc.compute_jac(n, x.flatten(), dy_dstates) dy_dstates = dy_dstates.reshape((n, num['dof'])) dstates_dytl = np.linalg.inv(self.mtx) ones = np.ones(self.nt) arange = np.arange(self.nt) dytl_dyt = csc_matrix((ones, (arange, arange)), shape=(num['dof'], self.nt)) dy_dyt = (dytl_dyt.T.dot(dstates_dytl.T).dot(dy_dstates.T)).T dy_dyt = np.einsum('ij,k->ijk', dy_dyt, np.ones(ny)) return {None: dy_dyt}
def get_power_spectral_density_matrix(observation, mask=None): """ Calculates the weighted power spectral density matrix. This does not yet work with more than one target mask. :param observation: Complex observations with shape (bins, sensors, frames) :param mask: Masks with shape (bins, frames) or (bins, 1, frames) :return: PSD matrix with shape (bins, sensors, sensors) """ bins, sensors, frames = observation.shape if mask is None: mask = np.ones((bins, frames)) if mask.ndim == 2: mask = mask[:, np.newaxis, :] normalization = np.maximum(np.sum(mask, axis=-1, keepdims=True), 1e-6) psd = np.einsum('...dt,...et->...de', mask * observation, observation.conj()) psd /= normalization return psd
def get_mvdr_vector(atf_vector, noise_psd_matrix): """ Returns the MVDR beamforming vector. :param atf_vector: Acoustic transfer function vector with shape (..., bins, sensors) :param noise_psd_matrix: Noise PSD matrix with shape (bins, sensors, sensors) :return: Set of beamforming vectors with shape (..., bins, sensors) """ while atf_vector.ndim > noise_psd_matrix.ndim - 1: noise_psd_matrix = np.expand_dims(noise_psd_matrix, axis=0) # Make sure matrix is hermitian noise_psd_matrix = 0.5 * ( noise_psd_matrix + np.conj(noise_psd_matrix.swapaxes(-1, -2))) numerator = solve(noise_psd_matrix, atf_vector) denominator = np.einsum('...d,...d->...', atf_vector.conj(), numerator) beamforming_vector = numerator / np.expand_dims(denominator, axis=-1) return beamforming_vector
def apply_sdw_mwf(mix, target_psd_matrix, noise_psd_matrix, mu=1, corr=None): """ Apply speech distortion weighted MWF: h = Tpsd * e1 / (Tpsd + mu*Npsd) :param mix: the signal complex FFT :param target_psd_matrix (bins, sensors, sensors) :param noise_psd_matrix :param mu: the lagrange factor :return """ bins, sensors, frames = mix.shape ref_vector = np.zeros((sensors,1), dtype=np.float) if corr is None: ref_ch = 0 else: # choose the channel with highest correlation with the others corr=corr.tolist() while len(corr) > sensors: corr.remove(np.min(corr)) ref_ch=np.argmax(corr) ref_vector[ref_ch,0]=1 mwf_vector = solve(target_psd_matrix + mu*noise_psd_matrix, target_psd_matrix[:,:,ref_ch]) return np.einsum('...a,...at->...t', mwf_vector.conj(), mix)
def test_against_numpy_einsum(self): """ Test against numpy.einsum """ a = np.arange(60.).reshape(3,4,5) b = np.arange(24.).reshape(4,3,2) stream = [a, b] from_numpy = np.einsum('ijk,jil->kl', a, b) from_stream = last(ieinsum(stream, 'ijk,jil->kl')) self.assertSequenceEqual(from_numpy.shape, from_stream.shape) self.assertTrue(np.allclose(from_numpy, from_stream))
