def test_divide_update( self, size, X_dtype, c_dtype, ): X = qu.randn(size, dtype=X_dtype) Y = np.empty_like(X) c = qu.randn(1, dtype=c_dtype).item() res = X / c qu.core.divide_update_(X, c, Y) assert_allclose(res, Y, rtol=1e-6)
def test_subtract_update( self, size, X_dtype, c_dtype, ): X = qu.randn(size, dtype=X_dtype) Y = qu.randn(size, dtype=X_dtype) c = qu.randn(1, dtype=c_dtype).item() res = X - c * Y qu.core.subtract_update_(X, c, Y) assert_allclose(res, X)
def test_unitize(self, method): mera = qt.MERA.rand(16, dangle=True) assert mera.H @ mera == pytest.approx(2.0) for t in mera: t.modify(data=qu.randn(t.shape)) assert mera.H @ mera != pytest.approx(2.0) mera.unitize_(method=method) assert mera.H @ mera == pytest.approx(2.0)
def rand_rank(m, n, k, dtype=complex): s = np.sort(qu.randn(k)**2)[::-1] U = qu.gen.rand.rand_iso(m, k, dtype=dtype) VH = qu.gen.rand.rand_iso(n, k, dtype=dtype).conj().T if U.dtype in ('float32', 'complex64'): s = s.astype('float32') return usv2dense(U, s, VH)
def test_vectorizer(): from quimb.tensor.optimize_autograd import Vectorizer shapes = [(2, 3), (4, 5), (6, 7, 8)] dtypes = ['complex64', 'float32', 'complex64'] arrays = [qu.randn(s, dtype=dtype) for s, dtype in zip(shapes, dtypes)] v = Vectorizer(arrays) grads = [qu.randn(s, dtype=dtype) for s, dtype in zip(shapes, dtypes)] v.pack(grads, 'grad') new_arrays = v.unpack(v.vector) for x, y in zip(arrays, new_arrays): assert_allclose(x, y) new_arrays = v.unpack(v.grad) for x, y in zip(grads, new_arrays): assert_allclose(x, y)
def test_subsystem(self): rho = qu.rand_rho(6) dims = [3, 2] I, X, Y, Z = (qu.pauli(s) for s in 'IXYZ') mi_i = qu.mutual_information(rho, dims) p = 0.1 Ek = [(1 - p)**0.5 * I, (p / 3)**0.5 * X, (p / 3)**0.5 * Y, (p / 3)**0.5 * Z] with pytest.raises(ValueError): qu.kraus_op(rho, qu.randn((3, 2, 2)), check=True, dims=dims, where=1) sigma = qu.kraus_op(rho, Ek, check=True, dims=dims, where=1) mi_f = qu.mutual_information(sigma, dims) assert mi_f < mi_i assert qu.tr(sigma) == pytest.approx(1.0) sig_exp = sum( (qu.eye(3) & E) @ rho @ qu.dag(qu.eye(3) & E) for E in Ek) assert_allclose(sig_exp, sigma)
def eigs_lobpcg(A, k, *, B=None, v0=None, which=None, return_vecs=True, sigma=None, isherm=True, P=None, sort=True, **lobpcg_opts): """Interface to scipy's lobpcg eigensolver, which can be good for generalized eigenproblems with matrix-free operators. Seems to a be a bit innacurate though (e.g. on the order of ~ 1e-6 for eigenvalues). Also only takes real, symmetric problems, targeting smallest eigenvalues (though scipy will soon have complex support, and its easy to add oneself). Note that the slepc eigensolver also has a lobpcg backend (``EPSType='lobpcg'``) which accepts complex input and is more accurate - though seems slower. Parameters ---------- A : array_like, sparse_matrix, LinearOperator or callable The operator to solve for. k : int Number of eigenpairs to return B : array_like, sparse_matrix, LinearOperator or callable, optional If given, the RHS operator (which should be positive) defining a generalized eigen problem. v0 : array_like (d, k), optional The initial subspace to iterate with. which : {'SA', 'LA'}, optional Find the smallest or largest eigenvalues. return_vecs : bool, optional Whether to return the eigenvectors found. P : array_like, sparse_matrix, LinearOperator or callable, optional Perform the eigensolve in the subspace defined by this projector. sort : bool, optional Whether to ensure the eigenvalues are sorted in ascending value. lobpcg_opts Supplied to :func:`scipy.sparse.linagl.lobpcg`. Returns ------- lk : array_like (k,) The eigenvalues. vk : array_like (d, k) The eigenvectors, if `return_vecs=True`. See Also -------- eigs_scipy, eigs_numpy, eigs_slepc """ if not isherm: raise ValueError("lobpcg can only solve symmetric problems.") if sigma is not None: raise ValueError("lobpcg can only solve extremal eigenvalues.") # remove invalid options for lobpcg lobpcg_opts.pop('ncv', None) lobpcg_opts.pop('EPSType', None) # convert some arguments and defaults lobpcg_opts.setdefault('maxiter', 30) if lobpcg_opts['maxiter'] is None: lobpcg_opts['maxiter'] = 30 largest = {'SA': False, 'LA': True}[which] if isinstance(A, qu.Lazy): A = A() if isinstance(B, qu.Lazy): B = B() if isinstance(P, qu.Lazy): P = P() # project into subspace if P is not None: A = qu.dag(P) @ (A @ P) # avoid matrix like behaviour if isinstance(A, qu.qarray): A = A.A d = A.shape[0] # set up the initial subsspace to iterate with if v0 is None: v0 = qu.randn((d, k), dtype=A.dtype) else: # check if intial space should be projected too if P is not None and v0.shape[0] != d: v0 = qu.dag(P) @ v0 v0 = v0.reshape(d, -1) # if not enough initial states given, flesh out with random if v0.shape[1] != k: v0 = np.hstack(v0, qu.randn((d, k - v0.shape[1]), dtype=A.dtype)) lk, vk = spla.lobpcg(A=A, X=v0, B=B, largest=largest, **lobpcg_opts) if return_vecs: vk = qu.qarray(vk) return maybe_sort_and_project(lk, vk, P, sort) else: return np.sort(lk) if sort else lk
def test_scale_and_loc(self): x = qu.randn(1000, scale=100, loc=50, dtype=float, seed=42) assert_allclose(np.mean(x), 50, rtol=1e-1) assert_allclose(np.std(x), 100, rtol=1e-1)
def test_can_seed(self): assert_allclose(qu.randn(5, seed=42), qu.randn(5, seed=42))
def test_basic(self, dtype): x = qu.randn((2, 3, 4), dtype=dtype) assert x.shape == (2, 3, 4) assert x.dtype == np.dtype(dtype)