Python numpy.tensordot方法代碼示例

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import tensordot [as 別名]
def test_vna_lih(self):
    dname = dirname(abspath(__file__))
    n = nao(label='lih', cd=dname)
    m = 200
    dvec,midv = 2*(n.atom2coord[1] - n.atom2coord[0])/m,  (n.atom2coord[1] + n.atom2coord[0])/2.0
    vgrid = np.tensordot(np.array(range(-m,m+1)), dvec, axes=0) + midv
    sgrid = np.array(range(-m,m+1)) * np.sqrt((dvec*dvec).sum())
    
    
    #vgrid = np.array([[-1.517908564663352e+00, 1.180550033093826e+00,0.000000000000000e+00]])
    vna = n.vna(vgrid)
    
    #for v,r in zip(vna,vgrid):
    #  print("%23.15e %23.15e %23.15e %23.15e"%(r[0], r[1], r[2], v))
    
    #print(vna.shape, sgrid.shape)
    np.savetxt('vna_lih_0004.txt', np.row_stack((sgrid, vna)).T)
    ref = np.loadtxt(dname+'/vna_lih_0004.txt-ref')
    for r,d in zip(ref[:,1],vna): self.assertAlmostEqual(r,d) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import tensordot [as 別名]
def deriv_wrt_params(self, wrtFilter=None):
        """
        Construct a matrix whose columns are the derivatives of the SPAM vector
        with respect to a single param.  Thus, each column is of length
        get_dimension and there is one column per SPAM vector parameter.

        Returns
        -------
        numpy array
            Array of derivatives, shape == (dimension, num_params)
        """
        dmVec = self.state_vec.todense()

        derrgen = self.error_map.deriv_wrt_params(wrtFilter)  # shape (dim*dim, nParams)
        derrgen.shape = (self.dim, self.dim, derrgen.shape[1])  # => (dim,dim,nParams)

        if self._prep_or_effect == "prep":
            #derror map acts on dmVec
            #return _np.einsum("ijk,j->ik", derrgen, dmVec) # return shape = (dim,nParams)
            return _np.tensordot(derrgen, dmVec, (1, 0))  # return shape = (dim,nParams)
        else:
            # self.error_map acts on the *state* vector before dmVec acts
            # as an effect:  E.dag -> dot(E.dag,errmap) ==> E -> dot(errmap.dag,E)
            #return _np.einsum("jik,j->ik", derrgen.conjugate(), dmVec) # return shape = (dim,nParams)
            return _np.tensordot(derrgen.conjugate(), dmVec, (0, 0))  # return shape = (dim,nParams) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import tensordot [as 別名]
def test_maximum_eigenvector_power_method(self):
    """Tests power method routine on some known left-stochastic matrices."""
    matrix1 = np.matrix([[0.6, 0.1, 0.1], [0.0, 0.6, 0.9], [0.4, 0.3, 0.0]])
    matrix2 = np.matrix([[0.4, 0.4, 0.2], [0.2, 0.1, 0.5], [0.4, 0.5, 0.3]])

    with self.wrapped_session() as session:
      eigenvector1 = session.run(
          proxy_lagrangian_optimizer._maximal_eigenvector_power_method(
              tf.constant(matrix1)))
      eigenvector2 = session.run(
          proxy_lagrangian_optimizer._maximal_eigenvector_power_method(
              tf.constant(matrix2)))

    # Check that eigenvector1 and eigenvector2 are eigenvectors of matrix1 and
    # matrix2 (respectively) with associated eigenvalue 1.
    matrix_eigenvector1 = np.tensordot(matrix1, eigenvector1, axes=1)
    matrix_eigenvector2 = np.tensordot(matrix2, eigenvector2, axes=1)
    self.assertAllClose(eigenvector1, matrix_eigenvector1, rtol=0, atol=1e-6)
    self.assertAllClose(eigenvector2, matrix_eigenvector2, rtol=0, atol=1e-6) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import tensordot [as 別名]
def middle_bond_hamiltonian(Jx, Jz, hx, hz, L):
    """" Returns the spin operators sigma_x and sigma_z for L sites."""
    sx = np.array([[0., 1.], [1., 0.]])
    sz = np.array([[1., 0.], [0., -1.]])

    H_bond = Jx * np.kron(sx, sx) + Jz * np.kron(sz, sz)
    H_bond = H_bond + hx / 2 * np.kron(sx, np.eye(2)) + hx / 2 * np.kron(np.eye(2), sx)
    H_bond = H_bond + hz / 2 * np.kron(sz, np.eye(2)) + hz / 2 * np.kron(np.eye(2), sz)
    H_bond = H_bond.reshape(2, 2, 2, 2).transpose(0, 2, 1, 3).reshape(4, 4)  #i1 i2 i1' i2' -->
    U, s, V = np.linalg.svd(H_bond)

    M1 = np.dot(U, np.diag(s)).reshape(2, 2, 1, 4).transpose(2, 3, 0, 1)
    M2 = V.reshape(4, 1, 2, 2)
    M0 = np.tensordot(np.tensordot([1], [1], axes=0), np.eye(2), axes=0)
    W = []

    for i in range(L):
        if i == L / 2 - 1:
            W.append(M1)
        elif i == L / 2:
            W.append(M2)
        else:
            W.append(M0)
    return W 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import tensordot [as 別名]
def test_npc_tensordot_extra():
    # check that the sorting of charges is fine with special test matrices
    # which gave me some headaches at some point :/
    chinfo = npc.ChargeInfo([1], ['Sz'])
    leg = npc.LegCharge.from_qflat(chinfo, [-1, 1])
    legs = [leg, leg, leg.conj(), leg.conj()]
    idx = [(0, 0, 0, 0), (0, 1, 0, 1), (0, 1, 1, 0), (1, 0, 0, 1), (1, 0, 1, 0), (1, 1, 1, 1)]
    Uflat = np.eye(4).reshape([2, 2, 2, 2])  # up to numerical rubbish the identity
    Uflat[0, 1, 1, 0] = Uflat[1, 0, 0, 1] = 1.e-20
    U = npc.Array.from_ndarray(Uflat, legs, cutoff=0.)
    theta_flat = np.zeros([2, 2, 2, 2])
    vals = np.random.random(len(idx))
    vals /= np.linalg.norm(vals)
    for i, val in zip(idx, vals):
        theta_flat[i] = val
    theta = npc.Array.from_ndarray(theta_flat, [leg, leg, leg.conj(), leg.conj()], cutoff=0.)
    assert abs(np.linalg.norm(theta_flat) - npc.norm(theta)) < 1.e-14
    Utheta_flat = np.tensordot(Uflat, theta_flat, axes=2)
    Utheta = npc.tensordot(U, theta, axes=2)
    npt.assert_array_almost_equal_nulp(Utheta.to_ndarray(), Utheta_flat, 10)
    assert abs(np.linalg.norm(theta_flat) - npc.norm(Utheta)) < 1.e-10 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import tensordot [as 別名]
def test_npc_outer():
    for sort in [True, False]:
        print("sort =", sort)
        a = random_Array((6, 7), chinfo3, sort=sort)
        b = random_Array((5, 5), chinfo3, sort=sort)
        aflat = a.to_ndarray()
        bflat = b.to_ndarray()
        c = npc.outer(a, b)
        c.test_sanity()
        cflat = np.tensordot(aflat, bflat, axes=0)
        npt.assert_equal(c.to_ndarray(), cflat)
        c = npc.tensordot(a, b, axes=0)  # (should as well call npc.outer)
        npt.assert_equal(c.to_ndarray(), cflat)

    print("for trivial charge")
    a = npc.Array.from_func(np.random.random, [lcTr, lcTr.conj()], shape_kw='size')
    aflat = a.to_ndarray()
    b = npc.tensordot(a, a, axes=0)
    bflat = np.tensordot(aflat, aflat, axes=0)
    npt.assert_array_almost_equal_nulp(b.to_ndarray(), bflat, sum(a.shape)) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import tensordot [as 別名]
def update_bond(self, i):
        j = (i + 1) % self.psi.L
        # get effective Hamiltonian
        Heff = SimpleHeff(self.LPs[i], self.RPs[j], self.H_mpo[i], self.H_mpo[j])
        # Diagonalize Heff, find ground state `theta`
        theta0 = np.reshape(self.psi.get_theta2(i), [Heff.shape[0]])  # initial guess
        e, v = arp.eigsh(Heff, k=1, which='SA', return_eigenvectors=True, v0=theta0)
        theta = np.reshape(v[:, 0], Heff.theta_shape)
        # split and truncate
        Ai, Sj, Bj = split_truncate_theta(theta, self.chi_max, self.eps)
        # put back into MPS
        Gi = np.tensordot(np.diag(self.psi.Ss[i]**(-1)), Ai, axes=[1, 0])  # vL [vL*], [vL] i vC
        self.psi.Bs[i] = np.tensordot(Gi, np.diag(Sj), axes=[2, 0])  # vL i [vC], [vC*] vC
        self.psi.Ss[j] = Sj  # vC
        self.psi.Bs[j] = Bj  # vC j vR
        self.update_LP(i)
        self.update_RP(j) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import tensordot [as 別名]
def correlation_length(self):
        """Diagonalize transfer matrix to obtain the correlation length."""
        import scipy.sparse.linalg.eigen.arpack as arp
        assert self.bc == 'infinite'  # works only in the infinite case
        B = self.Bs[0]  # vL i vR
        chi = B.shape[0]
        T = np.tensordot(B, np.conj(B), axes=[1, 1])  # vL [i] vR, vL* [i*] vR*
        T = np.transpose(T, [0, 2, 1, 3])  # vL vL* vR vR*
        for i in range(1, self.L):
            B = self.Bs[i]
            T = np.tensordot(T, B, axes=[2, 0])  # vL vL* [vR] vR*, [vL] i vR
            T = np.tensordot(T, np.conj(B), axes=[[2, 3], [0, 1]])
            # vL vL* [vR*] [i] vR, [vL*] [i*] vR*
        T = np.reshape(T, (chi**2, chi**2))
        # Obtain the 2nd largest eigenvalue
        eta = arp.eigs(T, k=2, which='LM', return_eigenvectors=False, ncv=20)
        return -self.L / np.log(np.min(np.abs(eta))) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import tensordot [as 別名]
def binary_to_decimal(X):
    """
    Parameters
    ----------
    X: xp.ndarray
        Feature maps
    """
    # This function expects X of shape (n_images, L2, y, x)
    # as an argument.
    # Let's say that X[k] (0 <= k < n_images) can be represented like
    # X[k] = [map_k[0], map_k[1], ..., map_k[L2-1]]
    # where the shape of each map_k is (y, x).
    # Then we calculate
    # a[0] * map_k[0] + a[1] * map_k[1] + ... + a[L2-1] * map_k[L2-1]
    # for each X[k], where a = [2^(L2-1), 2^(L2-2), ..., 2^0]
    # Therefore, the output shape must be (n_images, y, x)
    a = xp.arange(X.shape[1])[::-1]
    a = xp.power(2, a)
    return xp.tensordot(X, a, axes=([1], [0])) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import tensordot [as 別名]
def __init__(self, *dim):
        """
        >>> Id(1)
        Tensor(dom=Dim(1), cod=Dim(1), array=[1])
        >>> list(Id(2).array.flatten())
        [1.0, 0.0, 0.0, 1.0]
        >>> Id(2).array.shape
        (2, 2)
        >>> list(Id(2, 2).array.flatten())[:8]
        [1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0]
        >>> list(Id(2, 2).array.flatten())[8:]
        [0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0]
        """
        dim = dim[0] if isinstance(dim[0], Dim) else Dim(*dim)
        array = functools.reduce(
            lambda a, x: np.tensordot(a, np.identity(x), 0)
            if a.shape else np.identity(x), dim, np.array(1))
        array = np.moveaxis(
            array, [2 * i for i in range(len(dim))], list(range(len(dim))))
        super().__init__(dim, dim, array) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import tensordot [as 別名]
def _interleaved_identities(n: int, cutoff_dim: int):
    r"""Maximally entangled state of `n` modes.

    Returns the tensor :math:`\sum_{abc\ldots} \ket{abc\ldots}\bra{abc\ldots}`
    representing an unnormalized, maximally entangled state of `n` subsystems.

    Args:
        n (int): number of subsystems
        cutoff_dim (int): Fock basis truncation dimension

    Returns:
        array: unnormalized maximally entangled state, shape == (cutoff_dim,) * (2*n)
    """
    I = np.identity(cutoff_dim)
    temp = I
    for _ in range(1, n):
        temp = np.tensordot(temp, I, axes=0)

    # use einsum to permute the indices such that |a><a|*|b><b|*|c><c|*... becomes |abc...><abc...|
    sublist = [int(n) for n in np.arange(2 * n).reshape((2, n)).T.reshape([-1])]
    return np.einsum(temp, sublist) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import tensordot [as 別名]
def tensor(u, v, n, pure, pos=None):
    """
    Returns the tensor product of `u` and `v`, optionally spliced into a
    at location `pos`.
    """

    w = np.tensordot(u, v, axes=0)

    if pos is not None:
        if pure:
            scale = 1
        else:
            scale = 2
        for i in range(v.ndim):
            w = np.rollaxis(w, scale * n + i, scale * pos + i)

    return w 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import tensordot [as 別名]
def testTensordot(self, lhs_shape, lhs_dtype, rhs_shape, rhs_dtype, axes, rng_factory):
    rng = rng_factory()
    args_maker = lambda: [rng(lhs_shape, lhs_dtype), rng(rhs_shape, rhs_dtype)]
    lnp_fun = lambda a, b: lnp.tensordot(a, b, axes)
    def onp_fun(a, b):
      a = a if lhs_dtype != lnp.bfloat16 else a.astype(onp.float32)
      b = b if rhs_dtype != lnp.bfloat16 else b.astype(onp.float32)
      dtype = lnp.promote_types(lhs_dtype, rhs_dtype)
      return onp.tensordot(a, b, axes).astype(dtype)
    tol = {onp.float16: 1e-1, onp.float32: 1e-3, onp.float64: 1e-12,
           onp.complex64: 1e-3, onp.complex128: 1e-12}
    if jtu.device_under_test() == "tpu":
      tol[onp.float32] = tol[onp.complex64] = 2e-1
    self._CheckAgainstNumpy(onp_fun, lnp_fun, args_maker, check_dtypes=True,
                            tol=tol)
    self._CompileAndCheck(lnp_fun, args_maker, check_dtypes=True,
                          check_incomplete_shape=True) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import tensordot [as 別名]
def test_vna_n2(self):
    dname = dirname(abspath(__file__))
    n = nao(label='n2', cd=dname)
    m = 200
    dvec,midv = 2*(n.atom2coord[1] - n.atom2coord[0])/m,  (n.atom2coord[1] + n.atom2coord[0])/2.0
    vgrid = np.tensordot(np.array(range(-m,m+1)), dvec, axes=0) + midv
    sgrid = np.array(range(-m,m+1)) * np.sqrt((dvec*dvec).sum())
    
    vna = n.vna(vgrid)
    #print(vna.shape, sgrid.shape)
    #np.savetxt('vna_n2_0004.txt', np.row_stack((sgrid, vna)).T)
    ref = np.loadtxt(dname+'/vna_n2_0004.txt-ref')
    for r,d in zip(ref[:,1],vna): self.assertAlmostEqual(r,d) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import tensordot [as 別名]
def hessian_wrt_params(self, wrtFilter1=None, wrtFilter2=None):
        """
        Construct the Hessian of this SPAM vector with respect to its parameters.

        This function returns a tensor whose first axis corresponds to the
        flattened operation matrix and whose 2nd and 3rd axes correspond to the
        parameters that are differentiated with respect to.

        Parameters
        ----------
        wrtFilter1, wrtFilter2 : list
            Lists of indices of the paramters to take first and second
            derivatives with respect to.  If None, then derivatives are
            taken with respect to all of the vectors's parameters.

        Returns
        -------
        numpy array
            Hessian with shape (dimension, num_params1, num_params2)
        """
        dmVec = self.state_vec.todense()

        herrgen = self.error_map.hessian_wrt_params(wrtFilter1, wrtFilter2)  # shape (dim*dim, nParams1, nParams2)
        herrgen.shape = (self.dim, self.dim, herrgen.shape[1], herrgen.shape[2])  # => (dim,dim,nParams1, nParams2)

        if self._prep_or_effect == "prep":
            #derror map acts on dmVec
            #return _np.einsum("ijkl,j->ikl", herrgen, dmVec) # return shape = (dim,nParams)
            return _np.tensordot(herrgen, dmVec, (1, 0))  # return shape = (dim,nParams)
        else:
            # self.error_map acts on the *state* vector before dmVec acts
            # as an effect:  E.dag -> dot(E.dag,errmap) ==> E -> dot(errmap.dag,E)
            #return _np.einsum("jikl,j->ikl", herrgen.conjugate(), dmVec) # return shape = (dim,nParams)
            return _np.tensordot(herrgen.conjugate(), dmVec, (0, 0))  # return shape = (dim,nParams)