Python numpy.trace方法代码示例

# 需要导入模块: import numpy [as 别名]
# 或者: from numpy import trace [as 别名]
def test_circuit_generation_and_accuracy():
    for dim in range(2, 10):
        qubits = cirq.LineQubit.range(dim)
        u_generator = numpy.random.random(
            (dim, dim)) + 1j * numpy.random.random((dim, dim))
        u_generator = u_generator - numpy.conj(u_generator).T
        assert numpy.allclose(-1 * u_generator, numpy.conj(u_generator).T)

        unitary = scipy.linalg.expm(u_generator)
        circuit = cirq.Circuit()
        circuit.append(optimal_givens_decomposition(qubits, unitary))

        fermion_generator = QubitOperator(()) * 0.0
        for i, j in product(range(dim), repeat=2):
            fermion_generator += jordan_wigner(
                FermionOperator(((i, 1), (j, 0)), u_generator[i, j]))

        true_unitary = scipy.linalg.expm(
            get_sparse_operator(fermion_generator).toarray())
        assert numpy.allclose(true_unitary.conj().T.dot(true_unitary),
                              numpy.eye(2 ** dim, dtype=complex))

        test_unitary = cirq.unitary(circuit)
        assert numpy.isclose(
            abs(numpy.trace(true_unitary.conj().T.dot(test_unitary))), 2 ** dim) 

# 需要导入模块: import numpy [as 别名]
# 或者: from numpy import trace [as 别名]
def read_neci_1dms(fciqmcci, norb, nelec, filename='OneRDM.1', directory='.'):
    ''' Read spinned rdms, as they are in the neci output '''

    f = open(os.path.join(directory, filename),'r')

    dm1a = numpy.zeros((norb,norb))
    dm1b = numpy.zeros((norb,norb))
    for line in f.readlines():
        linesp = line.split()
        i, j = int(linesp[0]), int(linesp[1])
        assert((i % 2) == (j % 2))
        if i % 2 == 1:
            # alpha
            assert(all(x<norb for x in (i/2,j/2)))
            dm1a[i/2,j/2] = float(linesp[2])
            dm1a[j/2,i/2] = float(linesp[2])
        else:
            assert(all(x<norb for x in (i/2 - 1,j/2 - 1)))
            dm1b[i/2 - 1,j/2 - 1] = float(linesp[2])
            dm1b[j/2 - 1,i/2 - 1] = float(linesp[2])

    f.close()
    assert(numpy.allclose(dm1a.trace()+dm1b.trace(),sum(nelec)))
    return dm1a, dm1b 

# 需要导入模块: import numpy [as 别名]
# 或者: from numpy import trace [as 别名]
def is_normalized(self):
        '''
        Check if a basis is normalized, meaning that Tr(Bi Bi) = 1.0.

        Available only to bases whose elements are *matrices* for now.

        Returns
        -------
        bool
        '''
        if self.elndim == 2:
            for i, mx in enumerate(self.elements):
                t = _np.trace(_np.dot(mx, mx))
                t = _np.real(t)
                if not _np.isclose(t, 1.0): return False
            return True
        elif self.elndim == 1:
            raise NotImplementedError("TODO: add code so this works for *vector*-valued bases too!")
        else:
            raise ValueError("I don't know what normalized means for elndim == %d!" % self.elndim) 

# 需要导入模块: import numpy [as 别名]
# 或者: from numpy import trace [as 别名]
def tracenorm(A):
    """
    Compute the trace norm of matrix A given by:

      Tr( sqrt{ A^dagger * A } )

    Parameters
    ----------
    A : numpy array
        The matrix to compute the trace norm of.
    """
    if _np.linalg.norm(A - _np.conjugate(A.T)) < 1e-8:
        #Hermitian, so just sum eigenvalue magnitudes
        return _np.sum(_np.abs(_np.linalg.eigvals(A)))
    else:
        #Sum of singular values (positive by construction)
        return _np.sum(_np.linalg.svd(A, compute_uv=False)) 

# 需要导入模块: import numpy [as 别名]
# 或者: from numpy import trace [as 别名]
def jtracedist(A, B, mxBasis='pp'):  # Jamiolkowski trace distance:  Tr(|J(A)-J(B)|)
    """
    Compute the Jamiolkowski trace distance between operation matrices A and B,
    given by:

      D = 0.5 * Tr( sqrt{ (J(A)-J(B))^2 } )

    where J(.) is the Jamiolkowski isomorphism map that maps a operation matrix
    to it's corresponding Choi Matrix.

    Parameters
    ----------
    A, B : numpy array
        The matrices to compute the distance between.

    mxBasis : {'std', 'gm', 'pp', 'qt'} or Basis object
        The source and destination basis, respectively.  Allowed
        values are Matrix-unit (std), Gell-Mann (gm), Pauli-product (pp),
        and Qutrit (qt) (or a custom basis object).
    """
    JA = _jam.fast_jamiolkowski_iso_std(A, mxBasis)
    JB = _jam.fast_jamiolkowski_iso_std(B, mxBasis)
    return tracedist(JA, JB) 

# 需要导入模块: import numpy [as 别名]
# 或者: from numpy import trace [as 别名]
def povm_jtracedist(model, targetModel, povmlbl):
    """
    Computes the Jamiolkowski trace distance between POVM maps using :func:`jtracedist`.

    Parameters
    ----------
    model, targetModel : Model
        Models containing the two POVMs to compare.

    povmlbl : str
        The POVM label

    Returns
    -------
    float
    """
    povm_mx = get_povm_map(model, povmlbl)
    target_povm_mx = get_povm_map(targetModel, povmlbl)
    return jtracedist(povm_mx, target_povm_mx, targetModel.basis) 

# 需要导入模块: import numpy [as 别名]
# 或者: from numpy import trace [as 别名]
def reflection_matrix(point, normal):
    """Return matrix to mirror at plane defined by point and normal vector.
    >>> v0 = numpy.random.random(4) - 0.5
    >>> v0[3] = 1.0
    >>> v1 = numpy.random.random(3) - 0.5
    >>> R = reflection_matrix(v0, v1)
    >>> numpy.allclose(2., numpy.trace(R))
    True
    >>> numpy.allclose(v0, numpy.dot(R, v0))
    True
    >>> v2 = v0.copy()
    >>> v2[:3] += v1
    >>> v3 = v0.copy()
    >>> v2[:3] -= v1
    >>> numpy.allclose(v2, numpy.dot(R, v3))
    True
    """
    normal = unit_vector(normal[:3])
    M = numpy.identity(4)
    M[:3, :3] -= 2.0 * numpy.outer(normal, normal)
    M[:3, 3] = (2.0 * numpy.dot(point[:3], normal)) * normal
    return M 

# 需要导入模块: import numpy [as 别名]
# 或者: from numpy import trace [as 别名]
def axisangle_from_rotm(R):
  # logarithm of rotation matrix
  # R = R.reshape(-1,3,3)
  # tr = np.trace(R, axis1=1, axis2=2)
  # phi = np.arccos(np.clip((tr - 1) / 2, -1, 1))
  # scale = np.zeros_like(phi)
  # div = 2 * np.sin(phi)
  # np.divide(phi, div, out=scale, where=np.abs(div) > 1e-6)
  # A = (R - R.transpose(0,2,1)) * scale.reshape(-1,1,1)
  # aa = np.stack((A[:,2,1], A[:,0,2], A[:,1,0]), axis=1)
  # return aa.squeeze()
  R = R.reshape(-1,3,3)
  omega = np.empty((R.shape[0], 3), dtype=R.dtype)
  omega[:,0] = R[:,2,1] - R[:,1,2]
  omega[:,1] = R[:,0,2] - R[:,2,0]
  omega[:,2] = R[:,1,0] - R[:,0,1]
  r = np.linalg.norm(omega, axis=1).reshape(-1,1)
  t = np.trace(R, axis1=1, axis2=2).reshape(-1,1)
  omega = np.arctan2(r, t-1) * omega
  aa = np.zeros_like(omega)
  np.divide(omega, r, out=aa, where=r != 0)
  return aa.squeeze() 

# 需要导入模块: import numpy [as 别名]
# 或者: from numpy import trace [as 别名]
def reflection_matrix(point, normal):
    """Return matrix to mirror at plane defined by point and normal vector.

    >>> v0 = numpy.random.random(4) - 0.5
    >>> v0[3] = 1.0
    >>> v1 = numpy.random.random(3) - 0.5
    >>> R = reflection_matrix(v0, v1)
    >>> numpy.allclose(2., numpy.trace(R))
    True
    >>> numpy.allclose(v0, numpy.dot(R, v0))
    True
    >>> v2 = v0.copy()
    >>> v2[:3] += v1
    >>> v3 = v0.copy()
    >>> v2[:3] -= v1
    >>> numpy.allclose(v2, numpy.dot(R, v3))
    True

    """
    normal = unit_vector(normal[:3])
    M = numpy.identity(4)
    M[:3, :3] -= 2.0 * numpy.outer(normal, normal)
    M[:3, 3] = (2.0 * numpy.dot(point[:3], normal)) * normal
    return M 

# 需要导入模块: import numpy [as 别名]
# 或者: from numpy import trace [as 别名]
def compute_pose_error(gt, pred):
    RE = 0
    snippet_length = gt.shape[0]
    scale_factor = np.sum(gt[:,:,-1] * pred[:,:,-1])/np.sum(pred[:,:,-1] ** 2)
    ATE = np.linalg.norm((gt[:,:,-1] - scale_factor * pred[:,:,-1]).reshape(-1))
    for gt_pose, pred_pose in zip(gt, pred):
        # Residual matrix to which we compute angle's sin and cos
        R = gt_pose[:,:3] @ np.linalg.inv(pred_pose[:,:3])
        s = np.linalg.norm([R[0,1]-R[1,0],
                            R[1,2]-R[2,1],
                            R[0,2]-R[2,0]])
        c = np.trace(R) - 1
        # Note: we actually compute double of cos and sin, but arctan2 is invariant to scale
        RE += np.arctan2(s,c)

    return ATE/snippet_length, RE/snippet_length 

# 需要导入模块: import numpy [as 别名]
# 或者: from numpy import trace [as 别名]
def reflection_matrix(point, normal):
  """Return matrix to mirror at plane defined by point and normal vector.

  >>> v0 = numpy.random.random(4) - 0.5
  >>> v0[3] = 1.
  >>> v1 = numpy.random.random(3) - 0.5
  >>> R = reflection_matrix(v0, v1)
  >>> numpy.allclose(2, numpy.trace(R))
  True
  >>> numpy.allclose(v0, numpy.dot(R, v0))
  True
  >>> v2 = v0.copy()
  >>> v2[:3] += v1
  >>> v3 = v0.copy()
  >>> v2[:3] -= v1
  >>> numpy.allclose(v2, numpy.dot(R, v3))
  True

  """
  normal = unit_vector(normal[:3])
  M = numpy.identity(4)
  M[:3, :3] -= 2.0 * numpy.outer(normal, normal)
  M[:3, 3] = (2.0 * numpy.dot(point[:3], normal)) * normal
  return M 

# 需要导入模块: import numpy [as 别名]
# 或者: from numpy import trace [as 别名]
def test_trace():
    rng = numpy.random.RandomState(utt.fetch_seed())
    x = theano.tensor.matrix()
    g = trace(x)
    f = theano.function([x], g)

    for shp in [(2, 3), (3, 2), (3, 3)]:
        m = rng.rand(*shp).astype(config.floatX)
        v = numpy.trace(m)
        assert v == f(m)

    xx = theano.tensor.vector()
    ok = False
    try:
        trace(xx)
    except TypeError:
        ok = True
    assert ok 

# 需要导入模块: import numpy [as 别名]
# 或者: from numpy import trace [as 别名]
def test_reconstruction():
    dim = 20
    np.random.seed(42)
    mat = np.random.random((dim, dim))
    mat = 0.5 * (mat + mat.T)
    test_mat = np.zeros_like(mat)
    w, v = np.linalg.eigh(mat)
    for i in range(w.shape[0]):
        test_mat += w[i] * v[:, [i]].dot(v[:, [i]].T)
    assert np.allclose(test_mat - mat, 0.0)

    test_mat = fixed_trace_positive_projection(mat, np.trace(mat))
    assert np.isclose(np.trace(test_mat), np.trace(mat))
    w, v = np.linalg.eigh(test_mat)
    assert np.all(w >= -(float(4.0E-15)))

    mat = np.arange(16).reshape((4, 4))
    mat = 0.5 * (mat + mat.T)
    mat_tensor = map_to_tensor(mat)
    trace_mat = np.trace(mat)
    true_mat = fixed_trace_positive_projection(mat, trace_mat)
    test_mat = map_to_matrix(fixed_trace_positive_projection(mat_tensor,
                                                             trace_mat))
    assert np.allclose(true_mat, test_mat)

    w, v = np.linalg.eigh(true_mat)
    assert np.allclose(true_mat, fixed_trace_positive_projection(true_mat,
                                                                 trace_mat)) 

# 需要导入模块: import numpy [as 别名]
# 或者: from numpy import trace [as 别名]
def test_rdm1(self):
        cell = pbcgto.Cell()
        cell.atom = '''Al 0 0 0'''
        cell.basis = 'gth-szv'
        cell.pseudo = 'gth-pade'
        cell.a = '''
        2.47332919 0 1.42797728
        0.82444306 2.33187713 1.42797728
        0, 0, 2.85595455
        '''
        cell.unit = 'angstrom'
        cell.build()
        cell.verbose = 4
        cell.incore_anyway = True

        abs_kpts = cell.make_kpts((2, 1, 1), scaled_center=(.1, .2, .3))
        kmf = pbcscf.KRHF(cell, abs_kpts)
        kmf.conv_tol = 1e-12
        kmf.kernel()
        mp = pyscf.pbc.mp.kmp2.KMP2(kmf)
        mp.kernel(with_t2=True)
        self.assertAlmostEqual(mp.e_corr, -0.00162057921874043)
        dm = mp.make_rdm1()
        np.testing.assert_allclose(np.trace(dm[0]) + np.trace(dm[1]), 6)
        for kdm in dm:
            np.testing.assert_allclose(kdm, kdm.conj().T) 

# 需要导入模块: import numpy [as 别名]
# 或者: from numpy import trace [as 别名]
def test_det_ovlp(self):
        s, x = mf.det_ovlp(mf.mo_coeff, mf.mo_coeff, mf.mo_occ, mf.mo_occ)
        self.assertAlmostEqual(s, 1.000000000, 9)
        self.assertAlmostEqual(numpy.trace(x[0]), mol.nelec[0]*1.000000000, 9)
        self.assertAlmostEqual(numpy.trace(x[0]), mol.nelec[1]*1.000000000, 9)