Python numpy.eye方法代碼示例

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import eye [as 別名]
def classical_mds(self, D):
        ''' 
        Classical multidimensional scaling

        Parameters
        ----------
        D : square 2D ndarray
            Euclidean Distance Matrix (matrix containing squared distances between points
        '''

        # Apply MDS algorithm for denoising
        n = D.shape[0]
        J = np.eye(n) - np.ones((n,n))/float(n)
        G = -0.5*np.dot(J, np.dot(D, J))

        s, U = np.linalg.eig(G)

        # we need to sort the eigenvalues in decreasing order
        s = np.real(s)
        o = np.argsort(s)
        s = s[o[::-1]]
        U = U[:,o[::-1]]

        S = np.diag(s)[0:self.dim,:]
        self.X = np.dot(np.sqrt(S),U.T) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import eye [as 別名]
def output_shrink(K, L):
    """
    shrink the convolution output to half the size.
    used when both the annihilating filter and the uniform samples of sinusoids satisfy
    Hermitian symmetric.
    :param K: the annihilating filter size: K + 1
    :param L: length of the (complex-valued) b vector
    :return:
    """
    out_len = L - K
    if out_len % 2 == 0:
        half_out_len = np.int(out_len / 2.)
        mtx_r = np.hstack((np.eye(half_out_len),
                           np.zeros((half_out_len, half_out_len))))
        mtx_i = mtx_r
    else:
        half_out_len = np.int((out_len + 1) / 2.)
        mtx_r = np.hstack((np.eye(half_out_len),
                           np.zeros((half_out_len, half_out_len - 1))))
        mtx_i = np.hstack((np.eye(half_out_len - 1),
                           np.zeros((half_out_len - 1, half_out_len))))
    return linalg.block_diag(mtx_r, mtx_i) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import eye [as 別名]
def mtx_updated_G(phi_recon, M, mtx_amp2visi_ri, mtx_fri2visi_ri):
    """
    Update the linear transformation matrix that links the FRI sequence to the
    visibilities by using the reconstructed Dirac locations.
    :param phi_recon: the reconstructed Dirac locations (azimuths)
    :param M: the Fourier series expansion is between -M to M
    :param p_mic_x: a vector that contains microphones' x-coordinates
    :param p_mic_y: a vector that contains microphones' y-coordinates
    :param mtx_freq2visi: the linear mapping from Fourier series to visibilities
    :return:
    """
    L = 2 * M + 1
    ms_half = np.reshape(np.arange(-M, 1, step=1), (-1, 1), order='F')
    phi_recon = np.reshape(phi_recon, (1, -1), order='F')
    mtx_amp2freq = np.exp(-1j * ms_half * phi_recon)  # size: (M + 1) x K
    mtx_amp2freq_ri = np.vstack((mtx_amp2freq.real, mtx_amp2freq.imag[:-1, :]))  # size: (2M + 1) x K
    mtx_fri2amp_ri = linalg.lstsq(mtx_amp2freq_ri, np.eye(L))[0]
    # projection mtx_freq2visi to the null space of mtx_fri2amp
    mtx_null_proj = np.eye(L) - np.dot(mtx_fri2amp_ri.T,
                                       linalg.lstsq(mtx_fri2amp_ri.T, np.eye(L))[0])
    G_updated = np.dot(mtx_amp2visi_ri, mtx_fri2amp_ri) + \
                np.dot(mtx_fri2visi_ri, mtx_null_proj)
    return G_updated 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import eye [as 別名]
def _N(self,s,r):
        """
        Lagrange's interpolate function
        params:
            s,r:natural position of evalue point.2-array.
        returns:
            2x(2x4) shape function matrix.
        """
        la1=(1-s)/2
        la2=(1+s)/2
        lb1=(1-r)/2
        lb2=(1+r)/2
        N1=la1*lb1
        N2=la1*lb2
        N3=la2*lb1
        N4=la2*lb2

        N=np.hstack(N1*np.eye(2),N2*np.eye(2),N3*np.eye(2),N4*np.eye(2))
        return N 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import eye [as 別名]
def __init__(self):
        """Initialize variable used by Kalman Filter class
        Args:
            None
        Return:
            None
        """
        self.dt = 0.005  # delta time

        self.A = np.array([[1, 0], [0, 1]])  # matrix in observation equations
        self.u = np.zeros((2, 1))  # previous state vector

        # (x,y) tracking object center
        self.b = np.array([[0], [255]])  # vector of observations

        self.P = np.diag((3.0, 3.0))  # covariance matrix
        self.F = np.array([[1.0, self.dt], [0.0, 1.0]])  # state transition mat

        self.Q = np.eye(self.u.shape[0])  # process noise matrix
        self.R = np.eye(self.b.shape[0])  # observation noise matrix
        self.lastResult = np.array([[0], [255]]) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import eye [as 別名]
def betaseries_file(tmpdir_factory,
                    deriv_betaseries_fname=deriv_betaseries_fname):
    bfile = tmpdir_factory.mktemp("beta").ensure(deriv_betaseries_fname)
    np.random.seed(3)
    num_trials = 40
    tgt_corr = 0.1
    bs1 = np.random.rand(num_trials)
    # create another betaseries with a target correlation
    bs2 = minimize(lambda x: abs(tgt_corr - pearsonr(bs1, x)[0]),
                   np.random.rand(num_trials)).x

    # two identical beta series
    bs_data = np.array([[[bs1, bs2]]])

    # the nifti image
    bs_img = nib.Nifti1Image(bs_data, np.eye(4))
    bs_img.to_filename(str(bfile))

    return bfile 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import eye [as 別名]
def test_output():
    shape = (2,2)
    ones = mx.nd.ones(shape)
    zeros = mx.nd.zeros(shape)
    out = mx.nd.zeros(shape)
    mx.nd.ones(shape, out=out)
    assert_almost_equal(out.asnumpy(), ones.asnumpy())
    mx.nd.zeros(shape, out=out)
    assert_almost_equal(out.asnumpy(), zeros.asnumpy())
    mx.nd.full(shape, 2, out=out)
    assert_almost_equal(out.asnumpy(), ones.asnumpy() * 2)
    arange_out = mx.nd.arange(0, 20, dtype='int64')
    assert_almost_equal(arange_out.asnumpy(), np.arange(0, 20))
    N_array = np.random.randint(1, high=8, size=10)
    M_array = np.random.randint(1, high=8, size=10)
    k_array = np.random.randint(-10, high=10, size=10)
    for i in range(10):
        N = N_array[i]
        M = M_array[i]
        k = k_array[i]
        assert_almost_equal(np.eye(N, M, k), mx.nd.eye(N, M, k).asnumpy())
        assert_almost_equal(np.eye(N, k=k), mx.nd.eye(N, k=k).asnumpy()) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import eye [as 別名]
def set_camera(self, fov_vertical, z_near, z_far, aspect):
    width = 2*np.tan(np.deg2rad(fov_vertical)/2.0)*z_near*aspect;
    height = 2*np.tan(np.deg2rad(fov_vertical)/2.0)*z_near;
    egl_program = self.egl_program
    c = np.eye(4, dtype=np.float32)
    c[3,3] = 0
    c[3,2] = -1
    c[2,2] = -(z_near+z_far)/(z_far-z_near)
    c[2,3] = -2.0*(z_near*z_far)/(z_far-z_near)
    c[0,0] = 2.0*z_near/width
    c[1,1] = 2.0*z_near/height
    c = c.T
    
    projection_matrix_o = glGetUniformLocation(egl_program, 'uProjectionMatrix')
    projection_matrix = np.eye(4, dtype=np.float32)
    projection_matrix[...] = c
    projection_matrix = np.reshape(projection_matrix, (-1))
    glUniformMatrix4fv(projection_matrix_o, 1, GL_FALSE, projection_matrix) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import eye [as 別名]
def rotate_camera_to_point_at(up_from, lookat_from, up_to, lookat_to):
  inputs = [up_from, lookat_from, up_to, lookat_to]
  for i in range(4):
    inputs[i] = normalize(np.array(inputs[i]).reshape((-1,)))
  up_from, lookat_from, up_to, lookat_to = inputs
  r1 = r_between(lookat_from, lookat_to)

  new_x = np.dot(r1, np.array([1, 0, 0]).reshape((-1, 1))).reshape((-1))
  to_x = normalize(np.cross(lookat_to, up_to))
  angle = np.arccos(np.dot(new_x, to_x))
  if angle > ANGLE_EPS:
    if angle < np.pi - ANGLE_EPS:
      ax = normalize(np.cross(new_x, to_x))
      flip = np.dot(lookat_to, ax)
      if flip > 0:
        r2 = get_r_matrix(lookat_to, angle)
      elif flip < 0:
        r2 = get_r_matrix(lookat_to, -1. * angle)
    else:
      # Angle of rotation is too close to 180 degrees, direction of rotation
      # does not matter.
      r2 = get_r_matrix(lookat_to, angle)
  else:
    r2 = np.eye(3)
  return np.dot(r2, r1) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import eye [as 別名]
def test_givens_inverse():
    r"""
    The Givens rotation in OpenFermion is defined as

    .. math::

        \begin{pmatrix}
            \cos(\theta) & -e^{i \varphi} \sin(\theta) \\
            \sin(\theta) &     e^{i \varphi} \cos(\theta)
        \end{pmatrix}.

    confirm numerically its hermitian conjugate is it's inverse
    """
    a = numpy.random.random() + 1j * numpy.random.random()
    b = numpy.random.random() + 1j * numpy.random.random()
    ab_rotation = givens_matrix_elements(a, b, which='right')

    assert numpy.allclose(ab_rotation.dot(numpy.conj(ab_rotation).T),
                          numpy.eye(2))
    assert numpy.allclose(numpy.conj(ab_rotation).T.dot(ab_rotation),
                          numpy.eye(2)) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import eye [as 別名]
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) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import eye [as 別名]
def energy_from_opdm(opdm, constant, one_body_tensor, two_body_tensor):
    """
    Evaluate the energy of an opdm assuming the 2-RDM is opdm ^ opdm

    :param opdm: single spin-component of the full spin-orbital opdm.
    :param constant: constant shift to the Hamiltonian. Commonly this is the
                     nuclear repulsion energy.
    :param one_body_tensor: spatial one-body integrals
    :param two_body_tensor: spatial two-body integrals
    :return:
    """
    spin_opdm = np.kron(opdm, np.eye(2))
    spin_tpdm = 2 * wedge(spin_opdm, spin_opdm, (1, 1), (1, 1))
    molecular_hamiltonian = generate_hamiltonian(constant=constant,
                                                 one_body_integrals=one_body_tensor,
                                                 two_body_integrals=two_body_tensor)
    rdms = InteractionRDM(spin_opdm, spin_tpdm)
    return rdms.expectation(molecular_hamiltonian).real 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import eye [as 別名]
def netflix(es, ps, e0, l=.0001):
    """Combine predictions with the optimal weights to minimize RMSE.

    Args:
        es (list of float): RMSEs of predictions
        ps (list of np.array): predictions
        e0 (float): RMSE of all zero prediction
        l (float): lambda as in the ridge regression

    Returns:
        (tuple):

            - (np.array): ensemble predictions
            - (np.array): weights for input predictions
    """
    m = len(es)
    n = len(ps[0])

    X = np.stack(ps).T
    pTy = .5 * (n * e0**2 + (X**2).sum(axis=0) - n * np.array(es)**2)

    w = np.linalg.pinv(X.T.dot(X) + l * n * np.eye(m)).dot(pTy)

    return X.dot(w), w 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import eye [as 別名]
def fit(self, Xs, Xt):
        '''
        Fit source and target using KMM (compute the coefficients)
        :param Xs: ns * dim
        :param Xt: nt * dim
        :return: Coefficients (Pt / Ps) value vector (Beta in the paper)
        '''
        ns = Xs.shape[0]
        nt = Xt.shape[0]
        if self.eps == None:
            self.eps = self.B / np.sqrt(ns)
        K = kernel(self.kernel_type, Xs, None, self.gamma)
        kappa = np.sum(kernel(self.kernel_type, Xs, Xt, self.gamma) * float(ns) / float(nt), axis=1)

        K = matrix(K)
        kappa = matrix(kappa)
        G = matrix(np.r_[np.ones((1, ns)), -np.ones((1, ns)), np.eye(ns), -np.eye(ns)])
        h = matrix(np.r_[ns * (1 + self.eps), ns * (self.eps - 1), self.B * np.ones((ns,)), np.zeros((ns,))])

        sol = solvers.qp(K, -kappa, G, h)
        beta = np.array(sol['x'])
        return beta 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import eye [as 別名]
def fit(self, Xs, Xt):
        '''
        Transform Xs and Xt
        :param Xs: ns * n_feature, source feature
        :param Xt: nt * n_feature, target feature
        :return: Xs_new and Xt_new after TCA
        '''
        X = np.hstack((Xs.T, Xt.T))
        X /= np.linalg.norm(X, axis=0)
        m, n = X.shape
        ns, nt = len(Xs), len(Xt)
        e = np.vstack((1 / ns * np.ones((ns, 1)), -1 / nt * np.ones((nt, 1))))
        M = e * e.T
        M = M / np.linalg.norm(M, 'fro')
        H = np.eye(n) - 1 / n * np.ones((n, n))
        K = kernel(self.kernel_type, X, None, gamma=self.gamma)
        n_eye = m if self.kernel_type == 'primal' else n
        a, b = np.linalg.multi_dot([K, M, K.T]) + self.lamb * np.eye(n_eye), np.linalg.multi_dot([K, H, K.T])
        w, V = scipy.linalg.eig(a, b)
        ind = np.argsort(w)
        A = V[:, ind[:self.dim]]
        Z = np.dot(A.T, K)
        Z /= np.linalg.norm(Z, axis=0)
        Xs_new, Xt_new = Z[:, :ns].T, Z[:, ns:].T
        return Xs_new, Xt_new