Python linalg.block_diag方法代碼示例

# 需要導入模塊: from scipy import linalg [as 別名]
# 或者: from scipy.linalg import block_diag [as 別名]
def mtx_fri2visi_ri_multiband(M, p_mic_x_all, p_mic_y_all, D1, D2, aslist=False):
    """
    build the matrix that maps the Fourier series to the visibility in terms of
    REAL-VALUED entries only. (matrix size double)
    :param M: the Fourier series expansion is limited from -M to M
    :param p_mic_x_all: a matrix that contains microphones x coordinates
    :param p_mic_y_all: a matrix that contains microphones y coordinates
    :param D1: expansion matrix for the real-part
    :param D2: expansion matrix for the imaginary-part
    :return:
    """
    num_bands = p_mic_x_all.shape[1]
    if aslist:
        return [mtx_fri2visi_ri(M, p_mic_x_all[:, band_count],
                                p_mic_y_all[:, band_count], D1, D2)
                for band_count in range(num_bands)]
    else:
        return linalg.block_diag(*[mtx_fri2visi_ri(M, p_mic_x_all[:, band_count],
                                                   p_mic_y_all[:, band_count], D1, D2)
                                   for band_count in range(num_bands)]) 

# 需要導入模塊: from scipy import linalg [as 別名]
# 或者: from scipy.linalg import block_diag [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: from scipy import linalg [as 別名]
# 或者: from scipy.linalg import block_diag [as 別名]
def test_matrix_static_gain(self):
        """Regression: can we create matrix static gains?"""
        d1 = np.matrix([[1, 2, 3], [4, 5, 6]])
        d2 = np.matrix([[7, 8], [9, 10], [11, 12]])
        g1 = StateSpace([], [], [], d1)

        # _remove_useless_states was making A = [[0]]
        self.assertEqual((0, 0), g1.A.shape)

        g2 = StateSpace([], [], [], d2)
        g3 = StateSpace([], [], [], d2.T)

        h1 = g1 * g2
        np.testing.assert_array_equal(d1 * d2, h1.D)
        h2 = g1 + g3
        np.testing.assert_array_equal(d1 + d2.T, h2.D)
        h3 = g1.feedback(g2)
        np.testing.assert_array_almost_equal(
            solve(np.eye(2) + d1 * d2, d1), h3.D)
        h4 = g1.append(g2)
        np.testing.assert_array_equal(block_diag(d1, d2), h4.D) 

# 需要導入模塊: from scipy import linalg [as 別名]
# 或者: from scipy.linalg import block_diag [as 別名]
def test_matrix_static_gain(self):
        """Regression: can we create matrix static gains?"""
        d1 = np.array([[1, 2, 3], [4, 5, 6]])
        d2 = np.array([[7, 8], [9, 10], [11, 12]])
        g1 = StateSpace([], [], [], d1)

        # _remove_useless_states was making A = [[0]]
        self.assertEqual((0, 0), g1.A.shape)

        g2 = StateSpace([], [], [], d2)
        g3 = StateSpace([], [], [], d2.T)

        h1 = g1 * g2
        np.testing.assert_array_equal(np.dot(d1, d2), h1.D)
        h2 = g1 + g3
        np.testing.assert_array_equal(d1 + d2.T, h2.D)
        h3 = g1.feedback(g2)
        np.testing.assert_array_almost_equal(
            solve(np.eye(2) + np.dot(d1, d2), d1), h3.D)
        h4 = g1.append(g2)
        np.testing.assert_array_equal(block_diag(d1, d2), h4.D) 

# 需要導入模塊: from scipy import linalg [as 別名]
# 或者: from scipy.linalg import block_diag [as 別名]
def test_rotated_squeezed(self, setup_eng, hbar, tol):
        """Testing decomposed rotated squeezed state"""
        eng, prog = setup_eng(3)

        r = 0.1
        phi = 0.2312
        v1 = (hbar / 2) * np.diag([np.exp(-r), np.exp(r)])
        A = changebasis(3)
        cov = A.T @ block_diag(*[rot(phi) @ v1 @ rot(phi).T] * 3) @ A

        with prog.context as q:
            ops.Gaussian(cov) | q

        state = eng.run(prog).state
        assert np.allclose(state.cov(), cov, atol=tol)
        assert len(eng.run_progs[-1]) == 3 

# 需要導入模塊: from scipy import linalg [as 別名]
# 或者: from scipy.linalg import block_diag [as 別名]
def constr(self):
        def fun(x):
            x_coord, y_coord, z_coord = self._get_cordinates(x)
            return x_coord**2 + y_coord**2 + z_coord**2 - 1

        def jac(x):
            x_coord, y_coord, z_coord = self._get_cordinates(x)
            Jx = 2 * np.diag(x_coord)
            Jy = 2 * np.diag(y_coord)
            Jz = 2 * np.diag(z_coord)

            return csc_matrix(np.hstack((Jx, Jy, Jz)))

        def hess(x, v):
            D = 2 * np.diag(v)
            return block_diag(D, D, D)

        return NonlinearConstraint(fun, ("less",), jac, hess) 

# 需要導入模塊: from scipy import linalg [as 別名]
# 或者: from scipy.linalg import block_diag [as 別名]
def constr(self):
        def fun(x):
            x_coord, y_coord, z_coord = self._get_cordinates(x)
            return x_coord**2 + y_coord**2 + z_coord**2 - 1

        if self.constr_jac is None:
            def jac(x):
                x_coord, y_coord, z_coord = self._get_cordinates(x)
                Jx = 2 * np.diag(x_coord)
                Jy = 2 * np.diag(y_coord)
                Jz = 2 * np.diag(z_coord)
                return csc_matrix(np.hstack((Jx, Jy, Jz)))
        else:
            jac = self.constr_jac

        if self.constr_hess is None:
            def hess(x, v):
                D = 2 * np.diag(v)
                return block_diag(D, D, D)
        else:
            hess = self.constr_hess

        return NonlinearConstraint(fun, -np.inf, 0, jac, hess) 

# 需要導入模塊: from scipy import linalg [as 別名]
# 或者: from scipy.linalg import block_diag [as 別名]
def SO3_irreps(g, irreps):
    global Jd

    # First, compute sinusoids at all required frequencies, i.e.
    # cos(n x) for n=0, ..., max(irreps)
    # sin(n x) for n=-max(irreps), ..., max(irreps)
    # where x ranges over the three parameters of SO(3).

    # In theory, it may be faster to evaluate cos(x) once and then use
    # Chebyshev polynomials to obtain cos(n*x), but in practice this appears
    # to be slower than just evaluating cos(n*x).
    dim = np.sum(2 * np.array(irreps) + 1)
    T = np.empty((dim, dim, g.shape[1]))
    for i in range(g.shape[1]):
        T[:, :, i] = block_diag(*[rot_mat(g[0, i], g[1, i], g[2, i], l, Jd[l]) for l in irreps])
    return T 

# 需要導入模塊: from scipy import linalg [as 別名]
# 或者: from scipy.linalg import block_diag [as 別名]
def set_wrench(self, wrench):
        """
        Set contact wrench directly.

        Parameters
        ----------
        wrench : array, shape=(6,)
            Wrench coordinates given in the contact frame.

        Notes
        -----
        This function switches the contact to "managed" mode, as opposed to the
        default "supporting" mode where the wrench distributor finds contact
        wrenches by numerical optimization.
        """
        if not type(wrench) is ndarray:
            wrench = array(wrench)
        if not self.is_managed:
            self.set_color('b')
        self.is_managed = True
        self.wrench = dot(block_diag(self.R, self.R), wrench) 

# 需要導入模塊: from scipy import linalg [as 別名]
# 或者: from scipy.linalg import block_diag [as 別名]
def test_decompose(self, tol):
        """Test the two mode squeezing symplectic transform decomposes correctly."""
        r = 0.543
        phi = 0.123
        S = symplectic.two_mode_squeezing(r, phi)

        # test that S = B^\dagger(pi/4, 0) [S(z) x S(-z)] B(pi/4)
        # fmt: off
        B = np.array([[1, -1, 0, 0], [1, 1, 0, 0], [0, 0, 1, -1], [0, 0, 1, 1]])/np.sqrt(2)

        Sq1 = np.array([[np.cosh(r)-np.cos(phi)*np.sinh(r), -np.sin(phi)*np.sinh(r)],
                        [-np.sin(phi)*np.sinh(r), np.cosh(r)+np.cos(phi)*np.sinh(r)]])

        Sq2 = np.array([[np.cosh(-r)-np.cos(phi)*np.sinh(-r), -np.sin(phi)*np.sinh(-r)],
                        [-np.sin(phi)*np.sinh(-r), np.cosh(-r)+np.cos(phi)*np.sinh(-r)]])
        # fmt: on

        Sz = block_diag(Sq1, Sq2)[:, [0, 2, 1, 3]][[0, 2, 1, 3]]
        expected = B.conj().T @ Sz @ B
        assert np.allclose(S, expected, atol=tol, rtol=0) 

# 需要導入模塊: from scipy import linalg [as 別名]
# 或者: from scipy.linalg import block_diag [as 別名]
def _rotation(phi, bare=False):
    r"""Utility function, returns the Heisenberg transformation of a phase rotation gate.

    The transformation matrix returned is:

    .. math:: M = \begin{bmatrix}
        1 & 0 & 0\\
        0 & \cos\phi & -\sin\phi\\
        0 & \sin\phi & \cos\phi
        \end{bmatrix}

    Args:
        phi (float): rotation angle.
        bare (bool): if True, return a simple 2d rotation matrix

    Returns:
        array[float]: transformation matrix
    """
    c = math.cos(phi)
    s = math.sin(phi)
    temp = np.array([[c, -s], [s, c]])
    if bare:
        return temp
    return block_diag(1, temp)  # pylint: disable=no-member 

# 需要導入模塊: from scipy import linalg [as 別名]
# 或者: from scipy.linalg import block_diag [as 別名]
def test_two_mode_squeezing(self, tol):
        """Test the two mode squeezing symplectic transform."""

        r = 0.543
        phi = 0.123
        S = two_mode_squeezing(r, phi)

        # test that S = B^\dagger(pi/4, 0) [S(z) x S(-z)] B(pi/4)
        B = beamsplitter(np.pi/4, 0)
        Sz = block_diag(squeezing(r, phi), squeezing(-r, phi))[:, [0, 2, 1, 3]][[0, 2, 1, 3]]
        expected = B.conj().T @ Sz @ B
        assert S == pytest.approx(expected, abs=tol)

        # test that S |a1, a2> = |ta1+ra2, ta2+ra1>
        a1 = 0.23+0.12j
        a2 = 0.23+0.12j
        out = S @ np.array([a1.real, a2.real, a1.imag, a2.imag])*np.sqrt(2*hbar)

        T = np.cosh(r)
        R = np.exp(1j*phi)*np.sinh(r)
        a1out = T*a1 + R*np.conj(a2)
        a2out = T*a2 + R*np.conj(a1)
        expected = np.array([a1out.real, a2out.real, a1out.imag, a2out.imag])*np.sqrt(2*hbar)
        assert out == pytest.approx(expected, abs=tol) 

# 需要導入模塊: from scipy import linalg [as 別名]
# 或者: from scipy.linalg import block_diag [as 別名]
def test_controlled_addition(self, tol):
        """Test the CX symplectic transform."""

        s = 0.543
        S = controlled_addition(s)

        # test that S = B(theta+pi/2, 0) [S(z) x S(-z)] B(theta, 0)
        r = np.arcsinh(-s/2)
        theta = 0.5*np.arctan2(-1/np.cosh(r), -np.tanh(r))
        Sz = block_diag(squeezing(r, 0), squeezing(-r, 0))[:, [0, 2, 1, 3]][[0, 2, 1, 3]]

        expected = beamsplitter(theta+np.pi/2, 0) @ Sz @ beamsplitter(theta, 0)
        assert S == pytest.approx(expected, abs=tol)

        # test that S[x1, x2, p1, p2] -> [x1, x2+sx1, p1-sp2, p2]
        x1 = 0.5432
        x2 = -0.453
        p1 = 0.154
        p2 = -0.123
        out = S @ np.array([x1, x2, p1, p2])*np.sqrt(2*hbar)
        expected = np.array([x1, x2+s*x1, p1-s*p2, p2])*np.sqrt(2*hbar)
        assert out == pytest.approx(expected, abs=tol) 

# 需要導入模塊: from scipy import linalg [as 別名]
# 或者: from scipy.linalg import block_diag [as 別名]
def test_controlled_phase(self, tol):
        """Test the CZ symplectic transform."""

        s = 0.543
        S = controlled_phase(s)

        # test that S = R_2(pi/2) CX(s) R_2(pi/2)^\dagger
        R2 = block_diag(np.identity(2), rotation(np.pi/2))[:, [0, 2, 1, 3]][[0, 2, 1, 3]]
        expected = R2 @ controlled_addition(s) @ R2.conj().T
        assert S == pytest.approx(expected, abs=tol)

        # test that S[x1, x2, p1, p2] -> [x1, x2, p1+sx2, p2+sx1]
        x1 = 0.5432
        x2 = -0.453
        p1 = 0.154
        p2 = -0.123
        out = S @ np.array([x1, x2, p1, p2])*np.sqrt(2*hbar)
        expected = np.array([x1, x2, p1+s*x2, p2+s*x1])*np.sqrt(2*hbar)
        assert out == pytest.approx(expected, abs=tol) 

# 需要導入模塊: from scipy import linalg [as 別名]
# 或者: from scipy.linalg import block_diag [as 別名]
def Sa(self, x_surface, geom):
        """Covariance of prior distribution, calculated at state x. We find
        the covariance in a normalized space (normalizing by z) and then un-
        normalize the result for the calling function."""

        lamb = self.calc_lamb(x_surface, geom)
        lamb_ref = lamb[self.idx_ref]
        ci = self.component(x_surface, geom)
        Cov = self.components[ci][1]
        Cov = Cov * (self.norm(lamb_ref)**2)

        # If there are no other state vector elements, we're done.
        if len(self.statevec_names) == len(self.idx_lamb):
            return Cov

        # Embed into a larger state vector covariance matrix
        nprefix = self.idx_lamb[0]
        nsuffix = len(self.statevec_names) - self.idx_lamb[-1] - 1
        Cov_prefix = np.zeros((nprefix, nprefix))
        Cov_suffix = np.zeros((nsuffix, nsuffix))
        return block_diag(Cov_prefix, Cov, Cov_suffix)