Python numpy.outer() 使用实例

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Example 1

def treegauss_remove_row(
        data_row,
        tree_grid,
        latent_row,
        vert_ss,
        edge_ss,
        feat_ss, ):
    # Update sufficient statistics.
    for v in range(latent_row.shape[0]):
        z = latent_row[v, :]
        vert_ss[v, :, :] -= np.outer(z, z)
    for e in range(tree_grid.shape[1]):
        z1 = latent_row[tree_grid[1, e], :]
        z2 = latent_row[tree_grid[2, e], :]
        edge_ss[e, :, :] -= np.outer(z1, z2)
    for v, x in enumerate(data_row):
        if np.isnan(x):
            continue
        z = latent_row[v, :]
        feat_ss[v] -= 1
        feat_ss[v, 1] -= x
        feat_ss[v, 2:] -= x * z  # TODO Use central covariance. 

Example 2

def getTrainTestKernel(self, params, Xtest):
		self.checkParams(params)
		ell = np.exp(params[0])
		p = np.exp(params[1])
		
		Xtest_scaled = Xtest/np.sqrt(Xtest.shape[1])
		d2 = sq_dist(self.X_scaled.T/ell, Xtest_scaled.T/ell)	#precompute squared distances
		
		#compute dp
		dp = np.zeros(d2.shape)
		for d in xrange(self.X_scaled.shape[1]):
			dp += (np.outer(self.X_scaled[:,d], np.ones((1, Xtest_scaled.shape[0]))) - np.outer(np.ones((self.X_scaled.shape[0], 1)), Xtest_scaled[:,d]))
		dp /= p
				
		K = np.exp(-d2 / 2.0)
		return np.cos(2*np.pi*dp)*K 

Example 3

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 

Example 4

def unscentedTransform(X, Wm, Wc, f):
    Y = None
    Ymean = None
    fdim = None
    N = np.shape(X)[1]
    for j in range(0,N):
        fImage = f(X[:,j])
        if Y is None:
            fdim = np.size(fImage)
            Y = np.zeros((fdim, np.shape(X)[1]))
            Ymean = np.zeros(fdim)
        Y[:,j] = fImage
        Ymean += Wm[j] * Y[:,j]
    Ycov = np.zeros((fdim, fdim))
    for j in range(0, N):
        meanAdjustedYj = Y[:,j] - Ymean
        Ycov += np.outer(Wc[j] * meanAdjustedYj, meanAdjustedYj)
    return Y, Ymean, Ycov 

Example 5

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 

Example 6

def estimate_params(self, ess):
        """
        Estimate  Nomal param,
        given expecteed sufficient stats
        """
        n = len(ess)
        mu = np.asarray([0,0])
        for (m, c) in ess:
            mu = mu + m
        mu = mu * 1.0 / n

        C = np.asarray([[0,0],[0,0]])
        for (m, c) in ess:
            C = C + c

        C = C * 1.0 / n
        
        C = C - np.outer(mu, mu)

        if not self.full_cov:
            C = reduce_cov(C)

        return (mu, C) 

Example 7

def compute_pvalues_for_processes(self,U_matrix,chane_prob, num_bootstrapped_stats=100):
        N = U_matrix.shape[0]
        bootsraped_stats = np.zeros(num_bootstrapped_stats)

        # orsetinW = simulate(N,num_bootstrapped_stats,corr)

        for proc in range(num_bootstrapped_stats):
            # W = np.sign(orsetinW[:,proc])
            W = simulatepm(N,chane_prob)
            WW = np.outer(W, W)
            st = np.mean(U_matrix * WW)
            bootsraped_stats[proc] = N * st

        stat = N*np.mean(U_matrix)

        return float(np.sum(bootsraped_stats > stat)) / num_bootstrapped_stats 

Example 8

def genSphCoords():
    """ Generates cartesian (x,y,z) and spherical (theta, phi) coordinates of a sphere
    Returns
    -------
    coords : named tuple
        holds cartesian (x,y,z) and spherical (theta, phi) coordinates
    """
    coords = namedtuple('coords', ['x', 'y', 'z', 'az', 'el'])
    az = _np.linspace(0, 2 * _np.pi, 360)
    el = _np.linspace(0, _np.pi, 181)
    coords.x = _np.outer(_np.cos(az), _np.sin(el))
    coords.y = _np.outer(_np.sin(az), _np.sin(el))
    coords.z = _np.outer(_np.ones(360), _np.cos(el))

    coords.el, coords.az = _np.meshgrid(_np.linspace(0, _np.pi, 181),
                                        _np.linspace(0, 2 * _np.pi, 360))
    return coords 

Example 9

def _eig_local_op_mps(lv, ltens, rv):
    """Local operator contribution from an MPS"""
    # MPS 1 / ltens: Interpreted as |psiXpsi| part of the operator
    # MPS 2: The current eigvectector candidate
    op = lv.T
    # op axes: 0 mps2 bond, 1: mps1 bond
    s = op.shape
    op = op.reshape((s[0], 1, s[1]))
    # op axes: 0 mps2 bond, 1: physical legs, 2: mps1 bond
    for lt in ltens:
        # op axes: 0: mps2 bond, 1: physical legs, 2: mps1 bond
        op = np.tensordot(op, lt.conj(), axes=(2, 0))
        # op axes: 0: mps2 bond, 1, 2: physical legs, 3: mps1 bond
        s = op.shape
        op = op.reshape((s[0], -1, s[3]))
        # op axes: 0: mps2 bond, 1: physical legs, 2: mps1 bond
    op = np.tensordot(op, rv, axes=(2, 0))
    # op axes: 0: mps2 bond, 1: physical legs, 2: mps2 bond
    op = np.outer(op.conj(), op)
    # op axes:
    # 0: (0a: left cc mps2 bond, 0b: physical row leg, 0c: right cc mps2 bond),
    # 1: (1a: left mps2 bond, 1b: physical column leg, 1c: right mps2 bond)
    return op 

Example 10

def test_mps_to_mpo(nr_sites, local_dim, rank, rgen):
    mps = factory.random_mps(nr_sites, local_dim, rank, randstate=rgen)
    # Instead of calling the two functions, we call mps_to_mpo(),
    # which does exactly that:
    #   mps_as_puri = mp.mps_as_local_purification_mps(mps)
    #   mpo = mp.pmps_to_mpo(mps_as_puri)
    mpo = mm.mps_to_mpo(mps)
    # This is also a test of mp.mps_as_local_purification_mps() in the
    # following sense: Local purifications are representations of
    # mixed states. Therefore, compare mps and mps_as_puri by
    # converting them to mixed states.
    state = mps.to_array()
    state = np.outer(state, state.conj())
    state.shape = (local_dim,) * (2 * nr_sites)
    state2 = mpo.to_array_global()
    assert_array_almost_equal(state, state2) 

Example 11

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 

Example 12

def vol(self):
        """Construct cell volumes of the 3D model as 1d array."""
        if getattr(self, '_vol', None) is None:
            vh = self.h
            # Compute cell volumes
            if self.dim == 1:
                self._vol = utils.mkvc(vh[0])
            elif self.dim == 2:
                # Cell sizes in each direction
                self._vol = utils.mkvc(np.outer(vh[0], vh[1]))
            elif self.dim == 3:
                # Cell sizes in each direction
                self._vol = utils.mkvc(
                    np.outer(utils.mkvc(np.outer(vh[0], vh[1])), vh[2])
                )
        return self._vol 

Example 13

def test_minimummaximum_func(self):
        a = np.ones((2, 2))
        aminimum = minimum(a, a)
        self.assertTrue(isinstance(aminimum, MaskedArray))
        assert_equal(aminimum, np.minimum(a, a))

        aminimum = minimum.outer(a, a)
        self.assertTrue(isinstance(aminimum, MaskedArray))
        assert_equal(aminimum, np.minimum.outer(a, a))

        amaximum = maximum(a, a)
        self.assertTrue(isinstance(amaximum, MaskedArray))
        assert_equal(amaximum, np.maximum(a, a))

        amaximum = maximum.outer(a, a)
        self.assertTrue(isinstance(amaximum, MaskedArray))
        assert_equal(amaximum, np.maximum.outer(a, a)) 

Example 14

def test_TakeTransposeInnerOuter(self):
        # Test of take, transpose, inner, outer products
        x = arange(24)
        y = np.arange(24)
        x[5:6] = masked
        x = x.reshape(2, 3, 4)
        y = y.reshape(2, 3, 4)
        assert_equal(np.transpose(y, (2, 0, 1)), transpose(x, (2, 0, 1)))
        assert_equal(np.take(y, (2, 0, 1), 1), take(x, (2, 0, 1), 1))
        assert_equal(np.inner(filled(x, 0), filled(y, 0)),
                     inner(x, y))
        assert_equal(np.outer(filled(x, 0), filled(y, 0)),
                     outer(x, y))
        y = array(['abc', 1, 'def', 2, 3], object)
        y[2] = masked
        t = take(y, [0, 3, 4])
        assert_(t[0] == 'abc')
        assert_(t[1] == 2)
        assert_(t[2] == 3) 

Example 15

def test_testTakeTransposeInnerOuter(self):
        # Test of take, transpose, inner, outer products
        x = arange(24)
        y = np.arange(24)
        x[5:6] = masked
        x = x.reshape(2, 3, 4)
        y = y.reshape(2, 3, 4)
        assert_(eq(np.transpose(y, (2, 0, 1)), transpose(x, (2, 0, 1))))
        assert_(eq(np.take(y, (2, 0, 1), 1), take(x, (2, 0, 1), 1)))
        assert_(eq(np.inner(filled(x, 0), filled(y, 0)),
                   inner(x, y)))
        assert_(eq(np.outer(filled(x, 0), filled(y, 0)),
                   outer(x, y)))
        y = array(['abc', 1, 'def', 2, 3], object)
        y[2] = masked
        t = take(y, [0, 3, 4])
        assert_(t[0] == 'abc')
        assert_(t[1] == 2)
        assert_(t[2] == 3) 

Example 16

def test_4(self):
        """
        Test of take, transpose, inner, outer products.

        """
        x = self.arange(24)
        y = np.arange(24)
        x[5:6] = self.masked
        x = x.reshape(2, 3, 4)
        y = y.reshape(2, 3, 4)
        assert self.allequal(np.transpose(y, (2, 0, 1)), self.transpose(x, (2, 0, 1)))
        assert self.allequal(np.take(y, (2, 0, 1), 1), self.take(x, (2, 0, 1), 1))
        assert self.allequal(np.inner(self.filled(x, 0), self.filled(y, 0)),
                            self.inner(x, y))
        assert self.allequal(np.outer(self.filled(x, 0), self.filled(y, 0)),
                            self.outer(x, y))
        y = self.array(['abc', 1, 'def', 2, 3], object)
        y[2] = self.masked
        t = self.take(y, [0, 3, 4])
        assert t[0] == 'abc'
        assert t[1] == 2
        assert t[2] == 3 

Example 17

def outer(self, a, b):
        """
        Return the function applied to the outer product of a and b.

        """
        (da, db) = (getdata(a), getdata(b))
        d = self.f.outer(da, db)
        ma = getmask(a)
        mb = getmask(b)
        if ma is nomask and mb is nomask:
            m = nomask
        else:
            ma = getmaskarray(a)
            mb = getmaskarray(b)
            m = umath.logical_or.outer(ma, mb)
        if (not m.ndim) and m:
            return masked
        if m is not nomask:
            np.copyto(d, da, where=m)
        if not d.shape:
            return d
        masked_d = d.view(get_masked_subclass(a, b))
        masked_d._mask = m
        return masked_d 

Example 18

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 

Example 19

def update_kl_loss(p, lambdas, T, Cs):
    """
    Updates C according to the KL Loss kernel with the S Ts couplings calculated at each iteration


    Parameters
    ----------
    p  : ndarray, shape (N,)
         weights in the targeted barycenter
    lambdas : list of the S spaces' weights
    T : list of S np.ndarray(ns,N)
        the S Ts couplings calculated at each iteration
    Cs : list of S ndarray, shape(ns,ns)
         Metric cost matrices

    Returns
    ----------
    C : ndarray, shape (ns,ns)
        updated C matrix
    """
    tmpsum = sum([lambdas[s] * np.dot(T[s].T, Cs[s]).dot(T[s])
                  for s in range(len(T))])
    ppt = np.outer(p, p)

    return np.exp(np.divide(tmpsum, ppt)) 

Example 20

def __init__(self, n):
        self.degree = 2*n - 2

        a, A = numpy.polynomial.legendre.leggauss(n)

        w = numpy.outer((1 + a) * A, A)
        x = numpy.outer(1-a, numpy.ones(n)) / 2
        y = numpy.outer(1+a, 1-a) / 4

        self.weights = w.reshape(-1) / 4
        self.points = numpy.stack([x.reshape(-1), y.reshape(-1)]).T

        self.bary = numpy.array([
            self.points[:, 0],
            self.points[:, 1],
            1 - numpy.sum(self.points, axis=1)
            ]).T
        return 

Example 21

def rotation_matrix(u, theta):
    '''Return matrix that implements the rotation around the vector :math:`u`
    by the angle :math:`\\theta`, cf.
    https://en.wikipedia.org/wiki/Rotation_matrix#Rotation_matrix_from_axis_and_angle.

    :param u: rotation vector
    :param theta: rotation angle
    '''
    # Cross-product matrix.
    cpm = numpy.array([[0.0,   -u[2],  u[1]],
                      [u[2],    0.0, -u[0]],
                      [-u[1],  u[0],  0.0]])
    c = numpy.cos(theta)
    s = numpy.sin(theta)
    R = numpy.eye(3) * c \
        + s * cpm \
        + (1.0 - c) * numpy.outer(u, u)
    return R 

Example 22

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 

Example 23

def test_basic(self):
        vecs = [[1, 2, 3],
                [2],
                np.array([1, 2, 3]).reshape(1, -1),
                np.array([1, 2, 3]).reshape(-1, 1)]

        num_ones_list = [4, 1]

        for vec in vecs:
            for num_ones in num_ones_list:

                A = OnesOuterVec(num_ones=num_ones, vec=vec)
                M = np.outer([1]*num_ones, vec)

                V, v1, v2, U, u1, u2 = get_tst_mats(M.shape)

                assert_allclose(A.dot(V), M.dot(V))
                assert_allclose(A.dot(v1), M.dot(v1))
                assert_allclose(A.dot(v2), M.dot(v2))

                assert_allclose(A.T.dot(U), M.T.dot(U))
                assert_allclose(A.T.dot(u1), M.T.dot(u1))
                assert_allclose(A.T.dot(u2), M.T.dot(u2)) 

Example 24

def test_basic(self):

        shapes = [(50, 20), (1, 20), (50, 1)]

        # sparse
        for shape in shapes:
            mats = self.get_Xs(shape)

            m = mats[0].mean(axis=0).A1
            ones = np.ones(shape[0])
            M = mats[0].toarray() - np.outer(ones, m)

            for X in mats:

                A = col_mean_centered(X)

                V, v1, v2, U, u1, u2 = get_tst_mats(M.shape)

                assert_almost_equal(A.dot(V), M.dot(V))
                assert_almost_equal(A.dot(v1), M.dot(v1))
                assert_almost_equal(A.dot(v2), M.dot(v2))

                assert_almost_equal(A.T.dot(U), M.T.dot(U))
                assert_almost_equal(A.T.dot(u1), M.T.dot(u1))
                assert_almost_equal(A.T.dot(u2), M.T.dot(u2)) 

Example 25

def rotation_matrix(axis, angle):
    """
    Calculate a three dimensional rotation matrix for a rotation around
    the given angle and axis.

    @type axis: (3,) numpy array
    @param angle: angle in radians
    @type angle: float

    @rtype: (3,3) numpy.array
    """
    axis = numpy.asfarray(axis) / norm(axis)
    assert axis.shape == (3,)

    c = math.cos(angle)
    s = math.sin(angle)

    r = (1.0 - c) * numpy.outer(axis, axis)
    r.flat[[0,4,8]] += c
    r.flat[[5,6,1]] += s * axis
    r.flat[[7,2,3]] -= s * axis

    return r 

Example 26

def gower_matrix(X):
    """
    Gower, J.C. (1966). Some distance properties of latent root
    and vector methods used in multivariate analysis.
    Biometrika 53: 325-338

    @param X: ensemble coordinates
    @type X: (m,n,k) numpy.array

    @return: symmetric dissimilarity matrix
    @rtype: (n,n) numpy.array
    """
    X = numpy.asarray(X)

    B = sum(numpy.dot(x, x.T) for x in X) / float(len(X))
    b = B.mean(1)
    bb = b.mean()

    return (B - numpy.add.outer(b, b)) + bb 

Example 27

def nextfastpower(n):
    """Return the next integral power of small factors greater than the given
    number.  Specifically, return m such that
        m >= n
        m == 2**x * 3**y * 5**z
    where x, y, and z are integers.
    This is useful for ensuring fast FFT sizes.

    From https://gist.github.com/bhawkins/4479607 (Brian Hawkins)
    """
    if n < 7:
        return max (n, 1)
    # x, y, and z are all bounded from above by the formula of nextpower.
    # Compute all possible combinations for powers of 3 and 5.
    # (Not too many for reasonable FFT sizes.)
    def power_series (x, base):
        nmax = ceil (log (x) / log (base))
        return np.logspace (0.0, nmax, num=nmax+1, base=base)
    n35 = np.outer (power_series (n, 3.0), power_series (n, 5.0))
    n35 = n35[n35<=n]
    # Lump the powers of 3 and 5 together and solve for the powers of 2.
    n2 = nextpower (n / n35)
    return int (min (n2 * n35)) 

Example 28

def ests_ll_quad(self, params):
        """
        Calculate the loglikelihood given model parameters `params`.

        This method uses Gaussian quadrature, and thus returns an *approximate*
        integral.
        """
        mu0, gamma0, err0 = np.split(params, 3)
        x = np.tile(self.z, (self.cfg.QCOUNT, 1, 1))  # (QCOUNTXnhospXnmeas)
        loc = mu0 + np.outer(QC1, gamma0)
        loc = np.tile(loc, (self.n, 1, 1))
        loc = np.transpose(loc, (1, 0, 2))
        scale = np.tile(err0, (self.cfg.QCOUNT, self.n, 1))
        zs = lpdf_3d(x=x, loc=loc, scale=scale)

        w2 = np.tile(self.w, (self.cfg.QCOUNT, 1, 1))
        wted = np.nansum(w2 * zs, axis=2).T  # (nhosp X QCOUNT)
        qh = np.tile(QC1, (self.n, 1))  # (nhosp X QCOUNT)
        combined = wted + norm.logpdf(qh)  # (nhosp X QCOUNT)

        return logsumexp(np.nan_to_num(combined), b=QC2, axis=1)  # (nhosp) 

Example 29

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 

Example 30

def forward_prop_random_thru_post_mm(self, model, mx, vx, mu, Su):
        Kuu_noiseless = compute_kernel(
            2 * model.ls, 2 * model.sf, model.zu, model.zu)
        Kuu = Kuu_noiseless + np.diag(jitter * np.ones((self.M, )))
        # TODO: remove inv
        Kuuinv = np.linalg.inv(Kuu)
        A = np.dot(Kuuinv, mu)
        Smm = Su + np.outer(mu, mu)
        B_sto = np.dot(Kuuinv, np.dot(Smm, Kuuinv)) - Kuuinv
        psi0 = np.exp(2.0 * model.sf)
        psi1, psi2 = compute_psi_weave(
            2 * model.ls, 2 * model.sf, mx, vx, model.zu)
        mout = np.einsum('nm,md->nd', psi1, A)
        Bpsi2 = np.einsum('ab,nab->n', B_sto, psi2)[:, np.newaxis]
        vout = psi0 + Bpsi2 - mout**2
        return mout, vout 

Example 31

def score(self, y):
        groups = numpy.unique(y)
        a = len(groups)
        Ntx = len(y)
        self.a_ = a
        self.Ntx_ = Ntx
        self._SST = (self.pairs_**2).sum() / (2 * Ntx)
        pattern = numpy.zeros((Ntx, Ntx))
        for g in groups:
            pattern += numpy.outer(y == g, y == g) / \
                (numpy.float(numpy.sum(y == g)))

        self._SSW = ((self.pairs_**2) * (pattern)).sum() / 2

        self._SSA = self._SST - self._SSW

        self._F = (self._SSA / (a - 1)) / (self._SSW / (Ntx - a))

        return self._F
####################################################################### 

Example 32

def outer(v1, v2=None):
    """
    Construct the outer product of two vectors.

    The second vector argument is optional, if absent the projector
    of the first vector will be returned.

    Args:
        v1 (ndarray): the first vector.
        v2 (ndarray): the (optional) second vector.

    Returns:
        The matrix |v1><v2|.

    """
    if v2 is None:
        u = np.array(v1).conj()
    else:
        u = np.array(v2).conj()
    return np.outer(v1, u)


###############################################################
# Measures.
############################################################### 

Example 33

def concurrence(state):
    """Calculate the concurrence.

    Args:
        state (np.array): a quantum state
    Returns:
        concurrence.
    """
    rho = np.array(state)
    if rho.ndim == 1:
        rho = outer(state)
    if len(state) != 4:
        raise Exception("Concurence is not defined for more than two qubits")

    YY = np.fliplr(np.diag([-1, 1, 1, -1]))
    A = rho.dot(YY).dot(rho.conj()).dot(YY)
    w = la.eigh(A, eigvals_only=True)
    w = np.sqrt(np.maximum(w, 0))
    return max(0.0, w[-1]-np.sum(w[0:-1]))


###############################################################
# Other.
############################################################### 

Example 34

def _get_Smatrices(self, X, y):

        Sb = np.zeros((X.shape[1], X.shape[1]))

        S = np.inner(X.T, X.T)
        N = len(X)
        mu = np.mean(X, axis=0)
        classLabels = np.unique(y)
        for label in classLabels:
            classIdx = np.argwhere(y == label).T[0]
            Nl = len(classIdx)
            xL = X[classIdx]
            muL = np.mean(xL, axis=0)
            muLbar = muL - mu
            Sb = Sb + Nl * np.outer(muLbar, muLbar)

        Sbar = S - N * np.outer(mu, mu)
        Sw = Sbar - Sb
        self.mean_ = mu

        return (Sw, Sb) 

Example 35

def FOBI(X):
	"""Fourth Order Blind Identification technique is used.
	The function returns the unmixing matrix.
	X is assumed to be centered and whitened.
	The paper by J. Cardaso is in itself the best resource out there for it.
	SOURCE SEPARATION USING HIGHER ORDER MOMENTS - Jean-Francois Cardoso"""	

	rows = X.shape[0]
	n = X.shape[1]
	# Initializing the weighted covariance matrix which will hold the fourth order information
	weightedCovMatrix = np.zeros([rows, rows]) 

	# Approximating the expectation by diving with the number of data points
	for signal in X.T:
		norm = np.linalg.norm(signal)
		weightedCovMatrix += norm*norm*np.outer(signal, signal)

	weightedCovMatrix /= n

	# Doing the eigen value decomposition
	eigValue, eigVector = np.linalg.eigh(weightedCovMatrix)

	# print eigVector
	return eigVector 

Example 36

def ksvd(Y, D, X, n_cycles=1, verbose=True):
    n_atoms = D.shape[1]
    n_features, n_samples = Y.shape
    unused_atoms = []
    R = Y - fast_dot(D, X)

    for c in range(n_cycles):
        for k in range(n_atoms):
            if verbose:
                sys.stdout.write("\r" + "k-svd..." + ":%3.2f%%" % ((k / float(n_atoms)) * 100))
                sys.stdout.flush()
            # find all the datapoints that use the kth atom
            omega_k = X[k, :] != 0
            if not np.any(omega_k):
                unused_atoms.append(k)
                continue
            # the residual due to all the other atoms but k
            Rk = R[:, omega_k] + np.outer(D[:, k], X[k, omega_k])
            U, S, V = randomized_svd(Rk, n_components=1, n_iter=10, flip_sign=False)
            D[:, k] = U[:, 0]
            X[k, omega_k] = V[0, :] * S[0]
            # update the residual
            R[:, omega_k] = Rk - np.outer(D[:, k], X[k, omega_k])
        print ""
    return D, X, unused_atoms 

Example 37

def test_minimummaximum_func(self):
        a = np.ones((2, 2))
        aminimum = minimum(a, a)
        self.assertTrue(isinstance(aminimum, MaskedArray))
        assert_equal(aminimum, np.minimum(a, a))

        aminimum = minimum.outer(a, a)
        self.assertTrue(isinstance(aminimum, MaskedArray))
        assert_equal(aminimum, np.minimum.outer(a, a))

        amaximum = maximum(a, a)
        self.assertTrue(isinstance(amaximum, MaskedArray))
        assert_equal(amaximum, np.maximum(a, a))

        amaximum = maximum.outer(a, a)
        self.assertTrue(isinstance(amaximum, MaskedArray))
        assert_equal(amaximum, np.maximum.outer(a, a)) 

Example 38

def test_TakeTransposeInnerOuter(self):
        # Test of take, transpose, inner, outer products
        x = arange(24)
        y = np.arange(24)
        x[5:6] = masked
        x = x.reshape(2, 3, 4)
        y = y.reshape(2, 3, 4)
        assert_equal(np.transpose(y, (2, 0, 1)), transpose(x, (2, 0, 1)))
        assert_equal(np.take(y, (2, 0, 1), 1), take(x, (2, 0, 1), 1))
        assert_equal(np.inner(filled(x, 0), filled(y, 0)),
                     inner(x, y))
        assert_equal(np.outer(filled(x, 0), filled(y, 0)),
                     outer(x, y))
        y = array(['abc', 1, 'def', 2, 3], object)
        y[2] = masked
        t = take(y, [0, 3, 4])
        assert_(t[0] == 'abc')
        assert_(t[1] == 2)
        assert_(t[2] == 3) 

Example 39

def test_testTakeTransposeInnerOuter(self):
        # Test of take, transpose, inner, outer products
        x = arange(24)
        y = np.arange(24)
        x[5:6] = masked
        x = x.reshape(2, 3, 4)
        y = y.reshape(2, 3, 4)
        assert_(eq(np.transpose(y, (2, 0, 1)), transpose(x, (2, 0, 1))))
        assert_(eq(np.take(y, (2, 0, 1), 1), take(x, (2, 0, 1), 1)))
        assert_(eq(np.inner(filled(x, 0), filled(y, 0)),
                   inner(x, y)))
        assert_(eq(np.outer(filled(x, 0), filled(y, 0)),
                   outer(x, y)))
        y = array(['abc', 1, 'def', 2, 3], object)
        y[2] = masked
        t = take(y, [0, 3, 4])
        assert_(t[0] == 'abc')
        assert_(t[1] == 2)
        assert_(t[2] == 3) 

Example 40

def test_4(self):
        """
        Test of take, transpose, inner, outer products.

        """
        x = self.arange(24)
        y = np.arange(24)
        x[5:6] = self.masked
        x = x.reshape(2, 3, 4)
        y = y.reshape(2, 3, 4)
        assert self.allequal(np.transpose(y, (2, 0, 1)), self.transpose(x, (2, 0, 1)))
        assert self.allequal(np.take(y, (2, 0, 1), 1), self.take(x, (2, 0, 1), 1))
        assert self.allequal(np.inner(self.filled(x, 0), self.filled(y, 0)),
                            self.inner(x, y))
        assert self.allequal(np.outer(self.filled(x, 0), self.filled(y, 0)),
                            self.outer(x, y))
        y = self.array(['abc', 1, 'def', 2, 3], object)
        y[2] = self.masked
        t = self.take(y, [0, 3, 4])
        assert t[0] == 'abc'
        assert t[1] == 2
        assert t[2] == 3 

Example 41

def outer(self, a, b):
        """
        Return the function applied to the outer product of a and b.

        """
        (da, db) = (getdata(a), getdata(b))
        d = self.f.outer(da, db)
        ma = getmask(a)
        mb = getmask(b)
        if ma is nomask and mb is nomask:
            m = nomask
        else:
            ma = getmaskarray(a)
            mb = getmaskarray(b)
            m = umath.logical_or.outer(ma, mb)
        if (not m.ndim) and m:
            return masked
        if m is not nomask:
            np.copyto(d, da, where=m)
        if not d.shape:
            return d
        masked_d = d.view(get_masked_subclass(a, b))
        masked_d._mask = m
        return masked_d 

Example 42

def direct_ionization_rate(self):
        """
        Calculate direct ionization rate in cm3/s
        
        Needs an equation reference or explanation
        """
        xgl, wgl = np.polynomial.laguerre.laggauss(12)
        kBT = const.k_B.cgs*self.temperature
        energy = np.outer(xgl, kBT)*kBT.unit + self.ip
        cross_section = self.direct_ionization_cross_section(energy)
        if cross_section is None:
            return None
        term1 = np.sqrt(8./np.pi/const.m_e.cgs)*np.sqrt(kBT)*np.exp(-self.ip/kBT)
        term2 = ((wgl*xgl)[:,np.newaxis]*cross_section).sum(axis=0)
        term3 = (wgl[:,np.newaxis]*cross_section).sum(axis=0)*self.ip/kBT
        
        return term1*(term2 + term3) 

Example 43

def treegauss_add_row(
        data_row,
        tree_grid,
        program,
        latent_row,
        vert_ss,
        edge_ss,
        feat_ss, ):
    # Sample latent state using dynamic programming.
    TODO('https://github.com/posterior/treecat/issues/26')

    # Update sufficient statistics.
    for v in range(latent_row.shape[0]):
        z = latent_row[v, :]
        vert_ss[v, :, :] += np.outer(z, z)
    for e in range(tree_grid.shape[1]):
        z1 = latent_row[tree_grid[1, e], :]
        z2 = latent_row[tree_grid[2, e], :]
        edge_ss[e, :, :] += np.outer(z1, z2)
    for v, x in enumerate(data_row):
        if np.isnan(x):
            continue
        z = latent_row[v, :]
        feat_ss[v] += 1
        feat_ss[v, 1] += x
        feat_ss[v, 2:] += x * z  # TODO Use central covariance. 

Example 44

def __init__(self, X):
		Kernel.__init__(self)
		self.X_scaled = X/np.sqrt(X.shape[1])
		if (X.shape[1] >= X.shape[0] or True): self.K_sq = sq_dist(self.X_scaled.T)
		else: self.K_sq = None
		
		#compute dp
		self.dp = np.zeros((X.shape[0], X.shape[0]))
		for d in xrange(self.X_scaled.shape[1]):
			self.dp += (np.outer(self.X_scaled[:,d], np.ones((1, self.X_scaled.shape[0]))) - np.outer(np.ones((self.X_scaled.shape[0], 1)), self.X_scaled[:,d])) 

Example 45

def deriveKernel(self, params, i):
		self.checkParamsI(params, i)
		
		#find the relevant W
		numSNPs = self.X_scaled.shape[1]
		unitNum = i / numSNPs
		weightNum = i % numSNPs
		
		nnX_unitNum = self.applyNN(self.X_scaled, params, unitNum) / float(self.numUnits)
		w_deriv_relu = self.X_scaled[:, weightNum].copy()
		w_deriv_relu[nnX_unitNum <= 0] = 0
		
		K_deriv1 = np.outer(nnX_unitNum, w_deriv_relu)
		K_deriv = K_deriv1 + K_deriv1.T
		return K_deriv 

Example 46

def getTrainKernel(self, params):
		self.checkParams(params)
		if (self.sameParams(params)): return self.cache['getTrainKernel']				
		ell2 = np.exp(2*params[0])
		
		sqrt_ell2PSx = np.sqrt(ell2+self.sx)
		K = self.S / np.outer(sqrt_ell2PSx, sqrt_ell2PSx)
		self.cache['K'] = K
		K_arcsin = np.arcsin(K)
		
		self.cache['getTrainKernel'] = K_arcsin
		self.saveParams(params)
		return K_arcsin 

Example 47

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 

Example 48

def scale_matrix(factor, origin=None, direction=None):
    """Return matrix to scale by factor around origin in direction.

    Use factor -1 for point symmetry.

    >>> v = (numpy.random.rand(4, 5) - 0.5) * 20.0
    >>> v[3] = 1.0
    >>> S = scale_matrix(-1.234)
    >>> numpy.allclose(numpy.dot(S, v)[:3], -1.234*v[:3])
    True
    >>> factor = random.random() * 10 - 5
    >>> origin = numpy.random.random(3) - 0.5
    >>> direct = numpy.random.random(3) - 0.5
    >>> S = scale_matrix(factor, origin)
    >>> S = scale_matrix(factor, origin, direct)

    """
    if direction is None:
        # uniform scaling
        M = numpy.array(((factor, 0.0,    0.0,    0.0),
                         (0.0,    factor, 0.0,    0.0),
                         (0.0,    0.0,    factor, 0.0),
                         (0.0,    0.0,    0.0,    1.0)), dtype=numpy.float64)
        if origin is not None:
            M[:3, 3] = origin[:3]
            M[:3, 3] *= 1.0 - factor
    else:
        # nonuniform scaling
        direction = unit_vector(direction[:3])
        factor = 1.0 - factor
        M = numpy.identity(4)
        M[:3, :3] -= factor * numpy.outer(direction, direction)
        if origin is not None:
            M[:3, 3] = (factor * numpy.dot(origin[:3], direction)) * direction
    return M 

Example 49

def shear_matrix(angle, direction, point, normal):
    """Return matrix to shear by angle along direction vector on shear plane.

    The shear plane is defined by a point and normal vector. The direction
    vector must be orthogonal to the plane's normal vector.

    A point P is transformed by the shear matrix into P" such that
    the vector P-P" is parallel to the direction vector and its extent is
    given by the angle of P-P'-P", where P' is the orthogonal projection
    of P onto the shear plane.

    >>> angle = (random.random() - 0.5) * 4*math.pi
    >>> direct = numpy.random.random(3) - 0.5
    >>> point = numpy.random.random(3) - 0.5
    >>> normal = numpy.cross(direct, numpy.random.random(3))
    >>> S = shear_matrix(angle, direct, point, normal)
    >>> numpy.allclose(1.0, numpy.linalg.det(S))
    True

    """
    normal = unit_vector(normal[:3])
    direction = unit_vector(direction[:3])
    if abs(numpy.dot(normal, direction)) > 1e-6:
        raise ValueError("direction and normal vectors are not orthogonal")
    angle = math.tan(angle)
    M = numpy.identity(4)
    M[:3, :3] += angle * numpy.outer(direction, normal)
    M[:3, 3] = -angle * numpy.dot(point[:3], normal) * direction
    return M 

Example 50

def multiply_C(self, factor):
        """multiply ``self.C`` with ``factor`` updating internal states.

        ``factor`` can be a scalar, a vector or a matrix. The vector
        is used as outer product and multiplied element-wise, i.e.,
        ``multiply_C(diag(C)**-0.5)`` generates a correlation matrix.

        Details:
        """
        self._updateC()
        if np.isscalar(factor):
            self.C *= factor
            self.D *= factor**0.5
            try:
                self.inverse_root_C /= factor**0.5
            except AttributeError:
                pass
        elif len(np.asarray(factor).shape) == 1:
            self.C *= np.outer(factor, factor)
            self._decompose_C()
        elif len(factor.shape) == 2:
            self.C *= factor
            self._decompose_C()
        else:
            raise ValueError(str(factor))
        # raise NotImplementedError('never tested') 
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