Python numpy.linalg.eig() Examples

def _get_top_eigen_vectors(data: ndarray, n_components: int) -> ndarray:
        """The eigen vectors according to top n_components large eigen values.

        Arguments:
            data {ndarray} -- Training data.
            n_components {int} -- Number of components to keep.

        Returns:
            ndarray -- eigen vectors with shape(n_cols, n_components).
        """

        # Calculate eigen values and eigen vectors of covariance matrix.
        eigen_values, eigen_vectors = eig(data)
        # The indexes of top n_components large eigen values.
        _indexes = heapq.nlargest(n_components, enumerate(eigen_values),
                                  key=lambda x: x[1])
        indexes = [x[0] for x in _indexes]
        return eigen_vectors[:, indexes] 

def test_0_size(self):
        # Check that all kinds of 0-sized arrays work
        class ArraySubclass(np.ndarray):
            pass
        a = np.zeros((0, 1, 1), dtype=np.int_).view(ArraySubclass)
        res, res_v = linalg.eig(a)
        assert_(res_v.dtype.type is np.float64)
        assert_(res.dtype.type is np.float64)
        assert_equal(a.shape, res_v.shape)
        assert_equal((0, 1), res.shape)
        # This is just for documentation, it might make sense to change:
        assert_(isinstance(a, np.ndarray))

        a = np.zeros((0, 0), dtype=np.complex64).view(ArraySubclass)
        res, res_v = linalg.eig(a)
        assert_(res_v.dtype.type is np.complex64)
        assert_(res.dtype.type is np.complex64)
        assert_equal(a.shape, res_v.shape)
        assert_equal((0,), res.shape)
        # This is just for documentation, it might make sense to change:
        assert_(isinstance(a, np.ndarray)) 

def test_0_size(self):
        # Check that all kinds of 0-sized arrays work
        class ArraySubclass(np.ndarray):
            pass
        a = np.zeros((0, 1, 1), dtype=np.int_).view(ArraySubclass)
        res, res_v = linalg.eig(a)
        assert_(res_v.dtype.type is np.float64)
        assert_(res.dtype.type is np.float64)
        assert_equal(a.shape, res_v.shape)
        assert_equal((0, 1), res.shape)
        # This is just for documentation, it might make sense to change:
        assert_(isinstance(a, np.ndarray))

        a = np.zeros((0, 0), dtype=np.complex64).view(ArraySubclass)
        res, res_v = linalg.eig(a)
        assert_(res_v.dtype.type is np.complex64)
        assert_(res.dtype.type is np.complex64)
        assert_equal(a.shape, res_v.shape)
        assert_equal((0,), res.shape)
        # This is just for documentation, it might make sense to change:
        assert_(isinstance(a, np.ndarray)) 

def do(self, a, b):
        # note that eigenvalue arrays must be sorted since
        # their order isn't guaranteed.
        ev, evc = linalg.eigh(a)
        evalues, evectors = linalg.eig(a)
        ev.sort(axis=-1)
        evalues.sort(axis=-1)
        assert_almost_equal(ev, evalues)

        assert_allclose(dot_generalized(a, evc),
                        np.asarray(ev)[...,None,:] * np.asarray(evc),
                        rtol=get_rtol(ev.dtype))

        ev2, evc2 = linalg.eigh(a, 'U')
        ev2.sort(axis=-1)
        assert_almost_equal(ev2, evalues)

        assert_allclose(dot_generalized(a, evc2),
                        np.asarray(ev2)[...,None,:] * np.asarray(evc2),
                        rtol=get_rtol(ev.dtype), err_msg=repr(a)) 

def getPrincipalAxes(self):
        X = self.VPos - self.getCentroid()
        XTX = (X.T).dot(X)
        (lambdas, axes) = linalg.eig(XTX)
        #Put the eigenvalues in decreasing order
        idx = lambdas.argsort()[::-1]
        lambdas = lambdas[idx]
        axes = axes[:, idx]
        T = X.dot(axes)
        maxProj = T.max(0)
        minProj = T.min(0)
        axes = axes.T #Put each axis on each row to be consistent with everything else
        return (axes, maxProj, minProj)        
    
    #Delete the parts of the mesh below "plane".  If fillHoles
    #is true, plug up the holes that result from the cut 

def test_eig_build(self):
        # Ticket #652
        rva = array([1.03221168e+02 + 0.j,
                     -1.91843603e+01 + 0.j,
                     -6.04004526e-01 + 15.84422474j,
                     -6.04004526e-01 - 15.84422474j,
                     -1.13692929e+01 + 0.j,
                     -6.57612485e-01 + 10.41755503j,
                     -6.57612485e-01 - 10.41755503j,
                     1.82126812e+01 + 0.j,
                     1.06011014e+01 + 0.j,
                     7.80732773e+00 + 0.j,
                     -7.65390898e-01 + 0.j,
                     1.51971555e-15 + 0.j,
                     -1.51308713e-15 + 0.j])
        a = arange(13 * 13, dtype=float64)
        a.shape = (13, 13)
        a = a % 17
        va, ve = linalg.eig(a)
        va.sort()
        rva.sort()
        assert_array_almost_equal(va, rva) 

def spectral_radius(self):
        """Compute the spectral radius of the matrix of l1 norm of Hawkes
        kernels.

        Notes
        -----
        If the spectral radius is greater that 1, the hawkes process is not
        stable
        """

        get_norm = np.vectorize(lambda kernel: kernel.get_norm())
        norms = get_norm(self.kernels)

        # It might happens that eig returns a complex number but with a
        # negligible complex part, in this case we keep only the real part
        spectral_radius = max(eig(norms)[0])
        spectral_radius = np.real_if_close(spectral_radius)
        return spectral_radius 

def test_0_size(self):
        # Check that all kinds of 0-sized arrays work
        class ArraySubclass(np.ndarray):
            pass
        a = np.zeros((0, 1, 1), dtype=np.int_).view(ArraySubclass)
        res, res_v = linalg.eig(a)
        assert_(res_v.dtype.type is np.float64)
        assert_(res.dtype.type is np.float64)
        assert_equal(a.shape, res_v.shape)
        assert_equal((0, 1), res.shape)
        # This is just for documentation, it might make sense to change:
        assert_(isinstance(a, np.ndarray))

        a = np.zeros((0, 0), dtype=np.complex64).view(ArraySubclass)
        res, res_v = linalg.eig(a)
        assert_(res_v.dtype.type is np.complex64)
        assert_(res.dtype.type is np.complex64)
        assert_equal(a.shape, res_v.shape)
        assert_equal((0,), res.shape)
        # This is just for documentation, it might make sense to change:
        assert_(isinstance(a, np.ndarray)) 

def test_eig_build(self):
        # Ticket #652
        rva = array([1.03221168e+02 + 0.j,
                     -1.91843603e+01 + 0.j,
                     -6.04004526e-01 + 15.84422474j,
                     -6.04004526e-01 - 15.84422474j,
                     -1.13692929e+01 + 0.j,
                     -6.57612485e-01 + 10.41755503j,
                     -6.57612485e-01 - 10.41755503j,
                     1.82126812e+01 + 0.j,
                     1.06011014e+01 + 0.j,
                     7.80732773e+00 + 0.j,
                     -7.65390898e-01 + 0.j,
                     1.51971555e-15 + 0.j,
                     -1.51308713e-15 + 0.j])
        a = arange(13 * 13, dtype=float64)
        a.shape = (13, 13)
        a = a % 17
        va, ve = linalg.eig(a)
        va.sort()
        rva.sort()
        assert_array_almost_equal(va, rva) 

def _fit_ellipse_to_xy_points(x, y):
    """Fit an ellipse to a list of x and y points.

    Parameters
    ----------
    x, y : NumPy 2D array

    Returns
    -------
    ellipse_parameters : NumPy array

    """
    xx = x * x
    yy = y * y
    xy = x * y
    ones = np.ones_like(x)
    D = np.vstack((xx, xy, yy, x, y, ones))
    S = np.dot(D, D.T)
    C = np.zeros((6, 6))
    C[0, 2], C[2, 0] = 2, 2
    C[1, 1] = -1
    A, B = la.eig(np.dot(la.inv(S), C))
    i = np.argmax(np.abs(A))
    g = B[:, i]
    return g 

def test_eig_build(self, level=rlevel):
        # Ticket #652
        rva = array([1.03221168e+02 + 0.j,
                     -1.91843603e+01 + 0.j,
                     -6.04004526e-01 + 15.84422474j,
                     -6.04004526e-01 - 15.84422474j,
                     -1.13692929e+01 + 0.j,
                     -6.57612485e-01 + 10.41755503j,
                     -6.57612485e-01 - 10.41755503j,
                     1.82126812e+01 + 0.j,
                     1.06011014e+01 + 0.j,
                     7.80732773e+00 + 0.j,
                     -7.65390898e-01 + 0.j,
                     1.51971555e-15 + 0.j,
                     -1.51308713e-15 + 0.j])
        a = arange(13 * 13, dtype=float64)
        a.shape = (13, 13)
        a = a % 17
        va, ve = linalg.eig(a)
        va.sort()
        rva.sort()
        assert_array_almost_equal(va, rva) 

def do(self, a, b):
        # note that eigenvalue arrays returned by eig must be sorted since
        # their order isn't guaranteed.
        ev, evc = linalg.eigh(a)
        evalues, evectors = linalg.eig(a)
        evalues.sort(axis=-1)
        assert_almost_equal(ev, evalues)

        assert_allclose(dot_generalized(a, evc),
                        np.asarray(ev)[..., None, :] * np.asarray(evc),
                        rtol=get_rtol(ev.dtype))

        ev2, evc2 = linalg.eigh(a, 'U')
        assert_almost_equal(ev2, evalues)

        assert_allclose(dot_generalized(a, evc2),
                        np.asarray(ev2)[..., None, :] * np.asarray(evc2),
                        rtol=get_rtol(ev.dtype), err_msg=repr(a)) 

def test_0_size(self):
        # Check that all kinds of 0-sized arrays work
        class ArraySubclass(np.ndarray):
            pass
        a = np.zeros((0, 1, 1), dtype=np.int_).view(ArraySubclass)
        res, res_v = linalg.eig(a)
        assert_(res_v.dtype.type is np.float64)
        assert_(res.dtype.type is np.float64)
        assert_equal(a.shape, res_v.shape)
        assert_equal((0, 1), res.shape)
        # This is just for documentation, it might make sense to change:
        assert_(isinstance(a, np.ndarray))

        a = np.zeros((0, 0), dtype=np.complex64).view(ArraySubclass)
        res, res_v = linalg.eig(a)
        assert_(res_v.dtype.type is np.complex64)
        assert_(res.dtype.type is np.complex64)
        assert_equal(a.shape, res_v.shape)
        assert_equal((0,), res.shape)
        # This is just for documentation, it might make sense to change:
        assert_(isinstance(a, np.ndarray)) 

def test_eig_build(self):
        # Ticket #652
        rva = array([1.03221168e+02 + 0.j,
                     -1.91843603e+01 + 0.j,
                     -6.04004526e-01 + 15.84422474j,
                     -6.04004526e-01 - 15.84422474j,
                     -1.13692929e+01 + 0.j,
                     -6.57612485e-01 + 10.41755503j,
                     -6.57612485e-01 - 10.41755503j,
                     1.82126812e+01 + 0.j,
                     1.06011014e+01 + 0.j,
                     7.80732773e+00 + 0.j,
                     -7.65390898e-01 + 0.j,
                     1.51971555e-15 + 0.j,
                     -1.51308713e-15 + 0.j])
        a = arange(13 * 13, dtype=float64)
        a.shape = (13, 13)
        a = a % 17
        va, ve = linalg.eig(a)
        va.sort()
        rva.sort()
        assert_array_almost_equal(va, rva) 

def test_eig_build(self, level = rlevel):
        """Ticket #652"""
        rva = array([1.03221168e+02 +0.j,
               -1.91843603e+01 +0.j,
               -6.04004526e-01+15.84422474j,
               -6.04004526e-01-15.84422474j,
               -1.13692929e+01 +0.j,
               -6.57612485e-01+10.41755503j,
               -6.57612485e-01-10.41755503j,
               1.82126812e+01 +0.j,
               1.06011014e+01 +0.j,
               7.80732773e+00 +0.j,
               -7.65390898e-01 +0.j,
               1.51971555e-15 +0.j,
               -1.51308713e-15 +0.j])
        a = arange(13*13, dtype = float64)
        a.shape = (13, 13)
        a = a%17
        va, ve = linalg.eig(a)
        va.sort()
        rva.sort()
        assert_array_almost_equal(va, rva) 

def test_eig_build(self):
        # Ticket #652
        rva = array([1.03221168e+02 + 0.j,
                     -1.91843603e+01 + 0.j,
                     -6.04004526e-01 + 15.84422474j,
                     -6.04004526e-01 - 15.84422474j,
                     -1.13692929e+01 + 0.j,
                     -6.57612485e-01 + 10.41755503j,
                     -6.57612485e-01 - 10.41755503j,
                     1.82126812e+01 + 0.j,
                     1.06011014e+01 + 0.j,
                     7.80732773e+00 + 0.j,
                     -7.65390898e-01 + 0.j,
                     1.51971555e-15 + 0.j,
                     -1.51308713e-15 + 0.j])
        a = arange(13 * 13, dtype=float64)
        a.shape = (13, 13)
        a = a % 17
        va, ve = linalg.eig(a)
        va.sort()
        rva.sort()
        assert_array_almost_equal(va, rva) 

def test_0_size(self):
        # Check that all kinds of 0-sized arrays work
        class ArraySubclass(np.ndarray):
            pass
        a = np.zeros((0, 1, 1), dtype=np.int_).view(ArraySubclass)
        res, res_v = linalg.eig(a)
        assert_(res_v.dtype.type is np.float64)
        assert_(res.dtype.type is np.float64)
        assert_equal(a.shape, res_v.shape)
        assert_equal((0, 1), res.shape)
        # This is just for documentation, it might make sense to change:
        assert_(isinstance(a, np.ndarray))

        a = np.zeros((0, 0), dtype=np.complex64).view(ArraySubclass)
        res, res_v = linalg.eig(a)
        assert_(res_v.dtype.type is np.complex64)
        assert_(res.dtype.type is np.complex64)
        assert_equal(a.shape, res_v.shape)
        assert_equal((0,), res.shape)
        # This is just for documentation, it might make sense to change:
        assert_(isinstance(a, np.ndarray)) 

def test_0_size(self):
        # Check that all kinds of 0-sized arrays work
        class ArraySubclass(np.ndarray):
            pass
        a = np.zeros((0, 1, 1), dtype=np.int_).view(ArraySubclass)
        res, res_v = linalg.eig(a)
        assert_(res_v.dtype.type is np.float64)
        assert_(res.dtype.type is np.float64)
        assert_equal(a.shape, res_v.shape)
        assert_equal((0, 1), res.shape)
        # This is just for documentation, it might make sense to change:
        assert_(isinstance(a, np.ndarray))

        a = np.zeros((0, 0), dtype=np.complex64).view(ArraySubclass)
        res, res_v = linalg.eig(a)
        assert_(res_v.dtype.type is np.complex64)
        assert_(res.dtype.type is np.complex64)
        assert_equal(a.shape, res_v.shape)
        assert_equal((0,), res.shape)
        # This is just for documentation, it might make sense to change:
        assert_(isinstance(a, np.ndarray)) 

def lnc_correction(tree, points, k, alpha):
    e = 0
    n_sample = points.shape[0]
    for point in points:
        # Find k-nearest neighbors in joint space, p=inf means max norm
        knn = tree.query(point[None, :], k=k+1, return_distance=False)[0]
        knn_points = points[knn]
        # Substract mean of k-nearest neighbor points
        knn_points = knn_points - knn_points[0]
        # Calculate covariance matrix of k-nearest neighbor points, obtain eigen vectors
        covr = knn_points.T @ knn_points / k
        _, v = la.eig(covr)
        # Calculate PCA-bounding box using eigen vectors
        V_rect = np.log(np.abs(knn_points @ v).max(axis=0)).sum()
        # Calculate the volume of original box
        log_knn_dist = np.log(np.abs(knn_points).max(axis=0)).sum()

        # Perform local non-uniformity checking and update correction term
        if V_rect < log_knn_dist + np.log(alpha):
            e += (log_knn_dist - V_rect) / n_sample
    return e


# DISCRETE ESTIMATORS 

def test_eig_build(self):
        # Ticket #652
        rva = array([1.03221168e+02 + 0.j,
                     -1.91843603e+01 + 0.j,
                     -6.04004526e-01 + 15.84422474j,
                     -6.04004526e-01 - 15.84422474j,
                     -1.13692929e+01 + 0.j,
                     -6.57612485e-01 + 10.41755503j,
                     -6.57612485e-01 - 10.41755503j,
                     1.82126812e+01 + 0.j,
                     1.06011014e+01 + 0.j,
                     7.80732773e+00 + 0.j,
                     -7.65390898e-01 + 0.j,
                     1.51971555e-15 + 0.j,
                     -1.51308713e-15 + 0.j])
        a = arange(13 * 13, dtype=float64)
        a.shape = (13, 13)
        a = a % 17
        va, ve = linalg.eig(a)
        va.sort()
        rva.sort()
        assert_array_almost_equal(va, rva) 

def do(self, a, b):
        # note that eigenvalue arrays returned by eig must be sorted since
        # their order isn't guaranteed.
        ev, evc = linalg.eigh(a)
        evalues, evectors = linalg.eig(a)
        evalues.sort(axis=-1)
        assert_almost_equal(ev, evalues)

        assert_allclose(dot_generalized(a, evc),
                        np.asarray(ev)[..., None, :] * np.asarray(evc),
                        rtol=get_rtol(ev.dtype))

        ev2, evc2 = linalg.eigh(a, 'U')
        assert_almost_equal(ev2, evalues)

        assert_allclose(dot_generalized(a, evc2),
                        np.asarray(ev2)[..., None, :] * np.asarray(evc2),
                        rtol=get_rtol(ev.dtype), err_msg=repr(a)) 

def test_eig_build(self):
        # Ticket #652
        rva = array([1.03221168e+02 + 0.j,
                     -1.91843603e+01 + 0.j,
                     -6.04004526e-01 + 15.84422474j,
                     -6.04004526e-01 - 15.84422474j,
                     -1.13692929e+01 + 0.j,
                     -6.57612485e-01 + 10.41755503j,
                     -6.57612485e-01 - 10.41755503j,
                     1.82126812e+01 + 0.j,
                     1.06011014e+01 + 0.j,
                     7.80732773e+00 + 0.j,
                     -7.65390898e-01 + 0.j,
                     1.51971555e-15 + 0.j,
                     -1.51308713e-15 + 0.j])
        a = arange(13 * 13, dtype=float64)
        a.shape = (13, 13)
        a = a % 17
        va, ve = linalg.eig(a)
        va.sort()
        rva.sort()
        assert_array_almost_equal(va, rva) 

def test_0_size(self):
        # Check that all kinds of 0-sized arrays work
        class ArraySubclass(np.ndarray):
            pass
        a = np.zeros((0, 1, 1), dtype=np.int_).view(ArraySubclass)
        res, res_v = linalg.eig(a)
        assert_(res_v.dtype.type is np.float64)
        assert_(res.dtype.type is np.float64)
        assert_equal(a.shape, res_v.shape)
        assert_equal((0, 1), res.shape)
        # This is just for documentation, it might make sense to change:
        assert_(isinstance(a, np.ndarray))

        a = np.zeros((0, 0), dtype=np.complex64).view(ArraySubclass)
        res, res_v = linalg.eig(a)
        assert_(res_v.dtype.type is np.complex64)
        assert_(res.dtype.type is np.complex64)
        assert_equal(a.shape, res_v.shape)
        assert_equal((0,), res.shape)
        # This is just for documentation, it might make sense to change:
        assert_(isinstance(a, np.ndarray)) 

def do(self, a, b, tags):
        # note that eigenvalue arrays returned by eig must be sorted since
        # their order isn't guaranteed.
        ev = linalg.eigvalsh(a, 'L')
        evalues, evectors = linalg.eig(a)
        evalues.sort(axis=-1)
        assert_allclose(ev, evalues, rtol=get_rtol(ev.dtype))

        ev2 = linalg.eigvalsh(a, 'U')
        assert_allclose(ev2, evalues, rtol=get_rtol(ev.dtype)) 

def steady_state(P):
    """
    Calculates the steady state probability vector for a regular Markov
    transition matrix P
    Parameters
    ----------
    P        : matrix (kxk)
               an ergodic Markov transition probability matrix
    Returns
    -------
    implicit : matrix (kx1)
               steady state distribution
    Examples
    --------
    Taken from Kemeny and Snell. [1]_ Land of Oz example where the states are
    Rain, Nice and Snow - so there is 25 percent chance that if it
    rained in Oz today, it will snow tomorrow, while if it snowed today in
    Oz there is a 50 percent chance of snow again tomorrow and a 25
    percent chance of a nice day (nice, like when the witch with the monkeys
    is melting).
    >>> import numpy as np
    >>> p=np.matrix([[.5, .25, .25],[.5,0,.5],[.25,.25,.5]])
    >>> steady_state(p)
    matrix([[ 0.4],
            [ 0.2],
            [ 0.4]])
    Thus, the long run distribution for Oz is to have 40 percent of the
    days classified as Rain, 20 percent as Nice, and 40 percent as Snow
    (states are mutually exclusive).
    """

    v,d=la.eig(np.transpose(P))

    # for a regular P maximum eigenvalue will be 1
    mv=max(v)
    # find its position
    i=v.tolist().index(mv)

    # normalize eigenvector corresponding to the eigenvalue 1
    return d[:,i]/sum(d[:,i]) 

def get_epipole(self,F):
		'''
		Method to return the epipole from the fundamental matrix
		Args: 
			F: the fundamental matrix
		Retruns: 
			the epipole
		'''
		u,v=eig(F)
		dd=np.square(u);
		min_index=np.argmin(np.abs(dd))	# SOS: These are complex numbers, so compare their modulus
		epipole=v[:,min_index]
		epipole=epipole/epipole[2]
		return epipole.real 

def do(self, a, b, tags):
        # note that eigenvalue arrays returned by eig must be sorted since
        # their order isn't guaranteed.
        ev = linalg.eigvalsh(a, 'L')
        evalues, evectors = linalg.eig(a)
        evalues.sort(axis=-1)
        assert_allclose(ev, evalues, rtol=get_rtol(ev.dtype))

        ev2 = linalg.eigvalsh(a, 'U')
        assert_allclose(ev2, evalues, rtol=get_rtol(ev.dtype)) 

def test_types(self, dtype):
        x = np.array([[1, 0.5], [0.5, 1]], dtype=dtype)
        w, v = np.linalg.eig(x)
        assert_equal(w.dtype, dtype)
        assert_equal(v.dtype, dtype)

        x = np.array([[1, 0.5], [-1, 1]], dtype=dtype)
        w, v = np.linalg.eig(x)
        assert_equal(w.dtype, get_complex_dtype(dtype))
        assert_equal(v.dtype, get_complex_dtype(dtype)) 

def do(self, a, b, tags):
        ev = linalg.eigvals(a)
        evalues, evectors = linalg.eig(a)
        assert_almost_equal(ev, evalues) 

def do(self, a, b, tags):
        evalues, evectors = linalg.eig(a)
        assert_allclose(dot_generalized(a, evectors),
                        np.asarray(evectors) * np.asarray(evalues)[..., None, :],
                        rtol=get_rtol(evalues.dtype))
        assert_(consistent_subclass(evectors, a))