# Python numpy.polynomial.legendre.leggauss() Examples

The following are
code examples for showing how to use *numpy.polynomial.legendre.leggauss()*.
They are from open source Python projects. You can vote up the examples you like or vote down the ones you don't like.

Example 1

Project: lega Author: MiroK File: legendre_basis.py MIT License | 6 votes |

def backward_transformation_matrix(N): ''' Compute NxN matrix with values N_ij = L_i(x_j) where L_i are N Legendre polynomials and x_j are N GL quadrature points. This matrix is used for backward Legendre transformation: Suppose function f is represented in the wave number space by a vector F and let BL be the backward transformation matrix. Then f(x_j) = F.BL[:, j] or f = F.BL or BL.T.F, and vector f represents f in the real space. ''' BL = np.zeros((N, N)) # Get points of the guadrature points, _ = leggauss(N) for i in range(N): c = np.zeros(i+1) c[-1] = 1 # Evaluate the i-th polynomial at all the points row = legval(points, c) BL[i, :] = row return BL

Example 2

Project: shenfun Author: spectralDNS File: bases.py BSD 2-Clause "Simplified" License | 5 votes |

def points_and_weights(self, N=None, map_true_domain=False, weighted=True, **kw): if N is None: N = self.N if self.quad == "LG": points, weights = leg.leggauss(N) elif self.quad == "GL": points, weights = legendre_lobatto_nodes_and_weights(N) else: raise NotImplementedError if map_true_domain is True: points = self.map_true_domain(points) return points, weights

Example 3

Project: LaserTOF Author: kyleuckert File: test_legendre.py MIT License | 5 votes |

def test_100(self): x, w = leg.leggauss(100) # test orthogonality. Note that the results need to be normalized, # otherwise the huge values that can arise from fast growing # functions like Laguerre can be very confusing. v = leg.legvander(x, 99) vv = np.dot(v.T * w, v) vd = 1/np.sqrt(vv.diagonal()) vv = vd[:, None] * vv * vd assert_almost_equal(vv, np.eye(100)) # check that the integral of 1 is correct tgt = 2.0 assert_almost_equal(w.sum(), tgt)

Example 4

Project: FX-RER-Value-Extraction Author: tsKenneth File: test_legendre.py MIT License | 5 votes |

Example 5

Project: recruit Author: Frank-qlu File: test_legendre.py Apache License 2.0 | 5 votes |

Example 6

Project: att Author: Centre-Alt-Rendiment-Esportiu File: test_legendre.py GNU General Public License v3.0 | 5 votes |

Example 7

Project: FUTU_Stop_Loss Author: BigtoC File: test_legendre.py MIT License | 5 votes |

Example 8

Project: MARRtino-2.0 Author: DaniAffCH File: test_legendre.py GNU General Public License v3.0 | 5 votes |

Example 9

Project: auto-alt-text-lambda-api Author: abhisuri97 File: test_legendre.py MIT License | 5 votes |

Example 10

Project: vnpy_crypto Author: birforce File: test_legendre.py MIT License | 5 votes |

Example 11

Project: ble5-nrf52-mac Author: tomasero File: test_legendre.py MIT License | 5 votes |

Example 12

Project: Computable Author: ktraunmueller File: test_legendre.py MIT License | 5 votes |

Example 13

Project: poker Author: surgebiswas File: test_legendre.py MIT License | 5 votes |

Example 14

Project: P3_image_processing Author: latedude2 File: test_legendre.py MIT License | 5 votes |

Example 15

Project: GraphicDesignPatternByPython Author: Relph1119 File: test_legendre.py MIT License | 5 votes |

Example 16

Project: 3dprinteros-client Author: panasevychol File: test_legendre.py GNU Affero General Public License v3.0 | 5 votes |

Example 17

Project: 3dprinteros-client Author: panasevychol File: test_legendre.py GNU Affero General Public License v3.0 | 5 votes |

Example 18

Project: lie_learn Author: AMLab-Amsterdam File: S2.py MIT License | 5 votes |

def linspace(b, grid_type='Driscoll-Healy'): if grid_type == 'Driscoll-Healy': beta = np.arange(2 * b) * np.pi / (2. * b) alpha = np.arange(2 * b) * np.pi / b elif grid_type == 'SOFT': beta = np.pi * (2 * np.arange(2 * b) + 1) / (4. * b) alpha = np.arange(2 * b) * np.pi / b elif grid_type == 'Clenshaw-Curtis': # beta = np.arange(2 * b + 1) * np.pi / (2 * b) # alpha = np.arange(2 * b + 2) * np.pi / (b + 1) # Must use np.linspace to prevent numerical errors that cause beta > pi beta = np.linspace(0, np.pi, 2 * b + 1) alpha = np.linspace(0, 2 * np.pi, 2 * b + 2, endpoint=False) elif grid_type == 'Gauss-Legendre': x, _ = leggauss(b + 1) # TODO: leggauss docs state that this may not be only stable for orders > 100 beta = np.arccos(x) alpha = np.arange(2 * b + 2) * np.pi / (b + 1) elif grid_type == 'HEALPix': #TODO: implement this here so that we don't need the dependency on healpy / healpix_compat from healpix_compat import healpy_sphere_meshgrid return healpy_sphere_meshgrid(b) elif grid_type == 'equidistribution': raise NotImplementedError('Not implemented yet; see Fast evaluation of quadrature formulae on the sphere.') else: raise ValueError('Unknown grid_type:' + grid_type) return beta, alpha

Example 19

Project: predictive-maintenance-using-machine-learning Author: awslabs File: test_legendre.py Apache License 2.0 | 5 votes |

Example 20

Project: fund Author: Frank-qlu File: test_legendre.py Apache License 2.0 | 5 votes |

Example 21

Project: pySINDy Author: luckystarufo File: test_legendre.py MIT License | 5 votes |

Example 22

Project: Programming-for-Non-Technical-Roles- Author: PacktPublishing File: test_legendre.py MIT License | 5 votes |

Example 23

Project: linear_neuron Author: uglyboxer File: test_legendre.py MIT License | 5 votes |

Example 24

Project: facethin Author: ParkerGod File: test_legendre.py GNU General Public License v3.0 | 5 votes |

Example 25

Project: islam-buddy Author: hamir File: test_legendre.py MIT License | 5 votes |

Example 26

Project: mxnet-lambda Author: awslabs File: test_legendre.py Apache License 2.0 | 5 votes |

Example 27

Project: Deribit_funding_rate_indicator Author: Dimasik007 File: test_legendre.py MIT License | 5 votes |

Example 28

Project: psychrometric-chart-makeover Author: buds-lab File: test_legendre.py MIT License | 5 votes |

Example 29

Project: wine-ml-on-aws-lambda Author: pierreant File: test_legendre.py Apache License 2.0 | 5 votes |

Example 30

Project: linux-cross-gcc Author: nmercier File: test_legendre.py BSD 3-Clause "New" or "Revised" License | 5 votes |

Example 31

Project: SignLanguage_ML Author: mareep-raljodid File: test_legendre.py MIT License | 5 votes |

Example 32

Project: ImageFusion Author: pfchai File: test_legendre.py MIT License | 5 votes |

Example 33

Project: sarah Author: ChonchoFronto File: test_legendre.py MIT License | 5 votes |

Example 34

Project: honours_project Author: JFriel File: test_legendre.py GNU General Public License v3.0 | 5 votes |

Example 35

Project: honours_project Author: JFriel File: test_legendre.py GNU General Public License v3.0 | 5 votes |

Example 36

Project: Blackjack-Tracker Author: martinabeleda File: test_legendre.py MIT License | 5 votes |

Example 37

Project: PYPIC Author: max614 File: test_legendre.py BSD 2-Clause "Simplified" License | 5 votes |

Example 38

Project: PYPIC Author: max614 File: test_legendre.py BSD 2-Clause "Simplified" License | 5 votes |

Example 39

Project: PYPIC Author: max614 File: test_legendre.py BSD 2-Clause "Simplified" License | 5 votes |

Example 40

Project: Renormalizer Author: shuaigroup File: lib.py Apache License 2.0 | 5 votes |

def legendre(self, nb, x0, x1, ifsort=True): """ Legendre polynomial fit [x0, x1] to [-1,1] omega_m is the cutoff """ omega_value, w = le.leggauss(nb) omega_value = (omega_value + (x1 + x0) / (x1 - x0)) * (x1 - x0) / 2. c_j2 = w * (x1 - x0) / 2. * self.alpha * omega_value ** 2 * np.exp(-omega_value / self.omega_c) return self.post_process(omega_value, c_j2, ifsort)

Example 41

Project: lega Author: MiroK File: integration.py MIT License | 5 votes |

def __init__(self, N): '''Quadrature formulat using N points.''' self.points, self.weights = leggauss(N)

Example 42

Project: lega Author: MiroK File: integration.py MIT License | 5 votes |

def __init__(self, N): '''Quadrature formulat using N x Npoints.''' points, weights = leggauss(N) # Let's do the tensor product XY = np.array([list(xy) for xy in product(points, points)]) self.X = XY[:, 0] self.Y = XY[:, 1] self.weights = np.array([w0*w1 for w0, w1 in product(weights, weights)])

Example 43

Project: lega Author: MiroK File: legendre_basis.py MIT License | 5 votes |

def forward_transformation_matrix(N): ''' For any function f, we define its interpolant f_N as \sum_{i=0}^{N-1}F_i*L_i, where L_i is the i-th Legendre polynomial and the coeffcients F_i are given as F_i=\sum_{j=0}^{n-1}*f(xj)*w_j*L_i(x_j)/(L_i, L_i). The interpolant is thus a polynomial of degree N-1. The reasoning behind the definition is that is f were a polynomial of degre N-1 the integrals (f, L_i) having an integrand of max degree 2N-2 would be exactly evaluated by the N-1 point GL gradrature. Vector F is a representation of function f in the wave number space. Computing F can be represented as matrix-vector product and is reffered to as a forward Legendre transformation. Here we get the matrix for the operatation FL. ''' # Note that each row of FL could be computed by taking a dot of row of # matrix BL.inv(M) with the vector of weight. FL = np.zeros((N, N)) # Get point and weights of the guadrature points, weights = leggauss(N) for i in range(N): c = np.zeros(i+1) c[-1] = 1 # Evaluate te the i-th polynomial at all the points row = legval(points, c) # Now the element-wise with with weights, i.e. dot with weight vector row *= weights # Finally the (Li, Li) term, i.e. the inv(M) row /= 2/(2*i+1) FL[i, :] = row return FL

Example 44

Project: lega Author: MiroK File: legendre_basis.py MIT License | 5 votes |

def __init__(self, N): '''Compute the evaluation points.''' if not isinstance(N, list): N = [N] self.dim = len(N) # This would work for any dim but since only 1d and 2d is supported in # FLT and BLT I see no points in supporting it here. assert self.dim < 3 self.shape = tuple(N) # Get points for components points_i = [leggauss(n)[0] for n in N] # Combine as cartesian product self.points = np.array([list(pis) for pis in product(*points_i)])

Example 45

Project: offlow Author: satwikkansal File: test_legendre.py GNU General Public License v3.0 | 5 votes |

Example 46

Project: lambda-tensorflow-object-detection Author: mikylucky File: test_legendre.py GNU General Public License v3.0 | 5 votes |

Example 47

Project: elasticintel Author: securityclippy File: test_legendre.py GNU General Public License v3.0 | 5 votes |

Example 48

Project: cnidaria Author: sauloal File: test_legendre.py MIT License | 5 votes |

Example 49

Project: AutoDraw Author: yemi-Jump File: test_legendre.py MIT License | 5 votes |

Example 50

Project: fund-rank-dashboard Author: 1pani File: test_legendre.py Apache License 2.0 | 5 votes |

Example 51

Project: florence Author: romeric File: NumericIntegrator.py MIT License | 4 votes |

def GaussQuadrature(N,a=-1,b=1): if a==-1 and b==1: return leggauss(N) # The following is for historical purposes and when the range is different from [-1,1] N0=N-1 N1 = N0+1 N2 = N0+2 xu = np.linspace(-1.,1.,N1) # Legendre-Gauss-Vandermonde Matrix L = 1.0*np.zeros((N1,N2)) # Derivative of Legendre-Gauss-Vandermonde Matrix Lp = 1.0*np.zeros(N1) dum = np.linspace(0,N0,N1) y=np.cos((2*dum+1)*np.pi/(2*N0+2))+(0.27/N1)*np.sin(np.pi*xu*N0/N2) # PI = np.pi # y=ne.evaluate("cos((2*dum+1)*PI/(2*N0+2))+(0.27/N1)*sin(PI*xu*N0/N2)") deps = np.finfo(np.float64).eps # Initial Guess y0 = 2.0*np.ones(N1) while np.max(np.abs(y-y0)) > deps: L[:,0] = np.ones(N1) L[:,1] = y Lp = np.zeros(N1) for k in range(1,N1): L[:,k+1] = ((2*k+1)*L[:,k]*y - k*L[:,k-1])/(k+1) Lp = N2*(L[:,N0]-L[:,N1]*y)/(1-y**2) y0 = y y=y0-L[:,N1]/Lp z = (a*(1-y)+b*(1+y))/2.0 w = (b-a)/((1-y**2)*Lp**2)*pow((np.float64(N2)/N1),2) z = np.fliplr(z.reshape(1,z.shape[0])).reshape(z.shape[0]) w = np.fliplr(w.reshape(1,w.shape[0])).reshape(w.shape[0]) return (z,w)

Example 52

Project: lie_learn Author: AMLab-Amsterdam File: S2.py MIT License | 4 votes |

def quadrature_weights(b, grid_type='Gauss-Legendre'): """ Compute quadrature weights for a given grid-type. The function S2.meshgrid generates the points that correspond to the weights generated by this function. if convention == 'Gauss-Legendre': The quadrature formula is exact for polynomials up to degree M less than or equal to 2b + 1, so that we can compute exact Fourier coefficients for f a polynomial of degree at most b. if convention == 'Clenshaw-Curtis': The quadrature formula is exact for polynomials up to degree M less than or equal to 2b, so that we can compute exact Fourier coefficients for f a polynomial of degree at most b. :param b: the grid resolution. See S2.meshgrid :param grid_type: :return: """ if grid_type == 'Clenshaw-Curtis': # There is a faster fft based method to compute these weights # see "Fast evaluation of quadrature formulae on the sphere" # W = np.empty((2 * b + 2, 2 * b + 1)) # for j in range(2 * b + 1): # eps_j_2b = 0.5 if j == 0 or j == 2 * b else 1. # for k in range(2 * b + 2): # Doesn't seem to depend on k.. # W[k, j] = (4 * np.pi * eps_j_2b) / (b * (2 * b + 2)) # sum = 0. # for l in range(b + 1): # eps_l_b = 0.5 if l == 0 or l == b else 1. # sum += eps_l_b / (1 - 4 * l ** 2) * np.cos(j * l * np.pi / b) # W[k, j] *= sum w = _clenshaw_curtis_weights(n=2 * b) W = np.empty((2 * b + 1, 2 * b + 2)) W[:] = w[:, None] elif grid_type == 'Gauss-Legendre': # We found this formula in: # "A Fast Algorithm for Spherical Grid Rotations and its Application to Singular Quadrature" # eq. 10 _, w = leggauss(b + 1) W = w[:, None] * (2 * np.pi / (2 * b + 2) * np.ones(2 * b + 2)[None, :]) elif grid_type == 'SOFT': print("WARNING: SOFT quadrature weights don't work yet") k = np.arange(0, b) w = np.array([(2. / b) * np.sin(np.pi * (2. * j + 1.) / (4. * b)) * (np.sum((1. / (2 * k + 1)) * np.sin((2 * j + 1) * (2 * k + 1) * np.pi / (4. * b)))) for j in range(2 * b)]) W = w[:, None] * np.ones(2 * b)[None, :] else: raise ValueError('Unknown grid_type:' + str(grid_type)) return W