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Evaluate a 3-D Laguerre series at points (x, y, z). This function returns the values: .. math:: p(x,y,z) = \sum_{i,j,k} c_{i,j,k} * L_i(x) * L_j(y) * L_k(z) The parameters `x`, `y`, and `z` are converted to arrays only if they are tuples or a lists, otherwise they are treated as a scalars and they must have the same shape after conversion. In either case, either `x`, `y`, and `z` or their elements must support multiplication and(more...)

def lagval3d(x, y, z, c): """ Evaluate a 3-D Laguerre series at points (x, y, z). This function returns the values: .. math:: p(x,y,z) = \\sum_{i,j,k} c_{i,j,k} * L_i(x) * L_j(y) * L_k(z) The parameters `x`, `y`, and `z` are converted to arrays only if they are tuples or a lists, otherwise they are treated as a scalars and they must have the same shape after conversion. In either case, either `x`, `y`, and `z` or their elements must support multiplication and addition both with themselves and with the elements of `c`. If `c` has fewer than 3 dimensions, ones are implicitly appended to its shape to make it 3-D. The shape of the result will be c.shape[3:] + x.shape. Parameters ---------- x, y, z : array_like, compatible object The three dimensional series is evaluated at the points `(x, y, z)`, where `x`, `y`, and `z` must have the same shape. If any of `x`, `y`, or `z` is a list or tuple, it is first converted to an ndarray, otherwise it is left unchanged and if it isn't an ndarray it is treated as a scalar. c : array_like Array of coefficients ordered so that the coefficient of the term of multi-degree i,j,k is contained in ``c[i,j,k]``. If `c` has dimension greater than 3 the remaining indices enumerate multiple sets of coefficients. Returns ------- values : ndarray, compatible object The values of the multidimension polynomial on points formed with triples of corresponding values from `x`, `y`, and `z`. See Also -------- lagval, lagval2d, laggrid2d, laggrid3d Notes ----- .. versionadded::1.7.0 """ try: x, y, z = np.array((x, y, z), copy=0) except: raise ValueError('x, y, z are incompatible') c = lagval(x, c) c = lagval(y, c, tensor=False) c = lagval(z, c, tensor=False) return c

**nupic-linux64**(Download)

#test values tgt = y1*y2*y3 res = lag.lagval3d(x1, x2, x3, self.c3d) assert_almost_equal(res, tgt) #test shape z = np.ones((2,3)) res = lag.lagval3d(z, z, z, self.c3d)

c = np.random.random((2, 3, 4)) van = lag.lagvander3d(x1, x2, x3, [1, 2, 3]) tgt = lag.lagval3d(x1, x2, x3, c) res = np.dot(van, c.flat) assert_almost_equal(res, tgt)

src/n/u/numpy-1.8.1/numpy/polynomial/tests/test_laguerre.py

**numpy**(Download)

#test values tgt = y1*y2*y3 res = lag.lagval3d(x1, x2, x3, self.c3d) assert_almost_equal(res, tgt) #test shape z = np.ones((2, 3)) res = lag.lagval3d(z, z, z, self.c3d)

c = np.random.random((2, 3, 4)) van = lag.lagvander3d(x1, x2, x3, [1, 2, 3]) tgt = lag.lagval3d(x1, x2, x3, c) res = np.dot(van, c.flat) assert_almost_equal(res, tgt)