def tabulate_derivatives(self, n, pts):
"""Returns a tuple of length one (A,) such that
A[i,j] = D phi_i(pts[j]). The tuple is returned for
compatibility with the interfaces of the triangle and
tetrahedron expansions."""
ref_pts = numpy.array([self.mapping(pt) for pt in pts])
psitilde_as_derivs = jacobi.eval_jacobi_deriv_batch(0, 0, n, ref_pts)
# Jacobi polynomials defined on [-1, 1], first derivatives need scaling
psitilde_as_derivs *= 2.0 / self.ref_el.volume()
results = numpy.zeros((n + 1, len(pts)), "d")
for k in range(0, n + 1):
results[k, :] = psitilde_as_derivs[k, :] * numpy.sqrt(k + 0.5)
vals = self.tabulate(n, pts)
deriv_vals = (results,)
# Create the ordinary data structure.
dv = []
for i in range(vals.shape[0]):
dv.append([])
for j in range(vals.shape[1]):
dv[-1].append((vals[i][j], [deriv_vals[0][i][j]]))
return dv
def tabulate_derivatives(self, n, pts):
"""Returns a tuple of length one (A,) such that
A[i,j] = D phi_i(pts[j]). The tuple is returned for
compatibility with the interfaces of the triangle and
tetrahedron expansions."""
ref_pts = numpy.array([self.mapping(pt) for pt in pts])
psitilde_as_derivs = jacobi.eval_jacobi_deriv_batch(0, 0, n, ref_pts)
# Jacobi polynomials defined on [-1, 1], first derivatives need scaling
psitilde_as_derivs *= 2.0 / self.ref_el.volume()
results = numpy.zeros((n + 1, len(pts)), "d")
for k in range(0, n + 1):
results[k, :] = psitilde_as_derivs[k, :] * numpy.sqrt(k + 0.5)
vals = self.tabulate(n, pts)
deriv_vals = (results,)
# Create the ordinary data structure.
dv = []
for i in range(vals.shape[0]):
dv.append([])
for j in range(vals.shape[1]):
dv[-1].append((vals[i][j], [deriv_vals[0][i][j]]))
return dv