def __init__(self, ref_el, degree, shape=tuple()): if shape == tuple(): num_components = 1 else: flat_shape = numpy.ravel(shape) num_components = numpy.prod(flat_shape) num_exp_functions = expansions.polynomial_dimension(ref_el, degree) num_members = num_components * num_exp_functions embedded_degree = degree expansion_set = expansions.get_expansion_set(ref_el) sd = ref_el.get_spatial_dimension() # set up coefficients coeffs_shape = tuple([num_members] + list(shape) + [num_exp_functions]) coeffs = numpy.zeros(coeffs_shape, "d") # use functional's index_iterator function cur_bf = 0 if shape == tuple(): coeffs = numpy.eye(num_members) else: for idx in index_iterator(shape): n = expansions.polynomial_dimension(ref_el, embedded_degree) for exp_bf in range(n): cur_idx = tuple([cur_bf] + list(idx) + [exp_bf]) coeffs[cur_idx] = 1.0 cur_bf += 1 # construct dmats if degree == 0: dmats = [numpy.array([[0.0]], "d") for i in range(sd)] else: pts = ref_el.make_points(sd, 0, degree + sd + 1) v = numpy.transpose(expansion_set.tabulate(degree, pts)) vinv = numpy.linalg.inv(v) dv = expansion_set.tabulate_derivatives(degree, pts) dtildes = [[[a[1][i] for a in dvrow] for dvrow in dv] for i in range(sd)] dmats = [ numpy.dot(vinv, numpy.transpose(dtilde)) for dtilde in dtildes ] PolynomialSet.__init__(self, ref_el, degree, embedded_degree, expansion_set, coeffs, dmats)
def __init__(self, ref_el, degree, shape=tuple()): if shape == tuple(): num_components = 1 else: flat_shape = numpy.ravel(shape) num_components = numpy.prod(flat_shape) num_exp_functions = expansions.polynomial_dimension(ref_el, degree) num_members = num_components * num_exp_functions embedded_degree = degree expansion_set = expansions.get_expansion_set(ref_el) sd = ref_el.get_spatial_dimension() # set up coefficients coeffs_shape = tuple([num_members] + list(shape) + [num_exp_functions]) coeffs = numpy.zeros(coeffs_shape, "d") # use functional's index_iterator function cur_bf = 0 if shape == tuple(): coeffs = numpy.eye(num_members) else: for idx in index_iterator(shape): n = expansions.polynomial_dimension(ref_el, embedded_degree) for exp_bf in range(n): cur_idx = tuple([cur_bf] + list(idx) + [exp_bf]) coeffs[cur_idx] = 1.0 cur_bf += 1 # construct dmats if degree == 0: dmats = [numpy.array([[0.0]], "d") for i in range(sd)] else: pts = ref_el.make_points(sd, 0, degree + sd + 1) v = numpy.transpose(expansion_set.tabulate(degree, pts)) vinv = numpy.linalg.inv(v) dv = expansion_set.tabulate_derivatives(degree, pts) dtildes = [[[a[1][i] for a in dvrow] for dvrow in dv] for i in range(sd)] dmats = [numpy.dot(vinv, numpy.transpose(dtilde)) for dtilde in dtildes] PolynomialSet.__init__(self, ref_el, degree, embedded_degree, expansion_set, coeffs, dmats)
def __init__(self, ref_el, degree): entity_ids = {} nodes = [] sd = ref_el.get_spatial_dimension() t = ref_el.get_topology() # codimension 1 facets for i in range(len(t[sd - 1])): pts_cur = ref_el.make_points(sd - 1, i, sd + degree) for j in range(len(pts_cur)): pt_cur = pts_cur[j] f = functional.PointScaledNormalEvaluation(ref_el, i, pt_cur) nodes.append(f) # internal nodes. Let's just use points at a lattice if degree > 0: cpe = functional.ComponentPointEvaluation pts = ref_el.make_points(sd, 0, degree + sd) for d in range(sd): for i in range(len(pts)): l_cur = cpe(ref_el, d, (sd, ), pts[i]) nodes.append(l_cur) # Q = quadrature.make_quadrature(ref_el, 2 * ( degree + 1 )) # qpts = Q.get_points() # Pkm1 = polynomial_set.ONPolynomialSet(ref_el, degree - 1) # zero_index = tuple([0 for i in range(sd)]) # Pkm1_at_qpts = Pkm1.tabulate(qpts)[zero_index] # for d in range(sd): # for i in range(Pkm1_at_qpts.shape[0]): # phi_cur = Pkm1_at_qpts[i, :] # l_cur = functional.IntegralMoment(ref_el, Q, phi_cur, (d,), (sd,)) # nodes.append(l_cur) # sets vertices (and in 3d, edges) to have no nodes for i in range(sd - 1): entity_ids[i] = {} for j in range(len(t[i])): entity_ids[i][j] = [] cur = 0 # set codimension 1 (edges 2d, faces 3d) dof pts_facet_0 = ref_el.make_points(sd - 1, 0, sd + degree) pts_per_facet = len(pts_facet_0) entity_ids[sd - 1] = {} for i in range(len(t[sd - 1])): entity_ids[sd - 1][i] = list(range(cur, cur + pts_per_facet)) cur += pts_per_facet # internal nodes, if applicable entity_ids[sd] = {0: []} if degree > 0: num_internal_nodes = expansions.polynomial_dimension( ref_el, degree - 1) entity_ids[sd][0] = list(range(cur, cur + num_internal_nodes * sd)) super(RTDualSet, self).__init__(nodes, ref_el, entity_ids)
def __init__(self, ref_el, degree): entity_ids = {} nodes = [] sd = ref_el.get_spatial_dimension() t = ref_el.get_topology() # codimension 1 facets for i in range(len(t[sd - 1])): pts_cur = ref_el.make_points(sd - 1, i, sd + degree) for j in range(len(pts_cur)): pt_cur = pts_cur[j] f = functional.PointScaledNormalEvaluation(ref_el, i, pt_cur) nodes.append(f) # internal nodes. Let's just use points at a lattice if degree > 0: cpe = functional.ComponentPointEvaluation pts = ref_el.make_points(sd, 0, degree + sd) for d in range(sd): for i in range(len(pts)): l_cur = cpe(ref_el, d, (sd,), pts[i]) nodes.append(l_cur) # Q = quadrature.make_quadrature(ref_el, 2 * ( degree + 1 )) # qpts = Q.get_points() # Pkm1 = polynomial_set.ONPolynomialSet(ref_el, degree - 1) # zero_index = tuple([0 for i in range(sd)]) # Pkm1_at_qpts = Pkm1.tabulate(qpts)[zero_index] # for d in range(sd): # for i in range(Pkm1_at_qpts.shape[0]): # phi_cur = Pkm1_at_qpts[i, :] # l_cur = functional.IntegralMoment(ref_el, Q, phi_cur, (d,), (sd,)) # nodes.append(l_cur) # sets vertices (and in 3d, edges) to have no nodes for i in range(sd - 1): entity_ids[i] = {} for j in range(len(t[i])): entity_ids[i][j] = [] cur = 0 # set codimension 1 (edges 2d, faces 3d) dof pts_facet_0 = ref_el.make_points(sd - 1, 0, sd + degree) pts_per_facet = len(pts_facet_0) entity_ids[sd - 1] = {} for i in range(len(t[sd - 1])): entity_ids[sd - 1][i] = list(range(cur, cur + pts_per_facet)) cur += pts_per_facet # internal nodes, if applicable entity_ids[sd] = {0: []} if degree > 0: num_internal_nodes = expansions.polynomial_dimension(ref_el, degree - 1) entity_ids[sd][0] = list(range(cur, cur + num_internal_nodes * sd)) super(RTDualSet, self).__init__(nodes, ref_el, entity_ids)
def RTSpace(ref_el, deg): """Constructs a basis for the the Raviart-Thomas space (P_k)^d + P_k x""" sd = ref_el.get_spatial_dimension() vec_Pkp1 = polynomial_set.ONPolynomialSet(ref_el, deg + 1, (sd,)) dimPkp1 = expansions.polynomial_dimension(ref_el, deg + 1) dimPk = expansions.polynomial_dimension(ref_el, deg) dimPkm1 = expansions.polynomial_dimension(ref_el, deg - 1) vec_Pk_indices = list(chain(*(range(i * dimPkp1, i * dimPkp1 + dimPk) for i in range(sd)))) vec_Pk_from_Pkp1 = vec_Pkp1.take(vec_Pk_indices) Pkp1 = polynomial_set.ONPolynomialSet(ref_el, deg + 1) PkH = Pkp1.take(list(range(dimPkm1, dimPk))) Q = quadrature.make_quadrature(ref_el, 2 * deg + 2) # have to work on this through "tabulate" interface # first, tabulate PkH at quadrature points Qpts = numpy.array(Q.get_points()) Qwts = numpy.array(Q.get_weights()) zero_index = tuple([0 for i in range(sd)]) PkH_at_Qpts = PkH.tabulate(Qpts)[zero_index] Pkp1_at_Qpts = Pkp1.tabulate(Qpts)[zero_index] PkHx_coeffs = numpy.zeros((PkH.get_num_members(), sd, Pkp1.get_num_members()), "d") for i in range(PkH.get_num_members()): for j in range(sd): fooij = PkH_at_Qpts[i, :] * Qpts[:, j] * Qwts PkHx_coeffs[i, j, :] = numpy.dot(Pkp1_at_Qpts, fooij) PkHx = polynomial_set.PolynomialSet(ref_el, deg, deg + 1, vec_Pkp1.get_expansion_set(), PkHx_coeffs, vec_Pkp1.get_dmats()) return polynomial_set.polynomial_set_union_normalized(vec_Pk_from_Pkp1, PkHx)
def __init__(self, ref_el, degree, size=None): sd = ref_el.get_spatial_dimension() if size is None: size = sd shape = (size, size) num_exp_functions = expansions.polynomial_dimension(ref_el, degree) num_components = size * (size + 1) // 2 num_members = num_components * num_exp_functions embedded_degree = degree expansion_set = expansions.get_expansion_set(ref_el) # set up coefficients for symmetric tensors coeffs_shape = tuple([num_members] + list(shape) + [num_exp_functions]) coeffs = numpy.zeros(coeffs_shape, "d") cur_bf = 0 for [i, j] in index_iterator(shape): n = expansions.polynomial_dimension(ref_el, embedded_degree) if i == j: for exp_bf in range(n): cur_idx = tuple([cur_bf] + [i, j] + [exp_bf]) coeffs[cur_idx] = 1.0 cur_bf += 1 elif i < j: for exp_bf in range(n): cur_idx = tuple([cur_bf] + [i, j] + [exp_bf]) coeffs[cur_idx] = 1.0 cur_idx = tuple([cur_bf] + [j, i] + [exp_bf]) coeffs[cur_idx] = 1.0 cur_bf += 1 # construct dmats. this is the same as ONPolynomialSet. pts = ref_el.make_points(sd, 0, degree + sd + 1) v = numpy.transpose(expansion_set.tabulate(degree, pts)) vinv = numpy.linalg.inv(v) dv = expansion_set.tabulate_derivatives(degree, pts) dtildes = [[[a[1][i] for a in dvrow] for dvrow in dv] for i in range(sd)] dmats = [ numpy.dot(vinv, numpy.transpose(dtilde)) for dtilde in dtildes ] PolynomialSet.__init__(self, ref_el, degree, embedded_degree, expansion_set, coeffs, dmats)
def __init__(self, ref_el, degree, size=None): sd = ref_el.get_spatial_dimension() if size is None: size = sd shape = (size, size) num_exp_functions = expansions.polynomial_dimension(ref_el, degree) num_components = size * (size + 1) // 2 num_members = num_components * num_exp_functions embedded_degree = degree expansion_set = expansions.get_expansion_set(ref_el) # set up coefficients for symmetric tensors coeffs_shape = tuple([num_members] + list(shape) + [num_exp_functions]) coeffs = numpy.zeros(coeffs_shape, "d") cur_bf = 0 for [i, j] in index_iterator(shape): n = expansions.polynomial_dimension(ref_el, embedded_degree) if i == j: for exp_bf in range(n): cur_idx = tuple([cur_bf] + [i, j] + [exp_bf]) coeffs[cur_idx] = 1.0 cur_bf += 1 elif i < j: for exp_bf in range(n): cur_idx = tuple([cur_bf] + [i, j] + [exp_bf]) coeffs[cur_idx] = 1.0 cur_idx = tuple([cur_bf] + [j, i] + [exp_bf]) coeffs[cur_idx] = 1.0 cur_bf += 1 # construct dmats. this is the same as ONPolynomialSet. pts = ref_el.make_points(sd, 0, degree + sd + 1) v = numpy.transpose(expansion_set.tabulate(degree, pts)) vinv = numpy.linalg.inv(v) dv = expansion_set.tabulate_derivatives(degree, pts) dtildes = [[[a[1][i] for a in dvrow] for dvrow in dv] for i in range(sd)] dmats = [numpy.dot(vinv, numpy.transpose(dtilde)) for dtilde in dtildes] PolynomialSet.__init__(self, ref_el, degree, embedded_degree, expansion_set, coeffs, dmats)
def __init__(self, ref_el, degree, variant, quad_deg): entity_ids = {} nodes = [] sd = ref_el.get_spatial_dimension() t = ref_el.get_topology() if variant == "integral": facet = ref_el.get_facet_element() # Facet nodes are \int_F v\cdot n p ds where p \in P_{q-1} # degree is q - 1 Q = quadrature.make_quadrature(facet, quad_deg) Pq = polynomial_set.ONPolynomialSet(facet, degree) Pq_at_qpts = Pq.tabulate(Q.get_points())[tuple([0] * (sd - 1))] for f in range(len(t[sd - 1])): for i in range(Pq_at_qpts.shape[0]): phi = Pq_at_qpts[i, :] nodes.append( functional.IntegralMomentOfScaledNormalEvaluation( ref_el, Q, phi, f)) # internal nodes. These are \int_T v \cdot p dx where p \in P_{q-2}^d if degree > 0: Q = quadrature.make_quadrature(ref_el, quad_deg) qpts = Q.get_points() Pkm1 = polynomial_set.ONPolynomialSet(ref_el, degree - 1) zero_index = tuple([0 for i in range(sd)]) Pkm1_at_qpts = Pkm1.tabulate(qpts)[zero_index] for d in range(sd): for i in range(Pkm1_at_qpts.shape[0]): phi_cur = Pkm1_at_qpts[i, :] l_cur = functional.IntegralMoment( ref_el, Q, phi_cur, (d, ), (sd, )) nodes.append(l_cur) elif variant == "point": # codimension 1 facets for i in range(len(t[sd - 1])): pts_cur = ref_el.make_points(sd - 1, i, sd + degree) for j in range(len(pts_cur)): pt_cur = pts_cur[j] f = functional.PointScaledNormalEvaluation( ref_el, i, pt_cur) nodes.append(f) # internal nodes. Let's just use points at a lattice if degree > 0: cpe = functional.ComponentPointEvaluation pts = ref_el.make_points(sd, 0, degree + sd) for d in range(sd): for i in range(len(pts)): l_cur = cpe(ref_el, d, (sd, ), pts[i]) nodes.append(l_cur) # sets vertices (and in 3d, edges) to have no nodes for i in range(sd - 1): entity_ids[i] = {} for j in range(len(t[i])): entity_ids[i][j] = [] cur = 0 # set codimension 1 (edges 2d, faces 3d) dof pts_facet_0 = ref_el.make_points(sd - 1, 0, sd + degree) pts_per_facet = len(pts_facet_0) entity_ids[sd - 1] = {} for i in range(len(t[sd - 1])): entity_ids[sd - 1][i] = list(range(cur, cur + pts_per_facet)) cur += pts_per_facet # internal nodes, if applicable entity_ids[sd] = {0: []} if degree > 0: num_internal_nodes = expansions.polynomial_dimension( ref_el, degree - 1) entity_ids[sd][0] = list(range(cur, cur + num_internal_nodes * sd)) super(RTDualSet, self).__init__(nodes, ref_el, entity_ids)
def NedelecSpace3D(ref_el, k): """Constructs a nodal basis for the 3d first-kind Nedelec space""" sd = ref_el.get_spatial_dimension() if sd != 3: raise Exception("NedelecSpace3D requires 3d reference element") vec_Pkp1 = polynomial_set.ONPolynomialSet(ref_el, k + 1, (sd, )) dimPkp1 = expansions.polynomial_dimension(ref_el, k + 1) dimPk = expansions.polynomial_dimension(ref_el, k) if k > 0: dimPkm1 = expansions.polynomial_dimension(ref_el, k - 1) else: dimPkm1 = 0 vec_Pk_indices = list( chain(*(range(i * dimPkp1, i * dimPkp1 + dimPk) for i in range(sd)))) vec_Pk = vec_Pkp1.take(vec_Pk_indices) vec_Pke_indices = list( chain(*(range(i * dimPkp1 + dimPkm1, i * dimPkp1 + dimPk) for i in range(sd)))) vec_Pke = vec_Pkp1.take(vec_Pke_indices) Pkp1 = polynomial_set.ONPolynomialSet(ref_el, k + 1) Q = quadrature.make_quadrature(ref_el, 2 * (k + 1)) Qpts = numpy.array(Q.get_points()) Qwts = numpy.array(Q.get_weights()) zero_index = tuple([0 for i in range(sd)]) PkCrossXcoeffs = numpy.zeros( (vec_Pke.get_num_members(), sd, Pkp1.get_num_members()), "d") Pke_qpts = vec_Pke.tabulate(Qpts)[zero_index] Pkp1_at_Qpts = Pkp1.tabulate(Qpts)[zero_index] for i in range(vec_Pke.get_num_members()): for j in range(sd): # vector components qwts_cur_bf_val = ( Qpts[:, (j + 2) % 3] * Pke_qpts[i, (j + 1) % 3, :] - Qpts[:, (j + 1) % 3] * Pke_qpts[i, (j + 2) % 3, :]) * Qwts PkCrossXcoeffs[i, j, :] = numpy.dot(Pkp1_at_Qpts, qwts_cur_bf_val) # for k in range( Pkp1.get_num_members() ): # PkCrossXcoeffs[i,j,k] = sum( Qwts * cur_bf_val * Pkp1_at_Qpts[k,:] ) # for l in range( len( Qpts ) ): # cur_bf_val = Qpts[l][(j+2)%3] \ # * Pke_qpts[i,(j+1)%3,l] \ # - Qpts[l][(j+1)%3] \ # * Pke_qpts[i,(j+2)%3,l] # PkCrossXcoeffs[i,j,k] += Qwts[l] \ # * cur_bf_val \ # * Pkp1_at_Qpts[k,l] PkCrossX = polynomial_set.PolynomialSet(ref_el, k + 1, k + 1, vec_Pkp1.get_expansion_set(), PkCrossXcoeffs, vec_Pkp1.get_dmats()) return polynomial_set.polynomial_set_union_normalized(vec_Pk, PkCrossX)
def NedelecSpace2D(ref_el, k): """Constructs a basis for the 2d H(curl) space of the first kind which is (P_k)^2 + P_k rot( x )""" sd = ref_el.get_spatial_dimension() if sd != 2: raise Exception("NedelecSpace2D requires 2d reference element") vec_Pkp1 = polynomial_set.ONPolynomialSet(ref_el, k + 1, (sd, )) dimPkp1 = expansions.polynomial_dimension(ref_el, k + 1) dimPk = expansions.polynomial_dimension(ref_el, k) dimPkm1 = expansions.polynomial_dimension(ref_el, k - 1) vec_Pk_indices = list( chain(*(range(i * dimPkp1, i * dimPkp1 + dimPk) for i in range(sd)))) vec_Pk_from_Pkp1 = vec_Pkp1.take(vec_Pk_indices) Pkp1 = polynomial_set.ONPolynomialSet(ref_el, k + 1) PkH = Pkp1.take(list(range(dimPkm1, dimPk))) Q = quadrature.make_quadrature(ref_el, 2 * k + 2) Qpts = numpy.array(Q.get_points()) Qwts = numpy.array(Q.get_weights()) zero_index = tuple([0 for i in range(sd)]) PkH_at_Qpts = PkH.tabulate(Qpts)[zero_index] Pkp1_at_Qpts = Pkp1.tabulate(Qpts)[zero_index] PkH_crossx_coeffs = numpy.zeros( (PkH.get_num_members(), sd, Pkp1.get_num_members()), "d") def rot_x_foo(a): if a == 0: return 1, 1.0 elif a == 1: return 0, -1.0 for i in range(PkH.get_num_members()): for j in range(sd): (ind, sign) = rot_x_foo(j) for k in range(Pkp1.get_num_members()): PkH_crossx_coeffs[i, j, k] = sign * sum( Qwts * PkH_at_Qpts[i, :] * Qpts[:, ind] * Pkp1_at_Qpts[k, :]) # for l in range( len( Qpts ) ): # PkH_crossx_coeffs[i,j,k] += Qwts[ l ] \ # * PkH_at_Qpts[i,l] \ # * Qpts[l][ind] \ # * Pkp1_at_Qpts[k,l] \ # * sign PkHcrossx = polynomial_set.PolynomialSet(ref_el, k + 1, k + 1, vec_Pkp1.get_expansion_set(), PkH_crossx_coeffs, vec_Pkp1.get_dmats()) return polynomial_set.polynomial_set_union_normalized( vec_Pk_from_Pkp1, PkHcrossx)
def NedelecSpace3D(ref_el, k): """Constructs a nodal basis for the 3d first-kind Nedelec space""" sd = ref_el.get_spatial_dimension() if sd != 3: raise Exception("NedelecSpace3D requires 3d reference element") vec_Pkp1 = polynomial_set.ONPolynomialSet(ref_el, k + 1, (sd,)) dimPkp1 = expansions.polynomial_dimension(ref_el, k + 1) dimPk = expansions.polynomial_dimension(ref_el, k) if k > 0: dimPkm1 = expansions.polynomial_dimension(ref_el, k - 1) else: dimPkm1 = 0 vec_Pk_indices = list(chain(*(range(i * dimPkp1, i * dimPkp1 + dimPk) for i in range(sd)))) vec_Pk = vec_Pkp1.take(vec_Pk_indices) vec_Pke_indices = list(chain(*(range(i * dimPkp1 + dimPkm1, i * dimPkp1 + dimPk) for i in range(sd)))) vec_Pke = vec_Pkp1.take(vec_Pke_indices) Pkp1 = polynomial_set.ONPolynomialSet(ref_el, k + 1) Q = quadrature.make_quadrature(ref_el, 2 * (k + 1)) Qpts = numpy.array(Q.get_points()) Qwts = numpy.array(Q.get_weights()) zero_index = tuple([0 for i in range(sd)]) PkCrossXcoeffs = numpy.zeros((vec_Pke.get_num_members(), sd, Pkp1.get_num_members()), "d") Pke_qpts = vec_Pke.tabulate(Qpts)[zero_index] Pkp1_at_Qpts = Pkp1.tabulate(Qpts)[zero_index] for i in range(vec_Pke.get_num_members()): for j in range(sd): # vector components qwts_cur_bf_val = ( Qpts[:, (j + 2) % 3] * Pke_qpts[i, (j + 1) % 3, :] - Qpts[:, (j + 1) % 3] * Pke_qpts[i, (j + 2) % 3, :]) * Qwts PkCrossXcoeffs[i, j, :] = numpy.dot(Pkp1_at_Qpts, qwts_cur_bf_val) # for k in range( Pkp1.get_num_members() ): # PkCrossXcoeffs[i,j,k] = sum( Qwts * cur_bf_val * Pkp1_at_Qpts[k,:] ) # for l in range( len( Qpts ) ): # cur_bf_val = Qpts[l][(j+2)%3] \ # * Pke_qpts[i,(j+1)%3,l] \ # - Qpts[l][(j+1)%3] \ # * Pke_qpts[i,(j+2)%3,l] # PkCrossXcoeffs[i,j,k] += Qwts[l] \ # * cur_bf_val \ # * Pkp1_at_Qpts[k,l] PkCrossX = polynomial_set.PolynomialSet(ref_el, k + 1, k + 1, vec_Pkp1.get_expansion_set(), PkCrossXcoeffs, vec_Pkp1.get_dmats()) return polynomial_set.polynomial_set_union_normalized(vec_Pk, PkCrossX)
def NedelecSpace2D(ref_el, k): """Constructs a basis for the 2d H(curl) space of the first kind which is (P_k)^2 + P_k rot( x )""" sd = ref_el.get_spatial_dimension() if sd != 2: raise Exception("NedelecSpace2D requires 2d reference element") vec_Pkp1 = polynomial_set.ONPolynomialSet(ref_el, k + 1, (sd,)) dimPkp1 = expansions.polynomial_dimension(ref_el, k + 1) dimPk = expansions.polynomial_dimension(ref_el, k) dimPkm1 = expansions.polynomial_dimension(ref_el, k - 1) vec_Pk_indices = list(chain(*(range(i * dimPkp1, i * dimPkp1 + dimPk) for i in range(sd)))) vec_Pk_from_Pkp1 = vec_Pkp1.take(vec_Pk_indices) Pkp1 = polynomial_set.ONPolynomialSet(ref_el, k + 1) PkH = Pkp1.take(list(range(dimPkm1, dimPk))) Q = quadrature.make_quadrature(ref_el, 2 * k + 2) Qpts = numpy.array(Q.get_points()) Qwts = numpy.array(Q.get_weights()) zero_index = tuple([0 for i in range(sd)]) PkH_at_Qpts = PkH.tabulate(Qpts)[zero_index] Pkp1_at_Qpts = Pkp1.tabulate(Qpts)[zero_index] PkH_crossx_coeffs = numpy.zeros((PkH.get_num_members(), sd, Pkp1.get_num_members()), "d") def rot_x_foo(a): if a == 0: return 1, 1.0 elif a == 1: return 0, -1.0 for i in range(PkH.get_num_members()): for j in range(sd): (ind, sign) = rot_x_foo(j) for k in range(Pkp1.get_num_members()): PkH_crossx_coeffs[i, j, k] = sign * sum(Qwts * PkH_at_Qpts[i, :] * Qpts[:, ind] * Pkp1_at_Qpts[k, :]) # for l in range( len( Qpts ) ): # PkH_crossx_coeffs[i,j,k] += Qwts[ l ] \ # * PkH_at_Qpts[i,l] \ # * Qpts[l][ind] \ # * Pkp1_at_Qpts[k,l] \ # * sign PkHcrossx = polynomial_set.PolynomialSet(ref_el, k + 1, k + 1, vec_Pkp1.get_expansion_set(), PkH_crossx_coeffs, vec_Pkp1.get_dmats()) return polynomial_set.polynomial_set_union_normalized(vec_Pk_from_Pkp1, PkHcrossx)