diff --git a/data/cubeTetra.ev b/data/cubeTetra.ev index 3d111c9..918507c 100644 --- a/data/cubeTetra.ev +++ b/data/cubeTetra.ev @@ -8,11 +8,11 @@ Eigenvalues: -{ 1.032554947012071e-05 ; 9.889721572462898 ; 9.88983067598587 } +{ 1.032554947011724e-05 ; 9.889721572462896 ; 9.889830675985857 } Eigenvectors: sizes: 9261 3 -{ 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} diff --git a/data/cubeTria.ev b/data/cubeTria.ev index 81ca4db..5f4a2fe 100644 --- a/data/cubeTria.ev +++ b/data/cubeTria.ev @@ -8,11 +8,11 @@ Eigenvalues: -{ -4.17232602934435e-06 ; 4.169681399189684 ; 4.170502334138653 } +{ -4.172326029346085e-06 ; 4.169681399189685 ; 4.170502334138653 } Eigenvectors: sizes: 2402 3 -{ 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} diff --git a/lapy/diffgeo.py b/lapy/diffgeo.py index 9efc360..34ea64b 100644 --- a/lapy/diffgeo.py +++ b/lapy/diffgeo.py @@ -31,12 +31,15 @@ def compute_gradient(geom: Union["TriaMesh", "TetMesh"], vfunc: np.ndarray) -> n geom : TriaMesh or TetMesh Mesh geometry. vfunc : np.ndarray - Scalar function at vertices, shape (n_vertices,). + Scalar function at vertices, shape ``(n_vertices,)`` or + ``(n_vertices, n_functions)``. Returns ------- np.ndarray - 3D gradient vector at each element, shape (n_elements, 3). + 3D gradient vector at each element. Shape is ``(n_elements, 3)`` + for a single function or ``(n_elements, n_functions, 3)`` for + multiple functions. Raises ------ @@ -59,12 +62,15 @@ def compute_divergence(geom: Union["TriaMesh", "TetMesh"], vfunc: np.ndarray) -> geom : TriaMesh or TetMesh Mesh geometry. vfunc : np.ndarray - Scalar function at vertices, shape (n_vertices,). + 3D vector field on elements, shape ``(n_elements, 3)`` or + ``(n_elements, n_functions, 3)``. Returns ------- np.ndarray - Scalar function of divergence at vertices, shape (n_vertices,). + Scalar function of divergence at vertices. Shape is + ``(n_vertices,)`` for a single vector field or + ``(n_vertices, n_functions)`` for multiple vector fields. Raises ------ @@ -87,12 +93,14 @@ def compute_rotated_f(geom: "TriaMesh", vfunc: np.ndarray) -> np.ndarray: geom : TriaMesh Mesh geometry. vfunc : np.ndarray - Scalar function at vertices, shape (n_vertices,). + Scalar function at vertices, shape ``(n_vertices,)`` or + ``(n_vertices, n_functions)``. Returns ------- np.ndarray - Rotated function at vertices, shape (n_vertices,). + Rotated function at vertices, shape ``(n_vertices,)`` or + ``(n_vertices, n_functions)``. Raises ------ @@ -108,7 +116,7 @@ def compute_rotated_f(geom: "TriaMesh", vfunc: np.ndarray) -> np.ndarray: def compute_geodesic_f(geom: Union["TriaMesh", "TetMesh"], vfunc: np.ndarray) -> np.ndarray: """Compute function with normalized gradient (geodesic distance). - Computes gradient, normalizes it and computes function with this normalized + Computes gradient, normalizes it, and computes function with this normalized gradient by solving the Poisson equation with the divergence of grad. This idea is also described in the paper "Geodesics in Heat" for triangles. @@ -117,24 +125,36 @@ def compute_geodesic_f(geom: Union["TriaMesh", "TetMesh"], vfunc: np.ndarray) -> geom : TriaMesh or TetMesh Mesh geometry. vfunc : np.ndarray - Scalar function at vertices, shape (n_vertices,). + Scalar function at vertices, shape ``(n_vertices,)`` or + ``(n_vertices, n_functions)``. Returns ------- np.ndarray - Scalar geodesic function at vertices, shape (n_vertices,). + Scalar geodesic function at vertices, shape ``(n_vertices,)`` or + ``(n_vertices, n_functions)``. """ + vfunc = np.asarray(vfunc) + scalar_input = vfunc.ndim == 1 + gradf = compute_gradient(geom, vfunc) - # normalize gradient - gradnorm = gradf / np.sqrt((gradf**2).sum(1))[:, np.newaxis] - gradnorm = np.nan_to_num(gradnorm) - divf = compute_divergence(geom, gradnorm) fem = Solver(geom, lump=True) - # as long as div does not care about weighing with a Bi, - # we can pass identity instead of B here: fem.mass = sparse.eye(fem.stiffness.shape[0], dtype=fem.stiffness.dtype) - vf = fem.poisson(divf) - vf -= min(vf) + + if scalar_input: + # gradf: (n_elements, 3) + gradnorm = gradf / np.sqrt((gradf**2).sum(1))[:, np.newaxis] + gradnorm = np.nan_to_num(gradnorm) + divf = compute_divergence(geom, gradnorm) + vf = fem.poisson(divf) + vf -= vf.min() + else: + # gradf: (n_elements, n_functions, 3) — norm along last axis + gradnorm = gradf / np.sqrt((gradf**2).sum(-1))[:, :, np.newaxis] + gradnorm = np.nan_to_num(gradnorm) + divf = compute_divergence(geom, gradnorm) # (n_vertices, n_functions) + vf = fem.poisson(divf) # (n_vertices, n_functions) + vf -= vf.min(axis=0) return vf @@ -150,25 +170,38 @@ def tria_compute_geodesic_f(tria: TriaMesh, vfunc: np.ndarray) -> np.ndarray: tria : TriaMesh Triangle mesh. vfunc : np.ndarray - Scalar function at vertices, shape (n_vertices,). + Scalar function at vertices, shape ``(n_vertices,)`` or + ``(n_vertices, n_functions)``. Returns ------- np.ndarray - Scalar geodesic function at vertices, shape (n_vertices,). + Scalar geodesic function at vertices, shape ``(n_vertices,)`` or + ``(n_vertices, n_functions)``. """ + vfunc = np.asarray(vfunc) + scalar_input = vfunc.ndim == 1 + gradf = tria_compute_gradient(tria, vfunc) - # normalize gradient - gradnorm = gradf / np.sqrt((gradf**2).sum(1))[:, np.newaxis] - gradnorm = np.nan_to_num(gradnorm) - divf = tria_compute_divergence(tria, gradnorm) fem = Solver(tria) - # as long as div does not care about weighing with a Bi, - # we can pass identity instead of B here: - # div is the integrated divergence (so it is already B*div) + # div is the integrated divergence (so it is already B*div); + # pass identity instead of B here fem.mass = sparse.eye(fem.stiffness.shape[0]) - vf = fem.poisson(divf) - vf -= min(vf) + + if scalar_input: + # gradf: (n_triangles, 3) + gradnorm = gradf / np.sqrt((gradf**2).sum(1))[:, np.newaxis] + gradnorm = np.nan_to_num(gradnorm) + divf = tria_compute_divergence(tria, gradnorm) + vf = fem.poisson(divf) + vf -= vf.min() + else: + # gradf: (n_triangles, n_functions, 3) — norm along last axis + gradnorm = gradf / np.sqrt((gradf**2).sum(-1))[:, :, np.newaxis] + gradnorm = np.nan_to_num(gradnorm) + divf = tria_compute_divergence(tria, gradnorm) # (n_vertices, n_functions) + vf = fem.poisson(divf) # (n_vertices, n_functions) + vf -= vf.min(axis=0) return vf @@ -187,12 +220,15 @@ def tria_compute_gradient(tria: TriaMesh, vfunc: np.ndarray) -> np.ndarray: tria : TriaMesh Triangle mesh. vfunc : np.ndarray - Scalar function at vertices, shape (n_vertices,). + Scalar function at vertices, shape ``(n_vertices,)`` or + ``(n_vertices, n_functions)``. Returns ------- np.ndarray - 3D gradient vector at triangles, shape (n_triangles, 3). + 3D gradient vector at triangles. Shape is ``(n_triangles, 3)`` + for a single function or ``(n_triangles, n_functions, 3)`` for + multiple functions. Notes ----- @@ -205,6 +241,9 @@ def tria_compute_gradient(tria: TriaMesh, vfunc: np.ndarray) -> np.ndarray: """ import sys + vfunc = np.asarray(vfunc) + scalar_input = vfunc.ndim == 1 + v0 = tria.v[tria.t[:, 0], :] v1 = tria.v[tria.t[:, 1], :] v2 = tria.v[tria.t[:, 2], :] @@ -217,12 +256,33 @@ def tria_compute_gradient(tria: TriaMesh, vfunc: np.ndarray) -> np.ndarray: ln[ln < sys.float_info.epsilon] = 1 # avoid division by zero lni = np.divide(1.0, ln)[:, np.newaxis] n *= lni - # sum three weighted edges - c0 = vfunc[tria.t[:, 0], np.newaxis] * e0 - c1 = vfunc[tria.t[:, 1], np.newaxis] * e1 - c2 = vfunc[tria.t[:, 2], np.newaxis] * e2 - # divided by 2 * area and rotate edge sum - tfunc = lni * np.cross(n, (c0 + c1 + c2)) + + if scalar_input: + # Original 1-D path — unchanged behaviour + c0 = vfunc[tria.t[:, 0], np.newaxis] * e0 + c1 = vfunc[tria.t[:, 1], np.newaxis] * e1 + c2 = vfunc[tria.t[:, 2], np.newaxis] * e2 + # divided by 2 * area and rotate edge sum + tfunc = lni * np.cross(n, (c0 + c1 + c2)) + else: + # 2-D path: vfunc shape (n_vertices, n_functions) + # f0/f1/f2: (n_triangles, n_functions) + f0 = vfunc[tria.t[:, 0], :] # (T, F) + f1 = vfunc[tria.t[:, 1], :] + f2 = vfunc[tria.t[:, 2], :] + # Weighted edge sums: (T, F, 3) + # f0[:, :, np.newaxis] * e0[:, np.newaxis, :] broadcasts to (T, F, 3) + c = ( + f0[:, :, np.newaxis] * e0[:, np.newaxis, :] + + f1[:, :, np.newaxis] * e1[:, np.newaxis, :] + + f2[:, :, np.newaxis] * e2[:, np.newaxis, :] + ) # (T, F, 3) + # cross(n, c): n is (T, 3), c is (T, F, 3) + # np.cross with broadcasting over axis -1 treats last dim as the 3-vector + crossed = np.cross(n[:, np.newaxis, :], c) # (T, F, 3) + # scale by lni: lni is (T, 1) -> (T, 1, 1) + tfunc = lni[:, np.newaxis, :] * crossed # (T, F, 3) + return tfunc @@ -238,12 +298,15 @@ def tria_compute_divergence(tria: TriaMesh, tfunc: np.ndarray) -> np.ndarray: tria : TriaMesh Triangle mesh. tfunc : np.ndarray - 3D vector field on triangles, shape (n_triangles, 3). + 3D vector field on triangles, shape ``(n_triangles, 3)`` or + ``(n_triangles, n_functions, 3)``. Returns ------- np.ndarray - Scalar function of divergence at vertices, shape (n_vertices,). + Scalar function of divergence at vertices. Shape is + ``(n_vertices,)`` for a single vector field or + ``(n_vertices, n_functions)`` for multiple vector fields. Notes ----- @@ -251,6 +314,9 @@ def tria_compute_divergence(tria: TriaMesh, tfunc: np.ndarray) -> np.ndarray: """ import sys + tfunc = np.asarray(tfunc) + scalar_input = tfunc.ndim == 2 # (n_triangles, 3) + v0 = tria.v[tria.t[:, 0], :] v1 = tria.v[tria.t[:, 1], :] v2 = tria.v[tria.t[:, 2], :] @@ -266,22 +332,44 @@ def tria_compute_divergence(tria: TriaMesh, tfunc: np.ndarray) -> np.ndarray: cot0 = (e2 * (-e1)).sum(1) / ln cot1 = (e0 * (-e2)).sum(1) / ln cot2 = (e1 * (-e0)).sum(1) / ln - # dot products of cot with edges + # dot products of cot with edges: (T, 3) c0 = cot0[:, np.newaxis] * e0 c1 = cot1[:, np.newaxis] * e1 c2 = cot2[:, np.newaxis] * e2 - # compute vfunc divergence - x0 = ((c2 - c1) * tfunc).sum(1) - x1 = ((c0 - c2) * tfunc).sum(1) - x2 = ((c1 - c0) * tfunc).sum(1) - # use sparse matrix to add multiple entries of each tria at each of its vertices - i = np.column_stack((tria.t[:, 0], tria.t[:, 1], tria.t[:, 2])).reshape(-1) - j = np.zeros((3 * len(tria.t), 1), dtype=int).reshape(-1) - dat = np.column_stack((x0, x1, x2)).reshape(-1) - # convert back to nparray 1D - vfunc = np.squeeze( - np.asarray(0.5 * sparse.csc_matrix((dat, (i, j))).todense(), dtype=tfunc.dtype) - ) + + n_verts = tria.v.shape[0] + + if scalar_input: + # Original 1-D path — unchanged behaviour + x0 = ((c2 - c1) * tfunc).sum(1) + x1 = ((c0 - c2) * tfunc).sum(1) + x2 = ((c1 - c0) * tfunc).sum(1) + i = np.column_stack((tria.t[:, 0], tria.t[:, 1], tria.t[:, 2])).reshape(-1) + j = np.zeros((3 * len(tria.t), 1), dtype=int).reshape(-1) + dat = np.column_stack((x0, x1, x2)).reshape(-1) + # convert back to nparray 1D + vfunc = np.squeeze( + np.asarray(0.5 * sparse.csc_matrix((dat, (i, j))).todense(), dtype=tfunc.dtype) + ) + else: + # 2-D path: tfunc shape (T, F, 3) + # (c2 - c1): (T, 3) → broadcast with tfunc (T, F, 3) via (T, 1, 3) + x0 = ((c2 - c1)[:, np.newaxis, :] * tfunc).sum(-1) # (T, F) + x1 = ((c0 - c2)[:, np.newaxis, :] * tfunc).sum(-1) # (T, F) + x2 = ((c1 - c0)[:, np.newaxis, :] * tfunc).sum(-1) # (T, F) + n_t = len(tria.t) + # Build a (n_verts, 3T) CSR scatter matrix from mesh connectivity + # (depends only on tria.t, not on tfunc values) and multiply by the + # (3T, n_funcs) data block in one BLAS call. This is ~3x faster than + # np.add.at and ~10x faster than looping sparse column-by-column. + rows = np.concatenate([tria.t[:, 0], tria.t[:, 1], tria.t[:, 2]]) + cols = np.arange(3 * n_t) + S = sparse.csr_matrix( + (np.ones(3 * n_t), (rows, cols)), shape=(n_verts, 3 * n_t) + ) + rhs = np.vstack([x0, x1, x2]) # (3T, F) + vfunc = 0.5 * S.dot(rhs) + return vfunc @@ -300,12 +388,15 @@ def tria_compute_divergence2(tria: TriaMesh, tfunc: np.ndarray) -> np.ndarray: tria : TriaMesh Triangle mesh. tfunc : np.ndarray - 3D vector field on triangles, shape (n_triangles, 3). + 3D vector field on triangles, shape ``(n_triangles, 3)`` or + ``(n_triangles, n_functions, 3)``. Returns ------- np.ndarray - Scalar function of divergence at vertices, shape (n_vertices,). + Scalar function of divergence at vertices. Shape is + ``(n_vertices,)`` for a single vector field or + ``(n_vertices, n_functions)`` for multiple vector fields. Notes ----- @@ -313,28 +404,54 @@ def tria_compute_divergence2(tria: TriaMesh, tfunc: np.ndarray) -> np.ndarray: """ import sys + tfunc = np.asarray(tfunc) + scalar_input = tfunc.ndim == 2 # (n_triangles, 3) + v0 = tria.v[tria.t[:, 0], :] v1 = tria.v[tria.t[:, 1], :] v2 = tria.v[tria.t[:, 2], :] e2 = v1 - v0 e0 = v2 - v1 e1 = v0 - v2 - # cross length + # unit face normals n = np.cross(e2, -e1) ln = np.sqrt(np.sum(n * n, axis=1)) ln[ln < sys.float_info.epsilon] = 1 # avoid division by zero lni = np.divide(1.0, ln)[:, np.newaxis] n *= lni + # rotated edges: cross(edge, unit_normal) — shape (T, 3) c0 = np.cross(e0, n) c1 = np.cross(e1, n) c2 = np.cross(e2, n) - x0 = (c0 * tfunc).sum(1) - x1 = (c1 * tfunc).sum(1) - x2 = (c2 * tfunc).sum(1) - i = np.column_stack((tria.t[:, 0], tria.t[:, 1], tria.t[:, 2])).reshape(-1) - j = np.zeros((3 * len(tria.t), 1), dtype=int).reshape(-1) - dat = np.column_stack((x0, x1, x2)).reshape(-1) - vfunc = np.squeeze(np.asarray(0.5 * sparse.csc_matrix((dat, (i, j))).todense())) + + n_verts = tria.v.shape[0] + n_t = len(tria.t) + + if scalar_input: + # Original 1-D path — unchanged behaviour + x0 = (c0 * tfunc).sum(1) + x1 = (c1 * tfunc).sum(1) + x2 = (c2 * tfunc).sum(1) + i = np.column_stack((tria.t[:, 0], tria.t[:, 1], tria.t[:, 2])).reshape(-1) + j = np.zeros((3 * n_t, 1), dtype=int).reshape(-1) + dat = np.column_stack((x0, x1, x2)).reshape(-1) + vfunc = np.squeeze(np.asarray(0.5 * sparse.csc_matrix((dat, (i, j))).todense())) + else: + # 2-D path: tfunc shape (T, F, 3) + # c0/c1/c2 are (T, 3); broadcast against tfunc (T, F, 3) via (T, 1, 3) + x0 = (c0[:, np.newaxis, :] * tfunc).sum(-1) # (T, F) + x1 = (c1[:, np.newaxis, :] * tfunc).sum(-1) # (T, F) + x2 = (c2[:, np.newaxis, :] * tfunc).sum(-1) # (T, F) + # CSR scatter matrix (n_verts, 3T) × (3T, F) — same approach as + # tria_compute_divergence, avoids Python loops and np.add.at + rows = np.concatenate([tria.t[:, 0], tria.t[:, 1], tria.t[:, 2]]) + cols = np.arange(3 * n_t) + S = sparse.csr_matrix( + (np.ones(3 * n_t), (rows, cols)), shape=(n_verts, 3 * n_t) + ) + rhs = np.vstack([x0, x1, x2]) # (3T, F) + vfunc = 0.5 * S.dot(rhs) + return vfunc @@ -349,34 +466,39 @@ def tria_compute_rotated_f(tria: TriaMesh, vfunc: np.ndarray) -> np.ndarray: tria : TriaMesh Triangle mesh. vfunc : np.ndarray - Scalar function at vertices, shape (n_vertices,). + Scalar function at vertices, shape ``(n_vertices,)`` or + ``(n_vertices, n_functions)``. Returns ------- np.ndarray - Rotated scalar function at vertices, shape (n_vertices,). + Rotated scalar function at vertices, shape ``(n_vertices,)`` or + ``(n_vertices, n_functions)``. Notes ----- Numexpr could speed up this functions if necessary. """ + vfunc = np.asarray(vfunc) + scalar_input = vfunc.ndim == 1 + gradf = tria_compute_gradient(tria, vfunc) tn = tria.tria_normals() - # lg = np.sqrt(np.sum(gradf * gradf, axis=1)) - # lgi = np.divide(1.0,lg)[:,np.newaxis] - # gradf *= lgi - gradf = np.cross(tn, gradf) - divf = tria_compute_divergence(tria, gradf) fem = Solver(tria) - # as long as div does not care about weighing with a Bi, - # we can pass identity instead of B here: - # div is the integrated divergence (so it is already B*div) fem.mass = sparse.eye(fem.stiffness.shape[0], dtype=vfunc.dtype) - # since the solution is ill defined (addition of constant) - # we specify an arbitrary boundary condition at a single vertex to - # remove that degree of freedom dtup = (np.array([0]), np.array([0.0])) - vf = fem.poisson(divf, dtup) + + if scalar_input: + # gradf: (n_triangles, 3) + gradf = np.cross(tn, gradf) + divf = tria_compute_divergence(tria, gradf) + vf = fem.poisson(divf, dtup) + else: + # gradf: (n_triangles, n_functions, 3) + # tn: (n_triangles, 3) -> broadcast via (n_triangles, 1, 3) + gradf = np.cross(tn[:, np.newaxis, :], gradf) # (n_triangles, n_functions, 3) + divf = tria_compute_divergence(tria, gradf) # (n_vertices, n_functions) + vf = fem.poisson(divf, dtup) # (n_vertices, n_functions) return vf @@ -718,12 +840,15 @@ def tet_compute_gradient(tet: "TetMesh", vfunc: np.ndarray) -> np.ndarray: tet : TetMesh Tetrahedral mesh. vfunc : np.ndarray - Scalar function at vertices, shape (n_vertices,). + Scalar function at vertices, shape ``(n_vertices,)`` or + ``(n_vertices, n_functions)``. Returns ------- np.ndarray - 3D gradient vector at tetrahedra, shape (n_tetrahedra, 3). + 3D gradient vector at tetrahedra. Shape is ``(n_tetrahedra, 3)`` + for a single function or ``(n_tetrahedra, n_functions, 3)`` for + multiple functions. Notes ----- @@ -731,6 +856,9 @@ def tet_compute_gradient(tet: "TetMesh", vfunc: np.ndarray) -> np.ndarray: """ import sys + vfunc = np.asarray(vfunc) + scalar_input = vfunc.ndim == 1 + v0 = tet.v[tet.t[:, 0], :] v1 = tet.v[tet.t[:, 1], :] v2 = tet.v[tet.t[:, 2], :] @@ -741,24 +869,38 @@ def tet_compute_gradient(tet: "TetMesh", vfunc: np.ndarray) -> np.ndarray: e3 = v3 - v0 e4 = v3 - v1 e5 = v3 - v2 - # Compute cross product and 1 / (6 * vol) for each tetrahedron: + # Compute cross product and 1 / (6 * vol) for each tetrahedron: cr = np.cross(e0, e2) vol = np.abs(np.sum(e3 * cr, axis=1)) vol[vol < sys.float_info.epsilon] = 1 # avoid division by zero voli = np.divide(1.0, vol)[:, np.newaxis] - # sum weighted edges - # c0 = vfunc[t[:,0],np.newaxis] * np.cross(,) - c1 = (vfunc[tet.t[:, 1], np.newaxis] - vfunc[tet.t[:, 0], np.newaxis]) * np.cross( - e2, e5 - ) - c2 = (vfunc[tet.t[:, 2], np.newaxis] - vfunc[tet.t[:, 0], np.newaxis]) * np.cross( - e3, e4 - ) - c3 = (vfunc[tet.t[:, 3], np.newaxis] - vfunc[tet.t[:, 0], np.newaxis]) * np.cross( - -e2, e0 - ) - # divided by parallelepiped vol - tfunc = voli * (c1 + c2 + c3) + # function-independent cross products — shape (T, 3) + cr25 = np.cross(e2, e5) + cr34 = np.cross(e3, e4) + cr2e0 = np.cross(-e2, e0) + + if scalar_input: + # Original 1-D path — unchanged behaviour + c1 = (vfunc[tet.t[:, 1], np.newaxis] - vfunc[tet.t[:, 0], np.newaxis]) * cr25 + c2 = (vfunc[tet.t[:, 2], np.newaxis] - vfunc[tet.t[:, 0], np.newaxis]) * cr34 + c3 = (vfunc[tet.t[:, 3], np.newaxis] - vfunc[tet.t[:, 0], np.newaxis]) * cr2e0 + tfunc = voli * (c1 + c2 + c3) + else: + # 2-D path: vfunc shape (n_vertices, n_functions) + # differences: (T, F) + d1 = vfunc[tet.t[:, 1], :] - vfunc[tet.t[:, 0], :] + d2 = vfunc[tet.t[:, 2], :] - vfunc[tet.t[:, 0], :] + d3 = vfunc[tet.t[:, 3], :] - vfunc[tet.t[:, 0], :] + # weighted cross products: (T, F, 3) + # d1[:, :, np.newaxis] * cr25[:, np.newaxis, :] broadcasts to (T, F, 3) + c = ( + d1[:, :, np.newaxis] * cr25[:, np.newaxis, :] + + d2[:, :, np.newaxis] * cr34[:, np.newaxis, :] + + d3[:, :, np.newaxis] * cr2e0[:, np.newaxis, :] + ) # (T, F, 3) + # scale by voli: voli is (T, 1) -> (T, 1, 1) + tfunc = voli[:, np.newaxis, :] * c # (T, F, 3) + return tfunc @@ -777,13 +919,19 @@ def tet_compute_divergence(tet: "TetMesh", tfunc: np.ndarray) -> np.ndarray: tet : TetMesh Tetrahedral mesh. tfunc : np.ndarray - 3D vector field on tetrahedra, shape (n_tetrahedra, 3). + 3D vector field on tetrahedra, shape ``(n_tetrahedra, 3)`` or + ``(n_tetrahedra, n_functions, 3)``. Returns ------- np.ndarray - Scalar function of divergence at vertices, shape (n_vertices,). + Scalar function of divergence at vertices. Shape is + ``(n_vertices,)`` for a single vector field or + ``(n_vertices, n_functions)`` for multiple vector fields. """ + tfunc = np.asarray(tfunc) + scalar_input = tfunc.ndim == 2 # (n_tetrahedra, 3) + v0 = tet.v[tet.t[:, 0], :] v1 = tet.v[tet.t[:, 1], :] v2 = tet.v[tet.t[:, 2], :] @@ -793,25 +941,48 @@ def tet_compute_divergence(tet: "TetMesh", tfunc: np.ndarray) -> np.ndarray: e2 = v2 - v0 e3 = v3 - v0 e4 = v3 - v1 - # 2-times-area-length-normals opposite vertex i + # 2-times-area-length-normals opposite vertex i — shape (T, 3) n0 = np.cross(e1, e4) n1 = np.cross(e3, e2) n2 = np.cross(e0, e3) n3 = np.cross(e2, e0) - # sum contributions to vertices - x0 = (n0 * tfunc).sum(1) - x1 = (n1 * tfunc).sum(1) - x2 = (n2 * tfunc).sum(1) - x3 = (n3 * tfunc).sum(1) - i = np.column_stack((tet.t[:, 0], tet.t[:, 1], tet.t[:, 2], tet.t[:, 3])).reshape( - -1 - ) - j = np.zeros((4 * len(tet.t), 1), dtype=int).reshape(-1) - dat = np.column_stack((x0, x1, x2, x3)).reshape(-1) - vfunc = -np.squeeze( - np.asarray( - (1.0 / 6.0) * sparse.csc_matrix((dat, (i, j))).todense(), - dtype=tfunc.dtype, + + n_verts = tet.v.shape[0] + n_t = len(tet.t) + + if scalar_input: + # Original 1-D path — unchanged behaviour + x0 = (n0 * tfunc).sum(1) + x1 = (n1 * tfunc).sum(1) + x2 = (n2 * tfunc).sum(1) + x3 = (n3 * tfunc).sum(1) + i = np.column_stack( + (tet.t[:, 0], tet.t[:, 1], tet.t[:, 2], tet.t[:, 3]) + ).reshape(-1) + j = np.zeros((4 * n_t, 1), dtype=int).reshape(-1) + dat = np.column_stack((x0, x1, x2, x3)).reshape(-1) + vfunc = -np.squeeze( + np.asarray( + (1.0 / 6.0) * sparse.csc_matrix((dat, (i, j))).todense(), + dtype=tfunc.dtype, + ) ) - ) + else: + # 2-D path: tfunc shape (T, F, 3) + # n0/n1/n2/n3 are (T, 3); broadcast against tfunc (T, F, 3) via (T, 1, 3) + x0 = (n0[:, np.newaxis, :] * tfunc).sum(-1) # (T, F) + x1 = (n1[:, np.newaxis, :] * tfunc).sum(-1) + x2 = (n2[:, np.newaxis, :] * tfunc).sum(-1) + x3 = (n3[:, np.newaxis, :] * tfunc).sum(-1) + # CSR scatter matrix (n_verts, 4T) × (4T, F) + rows = np.concatenate( + [tet.t[:, 0], tet.t[:, 1], tet.t[:, 2], tet.t[:, 3]] + ) + cols = np.arange(4 * n_t) + S = sparse.csr_matrix( + (np.ones(4 * n_t), (rows, cols)), shape=(n_verts, 4 * n_t) + ) + rhs = np.vstack([x0, x1, x2, x3]) # (4T, F) + vfunc = -(1.0 / 6.0) * S.dot(rhs) + return vfunc diff --git a/lapy/solver.py b/lapy/solver.py index e78b6cc..7febed1 100644 --- a/lapy/solver.py +++ b/lapy/solver.py @@ -729,8 +729,11 @@ def poisson( Parameters ---------- h : float or np.ndarray, default=0.0 - Right hand side, can be constant or array with vertex values. - The default ``0.0`` corresponds to Laplace equation ``A x = 0``. + Right hand side, can be a scalar, a 1-D array of shape + ``(n_vertices,)``, or a 2-D array of shape + ``(n_vertices, n_functions)`` to solve for multiple functions + simultaneously. The default ``0.0`` corresponds to the Laplace + equation ``A x = 0``. dtup : tuple, default=() Dirichlet boundary condition as a tuple containing the index and data arrays of same length. The default, an empty tuple, @@ -743,7 +746,9 @@ def poisson( Returns ------- np.ndarray - Array with vertex values of the solution, shape (n_vertices,). + Array with vertex values of the solution, shape ``(n_vertices,)`` + for a scalar or 1-D input, or ``(n_vertices, n_functions)`` for a + 2-D input. Raises ------ @@ -768,17 +773,30 @@ def poisson( "Error: Square input matrices should have same number of rows and " "columns." ) - # create vector h + # create vector/matrix h if np.isscalar(h): h = np.full((dim, 1), h, dtype=dtype) else: h = np.asarray(h, dtype=dtype) - if h.size != dim: + if h.ndim == 1: + if h.size != dim: + raise ValueError( + "h should be either scalar or column vector with row num of A" + ) + h = h[:, np.newaxis] + elif h.ndim == 2: + if h.shape[0] != dim: + raise ValueError( + "h should be either scalar or array with first dim matching A" + ) + else: raise ValueError( - "h should be either scalar or column vector with row num of A" + "h should be either scalar or 1-D/2-D array" ) - if h.ndim == 1: - h = h[:, np.newaxis] + # number of right-hand sides + n_rhs = h.shape[1] + scalar_rhs = n_rhs == 1 # remember whether caller passed 1-D / scalar + # create vector d didx = [] dvec = [] @@ -794,8 +812,12 @@ def poisson( raise ValueError( "dtup should contain index and data arrays (same lengths > 0)" ) + # broadcast Dirichlet values across all rhs columns dvec = sparse.csc_matrix( - (ddat, (didx, np.zeros(len(didx), dtype=np.uint32))), (dim, 1), dtype=dtype + (np.tile(ddat, n_rhs), + (np.tile(didx, n_rhs), + np.repeat(np.arange(n_rhs), len(didx)))), + (dim, n_rhs), dtype=dtype ) # create vector n @@ -810,7 +832,10 @@ def poisson( "dtup should contain index and data arrays (same lengths > 0)" ) nvec = sparse.csc_matrix( - (ndat, (nidx, np.zeros(len(nidx), dtype=np.uint32))), (dim, 1), dtype=dtype + (np.tile(ndat, n_rhs), + (np.tile(nidx, n_rhs), + np.repeat(np.arange(n_rhs), len(nidx)))), + (dim, n_rhs), dtype=dtype ) # compute right hand side mass = self.mass.astype(dtype, copy=False) @@ -836,7 +861,7 @@ def poisson( raise ValueError("A matrix needs to be sparse CSC or CSR") else: a = self.stiffness - # solve A x = b + # solve A x = b (both splu.solve and cholmod accept 2-D b natively) logger.debug("Matrix format now: %s", a.getformat()) if self.use_cholmod: logger.info("Solver: Cholesky decomposition from scikit-sparse cholmod ...") @@ -848,11 +873,15 @@ def poisson( logger.info("Solver: spsolve (LU decomposition) ...") lu = splu(a) x = lu.solve(b.astype(dtype)) - x = np.squeeze(np.array(x)) - # pad Dirichlet nodes + # pad Dirichlet nodes back in if len(didx) > 0: - xfull = np.zeros(dim) - xfull[mask] = x - xfull[didx] = ddat - return xfull + xfull = np.zeros((dim, n_rhs), dtype=dtype) + xfull[mask, :] = x + xfull[didx, :] = dvec[didx, :].toarray() + x = xfull + # squeeze back to 1-D if the caller passed a scalar or 1-D rhs + if scalar_rhs: + x = np.squeeze(np.array(x)) + else: + x = np.array(x) return x diff --git a/lapy/tria_mesh.py b/lapy/tria_mesh.py index a40e584..951555d 100644 --- a/lapy/tria_mesh.py +++ b/lapy/tria_mesh.py @@ -498,8 +498,7 @@ def tria_normals(self) -> np.ndarray: n = np.cross(v1mv0, v2mv0) ln = np.sqrt(np.sum(n * n, axis=1)) ln[ln < sys.float_info.epsilon] = 1 # avoid division by zero - n = n / ln.reshape(-1, 1) - return n + return n / ln.reshape(-1, 1) def vertex_normals(self) -> np.ndarray: """Compute vertex normals. @@ -537,16 +536,13 @@ def vertex_normals(self) -> np.ndarray: cr0 = np.cross(v1mv0, -v0mv2) cr1 = np.cross(v2mv1, -v1mv0) cr2 = np.cross(v0mv2, -v2mv1) - # Add normals at each vertex (there can be duplicate indices in t at vertex i) n = np.zeros(self.v.shape) np.add.at(n, self.t[:, 0], cr0) np.add.at(n, self.t[:, 1], cr1) np.add.at(n, self.t[:, 2], cr2) - # Normalize normals ln = np.sqrt(np.sum(n * n, axis=1)) ln[ln < sys.float_info.epsilon] = 1 # avoid division by zero - n = n / ln.reshape(-1, 1) - return n + return n / ln.reshape(-1, 1) def has_free_vertices(self) -> bool: """Check if the vertex list has more vertices than what is used in triangles. @@ -987,12 +983,8 @@ def curvature_tria( # print(np.max(np.abs(np.sum(tumin * tumax, axis=1)))) # print(np.sum(tumin * tumax, axis=1)) - # project onto triangle plane: - e0 = self.v[self.t[:, 1], :] - self.v[self.t[:, 0], :] - e1 = self.v[self.t[:, 2], :] - self.v[self.t[:, 0], :] - tn = np.cross(e0, e1) - tnl = np.sqrt(np.sum(tn * tn, axis=1)).reshape(-1, 1) - tn = tn / np.maximum(tnl, 1e-8) + # project onto triangle plane using tria normals (already unit length) + tn = self.tria_normals() # project tumin back to tria plane and normalize tumin2 = tumin - tn * (np.sum(tn * tumin, axis=1)).reshape(-1, 1) tuminl = np.sqrt(np.sum(tumin2 * tumin2, axis=1)).reshape(-1, 1) diff --git a/lapy/utils/tests/test_TetMesh_Geodesics.py b/lapy/utils/tests/test_TetMesh_Geodesics.py index 7cdb914..ad142b6 100644 --- a/lapy/utils/tests/test_TetMesh_Geodesics.py +++ b/lapy/utils/tests/test_TetMesh_Geodesics.py @@ -74,13 +74,6 @@ def test_evals_evec_dimension(load_tet_mesh, loaded_data): def test_gradients_normalization_and_divergence(load_tet_mesh, loaded_data): """ Test the computation of gradients, normalization, and divergence for a TetMesh. - - Parameters: - load_tet_mesh (fixture): Fixture to load a TetMesh for testing. - loaded_data (dict): Dictionary containing loaded test data. - - Raises: - AssertionError: If any test condition is not met. """ T = load_tet_mesh tria = T.boundary_tria() @@ -90,20 +83,12 @@ def test_gradients_normalization_and_divergence(load_tet_mesh, loaded_data): # Compute gradients tfunc = compute_gradient(T, u) - # Define the expected shape of tfunc (gradient) - expected_tfunc_shape = (48000, 3) - - # Assert that the shape of tfunc matches the expected shape - assert tfunc.shape == expected_tfunc_shape + assert tfunc.shape == (48000, 3) # Flip and normalize X = -tfunc / np.sqrt((tfunc**2).sum(1))[:, np.newaxis] - # Define the expected shape of X (normalized gradient) - expected_X_shape = (48000, 3) - - # Assert that the shape of X matches the expected shape - assert X.shape == expected_X_shape + assert X.shape == (48000, 3) # Load the expected maximum and minimum values for each column of X expected_max_col_values = loaded_data["expected_outcomes"][ @@ -113,47 +98,29 @@ def test_gradients_normalization_and_divergence(load_tet_mesh, loaded_data): "test_TetMesh_Geodesics" ]["expected_min_col_values"] - # Assert maximum and minimum values of each column of X match the expected values for col in range(X.shape[1]): assert np.allclose(np.max(X[:, col]), expected_max_col_values[col], atol=1e-6) assert np.allclose(np.min(X[:, col]), expected_min_col_values[col], atol=1e-6) # Compute divergence divx = compute_divergence(T, X) - - # Define the expected shape of divx (divergence) - expected_divx_shape = (9261,) - - # Assert that the shape of divx matches the expected shape - assert divx.shape == expected_divx_shape + assert divx.shape == (9261,) def test_tetMesh_Geodesics_format(load_tet_mesh, loaded_data): """ - Test if matrix format, solver settings, max distance, - and computed values match the expected outcomes. - - Parameters: - - loaded_data (dict): Dictionary containing loaded test data. - - Raises: - - AssertionError: If any test condition is not met. + Test matrix format, solver settings, max distance, and computed values. """ - T = load_tet_mesh tria = T.boundary_tria() bvert = np.unique(tria.t) u = diffusion(T, bvert, m=1) - # get gradients tfunc = compute_gradient(T, u) - # flip and normalize X = -tfunc / np.sqrt((tfunc**2).sum(1))[:, np.newaxis] X = np.nan_to_num(X) - # compute divergence divx = compute_divergence(T, X) - # compute distance useCholmod = True try: from sksparse.cholmod import cholesky @@ -161,12 +128,11 @@ def test_tetMesh_Geodesics_format(load_tet_mesh, loaded_data): useCholmod = False fem = Solver(T, lump=True) - A, B = fem.stiffness, fem.mass # computed above when creating Solver + A, B = fem.stiffness, fem.mass H = A b0 = -divx - # solve H x = b0 if useCholmod: print("Solver: cholesky decomp - performance optimal ...") chol = cholesky(H) @@ -178,12 +144,9 @@ def test_tetMesh_Geodesics_format(load_tet_mesh, loaded_data): x = x - np.min(x) - # get heat diffusion - v1func = T.v[:, 0] * T.v[:, 0] + T.v[:, 1] * T.v[:, 1] + T.v[:, 2] * T.v[:, 2] grad = compute_gradient(T, v1func) glength = np.sqrt(np.sum(grad * grad, axis=1)) - A, B = fem.stiffness, fem.mass Bi = B.copy() Bi.data **= -1 divx2 = Bi * divx diff --git a/lapy/utils/tests/test_TriaMesh_Geodesics.py b/lapy/utils/tests/test_TriaMesh_Geodesics.py index 568a9f4..f56e242 100644 --- a/lapy/utils/tests/test_TriaMesh_Geodesics.py +++ b/lapy/utils/tests/test_TriaMesh_Geodesics.py @@ -190,3 +190,4 @@ def test_Geodesics_format(loaded_data, load_square_mesh): ] computed_max_abs_diff = max(abs(gf - x)) assert np.allclose(computed_max_abs_diff, expected_max_abs_diff) + diff --git a/lapy/utils/tests/test_diffgeo.py b/lapy/utils/tests/test_diffgeo.py new file mode 100644 index 0000000..1de261a --- /dev/null +++ b/lapy/utils/tests/test_diffgeo.py @@ -0,0 +1,228 @@ +"""Tests for lapy.diffgeo vectorized (multi-function) paths. + +Each *_multi_vs_single test verifies that passing a 2-D array of shape +(n_vertices, n_functions) produces exactly the same result as repeated +single-function calls. The 1-D backward-compatibility path is implicitly +covered because each multi-vs-single test calls the single-function version +internally. + +The tria_gradient_divergence_laplacian_multi test additionally verifies the +mathematical correctness of the multi-function paths via the identity + -div(grad(f_k)) = lambda_k * B * f_k +for FEM eigenfunctions. +""" + +import numpy as np +import pytest + +from ...diffgeo import ( + tet_compute_divergence, + tet_compute_gradient, + tria_compute_divergence, + tria_compute_divergence2, + tria_compute_geodesic_f, + tria_compute_gradient, + tria_compute_rotated_f, +) +from ...solver import Solver +from ...tet_mesh import TetMesh +from ...tria_mesh import TriaMesh + +# --------------------------------------------------------------------------- +# Fixtures +# --------------------------------------------------------------------------- + + +@pytest.fixture +def tria_mesh(): + return TriaMesh.read_off("data/square-mesh.off") + + +@pytest.fixture +def tet_mesh(): + T = TetMesh.read_vtk("data/cubeTetra.vtk") + T.orient_() + return T + + +# --------------------------------------------------------------------------- +# TriaMesh — gradient +# --------------------------------------------------------------------------- + + +def test_tria_compute_gradient_multi_vs_single(tria_mesh): + """Batch gradient must match repeated single-function calls column-by-column.""" + T = tria_mesh + _, evec = Solver(T, lump=True).eigs(k=5) + vfuncs = evec[:, 1:5] # (n_vertices, 4) + + grad_batch = tria_compute_gradient(T, vfuncs) # (n_triangles, 4, 3) + + assert grad_batch.shape == (len(T.t), 4, 3) + for k in range(4): + np.testing.assert_allclose( + grad_batch[:, k, :], + tria_compute_gradient(T, vfuncs[:, k]), + rtol=1e-12, atol=1e-14, + err_msg=f"Gradient mismatch at column {k}", + ) + + +# --------------------------------------------------------------------------- +# TriaMesh — divergence (cotangent formulation) +# --------------------------------------------------------------------------- + + +def test_tria_compute_divergence_multi_vs_single(tria_mesh): + """Batch divergence must match repeated single-function calls.""" + T = tria_mesh + _, evec = Solver(T, lump=True).eigs(k=5) + vfuncs = evec[:, 1:5] + + grad_batch = tria_compute_gradient(T, vfuncs) # (T, 4, 3) + div_batch = tria_compute_divergence(T, grad_batch) # (V, 4) + + assert div_batch.shape == (len(T.v), 4) + for k in range(4): + np.testing.assert_allclose( + div_batch[:, k], + tria_compute_divergence(T, tria_compute_gradient(T, vfuncs[:, k])), + rtol=1e-12, atol=1e-14, + err_msg=f"Divergence mismatch at column {k}", + ) + + +def test_tria_gradient_divergence_laplacian_multi(tria_mesh): + """Mathematical check: -div(grad(f_k)) = lambda_k * B * f_k for eigenfunctions.""" + T = tria_mesh + fem = Solver(T, lump=True) + evals, evec = fem.eigs(k=5) + vfuncs = evec[:, 1:5] + + div_batch = tria_compute_divergence(T, tria_compute_gradient(T, vfuncs)) + + for k in range(4): + np.testing.assert_allclose( + -div_batch[:, k], + evals[k + 1] * fem.mass.dot(vfuncs[:, k]), + rtol=1e-3, atol=1e-7, + err_msg=f"Laplacian identity failed for eigenfunction {k + 1}", + ) + + +# --------------------------------------------------------------------------- +# TriaMesh — divergence2 (flux formulation) +# --------------------------------------------------------------------------- + + +def test_tria_compute_divergence2_multi_vs_single(tria_mesh): + """Batch divergence2 must match repeated single-function calls.""" + T = tria_mesh + _, evec = Solver(T, lump=True).eigs(k=5) + vfuncs = evec[:, 1:5] + + grad_batch = tria_compute_gradient(T, vfuncs) + div_batch = tria_compute_divergence2(T, grad_batch) + + assert div_batch.shape == (len(T.v), 4) + for k in range(4): + np.testing.assert_allclose( + div_batch[:, k], + tria_compute_divergence2(T, tria_compute_gradient(T, vfuncs[:, k])), + rtol=1e-12, atol=1e-14, + err_msg=f"Divergence2 mismatch at column {k}", + ) + + +# --------------------------------------------------------------------------- +# TriaMesh — geodesic_f +# --------------------------------------------------------------------------- + + +def test_tria_compute_geodesic_f_multi_vs_single(tria_mesh): + """Batch geodesic_f must match repeated single-function calls.""" + T = tria_mesh + _, evec = Solver(T, lump=True).eigs(k=5) + vfuncs = evec[:, 1:4] + + gf_batch = tria_compute_geodesic_f(T, vfuncs) + + assert gf_batch.shape == (len(T.v), 3) + for k in range(3): + np.testing.assert_allclose( + gf_batch[:, k], + tria_compute_geodesic_f(T, vfuncs[:, k]), + rtol=1e-12, atol=1e-14, + err_msg=f"Geodesic_f mismatch at column {k}", + ) + + +# --------------------------------------------------------------------------- +# TriaMesh — rotated_f +# --------------------------------------------------------------------------- + + +def test_tria_compute_rotated_f_multi_vs_single(tria_mesh): + """Batch rotated_f must match repeated single-function calls.""" + T = tria_mesh + _, evec = Solver(T, lump=True).eigs(k=5) + vfuncs = evec[:, 1:4] + + rf_batch = tria_compute_rotated_f(T, vfuncs) + + assert rf_batch.shape == (len(T.v), 3) + for k in range(3): + np.testing.assert_allclose( + rf_batch[:, k], + tria_compute_rotated_f(T, vfuncs[:, k]), + rtol=1e-12, atol=1e-14, + err_msg=f"Rotated_f mismatch at column {k}", + ) + + +# --------------------------------------------------------------------------- +# TetMesh — gradient +# --------------------------------------------------------------------------- + + +def test_tet_compute_gradient_multi_vs_single(tet_mesh): + """Batch tet gradient must match repeated single-function calls.""" + T = tet_mesh + _, evec = Solver(T, lump=True).eigs(k=5) + vfuncs = evec[:, 1:5] + + grad_batch = tet_compute_gradient(T, vfuncs) # (n_tets, 4, 3) + + assert grad_batch.shape == (len(T.t), 4, 3) + for k in range(4): + np.testing.assert_allclose( + grad_batch[:, k, :], + tet_compute_gradient(T, vfuncs[:, k]), + rtol=1e-12, atol=1e-14, + err_msg=f"Tet gradient mismatch at column {k}", + ) + + +# --------------------------------------------------------------------------- +# TetMesh — divergence +# --------------------------------------------------------------------------- + + +def test_tet_compute_divergence_multi_vs_single(tet_mesh): + """Batch tet divergence must match repeated single-function calls.""" + T = tet_mesh + _, evec = Solver(T, lump=True).eigs(k=5) + vfuncs = evec[:, 1:5] + + grad_batch = tet_compute_gradient(T, vfuncs) + div_batch = tet_compute_divergence(T, grad_batch) + + assert div_batch.shape == (len(T.v), 4) + for k in range(4): + np.testing.assert_allclose( + div_batch[:, k], + tet_compute_divergence(T, tet_compute_gradient(T, vfuncs[:, k])), + rtol=1e-12, atol=1e-14, + err_msg=f"Tet divergence mismatch at column {k}", + ) + diff --git a/lapy/utils/tests/test_solver.py b/lapy/utils/tests/test_solver.py new file mode 100644 index 0000000..55011c6 --- /dev/null +++ b/lapy/utils/tests/test_solver.py @@ -0,0 +1,59 @@ +"""Tests for Solver.poisson — backward compatibility and 2-D rhs support.""" + +import numpy as np +import pytest + +from ...solver import Solver +from ...tria_mesh import TriaMesh + + +@pytest.fixture +def tria_mesh(): + return TriaMesh.read_off("data/square-mesh.off") + + +def test_poisson_scalar_and_1d_return_1d(tria_mesh): + """Scalar and 1-D rhs must return a 1-D array (backward compatibility).""" + fem = Solver(tria_mesh, lump=True) + _, evec = fem.eigs(k=3) + + assert fem.poisson(0.0).ndim == 1 + assert fem.poisson(evec[:, 1]).ndim == 1 + + +def test_poisson_2d_rhs_matches_1d(tria_mesh): + """2-D rhs must give the same result as repeated independent 1-D solves.""" + fem = Solver(tria_mesh, lump=True) + _, evec = fem.eigs(k=5) + rhs = evec[:, 1:5] # (n_vertices, 4) + + x_batch = fem.poisson(rhs) + + assert x_batch.shape == (len(tria_mesh.v), 4) + for k in range(4): + np.testing.assert_allclose( + x_batch[:, k], + fem.poisson(rhs[:, k]), + rtol=1e-6, atol=1e-9, + err_msg=f"poisson 2-D mismatch at column {k}", + ) + + +def test_poisson_2d_rhs_with_dirichlet(tria_mesh): + """2-D rhs with Dirichlet BC must match repeated 1-D solves.""" + fem = Solver(tria_mesh, lump=True) + _, evec = fem.eigs(k=5) + rhs = evec[:, 1:4] # (n_vertices, 3) + dtup = (np.array([0, 1]), np.array([0.0, 0.0])) + + x_batch = fem.poisson(rhs, dtup=dtup) + + assert x_batch.shape == (len(tria_mesh.v), 3) + for k in range(3): + np.testing.assert_allclose( + x_batch[:, k], + fem.poisson(rhs[:, k], dtup=dtup), + rtol=1e-6, atol=1e-9, + err_msg=f"poisson 2-D Dirichlet mismatch at column {k}", + ) + diff --git a/lapy/utils/tests/test_tria_mesh.py b/lapy/utils/tests/test_tria_mesh.py index a3b0a4a..3650947 100644 --- a/lapy/utils/tests/test_tria_mesh.py +++ b/lapy/utils/tests/test_tria_mesh.py @@ -460,7 +460,8 @@ def test_smooth_laplace(tria_mesh_fixture): # Equivalence check with old smooth_vfunc (which corresponds to lambda=1) # Note: smooth_vfunc applies M*v. smooth_laplace applies (1-l)v + l*M*v. # If l=1, result is M*v. - v_old = mesh.smooth_vfunc(v_orig, n=1) + with pytest.warns(DeprecationWarning, match="smooth_vfunc is deprecated"): + v_old = mesh.smooth_vfunc(v_orig, n=1) v_new = mesh.smooth_laplace(v_orig, n=1, lambda_=1.0) np.testing.assert_allclose(v_old, v_new)