importadaptiveimportnumpyasnpdefsphere(xyz):x,y,z=xyza=0.4returnx+z**2+np.exp(-(x**2+y**2+z**2-0.75**2)**2/a**4)learner=adaptive.LearnerND(sphere,bounds=[(-1,1), (-1,1), (-1,1)])runner=adaptive.runner.simple(learner,goal=lambdal:l.npoints>2000)

diff --git a/adaptive/learner/triangulation.py b/adaptive/learner/triangulation.pyindex 0cc0bde..4e29af1 100644--- a/adaptive/learner/triangulation.py+++ b/adaptive/learner/triangulation.py@@ -7,28 +7,29 @@ from math import factorial import numpy as np import scipy.spatial +from adaptive.triangulation import fast_norm, fast_2d_circumcircle, fast_3d_circumcircle, fast_2d_point_in_simplex -def fast_norm(v):-    # notice this method can be even more optimised-    if len(v) == 2:-        return math.sqrt(v[0] * v[0] + v[1] * v[1])-    if len(v) == 3:-        return math.sqrt(v[0] * v[0] + v[1] * v[1] + v[2] * v[2])-    return math.sqrt(np.dot(v, v))+# def fast_norm(v):+#     # notice this method can be even more optimised+#     if len(v) == 2:+#         return math.sqrt(v[0] * v[0] + v[1] * v[1])+#     if len(v) == 3:+#         return math.sqrt(v[0] * v[0] + v[1] * v[1] + v[2] * v[2])+#     return math.sqrt(np.dot(v, v))  -def fast_2d_point_in_simplex(point, simplex, eps=1e-8):-    (p0x, p0y), (p1x, p1y), (p2x, p2y) = simplex-    px, py = point+# def fast_2d_point_in_simplex(point, simplex, eps=1e-8):+#     (p0x, p0y), (p1x, p1y), (p2x, p2y) = simplex+#     px, py = point -    area = 0.5 * (-p1y * p2x + p0y * (p2x - p1x) + p1x * p2y + p0x * (p1y - p2y))+#     area = 0.5 * (-p1y * p2x + p0y * (p2x - p1x) + p1x * p2y + p0x * (p1y - p2y)) -    s = 1 / (2 * area) * (+p0y * p2x + (p2y - p0y) * px - p0x * p2y + (p0x - p2x) * py)-    if s < -eps or s > 1 + eps:-        return False-    t = 1 / (2 * area) * (+p0x * p1y + (p0y - p1y) * px - p0y * p1x + (p1x - p0x) * py)+#     s = 1 / (2 * area) * (+p0y * p2x + (p2y - p0y) * px - p0x * p2y + (p0x - p2x) * py)+#     if s < -eps or s > 1 + eps:+#         return False+#     t = 1 / (2 * area) * (+p0x * p1y + (p0y - p1y) * px - p0y * p1x + (p1x - p0x) * py) -    return (t >= -eps) and (s + t <= 1 + eps)+#     return (t >= -eps) and (s + t <= 1 + eps)   def point_in_simplex(point, simplex, eps=1e-8):@@ -42,80 +43,80 @@ def point_in_simplex(point, simplex, eps=1e-8):     return all(alpha > -eps) and sum(alpha) < 1 + eps  -def fast_2d_circumcircle(points):-    """Compute the center and radius of the circumscribed circle of a triangle--    Parameters-    -----------    points: 2D array-like-        the points of the triangle to investigate--    Returns-    --------    tuple-        (center point : tuple(int), radius: int)-    """-    points = np.array(points)-    # transform to relative coordinates-    pts = points[1:] - points[0]--    (x1, y1), (x2, y2) = pts-    # compute the length squared-    l1 = x1 * x1 + y1 * y1-    l2 = x2 * x2 + y2 * y2--    # compute some determinants-    dx = +l1 * y2 - l2 * y1-    dy = -l1 * x2 + l2 * x1-    aa = +x1 * y2 - x2 * y1-    a = 2 * aa--    # compute center-    x = dx / a-    y = dy / a-    radius = math.sqrt(x * x + y * y)  # radius = norm([x, y])--    return (x + points[0][0], y + points[0][1]), radius---def fast_3d_circumcircle(points):-    """Compute the center and radius of the circumscribed shpere of a simplex.--    Parameters-    -----------    points: 2D array-like-        the points of the triangle to investigate--    Returns-    --------    tuple-        (center point : tuple(int), radius: int)-    """-    points = np.array(points)-    pts = points[1:] - points[0]--    (x1, y1, z1), (x2, y2, z2), (x3, y3, z3) = pts--    l1 = x1 * x1 + y1 * y1 + z1 * z1-    l2 = x2 * x2 + y2 * y2 + z2 * z2-    l3 = x3 * x3 + y3 * y3 + z3 * z3--    # Compute some determinants:-    dx = +l1 * (y2 * z3 - z2 * y3) - l2 * (y1 * z3 - z1 * y3) + l3 * (y1 * z2 - z1 * y2)-    dy = +l1 * (x2 * z3 - z2 * x3) - l2 * (x1 * z3 - z1 * x3) + l3 * (x1 * z2 - z1 * x2)-    dz = +l1 * (x2 * y3 - y2 * x3) - l2 * (x1 * y3 - y1 * x3) + l3 * (x1 * y2 - y1 * x2)-    aa = +x1 * (y2 * z3 - z2 * y3) - x2 * (y1 * z3 - z1 * y3) + x3 * (y1 * z2 - z1 * y2)-    a = 2 * aa--    center = (dx / a, -dy / a, dz / a)-    radius = fast_norm(center)-    center = (-        center[0] + points[0][0],-        center[1] + points[0][1],-        center[2] + points[0][2],-    )--    return center, radius+# def fast_2d_circumcircle(points):+#     """Compute the center and radius of the circumscribed circle of a triangle++#     Parameters+#     ----------+#     points: 2D array-like+#         the points of the triangle to investigate++#     Returns+#     -------+#     tuple+#         (center point : tuple(int), radius: int)+#     """+#     points = np.array(points)+#     # transform to relative coordinates+#     pts = points[1:] - points[0]++#     (x1, y1), (x2, y2) = pts+#     # compute the length squared+#     l1 = x1 * x1 + y1 * y1+#     l2 = x2 * x2 + y2 * y2++#     # compute some determinants+#     dx = +l1 * y2 - l2 * y1+#     dy = -l1 * x2 + l2 * x1+#     aa = +x1 * y2 - x2 * y1+#     a = 2 * aa++#     # compute center+#     x = dx / a+#     y = dy / a+#     radius = math.sqrt(x * x + y * y)  # radius = norm([x, y])++#     return (x + points[0][0], y + points[0][1]), radius+++# def fast_3d_circumcircle(points):+#     """Compute the center and radius of the circumscribed shpere of a simplex.++#     Parameters+#     ----------+#     points: 2D array-like+#         the points of the triangle to investigate++#     Returns+#     -------+#     tuple+#         (center point : tuple(int), radius: int)+#     """+#     points = np.array(points)+#     pts = points[1:] - points[0]++#     (x1, y1, z1), (x2, y2, z2), (x3, y3, z3) = pts++#     l1 = x1 * x1 + y1 * y1 + z1 * z1+#     l2 = x2 * x2 + y2 * y2 + z2 * z2+#     l3 = x3 * x3 + y3 * y3 + z3 * z3++#     # Compute some determinants:+#     dx = +l1 * (y2 * z3 - z2 * y3) - l2 * (y1 * z3 - z1 * y3) + l3 * (y1 * z2 - z1 * y2)+#     dy = +l1 * (x2 * z3 - z2 * x3) - l2 * (x1 * z3 - z1 * x3) + l3 * (x1 * z2 - z1 * x2)+#     dz = +l1 * (x2 * y3 - y2 * x3) - l2 * (x1 * y3 - y1 * x3) + l3 * (x1 * y2 - y1 * x2)+#     aa = +x1 * (y2 * z3 - z2 * y3) - x2 * (y1 * z3 - z1 * y3) + x3 * (y1 * z2 - z1 * y2)+#     a = 2 * aa++#     center = (dx / a, -dy / a, dz / a)+#     radius = fast_norm(center)+#     center = (+#         center[0] + points[0][0],+#         center[1] + points[0][1],+#         center[2] + points[0][2],+#     )++#     return center, radius   def fast_det(matrix):