working on getting baker to work in 3D. the code runs, but the numbers are odd. I suspect the rectangular grid, and am going to try a random cloud of points.
This commit is contained in:
Stephen Mardson McQuay
+102
-9
@@ -41,9 +41,14 @@ def get_phis_3D(X, r):
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X -- the destination point (3D)
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X = [0,0,0]
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r -- the four points that make up the tetrahedron (3D)
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r = [[-1, -1], [0, 2], [1, -1]]
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r = [
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[0.0, 0.0, 1.0],
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[0.94280904333606508, 0.0, -0.3333333283722672],
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[-0.47140452166803232, 0.81649658244673617, -0.3333333283722672],
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[-0.47140452166803298, -0.81649658244673584, -0.3333333283722672],
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]
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this will return [0.333, 0.333, 0.333]
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this will return [0.25, 0.25, 0.25, 0.25]
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"""
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# baker: eq 7
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@@ -82,7 +87,7 @@ def qlinear(X, R):
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qlin = sum([q_i * phi_i for q_i, phi_i in zip(R.q, phis)])
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return phis, qlin
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def qlinear_3D(X, R, q):
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def qlinear_3D(X, R):
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"""
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this calculates the linear portion of q from X to r
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@@ -91,8 +96,8 @@ def qlinear_3D(X, R, q):
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q = CFD quantities of interest at the simplex points(R)
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"""
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phis = get_phis_3D(X, R)
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qlin = sum([q_i * phi_i for q_i, phi_i in zip(q, phis)])
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phis = get_phis_3D(X, R.points)
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qlin = sum([q_i * phi_i for q_i, phi_i in zip(R.q, phis)])
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return phis, qlin
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def run_baker(X, R, S):
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@@ -103,13 +108,11 @@ def run_baker(X, R, S):
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X = [0,0]
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R = Simplex
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S = extra points
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"""
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# calculate values only for the triangle
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phi, qlin = qlinear (X, R)
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phi, qlin = qlinear(X, R)
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if len(S.points) == 0:
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answer = {
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@@ -129,7 +132,13 @@ def run_baker(X, R, S):
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cur_phi, cur_qlin = qlinear(s, R)
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(phi1, phi2, phi3) = cur_phi
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B.append([phi1 * phi2, phi2 * phi3, phi3 * phi1])
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B.append(
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[
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phi1 * phi2,
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phi2 * phi3,
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phi3 * phi1,
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]
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)
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w.append(q - cur_qlin)
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B = np.array(B)
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@@ -161,3 +170,87 @@ def run_baker(X, R, S):
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}
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return answer
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def run_baker_3D(X, R, S):
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"""
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This is the main function to call to get an interpolation to X from the input meshes
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X -- the destination point (3D)
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X = [0,0,0]
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R = Simplex (4 points, contains X)
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S = extra points (surrounding, in some manner, R and X, but not in R)
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"""
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# calculate values only for the triangle
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phi, qlin = qlinear_3D(X, R)
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if len(S.points) == 0:
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answer = {
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'a': None,
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'b': None,
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'c': None,
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'd': None,
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'e': None,
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'f': None,
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'qlin': qlin,
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'error': None,
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'final': None,
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}
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return answer
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B = [] # baker eq 9
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w = [] # baker eq 11
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for (s, q) in zip(S.points, S.q):
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cur_phi, cur_qlin = qlinear_3D(s, R)
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(phi1, phi2, phi3, phi4) = cur_phi
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B.append(
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[
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phi1 * phi2,
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phi1 * phi3,
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phi1 * phi4,
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phi2 * phi3,
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phi2 * phi4,
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phi3 * phi4,
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]
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)
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w.append(q - cur_qlin)
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B = np.array(B)
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w = np.array(w)
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A = np.dot(B.T, B)
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b = np.dot(B.T, w)
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# baker solve eq 10
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try:
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(a, b, c, d, e, f) = np.linalg.solve(A,b)
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except:
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print >> sys.stderr, "warning: run_baker: linear calculation went bad, resorting to np.linalg.pinv"
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(a, b, c, d, e, f) = np.dot(np.linalg.pinv(A), b)
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error_term = a * phi[0] * phi[1]\
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+ b * phi[0] * phi[2]\
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+ c * phi[0] * phi[3]\
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+ d * phi[1] * phi[2]\
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+ e * phi[1] * phi[3]\
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+ f * phi[2] * phi[3]
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q_final = qlin + error_term
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answer = {
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'a': a,
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'b': b,
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'c': c,
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'd': d,
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'e': e,
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'f': f,
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'qlin': qlin,
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'error': error_term,
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'final': q_final,
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}
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return answer
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@@ -24,3 +24,12 @@ def exact_func(x, y):
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the exact function used from baker's article (for testing)
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"""
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return np.power((np.sin(x * np.pi) * np.cos(y * np.pi)), 2)
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def exact_func_3D(X):
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"""
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the exact function (3D) used from baker's article (for testing)
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"""
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x = X[0]
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y = X[1]
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z = X[2]
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return np.power((np.sin(x * np.pi / 2.0) * np.sin(y * np.pi / 2.0) * np.sin(z * np.pi / 2.0)), 2)
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+4
-105
@@ -7,49 +7,11 @@ from collections import defaultdict
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import numpy as np
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import scipy.spatial
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from baker import run_baker, get_phis
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from baker import run_baker
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from baker.tools import exact_func, smberror
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from simplex import face
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from smcqdelaunay import *
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class face(object):
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def __init__(self, name):
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self.name = name
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self.verts = []
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self.neighbors = []
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def add_vert(self, v):
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"""
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v should be an index into grid.points
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"""
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self.verts.append(v)
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def add_neighbor(self, n):
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"""
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reference to another face object
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"""
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self.neighbors.append(n)
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def contains(self, X, grid):
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R = [grid.points[i] for i in self.verts]
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phis = get_phis(X, R)
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r = True
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if [i for i in phis if i < 0.0]:
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r = False
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return r
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def __str__(self):
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neighbors = [i.name for i in self.neighbors]
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return '%s: verts: %s neighbors: [%s]' %\
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(
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self.name,
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self.verts,
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", ".join(neighbors)
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)
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class grid(object):
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@@ -97,7 +59,7 @@ class grid(object):
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R is a grid object that is the (a) containing simplex around point X
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S is S_j from baker's paper : some points from all point that are not the simplex
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"""
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(dist, indicies) = self.tree.query(X, 3 + extra_points)
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(dist, indicies) = self.tree.query(X, simplex_size + extra_points)
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# get the containing simplex
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@@ -152,7 +114,7 @@ class grid(object):
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try:
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(R, S) = self.get_simplex_and_nearest_points(X)
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answer = run_baker(X, R, S)
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except smberror as e:
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except smberror, e:
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print "caught error: %s, trying with connectivity-based mesh" % e
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(R, S) = self.get_points_conn(X)
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answer = run_baker(X, R, S)
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@@ -199,27 +161,6 @@ class grid(object):
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# self.facets_for_point[int(point[1:])] = [i for i in neighboring_facets.split() if i in self.faces]
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def for_qhull_generator(self):
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"""
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this returns a generator that should be fed into qdelaunay
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"""
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yield '2';
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yield '%d' % len(self.points)
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for p in self.points:
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yield "%f %f" % (p[0], p[1])
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def for_qhull(self):
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"""
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this returns a single string that should be fed into qdelaunay
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"""
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r = '2\n'
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r += '%d\n' % len(self.points)
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for p in self.points:
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r += "%f %f\n" % (p[0], p[1])
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return r
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def __str__(self):
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r = ''
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assert( len(self.points) == len(self.q) )
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@@ -233,49 +174,7 @@ class grid(object):
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r += "%s\n" % v
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return r
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class simple_rect_grid(grid):
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def __init__(self, xres = 5, yres = 5):
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xmin = -1.0
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xmax = 1.0
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xspan = xmax - xmin
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xdel = xspan / float(xres - 1)
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ymin = -1.0
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ymay = 1.0
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yspan = ymay - ymin
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ydel = yspan / float(yres - 1)
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points = []
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q = []
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for x in xrange(xres):
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cur_x = xmin + (x * xdel)
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for y in xrange(yres):
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cur_y = ymin + (y * ydel)
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points.append([cur_x, cur_y])
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q.append(exact_func(cur_x, cur_y))
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grid.__init__(self, points, q)
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self.construct_connectivity()
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class simple_random_grid(simple_rect_grid):
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def __init__(self, num_points = 10):
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points = []
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q = []
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r = np.random
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for i in xrange(num_points):
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cur_x = r.rand()
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cur_y = r.rand()
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points.append([cur_x, cur_y])
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q.append(exact_func(cur_x, cur_y))
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grid.__init__(self, points, q)
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self.points = np.array(self.points)
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self.q = np.array(self.q)
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if __name__ == '__main__':
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