153 lines
3.6 KiB
Python
153 lines
3.6 KiB
Python
from grid import exact_func
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import numpy as np
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import sys
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def get_phis(X, r):
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"""
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The get_phis function is used to get barycentric coordonites for a point on a triangle.
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X -- the destination point (2D)
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X = [0,0]
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r -- the three points that make up the triangular simplex (2D)
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r = [[-1, -1], [0, 2], [1, -1]]
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this will return [0.333, 0.333, 0.333]
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"""
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# baker: eq 7
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A = np.array([
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[ 1, 1, 1],
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[r[0][0], r[1][0], r[2][0]],
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[r[0][1], r[1][1], r[2][1]],
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])
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b = np.array([ 1,
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X[0],
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X[1]
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])
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try:
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phi = np.linalg.solve(A,b)
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except:
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print >> sys.stderr, "warning: calculation of phis yielded a linearly dependant system"
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phi = np.dot(np.linalg.pinv(A), b)
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return phi
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def get_phis_3D(X, r):
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"""
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The get_phis function is used to get barycentric coordonites for a point on a triangle.
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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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this will return [0.333, 0.333, 0.333]
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"""
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# baker: eq 7
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A = np.array([
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[ 1, 1, 1, 1 ],
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[r[0][0], r[1][0], r[2][0], r[3][0]],
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[r[0][1], r[1][1], r[2][1], r[3][1]],
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[r[0][2], r[1][2], r[2][2], r[3][2]],
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])
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b = np.array([ 1,
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X[0],
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X[1],
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X[2]
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])
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try:
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phi = np.linalg.solve(A,b)
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except:
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print >> sys.stderr, "warning: calculation of phis yielded a linearly dependant system"
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phi = np.dot(np.linalg.pinv(A), b)
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return phi
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def qlinear(X, R, q):
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"""
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this calculates the linear portion of q from X to r
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also, this is baker eq 3
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X = destination point
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R = simplex points
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q = CFD quantities of interest at the simplex points
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"""
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phis = get_phis(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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return qlin
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def qlinear_3D(X, R, q):
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"""
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this calculates the linear portion of q from X to r
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X = destination point
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R = simplex points
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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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return qlin
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def run_baker(X, R, S, extra_points = 3, verbose = False):
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"""
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This is the main function to call to get an interpolation to X from the tree
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X -- the destination point (2D)
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X = [0,0]
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g -- the grid object
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tree -- the kdtree search object (built from the g mesh)
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"""
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# calculate values only for the triangle
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phi = get_phis(X, S.points)
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qlin = qlinear (X, S.points, S.q)
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if extra_points == 0: return qlin
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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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(phi1, phi2, phi3) = get_phis(s, R.points)
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B.append([phi1 * phi2, phi2*phi3, phi3*phi1])
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w.append(q - qlinear(s, R.points, R.q))
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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) = np.linalg.solve(A,b)
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except:
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print >> sys.stderr, "warning: linear calculation went bad, resorting to np.linalg.pinv"
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(a, b, c) = np.dot(np.linalg.pinv(A), b)
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error_term = a * phi[0] * phi[1]\
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+ b * phi[1] * phi[2]\
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+ c * phi[2] * phi[0]
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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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'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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