smbinterp/lib/baker.py
Stephen Mardson McQuay 961b3b7b26 init
2009-12-27 10:48:27 -07:00

107 lines
2.7 KiB
Python

from grid import exact_func
import numpy as np
import sys
def get_phis(X, r):
"""
The get_phis function is used to get barycentric coordonites for a point on a triangle.
X -- the destination point (2D)
X = [0,0]
r -- the three points that make up the triangle (2D)
r = [[-1, -1], [0, 2], [1, -1]]
this will return [0.333, 0.333, 0.333]
"""
# baker: eq 7
A = np.array([
[1, 1, 1 ],
[r[0][0], r[1][0], r[2][0]],
[r[0][1], r[1][1], r[2][1]],
])
b = np.array([1, X[0], X[1]])
try:
phi = np.linalg.solve(A,b)
except:
print >> sys.stderr, "warning: calculation of phis yielded a linearly dependant system"
phi = np.dot(np.linalg.pinv(A), b)
return phi
def qlinear(X, r, q):
"""
this calculates the linear portion of q from X to r
X = destination point
r = simplex points
q = CFD quantities of interest at the simplex points
"""
phis = get_phis(X, r)
qlin = sum([q_i * phi_i for q_i, phi_i in zip(q[:len(phis)], phis)])
return qlin
def run_baker(X, g, tree, extra_points = 3, verbose = False):
"""
This is the main function to call to get an interpolation to X from the tree
X -- the destination point (2D)
X = [0,0]
g -- the grid object
tree -- the kdtree search object (built from the g mesh)
"""
(dist, indicies) = tree.query(X, 3 + extra_points)
nn = [g.points[i] for i in indicies]
nq = [g.q[i] for i in indicies]
phi = get_phis(X, nn[:3])
qlin = nq[0] * phi[0] + nq[1] * phi[1] + nq[2] * phi[2]
error_term = 0.0
if extra_points != 0:
B = [] # baker eq 9
w = [] # baker eq 11
for index in indicies[3:]:
(phi1,phi2,phi3) = get_phis(g.points[index], nn)
B.append([phi1 * phi2, phi2*phi3, phi3*phi1])
w.append(g.q[index] - qlinear(g.points[index], nn, nq))
B = np.array(B)
w = np.array(w)
A = np.dot(B.T, B)
b = np.dot(B.T, w)
# baker solve eq 10
try:
(a, b, c) = np.linalg.solve(A,b)
except:
print >> sys.stderr, "warning: linear calculation went bad, resorting to np.linalg.pinv"
(a, b, c) = np.dot(np.linalg.pinv(A), b)
error_term = a * phi[0] * phi[1]\
+ b * phi[1] * phi[2]\
+ c * phi[2] * phi[0]
exact = exact_func(X[0], X[1])
q_final = qlin + error_term
if verbose:
print "current point : %s" % X
print "exact : %0.4f" % exact
print "qlin : %0.4f" % qlin
print "qlinerr : %0.4f" % np.abs(exact - qlin)
print "q_final : %0.4f" % q_final
print "q_final_err : %0.4f" % np.abs(exact - q_final)
print
return (q_final, exact)