smbinterp/lib/baker/baker.py

259 lines
6.1 KiB
Python

import numpy as np
import sys
from tools import smberror
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 triangular simplex (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: get_phis: calculation of phis yielded a linearly dependant system"
raise smberror('get_phis')
phi = np.dot(np.linalg.pinv(A), b)
return phi
def get_phis_3D(X, r):
"""
The get_phis function is used to get barycentric coordonites for a point on a triangle.
X -- the destination point (3D)
X = [0,0,0]
r -- the four points that make up the tetrahedron (3D)
r = [
[0.0, 0.0, 1.0],
[0.94280904333606508, 0.0, -0.3333333283722672],
[-0.47140452166803232, 0.81649658244673617, -0.3333333283722672],
[-0.47140452166803298, -0.81649658244673584, -0.3333333283722672],
]
this will return [0.25, 0.25, 0.25, 0.25]
"""
# baker: eq 7
A = np.array([
[ 1, 1, 1, 1 ],
[r[0][0], r[1][0], r[2][0], r[3][0]],
[r[0][1], r[1][1], r[2][1], r[3][1]],
[r[0][2], r[1][2], r[2][2], r[3][2]],
])
b = np.array([ 1,
X[0],
X[1],
X[2]
])
try:
phi = np.linalg.solve(A,b)
except:
print >> sys.stderr, "warning: get_phis_3D: calculation of phis yielded a linearly dependant system"
phi = np.dot(np.linalg.pinv(A), b)
return phi
def qlinear(X, R):
"""
this calculates the linear portion of q from X to r
also, this is baker eq 3
X = destination point
R = simplex points
q = CFD quantities of interest at the simplex points
"""
phis = get_phis(X, R.points)
qlin = sum([q_i * phi_i for q_i, phi_i in zip(R.q, phis)])
return phis, qlin
def qlinear_3D(X, R):
"""
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(R)
"""
phis = get_phis_3D(X, R.points)
qlin = sum([q_i * phi_i for q_i, phi_i in zip(R.q, phis)])
return phis, qlin
def run_baker(X, R, S):
"""
This is the main function to call to get an interpolation to X from the input meshes
X -- the destination point (2D)
X = [0,0]
R = Simplex
S = extra points
"""
# calculate values only for the simplex triangle
phi, qlin = qlinear(X, R)
if [i for i in phi if i <= 0.0]:
print "failure"
if len(S.points) == 0:
answer = {
'a': None,
'b': None,
'c': None,
'qlin': qlin,
'error': None,
'final': None,
}
return answer
B = [] # baker eq 9
w = [] # baker eq 11
for (s, q) in zip(S.points, S.q):
cur_phi, cur_qlin = qlinear(s, R)
(phi1, phi2, phi3) = cur_phi
B.append(
[
phi1 * phi2,
phi2 * phi3,
phi3 * phi1,
]
)
w.append(q - cur_qlin)
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: run_baker: 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]
q_final = qlin + error_term
answer = {
'a': a,
'b': b,
'c': c,
'qlin': qlin,
'error': error_term,
'final': q_final,
}
return answer
def run_baker_3D(X, R, S):
"""
This is the main function to call to get an interpolation to X from the input meshes
X -- the destination point (3D)
X = [0,0,0]
R = Simplex (4 points, contains X)
S = extra points (surrounding, in some manner, R and X, but not in R)
"""
# calculate values only for the triangle
phi, qlin = qlinear_3D(X, R)
if len(S.points) == 0:
answer = {
'a': None,
'b': None,
'c': None,
'd': None,
'e': None,
'f': None,
'qlin': qlin,
'error': None,
'final': None,
}
return answer
B = [] # baker eq 9
w = [] # baker eq 11
for (s, q) in zip(S.points, S.q):
cur_phi, cur_qlin = qlinear_3D(s, R)
(phi1, phi2, phi3, phi4) = cur_phi
B.append(
[
phi1 * phi2,
phi1 * phi3,
phi1 * phi4,
phi2 * phi3,
phi2 * phi4,
phi3 * phi4,
]
)
w.append(q - cur_qlin)
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, d, e, f) = np.linalg.solve(A,b)
except:
print >> sys.stderr, "warning: run_baker: linear calculation went bad, resorting to np.linalg.pinv"
(a, b, c, d, e, f) = np.dot(np.linalg.pinv(A), b)
error_term = a * phi[0] * phi[1]\
+ b * phi[0] * phi[2]\
+ c * phi[0] * phi[3]\
+ d * phi[1] * phi[2]\
+ e * phi[1] * phi[3]\
+ f * phi[2] * phi[3]
q_final = qlin + error_term
answer = {
'a': a,
'b': b,
'c': c,
'd': d,
'e': e,
'f': f,
'qlin': qlin,
'error': error_term,
'final': q_final,
}
return answer