257 lines
6.1 KiB
Python
257 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 triangle
|
|
phi, qlin = qlinear(X, R)
|
|
|
|
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
|