336 lines
8.4 KiB
Python
336 lines
8.4 KiB
Python
from baker import *
|
|
from baker.tools import smblog
|
|
import numpy as np
|
|
import sys
|
|
|
|
import itertools
|
|
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 containing 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 np.linalg.LinAlgError as e:
|
|
msg = "calculation of phis yielded a linearly dependant system (%s)" % e
|
|
smblog.error(msg)
|
|
raise smberror(msg)
|
|
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 tetrahedron.
|
|
|
|
X -- the destination point (3D)
|
|
X = [0,0,0]
|
|
R -- the four points that make up the containing simplex, 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 (should) 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 np.linalg.LinAlgError as e:
|
|
smblog.error("calculation of phis yielded a linearly dependant system: %s" % e)
|
|
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 get_error_quadratic(phi, R, S):
|
|
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 np.linalg.LinAlgError as e:
|
|
smblog.error("linear calculation went bad, resorting to np.linalg.pinv: %s" % e)
|
|
(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]
|
|
|
|
return error_term
|
|
|
|
def get_error_cubic(phi, R, S):
|
|
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
|
|
|
|
# basing this on eq 17
|
|
B.append(
|
|
[
|
|
phi1 * phi2 * phi2, # a
|
|
phi1 * phi3 * phi3, # b
|
|
phi2 * phi1 * phi1, # c
|
|
phi2 * phi3 * phi3, # d
|
|
phi3 * phi1 * phi1, # e
|
|
phi3 * phi2 * phi2, # f
|
|
phi1 * phi2 * phi3, # g
|
|
]
|
|
)
|
|
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, g) = np.linalg.solve(A,b)
|
|
except np.linalg.LinAlgError as e:
|
|
smblog.error("linear calculation went bad, resorting to np.linalg.pinv: %s" % e)
|
|
(a, b, c, d, e, f, g) = np.dot(np.linalg.pinv(A), b)
|
|
|
|
error_term = a * phi[0] * phi[1] * phi[1]\
|
|
+ b * phi[0] * phi[2] * phi[2]\
|
|
+ c * phi[1] * phi[0] * phi[0]\
|
|
+ d * phi[1] * phi[2] * phi[2]\
|
|
+ e * phi[2] * phi[0] * phi[0]\
|
|
+ f * phi[2] * phi[1] * phi[1]\
|
|
+ g * phi[0] * phi[1] * phi[2]\
|
|
|
|
return error_term
|
|
|
|
|
|
def run_baker(X, R, S, order=2):
|
|
"""
|
|
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
|
|
"""
|
|
|
|
answer = {
|
|
'qlin': None,
|
|
'error': None,
|
|
'final': None,
|
|
}
|
|
# calculate values only for the simplex triangle
|
|
phi, qlin = qlinear(X, R)
|
|
|
|
if order == 1:
|
|
answer['qlin'] = qlin
|
|
return answer
|
|
elif order == 2:
|
|
error_term = get_error_quadratic(phi, R, S)
|
|
elif order == 3:
|
|
error_term = get_error_cubic(phi, R, S)
|
|
else:
|
|
raise smberror('unacceptable order for baker method')
|
|
|
|
q_final = qlin + error_term
|
|
|
|
answer['qlin' ] = qlin
|
|
answer['error'] = error_term
|
|
answer['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 np.linalg.LinAlgError as e:
|
|
smblog.error("linear calculation went bad, resorting to np.linalg.pinv: %s", e)
|
|
(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
|
|
|
|
def _boxings(n, k):
|
|
"""\
|
|
source for this function:
|
|
http://old.nabble.com/Simple-combinatorics-with-Numpy-td20086915.html
|
|
http://old.nabble.com/Re:-Simple-combinatorics-with-Numpy-p20099736.html
|
|
"""
|
|
seq, i = [n] * k + [0], k
|
|
while i:
|
|
yield tuple(seq[i] - seq[i+1] for i in xrange(k))
|
|
i = seq.index(0) - 1
|
|
seq[i:k] = [seq[i] - 1] * (k-i)
|
|
|
|
def _samples_ur(items, k, offset = 0):
|
|
"""Returns k unordered samples (with replacement) from items."""
|
|
n = len(items)
|
|
for sample in _boxings(k, n):
|
|
selections = [[items[i]]*count for i,count in enumerate(sample)]
|
|
yield tuple([x + offset for sel in selections for x in sel])
|
|
|
|
def pattern(power, phicount, offset = 0):
|
|
smblog.debug("(power = %s, phicount = %s)" % (power, phicount))
|
|
r = []
|
|
for i in _samples_ur(range(1, phicount + 1), power, offset):
|
|
if not len(set(i)) == 1:
|
|
r.append(i)
|
|
return r
|