smbinterp/lib/baker/__init__.py

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from baker import *
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 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 = "warning: get_phis: calculation of phis yielded a linearly dependant system (%s)" % e
# TODO: log this -- > print >> sys.stderr, 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:
print >> sys.stderr, "warning: get_phis_3D: calculation of phis yielded a linearly dependant system", 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:
print >> sys.stderr, "warning: run_baker: linear calculation went bad, resorting to np.linalg.pinv", 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, a, b, c
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, # a
phi1 * phi3, # b
phi2 * phi1, # c
phi2 * phi3, # d
phi3 * phi1, # e
phi3 * 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:
print >> sys.stderr, "warning: run_baker: linear calculation went bad, resorting to np.linalg.pinv", e
(a, b, c, d, e, f, g) = np.dot(np.linalg.pinv(A), b)
error_term = a * phi[0] * phi[1]\
+ b * phi[0] * phi[2]\
+ c * phi[1] * phi[0]\
+ d * phi[1] * phi[2]\
+ e * phi[2] * phi[0]\
+ f * phi[2] * phi[1]\
+ g * phi[0] * phi[1] * phi[2]\
return error_term, a, b, c
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
"""
# calculate values only for the simplex triangle
phi, qlin = qlinear(X, R)
if [i for i in phi if i <= 0.0]:
s = "this is not a containing simplex:\n"
s += " X: %s\n" % X
s += " R: %s\n" % R
s += " phi: %s, sum(%0.4e)\n" % (phi, sum(phi))
print >> sys.stderr, s
raise smberror("simplex does not contain point")
if len(S.points) == 0:
answer = {
'a': None,
'b': None,
'c': None,
'qlin': qlin,
'error': None,
'final': None,
}
return answer
if order == 2:
error_term, a, b, c = get_error_quadratic(phi, R, S)
elif order == 3:
error_term, a, b, c = get_error_cubic(phi, R, S)
else:
raise smberror('unacceptable order for baker method')
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 [i for i in phi if i <= 0.0]:
s = "this is not a containing simplex:\n"
s += " X: %s\n" % X
s += " R: %s\n" % R
s += " phi: %s, sum(%0.4e)\n" % (phi, sum(phi))
print >> sys.stderr, s
raise smberror("not containing simplex")
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:
print >> sys.stderr, "warning: run_baker: linear calculation went bad, resorting to np.linalg.pinv", 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