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major refactoring

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--HG--
rename : lib/baker/__init__.py => interp/baker/__init__.py
rename : lib/grid/DD.py => interp/grid/DD.py
rename : lib/grid/DDD.py => interp/grid/DDD.py
rename : lib/grid/__init__.py => interp/grid/__init__.py
rename : lib/grid/qhull.py => interp/grid/qhull.py
rename : lib/grid/simplex.py => interp/grid/simplex.py
rename : lib/grid/smcqdelaunay.py => interp/grid/smcqdelaunay.py
rename : lib/baker/tools.py => interp/tools.py
This commit is contained in:
sm
2010-10-22 16:10:58 -06:00
parent 98d7247497
commit 2db4169bfa
14 changed files with 56 additions and 565 deletions
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interp/baker/__init__.py
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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 = np.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 get_error_sauron(phi, R, S, order = 2):
smblog.debug("len(phi): %d"% len(phi))
B = [] # baker eq 9
w = [] # baker eq 11
p = pattern(order, len(phi), offset = -1)
smblog.debug("pattern: %s" % p)
for (s,q) in zip(S.points, S.q):
cur_phi, cur_qlin = qlinear(s, R)
l = []
for i in p:
cur_sum = cur_phi[i[0]]
for j in i[1:]:
cur_sum *= cur_phi[j]
l.append(cur_sum)
B.append(l)
w.append(q - cur_qlin)
smblog.debug("B: %s" % B)
smblog.debug("w: %s" % w)
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:
abc = np.linalg.solve(A,b)
except np.linalg.LinAlgError as e:
smblog.error("linear calculation went bad, resorting to np.linalg.pinv: %s" % e)
abc = np.dot(np.linalg.pinv(A), b)
smblog.debug(len(abc) == len(p))
error_term = 0.0
for (a, i) in zip(abc, p):
cur_sum = a
for j in i:
cur_sum *= phi[j]
error_term += cur_sum
smblog.debug("error_term smb: %s" % error_term)
return error_term, abc
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
"""
smblog.debug("order = %d" % order)
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 in (2,3):
error_term, abc = get_error_sauron(phi, R, S, order)
else:
raise smberror('unsupported 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