putting together a simple test case so that I can test my quad/cubic interpolator
This commit is contained in:
Stephen Mardson McQuay
parent
993c901cec
commit
1fc988428d
@ -6,18 +6,18 @@ from optparse import OptionParser
|
||||
import numpy as np
|
||||
|
||||
from baker.tools import rms, exact_func
|
||||
from grid.DD import simple_random_grid, simple_rect_grid
|
||||
from grid.DD import random_grid, rect_grid
|
||||
|
||||
|
||||
def get_mesh(source, destination, use_structured_grid = False):
|
||||
mesh_source = None
|
||||
mesh_dest = None
|
||||
if use_structured_grid:
|
||||
mesh_source = simple_rect_grid(source, source)
|
||||
mesh_dest = simple_rect_grid(destination, destination)
|
||||
mesh_source = rect_grid(source, source)
|
||||
mesh_dest = rect_grid(destination, destination)
|
||||
else:
|
||||
mesh_source = simple_random_grid(source)
|
||||
mesh_dest = simple_random_grid(destination)
|
||||
mesh_source = random_grid(source)
|
||||
mesh_dest = random_grid(destination)
|
||||
|
||||
if not (mesh_dest and mesh_source):
|
||||
raise smberror('problem creating mesh objects')
|
||||
@ -88,7 +88,7 @@ if __name__ == '__main__':
|
||||
errors.append(0)
|
||||
continue
|
||||
|
||||
exact = exact_func(X[0], X[1])
|
||||
exact = exact_func(X)
|
||||
if np.abs(exact - answer['final']) <= np.abs(exact - answer['qlin']):
|
||||
success += 1
|
||||
|
||||
|
||||
@ -1,16 +0,0 @@
|
||||
#!/usr/bin/perl
|
||||
|
||||
use strict;
|
||||
use warnings;
|
||||
|
||||
my $output_filename = $ARGV[0] or die "no args";
|
||||
my $tmp_grid_file = "$output_filename.grid.txt";
|
||||
|
||||
system("grid.py > $tmp_grid_file");
|
||||
|
||||
|
||||
system("cat $tmp_grid_file | qdelaunay GD2 s > $output_filename.txt\n" );
|
||||
system("cat $tmp_grid_file | qdelaunay GD2 s Qt > ${output_filename}_qt.txt\n");
|
||||
system("cat $tmp_grid_file | qdelaunay GD2 s QJ > ${output_filename}_qj.txt\n");
|
||||
|
||||
unlink($tmp_grid_file);
|
||||
@ -3,9 +3,9 @@
|
||||
import sys
|
||||
import pickle
|
||||
|
||||
from grid.DD import simple_rect_grid, simple_random_grid
|
||||
from grid.DD import rect_grid, random_grid
|
||||
from baker import run_baker
|
||||
from baker.tools import smberror
|
||||
from baker.tools import exact_func, smberror
|
||||
|
||||
qfile = '/tmp/grid_regular.txt'
|
||||
|
||||
@ -18,19 +18,23 @@ if __name__ == '__main__':
|
||||
rx = 4
|
||||
ry = 4 * rx
|
||||
|
||||
source_mesh = simple_rect_grid(rx, ry)
|
||||
source_mesh = rect_grid(rx, ry)
|
||||
|
||||
# print source_mesh
|
||||
|
||||
X = [0.1, 0.1]
|
||||
X = [0.1, 0.01]
|
||||
|
||||
try:
|
||||
print "trying to get simplex and nearest points using nearest points (kdtree)"
|
||||
(R, S) = source_mesh.get_simplex_and_nearest_points(X, extra_points=4)
|
||||
print "R for nearest-neighbor:\n", R
|
||||
print "S for nearest-neighbor:\n", S
|
||||
print "trying to run baker"
|
||||
print run_baker(X, R, S)
|
||||
except smberror as e:
|
||||
print "caught error: %s" % e
|
||||
|
||||
print "trying to get simplex and nearest points using connectivity scheme"
|
||||
(R, S) = source_mesh.get_points_conn(X)
|
||||
print "R for connectivity:\n", R
|
||||
print "S for connectivity:\n", S
|
||||
@ -38,5 +42,16 @@ if __name__ == '__main__':
|
||||
|
||||
|
||||
print "repeating the above just using the grid object:"
|
||||
print source_mesh.run_baker(X)
|
||||
r = source_mesh.run_baker(X)
|
||||
exact = exact_func(X)
|
||||
print r
|
||||
print 'exact', exact
|
||||
print 'qlin' , r['qlin']
|
||||
print 'error', r['error']
|
||||
print 'final', r['final']
|
||||
|
||||
if abs(r['final'] - exact) <= abs(r['qlin'] - exact):
|
||||
print "win"
|
||||
else:
|
||||
print "failure"
|
||||
open(qfile, 'w').write(source_mesh.for_qhull())
|
||||
|
||||
27
bin/test.py
27
bin/test.py
@ -1,9 +1,9 @@
|
||||
#!/usr/bin/python2.6
|
||||
|
||||
import sys
|
||||
from grid.DDD import simple_random_grid
|
||||
from grid.DDD import random_grid
|
||||
from baker import get_phis_3D, run_baker_3D
|
||||
from baker.tools import exact_func_3D
|
||||
from baker.tools import exact_func_3D, smberror
|
||||
|
||||
try:
|
||||
total_points = int(sys.argv[1])
|
||||
@ -12,7 +12,7 @@ except:
|
||||
|
||||
|
||||
print total_points
|
||||
g = simple_random_grid(total_points)
|
||||
g = random_grid(total_points)
|
||||
|
||||
open('/tmp/for_qhull.txt', 'w').write(g.for_qhull())
|
||||
|
||||
@ -31,13 +31,16 @@ print "phi values (should all be positive): ", phis, sum(phis)
|
||||
if [i for i in phis if i < 0.0]:
|
||||
print "problems"
|
||||
|
||||
r = run_baker_3D(X, R, S)
|
||||
try:
|
||||
r = run_baker_3D(X, R, S)
|
||||
print 'qlin' , r['qlin']
|
||||
print 'error', r['error']
|
||||
print 'final', r['final']
|
||||
|
||||
print 'qlin' , r['qlin']
|
||||
print 'error', r['error']
|
||||
print 'final', r['final']
|
||||
|
||||
if abs(r['final'] - exact) <= abs(r['qlin'] - exact):
|
||||
print "win"
|
||||
else:
|
||||
print "failure"
|
||||
if abs(r['final'] - exact) <= abs(r['qlin'] - exact):
|
||||
print "win"
|
||||
else:
|
||||
print "failure"
|
||||
except smberror as e:
|
||||
print e
|
||||
print 'TAINT'
|
||||
|
||||
@ -1 +1,274 @@
|
||||
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 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]:
|
||||
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
|
||||
|
||||
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]
|
||||
|
||||
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
|
||||
|
||||
@ -1,272 +0,0 @@
|
||||
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 np.linalg.LinAlgError as e:
|
||||
print >> sys.stderr, "warning: get_phis: calculation of phis yielded a linearly dependant system", e
|
||||
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 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 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]:
|
||||
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,
|
||||
'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 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]
|
||||
|
||||
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
|
||||
@ -19,10 +19,12 @@ def rms(errors):
|
||||
r = np.sqrt(r / len(errors))
|
||||
return r
|
||||
|
||||
def exact_func(x, y):
|
||||
def exact_func(X):
|
||||
"""
|
||||
the exact function used from baker's article (for testing)
|
||||
"""
|
||||
x = X[0]
|
||||
y = X[0]
|
||||
return np.power((np.sin(x * np.pi) * np.cos(y * np.pi)), 2)
|
||||
|
||||
def exact_func_3D(X):
|
||||
|
||||
@ -1,32 +1,13 @@
|
||||
from grid import grid
|
||||
from grid import grid as basegrid
|
||||
|
||||
from baker.tools import exact_func
|
||||
|
||||
import numpy as np
|
||||
|
||||
|
||||
class simple_rect_grid(grid):
|
||||
def __init__(self, xres = 5, yres = 5):
|
||||
xmin = -1.0
|
||||
xmax = 1.0
|
||||
xspan = xmax - xmin
|
||||
xdel = xspan / float(xres - 1)
|
||||
|
||||
ymin = -1.0
|
||||
ymay = 1.0
|
||||
yspan = ymay - ymin
|
||||
ydel = yspan / float(yres - 1)
|
||||
|
||||
|
||||
points = []
|
||||
q = []
|
||||
for x in xrange(xres):
|
||||
cur_x = xmin + (x * xdel)
|
||||
for y in xrange(yres):
|
||||
cur_y = ymin + (y * ydel)
|
||||
points.append([cur_x, cur_y])
|
||||
q.append(exact_func(cur_x, cur_y))
|
||||
grid.__init__(self, points, q)
|
||||
self.construct_connectivity()
|
||||
class grid(basegrid):
|
||||
def __init__(self, points, q):
|
||||
basegrid.__init__(self, points, q)
|
||||
|
||||
def for_qhull_generator(self):
|
||||
"""
|
||||
@ -49,8 +30,32 @@ class simple_rect_grid(grid):
|
||||
r += "%f %f\n" % (p[0], p[1])
|
||||
return r
|
||||
|
||||
class rect_grid(grid):
|
||||
def __init__(self, xres = 5, yres = 5):
|
||||
xmin = -1.0
|
||||
xmax = 1.0
|
||||
xspan = xmax - xmin
|
||||
xdel = xspan / float(xres - 1)
|
||||
|
||||
class simple_random_grid(simple_rect_grid):
|
||||
ymin = -1.0
|
||||
ymay = 1.0
|
||||
yspan = ymay - ymin
|
||||
ydel = yspan / float(yres - 1)
|
||||
|
||||
|
||||
points = []
|
||||
q = []
|
||||
for x in xrange(xres):
|
||||
cur_x = xmin + (x * xdel)
|
||||
for y in xrange(yres):
|
||||
cur_y = ymin + (y * ydel)
|
||||
points.append([cur_x, cur_y])
|
||||
q.append(exact_func((cur_x, cur_y)))
|
||||
grid.__init__(self, points, q)
|
||||
self.construct_connectivity()
|
||||
|
||||
|
||||
class random_grid(rect_grid):
|
||||
def __init__(self, num_points = 10):
|
||||
points = []
|
||||
q = []
|
||||
@ -62,7 +67,7 @@ class simple_random_grid(simple_rect_grid):
|
||||
cur_y = r.rand()
|
||||
|
||||
points.append([cur_x, cur_y])
|
||||
q.append(exact_func(cur_x, cur_y))
|
||||
q.append( exact_func( (cur_x, cur_y) ) )
|
||||
grid.__init__(self, points, q)
|
||||
|
||||
self.points = np.array(self.points)
|
||||
|
||||
@ -1,10 +1,35 @@
|
||||
from grid import grid
|
||||
from grid import grid as basegrid
|
||||
from baker.tools import exact_func_3D
|
||||
|
||||
import numpy as np
|
||||
|
||||
|
||||
class simple_rect_grid(grid):
|
||||
class grid(basegrid):
|
||||
def __init__(self, points, q):
|
||||
basegrid.__init__(self, points, q)
|
||||
|
||||
def for_qhull_generator(self):
|
||||
"""
|
||||
this returns a generator that should be fed into qdelaunay
|
||||
"""
|
||||
|
||||
yield '3';
|
||||
yield '%d' % len(self.points)
|
||||
|
||||
for p in self.points:
|
||||
yield "%f %f %f" % tuple(p)
|
||||
|
||||
def for_qhull(self):
|
||||
"""
|
||||
this returns a single string that should be fed into qdelaunay
|
||||
"""
|
||||
r = '3\n'
|
||||
r += '%d\n' % len(self.points)
|
||||
for p in self.points:
|
||||
r += "%f %f %f\n" % tuple(p)
|
||||
return r
|
||||
|
||||
class rect_grid(grid):
|
||||
def __init__(self, xres = 5, yres = 5, zres = 5):
|
||||
xmin = -1.0
|
||||
xmax = 1.0
|
||||
@ -56,7 +81,7 @@ class simple_rect_grid(grid):
|
||||
r += "%f %f %f\n" % tuple(p)
|
||||
return r
|
||||
|
||||
class simple_random_grid(simple_rect_grid):
|
||||
class random_grid(rect_grid):
|
||||
def __init__(self, num_points = 10):
|
||||
points = []
|
||||
q = []
|
||||
|
||||
174
lib/grid/__init__.py
Executable file → Normal file
174
lib/grid/__init__.py
Executable file → Normal file
@ -1 +1,173 @@
|
||||
from grid import *
|
||||
import sys
|
||||
import re
|
||||
from collections import defaultdict
|
||||
|
||||
import numpy as np
|
||||
import scipy.spatial
|
||||
|
||||
from baker import run_baker
|
||||
from baker.tools import exact_func, smberror
|
||||
from simplex import face
|
||||
from smcqdelaunay import *
|
||||
|
||||
|
||||
|
||||
class grid(object):
|
||||
facet_re = re.compile(r'''
|
||||
-\s+(?P<facet>f\d+).*?
|
||||
vertices:\s(?P<verts>.*?)\n.*?
|
||||
neighboring\s facets:\s+(?P<neigh>[\sf\d]*)
|
||||
''', re.S|re.X)
|
||||
|
||||
point_re = re.compile(r'''
|
||||
-\s+(?P<point>p\d+).*?
|
||||
neighbors:\s+(?P<neigh>[\sf\d]*)
|
||||
''', re.S|re.X)
|
||||
|
||||
vert_re = re.compile(r'''
|
||||
(p\d+)
|
||||
''', re.S|re.X)
|
||||
|
||||
|
||||
def __init__(self, points, q):
|
||||
"""
|
||||
this thing eats two pre-constructed arrays of stuff:
|
||||
points = array of arrays (i will convert to numpy.array)
|
||||
[[x0,y0], [x1,y1], ...]
|
||||
q = array (1D) of important values
|
||||
"""
|
||||
|
||||
self.points = np.array(points)
|
||||
self.q = np.array(q)
|
||||
self.tree = scipy.spatial.KDTree(self.points)
|
||||
self.faces = {}
|
||||
self.facets_for_point = defaultdict(list)
|
||||
|
||||
|
||||
def create_mesh(self, indicies):
|
||||
p = [self.points[i] for i in indicies]
|
||||
q = [self.q[i] for i in indicies]
|
||||
return grid(p, q)
|
||||
|
||||
|
||||
def get_simplex_and_nearest_points(self, X, extra_points = 3, simplex_size = 3):
|
||||
"""
|
||||
this returns two grid objects: R and S.
|
||||
|
||||
R is a grid object that is the (a) containing simplex around point X
|
||||
S is S_j from baker's paper : some points from all point that are not the simplex
|
||||
"""
|
||||
(dist, indicies) = self.tree.query(X, simplex_size + extra_points)
|
||||
|
||||
|
||||
# get the containing simplex
|
||||
r_mesh = self.create_mesh(indicies[:simplex_size])
|
||||
# and some extra points
|
||||
s_mesh = self.create_mesh(indicies[simplex_size:])
|
||||
|
||||
return (r_mesh, s_mesh)
|
||||
|
||||
def get_points_conn(self, X):
|
||||
"""
|
||||
this returns two grid objects: R and S.
|
||||
|
||||
this function differes from the get_simplex_and_nearest_points
|
||||
function in that it builds up the extra points based on
|
||||
connectivity information, not just nearest-neighbor.
|
||||
in theory, this will work much better for situations like
|
||||
points near a short edge in a boundary layer cell where the
|
||||
nearest points would all be colinear
|
||||
|
||||
R is a grid object that is the (a) containing simplex around point X
|
||||
S is a connectivity-based nearest-neighbor lookup, limited to 3 extra points
|
||||
"""
|
||||
if not self.faces:
|
||||
self.construct_connectivity()
|
||||
|
||||
# get closest point
|
||||
(dist, indicies) = self.tree.query(X, 2)
|
||||
|
||||
simplex = None
|
||||
for i in self.facets_for_point[indicies[0]]:
|
||||
if i.contains(X, self):
|
||||
simplex = i
|
||||
break
|
||||
|
||||
if not simplex:
|
||||
raise AssertionError('no containing simplex found')
|
||||
|
||||
R = self.create_mesh(simplex.verts)
|
||||
|
||||
|
||||
s = []
|
||||
for c,i in enumerate(simplex.neighbors):
|
||||
s.extend([guy for guy in i.verts if not guy in simplex.verts])
|
||||
S = self.create_mesh(s)
|
||||
|
||||
return R, S
|
||||
|
||||
def run_baker(self, X):
|
||||
answer = None
|
||||
|
||||
try:
|
||||
(R, S) = self.get_simplex_and_nearest_points(X)
|
||||
answer = run_baker(X, R, S)
|
||||
except smberror, e:
|
||||
print >> sys.stderr, "caught error: %s, trying with connectivity-based mesh" % e
|
||||
(R, S) = self.get_points_conn(X)
|
||||
answer = run_baker(X, R, S)
|
||||
|
||||
return answer
|
||||
|
||||
|
||||
|
||||
def construct_connectivity(self):
|
||||
"""
|
||||
a call to this method prepares the internal connectivity structure.
|
||||
|
||||
this is part of the __init__ for a rect_grid, but can be called from any grid object
|
||||
"""
|
||||
qdelaunay_string = get_qdelaunay_dump_str(self)
|
||||
facet_to_facets = []
|
||||
for matcher in grid.facet_re.finditer(qdelaunay_string):
|
||||
d = matcher.groupdict()
|
||||
|
||||
facet_name = d['facet']
|
||||
verticies = d['verts']
|
||||
neighboring_facets = d['neigh']
|
||||
|
||||
cur_face = face(facet_name)
|
||||
self.faces[facet_name] = cur_face
|
||||
|
||||
for v in grid.vert_re.findall(verticies):
|
||||
vertex_index = int(v[1:])
|
||||
cur_face.add_vert(vertex_index)
|
||||
self.facets_for_point[vertex_index].append(cur_face)
|
||||
|
||||
nghbrs = [(facet_name, i) for i in neighboring_facets.split()]
|
||||
facet_to_facets.extend(nghbrs)
|
||||
|
||||
for rel in facet_to_facets:
|
||||
if rel[1] in self.faces:
|
||||
self.faces[rel[0]].add_neighbor(self.faces[rel[1]])
|
||||
|
||||
# for matcher in grid.point_re.finditer(qdelaunay_string):
|
||||
# d = matcher.groupdict()
|
||||
|
||||
# point = d['point']
|
||||
# neighboring_facets = d['neigh']
|
||||
|
||||
# self.facets_for_point[int(point[1:])] = [i for i in neighboring_facets.split() if i in self.faces]
|
||||
|
||||
def __str__(self):
|
||||
r = ''
|
||||
assert( len(self.points) == len(self.q) )
|
||||
for c, i in enumerate(zip(self.points, self.q)):
|
||||
r += "%d %r: %0.4f" % (c,i[0], i[1])
|
||||
facet_str = ", ".join([f.name for f in self.facets_for_point[c]])
|
||||
r += " faces: [%s]" % facet_str
|
||||
r += "\n"
|
||||
if self.faces:
|
||||
for v in self.faces.itervalues():
|
||||
r += "%s\n" % v
|
||||
return r
|
||||
|
||||
186
lib/grid/grid.py
186
lib/grid/grid.py
@ -1,186 +0,0 @@
|
||||
#!/usr/bin/python
|
||||
|
||||
import sys
|
||||
import re
|
||||
from collections import defaultdict
|
||||
|
||||
import numpy as np
|
||||
import scipy.spatial
|
||||
|
||||
from baker import run_baker
|
||||
from baker.tools import exact_func, smberror
|
||||
from simplex import face
|
||||
from smcqdelaunay import *
|
||||
|
||||
|
||||
|
||||
class grid(object):
|
||||
facet_re = re.compile(r'''
|
||||
-\s+(?P<facet>f\d+).*?
|
||||
vertices:\s(?P<verts>.*?)\n.*?
|
||||
neighboring\s facets:\s+(?P<neigh>[\sf\d]*)
|
||||
''', re.S|re.X)
|
||||
|
||||
point_re = re.compile(r'''
|
||||
-\s+(?P<point>p\d+).*?
|
||||
neighbors:\s+(?P<neigh>[\sf\d]*)
|
||||
''', re.S|re.X)
|
||||
|
||||
vert_re = re.compile(r'''
|
||||
(p\d+)
|
||||
''', re.S|re.X)
|
||||
|
||||
|
||||
def __init__(self, points, q):
|
||||
"""
|
||||
this thing eats two pre-constructed arrays of stuff:
|
||||
points = array of arrays (i will convert to numpy.array)
|
||||
[[x0,y0], [x1,y1], ...]
|
||||
q = array (1D) of important values
|
||||
"""
|
||||
|
||||
self.points = np.array(points)
|
||||
self.q = np.array(q)
|
||||
self.tree = scipy.spatial.KDTree(self.points)
|
||||
self.faces = {}
|
||||
self.facets_for_point = defaultdict(list)
|
||||
|
||||
|
||||
def create_mesh(self, indicies):
|
||||
p = [self.points[i] for i in indicies]
|
||||
q = [self.q[i] for i in indicies]
|
||||
return grid(p, q)
|
||||
|
||||
|
||||
def get_simplex_and_nearest_points(self, X, extra_points = 3, simplex_size = 3):
|
||||
"""
|
||||
this returns two grid objects: R and S.
|
||||
|
||||
R is a grid object that is the (a) containing simplex around point X
|
||||
S is S_j from baker's paper : some points from all point that are not the simplex
|
||||
"""
|
||||
(dist, indicies) = self.tree.query(X, simplex_size + extra_points)
|
||||
|
||||
|
||||
# get the containing simplex
|
||||
r_mesh = self.create_mesh(indicies[:simplex_size])
|
||||
# and some extra points
|
||||
s_mesh = self.create_mesh(indicies[simplex_size:])
|
||||
|
||||
return (r_mesh, s_mesh)
|
||||
|
||||
def get_points_conn(self, X):
|
||||
"""
|
||||
this returns two grid objects: R and S.
|
||||
|
||||
this function differes from the get_simplex_and_nearest_points
|
||||
function in that it builds up the extra points based on
|
||||
connectivity information, not just nearest-neighbor.
|
||||
in theory, this will work much better for situations like
|
||||
points near a short edge in a boundary layer cell where the
|
||||
nearest points would all be colinear
|
||||
|
||||
R is a grid object that is the (a) containing simplex around point X
|
||||
S is a connectivity-based nearest-neighbor lookup, limited to 3 extra points
|
||||
"""
|
||||
if not self.faces:
|
||||
self.construct_connectivity()
|
||||
|
||||
# get closest point
|
||||
(dist, indicies) = self.tree.query(X, 2)
|
||||
|
||||
simplex = None
|
||||
for i in self.facets_for_point[indicies[0]]:
|
||||
if i.contains(X, self):
|
||||
simplex = i
|
||||
break
|
||||
|
||||
if not simplex:
|
||||
raise AssertionError('no containing simplex found')
|
||||
|
||||
R = self.create_mesh(simplex.verts)
|
||||
|
||||
|
||||
s = []
|
||||
for c,i in enumerate(simplex.neighbors):
|
||||
s.extend([guy for guy in i.verts if not guy in simplex.verts])
|
||||
S = self.create_mesh(s)
|
||||
|
||||
return R, S
|
||||
|
||||
def run_baker(self, X):
|
||||
answer = None
|
||||
|
||||
try:
|
||||
(R, S) = self.get_simplex_and_nearest_points(X)
|
||||
answer = run_baker(X, R, S)
|
||||
except smberror, e:
|
||||
print "caught error: %s, trying with connectivity-based mesh" % e
|
||||
(R, S) = self.get_points_conn(X)
|
||||
answer = run_baker(X, R, S)
|
||||
|
||||
return answer
|
||||
|
||||
|
||||
|
||||
def construct_connectivity(self):
|
||||
"""
|
||||
a call to this method prepares the internal connectivity structure.
|
||||
|
||||
this is part of the __init__ for a simple_rect_grid, but can be called from any grid object
|
||||
"""
|
||||
qdelaunay_string = get_qdelaunay_dump_str(self)
|
||||
facet_to_facets = []
|
||||
for matcher in grid.facet_re.finditer(qdelaunay_string):
|
||||
d = matcher.groupdict()
|
||||
|
||||
facet_name = d['facet']
|
||||
verticies = d['verts']
|
||||
neighboring_facets = d['neigh']
|
||||
|
||||
cur_face = face(facet_name)
|
||||
self.faces[facet_name] = cur_face
|
||||
|
||||
for v in grid.vert_re.findall(verticies):
|
||||
vertex_index = int(v[1:])
|
||||
cur_face.add_vert(vertex_index)
|
||||
self.facets_for_point[vertex_index].append(cur_face)
|
||||
|
||||
nghbrs = [(facet_name, i) for i in neighboring_facets.split()]
|
||||
facet_to_facets.extend(nghbrs)
|
||||
|
||||
for rel in facet_to_facets:
|
||||
if rel[1] in self.faces:
|
||||
self.faces[rel[0]].add_neighbor(self.faces[rel[1]])
|
||||
|
||||
# for matcher in grid.point_re.finditer(qdelaunay_string):
|
||||
# d = matcher.groupdict()
|
||||
|
||||
# point = d['point']
|
||||
# neighboring_facets = d['neigh']
|
||||
|
||||
# self.facets_for_point[int(point[1:])] = [i for i in neighboring_facets.split() if i in self.faces]
|
||||
|
||||
def __str__(self):
|
||||
r = ''
|
||||
assert( len(self.points) == len(self.q) )
|
||||
for c, i in enumerate(zip(self.points, self.q)):
|
||||
r += "%d %r: %0.4f" % (c,i[0], i[1])
|
||||
facet_str = ", ".join([f.name for f in self.facets_for_point[c]])
|
||||
r += " faces: [%s]" % facet_str
|
||||
r += "\n"
|
||||
if self.faces:
|
||||
for v in self.faces.itervalues():
|
||||
r += "%s\n" % v
|
||||
return r
|
||||
|
||||
|
||||
|
||||
|
||||
if __name__ == '__main__':
|
||||
try:
|
||||
resolution = int(sys.argv[1])
|
||||
except:
|
||||
resolution = 10
|
||||
g = simple_rect_grid(resolution, resolution)
|
||||
print g.for_qhull()
|
||||
@ -1,5 +1,15 @@
|
||||
from baker import get_phis
|
||||
|
||||
TOL = 1e-3
|
||||
|
||||
def contains(X, R):
|
||||
phis = get_phis(X, R)
|
||||
r = True
|
||||
if [i for i in phis if i < 0.0 - TOL]:
|
||||
r = False
|
||||
return r
|
||||
|
||||
|
||||
class face(object):
|
||||
def __init__(self, name):
|
||||
self.name = name
|
||||
@ -19,14 +29,7 @@ class face(object):
|
||||
self.neighbors.append(n)
|
||||
|
||||
def contains(self, X, grid):
|
||||
R = [grid.points[i] for i in self.verts]
|
||||
|
||||
phis = get_phis(X, R)
|
||||
|
||||
r = True
|
||||
if [i for i in phis if i < 0.0]:
|
||||
r = False
|
||||
return r
|
||||
return contains(X, grid.points)
|
||||
|
||||
def __str__(self):
|
||||
neighbors = [i.name for i in self.neighbors]
|
||||
|
||||
54
test/quad.test.py
Executable file
54
test/quad.test.py
Executable file
@ -0,0 +1,54 @@
|
||||
#!/usr/bin/python
|
||||
|
||||
import unittest
|
||||
|
||||
from baker import run_baker
|
||||
from baker.tools import exact_func
|
||||
|
||||
from grid.DD import grid
|
||||
from grid.simplex import contains
|
||||
|
||||
|
||||
class TestSequenceFunctions(unittest.TestCase):
|
||||
def setUp(self):
|
||||
self.points = [
|
||||
[ 0.25, 0.40], # 0
|
||||
[ 0.60, 0.80], # 1
|
||||
[ 0.65, 0.28], # 2
|
||||
[ 0.28, 0.65], # 3
|
||||
[ 1.00, 0.75], # 4
|
||||
[ 0.30, 0.95], # 5
|
||||
[ 0.80, 0.50], # 6
|
||||
[ 0.35, 0.15], # 7
|
||||
]
|
||||
self.q = [exact_func(p) for p in self.points]
|
||||
|
||||
self.X = [0.55, 0.45]
|
||||
self.X = [0.25, 0.4001]
|
||||
|
||||
self.g = grid(self.points, self.q)
|
||||
self.g.construct_connectivity()
|
||||
self.R = self.g.create_mesh(range(3))
|
||||
self.S = self.g.create_mesh(range(3,len(self.points)))
|
||||
|
||||
self.exact = exact_func(self.X)
|
||||
|
||||
self.answer = run_baker(self.X, self.R, self.S)
|
||||
|
||||
self.accuracy = 8
|
||||
|
||||
def test_R_contains_X(self):
|
||||
self.assertTrue(contains(self.X, self.R.points))
|
||||
|
||||
def test_RunBaker(self):
|
||||
print
|
||||
print "X\n", self.X
|
||||
print "R\n", self.R
|
||||
print "S\n", self.S
|
||||
print "exact\n",self.exact
|
||||
print "qlin\n",self.answer['qlin']
|
||||
self.assertTrue(self.answer)
|
||||
|
||||
if __name__ == '__main__':
|
||||
suite = unittest.TestLoader().loadTestsFromTestCase(TestSequenceFunctions)
|
||||
unittest.TextTestRunner(verbosity=3).run(suite)
|
||||
@ -1,9 +1,9 @@
|
||||
from Blender import *
|
||||
import bpy
|
||||
|
||||
from grid.test3d import simple_rect_grid
|
||||
from grid.test3d import rect_grid
|
||||
|
||||
g = simple_rect_grid(10, 10, 20)
|
||||
g = rect_grid(10, 10, 20)
|
||||
|
||||
me = bpy.data.meshes.new('points')
|
||||
me.verts.extend(g.points)
|
||||
|
||||
Loading…
Reference in New Issue
Block a user