updated library files so that i don't have to edit the __init__.py files

--HG--
rename : lib/baker/__init__.py => lib/baker/baker.py
rename : lib/grid/__init__.py => lib/grid/grid.py
This commit is contained in:
Stephen Mardson McQuay 2010-03-08 14:30:22 -07:00
parent b9ea6a3ac2
commit a2d7b3f063
5 changed files with 453 additions and 450 deletions

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\.pyc$ \.pyc$
\.blend$ \.blend$
egg

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import numpy as np from baker import *
import sys
from baker.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 = [[-1, -1], [0, 2], [1, -1]]
this will return [0.333, 0.333, 0.333]
"""
# 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, q):
"""
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)
qlin = sum([q_i * phi_i for q_i, phi_i in zip(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

163
lib/baker/baker.py Normal file
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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 = [[-1, -1], [0, 2], [1, -1]]
this will return [0.333, 0.333, 0.333]
"""
# 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, q):
"""
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)
qlin = sum([q_i * phi_i for q_i, phi_i in zip(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

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#!/usr/bin/python from grid import *
import sys
import re
from collections import defaultdict
import numpy as np
import scipy.spatial
from baker import run_baker, get_phis
from baker.tools import exact_func, smberror
from grid.smcqdelaunay import *
class face(object):
def __init__(self, name):
self.name = name
self.verts = []
self.neighbors = []
def add_vert(self, v):
"""
v should be an index into grid.points
"""
self.verts.append(v)
def add_neighbor(self, n):
"""
reference to another 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
def __str__(self):
neighbors = [i.name for i in self.neighbors]
return '%s: verts: %s neighbors: [%s]' %\
(
self.name,
self.verts,
", ".join(neighbors)
)
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, 3 + 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 as 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 for_qhull_generator(self):
"""
this returns a generator that should be fed into qdelaunay
"""
yield '2';
yield '%d' % len(self.points)
for p in self.points:
yield "%f %f" % (p[0], p[1])
def for_qhull(self):
"""
this returns a single string that should be fed into qdelaunay
"""
r = '2\n'
r += '%d\n' % len(self.points)
for p in self.points:
r += "%f %f\n" % (p[0], p[1])
return r
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
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 simple_random_grid(simple_rect_grid):
def __init__(self, num_points = 10):
points = []
q = []
r = np.random
for i in xrange(num_points):
cur_x = r.rand()
cur_y = r.rand()
points.append([cur_x, cur_y])
q.append(exact_func(cur_x, cur_y))
grid.__init__(self, points, q)
self.points = np.array(self.points)
self.q = np.array(self.q)
if __name__ == '__main__':
try:
resolution = int(sys.argv[1])
except:
resolution = 10
g = simple_rect_grid(resolution, resolution)
print g.for_qhull()

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lib/grid/grid.py Executable file
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#!/usr/bin/python
import sys
import re
from collections import defaultdict
import numpy as np
import scipy.spatial
from baker import run_baker, get_phis
from baker.tools import exact_func, smberror
from smcqdelaunay import *
class face(object):
def __init__(self, name):
self.name = name
self.verts = []
self.neighbors = []
def add_vert(self, v):
"""
v should be an index into grid.points
"""
self.verts.append(v)
def add_neighbor(self, n):
"""
reference to another 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
def __str__(self):
neighbors = [i.name for i in self.neighbors]
return '%s: verts: %s neighbors: [%s]' %\
(
self.name,
self.verts,
", ".join(neighbors)
)
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, 3 + 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 as 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 for_qhull_generator(self):
"""
this returns a generator that should be fed into qdelaunay
"""
yield '2';
yield '%d' % len(self.points)
for p in self.points:
yield "%f %f" % (p[0], p[1])
def for_qhull(self):
"""
this returns a single string that should be fed into qdelaunay
"""
r = '2\n'
r += '%d\n' % len(self.points)
for p in self.points:
r += "%f %f\n" % (p[0], p[1])
return r
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
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 simple_random_grid(simple_rect_grid):
def __init__(self, num_points = 10):
points = []
q = []
r = np.random
for i in xrange(num_points):
cur_x = r.rand()
cur_y = r.rand()
points.append([cur_x, cur_y])
q.append(exact_func(cur_x, cur_y))
grid.__init__(self, points, q)
self.points = np.array(self.points)
self.q = np.array(self.q)
if __name__ == '__main__':
try:
resolution = int(sys.argv[1])
except:
resolution = 10
g = simple_rect_grid(resolution, resolution)
print g.for_qhull()