smbinterp/lib/baker.py

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from grid import exact_func
import numpy as np
import sys
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)
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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],
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[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]
])
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try:
phi = np.linalg.solve(A,b)
except:
print >> sys.stderr, "warning: calculation of phis yielded a linearly dependant system"
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: calculation of phis yielded a linearly dependant system"
phi = np.dot(np.linalg.pinv(A), b)
return phi
def qlinear(X, R, q):
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"""
this calculates the linear portion of q from X to r
also, this is baker eq 3
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X = destination point
R = simplex points
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q = CFD quantities of interest at the simplex points
"""
phis = get_phis(X, R)
qlin = sum([q_i * phi_i for q_i, phi_i in zip(q, phis)])
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return 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 qlin
def run_baker(X, R, S, extra_points = 3, verbose = False):
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"""
This is the main function to call to get an interpolation to X from the tree
X -- the destination point (2D)
X = [0,0]
g -- the grid object
tree -- the kdtree search object (built from the g mesh)
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"""
# calculate values only for the triangle
phi = get_phis(X, S.points)
qlin = qlinear (X, S.points, S.q)
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if extra_points == 0: return qlin
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B = [] # baker eq 9
w = [] # baker eq 11
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for (s, q) in zip(S.points, S.q):
(phi1, phi2, phi3) = get_phis(s, R.points)
B.append([phi1 * phi2, phi2*phi3, phi3*phi1])
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w.append(q - qlinear(s, R.points, R.q))
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B = np.array(B)
w = np.array(w)
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A = np.dot(B.T, B)
b = np.dot(B.T, w)
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# baker solve eq 10
try:
(a, b, c) = np.linalg.solve(A,b)
except:
print >> sys.stderr, "warning: linear calculation went bad, resorting to np.linalg.pinv"
(a, b, c) = np.dot(np.linalg.pinv(A), b)
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error_term = a * phi[0] * phi[1]\
+ b * phi[1] * phi[2]\
+ c * phi[2] * phi[0]
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q_final = qlin + error_term
answer = {
'a': a,
'b': b,
'c': c,
'qlin': qlin,
'error': error_term,
'final': q_final,
}
return answer