323 lines
8.1 KiB
Python
323 lines
8.1 KiB
Python
from baker import *
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import numpy as np
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import sys
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from tools import smberror
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def get_phis(X, R):
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"""
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The get_phis function is used to get barycentric coordonites for a point on a triangle.
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X -- the destination point (2D)
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X = [0,0]
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r -- the three points that make up the containing triangular simplex (2D)
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r = [[-1, -1], [0, 2], [1, -1]]
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this will return [0.333, 0.333, 0.333]
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"""
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# baker: eq 7
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A = np.array([
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[ 1, 1, 1],
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[R[0][0], R[1][0], R[2][0]],
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[R[0][1], R[1][1], R[2][1]],
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])
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b = np.array([ 1,
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X[0],
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X[1]
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])
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try:
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phi = np.linalg.solve(A,b)
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except np.linalg.LinAlgError as e:
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msg = "warning: get_phis: calculation of phis yielded a linearly dependant system (%s)" % e
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# TODO: log this -- > print >> sys.stderr, msg
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raise smberror(msg)
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phi = np.dot(np.linalg.pinv(A), b)
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return phi
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def get_phis_3D(X, R):
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"""
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The get_phis function is used to get barycentric coordonites for a point on a tetrahedron.
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X -- the destination point (3D)
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X = [0,0,0]
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R -- the four points that make up the containing simplex, tetrahedron (3D)
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R = [
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[0.0, 0.0, 1.0],
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[0.94280904333606508, 0.0, -0.3333333283722672],
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[-0.47140452166803232, 0.81649658244673617, -0.3333333283722672],
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[-0.47140452166803298, -0.81649658244673584, -0.3333333283722672],
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]
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this (should) will return [0.25, 0.25, 0.25, 0.25]
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"""
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# baker: eq 7
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A = np.array([
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[ 1, 1, 1, 1 ],
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[R[0][0], R[1][0], R[2][0], R[3][0]],
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[R[0][1], R[1][1], R[2][1], R[3][1]],
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[R[0][2], R[1][2], R[2][2], R[3][2]],
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])
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b = np.array([ 1,
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X[0],
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X[1],
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X[2]
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])
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try:
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phi = np.linalg.solve(A,b)
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except np.linalg.LinAlgError as e:
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print >> sys.stderr, "warning: get_phis_3D: calculation of phis yielded a linearly dependant system", e
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phi = np.dot(np.linalg.pinv(A), b)
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return phi
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def qlinear(X, R):
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"""
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this calculates the linear portion of q from X to R
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also, this is baker eq 3
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X = destination point
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R = simplex points
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q = CFD quantities of interest at the simplex points
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"""
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phis = get_phis(X, R.points)
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qlin = sum([q_i * phi_i for q_i, phi_i in zip(R.q, phis)])
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return phis, qlin
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def qlinear_3D(X, R):
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"""
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this calculates the linear portion of q from X to R
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X = destination point
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R = simplex points
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q = CFD quantities of interest at the simplex points(R)
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"""
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phis = get_phis_3D(X, R.points)
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qlin = sum([q_i * phi_i for q_i, phi_i in zip(R.q, phis)])
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return phis, qlin
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def get_error_quadratic(phi, R, S):
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B = [] # baker eq 9
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w = [] # baker eq 11
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for (s, q) in zip(S.points, S.q):
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cur_phi, cur_qlin = qlinear(s, R)
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(phi1, phi2, phi3) = cur_phi
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B.append(
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[
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phi1 * phi2,
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phi2 * phi3,
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phi3 * phi1,
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]
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)
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w.append(q - cur_qlin)
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B = np.array(B)
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w = np.array(w)
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A = np.dot(B.T, B)
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b = np.dot(B.T, w)
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# baker solve eq 10
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try:
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(a, b, c) = np.linalg.solve(A,b)
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except np.linalg.LinAlgError as e:
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print >> sys.stderr, "warning: run_baker: linear calculation went bad, resorting to np.linalg.pinv", e
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(a, b, c) = np.dot(np.linalg.pinv(A), b)
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error_term = a * phi[0] * phi[1]\
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+ b * phi[1] * phi[2]\
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+ c * phi[2] * phi[0]
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return error_term, a, b, c
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def get_error_cubic(phi, R, S):
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B = [] # baker eq 9
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w = [] # baker eq 11
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for (s, q) in zip(S.points, S.q):
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cur_phi, cur_qlin = qlinear(s, R)
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(phi1, phi2, phi3) = cur_phi
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# basing this on eq 17
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B.append(
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[
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phi1 * phi2 * phi2, # a
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phi1 * phi3 * phi3, # b
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phi2 * phi1 * phi1, # c
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phi2 * phi3 * phi3, # d
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phi3 * phi1 * phi1, # e
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phi3 * phi2 * phi2, # f
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phi1 * phi2 * phi3, # g
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]
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)
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w.append(q - cur_qlin)
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B = np.array(B)
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w = np.array(w)
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A = np.dot(B.T, B)
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b = np.dot(B.T, w)
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# baker solve eq 10
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try:
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(a, b, c, d, e, f, g) = np.linalg.solve(A,b)
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except np.linalg.LinAlgError as e:
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print >> sys.stderr, "warning: run_baker: linear calculation went bad, resorting to np.linalg.pinv", e
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(a, b, c, d, e, f, g) = np.dot(np.linalg.pinv(A), b)
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error_term = a * phi[0] * phi[1] * phi[1]\
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+ b * phi[0] * phi[2] * phi[2]\
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+ c * phi[1] * phi[0] * phi[0]\
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+ d * phi[1] * phi[2] * phi[2]\
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+ e * phi[2] * phi[0] * phi[0]\
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+ f * phi[2] * phi[1] * phi[1]\
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+ g * phi[0] * phi[1] * phi[2]\
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return error_term, a, b, c
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def run_baker(X, R, S, order=2):
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"""
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This is the main function to call to get an interpolation to X from the input meshes
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X -- the destination point (2D)
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X = [0,0]
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R = Simplex
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S = extra points
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"""
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# calculate values only for the simplex triangle
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phi, qlin = qlinear(X, R)
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if len(S.points) == 0:
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answer = {
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'a': None,
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'b': None,
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'c': None,
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'qlin': qlin,
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'error': None,
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'final': None,
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}
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return answer
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if order == 2:
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error_term, a, b, c = get_error_quadratic(phi, R, S)
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elif order == 3:
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error_term, a, b, c = get_error_cubic(phi, R, S)
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else:
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raise smberror('unacceptable order for baker method')
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q_final = qlin + error_term
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answer = {
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'a': a,
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'b': b,
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'c': c,
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'qlin': qlin,
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'error': error_term,
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'final': q_final,
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}
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return answer
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def run_baker_3D(X, R, S):
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"""
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This is the main function to call to get an interpolation to X from the input meshes
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X -- the destination point (3D)
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X = [0,0,0]
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R = Simplex (4 points, contains X)
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S = extra points (surrounding, in some manner, R and X, but not in R)
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"""
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# calculate values only for the triangle
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phi, qlin = qlinear_3D(X, R)
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if [i for i in phi if i <= 0.0]:
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s = "this is not a containing simplex:\n"
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s += " X: %s\n" % X
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s += " R: %s\n" % R
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s += " phi: %s, sum(%0.4e)\n" % (phi, sum(phi))
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print >> sys.stderr, s
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raise smberror("not containing simplex")
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if len(S.points) == 0:
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answer = {
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'a': None,
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'b': None,
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'c': None,
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'd': None,
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'e': None,
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'f': None,
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'qlin': qlin,
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'error': None,
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'final': None,
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}
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return answer
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B = [] # baker eq 9
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w = [] # baker eq 11
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for (s, q) in zip(S.points, S.q):
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cur_phi, cur_qlin = qlinear_3D(s, R)
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(phi1, phi2, phi3, phi4) = cur_phi
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B.append(
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[
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phi1 * phi2,
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phi1 * phi3,
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phi1 * phi4,
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phi2 * phi3,
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phi2 * phi4,
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phi3 * phi4,
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]
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)
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w.append(q - cur_qlin)
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B = np.array(B)
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w = np.array(w)
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A = np.dot(B.T, B)
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b = np.dot(B.T, w)
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# baker solve eq 10
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try:
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(a, b, c, d, e, f) = np.linalg.solve(A,b)
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except np.linalg.LinAlgError as e:
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print >> sys.stderr, "warning: run_baker: linear calculation went bad, resorting to np.linalg.pinv", e
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(a, b, c, d, e, f) = np.dot(np.linalg.pinv(A), b)
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error_term = a * phi[0] * phi[1]\
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+ b * phi[0] * phi[2]\
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+ c * phi[0] * phi[3]\
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+ d * phi[1] * phi[2]\
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+ e * phi[1] * phi[3]\
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+ f * phi[2] * phi[3]
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q_final = qlin + error_term
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answer = {
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'a': a,
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'b': b,
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'c': c,
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'd': d,
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'e': e,
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'f': f,
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'qlin': qlin,
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'error': error_term,
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'final': q_final,
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}
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return answer
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