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TestTemp.py
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TestTemp.py
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# -*- coding: utf-8 -*-
"""
Created on Wed Jan 4 22:13:33 2017
Tests on attempts to find a simpler way to solve for pressures in
bryozoan model.
@author: Michelangelo
"""
from Bryozoan import *
import numpy
import scipy
import scipy.sparse as sparse
import scipy.sparse.linalg as ssl
import matplotlib.pyplot as plt
c1 = Colony(nz=6, mz=7, OutflowConductivity=0.01, dCdt=dCdt_default,
dCdt_in_params={'yminusx': 1, 'b': 1, 'r': 1, 'w': 3},
dCdt_out_params={'yminusx': 1, 'b': 0.1, 'r': 1, 'w': 3})
# Set a central outflow conduit (edge) to have higher conductivity
c1.setouterconductivities([41], [0.02])
temp = c1.solvecolony()
Bz = temp['IncidenceFull']
P = np.asmatrix(temp['Pressures']).transpose()
C = sparse.diags(temp['conductivityfull'],0)
Cinv = sparse.diags(1/temp['conductivityfull'],0)
q = np.asmatrix(c1.InFlow).transpose()
mpiBz = scipy.linalg.pinv(Bz.todense())
q_newmethod = Bz.transpose()*C*Bz*(mpiBz*(Cinv*(mpiBz.transpose()*q)))
q_originalmethod = Bz.transpose()*C*Bz*P
print('original method works?', np.allclose(q, q_originalmethod,
rtol=np.mean(abs(q))*10**-4,
atol=np.mean(abs(q))*10**-4))
print('new method works?', np.allclose(q, q_newmethod,
rtol=np.mean(abs(q))*10**-4,
atol=np.mean(abs(q))*10**-4))
print('Is it a right inverse?',
np.allclose(q, Bz.transpose()*mpiBz.transpose()*q,
rtol=np.mean(abs(q))*10**-4, atol=np.mean(abs(q))*10**-4))
print('Is it a right inverse?',
np.allclose(Bz.transpose()*C*Bz*P, Bz.transpose()*mpiBz.transpose()*q,
rtol=np.mean(abs(q))*10**-4, atol=np.mean(abs(q))*10**-4))
print('Is it a right inverse?',
np.allclose(C*Bz*P, mpiBz.transpose()*q,
rtol=np.mean(abs(q))*10**-4, atol=np.mean(abs(q))*10**-4))
print('Is it a right inverse?',
np.allclose(Bz*P, ssl.inv(C)*mpiBz.transpose()*q,
rtol=np.mean(abs(q))*10**-4, atol=np.mean(abs(q))*10**-4))