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ehaber99
50 lines
1.4 KiB
Python
50 lines
1.4 KiB
Python
import numpy as np
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from utils import mkvc
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import scipy.sparse.linalg.dsolve as dsl
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def getMisfit(m,mesh,forward):
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mu0 = 4*np.pi*1e-7
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omega = forward['omega'] #[param['indomega']]
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rhs = forward['rhs'] #[:,param['indrhs']]
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misfit = 0
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# Maxwell's system for E
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for i in range(len(omega)):
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for j in range(rhs.shape[1]):
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Curl = mesh.edgeCurl
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#Grad = mesh.nodalGrad
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sigma = np.exp(m)
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Me,PP = mesh.getEdgeMass(sigma)
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Mf = 1/mu0 * mesh.getFaceMass() # assume mu = mu0
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A = Curl.T * Mf * Curl - 1j * omega[i] * Me
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b = mkvc(np.array(rhs[:,j]))
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e = dsl.spsolve(A,b)
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e = mkvc(e,2)
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#print np.linalg.norm(A*e-b)/np.linalg.norm(b)
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P = forward['projection']
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d = P*e
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r = mkvc(d - param.dobs[i,j,:],2)
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mis = mis + 0.5*(r.T*r)
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# get derivatives
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lam = dsl.spsolve(A.T,P.T*r)
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Gij = PP.T*diag((PP*e)*mesh.vol)
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dmis = dmis - Gij.T*lam
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if __name__ == '__main__':
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from TensorMesh import TensorMesh
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h = [np.ones(7),np.ones(8),np.ones(9)]
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mesh = TensorMesh(h)
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ne = np.sum(mesh.nE)
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Q = np.matrix(np.random.randn(ne,5))
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P = np.matrix(Q.T)
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forward = {'omega':[1,2,3], 'rhs':Q,'projection':P}
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m = np.ones(mesh.nC)
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getMisfit(m,mesh,forward)
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