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ehaber99
dcae030d81
2. The getMisfit may be working but needs a little bit more work We need to go through our code to make sure that all vectors that can be multiplied by a matrix are set to vec = mkvc(vec,2)
77 lines
2.2 KiB
Python
77 lines
2.2 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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from InnerProducts import getFaceInnerProduct, getEdgeInnerProduct
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def getMisfit(m,mesh,forward,param):
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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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mis = 0
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dmis = m*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 = getEdgeInnerProduct(mesh,sigma)
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Mf = 1/mu0 * getFaceInnerProduct(mesh) # 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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lam = mkvc(lam,2)
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Gij = - 1j * omega[i] * PP.T*sp.diag((PP*e)*mesh.vol)
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dmis = dmis - Gij.T*lam
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return mis, dmis, d
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if __name__ == '__main__':
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from TensorMesh import TensorMesh
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from interpmat import interpmat
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from scipy import sparse as sp
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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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xs = np.array([3.1,4.3,5.4,6.5])
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ys = np.array([3.2,4.1,5.4,6.2])
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zs = np.array([4.3,4.2,4.1,4.1]);
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xyz = mesh.gridEx
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x = xyz[:,0]; y = xyz[:,1]; z = xyz[:,2]
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Px = interpmat(x,y,z,xs,ys,zs)
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xyz = mesh.gridEy
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x = xyz[:,0]; y = xyz[:,1]; z = xyz[:,2]
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Py = interpmat(x,y,z,xs,ys,zs)
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xyz = mesh.gridEz
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x = xyz[:,0]; y = xyz[:,1]; z = xyz[:,2]
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Pz = interpmat(x,y,z,xs,ys,zs)
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P = sp.hstack((Px,Py,Pz))
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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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omega = [1,2,3]
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forward = {'omega':omega, 'rhs':Q,'projection':P}
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dobs = np.ones(np.size(xs),np.shape(Q,2),np.size(omega))
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param = {'dobs':dobs}
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m = np.ones(mesh.nC)
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getMisfit(m,mesh,forward,param)
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