mirror of
https://github.com/wassname/simpeg.git
synced 2026-06-28 04:23:26 +08:00
Lindsey Heagy
69 lines
1.7 KiB
Python
69 lines
1.7 KiB
Python
from SimPEG import *
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def run(N=100, plotIt=True):
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"""
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Inversion: Linear Problem
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=========================
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Here we go over the basics of creating a linear problem and inversion.
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"""
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np.random.seed(1)
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mesh = Mesh.TensorMesh([N])
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nk = 20
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jk = np.linspace(1.,20.,nk)
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p = -0.25
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q = 0.25
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g = lambda k: np.exp(p*jk[k]*mesh.vectorCCx)*np.cos(2*np.pi*q*jk[k]*mesh.vectorCCx)
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G = np.empty((nk, mesh.nC))
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for i in range(nk):
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G[i,:] = g(i)
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mtrue = np.zeros(mesh.nC)
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mtrue[mesh.vectorCCx > 0.3] = 1.
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mtrue[mesh.vectorCCx > 0.45] = -0.5
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mtrue[mesh.vectorCCx > 0.6] = 0
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prob = Problem.LinearProblem(mesh, G)
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survey = Survey.LinearSurvey()
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survey.pair(prob)
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survey.makeSyntheticData(mtrue, std=0.01)
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M = prob.mesh
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reg = Regularization.Tikhonov(mesh)
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dmis = DataMisfit.l2_DataMisfit(survey)
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opt = Optimization.InexactGaussNewton(maxIter=35)
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invProb = InvProblem.BaseInvProblem(dmis, reg, opt)
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beta = Directives.BetaSchedule()
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betaest = Directives.BetaEstimate_ByEig()
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inv = Inversion.BaseInversion(invProb, directiveList=[beta, betaest])
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m0 = np.zeros_like(survey.mtrue)
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mrec = inv.run(m0)
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if plotIt:
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import matplotlib.pyplot as plt
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fig, axes = plt.subplots(1,2,figsize=(12*1.2,4*1.2))
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for i in range(prob.G.shape[0]):
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axes[0].plot(prob.G[i,:])
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axes[0].set_title('Columns of matrix G')
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axes[1].plot(M.vectorCCx, survey.mtrue, 'b-')
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axes[1].plot(M.vectorCCx, mrec, 'r-')
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axes[1].legend(('True Model', 'Recovered Model'))
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plt.show()
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return prob, survey, mesh, mrec
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if __name__ == '__main__':
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run()
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