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Test interpolation methods.
Attempt at using FFT to resample grid. Need to can an FFT method for 2 grid ( pad, taper, resample, extract)
This commit is contained in:
D Fournier
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import os
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home_dir = 'C:\\LC\\Private\\dominiquef\\Projects\\4414_Minsim\\Modeling\\MAG'
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os.chdir(home_dir)
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#%%
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from SimPEG import *
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import matplotlib.pyplot as plt
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import simpegPF as PF
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import scipy.interpolate as interpolation
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#from fwr_MAG_data import fwr_MAG_data
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plt.close('all')
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topofile = 'Gaussian.topo'
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zoffset = 2
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#%% Create survey
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# Load in topofile or create flat surface
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if not topofile:
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actv = np.ones(mesh.nC)
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else:
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topo = np.genfromtxt(topofile,skip_header=1)
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B = np.array(([90.,0.,50000.]))
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M = np.array(([90.,0.,315.]))
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# Sphere radius
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R = 25.
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# # Or create juste a plane grid
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xr = np.linspace(-99., 99., 40)
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yr = np.linspace(-49., 49., 20)
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X, Y = np.meshgrid(xr, yr)
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d_iter = 1
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lrl = np.zeros(d_iter)
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sclx = 100.
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dx = 5
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#%% Loop through decreasing meshes and measure the residual
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# Create mesh using simpeg and write out in GIF format
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for ii in range(d_iter):
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nc = int(sclx/dx)
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hxind = [(dx, 2*nc)]
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hyind = [(dx, nc)]
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hzind = [(dx, nc)]
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mesh = Mesh.TensorMesh([hxind, hyind, hzind], 'CCN')
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actv = PF.Magnetics.getActiveTopo(mesh,topo,'N')
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# Drape observations on topo + offset
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if not topofile:
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Z = np.ones((xr.size, yr.size)) * 2.5
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else:
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F = interpolation.NearestNDInterpolator(topo[:,0:2],topo[:,2])
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Z = F(X,Y) + zoffset
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rxLoc = np.c_[Utils.mkvc(X.T), Utils.mkvc(Y.T), Utils.mkvc(Z.T)]
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ndata = rxLoc.shape[0]
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xn = mesh.vectorNx
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yn = mesh.vectorNy
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zn = mesh.vectorNz
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mcell = mesh.nC
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print 'Mesh size: ' + str(mcell)
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#%% Create model
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chibkg = 0.
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chiblk = 0.01
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model = np.ones(mcell)*chibkg
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# Do a three sphere problem for more frequencies
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sph_ind = PF.MagAnalytics.spheremodel(mesh, 0., 0., -sclx/3, R)
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model[sph_ind] = 0.5*chiblk
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sph_ind = PF.MagAnalytics.spheremodel(mesh, -sclx/2., 0., -sclx/3., R/3.)
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model[sph_ind] = 4.*chiblk
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sph_ind = PF.MagAnalytics.spheremodel(mesh, sclx/2., 0., -sclx/2.5, R/2.5)
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model[sph_ind] = 2.5*chiblk
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Utils.writeUBCTensorMesh('Mesh.msh',mesh)
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Utils.writeUBCTensorModel('Model.sus',mesh,model)
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actv = np.ones(mesh.nC)
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#%% Forward mode ldata
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d = PF.Magnetics.Intgrl_Fwr_Data(mesh,B,M,rxLoc,model,actv,'tmi')
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#fwr_tmi = d[0:ndata]
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#fwr_y = d[ndata:2*ndata]
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#fwr_z = d[2*ndata:]
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#%% Get the analystical answer and compute the residual
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#bxa,bya,bza = PF.MagAnalytics.MagSphereAnaFunA(rxLoc[:,0],rxLoc[:,1],rxLoc[:,2],R,0.,0.,0.,chiblk, np.array(([0.,0.,B[2]])),'secondary')
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Bd = (450.-float(B[1]))%360.
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Bi = B[0]; # Convert dip to horizontal to cartesian
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Bx = np.cos(np.deg2rad(Bi)) * np.cos(np.deg2rad(Bd)) * B[2]
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By = np.cos(np.deg2rad(Bi)) * np.sin(np.deg2rad(Bd)) * B[2]
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Bz = np.sin(np.deg2rad(Bi)) * B[2]
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Bo = np.c_[Bx, By, Bz]
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Ptmi = mkvc(np.r_[np.cos(np.deg2rad(Bi))*np.cos(np.deg2rad(Bd)),np.cos(np.deg2rad(Bi))*np.sin(np.deg2rad(Bd)),np.sin(np.deg2rad(Bi))],2).T;
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bxa,bya,bza = PF.MagAnalytics.MagSphereFreeSpace(rxLoc[:,0],rxLoc[:,1],rxLoc[:,2],R,0., 0., -sclx/3, 0.5*chiblk, Bo)
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bxb,byb,bzb = PF.MagAnalytics.MagSphereFreeSpace(rxLoc[:,0],rxLoc[:,1],rxLoc[:,2],R/3., -sclx/2., 0., -sclx/3.,4.*chiblk, Bo)
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bxc,byc,bzc = PF.MagAnalytics.MagSphereFreeSpace(rxLoc[:,0],rxLoc[:,1],rxLoc[:,2],R/2.5, sclx/2., 0., -sclx/2.5,2.5*chiblk, Bo)
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bx = bxa + bxb + bxc
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by = bya + byb + byc
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bz = bza + bzb + bzc
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b_tmi = mkvc(Ptmi.dot(np.c_[bx,by,bz].T))
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r_tmi = d - b_tmi
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#r_By = fwr_y - bya
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#r_Bz = fwr_z - bza
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lrl[ii] = sum( r_tmi**2 ) **0.5
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#%% Write predicted to file
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PF.Magnetics.writeUBCobs('Obsloc.loc',B,M,rxLoc,d,np.ones(len(d)))
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#%% Plot results
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print 'Residual between analytical sphere and integral forward'
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for ii in range(d_iter):
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nc = 3**(ii+1)
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print "||r||= " + str(lrl[ii]) + "\t dx= " + str(1./nc)
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#%% Plot fields
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plt.figure(1)
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#ax = plt.subplot(221)
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plt.imshow(np.reshape(b_tmi,X.shape), interpolation="bicubic", extent=[xr.min(), xr.max(), yr.min(), yr.max()], origin = 'lower')
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plt.colorbar(fraction=0.04)
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plt.contour(X,Y, np.reshape(b_tmi,X.shape),10)
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plt.scatter(X,Y, c=np.reshape(b_tmi,X.shape), s=20)
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ax.set_title('Analytical')
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#%% Plot the forward solution from integral
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plt.figure(2)
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#ax = plt.subplot(222)
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plt.imshow(np.reshape(d,X.shape), interpolation="bicubic", extent=[xr.min(), xr.max(), yr.min(), yr.max() ], origin = 'lower')
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plt.colorbar(fraction=0.04)
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plt.contour(X,Y, np.reshape(d,X.shape),10)
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plt.scatter(X,Y, c=np.reshape(d,X.shape), s=20)
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ax.set_title('Numerical')
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#%% Plot residual data
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plt.figure(3)
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#ax = plt.subplot(212)
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plt.imshow(np.reshape(r_tmi,X.shape), interpolation="bicubic", extent=[xr.min(), xr.max(), yr.min(), yr.max()], origin = 'lower')
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plt.colorbar(fraction=0.04)
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plt.contour(X,Y, np.reshape(r_tmi,X.shape),10)
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plt.scatter(X,Y, c=np.reshape(r_tmi,X.shape), s=20)
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ax.set_title('Sphere Ana Bx')
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import os
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home_dir = 'C:\\LC\\Private\\dominiquef\\Projects\\4414_Minsim\\Modeling\\MAG'
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os.chdir(home_dir)
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#%%
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from SimPEG import *
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import matplotlib.pyplot as plt
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import simpegPF as PF
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import scipy.interpolate as interpolation
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import scipy.signal as sn
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import time
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#from fwr_MAG_data import fwr_MAG_data
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plt.close('all')
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topofile = 'Gaussian.topo'
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zoffset = 5
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#%% Create survey
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# Load in topofile or create flat surface
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if not topofile:
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actv = np.ones(mesh.nC)
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else:
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topo = np.genfromtxt(topofile,skip_header=1)
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B = np.array(([90.,0.,50000.]))
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M = np.array(([90.,0.,315.]))
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# Sphere radius
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R = 25.
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sclx = 100.
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dx = 5.
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#%% Loop through decreasing meshes and measure the residual
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# Create mesh using simpeg and write out in GIF format
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# # Or create juste a plane grid
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xr = np.linspace(-102.5, 97.5, 41)
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yr = np.linspace(-52.5, 47.5, 21)
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X, Y = np.meshgrid(xr, yr)
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nc = int(sclx/dx)
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hxind = [(dx, 2*nc)]
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hyind = [(dx, nc)]
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hzind = [(dx, nc)]
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mesh = Mesh.TensorMesh([hxind, hyind, hzind], 'CCN')
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actv = PF.Magnetics.getActiveTopo(mesh,topo,'N')
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# Drape observations on topo + offset
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if not topofile:
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Z = np.ones((xr.size, yr.size)) * 2.5
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else:
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F = interpolation.interp2d(topo[:,0],topo[:,1],topo[:,2])
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#F = interpolation.NearestNDInterpolator(topo[:,0:2],topo[:,2])
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Z = F(xr,yr) + zoffset
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rxLoc = np.c_[Utils.mkvc(X.T), Utils.mkvc(Y.T), Utils.mkvc(Z.T)]
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ndata = rxLoc.shape[0]
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xn = mesh.vectorNx
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yn = mesh.vectorNy
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zn = mesh.vectorNz
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mcell = mesh.nC
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print 'Mesh size: ' + str(mcell)
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#%% Create model
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chibkg = 0.000
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chiblk = 0.01
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model = np.ones(mcell)*chibkg
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# Do a three sphere problem for more frequencies
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sph_ind = PF.MagAnalytics.spheremodel(mesh, 0., 0., -sclx/3, R)
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model[sph_ind] = 0.5*chiblk
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sph_ind = PF.MagAnalytics.spheremodel(mesh, -sclx/2., 0., -sclx/3., R/3.)
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model[sph_ind] = 4.*chiblk
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sph_ind = PF.MagAnalytics.spheremodel(mesh, sclx/2., 0., -sclx/2.5, R/2.5)
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model[sph_ind] = 2.5*chiblk
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Utils.writeUBCTensorMesh('Mesh.msh',mesh)
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Utils.writeUBCTensorModel('Model.sus',mesh,model)
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actv = np.ones(mesh.nC)
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#%% Forward mode ldata
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d = PF.Magnetics.Intgrl_Fwr_Data(mesh,B,M,rxLoc,model,actv,'tmi')
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#fwr_tmi = d[0:ndata]
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#fwr_y = d[ndata:2*ndata]
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#fwr_z = d[2*ndata:]
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#%% Compute data on a line
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xx = np.linspace(-101., 99., 200)
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yy = np.zeros(len(xx))
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zz = F(xx,0.) + zoffset
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rxLoc = np.c_[xx,yy,zz]
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d_line = PF.Magnetics.Intgrl_Fwr_Data(mesh,B,M,rxLoc,model,actv,'tmi')
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d_iter = 4
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l1_r = np.zeros((d_iter,5))
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l2_r = np.zeros((d_iter,5))
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linf_r = np.zeros((d_iter,5))
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timer = np.zeros((d_iter,5))
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#%% Try different interpolation schemes
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for ii in range(d_iter):
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indx = ii+1
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d2d = np.reshape(d, (len(yr),len(xr)))
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d2d = mkvc(d2d[::indx,::indx].T)
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xsub = xr[::indx]
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ysub = yr[::indx]
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# Nearest Neighbourg
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start_time = time.time()
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F = interpolation.NearestNDInterpolator(np.c_[mkvc(Y[::indx,::indx].T),mkvc(X[::indx,::indx].T)],d2d)
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d_i2d_nnb = mkvc( F(0.,xx) )
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l1_r[ii,0] = np.sum( np.abs(d_line - d_i2d_nnb) )**0.5
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l2_r[ii,0] = np.sum( (d_line - d_i2d_nnb)**2. )
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linf_r[ii,0] = np.max( np.abs(d_line - d_i2d_nnb) )
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timer[ii,0] = (time.time() - start_time)
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# Linear interpolation
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start_time = time.time()
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F = interpolation.interp2d(ysub,xsub,d2d)
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d_i2d_lin = mkvc( F(0.,xx) )
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l1_r[ii,1] = np.sum( np.abs(d_line - d_i2d_lin) )**0.5
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l2_r[ii,1] = np.sum( (d_line - d_i2d_lin)**2. )
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linf_r[ii,1] = np.max( np.abs(d_line - d_i2d_lin) )
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timer[ii,1] = (time.time() - start_time)
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# Cubic interpolation
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start_time = time.time()
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F = interpolation.interp2d(ysub,xsub,d2d,kind='cubic')
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d_i2d_cub = mkvc( F(0.,xx) )
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l1_r[ii,2] = np.sum( np.abs(d_line - d_i2d_cub) )**0.5
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l2_r[ii,2] = np.sum( (d_line - d_i2d_cub)**2. )
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linf_r[ii,2] = np.max( np.abs(d_line - d_i2d_cub) )
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timer[ii,2] = (time.time() - start_time)
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# Quintic interpolation
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start_time = time.time()
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F = interpolation.interp2d(ysub,xsub,d2d,kind='quintic')
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d_i2d_qui = mkvc( F(0.,xx) )
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l1_r[ii,3] = np.sum( np.abs(d_line - d_i2d_qui) )**0.5
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l2_r[ii,3] = np.sum( (d_line - d_i2d_qui)**2. )
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linf_r[ii,3] = np.max( np.abs(d_line - d_i2d_qui) )
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timer[ii,3] = (time.time() - start_time)
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#%% FFT interpolation
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d2d = np.reshape(d, (len(yr),len(xr)))
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# Add padding values by reflection (2**n)
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lenx = np.floor( np.log2( 2*len(xr) ) )
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npadx = int(np.floor( ( 2**lenx - len(xr) ) /2. ))
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#Create hemming taper
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if np.mod(npadx*2+len(xr),2) != 0:
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oddx = 1
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else:
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oddx = 0
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tap0 = sn.hamming(npadx*2)
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tapl = sp.spdiags(tap0[0:npadx],0,npadx,npadx)
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tapr = sp.spdiags(tap0[npadx:],0,npadx,npadx+oddx)
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# Mirror the 2d data over the half lenght and apply 0-taper
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d2dpad = np.hstack([np.fliplr(d2d[:,0:npadx]) * tapl, d2d, np.fliplr(d2d[:,-npadx:]) * tapr])
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# Repeat along the second dimension
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leny = np.floor( np.log2( 2*len(yr) ) )
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npady = int(np.floor( ( 2**leny - len(yr) ) /2. ))
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#Create hemming taper
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if np.mod(npady*2+len(yr),2) != 0:
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oddy = 1
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else:
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oddy = 0
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tap0 = sn.hamming(npady*2)
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tapu = sp.spdiags(tap0[0:npady],0,npady,npady)
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tapd = sp.spdiags(tap0[npady:],0,npady+oddy,npady)
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d2dpad = np.vstack([tapu*np.flipud(d2dpad[0:npady,:]), d2dpad, tapd*np.flipud(d2dpad[-npady:,:])])
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# Compute FFT
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FFTd2d = np.fft.fft2(d2dpad)
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# Compute IFFT at a given location
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# Do an FFT shift
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#FFTshift = np.fft.fftshift(FFTd2d)
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FFTd2d = np.hstack([FFTd2d[:,0:31],np.zeros((32,64)),FFTd2d[:,31:]])
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FFTd2d = np.vstack([FFTd2d[0:15,:],np.zeros((32,128)),FFTd2d[15:,:]])
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# Pad with zeros
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#temp = np.zeros((FFTd2d.shape[0]*2,FFTd2d.shape[1]*2))
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# Compute inverse FFT
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IFFTd2d = np.fft.ifft2(FFTd2d)*FFTd2d.size/d2dpad.size
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# Extract core
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#d2d_out = np.real(IFFTd2d[npady*2:-(npady*2+oddy+1),npadx*2:-(npadx*2+oddx+1)])
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d2d_out = np.real(IFFTd2d[:-1,:-1])
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d2d_out = d2d_out[npady*2:-(npady*2+oddy),npadx*2:-(npadx*2+oddx)]
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# Create new distance vector
|
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XX = np.linspace(np.min(xr),np.max(xr),d2d_out.shape[1])
|
||||
YY = np.linspace(np.min(yr),np.max(yr),d2d_out.shape[0])
|
||||
|
||||
start_time = time.time()
|
||||
F = interpolation.interp2d(XX,YY,d2d_out)
|
||||
d_i2d_fft = mkvc( F(xx,0.) )
|
||||
l1_r[ii,4] = np.sum( np.abs(d_line - d_i2d_nnb) )**0.5
|
||||
l2_r[ii,4] = np.sum( (d_line - d_i2d_nnb)**2. )
|
||||
linf_r[ii,4] = np.max( np.abs(d_line - d_i2d_nnb) )
|
||||
timer[ii,4] = (time.time() - start_time)
|
||||
|
||||
print("--- FFT completed in %s seconds ---" % (time.time() - start_time))
|
||||
|
||||
plt.figure()
|
||||
ax = plt.subplot()
|
||||
plt.imshow(d2d_out, interpolation="bicubic", extent=[xr.min(), xr.max(), yr.min(), yr.max() ], origin = 'lower')
|
||||
plt.colorbar(fraction=0.04)
|
||||
|
||||
|
||||
#%% Write predicted to file
|
||||
|
||||
#PF.Magnetics.writeUBCobs('Obsloc.loc',B,M,rxLoc,d,np.ones(len(d)))
|
||||
|
||||
#%% Plot results
|
||||
#==============================================================================
|
||||
# print 'Residual between analytical sphere and integral forward'
|
||||
# for ii in range(d_iter):
|
||||
# nc = 3**(ii+1)
|
||||
#
|
||||
# print "||r||= " + str(lrl[ii]) + "\t dx= " + str(1./nc)
|
||||
#==============================================================================
|
||||
|
||||
|
||||
#%% Plot the forward solution from integral
|
||||
plt.figure()
|
||||
ax = plt.subplot()
|
||||
plt.imshow(d2d, interpolation="bicubic", extent=[xr.min(), xr.max(), yr.min(), yr.max() ], origin = 'lower')
|
||||
plt.colorbar(fraction=0.04)
|
||||
|
||||
plt.figure()
|
||||
plt.contour(X,Y, np.reshape(d,X.shape),10)
|
||||
plt.scatter(X,Y, c=np.reshape(d,X.shape), s=10)
|
||||
plt.scatter(xx,yy, c='k', s=20, marker='o')
|
||||
ax.set_title('Numerical')
|
||||
|
||||
|
||||
#%%
|
||||
|
||||
plt.figure()
|
||||
ax = plt.subplot()
|
||||
plt.plot(xx,d_line,c='r', linewidth=3)
|
||||
plt.plot(xx,d_i2d_lin,c='b')
|
||||
plt.plot(xx,d_i2d_cub,c='g')
|
||||
plt.plot(xx,d_i2d_qui,c='m')
|
||||
plt.plot(xx,d_i2d_nnb,c='k')
|
||||
plt.plot(xx,d_i2d_fft,c='c',marker='o')
|
||||
plt.plot(xr[::indx],np.zeros(len(xr[::indx])),c='r',linewidth=0.,marker='o')
|
||||
ax.set_title('Analytical')
|
||||
|
||||
#%% Write result to file
|
||||
with file('l2_residual.dat','w') as fid:
|
||||
fid.write('NearestN \t Linear \t Cubic \t Quintic \t FFT\n')
|
||||
np.savetxt(fid, l2_r, fmt='%e',delimiter=' ',newline='\n')
|
||||
|
||||
with file('l1_residual.dat','w') as fid:
|
||||
fid.write('NearestN \t Linear \t Cubic \t Quintic \t FFT\n')
|
||||
np.savetxt(fid, l1_r, fmt='%e',delimiter=' ',newline='\n')
|
||||
+19
-18
@@ -637,6 +637,7 @@ def get_T_mat(Xn,Yn,Zn,rxLoc):
|
||||
@author: dominiquef
|
||||
"""
|
||||
|
||||
|
||||
mcell = Xn.shape[0]
|
||||
|
||||
# Pre-allocate space for 1D array
|
||||
@@ -644,29 +645,29 @@ def get_T_mat(Xn,Yn,Zn,rxLoc):
|
||||
Ty = np.zeros((1,3*mcell))
|
||||
Tz = np.zeros((1,3*mcell))
|
||||
|
||||
dz2 = rxLoc[2] - Zn[:,0];
|
||||
dz1 = rxLoc[2] - Zn[:,1];
|
||||
dz2 = rxLoc[2] - Zn[:,0]
|
||||
dz1 = rxLoc[2] - Zn[:,1]
|
||||
|
||||
dy2 = Yn[:,1] - rxLoc[1];
|
||||
dy1 = Yn[:,0] - rxLoc[1];
|
||||
dy2 = Yn[:,1] - rxLoc[1]
|
||||
dy1 = Yn[:,0] - rxLoc[1]
|
||||
|
||||
dx2 = Xn[:,1] - rxLoc[0];
|
||||
dx1 = Xn[:,0] - rxLoc[0];
|
||||
dx2 = Xn[:,1] - rxLoc[0]
|
||||
dx1 = Xn[:,0] - rxLoc[0]
|
||||
|
||||
R1 = ( dy2**2 + dx2**2 );
|
||||
R2 = ( dy2**2 + dx1**2 );
|
||||
R3 = ( dy1**2 + dx2**2 );
|
||||
R4 = ( dy1**2 + dx1**2 );
|
||||
R1 = ( dy2**2 + dx2**2 )
|
||||
R2 = ( dy2**2 + dx1**2 )
|
||||
R3 = ( dy1**2 + dx2**2 )
|
||||
R4 = ( dy1**2 + dx1**2 )
|
||||
|
||||
|
||||
arg1 = np.sqrt( dz2**2 + R2 );
|
||||
arg2 = np.sqrt( dz2**2 + R1 );
|
||||
arg3 = np.sqrt( dz1**2 + R1 );
|
||||
arg4 = np.sqrt( dz1**2 + R2 );
|
||||
arg5 = np.sqrt( dz2**2 + R3 );
|
||||
arg6 = np.sqrt( dz2**2 + R4 );
|
||||
arg7 = np.sqrt( dz1**2 + R4 );
|
||||
arg8 = np.sqrt( dz1**2 + R3 );
|
||||
arg1 = np.sqrt( dz2**2 + R2 )
|
||||
arg2 = np.sqrt( dz2**2 + R1 )
|
||||
arg3 = np.sqrt( dz1**2 + R1 )
|
||||
arg4 = np.sqrt( dz1**2 + R2 )
|
||||
arg5 = np.sqrt( dz2**2 + R3 )
|
||||
arg6 = np.sqrt( dz2**2 + R4 )
|
||||
arg7 = np.sqrt( dz1**2 + R4 )
|
||||
arg8 = np.sqrt( dz1**2 + R3 )
|
||||
|
||||
|
||||
|
||||
|
||||
Reference in New Issue
Block a user