mirror of
https://github.com/wassname/simpeg.git
synced 2026-07-03 11:10:47 +08:00
Rowan Cockett
128 lines
3.4 KiB
Python
128 lines
3.4 KiB
Python
import numpy as np
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import scipy.sparse as sp
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from sputils import spzeros
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from matutils import mkvc, sub2ind
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def _interp_point_1D(x, xr_i):
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im = np.argmin(abs(x-xr_i))
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if xr_i - x[im] >= 0: # Point on the left
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ind_x1 = im
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ind_x2 = im+1
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elif xr_i - x[im] < 0: # Point on the right
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ind_x1 = im-1
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ind_x2 = im
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dx1 = xr_i - x[ind_x1]
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dx2 = x[ind_x2] - xr_i
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return ind_x1, ind_x2, dx1, dx2
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def interpmat(locs, x, y=None, z=None):
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""" Local interpolation computed for each receiver point in turn """
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if y is None and z is None:
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return interpmat1D(locs, x)
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elif z is None:
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return interpmat2D(locs, x, y)
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else:
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return interpmat3D(locs, x, y, z)
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def interpmat1D(locs, x):
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nx = x.size
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locs = mkvc(locs)
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npts = locs.shape[0]
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Q = sp.lil_matrix((npts, nx))
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for i in range(npts):
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ind_x1, ind_x2, dx1, dx2 = _interp_point_1D(x, locs[i])
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dv = (x[ind_x2] - x[ind_x1])
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Dx = x[ind_x2] - x[ind_x1]
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# Get the row in the matrix
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inds = [ind_x1, ind_x2]
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vals = [(1-dx1/Dx),(1-dx2/Dx)]
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Q[i, inds] = vals
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return Q.tocsr()
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def interpmat2D(locs, x, y):
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nx = x.size
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ny = y.size
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npts = locs.shape[0]
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Q = sp.lil_matrix((npts, nx*ny))
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for i in range(npts):
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ind_x1, ind_x2, dx1, dx2 = _interp_point_1D(x, locs[i, 0])
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ind_y1, ind_y2, dy1, dy2 = _interp_point_1D(y, locs[i, 1])
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dv = (x[ind_x2] - x[ind_x1]) * (y[ind_y2] - y[ind_y1])
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Dx = x[ind_x2] - x[ind_x1]
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Dy = y[ind_y2] - y[ind_y1]
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# Get the row in the matrix
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inds = sub2ind((nx,ny),[
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( ind_x1, ind_y2),
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( ind_x1, ind_y1),
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( ind_x2, ind_y1),
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( ind_x2, ind_y2)])
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vals = [(1-dx1/Dx)*(1-dy2/Dy),
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(1-dx1/Dx)*(1-dy1/Dy),
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(1-dx2/Dx)*(1-dy1/Dy),
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(1-dx2/Dx)*(1-dy2/Dy)]
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Q[i, mkvc(inds)] = vals
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return Q.tocsr()
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def interpmat3D(locs, x, y, z):
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nx = x.size
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ny = y.size
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nz = z.size
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npts = locs.shape[0]
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Q = sp.lil_matrix((npts, nx*ny*nz))
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for i in range(npts):
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ind_x1, ind_x2, dx1, dx2 = _interp_point_1D(x, locs[i, 0])
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ind_y1, ind_y2, dy1, dy2 = _interp_point_1D(y, locs[i, 1])
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ind_z1, ind_z2, dz1, dz2 = _interp_point_1D(z, locs[i, 2])
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dv = (x[ind_x2] - x[ind_x1]) * (y[ind_y2] - y[ind_y1]) *(z[ind_z2] - z[ind_z1])
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Dx = x[ind_x2] - x[ind_x1]
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Dy = y[ind_y2] - y[ind_y1]
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Dz = z[ind_z2] - z[ind_z1]
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# Get the row in the matrix
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inds = sub2ind((nx,ny,nz),[
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( ind_x1, ind_y2, ind_z1),
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( ind_x1, ind_y1, ind_z1),
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( ind_x2, ind_y1, ind_z1),
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( ind_x2, ind_y2, ind_z1),
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( ind_x1, ind_y1, ind_z2),
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( ind_x1, ind_y2, ind_z2),
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( ind_x2, ind_y1, ind_z2),
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( ind_x2, ind_y2, ind_z2)])
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vals = [(1-dx1/Dx)*(1-dy2/Dy)*(1-dz1/Dz),
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(1-dx1/Dx)*(1-dy1/Dy)*(1-dz1/Dz),
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(1-dx2/Dx)*(1-dy1/Dy)*(1-dz1/Dz),
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(1-dx2/Dx)*(1-dy2/Dy)*(1-dz1/Dz),
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(1-dx1/Dx)*(1-dy1/Dy)*(1-dz2/Dz),
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(1-dx1/Dx)*(1-dy2/Dy)*(1-dz2/Dz),
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(1-dx2/Dx)*(1-dy1/Dy)*(1-dz2/Dz),
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(1-dx2/Dx)*(1-dy2/Dy)*(1-dz2/Dz)]
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Q[i, mkvc(inds)] = vals
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return Q.tocsr()
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