renaming to ensure capitals

SimPEG/Utils/interputils.py

@@ -0,0 +1,181 @@
+import numpy as np
+import scipy.sparse as sp
+from sputils import spzeros
+from matutils import mkvc, sub2ind
+
+def _interp_point_1D(x, xr_i):
+    """
+        given a point, xr_i, this will find which two integers it lies between.
+
+        :param numpy.ndarray x: Tensor vector of 1st dimension of grid.
+        :param float xr_i: Location of a point
+        :rtype: int,int,float,float
+        :return: index1, index2, portion1, portion2
+    """
+    # TODO: This fails if the point is on the outside of the mesh. We may want to replace this by extrapolation?
+    im = np.argmin(abs(x-xr_i))
+    if  xr_i - x[im] >= 0:  # Point on the left
+        ind_x1 = im
+        ind_x2 = im+1
+    elif  xr_i - x[im] < 0:  # Point on the right
+        ind_x1 = im-1
+        ind_x2 = im
+    dx1 = xr_i - x[ind_x1]
+    dx2 = x[ind_x2] - xr_i
+    return ind_x1, ind_x2, dx1, dx2
+
+
+def interpmat(locs, x, y=None, z=None):
+    """
+        Local interpolation computed for each receiver point in turn
+
+        :param numpy.ndarray loc: Location of points to interpolate to
+        :param numpy.ndarray x: Tensor vector of 1st dimension of grid.
+        :param numpy.ndarray y: Tensor vector of 2nd dimension of grid. None by default.
+        :param numpy.ndarray z: Tensor vector of 3rd dimension of grid. None by default.
+        :rtype: scipy.sparse.csr.csr_matrix
+        :return: Interpolation matrix
+
+        .. plot::
+
+            import SimPEG
+            import numpy as np
+            import matplotlib.pyplot as plt
+            locs = np.random.rand(50)*0.8+0.1
+            x = np.linspace(0,1,7)
+            dense = np.linspace(0,1,200)
+            fun = lambda x: np.cos(2*np.pi*x)
+            Q = SimPEG.Utils.interpmat(locs, x)
+            plt.plot(x, fun(x), 'bs-')
+            plt.plot(dense, fun(dense), 'y:')
+            plt.plot(locs, Q*fun(x), 'mo')
+            plt.plot(locs, fun(locs), 'rx')
+            plt.show()
+
+    """
+    if y is None and z is None:
+        return _interpmat1D(locs, x)
+    elif z is None:
+        return _interpmat2D(locs, x, y)
+    else:
+        return _interpmat3D(locs, x, y, z)
+
+
+def _interpmat1D(locs, x):
+    """Use interpmat with only x component provided."""
+    nx = x.size
+    locs = mkvc(locs)
+    npts = locs.shape[0]
+
+    Q = sp.lil_matrix((npts, nx))
+
+    for i in range(npts):
+        ind_x1, ind_x2, dx1, dx2 = _interp_point_1D(x, locs[i])
+        dv = (x[ind_x2] - x[ind_x1])
+        Dx =  x[ind_x2] - x[ind_x1]
+        # Get the row in the matrix
+        inds = [ind_x1, ind_x2]
+        vals = [(1-dx1/Dx),(1-dx2/Dx)]
+        Q[i, inds] = vals
+    return Q.tocsr()
+
+
+
+def _interpmat2D(locs, x, y):
+    """Use interpmat with only x and y components provided."""
+    nx = x.size
+    ny = y.size
+    npts = locs.shape[0]
+
+    Q = sp.lil_matrix((npts, nx*ny))
+
+
+    for i in range(npts):
+        ind_x1, ind_x2, dx1, dx2 = _interp_point_1D(x, locs[i, 0])
+        ind_y1, ind_y2, dy1, dy2 = _interp_point_1D(y, locs[i, 1])
+
+        dv = (x[ind_x2] - x[ind_x1]) * (y[ind_y2] - y[ind_y1])
+
+        Dx =  x[ind_x2] - x[ind_x1]
+        Dy =  y[ind_y2] - y[ind_y1]
+
+        # Get the row in the matrix
+
+        inds = sub2ind((nx,ny),[
+            ( ind_x1,  ind_y2),
+            ( ind_x1,  ind_y1),
+            ( ind_x2,  ind_y1),
+            ( ind_x2,  ind_y2)])
+
+        vals = [(1-dx1/Dx)*(1-dy2/Dy),
+                (1-dx1/Dx)*(1-dy1/Dy),
+                (1-dx2/Dx)*(1-dy1/Dy),
+                (1-dx2/Dx)*(1-dy2/Dy)]
+
+        Q[i, mkvc(inds)] = vals
+
+    return Q.tocsr()
+
+
+
+def _interpmat3D(locs, x, y, z):
+    """Use interpmat."""
+    nx = x.size
+    ny = y.size
+    nz = z.size
+    npts = locs.shape[0]
+
+    Q = sp.lil_matrix((npts, nx*ny*nz))
+
+
+    for i in range(npts):
+        ind_x1, ind_x2, dx1, dx2 = _interp_point_1D(x, locs[i, 0])
+        ind_y1, ind_y2, dy1, dy2 = _interp_point_1D(y, locs[i, 1])
+        ind_z1, ind_z2, dz1, dz2 = _interp_point_1D(z, locs[i, 2])
+
+        dv = (x[ind_x2] - x[ind_x1]) * (y[ind_y2] - y[ind_y1]) *(z[ind_z2] - z[ind_z1])
+
+        Dx =  x[ind_x2] - x[ind_x1]
+        Dy =  y[ind_y2] - y[ind_y1]
+        Dz =  z[ind_z2] - z[ind_z1]
+
+        # Get the row in the matrix
+
+        inds = sub2ind((nx,ny,nz),[
+            ( ind_x1,  ind_y2,  ind_z1),
+            ( ind_x1,  ind_y1,  ind_z1),
+            ( ind_x2,  ind_y1,  ind_z1),
+            ( ind_x2,  ind_y2,  ind_z1),
+            ( ind_x1,  ind_y1,  ind_z2),
+            ( ind_x1,  ind_y2,  ind_z2),
+            ( ind_x2,  ind_y1,  ind_z2),
+            ( ind_x2,  ind_y2,  ind_z2)])
+
+        vals = [(1-dx1/Dx)*(1-dy2/Dy)*(1-dz1/Dz),
+                (1-dx1/Dx)*(1-dy1/Dy)*(1-dz1/Dz),
+                (1-dx2/Dx)*(1-dy1/Dy)*(1-dz1/Dz),
+                (1-dx2/Dx)*(1-dy2/Dy)*(1-dz1/Dz),
+                (1-dx1/Dx)*(1-dy1/Dy)*(1-dz2/Dz),
+                (1-dx1/Dx)*(1-dy2/Dy)*(1-dz2/Dz),
+                (1-dx2/Dx)*(1-dy1/Dy)*(1-dz2/Dz),
+                (1-dx2/Dx)*(1-dy2/Dy)*(1-dz2/Dz)]
+
+        Q[i, mkvc(inds)] = vals
+
+    return Q.tocsr()
+
+
+if __name__ == '__main__':
+    import SimPEG
+    import numpy as np
+    import matplotlib.pyplot as plt
+    locs = np.random.rand(50)*0.8+0.1
+    x = np.linspace(0,1,7)
+    dense = np.linspace(0,1,200)
+    fun = lambda x: np.cos(2*np.pi*x)
+    Q = SimPEG.Utils.interpmat(locs, x)
+    plt.plot(x, fun(x), 'bs-')
+    plt.plot(dense, fun(dense), 'y:')
+    plt.plot(locs, Q*fun(x), 'mo')
+    plt.plot(locs, fun(locs), 'rx')
+    plt.show()