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()
"""
npts = locs.shape[0]
locs = locs.astype(float)
x = x.astype(float)
if y is None and z is None:
shape = [
x.size,
]
inds, vals = _interpmat1D(mkvc(locs), x)
elif z is None:
y = y.astype(float)
shape = [x.size, y.size]
inds, vals = _interpmat2D(locs, x, y)
else:
y = y.astype(float)
z = z.astype(float)
shape = [x.size, y.size, z.size]
inds, vals = _interpmat3D(locs, x, y, z)
I = np.repeat(range(npts), 2**len(shape))
J = sub2ind(shape, inds)
Q = sp.csr_matrix((vals, (I, J)), shape=(npts, np.prod(shape)))
return Q
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_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()
"""
npts = locs.shape[0]
locs = locs.astype(float)
x = x.astype(float)
if y is None and z is None:
shape = [x.size,]
inds, vals = _interpmat1D(mkvc(locs), x)
elif z is None:
y = y.astype(float)
shape = [x.size, y.size]
inds, vals = _interpmat2D(locs, x, y)
else:
y = y.astype(float)
z = z.astype(float)
shape = [x.size, y.size, z.size]
inds, vals = _interpmat3D(locs, x, y, z)
I = np.repeat(range(npts),2**len(shape))
J = sub2ind(shape,inds)
Q = sp.csr_matrix((vals,(I, J)),
shape=(npts, np.prod(shape)))
return Q
def indexCube(nodes, gridSize, n=None):
"""
Returns the index of nodes on the mesh.
Input:
nodes - string of which nodes to return. e.g. 'ABCD'
gridSize - size of the nodal grid
n - number of nodes each i,j,k direction: [ni,nj,nk]
Output:
index - index in the order asked e.g. 'ABCD' --> (A,B,C,D)
TWO DIMENSIONS::
node(i,j) node(i,j+1)
A -------------- B
| |
| cell(i,j) |
| I |
| |
D -------------- C
node(i+1,j) node(i+1,j+1)
THREE DIMENSIONS::
node(i,j,k+1) node(i,j+1,k+1)
E --------------- F
/| / |
/ | / |
/ | / |
node(i,j,k) node(i,j+1,k)
A -------------- B |
| H ----------|---- G
| /cell(i,j) | /
| / I | /
| / | /
D -------------- C
node(i+1,j,k) node(i+1,j+1,k)
"""
assert type(nodes) == str, "Nodes must be a str variable: e.g. 'ABCD'"
assert isinstance(gridSize,
np.ndarray), "Number of nodes must be an ndarray"
nodes = nodes.upper()
# Make sure that we choose from the possible nodes.
possibleNodes = 'ABCD' if gridSize.size == 2 else 'ABCDEFGH'
for node in nodes:
assert node in possibleNodes, "Nodes must be chosen from: '{0!s}'".format(
possibleNodes)
dim = gridSize.size
if n is None:
n = gridSize - 1
if dim == 2:
ij = ndgrid(np.arange(n[0]), np.arange(n[1]))
i, j = ij[:, 0], ij[:, 1]
elif dim == 3:
ijk = ndgrid(np.arange(n[0]), np.arange(n[1]), np.arange(n[2]))
i, j, k = ijk[:, 0], ijk[:, 1], ijk[:, 2]
else:
raise Exception('Only 2 and 3 dimensions supported.')
nodeMap = {
'A': [0, 0, 0],
'B': [0, 1, 0],
'C': [1, 1, 0],
'D': [1, 0, 0],
'E': [0, 0, 1],
'F': [0, 1, 1],
'G': [1, 1, 1],
'H': [1, 0, 1]
}
out = ()
for node in nodes:
shift = nodeMap[node]
if dim == 2:
out += (sub2ind(gridSize, np.c_[i + shift[0],
j + shift[1]]).flatten(), )
elif dim == 3:
out += (sub2ind(gridSize, np.c_[i + shift[0], j + shift[1],
k + shift[2]]).flatten(), )
return out
def indexCube(nodes, gridSize, n=None):
"""
Returns the index of nodes on the mesh.
Input:
nodes - string of which nodes to return. e.g. 'ABCD'
gridSize - size of the nodal grid
n - number of nodes each i,j,k direction: [ni,nj,nk]
Output:
index - index in the order asked e.g. 'ABCD' --> (A,B,C,D)
TWO DIMENSIONS::
node(i,j) node(i,j+1)
A -------------- B
| |
| cell(i,j) |
| I |
| |
D -------------- C
node(i+1,j) node(i+1,j+1)
THREE DIMENSIONS::
node(i,j,k+1) node(i,j+1,k+1)
E --------------- F
/| / |
/ | / |
/ | / |
node(i,j,k) node(i,j+1,k)
A -------------- B |
| H ----------|---- G
| /cell(i,j) | /
| / I | /
| / | /
D -------------- C
node(i+1,j,k) node(i+1,j+1,k)
"""
assert type(nodes) == str, "Nodes must be a str variable: e.g. 'ABCD'"
assert isinstance(gridSize, np.ndarray), "Number of nodes must be an ndarray"
nodes = nodes.upper()
# Make sure that we choose from the possible nodes.
possibleNodes = 'ABCD' if gridSize.size == 2 else 'ABCDEFGH'
for node in nodes:
assert node in possibleNodes, "Nodes must be chosen from: '%s'" % possibleNodes
dim = gridSize.size
if n is None:
n = gridSize - 1
if dim == 2:
ij = ndgrid(np.arange(n[0]), np.arange(n[1]))
i, j = ij[:, 0], ij[:, 1]
elif dim == 3:
ijk = ndgrid(np.arange(n[0]), np.arange(n[1]), np.arange(n[2]))
i, j, k = ijk[:, 0], ijk[:, 1], ijk[:, 2]
else:
raise Exception('Only 2 and 3 dimensions supported.')
nodeMap = {'A': [0, 0, 0], 'B': [0, 1, 0], 'C': [1, 1, 0], 'D': [1, 0, 0],
'E': [0, 0, 1], 'F': [0, 1, 1], 'G': [1, 1, 1], 'H': [1, 0, 1]}
out = ()
for node in nodes:
shift = nodeMap[node]
if dim == 2:
out += (sub2ind(gridSize, np.c_[i+shift[0], j+shift[1]]).flatten(), )
elif dim == 3:
out += (sub2ind(gridSize, np.c_[i+shift[0], j+shift[1], k+shift[2]]).flatten(), )
return out