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Update grad.py #65

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87 changes: 49 additions & 38 deletions python/nt_toolbox/grad.py
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Original file line number Diff line number Diff line change
@@ -1,83 +1,94 @@
import numpy as np


def grad(M, bound="sym", order=1):
"""
grad - gradient, forward differences

[gx,gy] = grad(M, options);
or
g = grad(M, options);

options.bound = 'per' or 'sym'
options.order = 1 (backward differences)
= 2 (centered differences)

Works also for 3D array.
Assme that the function is evenly sampled with sampling step 1.

See also: div.

Copyright (c) Gabriel Peyre
"""
"""

ny = None
fy = None
fz = None

# retrieve number of dimensions
nbdims = np.ndim(M)


if bound == "sym":
if bound == "sym":
nx = np.shape(M)[0]

if order == 1:
fx = M[np.hstack((np.arange(1,nx),[nx-1])),:] - M
fx = M[np.hstack((np.arange(1, nx), [nx-1])), :] - M
else:
fx = (M[np.hstack((np.arange(1,nx),[nx-1])),:] - M[np.hstack(([0],np.arange(0,nx-1))),:])/2.
fx = (M[np.hstack((np.arange(1, nx), [nx-1])), :] -
M[np.hstack(([0], np.arange(0, nx-1))), :])/2.
# boundary
fx[0,:] = M[1,:]-M[0,:]
fx[nx-1,:] = M[nx-1,:]-M[nx-2,:]
fx[0, :] = M[1, :]-M[0, :]
fx[nx-1, :] = M[nx-1, :]-M[nx-2, :]

if nbdims >= 2:
ny = np.shape(M)[1]
if order == 1:
fy = M[:,np.hstack((np.arange(1,ny),[ny-1]))] - M
fy = M[:, np.hstack((np.arange(1, ny), [ny-1]))] - M
else:
fy = (M[:,np.hstack((np.arange(1,ny),[ny-1]))] - M[:,np.hstack(([0],np.arange(ny-1)))])/2.
fy = (M[:, np.hstack((np.arange(1, ny), [ny-1]))] -
M[:, np.hstack(([0], np.arange(ny-1)))])/2.
# boundary
fy[:,0] = M[:,1]-M[:,0]
fy[:,ny-1] = M[:,ny-1]-M[:,ny-2]
fy[:, 0] = M[:, 1]-M[:, 0]
fy[:, ny-1] = M[:, ny-1]-M[:, ny-2]

if nbdims >= 3:
nz = np.shape(M)[2]
if order == 1:
fz = M[:,:,np.hstack((np.arange(1,nz),[nz-1]))] - M
fz = M[:, :, np.hstack((np.arange(1, nz), [nz-1]))] - M
else:
fz = (M[:,:,np.hstack((np.arange(1,nz),[nz-1]))] - M[:,:,np.hstack(([0],np.arange(nz-1)))])/2.
fz = (M[:, :, np.hstack((np.arange(1, nz), [nz-1]))] -
M[:, :, np.hstack(([0], np.arange(nz-1)))])/2.
# boundary
fz[:,:,0] = M[:,:,1]-M[:,:,0]
fz[:,:,ny-1] = M[:,:,nz-1]-M[:,:,nz-2]
fz[:, :, 0] = M[:, :, 1]-M[:, :, 0]
fz[:, :, ny-1] = M[:, :, nz-1]-M[:, :, nz-2]
else:
nx = np.shape(M)[0]
if order == 1:
fx = M[np.hstack((np.arange(1,nx),[0])),:] - M
fx = M[np.hstack((np.arange(1, nx), [0])), :] - M
else:
fx = (M[np.hstack((np.arange(1,nx),[0])),:] - M[np.hstack(([nx-1],np.arange(nx-1))),:])/2.

fx = (M[np.hstack((np.arange(1, nx), [0])), :] -
M[np.hstack(([nx-1], np.arange(nx-1))), :])/2.

if nbdims >= 2:
ny = np.shape(M)[1]
if order == 1:
fy = M[:,np.hstack((np.arange(1,ny),[0]))] - M
fy = M[:, np.hstack((np.arange(1, ny), [0]))] - M
else:
fy = (M[:,np.hstack((np.arange(1,ny),[0]))] - M[:,np.hstack(([ny-1],np.arange(ny-1)))])/2.

fy = (M[:, np.hstack((np.arange(1, ny), [0]))] -
M[:, np.hstack(([ny-1], np.arange(ny-1)))])/2.

if nbdims >= 3:
nz = np.shape(M)[2]
if order == 1:
fz = M[:,:,np.hstack((np.arange(1,nz),[0]))] - M
fz = M[:, :, np.hstack((np.arange(1, nz), [0]))] - M
else:
fz = (M[:,:,np.hstack((np.arange(1,nz),[0]))] - M[:,:,np.hstack(([nz-1],np.arange(nz-1)))])/2.

if nbdims==2:
fx = np.concatenate((fx[:,:,np.newaxis],fy[:,:,np.newaxis]), axis=2)
elif nbdims==3:
fx = np.concatenate((fx[:,:,:,np.newaxis],fy[:,:,:,np.newaxis],fz[:,:,:,np.newaxis]),axis=3)

return fx
fz = (M[:, :, np.hstack((np.arange(1, nz), [0]))] -
M[:, :, np.hstack(([nz-1], np.arange(nz-1)))])/2.

if nbdims == 2:
fx = np.concatenate(
(fx[:, :, np.newaxis], fy[:, :, np.newaxis]), axis=2)
elif nbdims == 3:
fx = np.concatenate(
(fx[:, :, :, np.newaxis], fy[:, :, :, np.newaxis], fz[:, :, :, np.newaxis]), axis=3)

return fx