Stream thickness

• from pr #95
• commits from @micmitch
• review from @lheagy

Description

Added stream_thickness keyword argument to plotSlice and _plotImage2D functions so that it is possible to scale the thickness of streamlines to reflect the amplitude of the vector field. This functionality was added in a manner similar to the stream_threshold keyword.

stream_thickness keyword currently takes a float which acts as a scaling factor for the streamline thickness. Bounds are hardwired to fix the thickness of the 10% largest and smallest vector amplitudes. Provides good results with the DC current density plots I've made but could probably be generalized in the future for more flexibility.

e.g.

mesh.plotSlice(
    u, ax=ax, normal='X', vType='F', view='vec', stream_threshold=1e-8, stream_thickness=3
)

Expand the `plot_3d_slicer` to other `vTypes` and `views`

• from pr: #121
• commits from: @prisae
• review from: @lheagy

Expand plot_3d_slicer

Addresses #116 .

Bug fix

First, it contains a minor bug-fix in the scrolling behavior (last element in each direction was not acceptable, only noticeable in small grids).

vType

Included all non-vector vType's: CC, Ex, Ey, Ez, Fx, Fy, Fz.

view

Included all view's except vec (real [default]; imag; abs; tested them all, seems to be fine).

Name-clash
There is a problem with the view-parameter, which I stupidly used to switch the x-y-axis. I changed the previous view-parameter to axis (hence axis='xy' or 'yx'). It is better to change this than to have different parameters as, for instance, in plotSlice. I added a switch for backwards-compatibility (if view in ['xy', 'yx'] => it sets axis = view; view = 'real').

Add VTK object interface

• from pr: #114
• commits from: @banesullivan
• review from: @rowanc1, @lheagy

Description

These new features enable discretize to have a direct interface for VTK base software by implementing toVTK() methods on all the mesh types (excluding CylMesh at this time). Notably, @banesullivan will be using this to provide interoperability with PVGeo to provide direct file IO into ParaView using discretize as well as ways to interactively create discretize meshes in ParaView similar to this example in the PVGeo docs. This new interface also enables discretize meshes to be passed on directly to VTK algorithms for post-processing analysis (note if you couple the interface with PVGeo like shown in this notebook, the process is somewhat simplified).

To learn more about the new VTK object interface, see the docs for the vtkInterface.

Example Usage

The VTK object interface can be used on TensorMesh, TreeMesh, and CurvilinearMesh objects to yield a VTK object in your active Python environment or used to save VTK files for easy sharing.

import discretize
import numpy as np
h1 = np.linspace(.1, .5, 3)
h2 = np.linspace(.1, .5, 5)
h3 = np.linspace(.1, .5, 3)
mesh = discretize.TensorMesh([h1, h2, h3])

# Yield a VTK data object for passing this mesh onto VTK algorithms
vtkobj = mesh.toVTK()

# Or save out the tree mesh for sharing with others
mesh.writeVTK('sample_mesh')

Note that these new features also give users the ability to specify the axes orientation of any given mesh. For example, the above TensorMesh is oriented on the traditional Cartesian reference frame by default but we could change this. To define what that orientation is, we can use the new axis_* properties:

# Defined a rotated reference frame
mesh.axis_u = (1,-1,0)
mesh.axis_v = (-1,-1,0)
mesh.axis_w = (0,0,1)
# Check that the reference frame is valid
mesh._validate_orientation()

Now we have a TensorMesh explicitly defined on a rotated reference frame! This is quite useful for when we want to convert this to a VTK data object that must have its location in a traditional XYZ Cartesian space defined.

Please take a look at the docs to learn more about using these new features!

plot_3d_slicer

• from pr #104
• commits from @prisae
• review from @lheagy

plot_3d_slicer

Add an interactive slicer for 3D volumes. At the moment only implemented for tensor meshes.

Features

• Mouse wheel scroll while hovering over a subplot scrolls through the third axis (e.g., hovering over the xy-slice and scrolling your mouse wheel will go through the z-axis).
• The three subplots are synced, also for zooming and moving.
• The initial slices can be provided via the xslice, yslice, and zslice parameters (default is in the middle of the volume).
• Transparency values and ranges can be provided (a list of floats and tuples/lists of two values), e.g. to hide the seawater or to focus on an interesting part, e.g., [0.3, [1, 4], [-np.infty, -10]] to remove all values equal to 0.3, all values between 1 and 4, and all values smaller than -10. For interactive range selection set transparency='slider'.
• Takes clim and pcolorOpts as other mesh-plotting functions, which will be passed to pcolormesh.
• By default the horizontal axis is x, and the vertical axis is y; this can be flipped by setting view='yx'.

By default, the aspect ratio of the three subplots is set to 'auto'. You can change this with the aspect
parameter, however, expect the unexpected by doing this. Most importantly, the three subplots won't be nicely aligned, and zooming might result in funny arrangements. Two parameters can be used in this respect:

• aspect takes 'auto', 'equal', or num. A list of two of them can be provided, in which case the first element is for the xy-slice, and the second element for the xz- and zy-slices. E.g., aspect=['equal', 2] sets the xy-slice to equal, and in the other two the vertical dimension is exaggerated by a factor of 2.
• The plot_3d_slicer is on a subplot2grid-grid, by default on a 3x3 grid, where 2x2 are used for the xy-slice, 2x1 for the xz-slice, and 1x2 for the zy-slice. You can provide a list of three integers via the grid-parameter, which stand for the number of grid-units occupied for the x-, y-, and z-dimension (default is [2, 2, 1]).

Usage

mesh.plot_3d_slicer(data)

It requires %matplotlib notebook in Jupyter. In regular IPython shells it should just work.

options on plotSlice, grid=True

• allow kwargs for color and linewidth in the plotgrid function
• helpful when plotting the mesh and model on a highly discretized mesh. e.g.
  

Include tree.pxd in source distribution

• from #102

• commits from: @cgohlke

• review from: @jcapriot, @lheagy

• Include tree.pxd in source distribution

Minor update: plotGrid - linestyle

• from pr #101
• ".-" is no longer valid for a linestyle input in matplotlib, it should instead be "-." (however, a solid line looks better anyways for the 1d).

TreeMesh Re-write

• originally from pr #94
• commits from: @jcapriot
• review from: @rowanc1, @fourndo, @lheagy

New Implementation of the TreeMesh

At this point consider this branch as EXPERIMENTAL. There are many possible unsafe operations that could arise, so be careful (which will need to be enforced at a later time). The code is certainly not completely up to format standards, but at this point, just wanted to get a pull request going and allow anyone who wants to use it to test it out to find any bugs.

There are many changes to the TreeMesh implementation within this pull request, However it is mostly feature complete compared to the previous implementation with regards to the public members of the class.

It was mostly rewritten in a way that made the construction of the mesh and construction of the operators all done in c++/cython, which resulted in dramatic speedups. As a reference, the 97 nosetests on the tree in the previous implementation took 238.476s on my personal computer. This implementation took 20.281s.

The basic idea is that each object, (node, edge, etc.) is aware of the structure of the TreeMesh as each is a cpp class that contains references to other objects.

A few key differences:

• All tree construction is balanced (no need to call tree.balance, or pass balance=True to functions)

• tree.refine should only be called once (at this point) as it "finalizes" the tree. It might be good to add a flag to the tree initialization that would allow incremental additions (similar to scipy.spatial.ConvexHull) and then require a finalization operation to be done before any other operations.

• Interpolation is "lazy" 2nd order now for all E, CC, and F interpolation, meaning we triangulate the grid points to interpolate. Interpolating without triangulation on the TreeMesh is still a point of research. This is not as fast as it could be, but still faster than previously.

• Both face and edge operations are defined for 2D, (basically a re-ording of x-edges -> y-faces)

• Do not expect any ordering for the faces, edges, and nodes. They are whatever they have decided to be.

• Do not expect any of the private members of the class to have remained consistent between implementations.

• There are many other changes which should hopefully be apparent as you look through the code.

Big things that still need to be implemented

• Serialization, (do not expect to pickle this object and have it work, however with construction being much faster, this shouldn't slow down anyone too much while it is being worked on).

• PlotImage and PlotSlice.

There are also many areas that this code could be extended to handle different types of underlying meshs, as well as support for differing sizes of axes, but as I said before, the initial goal of this pull request is to mimic the behavior of the current implementation.

Other than that, I hope this speeds up the operations for those who need them.

Update

• Serialization should be implemented now (the TreeMesh is pickle-able)
• PlotImage and PlotSlice are also implemented.
• It also now support differing dimensions of the underlying TensorMesh
• Interpolation is now NOT triangulated, so do there is no longer 2nd order convergence of the non-node interpolation matrices.
• the refine and insert_cells function now have a finalize keyword arg that can be set to false if you want to do multiple steps of tree building

pypi deploys

• from pr #97
• update pypi credentials
• update appveyor and travis to auto-deploy to pypi on tags
  • includes upload of wheel files from appveyor

3D cyl mesh

• originally from pr: #36
• commits from: @lheagy
• review from: @rowanc1

3D Cyl Mesh

First implementation of a 3D cylindrical mesh. We discretize in r, theta and z.

Operators

• edgeCurl
• faceDiv
• aveF2CC
• aveF2CCV
• aveE2CC
• aveE2CCV

are all implemented and tested for second order convergence

Examples

There are some examples running this code in http://github.com/lheagy/casingResearch

• added a simple example that plots a 3D cyl mesh

Plotting

• add plot capabilities for plotSlice (and I think two slices through the mesh for plotGrid())

Testing

• basic elements like the grids, counting of things.
• operator tests for mimetic properties

Other updates

Cell Grad Stencils are properties

• cell grad stencils are properties rather than methods. This pr will need to be followed by an update in the SimPEG regularization (addressed in simpeg/simpeg#699)

minor updates

• plotting now uses the C0, C1, ... colors in matplotlib
• added *.ipynb to .gitignore