simpeg/SimPEG/Utils/meshutils.py

import numpy as np
from scipy import sparse as sp
from matutils import mkvc, ndgrid, sub2ind, sdiag
from codeutils import asArray_N_x_Dim
from codeutils import isScalar
import os

def exampleLrmGrid(nC, exType):
    assert type(nC) == list, "nC must be a list containing the number of nodes"
    assert len(nC) == 2 or len(nC) == 3, "nC must either two or three dimensions"
    exType = exType.lower()

    possibleTypes = ['rect', 'rotate']
    assert exType in possibleTypes, "Not a possible example type."

    if exType == 'rect':
        return list(ndgrid([np.cumsum(np.r_[0, np.ones(nx)/nx]) for nx in nC], vector=False))
    elif exType == 'rotate':
        if len(nC) == 2:
            X, Y = ndgrid([np.cumsum(np.r_[0, np.ones(nx)/nx]) for nx in nC], vector=False)
            amt = 0.5-np.sqrt((X - 0.5)**2 + (Y - 0.5)**2)
            amt[amt < 0] = 0
            return [X + (-(Y - 0.5))*amt, Y + (+(X - 0.5))*amt]
        elif len(nC) == 3:
            X, Y, Z = ndgrid([np.cumsum(np.r_[0, np.ones(nx)/nx]) for nx in nC], vector=False)
            amt = 0.5-np.sqrt((X - 0.5)**2 + (Y - 0.5)**2 + (Z - 0.5)**2)
            amt[amt < 0] = 0
            return [X + (-(Y - 0.5))*amt, Y + (-(Z - 0.5))*amt, Z + (-(X - 0.5))*amt]

def meshTensor(value):
    """
        **meshTensor** takes a list of numbers and tuples that have the form::

            mT = [ float, (cellSize, numCell), (cellSize, numCell, factor) ]

        For example, a time domain mesh code needs
        many time steps at one time::

            [(1e-5, 30), (1e-4, 30), 1e-3]

        Means take 30 steps at 1e-5 and then 30 more at 1e-4,
        and then one step of 1e-3.

        Tensor meshes can also be created by increase factors::

            [(10.0, 5, -1.3), (10.0, 50), (10.0, 5, 1.3)]

        When there is a third number in the tuple, it
        refers to the increase factor, if this number
        is negative this section of the tensor is flipped right-to-left.

        .. plot::

            from SimPEG import Mesh
            tx = [(10.0,10,-1.3),(10.0,40),(10.0,10,1.3)]
            ty = [(10.0,10,-1.3),(10.0,40)]
            M = Mesh.TensorMesh([tx, ty])
            M.plotGrid(showIt=True)

    """
    if type(value) is not list:
        raise Exception('meshTensor must be a list of scalars and tuples.')

    proposed = []
    for v in value:
        if isScalar(v):
            proposed += [float(v)]
        elif type(v) is tuple and len(v) == 2:
            proposed += [float(v[0])]*int(v[1])
        elif type(v) is tuple and len(v) == 3:
            start = float(v[0])
            num = int(v[1])
            factor = float(v[2])
            pad = ((np.ones(num)*np.abs(factor))**(np.arange(num)+1))*start
            if factor < 0: pad = pad[::-1]
            proposed += pad.tolist()
        else:
            raise Exception('meshTensor must contain only scalars and len(2) or len(3) tuples.')

    return np.array(proposed)

def closestPoints(mesh, pts, gridLoc='CC'):
    """
        Move a list of points to the closest points on a grid.

        :param BaseMesh mesh: The mesh
        :param numpy.ndarray pts: Points to move
        :param string gridLoc: ['CC', 'N', 'Fx', 'Fy', 'Fz', 'Ex', 'Ex', 'Ey', 'Ez']
        :rtype: numpy.ndarray
        :return: nodeInds
    """

    pts = asArray_N_x_Dim(pts, mesh.dim)
    grid = getattr(mesh, 'grid' + gridLoc)
    nodeInds = np.empty(pts.shape[0], dtype=int)

    for i, pt in enumerate(pts):
        if mesh.dim == 1:
            nodeInds[i] = ((pt - grid)**2).argmin()
        else:
            nodeInds[i] = ((np.tile(pt, (grid.shape[0],1)) - grid)**2).sum(axis=1).argmin()

    return nodeInds

def ExtractCoreMesh(xyzlim, mesh, meshType='tensor'):
    """
    Extracts Core Mesh from Global mesh

    :param numpy.ndarray xyzlim: 2D array [ndim x 2]
    :param BaseMesh mesh: The mesh

    This function ouputs::

        - actind: corresponding boolean index from global to core
        - meshcore: core SimPEG mesh

    Warning: 1D and 2D has not been tested
    """
    from SimPEG import Mesh
    if mesh.dim == 1:
        xyzlim = xyzlim.flatten()
        xmin, xmax = xyzlim[0], xyzlim[1]

        xind = np.logical_and(mesh.vectorCCx>xmin, mesh.vectorCCx<xmax)

        xc = mesh.vectorCCx[xind]

        hx = mesh.hx[xind]

        x0 = [xc[0]-hx[0]*0.5, yc[0]-hy[0]*0.5]

        meshCore = Mesh.TensorMesh([hx, hy], x0=x0)

        actind = (mesh.gridCC[:,0]>xmin) & (mesh.gridCC[:,0]<xmax)

    elif mesh.dim == 2:
        xmin, xmax = xyzlim[0,0], xyzlim[0,1]
        ymin, ymax = xyzlim[1,0], xyzlim[1,1]

        yind = np.logical_and(mesh.vectorCCy>ymin, mesh.vectorCCy<ymax)
        zind = np.logical_and(mesh.vectorCCz>zmin, mesh.vectorCCz<zmax)

        xc = mesh.vectorCCx[xind]
        yc = mesh.vectorCCy[yind]

        hx = mesh.hx[xind]
        hy = mesh.hy[yind]

        x0 = [xc[0]-hx[0]*0.5, yc[0]-hy[0]*0.5]

        meshCore = Mesh.TensorMesh([hx, hy], x0=x0)

        actind = (mesh.gridCC[:,0]>xmin) & (mesh.gridCC[:,0]<xmax) \
               & (mesh.gridCC[:,1]>ymin) & (mesh.gridCC[:,1]<ymax) \

    elif mesh.dim == 3:
        xmin, xmax = xyzlim[0,0], xyzlim[0,1]
        ymin, ymax = xyzlim[1,0], xyzlim[1,1]
        zmin, zmax = xyzlim[2,0], xyzlim[2,1]

        xind = np.logical_and(mesh.vectorCCx>xmin, mesh.vectorCCx<xmax)
        yind = np.logical_and(mesh.vectorCCy>ymin, mesh.vectorCCy<ymax)
        zind = np.logical_and(mesh.vectorCCz>zmin, mesh.vectorCCz<zmax)

        xc = mesh.vectorCCx[xind]
        yc = mesh.vectorCCy[yind]
        zc = mesh.vectorCCz[zind]

        hx = mesh.hx[xind]
        hy = mesh.hy[yind]
        hz = mesh.hz[zind]

        x0 = [xc[0]-hx[0]*0.5, yc[0]-hy[0]*0.5, zc[0]-hz[0]*0.5]

        meshCore = Mesh.TensorMesh([hx, hy, hz], x0=x0)

        actind = (mesh.gridCC[:,0]>xmin) & (mesh.gridCC[:,0]<xmax) \
               & (mesh.gridCC[:,1]>ymin) & (mesh.gridCC[:,1]<ymax) \
               & (mesh.gridCC[:,2]>zmin) & (mesh.gridCC[:,2]<zmax)

    else:
        raise(Exception("Not implemented!"))


    return actind, meshCore


if __name__ == '__main__':
    from SimPEG import Mesh
    import matplotlib.pyplot as plt
    tx = [(10.0,10,-1.3),(10.0,40),(10.0,10,1.3)]
    ty = [(10.0,10,-1.3),(10.0,40)]
    M = Mesh.TensorMesh([tx, ty])
    M.plotGrid()
    plt.gca().axis('tight')
    plt.show()