simpeg/SimPEG/TensorMesh.py

import numpy as np
from BaseMesh import BaseMesh
from TensorView import TensorView
from DiffOperators import DiffOperators
from InnerProducts import InnerProducts
from utils import ndgrid, mkvc


class TensorMesh(BaseMesh, TensorView, DiffOperators, InnerProducts):
    """
    TensorMesh is a mesh class that deals with tensor product meshes.

    Any Mesh that has a constant width along the entire axis
    such that it can defined by a single width vector, called 'h'.

    e.g.

        hx = np.array([1,1,1])
        hy = np.array([1,2])
        hz = np.array([1,1,1,1])

        mesh = TensorMesh([hx, hy, hz])

    """
    _meshType = 'TENSOR'

    def __init__(self, h, x0=None):
        super(TensorMesh, self).__init__(np.array([x.size for x in h]), x0)

        assert len(h) == len(self.x0), "Dimension mismatch. x0 != len(h)"

        for i, h_i in enumerate(h):
            assert type(h_i) == np.ndarray, ("h[%i] is not a numpy array." % i)
            assert len(h_i.shape) == 1, ("h[%i] must be a 1D numpy array." % i)

        # Ensure h contains 1D vectors
        self._h = [mkvc(x) for x in h]

    def __str__(self):
        outStr = '  ---- {0:d}-D TensorMesh ----  '.format(self.dim)
        def printH(hx, outStr=''):
            i = -1
            while True:
                i = i + 1
                if i > hx.size:
                    break
                elif i == hx.size:
                    break
                h = hx[i]
                n = 1
                for j in range(i+1, hx.size):
                    if hx[j] == h:
                        n = n + 1
                        i = i + 1
                    else:
                        break

                if n == 1:
                    outStr = outStr + ' {0:.2f},'.format(h)
                else:
                    outStr = outStr + ' {0:d}*{1:.2f},'.format(n,h)

            return outStr[:-1]
        
        if self.dim == 1:
            outStr = outStr + '\n   x0: {0:.2f}'.format(self.x0[0])
            outStr = outStr + '\n  nCx: {0:d}'.format(self.nCx)
            outStr = outStr + printH(self.hx, outStr='\n   hx:')
            pass
        elif self.dim == 2:
            outStr = outStr + '\n   x0: {0:.2f}'.format(self.x0[0])
            outStr = outStr + '\n   y0: {0:.2f}'.format(self.x0[1])
            outStr = outStr + '\n  nCx: {0:d}'.format(self.nCx)
            outStr = outStr + '\n  nCy: {0:d}'.format(self.nCy)
            outStr = outStr + printH(self.hx, outStr='\n   hx:')
            outStr = outStr + printH(self.hy, outStr='\n   hy:')
        elif self.dim == 3:
            outStr = outStr + '\n   x0: {0:.2f}'.format(self.x0[0])
            outStr = outStr + '\n   y0: {0:.2f}'.format(self.x0[1])
            outStr = outStr + '\n   z0: {0:.2f}'.format(self.x0[2])
            outStr = outStr + '\n  nCx: {0:d}'.format(self.nCx)
            outStr = outStr + '\n  nCy: {0:d}'.format(self.nCy)
            outStr = outStr + '\n  nCz: {0:d}'.format(self.nCz)
            outStr = outStr + printH(self.hx, outStr='\n   hx:')
            outStr = outStr + printH(self.hy, outStr='\n   hy:')
            outStr = outStr + printH(self.hz, outStr='\n   hz:')

        return outStr

    def h():
        doc = "h is a list containing the cell widths of the tensor mesh in each dimension."
        fget = lambda self: self._h
        return locals()
    h = property(**h())

    def hx():
        doc = "Width of cells in the x direction"
        fget = lambda self: self._h[0]
        return locals()
    hx = property(**hx())

    def hy():
        doc = "Width of cells in the y direction"
        fget = lambda self: None if self.dim < 2 else self._h[1]
        return locals()
    hy = property(**hy())

    def hz():
        doc = "Width of cells in the z direction"
        fget = lambda self: None if self.dim < 3 else self._h[2]
        return locals()
    hz = property(**hz())

    def vectorNx():
        doc = "Nodal grid vector (1D) in the x direction."
        fget = lambda self: np.r_[0., self.hx.cumsum()] + self.x0[0]
        return locals()
    vectorNx = property(**vectorNx())

    def vectorNy():
        doc = "Nodal grid vector (1D) in the y direction."
        fget = lambda self: None if self.dim < 2 else np.r_[0., self.hy.cumsum()] + self.x0[1]
        return locals()
    vectorNy = property(**vectorNy())

    def vectorNz():
        doc = "Nodal grid vector (1D) in the z direction."
        fget = lambda self: None if self.dim < 3 else np.r_[0., self.hz.cumsum()] + self.x0[2]
        return locals()
    vectorNz = property(**vectorNz())

    def vectorCCx():
        doc = "Cell-centered grid vector (1D) in the x direction."
        fget = lambda self: np.r_[0, self.hx[:-1].cumsum()] + self.hx*0.5 + self.x0[0]
        return locals()
    vectorCCx = property(**vectorCCx())

    def vectorCCy():
        doc = "Cell-centered grid vector (1D) in the y direction."
        fget = lambda self: None if self.dim < 2 else np.r_[0, self.hy[:-1].cumsum()] + self.hy*0.5 + self.x0[1]
        return locals()
    vectorCCy = property(**vectorCCy())

    def vectorCCz():
        doc = "Cell-centered grid vector (1D) in the z direction."
        fget = lambda self: None if self.dim < 3 else np.r_[0, self.hz[:-1].cumsum()] + self.hz*0.5 + self.x0[2]
        return locals()
    vectorCCz = property(**vectorCCz())

    def gridCC():
        doc = "Cell-centered grid."

        def fget(self):
            if self._gridCC is None:
                self._gridCC = ndgrid([x for x in [self.vectorCCx, self.vectorCCy, self.vectorCCz] if not x is None])
            return self._gridCC
        return locals()
    _gridCC = None  # Store grid by default
    gridCC = property(**gridCC())

    def gridN():
        doc = "Nodal grid."

        def fget(self):
            if self._gridN is None:
                self._gridN = ndgrid([x for x in [self.vectorNx, self.vectorNy, self.vectorNz] if not x is None])
            return self._gridN
        return locals()
    _gridN = None  # Store grid by default
    gridN = property(**gridN())

    def gridFx():
        doc = "Face staggered grid in the x direction."

        def fget(self):
            if self._gridFx is None:
                self._gridFx = ndgrid([x for x in [self.vectorNx, self.vectorCCy, self.vectorCCz] if not x is None])
            return self._gridFx
        return locals()
    _gridFx = None  # Store grid by default
    gridFx = property(**gridFx())

    def gridFy():
        doc = "Face staggered grid in the y direction."

        def fget(self):
            if self._gridFy is None and self.dim > 1:
                self._gridFy = ndgrid([x for x in [self.vectorCCx, self.vectorNy, self.vectorCCz] if not x is None])
            return self._gridFy
        return locals()
    _gridFy = None  # Store grid by default
    gridFy = property(**gridFy())

    def gridFz():
        doc = "Face staggered grid in the z direction."

        def fget(self):
            if self._gridFz is None and self.dim > 2:
                self._gridFz = ndgrid([x for x in [self.vectorCCx, self.vectorCCy, self.vectorNz] if not x is None])
            return self._gridFz
        return locals()
    _gridFz = None  # Store grid by default
    gridFz = property(**gridFz())

    def gridEx():
        doc = "Edge staggered grid in the x direction."

        def fget(self):
            if self._gridEx is None:
                self._gridEx = ndgrid([x for x in [self.vectorCCx, self.vectorNy, self.vectorNz] if not x is None])
            return self._gridEx
        return locals()
    _gridEx = None  # Store grid by default
    gridEx = property(**gridEx())

    def gridEy():
        doc = "Edge staggered grid in the y direction."

        def fget(self):
            if self._gridEy is None and self.dim > 1:
                self._gridEy = ndgrid([x for x in [self.vectorNx, self.vectorCCy, self.vectorNz] if not x is None])
            return self._gridEy
        return locals()
    _gridEy = None  # Store grid by default
    gridEy = property(**gridEy())

    def gridEz():
        doc = "Edge staggered grid in the z direction."

        def fget(self):
            if self._gridEz is None and self.dim > 2:
                self._gridEz = ndgrid([x for x in [self.vectorNx, self.vectorNy, self.vectorCCz] if not x is None])
            return self._gridEz
        return locals()
    _gridEz = None  # Store grid by default
    gridEz = property(**gridEz())

    # --------------- Geometries ---------------------
    def vol():
        doc = "Construct cell volumes of the 3D model as 1d array."

        def fget(self):
            if(self._vol is None):
                vh = self.h
                # Compute cell volumes
                if(self.dim == 1):
                    self._vol = mkvc(vh[0])
                elif(self.dim == 2):
                    # Cell sizes in each direction
                    self._vol = mkvc(np.outer(vh[0], vh[1]))
                elif(self.dim == 3):
                    # Cell sizes in each direction
                    self._vol = mkvc(np.outer(mkvc(np.outer(vh[0], vh[1])), vh[2]))
            return self._vol
        return locals()
    _vol = None
    vol = property(**vol())

    def area():
        doc = "Construct face areas of the 3D model as 1d array."

        def fget(self):
            if(self._area is None):
                # Ensure that we are working with column vectors
                vh = self.h
                # The number of cell centers in each direction
                n = self.n
                # Compute areas of cell faces
                if(self.dim == 1):
                    self._area = np.ones(n[0]+1)
                elif(self.dim == 2):
                    area1 = np.outer(np.ones(n[0]+1), vh[1])
                    area2 = np.outer(vh[0], np.ones(n[1]+1))
                    self._area = np.r_[mkvc(area1), mkvc(area2)]
                elif(self.dim == 3):
                    area1 = np.outer(np.ones(n[0]+1), mkvc(np.outer(vh[1], vh[2])))
                    area2 = np.outer(vh[0], mkvc(np.outer(np.ones(n[1]+1), vh[2])))
                    area3 = np.outer(vh[0], mkvc(np.outer(vh[1], np.ones(n[2]+1))))
                    self._area = np.r_[mkvc(area1), mkvc(area2), mkvc(area3)]
            return self._area
        return locals()
    _area = None
    area = property(**area())

    def edge():
        doc = "Construct edge legnths of the 3D model as 1d array."

        def fget(self):
            if(self._edge is None):
                # Ensure that we are working with column vectors
                vh = self.h
                # The number of cell centers in each direction
                n = self.n
                # Compute edge lengths
                if(self.dim == 1):
                    self._edge = mkvc(vh[0])
                elif(self.dim == 2):
                    l1 = np.outer(vh[0], np.ones(n[1]+1))
                    l2 = np.outer(np.ones(n[0]+1), vh[1])
                    self._edge = np.r_[mkvc(l1), mkvc(l2)]
                elif(self.dim == 3):
                    l1 = np.outer(vh[0], mkvc(np.outer(np.ones(n[1]+1), np.ones(n[2]+1))))
                    l2 = np.outer(np.ones(n[0]+1), mkvc(np.outer(vh[1], np.ones(n[2]+1))))
                    l3 = np.outer(np.ones(n[0]+1), mkvc(np.outer(np.ones(n[1]+1), vh[2])))
                    self._edge = np.r_[mkvc(l1), mkvc(l2), mkvc(l3)]
            return self._edge
        return locals()
    _edge = None
    edge = property(**edge())


if __name__ == '__main__':
    print('Welcome to tensor mesh!')

    testDim = 1
    h1 = 0.3*np.ones(7)
    h1[0] = 0.5
    h1[-1] = 0.6
    h2 = .5 * np.ones(4)
    h3 = .4 * np.ones(6)

    h = [h1, h2, h3]
    h = h[:testDim]

    M = TensorMesh(h)

    xn = M.plotGrid()