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 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 simpeg.Mesh.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): nodeInds[i] = ((np.tile(pt, (grid.shape[0],1)) - grid)**2).sum(axis=1).argmin() return nodeInds def readUBCTensorMesh(fileName): """ Read UBC GIF 3DTensor mesh and generate 3D Tensor mesh in simpegTD Input: :param fileName, path to the UBC GIF mesh file Output: :param SimPEG TensorMesh object :return """ # Interal function to read cell size lines for the UBC mesh files. def readCellLine(line): for seg in line.split(): if '*' in seg: st = seg sp = seg.split('*') re = np.array(sp[0],dtype=int)*(' ' + sp[1]) line = line.replace(st,re.strip()) return np.array(line.split(),dtype=float) # Read the file as line strings, remove lines with comment = ! msh = np.genfromtxt(fileName,delimiter='\n',dtype=np.str,comments='!') # Fist line is the size of the model sizeM = np.array(msh[0].split(),dtype=float) # Second line is the South-West-Top corner coordinates. x0 = np.array(msh[1].split(),dtype=float) # Read the cell sizes h1 = readCellLine(msh[2]) h2 = readCellLine(msh[3]) h3temp = readCellLine(msh[4]) h3 = h3temp[::-1] # Invert the indexing of the vector to start from the bottom. # Adjust the reference point to the bottom south west corner x0[2] = x0[2] - np.sum(h3) # Make the mesh from SimPEG import Mesh tensMsh = Mesh.TensorMesh([h1,h2,h3],x0) return tensMsh def readUBCTensorModel(fileName, mesh): """ ReadUBC 3DTensor mesh model and generate 3D Tensor mesh model in simpegTD """ f = open(fileName, 'r') model = np.array(map(float, f.readlines())) f.close() model = np.reshape(model, (mesh.nCz, mesh.nCx, mesh.nCy), order = 'F') model = model[::-1,:,:] model = np.transpose(model, (1, 2, 0)) model = mkvc(model) return model def writeUBCTensorMesh(mesh, fileName): """ Writes a SimPEG TensorMesh to a UBC-GIF format mesh file. :param simpeg.Mesh.TensorMesh mesh: The mesh :param str fileName: File to write to """ assert mesh.dim == 3 s = '' s += '%i %i %i\n' %tuple(mesh.vnC) origin = mesh.x0 origin.dtype = float origin[2] = origin[2]+mesh.hz.sum() s += '%.2f %.2f %.2f\n' %tuple(origin) s += ('%.2f '*mesh.nCx+'\n')%tuple(mesh.hx) s += ('%.2f '*mesh.nCy+'\n')%tuple(mesh.hy) s += ('%.2f '*mesh.nCz+'\n')%tuple(mesh.hz[::-1]) f = open(fileName, 'w') f.write(s) f.close() def writeUBCTensorModel(mesh, model, fileName): """ Writes a model associated with a SimPEG TensorMesh to a UBC-GIF format model file. :param simpeg.Mesh.TensorMesh mesh: The mesh :param numpy.ndarray model: The model :param str fileName: File to write to """ # Reshape model to a matrix modelMat = mesh.r(model,'CC','CC','M') # Transpose the axes modelMatT = modelMat.transpose((2,0,1)) # Flip z to positive down modelMatTR = mkvc(modelMatT[::-1,:,:]) np.savetxt(fileName, modelMatTR.ravel()) 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()