import numpy as np import matplotlib.pyplot as plt import matplotlib from mpl_toolkits.mplot3d import Axes3D class TensorView(object): """ Provides viewing functions for TensorMesh This class is inherited by TensorMesh """ def __init__(self): pass def plotImage(self, I, imageType='CC', figNum=1,ax=None,direction='z',numbering=True): """ Mesh.plotImage(I) Plots scalar fields on the given mesh. Input: I - scalar field (np.array) Optional Input: imageType - type of image ('CC','N','Fx','Fy','Fz','Ex','Ey','Ez') figNum - number of figure to plot to ax - axis to plot to direction - 3D only. slice dimensions numbering - 3D only. show numbering of slices """ assert type(I) == np.ndarray, "I must be a numpy array" assert type(numbering) == bool, "numbering must be a bool" assert imageType in ["CC", "N","Fx","Fy","Fz","Ex","Ey","Ez"], "imageType must be 'CC', 'N','Fx','Fy','Fz','Ex','Ey','Ez'" assert direction in ["x", "y","z"], "direction must be either x,y, or z" if imageType == 'CC': assert I.size == self.nC, "Incorrect dimensions for CC." elif imageType == 'N': assert I.size == self.nN, "Incorrect dimensions for N." elif imageType == 'Fx': assert I.size == np.prod(self.nFx), "Incorrect dimensions for Fx." elif imageType == 'Fy': assert I.size == np.prod(self.nFy), "Incorrect dimensions for Fy." elif imageType == 'Fz': assert I.size == np.prod(self.nFz), "Incorrect dimensions for Fz." elif imageType == 'Ex': assert I.size == np.prod(self.nEx), "Incorrect dimensions for Ex." elif imageType == 'Ey': assert I.size == np.prod(self.nEy), "Incorrect dimensions for Ey." elif imageType == 'Ez': assert I.size == np.prod(self.nEz), "Incorrect dimensions for Ez." if ax is None: fig = plt.figure(figNum) fig.clf() ax = plt.subplot(111) else: assert isinstance(ax,matplotlib.axes.Axes), "ax must be an Axes!" fig = ax.figure if self.dim == 1: if imageType == 'CC': ph = ax.plot(self.vectorCCx, I, '-ro') elif imageType == 'N': ph = ax.plot(self.vectorNx, I, '-bs') ax.set_xlabel("x") ax.axis('tight') elif self.dim == 2: if imageType == 'CC': C = I[:].reshape(self.n, order='F') elif imageType == 'N': C = I[:].reshape(self.n+1, order='F') C = 0.25*(C[:-1, :-1] + C[1:, :-1] + C[:-1, 1:] + C[1:, 1:]) elif imageType == 'Fx': C = I[:].reshape(self.nFx, order='F') C = 0.5*(C[:-1, :] + C[1:, :] ) elif imageType == 'Fy': C = I[:].reshape(self.nFy, order='F') C = 0.5*(C[:, :-1] + C[:, 1:] ) elif imageType == 'Ex': C = I[:].reshape(self.nEx, order='F') C = 0.5*(C[:,:-1] + C[:,1:] ) elif imageType == 'Ey': C = I[:].reshape(self.nEy, order='F') C = 0.5*(C[:-1,:] + C[1:,:] ) ph = ax.pcolormesh(self.vectorNx, self.vectorNy, C.T) ax.axis('tight') ax.set_xlabel("x") ax.set_ylabel("y") elif self.dim == 3: if direction == 'z': # get copy of image and average to cell-centres is necessary if imageType == 'CC': Ic = I[:].reshape(self.n, order='F') elif imageType == 'N': Ic = I[:].reshape(self.n+1, order='F') Ic = .125*(Ic[:-1,:-1,:-1]+Ic[1:,:-1,:-1] + Ic[:-1,1:,:-1]+ Ic[1:,1:,:-1]+ Ic[:-1,:-1,1:]+Ic[1:,:-1,1:] + Ic[:-1,1:,1:]+ Ic[1:,1:,1:] ) elif imageType == 'Fx': Ic = I[:].reshape(self.nFx, order='F') Ic = .5*(Ic[:-1,:,:]+Ic[1:,:,:]) elif imageType == 'Fy': Ic = I[:].reshape(self.nFy, order='F') Ic = .5*(Ic[:,:-1,:]+Ic[:,1:,:]) elif imageType == 'Fz': Ic = I[:].reshape(self.nFz, order='F') Ic = .5*(Ic[:,:,:-1]+Ic[:,:,1:]) elif imageType == 'Ex': Ic = I[:].reshape(self.nEx, order='F') Ic = .25*(Ic[:,:-1,:-1]+Ic[:,1:,:-1]+Ic[:,:-1,1:]+Ic[:,1:,:1]) elif imageType == 'Ey': Ic = I[:].reshape(self.nEy, order='F') Ic = .25*(Ic[:-1,:,:-1]+Ic[1:,:,:-1]+Ic[:-1,:,1:]+Ic[1:,:,:1]) elif imageType == 'Ez': Ic = I[:].reshape(self.nEz, order='F') Ic = .25*(Ic[:-1,:-1,:]+Ic[1:,:-1,:]+Ic[:-1,1:,:]+Ic[1:,:1,:]) # determine number oE slices in x and y dimension nX = np.ceil(np.sqrt(self.nCz)) nY = np.ceil(self.nCz/nX) # allocate space for montage C = np.zeros((nX*self.nCx,nY*self.nCz)) nCx = self.nCx nCy = self.nCy for iy in range(int(nY)): for ix in range(int(nX)): iz = ix + iy*nX if iz < self.nCz: C[ix*nCx:(ix+1)*nCx, iy*nCy:(iy+1)*nCy] = Ic[:, :, iz] else: C[ix*nCx:(ix+1)*nCx, iy*nCy:(iy+1)*nCy] = np.nan C = np.ma.masked_where(np.isnan(C), C) xx = np.r_[0, np.cumsum(np.kron(np.ones((nX, 1)), self.hx).ravel())] yy = np.r_[0, np.cumsum(np.kron(np.ones((nY, 1)), self.hy).ravel())] ph = ax.pcolormesh(xx, yy, C.T) # Plot the lines gx = np.r_[0, np.cumsum(np.kron(np.ones((nX, 1)), np.sum(self.hy)).ravel())] gy = np.r_[0, np.cumsum(np.kron(np.ones((nY, 1)), np.sum(self.hx)).ravel())] # Repeat and seperate with NaN gxX = np.c_[gx, gx, gx+np.nan].ravel() gxY = np.kron(np.ones((nX+1, 1)), np.array([0, sum(self.hy)*nY, np.nan])).ravel() gyX = np.kron(np.ones((nY+1, 1)), np.array([0, sum(self.hx)*nX, np.nan])).ravel() gyY = np.c_[gy, gy, gy+np.nan].ravel() ax.plot(gxX, gxY, 'w-', linewidth=2) ax.plot(gyX, gyY, 'w-', linewidth=2) if numbering: pad = np.sum(self.hx)*0.04 for iy in range(int(nY)): for ix in range(int(nX)): iz = ix + iy*nX if iz < self.nCz: ax.text((ix+1)*self.vectorNx[-1]-pad,(iy)*self.vectorNy[-1]+pad, '#%i'%iz,color='w',verticalalignment='bottom',horizontalalignment='right',size='x-large') fig.show() return ph def plotGrid(self): """Plot the nodal, cell-centered and staggered grids for 1,2 and 3 dimensions.""" if self.dim == 1: fig = plt.figure(1) fig.clf() ax = plt.subplot(111) xn = self.gridN xc = self.gridCC ax.hold(True) ax.plot(xn, np.ones(np.shape(xn)), 'bs') ax.plot(xc, np.ones(np.shape(xc)), 'ro') ax.plot(xn, np.ones(np.shape(xn)), 'k--') ax.grid(True) ax.hold(False) ax.set_xlabel('x1') fig.show() elif self.dim == 2: fig = plt.figure(2) fig.clf() ax = plt.subplot(111) xn = self.gridN xc = self.gridCC xs1 = self.gridFx xs2 = self.gridFy ax.hold(True) ax.plot(xn[:, 0], xn[:, 1], 'bs') ax.plot(xc[:, 0], xc[:, 1], 'ro') ax.plot(xs1[:, 0], xs1[:, 1], 'g>') ax.plot(xs2[:, 0], xs2[:, 1], 'g^') ax.grid(True) ax.hold(False) ax.set_xlabel('x1') ax.set_ylabel('x2') fig.show() elif self.dim == 3: fig = plt.figure(3) fig.clf() ax = fig.add_subplot(111, projection='3d') xn = self.gridN xc = self.gridCC xfs1 = self.gridFx xfs2 = self.gridFy xfs3 = self.gridFz xes1 = self.gridEx xes2 = self.gridEy xes3 = self.gridEz ax.hold(True) ax.plot(xn[:, 0], xn[:, 1], 'bs', zs=xn[:, 2]) ax.plot(xc[:, 0], xc[:, 1], 'ro', zs=xc[:, 2]) ax.plot(xfs1[:, 0], xfs1[:, 1], 'g>', zs=xfs1[:, 2]) ax.plot(xfs2[:, 0], xfs2[:, 1], 'g<', zs=xfs2[:, 2]) ax.plot(xfs3[:, 0], xfs3[:, 1], 'g^', zs=xfs3[:, 2]) ax.plot(xes1[:, 0], xes1[:, 1], 'k>', zs=xes1[:, 2]) ax.plot(xes2[:, 0], xes2[:, 1], 'k<', zs=xes2[:, 2]) ax.plot(xes3[:, 0], xes3[:, 1], 'k^', zs=xes3[:, 2]) ax.grid(True) ax.hold(False) ax.set_xlabel('x1') ax.set_ylabel('x2') ax.set_zlabel('x3') fig.show()