def plotEllipse(self,barotropic=False,k=0,con='M2',scale=1e4,subsample=4,\
xlims=None,ylims=None,cbarpos=[0.15, 0.15, 0.03, 0.3],**kwargs):
"""
Plots tidal ellipses on a map
"""
from matplotlib.collections import EllipseCollection
plt.ioff()
fig = plt.gcf()
ax = fig.gca()
iicon = findCon(con,self.frqnames)
if self.clim==None:
self.clim=[]
self.clim.append(np.min(self.Amp))
self.clim.append(np.max(self.Amp))
if xlims==None or ylims==None:
xlims=self.xlims
ylims=self.ylims
ell = self.getEllipse(barotropic=barotropic,k=k,con=con)
# Create the ellipse collection
indices = range(0,self.Nc,subsample)
widths = [ell[0][ii]*scale for ii in indices]
heights = [ell[1][ii]*scale for ii in indices]
angles = [ell[2][ii]*180.0/np.pi for ii in indices]
#angles = [ell[2][ii] for ii in indices]
offsets = [(self.xv[ii],self.yv[ii]) for ii in indices]
collection = EllipseCollection(widths,heights,angles,units='xy',\
offsets=offsets, transOffset=ax.transData,**kwargs)
z=ell[0][indices]
collection.set_array(np.array(z))
collection.set_clim(vmin=self.clim[0],vmax=self.clim[1])
collection.set_edgecolors(collection.to_rgba(np.array(z)))
ax.set_aspect('equal')
ax.set_xlim(xlims)
ax.set_ylim(ylims)
titlestr='%s - Semi-major Ellipse Amplitude'%(self.frqnames[iicon])
plt.title(titlestr)
ax.add_collection(collection)
# Add a decent looking colorbar
if not cbarpos==None:
cbaxes = fig.add_axes(cbarpos)
cb = fig.colorbar(collection,cax = cbaxes,orientation='vertical')
cb.ax.set_title('[m s$^{-1}$]')
plt.sca(ax)
#axcb = fig.colorbar(collection)
return collection
def display_matrices(ax, grid, texture, scale=None, col=None):
"""Display on a matplotlib axis an ellipse representing a symmetric matrix at each grid element. Each axis of the ellipse corresponds to an eigenvalue and is oriented along its eigenvector. An axis corresponding to a positive eigenvalue is drawn. A 'coffee bean' has a negative eigenvalue smaller in absolute value than its positive eigenvalue. A 'capsule' has a negative eigenvalue larger in absolute value than its positive eigenvalue. A circle is when the two eigenvalues are equal in absolute value."""
XY = grid.mesh()
mask = grid.mask()
#convert the texture back to an array of matrices
mat = tri2square(texture)
#compute egenvalues and eigenvectors of texture for each cell of the grid
evalues, evectors = np.linalg.eigh(mat)
#width and height are the larger and smaller eigenvalues respectively
ww = evalues[..., 1][mask]
hh = evalues[..., 0][mask]
#angle is given by the angle of the larger eigenvector
aa = np.rad2deg(np.arctan2(evectors[..., 1, 1], evectors[..., 0, 1]))[mask]
#sum of the eigenvalues (trace of the matrix)
trace = ww + hh #np.where(np.abs(ww)>np.abs(hh), ww, hh)#ww*hh
#color
#if col is None:
# if trace.ptp()>0:
# col = plt.cm.viridis((trace.ravel() - trace.min())/trace.ptp())
# else:
# col = plt.cm.viridis(np.ones_like(trace))
if scale is None:
#scale = 1
ellipse_areas = np.pi * np.abs(np.prod(evalues, axis=-1))
rarea = ellipse_areas / grid.areas()
scale = np.nanpercentile(np.sqrt(rarea[mask]), 90)
if scale == 0:
scale = np.nanmax(np.sqrt(rarea[mask]))
if scale == 0:
raise ValueError("All matrices are null")
scale = 1 / scale
#show ellipses
ec = EllipseCollection(
ww * scale,
hh * scale,
aa,
units='xy',
offsets=XY,
transOffset=ax.transData,
edgecolors=col,
facecolors='none',
)
#major and minor axes (only for positive eigenvalues)
xyps = scale * np.transpose(
evectors * np.maximum(0, evalues)[..., None, :],
(0, 1, 3, 2))[mask].reshape(2 * len(ww), 2) * 0.5
ma = LineCollection([[-xyp, xyp] for xyp in xyps],
offsets=np.repeat(XY, 2, axis=0),
color=(0.5, 0.5, 0.5))
if col is None:
if trace.ptp() > 0:
ec.set_array(trace)
ma.set_array(trace[mask.ravel()])
else:
ec.set_edgecolors(col)
ma.set_edgecolors(col)
ax.add_collection(ec)
ax.add_collection(ma)
return ec