def plotmesh(self, **how):
""" Draw a plot of the mesh.
Inner edges in blue lines. Boundary edges in magenta lines. Centers as
circles. Vertices as squares. x_sigma as x. nKs as arrows.
"""
ax = plt.gca()
ax.set_xlim(
(1.1 * self.mx - 0.1 * self.Mx, -0.1 * self.mx + 1.1 * self.Mx))
ax.set_ylim(
(1.1 * self.my - 0.1 * self.My, -0.1 * self.my + 1.1 * self.My))
ax.set_aspect('equal')
s_i = self.vert[self.inner]
s_b = self.vert[self.bnd]
X_i = np.stack((s_i[0, :, 0], s_i[1, :, 0]))
Y_i = np.stack((s_i[0, :, 1], s_i[1, :, 1]))
X_b = np.stack((s_b[0, :, 0], s_b[1, :, 0]))
Y_b = np.stack((s_b[0, :, 1], s_b[1, :, 1]))
plt.plot(X_i, Y_i, '-b')
plt.plot(X_b, Y_b, '-m')
plt.plot(self.vert[:, 0], self.vert[:, 1], 's', **how)
plt.plot(self.centres[:, 0], self.centres[:, 1], 'go', **how)
plt.plot(self.xs_b[:, 0], self.xs_b[:, 1], 'rx', **how)
plt.plot(self.xs_i[:, 0], self.xs_i[:, 1], 'rx', **how)
plt.quiver(self.xs_i[:, 0], self.xs_i[:, 1], self.nKs_i[:, 0],
self.nKs_i[:, 1])
plt.quiver(self.xs_b[:, 0], self.xs_b[:, 1], self.nKs_b[:, 0],
self.nKs_b[:, 1])
def main():
F, I = ag.io.load_example('two-faces')
t1 = time()
imdef, info = ag.stats.image_deformation(F, I, penalty=0.1, rho=2.0, last_level=3, tol=0.00001, maxiter=100, \
start_level=1, wavelet='db8', debug_plot=False)
t2 = time()
Fdef = imdef.deform(F)
print "Time:", t2 - t1
print "Cost:", info['cost']
x, y = imdef.meshgrid()
Ux, Uy = imdef.deform_map(x, y)
for i in range(Ux.shape[0]):
for j in range(Ux.shape[1]):
print Ux[i, j], Uy[i, j]
print 'mins', Ux.min(), Uy.min()
print 'maxs', Ux.max(), Uy.max()
import matplotlib.pylab as plt
plt.quiver(x, y, Ux, Uy) #, Ux, Uy)
plt.show()
PLOT = False
if PLOT:
import matplotlib.pylab as plt
ag.plot.deformation(F, I, imdef)
def main():
F, I = ag.io.load_example('two-faces')
t1 = time()
imdef, info = ag.stats.image_deformation(F, I, penalty=0.1, rho=2.0, last_level=3, tol=0.00001, maxiter=100, \
start_level=1, wavelet='db8', debug_plot=False)
t2 = time()
Fdef = imdef.deform(F)
print "Time:", t2-t1
print "Cost:", info['cost']
x, y = imdef.meshgrid()
Ux, Uy = imdef.deform_map(x, y)
for i in range(Ux.shape[0]):
for j in range(Ux.shape[1]):
print Ux[i,j], Uy[i,j]
print 'mins', Ux.min(), Uy.min()
print 'maxs', Ux.max(), Uy.max()
import matplotlib.pylab as plt
plt.quiver(x, y, Ux, Uy)#, Ux, Uy)
plt.show()
PLOT = False
if PLOT:
import matplotlib.pylab as plt
ag.plot.deformation(F, I, imdef)
def plot_electric_field(self,sp=10,scales = 500000,cont_scale=90,savefigs = False):
fig = plt.figure(figsize=(7.0, 7.0))
xplot = self.x*1e6
yplot = self.y*1e6
X,Y = np.meshgrid(xplot,yplot)
try:
plt.contourf(X,Y,self.mode_field,cont_scale)
except AttributeError:
raise NotImplementedError("interpolate before plotting")
plt.quiver(X[::sp,::sp], Y[::sp,::sp], np.real(self.E[::sp,::sp,0]), np.real(self.E[::sp,::sp,1]),scale = scales,headlength=7)
plt.xlabel(r'$x(\mu m)$')
plt.ylabel(r'$y(\mu m)$')
#plt.title(r'mode$=$'+str(self.mode)+', '+' $n_{eff}=$'+str(self.neff.real)+str(self.neff.imag)+'j')
if savefigs == True:
plt.savefig('mode'+str(self.mode)+'.eps',bbox_inches ='tight')
D = {}
D['X'] = X
D['Y'] = Y
D['Z'] = self.mode_field
D['u'] = np.real(self.E[::sp,::sp,0])
D['v'] = np.real(self.E[::sp,::sp,1])
D['scale'] = scales
D['cont_scale'] = 90
D['sp'] = sp
savemat('mode'+str(self.mode)+'.mat',D)
return None
def plot_field(self,x,y,u=None,v=None,F=None,contour=False,outdir=None,plot='quiver',figname='_field',format='eps'):
outdir = self.set_dir(outdir)
p = 64
if F is None: F=self.calc_F(u,v)
plt.close('all')
plt.figure()
#fig, axes = plt.subplots(nrows=1)
if contour:
plt.hold(True)
plt.contourf(x,y,F)
if plot=='quiver':
plt.quiver(x[::p],y[::p],u[::p],v[::p],scale=0.1)
if plot=='pcolor':
plt.pcolormesh(x[::4],y[::4],F[::4],cmap=plt.cm.Pastel1)
plt.colorbar()
if plot=='stream':
speed = F[::16]
plt.streamplot(x[::16], y[::16], u[::16], v[::16], density=(1,1),color='k')
plt.xlabel('$x$ (a.u.)')
plt.ylabel('$y$ (a.u.)')
plt.savefig(os.path.join(outdir,figname+'.'+format),format=format,dpi=320,bbox_inches='tight')
plt.close()
def handle_2d_plot(
embedding,
kind,
color=None,
xlabel=None,
ylabel=None,
title=None,
show_operations=False,
annot=True,
axis_option=None,
):
"""
Handles the logic to perform a 2d plot in matplotlib.
**Input**
- embedding.md: a `whatlies.Embedding` object to plot
- kind: what kind of plot to make, can be `scatter`, `arrow` or `text`
- color: the color to apply, only works for `scatter` and `arrow`
- xlabel: manually override the xlabel
- ylabel: manually override the ylabel
- title: optional title used for the plot
- show_operations: setting to also show the applied operations, only works for `text`
- axis_option: a string which is passed to `matplotlib.pyplot.axis` function.
"""
if not isinstance(embedding, list):
# It's a single Embedding instance
embedding = [embedding]
vectors = np.array([e.vector for e in embedding])
names = [e.name if show_operations else e.orig for e in embedding]
if kind == "scatter":
if color is None:
color = "steelblue"
plt.scatter(vectors[:, 0], vectors[:, 1], c=color)
if kind == "arrow":
plt.scatter(vectors[:, 0], vectors[:, 1], c="white", s=0.01)
plt.quiver(
np.zeros_like(vectors[:, 0]),
np.zeros_like(vectors[:, 1]),
vectors[:, 0],
vectors[:, 1],
color=color,
angles="xy",
scale_units="xy",
scale=1,
)
if (kind == "text") or annot:
for vec, name in zip(vectors, names):
plt.text(vec[0] + 0.01, vec[1], name)
plt.xlabel("x" if xlabel is None else xlabel)
plt.ylabel("y" if ylabel is None else ylabel)
if title is not None:
plt.title(title)
if axis_option is not None:
plt.axis(axis_option)
def visualize_momentum(m, step=5):
m = m.__array__()
u = m[0, 0:-1:step, 0:-1:step]
v = m[1, 0:-1:step, 0:-1:step]
x = np.linspace(0, 1, u.shape[0])
y = np.linspace(0, 1, u.shape[1])
plt.quiver(x, y, u, v, scale=1)
def potential(x_axis,
y_axis,
cbar,
x_label,
y_label,
cbar_label,
int_pol,
colorMap,
xmin=None,
xmax=None,
ymin=None,
ymax=None,
plot=None):
"""A general plotter allowing for the plotting of a heatmap(primarily used
here for potential function) which takes in relevant data about the
graph. It also allows for the option of overlaying either a quiver or a
streamline plot, or not!
Parameters:
x_axis, y_axis : The corresponding x and y axis data lists of a plot
cbar: The heatmap list data which usually corresponds to x and y axis
x_label, y_label, : The x, y and z label of the graph dtype = string
cbar_label : The colourbar label dtype = string
int_pol: The colour interpolation of the heatmap dtype = integer
colorMap: The style and colour of heatmap dtype = string
xmin, xmax: The minimum and maximum value of the x-axis
ymin, ymax: The minimum and maximum value of the y-axis
plot: "quiver", "stream" allowing for the overlay of quiver or streamline
plot
Returns:
Image : AxesImage
"""
plt.contourf(x_axis, y_axis, cbar, int_pol, cmap=colorMap)
cbar_tag = plt.colorbar()
Z = cbar
plt.xlabel(x_label)
plt.ylabel(y_label)
cbar_tag.set_label(cbar_label, rotation=270)
cbar_tag.set_clim(-1000.0, 1000.0)
E = np.gradient(Z)
E = E / np.sqrt(E[0]**2 + E[1]**2)
if plot is not None:
if plot == "quiver":
print("\nQuiver plot:")
plt.quiver(x_axis, y_axis, E[1], E[0])
if plot == "stream":
print("\nStreamline Plot:")
plt.streamplot(x_axis, y_axis, -E[1], -E[0], color='black')
if xmin is not None and xmax is not None:
plt.xlim(xmin, xmax)
if ymin is not None and ymax is not None:
plt.ylim(ymin, ymax)
plt.show()
def pltShow2d(X, Y, grad):
plt.figure()
plt.quiver(X, Y, -grad[0], -grad[1], angles="xy",
color="#666666") #,headwidth=10,scale=40,color="#444444")
plt.xlim([-2, 2])
plt.ylim([-2, 2])
plt.xlabel('x0')
plt.ylabel('x1')
plt.grid()
plt.legend()
plt.draw()
plt.show()
def deformation(F, I, displacement_field, show_diff=False, show=True):
"""
Plot how a :class:`DisplacementField` applies to a prototype image `F` to qualitatively compare it with `I`.
Especially designed to plot the results of :func:`image_deformation`.
Parameters
----------
F : ndarray
Prototype image.
I : ndarray
Data image. This is included for comparison.
displacement_field : DisplacementField
A displacement field that will be applied to `F` and also plotted by itself.
show_diff : bool
If True, displays the difference map instead of the vector field.
show : bool
Call `pylab.show()` inside the function.
"""
import matplotlib.pylab as plt
assert isinstance(displacement_field, ag.util.DisplacementField)
x, y = displacement_field.meshgrid()
Ux, Uy = displacement_field.deform_map(x, y)
Fdef = displacement_field.deform(F)
d = dict(interpolation='nearest', cmap=plt.cm.gray)
plt.figure(figsize=(7, 7))
plt.subplot(221)
plt.title("Prototype")
plt.imshow(F, **d)
plt.subplot(222)
plt.title("Data image")
plt.imshow(I, **d)
plt.subplot(223)
plt.title("Deformed prototype")
plt.imshow(Fdef, **d)
plt.subplot(224)
if show_diff:
plt.title("Difference")
plt.imshow(Fdef - I, interpolation='nearest')
plt.colorbar()
else:
plt.title("Displacement field")
plt.quiver(np.asarray(y),
np.asarray(-x),
np.asarray(Uy),
np.asarray(-Ux),
linewidth=2.0)
if show:
plt.show()
def plot_current(GLORYS_path, numday):
""" """
# Read data.
U_cur, V_cur, xu, xv, yu, yv = read_current(GLORYS_path, numday)
# Interpolate V over U grid :
V_interp = np.zeros(np.shape(V_cur))
for i in range(np.shape(V_interp)[0]):
for j in range(np.shape(V_interp)[1]):
V_interp[i, j] = interpolate_var(V_cur, xv, yv, xu[i], yu[j])
xu, U_cur = shift_lon(xu, U_cur)
xv, V_interp = shift_lon(xv, V_interp)
pl.quiver(xu, yu, U_cur, V_interp)
pl.show()
def __call__(self, **params):
p = ParamOverrides(self, params)
name = p.plot_template.keys().pop(0)
plot = make_template_plot(p.plot_template,
p.sheet.views.Maps,
p.sheet.xdensity,
p.sheet.bounds,
p.normalize,
name=p.plot_template[name])
fig = plt.figure(figsize=(5, 5))
if plot:
bitmap = plot.bitmap
isint = plt.isinteractive(
) # Temporarily make non-interactive for plotting
plt.ioff() # Turn interactive mode off
plt.imshow(bitmap.image, origin='lower', interpolation='nearest')
plt.axis('off')
for (t, pref, sel, c) in p.overlay:
v = plt.flipud(p.sheet.views.Maps[pref].view()[0])
if (t == 'contours'):
plt.contour(v, [sel, sel], colors=c, linewidths=2)
if (t == 'arrows'):
s = plt.flipud(p.sheet.views.Maps[sel].view()[0])
scale = int(np.ceil(np.log10(len(v))))
X = np.array([x for x in xrange(len(v) / scale)])
v_sc = np.zeros((len(v) / scale, len(v) / scale))
s_sc = np.zeros((len(v) / scale, len(v) / scale))
for i in X:
for j in X:
v_sc[i][j] = v[scale * i][scale * j]
s_sc[i][j] = s[scale * i][scale * j]
plt.quiver(scale * X,
scale * X,
-np.cos(2 * np.pi * v_sc) * s_sc,
-np.sin(2 * np.pi * v_sc) * s_sc,
color=c,
edgecolors=c,
minshaft=3,
linewidths=1)
p.title = '%s overlaid with %s at time %s' % (plot.name, pref,
topo.sim.timestr())
if isint: plt.ion()
p.filename_suffix = "_" + p.sheet.name
self._generate_figure(p)
return fig
def deformation(F, I, displacement_field, show_diff=False, show=True):
"""
Plot how a :class:`DisplacementField` applies to a prototype image `F` to qualitatively compare it with `I`.
Especially designed to plot the results of :func:`image_deformation`.
Parameters
----------
F : ndarray
Prototype image.
I : ndarray
Data image. This is included for comparison.
displacement_field : DisplacementField
A displacement field that will be applied to `F` and also plotted by itself.
show_diff : bool
If True, displays the difference map instead of the vector field.
show : bool
Call `pylab.show()` inside the function.
"""
import matplotlib.pylab as plt
assert isinstance(displacement_field, ag.util.DisplacementField)
x, y = displacement_field.meshgrid()
Ux, Uy = displacement_field.deform_map(x, y)
Fdef = displacement_field.deform(F)
d = dict(interpolation='nearest', cmap=plt.cm.gray)
plt.figure(figsize=(7,7))
plt.subplot(221)
plt.title("Prototype")
plt.imshow(F, **d)
plt.subplot(222)
plt.title("Data image")
plt.imshow(I, **d)
plt.subplot(223)
plt.title("Deformed prototype")
plt.imshow(Fdef, **d)
plt.subplot(224)
if show_diff:
plt.title("Difference")
plt.imshow(Fdef - I, interpolation='nearest')
plt.colorbar()
else:
plt.title("Displacement field")
plt.quiver(np.asarray(y), np.asarray(-x), np.asarray(Uy), np.asarray(-Ux), linewidth=2.0)
if show:
plt.show()
def direction_field():
# get axis limits
ymax = plt.ylim(ymin=0)[1]
xmax = plt.xlim(xmin=0)[1]
nb_points = 30
x = np.linspace(0, xmax, nb_points)
y = np.linspace(0, ymax, nb_points)
# create a grid with the axis limits
X, Y = np.meshgrid(x, y)
# compute growth rate on the grid
U = 1
V = dp_dt(Y, A, K)
# to synchronize the scale of grid between solution plot ft_increase, ft_derease and direction fields
# otherwise, the direction of arrows do not look to be tangential to the solution plot.
V = V * xmax / ymax
# norm of logistics
M = np.sqrt(U**2 + V**2, dtype=np.float64)
# avoid zero division errors
M[M == 0] = 1.
# normalize each arrow
U /= M
V /= M
# plot the direction field for the range of parameters
# define a grid and compute direction at each point
Q = plt.quiver(X, Y, U, V, M, pivot='mid', cmap=plt.cm.jet)
def plot_neuron_arrows(self, colorrange=[0, 2],visualize=False):
""" Plot arrows from each neuron center and color with strength """
best_actions = np.argmax(self.weights_, 2)
action_strength = np.max(self.weights_, 2)
dX = np.cos(2 * np.pi / 8 * best_actions)
dY = np.sin(2 * np.pi / 8 * best_actions)
plt.figure(figsize=(5.5, 5.5))
plt.subplot(aspect='equal')
arrows = plt.quiver(self.centers_[0], self.centers_[1], dX, dY, action_strength, scale=10, headwidth=5,
cmap='autumn_r', clim=colorrange)
if visualize:
positions = np.array(self.pos_history_)
plt.plot(positions[:, 0], positions[:, 1], 'ko-', alpha=0.2,markersize=5)
plt.xlim(-0.05, 1.05)
plt.ylim(-0.05, 1.05)
self._plot_dots()
from mpl_toolkits.axes_grid1 import make_axes_locatable
divider = make_axes_locatable(plt.gca())
cax = divider.append_axes("right", "5%", pad="3%")
cbar = plt.colorbar(arrows, cax=cax)
cbar.ax.set_ylabel('highest weight value')
plt.tight_layout()
plt.draw()
def gradient_descent(f, init_x, lr=0.01, step_num=100):
x = init_x
x_history = []
for i in range(step_num):
x_history.append(x.copy())
grad = numerical_gradient(f, x)
plt.quiver(x[0],
x[1],
-grad[0],
-grad[1],
angles="xy",
color="#666666")
x -= lr * grad
return x, np.array(x_history)
def vector_field2d(barycenters, vector_field, N, figure=None):
dn = 1. / N
N = complex(0, N)
xmin, xmax = barycenters[:, 0].min(), barycenters[:, 0].max()
ymin, ymax = barycenters[:, 1].min(), barycenters[:, 1].max()
vector_field *= dn / sqrt((vector_field ** 2).sum(1).max())
grid = mgrid[xmin + dn*(xmax-xmin):xmax:N, ymin + dn*(ymax-ymin):ymax:N]
z1 = [griddata(barycenters, z0, grid.transpose((1,2,0)), method='linear') for z0 in vector_field.T]
from matplotlib import pylab
X, Y = grid
VX, VY = z1
if figure == None:
fig = pylab.figure(figsize=(10,10))
pylab.quiver(X, Y, VX, VY, sqrt(VX ** 2 + VY ** 2), scale=1, figure=figure)
pylab.axis([xmin, xmax, ymin, ymax])
def plot_quiver(self, n):
""" Plot the curve and the vector field at a particular timestep """
self.new_figure()
x,y = self.split_array(self.Q[n])
u,v = self.split_array(self.U[n])
mag = [np.sqrt(u[i]**2+v[i]**2) for i in xrange(np.size(u))]
norm = plt.normalize(np.min(mag), np.max(mag))
C = [plt.cm.jet(norm(m)) for m in mag]
plt.plot(x,y)
plt.quiver(x,y,-u,-v,color=C)
#plt.plot(*self.split_array(self.qA),color='grey',ls=':')
plt.plot(*self.split_array(self.qB),color='grey',ls=':')
def handle_2d_plot(
embedding,
kind,
color=None,
xlabel=None,
ylabel=None,
show_operations=False,
annot=False,
):
"""
Handles the logic to perform a 2d plot in matplotlib.
**Input**
- embedding.md: a `whatlies.Embedding` object to plot
- kind: what kind of plot to make, can be `scatter`, `arrow` or `text`
- color: the color to apply, only works for `scatter` and `arrow`
- xlabel: manually override the xlabel
- ylabel: manually override the ylabel
- show_operations: setting to also show the applied operations, only works for `text`
"""
name = embedding.name if show_operations else embedding.orig
if kind == "scatter":
if color is None:
color = "steelblue"
plt.scatter([embedding.vector[0]], [embedding.vector[1]], c=color)
if kind == "arrow":
plt.scatter([embedding.vector[0]], [embedding.vector[1]],
c="white",
s=0.01)
plt.quiver(
[0],
[0],
[embedding.vector[0]],
[embedding.vector[1]],
color=color,
angles="xy",
scale_units="xy",
scale=1,
)
plt.text(embedding.vector[0] + 0.01, embedding.vector[1], name)
if (kind == "text") or annot:
plt.text(embedding.vector[0] + 0.01, embedding.vector[1], name)
plt.xlabel("x" if not xlabel else xlabel)
plt.ylabel("y" if not ylabel else ylabel)
def plot_field(self,
x,
y,
u=None,
v=None,
F=None,
contour=False,
outdir=None,
plot='quiver',
figname='_field',
format='eps'):
outdir = self.set_dir(outdir)
p = 64
if F is None: F = self.calc_F(u, v)
plt.close('all')
plt.figure()
#fig, axes = plt.subplots(nrows=1)
if contour:
plt.hold(True)
plt.contourf(x, y, F)
if plot == 'quiver':
plt.quiver(x[::p], y[::p], u[::p], v[::p], scale=0.1)
if plot == 'pcolor':
plt.pcolormesh(x[::4], y[::4], F[::4], cmap=plt.cm.Pastel1)
plt.colorbar()
if plot == 'stream':
speed = F[::16]
plt.streamplot(x[::16],
y[::16],
u[::16],
v[::16],
density=(1, 1),
color='k')
plt.xlabel('$x$ (a.u.)')
plt.ylabel('$y$ (a.u.)')
plt.savefig(os.path.join(outdir, figname + '.' + format),
format=format,
dpi=320,
bbox_inches='tight')
plt.close()
def on_means(limits, count, mean_vx, mean_vy):
if normalize:
length = np.sqrt(mean_vx**2 + mean_vy**2)
mean_vx = mean_vx / length
mean_vy = mean_vy / length
x_centers = self.bin_centers(x, limits[0], shape=shape[0])
y_centers = self.bin_centers(y, limits[1], shape=shape[1])
Y, X = np.meshgrid(x_centers, y_centers) # , indexing='ij')
count = count.flatten()
mask = count >= min_count
kwargs['alpha'] = kwargs.get('alpha', 0.7)
plt.quiver(X.flatten()[mask],
Y.flatten()[mask],
mean_vx.flatten()[mask],
mean_vy.flatten()[mask], **kwargs)
if show:
plt.show()
return
def navigation_map(self, K=25):
plt.figure(figsize=(5.5, 5.5))
plt.subplot(aspect='equal')
X, Y = np.meshgrid(np.linspace(0, 1, K + 1), np.linspace(0, 1, K + 1))
best_actions = np.zeros((K + 1, K + 1))
for i in range(K + 1):
for j in range(K + 1):
best_actions[i, j] = np.argmax(self.get_Qvalue_(X[i, j], Y[i, j]))
dX = np.cos(2 * np.pi / self.n_actions_ * best_actions)
dY = np.sin(2 * np.pi / self.n_actions_ * best_actions)
plt.quiver(X, Y, dX, dY, scale=20)
self._plot_dots()
plt.draw()
def quiver(self,coordinate,attribute):
'''
Quiver plot the attribute of the body.chord
Input
-----
coordinates - the coordinates of the quiver plot. Standard coordinates
of the body: 'geometry'.
attribute - body parameter that needs to plotted. Ex. 'geometry'
Returns
-------
quiver plot with attributes plotted at given coordinates. Figure not
configured.
'''
plt.quiver(self.__dict__[coordinate][0], self.__dict__[coordinate][1],
self.__dict__[attribute][0], self.__dict__[attribute][1])
def on_means(limits, count, mean_vx, mean_vy):
if normalize:
length = np.sqrt(mean_vx**2 + mean_vy**2)
mean_vx = mean_vx / length
mean_vy = mean_vy / length
x_centers = self.bin_centers(x, limits[0], shape=shape[0])
y_centers = self.bin_centers(y, limits[1], shape=shape[1])
Y, X = np.meshgrid(y_centers, x_centers) # , indexing='ij')
count = count.flatten()
mask = count >= min_count
kwargs['alpha'] = kwargs.get('alpha', 0.7)
plt.quiver(X.flatten()[mask],
Y.flatten()[mask],
mean_vx.flatten()[mask],
mean_vy.flatten()[mask],
**kwargs)
if show:
plt.show()
return
def _plot_vector_field(self, resolution):
"""
Plot vector field.
Arguments
resolution
Resolution of plot
"""
x_mesh, y_mesh, ode_x, ode_y = self._get_ode_values(resolution)
# scale vector field
hyp = np.hypot(ode_x, ode_y)
hyp[hyp==0] = 1.
ode_x /= hyp
ode_y /= hyp
plt.quiver(
x_mesh, y_mesh,
ode_x, ode_y,
pivot='mid', color='lightgray')
def draw_gradient_2d():
x0 = np.arange(-2, 2.5, 0.25)
x1 = np.arange(-2, 2.5, 0.25)
X, Y = np.meshgrid(x0, x1)
X = X.flatten()
Y = Y.flatten()
grad = numerical_gradient(function_2, np.array([X, Y]))
plt.figure()
plt.quiver(X, Y, -grad[0], -grad[1], angles="xy", color="#666666")
plt.xlim([-2, 2])
plt.ylim([-2, 2])
plt.xlabel('x0')
plt.ylabel('x1')
plt.grid()
plt.legend()
plt.draw()
plt.show()
def vector_field2d(barycenters, vector_field, N, figure=None):
dn = 1. / N
N = complex(0, N)
xmin, xmax = barycenters[:, 0].min(), barycenters[:, 0].max()
ymin, ymax = barycenters[:, 1].min(), barycenters[:, 1].max()
vector_field *= dn / sqrt((vector_field**2).sum(1).max())
grid = mgrid[xmin + dn * (xmax - xmin):xmax:N,
ymin + dn * (ymax - ymin):ymax:N]
z1 = [
griddata(barycenters, z0, grid.transpose((1, 2, 0)), method='linear')
for z0 in vector_field.T
]
from matplotlib import pylab
X, Y = grid
VX, VY = z1
if figure == None:
fig = pylab.figure(figsize=(10, 10))
pylab.quiver(X, Y, VX, VY, sqrt(VX**2 + VY**2), scale=1, figure=figure)
pylab.axis([xmin, xmax, ymin, ymax])
def __call__(self, **params):
p=ParamOverrides(self,params)
name=p.plot_template.keys().pop(0)
plot=make_template_plot(p.plot_template,
p.sheet.views.Maps, p.sheet.xdensity,p.sheet.bounds,
p.normalize,name=p.plot_template[name])
fig = plt.figure(figsize=(5,5))
if plot:
bitmap=plot.bitmap
isint=plt.isinteractive() # Temporarily make non-interactive for plotting
plt.ioff() # Turn interactive mode off
plt.imshow(bitmap.image,origin='lower',interpolation='nearest')
plt.axis('off')
for (t,pref,sel,c) in p.overlay:
v = plt.flipud(p.sheet.views.Maps[pref].view()[0])
if (t=='contours'):
plt.contour(v,[sel,sel],colors=c,linewidths=2)
if (t=='arrows'):
s = plt.flipud(p.sheet.views.Maps[sel].view()[0])
scale = int(np.ceil(np.log10(len(v))))
X = np.array([x for x in xrange(len(v)/scale)])
v_sc = np.zeros((len(v)/scale,len(v)/scale))
s_sc = np.zeros((len(v)/scale,len(v)/scale))
for i in X:
for j in X:
v_sc[i][j] = v[scale*i][scale*j]
s_sc[i][j] = s[scale*i][scale*j]
plt.quiver(scale*X, scale*X, -np.cos(2*np.pi*v_sc)*s_sc,
-np.sin(2*np.pi*v_sc)*s_sc, color=c,
edgecolors=c, minshaft=3, linewidths=1)
p.title='%s overlaid with %s at time %s' %(plot.name,pref,topo.sim.timestr())
if isint: plt.ion()
p.filename_suffix="_"+p.sheet.name
self._generate_figure(p)
return fig
def plot_motion_field_quiver(UV, geodata=None, step=15):
"""Function to plot a precipitation field witha a colorbar.
Parameters
----------
UV : array-like
Array of shape (2, m,n) containing the input motion field.
geodata : dictionary
step : int
Returns:
----------
ax : fig axes
Figure axes. Needed if one wants to add e.g. text inside the plot.
"""
# prepare X Y coordinates
if geodata is not None:
X, Y = np.meshgrid(
np.arange(geodata['x1'] / 1000, geodata['x2'] / 1000),
np.arange(geodata['y1'] / 1000, geodata['y2'] / 1000))
else:
X, Y = np.meshgrid(np.arange(UV.shape[2]), np.arange(UV.shape[1]))
# reduce number of vectors to plot
UV_ = UV[:, 0:UV.shape[1]:step, 0:UV.shape[2]:step]
X_ = X[0:UV.shape[1]:step, 0:UV.shape[2]:step]
Y_ = Y[0:UV.shape[1]:step, 0:UV.shape[2]:step]
plt.quiver(X_, Y_, UV_[0, :, :], -UV_[1, :, :], pivot='tip')
axes = plt.gca()
if geodata is None:
axes.xaxis.set_ticklabels([])
axes.yaxis.set_ticklabels([])
return axes
def _plot_vector_field(self, resolution):
"""
Plot vector field.
Arguments
resolution
Resolution of plot
"""
x_mesh, y_mesh, ode_x, ode_y = self._get_ode_values(resolution)
# scale vector field
hyp = np.hypot(ode_x, ode_y)
hyp[hyp == 0] = 1.
ode_x /= hyp
ode_y /= hyp
plt.quiver(x_mesh,
y_mesh,
ode_x,
ode_y,
pivot='mid',
color='lightgray')
def test_east_w1_lonlat(grid, target_points, connectivity):
"""
Test computation of edge integrals using an eastward vector field
"""
nedge = grid.getNumberOfEdges()
ntarget = target_points.shape[0]
lon = connectivity['lon']
lat = connectivity['lat']
edge_node_connect = connectivity['edge_node_connect']
# set the components
u1 = numpy.ones((nedge, ), numpy.float64) # east
u2 = numpy.zeros((nedge, ), numpy.float64)
ue_integrated = getIntegralsInLonLat(lon,
lat,
edge_node_connect,
u1,
u2,
w1=True)
vi = VectorInterp()
vi.setGrid(grid)
vi.buildLocator(numCellsPerBucket=100)
vi.findPoints(target_points, tol2=1.e-10)
vects = vi.getEdgeVectors(ue_integrated, placement=1)
error = numpy.sum(numpy.fabs(vects[:, 1] / (vects[:, 0] + EPS))) / ntarget
print(f'test_east_w1_lonlat: error = {error}')
assert (error < 0.06)
if False:
from matplotlib import pylab
pylab.quiver(target_points[:, 0], target_points[:, 1], vects[:, 0],
vects[:, 1])
pylab.title('test_east_w1_lonlat')
pylab.show()
def gradient(
func, x0_max=2.5, x0_min=-2., x0_step=0.25,
x1_max=2.5, x1_min=-2., x1_step=0.25,
x_max=2., x_min=-2., y_max=2., y_min=-2.):
x0_elements = np.arange(x0_min, x0_max, x0_step)
x1_elements = np.arange(x1_min, x1_max, x1_step)
X, Y = np.meshgrid(x0_elements, x1_elements)
X = X.flatten()
Y = Y.flatten()
y = differentiations.numerical_gradient(func, np.array([X, Y]))
plt.figure()
plt.quiver(X, Y, y[0], y[1], angles="xy",color="#666666")
plt.xlim([x_min, x_max])
plt.ylim([y_min, y_max])
plt.xlabel('x0')
plt.ylabel('x1')
plt.grid()
plt.legend()
plt.draw()
plt.show()
def quiver(grid, u_field_name, v_field_name, **kwargs):
fig = plt.figure()
plt.axes().set_aspect('equal')
u, v = grid.get_cell_fields(u_field_name, v_field_name)
cell_nodes = grid.cell_nodes
plt.quiver(cell_nodes[:, :, 0], cell_nodes[:, :, 1], u, v)
if kwargs.get('show_grid', False):
plt.plot(cell_nodes[:, :, 0], cell_nodes[:, :, 1], '-', color='black')
plt.plot(np.transpose(cell_nodes[:, :, 0]), np.transpose(cell_nodes[:, :, 1]), '-', color='black')
if kwargs.get('mark_cell_centers', False):
plt.plot(cell_nodes[:, :, 0], cell_nodes[:, :, 1], 'o', color='black')
if kwargs.get('show', False):
plt.show()
f = BytesIO()
plt.savefig(f)
return f
def main():
F = np.load("faces.npz")['F']
F = F[:, :, ::-1]
testing = ag.io.load_example('mnist')
testing = testing[:, ::-1]
settings = dict(origin='lower', interpolation='nearest', cmap=plt.cm.gray)
for d in [9]:
print("Digit:", d)
imdef, info = ag.ml.bernoulli_model(testing[0], F[d], calc_costs=True)
print(info['iterations_per_level'])
print(-info['loglikelihoods'][-1] - info['logpriors'][-1])
subject = testing[1]
#imdef = ag.util.DisplacementFieldWavelet(testing[0].shape)
#imdef.u[0][0,0] = 0.6
x, y = imdef.get_x(subject.shape)
Ux, Uy = imdef.deform_map(x, y)
print('U-max:', Ux.max(), Uy.max())
#print(imdef.u)
im = imdef.deform(subject)
plt.figure(figsize=(7, 7))
plt.subplot(221)
plt.imshow(subject, **settings)
plt.subplot(222)
plt.imshow(im, **settings)
plt.subplot(223)
plt.imshow(F[d].sum(axis=0), **settings)
plt.subplot(224)
plt.quiver(y, x, Uy, Ux)
#plt.plot(-(info['loglikelihoods']+info['logpriors']))
plt.show()
def visualize():
x = np.arange(3, 7., 0.15)
y = np.arange(3, 7., 0.5)
xx, yy = np.meshgrid(x, y)
d = 1.
start = np.array([4.75, 4.75])
# Location of points
# 1 2
# 0 3
loc = np.array(([start[0], start[1]], [start[0], start[1] + d],
[start[0] + d, start[1] + d], [start[0] + d, start[1]]))
psi = np.zeros_like(xx)
vxx = np.zeros_like(xx)
vyy = np.zeros_like(xx)
gamma = np.array([1., -1., -1., 1.])
for i in np.arange(0, 4):
p, vx, vy = vortex_flow(xx, yy, loc[i, 0], loc[i, 1], gamma=gamma[i])
psi += p
vxx += vx
vyy += vy
# plt.contour(xx, yy, vxx, 100)
# plt.contourf(xx, yy, vyy, 100)
# plt.contourf(xx, yy, psi, 100)
plt.contour(xx, yy, np.sqrt(vxx**2 + vyy**2), 100)
plt.quiver(xx, yy, vxx, vyy)
plt.scatter(loc[:, 0], loc[:, 1])
plt.show()
return
def __init__(self, cells, t, **kwargs):
"""
Creates a new flux map
:param cells: The cells to be used
:param t: The current time step
:param kwargs: Keyword arguments for plt.quiver
"""
self.cells = cells
# get position vector
p = cmf.cell_positions(cells)
# get flux vector
f = cmf.cell_flux_directions(cells, t)
self.t = t
a = numpy.array
self.quiver = plt.quiver(a(p.X), a(p.Y), a(f.X), a(f.Y), **kwargs)
def main():
F = np.load("faces.npz")['F']
F = F[:,:,::-1]
testing = ag.io.load_example('mnist')
testing = testing[:,::-1]
settings = dict(origin='lower', interpolation='nearest', cmap=plt.cm.gray)
for d in [9]:
print("Digit:", d)
imdef, info = ag.ml.bernoulli_model(testing[0], F[d], calc_costs=True)
print(info['iterations_per_level'])
print(-info['loglikelihoods'][-1] - info['logpriors'][-1])
subject = testing[1]
#imdef = ag.util.DisplacementFieldWavelet(testing[0].shape)
#imdef.u[0][0,0] = 0.6
x, y = imdef.get_x(subject.shape)
Ux, Uy = imdef.deform_map(x, y)
print('U-max:',Ux.max(), Uy.max())
#print(imdef.u)
im = imdef.deform(subject)
plt.figure(figsize=(7,7))
plt.subplot(221)
plt.imshow(subject, **settings)
plt.subplot(222)
plt.imshow(im, **settings)
plt.subplot(223)
plt.imshow(F[d].sum(axis=0), **settings)
plt.subplot(224)
plt.quiver(y, x, Uy, Ux)
#plt.plot(-(info['loglikelihoods']+info['logpriors']))
plt.show()
def twoD_ArrayQuiver(X, Y, Z):
"""
Represent a 2D array with arrows
Parameters
----------
X : numpy.ndarray
メッシュのX座標
Y : numpy.ndarray
メッシュのY座標
Z : numpy.ndarray
メッシュのZ座標
"""
plt.figure()
plt.quiver(X, Y, -Z[0], -Z[1], angles='xy', color='#666666')
plt.xlim([-2, 2])
plt.ylim([-2, 2])
plt.xlabel('x0')
plt.ylabel('x1')
plt.grid()
plt.legend()
plt.draw()
plt.show()
def main(F, coef, filename=None, test_index=1):
#Fmax = F.max()
#F *= 1.0
#F = np.clip(F, 0.01, 1.0 - 0.01)
#print("Normalizing with {0}".format(Fmax))
#testing = ag.io.load_example('mnist')
testing = np.load('digits.npz')['nines']
testing = testing[:,::-1]
settings = dict(origin='lower', interpolation='nearest', cmap=None, vmin=0.0, vmax=1.0)
feat = int(sys.argv[1])
costs = []
for d in [9]:
print("Digit:", d)
imdef, info = ag.ml.bernoulli_model(F[d], testing[test_index], calc_costs=True, tol=1e-4)
#imdef, info = ag.ml.imagedef(F[d], testing[test_index], coef=1e-2, stepsize=0.3, calc_costs=True)
print(info['iterations_per_level'])
print("Cost:", -info['loglikelihoods'][-1] - info['logpriors'][-1])
subject = ag.features.bedges(testing[test_index])[:,:,feat].astype(np.float64)
#subject = testing[1]
#imdef = ag.util.DisplacementFieldWavelet(testing[0].shape)
#imdef.u[0][0,0] = 0.6
x, y = imdef.get_x(subject.shape)
Ux, Uy = imdef.deform_map(x, y)
print('U-max:',Ux.max(), Uy.max())
#print(imdef.u)
imf = imdef.deform(subject)
canon_nine = np.load('canonical-digits.npz')['F'][9]
#im = imdef.deform(F[d,feat])
im = imdef.deform(canon_nine)
costs.append(-info['loglikelihoods'][-1] - info['loglikelihoods'][-1])
if PLOT:
plt.figure(figsize=(11,7))
plt.subplot(231)
plt.imshow(subject, **settings)
plt.subplot(232)
plt.imshow(imf, **settings)
plt.subplot(233)
#plt.imshow(F[d,feat], **settings)
plt.imshow(F[d,feat], **settings)
plt.subplot(234)
plt.quiver(y, x, Uy, Ux, scale=1.0)
plt.subplot(235)
plt.imshow(testing[test_index], **settings)
plt.subplot(236)
plt.imshow(im, **settings)
plt.colorbar()
#plt.plot(-(info['loglikelihoods']+info['logpriors']))
print("RESULT Digit: {0}".format(np.argmin(costs)))
if PLOT:
if filename:
plt.savefig(filename)
else:
plt.show()
g = lambda y: -(y - W/2.)
#f = lambda x: np.sin(x/175. + 100)
for i in xrange(0,N):
for j in xrange(0,N):
U[i,j] = f(p*i)
V[i,j] = g(p*j)
X[i,j] = p*i
Y[i,j] = p*j
im.new_figure()
#plt.figure()
#plt.axis("equal")
plt.quiver(X,Y,U,V,color='k',scale_units='inches', scale=3000)
qx,qy = im.split_array(q)
plt.plot(qx,qy,color="k", lw=3)
plt.axis((0,W,0,W))
plt.savefig("misc/outer_field.pdf",bbox_inches='tight')
#no build the quiver for the inner metric plot
u = [f(x) for x in qx]
v = [g(y) for y in qy]
ut = []
vt = []
xt = []
yt = []
for i in np.arange(0,201,2):
def tangent_line(f, x):
d = numerical_gradient(f, x)
print(d)
y = f(x) - d * x
return lambda t: d * t + y
if __name__ == '__main__':
x0 = np.arange(-2, 2.5, 0.25)
x1 = np.arange(-2, 2.5, 0.25)
X, Y = np.meshgrid(x0, x1)
X = X.flatten()
Y = Y.flatten()
grad = numerical_gradient(function_2, np.array([X, Y]))
plt.figure()
plt.quiver(X, Y, -grad[0], -grad[1], angles="xy",
color="#666666") #,headwidth=10,scale=40,color="#444444")
plt.xlim([-2, 2])
plt.ylim([-2, 2])
plt.xlabel('x0')
plt.ylabel('x1')
plt.grid()
plt.legend()
plt.draw()
plt.show()
import numpy as np
import matplotlib.pylab as plt
images = np.load('nines.npz')['images']
im = images[0]
im = im[::-1,:]
plt.figure(figsize=(14,6))
plt.subplot(121)
plt.xlabel('x')
plt.ylabel('y')
plt.imshow(im, interpolation='nearest', origin='lower')
plt.subplot(122)
plt.quiver(im, np.zeros(im.shape))
plt.show()
def symimage(*args,**kwargs):
I = plp.Image()
T = plp.Tools()
#fig = plt.figure()
Dmhd = plp.pload(319,w_dir='/Users/bhargavvaidya/pyPLUTO-wdir/M30a055b5_data/')
Data = args[0]
sclf = kwargs.get('scalefact',1.0)
if kwargs.get('log',False)==True:
var = np.log10(sclf*Data.__getattribute__(args[1]))
else:
var = sclf*Data.__getattribute__(args[1])
x1 = Data.x1
x2 = Data.x2
plt.axis([-x1.max(),x1.max(),0.0,x2.max()])
plt.title(kwargs.get('title',"Title"),size=kwargs.get('size'))
plt.xlabel(kwargs.get('label1',"Xlabel"),size=kwargs.get('size'),labelpad=6)
plt.ylabel(kwargs.get('label2',"Ylabel"),size=kwargs.get('size'),labelpad=6)
xm,ym = np.meshgrid(x1.T,x2.T)
xmc = T.congrid(xm,2*([kwargs.get('arrows')[1]]),method='linear')
ymc = T.congrid(ym,2*([kwargs.get('arrows')[1]]),method='linear')
v1c = T.congrid(Data.v1.T,2*([kwargs.get('arrows')[1]]),method='linear')
v2c = T.congrid(Data.v2.T,2*([kwargs.get('arrows')[1]]),method='linear')
v1cn,v2cn = v1c/np.sqrt(v1c**2+v2c**2),v2c/np.sqrt(v1c**2+v2c**2)
if kwargs.get('ysym',False) == True:
ysymvar = np.flipud(var)
plc1=plt.pcolormesh(-x1[::-1],x2,ysymvar.T,vmin=kwargs.get('vmin',np.min(var)),vmax=kwargs.get('vmax',np.max(var)))
plc2=plt.pcolormesh(x1,x2,var.T,vmin=kwargs.get('vmin',np.min(var)),vmax=kwargs.get('vmax',np.max(var)))
if kwargs.get('cbar',(False,''))[0] == True:
plcol=plt.colorbar(orientation=kwargs.get('cbar')[1])
if kwargs.get('arrows',(False,20))[0]==True:
plq1=plt.quiver(xmc,ymc,v1cn,v2cn,color='k')
plq2=plt.quiver(-xmc,ymc,-v1cn,v2cn,color='k')
if kwargs.get('flines',(False,[3.0,6.0,10.0,15.0],[0.001,0.001,0.001,0.001]))[0]==True:
x0arr = kwargs.get('flines')[1]
y0arr = kwargs.get('flines')[2]
for i in range(np.size(x0arr)):
flmhd = I.field_line(Dmhd.b1,Dmhd.b2,Dmhd.x1,Dmhd.x2,Dmhd.dx1,Dmhd.dx2,x0arr[i],y0arr[i])
Qxmhd = flmhd.get('qx')
Qymhd = flmhd.get('qy')
fl =I.field_line(Data.b1,Data.b2,Data.x1,Data.x2,Data.dx1,Data.dx2,x0arr[i],y0arr[i])
Qx= fl.get('qx')
Qy= fl.get('qy')
plfl1=plt.plot(Qx,Qy,color=kwargs.get('colors','r'),ls=kwargs.get('ls','-'),lw=kwargs.get('lw',2.0))
plfl2=plt.plot(-Qx,Qy,color=kwargs.get('colors','r'),ls=kwargs.get('ls','-'),lw=kwargs.get('lw',2.0))
plfl3=plt.plot(Qxmhd,Qymhd,color=kwargs.get('colors','w'),ls=kwargs.get('ls','--'),lw=kwargs.get('lw',2.0))
plfl4=plt.plot(-Qxmhd,Qymhd,color=kwargs.get('colors','w'),ls=kwargs.get('ls','--'),lw=kwargs.get('lw',2.0))
if kwargs.get('xsym',False) == True:
xsymvar = np.fliplr(var)
plc1=plt.pcolormesh(x1,-x2[::-1],xsymvar.T,vmin=kwargs.get('vmin',np.min(var)),vmax=kwargs.get('vmax',np.max(var)))
plc2=plt.pcolormesh(x1,x2,var.T,vmin=kwargs.get('vmin',np.min(var)),vmax=kwargs.get('vmax',np.max(var)))
if kwargs.get('cbar',(False,''))[0] == True:
plcol=plt.colorbar(orientation=kwargs.get('cbar')[1])
if kwargs.get('arrows',(False,20))[0]==True:
plq1=plt.quiver(xmc,ymc,v1cn,v2cn,color='g')
plq2=plt.quiver(xmc,-ymc,v1cn,-v2cn,color='g')
if kwargs.get('flines',(False,[3.0,6.0,10.0,15.0],[0.001,0.001,0.001,0.001]))[0]==True:
x0arr = kwargs.get('flines')[1]
y0arr = kwargs.get('flines')[2]
for i in range(np.size(x0arr)):
flmhd = I.field_line(Dmhd.b1,Dmhd.b2,Dmhd.x1,Dmhd.x2,Dmhd.dx1,Dmhd.dx2,x0arr[i],y0arr[i])
Qxmhd = flmhd.get('qx')
Qymhd = flmhd.get('qy')
fl =I.field_line(Data.b1,Data.b2,Data.x1,Data.x2,Data.dx1,Data.dx2,x0arr[i],y0arr[i])
Qx= fl.get('qx')
Qy= fl.get('qy')
plfl1= plt.plot(Qx,Qy,color=kwargs.get('colors','r'),ls=kwargs.get('ls','-'),lw=kwargs.get('lw',2.0))
plfl2= plt.plot(Qx,-Qy,color=kwargs.get('colors','r'),ls=kwargs.get('ls','-'),lw=kwargs.get('lw',2.0))
plfl1= plt.plot(Qxmhd,Qymhd,color=kwargs.get('colors','w'),ls=kwargs.get('ls','--'),lw=kwargs.get('lw',2.0))
plfl2= plt.plot(Qxmhd,-Qymhd,color=kwargs.get('colors','w'),ls=kwargs.get('ls','--'),lw=kwargs.get('lw',2.0))
if kwargs.get('fullsym',False) == True:
ysymvar = np.flipud(var)
plc1=plt.pcolormesh(-x1[::-1],x2,ysymvar.T,vmin=kwargs.get('vmin',np.min(var)),vmax=kwargs.get('vmax',np.max(var)))
xsymvar = np.fliplr(var)
plc2=plt.pcolormesh(x1,-x2[::-1],xsymvar.T,vmin=kwargs.get('vmin',np.min(var)),vmax=kwargs.get('vmax',np.max(var)))
plc3=plt.pcolormesh(-x1,-x2,var.T,vmin=kwargs.get('vmin',np.min(var)),vmax=kwargs.get('vmax',np.max(var)))
plc4=plt.pcolormesh(x1,x2,var.T,vmin=kwargs.get('vmin',np.min(var)),vmax=kwargs.get('vmax',np.max(var)))
if kwargs.get('cbar',(False,''))[0] == True:
plcol=plt.colorbar(orientation=kwargs.get('cbar')[1])
if kwargs.get('arrows',(False,20))[0]==True:
plq1=plt.quiver(-xmc,ymc,-v1cn,v2cn,color='w')
plq2=plt.quiver(xmc,-ymc,v1cn,-v2cn,color='w')
plq3=plt.quiver(xmc,ymc,v1cn,v2cn,color='w')
plq4=plt.quiver(-xmc,-ymc,-v1cn,-v2cn,color='w')
if kwargs.get('flines',(False,[2.0,4.0,7.0,13.0],[0.001,0.001,0.001,0.001]))[0]==True:
x0arr = kwargs.get('flines')[1]
y0arr = kwargs.get('flines')[2]
for i in range(np.size(x0arr)):
fl =I.field_line(Data.b1,Data.b2,Data.x1,Data.x2,Data.dx1,Data.dx2,x0arr[i],y0arr[i])
Qx= fl.get('qx')
Qy= fl.get('qy')
plfl1=plt.plot(Qx,Qy,color=kwargs.get('colors','r'),ls=kwargs.get('ls','-'),lw=kwargs.get('lw',2.0))
plfl2=plt.plot(-Qx,Qy,color=kwargs.get('colors','r'),ls=kwargs.get('ls','-'),lw=kwargs.get('lw',2.0))
plfl3=plt.plot(Qx,-Qy,color=kwargs.get('colors','r'),ls=kwargs.get('ls','-'),lw=kwargs.get('lw',2.0))
plfl4=plt.plot(-Qx,-Qy,color=kwargs.get('colors','r'),ls=kwargs.get('ls','-'),lw=kwargs.get('lw',2.0))
return [plc1,plc2,plcol,plq1,plq2,plfl1,plfl2,plfl3,plfl4]
def interpolate_sparse_vectors(x, y, u, v, domain_size, function="inverse",
k=20, epsilon=None, nchunks=5):
"""Interpolation of sparse motion vectors to produce a dense field of motion
vectors.
Parameters
----------
x : array-like
x coordinates of the sparse motion vectors
y : array-like
y coordinates of the sparse motion vectors
u : array_like
u components of the sparse motion vectors
v : array_like
v components of the sparse motion vectors
domain_size : tuple
size of the domain of the dense motion field [px]
function : string
the radial basis function, based on the Euclidian norm, d.
default : inverse
available : nearest, inverse, gaussian
k : int or "all"
the number of nearest neighbors used to speed-up the interpolation
If set equal to "all", it employs all the sparse vectors
default : 20
epsilon : float
adjustable constant for gaussian or inverse functions
default : median distance between sparse vectors
nchunks : int
split the grid points in n chunks to limit the memory usage during the
interpolation
default : 5
Returns
-------
X : array-like
grid
Y : array-like
grid
UV : array-like
Three-dimensional array (2,domain_size[0],domain_size[1])
containing the dense U, V motion fields.
"""
testinterpolation = False
# make sure these are vertical arrays
x = x[:,None]
y = y[:,None]
u = u[:,None]
v = v[:,None]
points = np.column_stack((x, y))
if len(domain_size)==1:
domain_size = (domain_size, domain_size)
# generate the grid
xgrid = np.arange(domain_size[1])
ygrid = np.arange(domain_size[0])
X, Y = np.meshgrid(xgrid, ygrid)
grid = np.column_stack((X.ravel(), Y.ravel()))
U = np.zeros(grid.shape[0])
V = np.zeros(grid.shape[0])
# create cKDTree object to represent source grid
if k is not "all":
k = np.min((k, points.shape[0]))
tree = scipy.spatial.cKDTree(points)
# split grid points in n chunks
subgrids = np.array_split(grid, nchunks, 0)
subgrids = [x for x in subgrids if x.size > 0]
# loop subgrids
i0=0
for i,subgrid in enumerate(subgrids):
idelta = subgrid.shape[0]
if function.lower() == "nearest":
# find indices of the nearest neighbors
_, inds = tree.query(subgrid, k=1)
U[i0:(i0+idelta)] = u.flatten()[inds]
V[i0:(i0+idelta)] = v.flatten()[inds]
else:
if k == "all":
d = scipy.spatial.distance.cdist(points, subgrid, 'euclidean').transpose()
inds = np.arange(u.size)[None,:]*np.ones((subgrid.shape[0],u.size)).astype(int)
else:
# find indices of the k-nearest neighbors
d, inds = tree.query(subgrid, k=k)
# the bandwidth
if epsilon is None:
dpoints = scipy.spatial.distance.pdist(points, 'euclidean')
epsilon = np.median(dpoints)
# the interpolation weights
if function.lower() == "inverse":
w = 1.0/np.sqrt((d/epsilon)**2 + 1)
elif function.lower() == "gaussian":
w = np.exp(-0.5*(d/epsilon)**2)
else:
raise ValueError("unknown radial fucntion %s" % function)
U[i0:(i0+idelta)] = np.sum(w * u.flatten()[inds], axis=1) / np.sum(w, axis=1)
V[i0:(i0+idelta)] = np.sum(w * v.flatten()[inds], axis=1) / np.sum(w, axis=1)
i0 += idelta
# reshape back to original size
U = U.reshape(domain_size[0], domain_size[1])
V = V.reshape(domain_size[0], domain_size[1])
UV = np.stack([U, V])
if testinterpolation:
import matplotlib.pylab as plt
step=15
UV_ = UV[:, 0:UV.shape[1]:step, 0:UV.shape[2]:step]
X_ = X[0:UV.shape[1]:step, 0:UV.shape[2]:step]
Y_ = Y[0:UV.shape[1]:step, 0:UV.shape[2]:step]
plt.quiver(X_, np.flipud(Y_), UV_[0,:,:], -UV_[1,:,:])
plt.quiver(x, np.flipud(y), u, -v, color="red")
plt.show()
return X, Y, UV
def drainage_plot(
mg,
surface="topographic__elevation",
receivers=None,
proportions=None,
surf_cmap="gray",
quiver_cmap="viridis",
title="Drainage Plot",
):
if isinstance(surface, six.string_types):
colorbar_label = surface
else:
colorbar_label = "topographic_elevation"
imshow_grid(mg, surface, cmap=surf_cmap, colorbar_label=colorbar_label)
if receivers is None:
receivers = mg.at_node["flow__receiver_node"]
if proportions is None:
if "flow__receiver_proportions" in mg.at_node:
proportions = mg.at_node["flow__receiver_proportions"]
else:
receivers = np.asarray(receivers)
if receivers.ndim == 1:
receivers = np.expand_dims(receivers, axis=1)
nreceievers = receivers.shape[-1]
propColor = plt.get_cmap(quiver_cmap)
for j in range(nreceievers):
rec = receivers[:, j]
is_bad = rec == -1
xdist = -0.8 * (mg.x_of_node - mg.x_of_node[rec])
ydist = -0.8 * (mg.y_of_node - mg.y_of_node[rec])
if proportions is None:
proportions = np.ones_like(receivers, dtype=float)
is_bad[proportions[:, j] == 0.0] = True
xdist[is_bad] = np.nan
ydist[is_bad] = np.nan
prop = proportions[:, j] * 256.0
lu = np.floor(prop)
colors = propColor(lu.astype(int))
shape = (mg.number_of_nodes, 1)
plt.quiver(
mg.x_of_node.reshape(shape),
mg.y_of_node.reshape(shape),
xdist.reshape(shape),
ydist.reshape(shape),
color=colors,
angles="xy",
scale_units="xy",
scale=1,
zorder=3,
)
# Plot differen types of nodes:
o, = plt.plot(
mg.x_of_node[mg.status_at_node == CORE_NODE],
mg.y_of_node[mg.status_at_node == CORE_NODE],
"b.",
label="Core Nodes",
zorder=4,
)
fg, = plt.plot(
mg.x_of_node[mg.status_at_node == FIXED_VALUE_BOUNDARY],
mg.y_of_node[mg.status_at_node == FIXED_VALUE_BOUNDARY],
"c.",
label="Fixed Gradient Nodes",
zorder=5,
)
fv, = plt.plot(
mg.x_of_node[mg.status_at_node == FIXED_GRADIENT_BOUNDARY],
mg.y_of_node[mg.status_at_node == FIXED_GRADIENT_BOUNDARY],
"g.",
label="Fixed Value Nodes",
zorder=6,
)
c, = plt.plot(
mg.x_of_node[mg.status_at_node == CLOSED_BOUNDARY],
mg.y_of_node[mg.status_at_node == CLOSED_BOUNDARY],
"r.",
label="Closed Nodes",
zorder=7,
)
node_id = np.arange(mg.number_of_nodes)
flow_to_self = receivers[:, 0] == node_id
fts, = plt.plot(
mg.x_of_node[flow_to_self],
mg.y_of_node[flow_to_self],
"kx",
markersize=6,
label="Flows To Self",
zorder=8,
)
ax = plt.gca()
ax.legend(
labels=[
"Core Nodes",
"Fixed Gradient Nodes",
"Fixed Value Nodes",
"Closed Nodes",
"Flows To Self",
],
handles=[o, fg, fv, c, fts],
numpoints=1,
loc="center left",
bbox_to_anchor=(1.7, 0.5),
)
sm = plt.cm.ScalarMappable(cmap=propColor, norm=plt.Normalize(vmin=0, vmax=1))
sm._A = []
cx = plt.colorbar(sm)
cx.set_label("Proportion of Flow")
plt.title(title)
U[j,-1] = UVP[loc_glob[j*Nx+Nx-1,N]]
V[j,-1] = UVP[loc_glob[j*Nx+Nx-1,N]+dofs]
for i in range(Nx):
#Leftmost point:
U[-1,i] = UVP[loc_glob[Nx*(Ny-1)+i, N*(N-1)]]
V[-1,i] = UVP[loc_glob[Nx*(Ny-1)+i, N*(N-1)]+dofs]
#General point:
U[j,i] = UVP[loc_glob[Nx*j+i,0]]
V[j,i] = UVP[loc_glob[Nx*j+i,0]+dofs]
#Right- and topmost corner:
U[-1,-1] = UVP[loc_glob[-1,-1]]
V[-1,-1] = UVP[loc_glob[-1,-1]+dofs]
pl.quiver(X_el, Y_el, U, V, scale=10.0)
plt.plot( X_el[0, patches:(idim-patches)], Y_el[0, patches:(idim-patches)], 'b')
pl.xlabel('$x$')
pl.ylabel('$y$')
pl.axis('image')
'''
# PRESSURE PLOT:
plt.subplot(122)
ax = fig.add_subplot(122, projection='3d')
for K in range(num_el):
ax.plot_wireframe( X[K, 1:-1, 1:-1], Y[K, 1:-1, 1:-1], UVP[loc_glob_p[K]+2*dofs].reshape((N-2,N-2)))
'''
pl.show()
"""
Plot of wind speed, wind vectors and surface pressure
By Richard Essery
"""
import numpy as np
import matplotlib.pylab as plt
plt.figure(figsize=(10, 10))
P = np.loadtxt('Psurf.txt')
U = np.loadtxt('Uwind.txt')
V = np.loadtxt('Vwind.txt')
W = np.sqrt(U**2 + V**2)
# wind speed as an image with a colour bar
plt.imshow(W, cmap='PuBu', origin='lower')
cbar = plt.colorbar(shrink=0.6)
cbar.set_label('wind speed (m s$^{-1}$)', fontsize=16, rotation=270)
# surface pressure as a contour plot with 4 hPa spacing
levels = 960 + 4*np.arange(20)
cs = plt.contour(P, colors='black', levels=levels)
plt.clabel(cs, fmt='%d')
# wind vectors
plt.quiver(U,V)
plt.xticks([])
plt.yticks([])
plt.show()
# TIME TO SOLVE:
####################
print "Done solving..."
P = UVP[2*N**2:]
P = np.reshape ( P, (N-2,N-2) )
U1 = np.reshape ( U1, (N,N) )
U2 = np.reshape ( U2, (N,N) )
t2 = time.time()-t1
print "Total time: ", t2
############################
# PLOTTING THE SHIT:
############################
# Quiverplot
fig = plt.figure(1)
plt.subplot(121)
pl.quiver(X, Y, U1, U2, pivot='middle', headwidth=4, headlength=6)
pl.xlabel('$x$')
pl.ylabel('$y$')
pl.axis('image')
# Pressureplot
plt.subplot(122)
ax = fig.add_subplot(122, projection='3d')
ax.plot_wireframe(X_p, Y_p, P)#-np.sin(2*np.pi*(X**2 + Y**2)))
plt.xlabel('$x$')
plt.ylabel('$y$')
plt.show()
break
print "Time to solve: ", time.time()-t1
counter += 1
print "error : ", error
################################
# PLOTTING:
################################
# Making global X and Y coordinates
fig = plt.figure(1)
# QUIVERPLOT #
P = UVP[2*dofs:]
for i in range(num_el):
X,Y = gh.gordon_hall_grid(gm.gammas(i,1),gm.gammas(i,2),gm.gammas(i,3),gm.gammas(i,4), xis, xis)
plt.subplot(121)
pl.quiver(X,Y, U1[loc_glob[i]].reshape( (N,N) ), U2[loc_glob[i]].reshape( (N,N) ))
pl.xlabel('$x$')
pl.ylabel('$y$')
pl.axis('image')
# PRESSURE PLOT:
plt.subplot(122)
ax = fig.add_subplot(122, projection='3d')
for i in range(num_el):
X,Y = gh.gordon_hall_grid(gm.gammas(i,1),gm.gammas(i,2),gm.gammas(i,3),gm.gammas(i,4), xis, xis)
ax.plot_wireframe(X[1:-1,1:-1],Y[1:-1,1:-1], P[loc_glob_p[i]].reshape( (N-2,N-2)))
pl.show()
else:
return np.sum(x**2, axis=1)
def tangent_line(f, x):
d = numerical_gradient(f, x)
print(d)
y = f(x) - d*x
return lambda t: d*t + y
if __name__ == '__main__':
x0 = np.arange(-2, 2.5, 0.25)
x1 = np.arange(-2, 2.5, 0.25)
X, Y = np.meshgrid(x0, x1)
X = X.flatten()
Y = Y.flatten()
grad = numerical_gradient(function_2, np.array([X, Y]) )
plt.figure()
plt.quiver(X, Y, -grad[0], -grad[1], angles="xy",color="#666666")#,headwidth=10,scale=40,color="#444444")
plt.xlim([-2, 2])
plt.ylim([-2, 2])
plt.xlabel('x0')
plt.ylabel('x1')
plt.grid()
plt.legend()
plt.draw()
plt.show()
y = f(x) - d * x
return lambda t: d * t + y #lambda:引数で関数を返す
if __name__ == '__main__': #気にしない
x0 = np.arange(-2, 2, 0.25)
x1 = np.arange(-2, 2, 0.25)
X, Y = np.meshgrid(x0, x1)
X = X.flatten() #flatten:多次元配列を一次元に
Y = Y.flatten()
grad = numerical_gradient(function_2, np.array([X, Y]).T).T
plt.figure()
plt.quiver(X, Y, -grad[0], -grad[1], angles="xy", color="#666666")
plt.xlim([-2, 2])
plt.ylim([-2, 2])
plt.xlabel('x0')
plt.ylabel('x1')
plt.grid()
plt.draw()
plt.show()
_______________________________________________________________________________
#勾配法
#勾配が最も小さくなる方向に少しずつ移動する：勾配降下法
#x=x-η*(∂f/∂x)
#η：学習率
#勾配降下法の実装
for i in range(len(u[q])):
if i == 0:
levcoefs[i] += (u[q][i]**2 ).sum()
else:
for alpha in range(3):
levcoefs[i] += (u[q][i][alpha]**2 ).sum()
#print levcoefs
from itertools import product
shape = im1.shape
xs = np.empty(shape + (2,))
for x0, x1 in product(range(shape[0]), range(shape[1])):
xs[x0,x1] = np.array([float(x0)/(shape[0]), float(x1)/shape[1]])
defmap = ag.ml.imagedefw.deform_map(xs, u)
face2 = ag.ml.imagedefw.deform(face, u)
d = dict(origin='lower', interpolation='nearest', cmap=plt.cm.gray)
plt.figure(figsize=(9,9))
plt.subplot(221)
plt.imshow(face, **d)
plt.subplot(222)
plt.imshow(face2, **d)
plt.subplot(223)
plt.plot(levcoefs)
#plt.pcolor(u[1][0])
#plt.colorbar()
plt.subplot(224)
plt.quiver(xs[:,:,1], xs[:,:,0], defmap[:,:,1], defmap[:,:,0])
plt.show()
def singleVector():
dx = 0.05
x = np.arange(-1,1+dx,dx)
y = np.arange(-1,1+dx,dx)
X,Y = np.meshgrid(x,y)
x2 = np.reshape(X,[-1])
y2 = np.reshape(Y,[-1])
xo = np.array([0.])
yo = np.array([0.])
uo = np.array([1.])
vo = np.array([0.])
ob = np.concatenate([uo,vo])
ob = np.reshape(ob,[ob.size,1])
K1 = sqExp(xo,xo,xo,xo,0.1)
Ki1 = np.linalg.inv(K1)
Ks1 = sqExp(x2,y2,xo,yo,0.1)
u1 = np.dot(Ks1,np.dot(Ki1,uo))
u1 = np.reshape(u1,[x.size,-1])
v1 = np.dot(Ks1,np.dot(Ki1,vo))
v1 = np.reshape(v1,[x.size,-1])
K2 = compute_K(xo,xo,0.1,1)
Ks2 = compute_Ks(xo,xo,x2,y2,0.1,1)
Ki2 = np.linalg.inv(K2)
f2 = getMean(Ks2,Ki2,ob)
u2 = np.reshape(f2[0:f2.size/2],[x.size,-1])
v2 = np.reshape(f2[f2.size/2:],[x.size,-1])
K3 = compute_K(xo,xo,0.1,2)
Ks3 = compute_Ks(xo,xo,x2,y2,0.1,2)
Ki3 = np.linalg.inv(K3)
f3 = getMean(Ks3,Ki3,ob)
u3 = np.reshape(f3[0:f3.size/2],[x.size,-1])
v3 = np.reshape(f3[f3.size/2:],[x.size,-1])
figH = 20
figW = 9.5
bottom = [0.69,0.36,0.03]
height = 0.27
left = 0.085
width = 0.88
FS = 38
FS2 = 32
scal = 15.
fig = pl.figure(figsize=(figW,figH))
plot=fig.add_axes([left,bottom[0],width,height])
cs=plot.quiver(x,y,u1,v1,scale=scal)
pl.quiver(xo,yo,uo,vo,scale=scal,color='r')
plot.tick_params(axis='both',which='major',labelsize=FS2)
plot.set_title('Isotropic kernel',fontsize = FS)
plot.set_xlim([-0.3,0.3])
plot.set_ylim([-0.3,0.3])
plot.set_xticks([-0.3,-0.2,-0.1,0.,0.1,0.2,0.3])
plot.set_yticks([-0.2,-0.1,0.0,0.1,0.2])
plot=fig.add_axes([left,bottom[1],width,height])
cs=plot.quiver(x,y,u2,v2,scale=scal)
pl.quiver(xo,yo,uo,vo,scale=scal,color='r')
plot.tick_params(axis='both',which='major',labelsize=FS2)
plot.set_title('Divergence-free kernel',fontsize = FS)
plot.set_xlim([-0.3,0.3])
plot.set_ylim([-0.3,0.3])
plot.set_xticks([-0.3,-0.2,-0.1,0.,0.1,0.2,0.3])
plot.set_yticks([-0.2,-0.1,0.0,0.1,0.2])
plot=fig.add_axes([left,bottom[2],width,height])
cs=plot.quiver(x,y,u3,v3,scale=scal)
pl.quiver(xo,yo,uo,vo,scale=scal,color='r')
plot.tick_params(axis='both',which='major',labelsize=FS2)
plot.set_title('Curl-free kernel',fontsize = FS)
plot.set_xlim([-0.3,0.3])
plot.set_ylim([-0.3,0.3])
plot.set_xticks([-0.3,-0.2,-0.1,0.,0.1,0.2,0.3])
plot.set_yticks([-0.2,-0.1,0.0,0.1,0.2])
pl.savefig('plots/one_obs.png', bbox_inches=0)
for i in xrange(Nres):
for j in xrange(Nres):
r = np.array([Xarray[i], Yarray[j]])
phi2[i, j] = Phi(r, rp2, q2)
E = Electric(r, rp2, q2)
E2x[i, j], E2y[i, j] = E / np.linalg.norm(E)
# CONSTRUCCION DE CAMPO E Y POTENCIAL PHI, TOTAL
phi_tot = phi1 + phi2
# Incializacion Campo Electrico
Ex_tot = np.ones((Nres, Nres))
Ey_tot = np.ones((Nres, Nres))
# Calculo Potencial Electrico y Campo Electrico Total
for i in xrange(Nres):
for j in xrange(Nres):
E = np.array([E1x[i, j] + E2x[i, j], E1y[i, j] + E2y[i, j]])
E = E / np.linalg.norm(E)
Ex_tot[i, j], Ey_tot[i, j] = E
# Grafica de equipotenciales
plt.contour(X, Y, phi_tot, 100)
# Grafica de lineas de campo
plt.quiver(X, Y, Ey_tot, Ex_tot)
# Limites del eje X
plt.xlim((0, 10))
# Limites del eje Y
plt.ylim((0, 10))
plt.legend()
plt.show()
help='Which velocity field to plot.',
choices=['obstacle', 'goal', 'all'])
args, unknown = parser.parse_known_args()
fig, ax = plt.subplots()
# Plot field.
X, Y = np.meshgrid(np.linspace(-WALL_OFFSET, WALL_OFFSET, 30),
np.linspace(-WALL_OFFSET, WALL_OFFSET, 30))
U = np.zeros_like(X)
V = np.zeros_like(X)
for i in range(len(X)):
for j in range(len(X[0])):
velocity = get_velocity(np.array([X[i, j], Y[i, j]]), args.mode)
U[i, j] = velocity[0]
V[i, j] = velocity[1]
plt.quiver(X, Y, U, V, units='width')
# Plot environment.
ax.add_artist(plt.Circle(CYLINDER_POSITION1, CYLINDER_RADIUS,
color='gray'))
ax.add_artist(plt.Circle(CYLINDER_POSITION2, CYLINDER_RADIUS,
color='gray'))
plt.plot([-WALL_OFFSET, WALL_OFFSET], [-WALL_OFFSET, -WALL_OFFSET], 'k')
plt.plot([-WALL_OFFSET, WALL_OFFSET], [WALL_OFFSET, WALL_OFFSET], 'k')
plt.plot([-WALL_OFFSET, -WALL_OFFSET], [-WALL_OFFSET, WALL_OFFSET], 'k')
plt.plot([WALL_OFFSET, WALL_OFFSET], [-WALL_OFFSET, WALL_OFFSET], 'k')
# Plot a simple trajectory from the start position.
# Uses Euler integration.
dt = 0.01
x = START_POSITION
def main():
#import amitgroup.io.mnist
#images, _ = read('training', '/local/mnist', [9])
#shifted = np.zeros(images[0].shape)
#shifted[:-3,:] = images[0,3:,:]
im1, im2 = np.zeros((32, 32)), np.zeros((32, 32))
wl_name = "db2"
levels = len(pywt.wavedec(range(32), wl_name)) - 1
scriptNs = map(len, pywt.wavedec(range(32), wl_name, level=levels))
if 0:
images = np.load("data/nines.npz")['images']
im1[:28,:28] = images[0]
im2[:28,:28] = images[2]
else:
im1 = ag.io.load_image('data/Images_0', 45)
im2 = ag.io.load_image('data/Images_1', 23)
im1 = im1[::-1,:]
im2 = im2[::-1,:]
A = 2
if 1:
# Blur images
im1b = im1#ag.math.blur_image(im1, 2)
im2b = im2#ag.math.blur_image(im2, 2)
show_costs = True
imgdef, info = ag.ml.imagedef(im1b, im2b, rho=3.0, calc_costs=show_costs)
print info['iterations_per_level']
if PLOT and show_costs:
logpriors = -info['logpriors']
loglikelihoods = -info['loglikelihoods']
np.savez('logs', logpriors=logpriors, loglikelihoods=loglikelihoods)
plotfunc = plt.semilogy
plt.figure(figsize=(8,12))
plt.subplot(211)
costs = logpriors + loglikelihoods
plotfunc(costs, label="J")
plotfunc(loglikelihoods, label="log likelihood")
plt.legend()
plt.subplot(212)
plotfunc(logpriors, label="log prior")
plt.legend()
plt.show()
im3 = imgdef.deform(im1)
if PLOT:
d = dict(origin='lower', interpolation='nearest', cmap=plt.cm.gray)
plt.figure(figsize=(9,9))
plt.subplot(221)
plt.title("Prototype")
plt.imshow(im1, **d)
plt.subplot(222)
plt.title("Original")
plt.imshow(im2, **d)
plt.subplot(223)
plt.title("Deformed")
plt.imshow(im3, **d)
plt.subplot(224)
if 0:
plt.title("Deformed")
plt.imshow(im2-im3, **d)
plt.colorbar()
else:
plt.title("Deformation map")
x, y = imgdef.get_x(im1.shape)
Ux, Uy = imgdef.deform_map(x, y)
plt.quiver(y, x, Uy, Ux)
plt.show()
elif 1:
plt.figure(figsize=(14,6))
plt.subplot(121)
plt.title("F")
plt.imshow(im1, origin='lower')
plt.subplot(122)
plt.title("I")
plt.imshow(im2, origin='lower')
plt.show()
import pickle
if TEST:
im3correct = pickle.load(open('im3.p', 'rb'))
passed = (im3 == im3correct).all()
print "PASSED:", ['NO', 'YES'][passed]
print ((im3 - im3correct)**2).sum()
else:
pickle.dump(im3, open('im3.p', 'wb'))
def drainage_plot(mg,
surface='topographic__elevation',
receivers=None,
proportions=None,
surf_cmap='gray',
quiver_cmap='viridis',
title = 'Drainage Plot'):
if isinstance(surface, six.string_types):
colorbar_label = surface
else:
colorbar_label = 'topographic_elevation'
imshow_node_grid(mg, surface, cmap=surf_cmap, colorbar_label=colorbar_label)
if receivers is None:
try:
receivers = mg.at_node['flow__receiver_nodes']
if proportions is None:
try:
proportions = mg.at_node['flow__receiver_proportions']
except:
pass
except:
receivers = np.reshape(mg.at_node['flow__receiver_node'],(mg.number_of_nodes,1))
nreceievers = int(receivers.size/receivers.shape[0])
propColor=plt.get_cmap(quiver_cmap)
for j in range(nreceievers):
rec = receivers[:,j]
is_bad = rec == -1
xdist = -0.8*(mg.node_x-mg.node_x[rec])
ydist = -0.8*(mg.node_y-mg.node_y[rec])
if proportions is None:
proportions = np.ones_like(receivers, dtype=float)
is_bad[proportions[:,j]==0.]=True
xdist[is_bad] = np.nan
ydist[is_bad] = np.nan
prop = proportions[:,j]*256.
lu = np.floor(prop)
colors = propColor(lu.astype(int))
shape = (mg.number_of_nodes, 1)
plt.quiver(mg.node_x.reshape(shape), mg.node_y.reshape(shape),
xdist.reshape(shape), ydist.reshape(shape),
color=colors,
angles='xy',
scale_units='xy',
scale=1,
zorder=3)
# Plot differen types of nodes:
o, = plt.plot(mg.node_x[mg.status_at_node == CORE_NODE], mg.node_y[mg.status_at_node == CORE_NODE], 'b.', label='Core Nodes', zorder=4)
fg, = plt.plot(mg.node_x[mg.status_at_node == FIXED_VALUE_BOUNDARY], mg.node_y[mg.status_at_node == FIXED_VALUE_BOUNDARY], 'c.', label='Fixed Gradient Nodes', zorder=5)
fv, = plt.plot(mg.node_x[mg.status_at_node == FIXED_GRADIENT_BOUNDARY], mg.node_y[mg.status_at_node ==FIXED_GRADIENT_BOUNDARY], 'g.', label='Fixed Value Nodes', zorder=6)
c, = plt.plot(mg.node_x[mg.status_at_node == CLOSED_BOUNDARY], mg.node_y[mg.status_at_node ==CLOSED_BOUNDARY], 'r.', label='Closed Nodes', zorder=7)
node_id = np.arange(mg.number_of_nodes)
flow_to_self = receivers[:,0]==node_id
fts, = plt.plot(mg.node_x[flow_to_self], mg.node_y[flow_to_self], 'kx', markersize=6, label = 'Flows To Self', zorder=8)
ax = plt.gca()
ax.legend(labels = ['Core Nodes', 'Fixed Gradient Nodes', 'Fixed Value Nodes', 'Closed Nodes', 'Flows To Self'],
handles = [o, fg, fv, c, fts], numpoints=1, loc='center left', bbox_to_anchor=(1.7, 0.5))
sm = plt.cm.ScalarMappable(cmap=propColor, norm=plt.Normalize(vmin=0, vmax=1))
sm._A = []
cx = plt.colorbar(sm)
cx.set_label('Proportion of Flow')
plt.title(title)
plt.show()
import sympy as sp
import numpy as np
import matplotlib.pylab as plt
x, v = sp.symbols('x v')
f = sp.Function('f')(x, v)
expr = -x - v
f = sp.lambdify((x, v), expr)
x = np.linspace(-1, 1, 10)
v = np.linspace(-1, 1, 10)
x, v = np.meshgrid(x, v)
result = f(x, v)
scale = np.sqrt(1 / (v ** 2 + result ** 2))
plt.quiver(x, v, v * scale, result * scale)
plt.show()
def twoVectors(sigma = 0.2):
#
figH = 18
figW = 13
bottom = [0.68,0.35,0.02]
height = 0.3
left = [0.07,0.56]
width = 0.4
FS = 42
FS2 = 32
scal = 25.
#
dx = 0.05
x = np.arange(-1,1+dx,dx)
y = np.arange(-1,1+dx,dx)
X,Y = np.meshgrid(x,y)
Xs = np.reshape(X,[X.size])
Ys = np.reshape(Y,[Y.size])
# observation 1, at origin
xo1 = 0.
yo1 = 0.
uo1 = 1.
vo1 = 0.
# observation 2, varying direction, intensity and location
# xo2 = np.array([0.07,0.14,0.28])
# yo2 = np.array([0.07,0.14,0.28])
xo2 = np.array([0.07,0.28])
yo2 = np.array([0.07,0.28])
angle = np.array([45,90,180])
absVel = np.array([0.5,1,2])
#
for i in range(angle.size):
fig = pl.figure(figsize=(figW,figH))
jk=1
filename = 'plots/2_vectors_angle_'+str(angle[i])+'.png'
for j in range(absVel.size):
uo2 = absVel[j]*np.cos(np.deg2rad(angle[i]))
vo2 = absVel[j]*np.sin(np.deg2rad(angle[i]))
uo = np.array([uo1,uo2])
vo = np.array([vo1,vo2])
ob = np.concatenate([uo,vo])
ob = np.reshape(ob,[ob.size,1])
for k in range(xo2.size):
xo = np.array([xo1,xo2[k]])
yo = np.array([yo1,yo2[k]])
# compute kernel
K = compute_K(xo,yo,sigma)
Ki = np.linalg.inv(K)
Ks = compute_Ks(xo,yo,Xs,Ys,sigma)
f = getMean(Ks,Ki,ob)
uf = np.reshape(f[:f.size/2],[y.size,-1])
vf = np.reshape(f[f.size/2:],[y.size,-1])
# plot
print jk
print i,j,k
# plot = fig.add_subplot(3,3,jk)
plot=fig.add_axes([left[k],bottom[j],width,height])
plot.quiver(X,Y,uf,vf,scale=scal)
pl.quiver(xo,yo,uo,vo,scale=scal,color='r')
plot.set_xlim([-0.6,0.8])
plot.set_ylim([-0.6,0.8])
plot.set_xticks([-0.6,-0.3,0.,0.3,0.6])
plot.set_yticks([-0.5,-0.2,0.1,0.4,0.7])
# titleText = plot.text(0.7, 1.05, '',transform=plot.transAxes,
# fontsize=FS,fontweight='bold')
titleText1 = plot.text(0.05, 0.9, '',transform=plot.transAxes,
fontsize=FS2,fontweight='bold',color='b')
titleText2 = plot.text(0.03, 0.03, '',transform=plot.transAxes,
fontsize=FS2,fontweight='bold',color='b')
titleText3 = plot.text(0.7, 0.03, '',transform=plot.transAxes,
fontsize=FS2,fontweight='bold',color='b')
titleText3.set_text('$\Theta='+str(angle[i])+'$')
titleText2.set_text('$|v_2|='+str(absVel[j])+'$')
dx2= np.round(np.sqrt(np.square(xo1-xo2[k])+np.square(yo1-yo2[k])),decimals=2)
titleText1.set_text('$|x_2-x_1|='+str(dx2)+'$')
plot.tick_params(axis='both',which='major',labelsize=FS2)
jk+=1
pl.savefig(filename, bbox_inches=0)
def mag_forces(*args,**kwargs):
Tool = plp.Tools()
Fc = jana.Force()
I = plp.Image()
D = args[0]
#Lorentz_Force_Dict = Fc.Lorentz(D)
StForce_Dict = Fc.Pressure(D)
Flr = StForce_Dict['Fp_r']
Flz = StForce_Dict['Fp_z']
#Flr = Lorentz_Force_Dict['Fl_r']
#Flz = Lorentz_Force_Dict['Fl_z']
spx= kwargs.get('spacingx',40)
spy= kwargs.get('spacingx',80)
nxr = D.n1/spx
nyr = D.n2/spy
nshape = ([nxr,nyr])
b1new = Tool.congrid(D.b1,nshape)
b2new = Tool.congrid(D.b2,nshape)
x1new = Tool.congrid(D.x1,([nxr]))
x2new = Tool.congrid(D.x2,([nyr]))
Flr_p = Tool.congrid(Flr,nshape)
Flz_p = Tool.congrid(Flz,nshape)
magpol_p = np.sqrt(Flr_p*Flr_p + Flz_p*Flz_p)
#plt.quiver(x1new,x2new,(Flr_p/magpol_p).T,(Flz_p/magpol_p).T,color=kwargs.get('color','k'),headwidth=kwargs.get('hw',3))
#FOR THE PARALLEL FORCES WE HAVE TO PROJECT THE Fl TO THE Bp
if kwargs.get('Para',False)==True:
phi = np.arctan2(b2new,b1new)
f2 = plt.figure(num=2)
theta = np.zeros(phi.shape)
alpha = np.arctan2(Flz_p,Flr_p)
for i in range(phi.shape[0]):
for j in range(phi.shape[1]):
if (alpha[i,j] > phi[i,j]):
theta[i,j] = (alpha[i,j] - phi[i,j])
else:
theta[i,j] = 2.0*np.pi + (alpha[i,j] - phi[i,j])
magFlpara = magpol_p*np.cos(theta)
Flpara_r_p = magFlpara*np.cos(phi)
Flpara_z_p = magFlpara*np.sin(phi)
magFlpara_p = np.sqrt(Flpara_r_p*Flpara_r_p + Flpara_z_p*Flpara_z_p)
f1 = plt.figure(num=1)
ax1 = f1.add_subplot(111)
ax1.set_aspect(1.0)
plt.quiver(x1new,x2new,(Flpara_r_p/magFlpara_p).T,(Flpara_z_p/magFlpara_p).T,color=kwargs.get('color','k'),headwidth=kwargs.get('hw',5),width=kwargs.get('width',0.001),scale_units='xy')
I.myfieldlines(D,[3.0,6.0,10.0,15.0],[0.01,0.01,0.01,0.01],stream=True,colors='k')
#FOR THE PERPENDICULAR FORCES WE HAVE TO PROJECT THE Fl TO THE Bp
if kwargs.get('Perp',False)==True:
phi = np.arctan2(b2new,b1new)
theta = np.zeros(phi.shape)
Flper_r_p=np.zeros(phi.shape)
Flper_z_p=np.zeros(phi.shape)
magFlper=np.zeros(phi.shape)
alpha = np.arctan2(Flz_p,Flr_p)
for i in range(phi.shape[0]):
for j in range(phi.shape[1]):
if (alpha[i,j] > phi[i,j]):
theta[i,j] = (alpha[i,j] - phi[i,j])
magFlper[i,j] = magpol_p[i,j]*np.sin(theta[i,j])
Flper_r_p[i,j] = -1.0*magFlper[i,j]*np.sin(phi[i,j])
Flper_z_p[i,j] = magFlper[i,j]*np.cos(phi[i,j])
else:
theta[i,j] = 2.0*np.pi + (alpha[i,j] - phi[i,j])
magFlper[i,j] = magpol_p[i,j]*np.sin(theta[i,j])
Flper_r_p[i,j] = -1.0*magFlper[i,j]*np.sin(phi[i,j])
Flper_z_p[i,j] = magFlper[i,j]*np.cos(phi[i,j])
magFlper_p = np.sqrt(Flper_r_p*Flper_r_p + Flper_z_p*Flper_z_p)
f1 = plt.figure(num=1)
ax2 = f1.add_subplot(111)
ax2.set_aspect(1.0)
plt.quiver(x1new,x2new,(Flper_r_p/magFlper_p).T,(Flper_z_p/magFlper_p).T,color=kwargs.get('color','k'),headwidth=kwargs.get('hw',5),width=kwargs.get('width',0.001),scale_units='xy')
I.myfieldlines(D,[3.0,6.0,10.0,15.0],[0.01,0.01,0.01,0.01],stream=True,colors='k')
