def f(x, interp_mode):
xgr = xg.ravel()
ygr = yg.ravel()
if interp_mode == 'linear':
interp = LinearTriInterpolator(triang, x)
else:
interp = CubicTriInterpolator(triang, x)
return interp(xgr, ygr).reshape(grid_pts)
def plot_GRAD(UC,
nodes,
elements,
Ngra,
plt_type="contourf",
levels=12,
savefigs=False,
title="Solution:"):
"""Plots the gradient of a user defined scalar field using triangulation.
Parameters
----------
UC : ndarray (float)
Array with the scalar field.
nodes : ndarray (float)
Array with number and nodes coordinates:
`number coordX coordY`
elements : ndarray (int)
Array with the node number for the nodes that correspond to each
element.
"""
tri = mesh2tri(nodes, elements)
tcu = CubicTriInterpolator(tri, UC)
(DuDx, DuDy) = tcu.gradient(tri.x, tri.y)
tri_plot(tri,
DuDx,
Ngra,
title=r'$\frac{{\partial }}{{\partial x}}$',
figtitle="x gradient",
levels=levels,
plt_type=plt_type,
savefigs=savefigs,
filename="dudx.pdf")
tri_plot(tri,
DuDy,
Ngra,
title=r'$\frac{{\partial }}{{\partial y}}$',
figtitle="y gradient",
levels=levels,
plt_type=plt_type,
savefigs=savefigs,
filename="dudy.pdf")
return DuDx, DuDy
def _setup_Te_interpolator(self, kind='linear'):
"""setup interpolator for measured Te
:param string kind: default is 'linear', can be 'cubic' or 'linear'
"""
self._Delaunay = Delaunay(self._points)
self._triangulation = triangulation.Triangulation(
self._Y, self._X, triangles=self._Delaunay.simplices)
self._trifinder = DelaunayTriFinder(self._Delaunay,
self._triangulation)
if kind == 'linear':
self._kind = kind
self._Te_interpolator = LinearTriInterpolator(
self._triangulation, self._Te, trifinder=self._trifinder)
elif kind == 'cubic':
self._kind = kind
self._Te_interpolator = CubicTriInterpolator(
self._triangulation, self._Te, trifinder=self._trifinder)
else:
raise ValueError('Wrong kind of interpolation: {0}. Available \
options are "linear" and "cubic".'.format(kind))
def __draw_plot(self):
freqCentre = self.spinCentre.GetValue()
freqBw = self.spinBw.GetValue()
freqMin = (freqCentre - freqBw) / 1000.
freqMax = (freqCentre + freqBw) / 1000.
coords = {}
for timeStamp in self.spectrum:
spectrum = self.spectrum[timeStamp]
sweep = [
yv for xv, yv in spectrum.items() if freqMin <= xv <= freqMax
]
if len(sweep):
peak = max(sweep)
try:
location = self.location[timeStamp]
except KeyError:
continue
coord = tuple(location[0:2])
if coord not in coords:
coords[coord] = peak
else:
coords[coord] = (coords[coord] + peak) / 2
x = []
y = []
z = []
for coord, peak in coords.items():
x.append(coord[1])
y.append(coord[0])
z.append(peak)
self.extent = (min(x), max(x), min(y), max(y))
self.xyz = (x, y, z)
xi, yi = numpy.meshgrid(
numpy.linspace(min(x), max(x), self.IMAGE_SIZE),
numpy.linspace(min(y), max(y), self.IMAGE_SIZE))
if self.plotMesh or self.plotCont:
triangle = Triangulation(x, y)
interp = CubicTriInterpolator(triangle, z, kind='geom')
zi = interp(xi, yi)
if self.plotMesh:
self.plot = self.axes.pcolormesh(xi,
yi,
zi,
cmap=self.colourMap)
self.plot.set_zorder(1)
if self.plotCont:
contours = self.axes.contour(xi,
yi,
zi,
linewidths=0.5,
colors='k')
self.axes.clabel(contours,
inline=1,
fontsize='x-small',
gid='clabel',
zorder=3)
if self.plotHeat:
image = create_heatmap(x, y, self.IMAGE_SIZE, self.IMAGE_SIZE / 10,
self.colourHeat)
heatMap = self.axes.imshow(image,
aspect='auto',
extent=self.extent)
heatMap.set_zorder(2)
if self.plotPoint:
self.axes.plot(x, y, 'wo')
for posX, posY, posZ in zip(x, y, z):
points = self.axes.annotate('{0:.2f}dB'.format(posZ),
xy=(posX, posY),
xytext=(-5, 5),
ha='right',
textcoords='offset points')
points.set_zorder(3)
if matplotlib.__version__ >= '1.3':
effect = patheffects.withStroke(linewidth=2,
foreground="w",
alpha=0.75)
for child in self.axes.get_children():
child.set_path_effects([effect])
if self.plotAxes:
self.axes.set_axis_on()
else:
self.axes.set_axis_off()
self.canvas.draw()
# Mask off unwanted triangles.
triang.set_mask(np.hypot(x[triang.triangles].mean(axis=1),
y[triang.triangles].mean(axis=1))
< min_radius)
#-----------------------------------------------------------------------------
# Refine data - interpolates the electrical potential V
#-----------------------------------------------------------------------------
refiner = UniformTriRefiner(triang)
tri_refi, z_test_refi = refiner.refine_field(V, subdiv=3)
#-----------------------------------------------------------------------------
# Computes the electrical field (Ex, Ey) as gradient of electrical potential
#-----------------------------------------------------------------------------
tci = CubicTriInterpolator(triang, -V)
# Gradient requested here at the mesh nodes but could be anywhere else:
(Ex, Ey) = tci.gradient(triang.x, triang.y)
E_norm = np.sqrt(Ex**2 + Ey**2)
#-----------------------------------------------------------------------------
# Plot the triangulation, the potential iso-contours and the vector field
#-----------------------------------------------------------------------------
fig, ax = plt.subplots()
ax.set_aspect('equal')
# Enforce the margins, and enlarge them to give room for the vectors.
ax.use_sticky_edges = False
ax.margins(0.07)
ax.triplot(triang, color='0.8')
# Mask off unwanted triangles.
triang.set_mask(
np.hypot(x[triang.triangles].mean(axis=1), y[triang.triangles].mean(
axis=1)) < min_radius)
#-----------------------------------------------------------------------------
# Refine data - interpolates the electrical potential V
#-----------------------------------------------------------------------------
refiner = UniformTriRefiner(triang)
tri_refi, z_test_refi = refiner.refine_field(V, subdiv=3)
#-----------------------------------------------------------------------------
# Computes the electrical field (Ex, Ey) as gradient of electrical potential
#-----------------------------------------------------------------------------
tci = CubicTriInterpolator(triang, -V)
# Gradient requested here at the mesh nodes but could be anywhere else:
(Ex, Ey) = tci.gradient(triang.x, triang.y)
E_norm = np.sqrt(Ex**2 + Ey**2)
#-----------------------------------------------------------------------------
# Plot the triangulation, the potential iso-contours and the vector field
#-----------------------------------------------------------------------------
fig, ax = plt.subplots()
ax.set_aspect('equal')
# Enforce the margins, and enlarge them to give room for the vectors.
ax.use_sticky_edges = False
ax.margins(0.07)
ax.triplot(triang, color='0.8')
def spatial_autocorr_fft(tri,
U,
V,
N_grid=512,
auto=False,
transform=False,
tree=None,
interp='Lanczos'):
"""
Function to estimate autocorrelation from a single increment in cartesian
coordinates(tau, eta)
Input:
-----
tri - Delaunay triangulation object of unstructured grid.
N_grid - Squared, structured grid resolution to apply FFT.
U, V - Arrays with cartesian components of wind speed.
Output:
------
r_u,r_v - 2D arrays with autocorrelation function rho(tau,eta)
for U and V, respectively.
"""
if transform:
U_mean = avetriangles(np.c_[tri.x, tri.y], U, tri)
V_mean = avetriangles(np.c_[tri.x, tri.y], V, tri)
# Wind direction
gamma = np.arctan2(V_mean, U_mean)
# Components in matrix of coefficients
S11 = np.cos(gamma)
S12 = np.sin(gamma)
T = np.array([[S11, S12], [-S12, S11]])
vel = np.array(np.c_[U, V]).T
vel = np.dot(T, vel)
X = np.array(np.c_[tri.x, tri.y]).T
X = np.dot(T, X)
U = vel[0, :]
V = vel[1, :]
tri = Triangulation(X[0, :], X[1, :])
mask = TriAnalyzer(tri).get_flat_tri_mask(.05)
tri = Triangulation(tri.x, tri.y, triangles=tri.triangles[~mask])
U_mean = avetriangles(np.c_[tri.x, tri.y], U, tri)
V_mean = avetriangles(np.c_[tri.x, tri.y], V, tri)
else:
# Demeaning
U_mean = avetriangles(np.c_[tri.x, tri.y], U, tri)
V_mean = avetriangles(np.c_[tri.x, tri.y], V, tri)
grid = np.meshgrid(np.linspace(np.min(tri.x), np.max(tri.x), N_grid),
np.linspace(np.min(tri.y), np.max(tri.y), N_grid))
U = U - U_mean
V = V - V_mean
# Interpolated values of wind field to a squared structured grid
if interp == 'cubic':
U_int = CubicTriInterpolator(tri, U)(grid[0].flatten(),
grid[1].flatten()).data
V_int = CubicTriInterpolator(tri, V)(grid[0].flatten(),
grid[1].flatten()).data
U_int = np.reshape(U_int, grid[0].shape)
V_int = np.reshape(V_int, grid[0].shape)
else:
# U_int= lanczos_int_sq(grid,tree,U)
# V_int= lanczos_int_sq(grid,tree,V)
U_int = LinearTriInterpolator(tri, U)(grid[0].flatten(),
grid[1].flatten()).data
V_int = LinearTriInterpolator(tri, V)(grid[0].flatten(),
grid[1].flatten()).data
U_int = np.reshape(U_int, grid[0].shape)
V_int = np.reshape(V_int, grid[0].shape)
#zero padding
U_int[np.isnan(U_int)] = 0.0
V_int[np.isnan(V_int)] = 0.0
fftU = np.fft.fft2(U_int)
fftV = np.fft.fft2(V_int)
if auto:
# Autocorrelation
r_u = np.real(np.fft.fftshift(np.fft.ifft2(np.absolute(fftU)**
2))) / len(U_int.flatten())
r_v = np.real(np.fft.fftshift(np.fft.ifft2(np.absolute(fftV)**
2))) / len(U_int.flatten())
r_uv = np.real(
np.fft.fftshift(np.fft.ifft2(np.real(
fftU * np.conj(fftV))))) / len(U_int.flatten())
dx = np.max(np.diff(grid[0].flatten()))
dy = np.max(np.diff(grid[1].flatten()))
n = grid[0].shape[0]
m = grid[1].shape[0]
# Spectra
fftU = np.fft.fftshift(fftU)
fftV = np.fft.fftshift(fftV)
fftUV = fftU * np.conj(fftV)
Suu = 2 * (np.abs(fftU)**2) * (dx * dy) / (n * m)
Svv = 2 * (np.abs(fftV)**2) * (dx * dy) / (n * m)
Suv = 2 * np.real(fftUV) * (dx * dy) / (n * m)
k1 = np.fft.fftshift((np.fft.fftfreq(n, d=dx)))
k2 = np.fft.fftshift((np.fft.fftfreq(m, d=dy)))
if auto:
return (r_u, r_v, r_uv, Suu, Svv, Suv, k1, k2)
else:
return (Suu, Svv, Suv, k1, k2)
for line in open('data.1'):
row = line.strip().split(" ")
x.append(float(row[0]))
y.append(float(row[1]))
for line in open('data.2'):
row = line.strip().split(" ")
v.append(float(row[0]))
for line in open('data.3'):
row = line.strip().split(" ")
m.append([int(row[0]) - 1,
int(row[1]) - 1,
int(row[2]) - 1])
triangles = Triangulation(x, y, m)
tci = CubicTriInterpolator(triangles, -numpy.array(v))
(u, v) = tci.gradient(triangles.x, triangles.y)
v_norm = numpy.sqrt(u**2, v**2)
fig, ax = plt.subplots()
ax.set_aspect('equal')
ax.use_sticky_edges = False
ax.margins(0.07)
ax.triplot(triangles, color='0.8', lw=0.5)
#tcf = ax.tricontourf(triangles, -numpy.array(v));
#fig.colorbar(tcf);
ax.quiver(triangles.x, triangles.y, u / v_norm, v / v_norm, color='blue')
plt.savefig('1.svg')
