def generate_offset_map(self, source, target):
anchor_pts = [[0, 0], [0, 256], [256, 0], [256, 256], [0, 128],
[128, 0], [256, 128], [128, 256], [0, 64], [0, 192],
[256, 64], [256, 192], [64, 0], [192, 0], [64, 256],
[192, 256]]
anchor_pts = np.asarray(anchor_pts) / 256
# print(f"shape of spoof: {source.shape}, shape of live: {target.shape}")
# print(f"shape of anch: {anchor_pts.shape}")
xi, yi = np.meshgrid(np.linspace(0, 1, 256), np.linspace(0, 1, 256))
# print(f"shape of xi: {xi.shape}, shape of yi: {yi.shape}")
_source = np.concatenate([source, anchor_pts],
axis=0).astype(np.float32)
_target = np.concatenate([target, anchor_pts],
axis=0).astype(np.float32)
# print(f"shape of spoof after meshgrid: {_source.shape}, shape of live: {_target.shape}")
_offset = _source - _target
# print(f"shape of offset: {_offset.shape}")
# interp2d
_triang = mtri.Triangulation(_target[:, 0], _target[:, 1])
# print(f"after triangulation: {_triang}")
_interpx = mtri.LinearTriInterpolator(_triang, _offset[:, 0])
_interpy = mtri.LinearTriInterpolator(_triang, _offset[:, 1])
# print(f"shapes interps: {_interpx}, {_interpy}")
_offsetmapx = _interpx(xi, yi)
_offsetmapy = _interpy(xi, yi)
# print(f"x, y offset: {_offsetmapx.shape}, {_offsetmapy.shape}")
offsetmap = np.stack([_offsetmapy, _offsetmapx, _offsetmapx * 0],
axis=2)
# print(f"final offsetmap: {offsetmap.shape}")
return offsetmap
def addInterpolator(self, interpolation='cubic', kind='geom'):
'''
Add interpolator Object to the vector field.
Arguments:
*interpolation: string. 'cubic' or 'linear'
'''
self.interType = interpolation
self.interKind = kind
if self.interType == 'cubic':
self.vx_i = tri.CubicTriInterpolator(self.triangulation,
self.vx,
kind=self.interKind)
self.vy_i = tri.CubicTriInterpolator(self.triangulation,
self.vy,
kind=self.interKind)
self.vz_i = tri.CubicTriInterpolator(self.triangulation,
self.vz,
kind=self.interKind)
elif self.interType == 'linear':
self.vx_i = tri.LinearTriInterpolator(self.triangulation, self.vx)
self.vy_i = tri.LinearTriInterpolator(self.triangulation, self.vy)
self.vz_i = tri.LinearTriInterpolator(self.triangulation, self.vz)
else:
raise ValueError('Interpolation must be "cubic" or "linear".')
def streamlines(ax, mesh, umean):
"""
Plot velocity streamlines. Interpolate data to background Cartesian grid,
then use matplotlib's ``streamplot()``.
"""
Nx, Ny = 1001, 401
xcart = np.linspace(0, 10, Nx)
ycart = np.linspace(0, 4, Ny)
meshcart = np.vstack(map(lambda x: x.flatten(), np.meshgrid(xcart,
ycart))).T
interp_u = tri.LinearTriInterpolator(mesh, umean[:, 0])
interp_v = tri.LinearTriInterpolator(mesh, umean[:, 1])
ucart = interp_u(meshcart[:, 0], meshcart[:, 1])
vcart = interp_v(meshcart[:, 0], meshcart[:, 1])
X = meshcart[:, 0].reshape(Ny, Nx)
Y = meshcart[:, 1].reshape(Ny, Nx)
U = ucart.reshape(Ny, Nx)
V = vcart.reshape(Ny, Nx)
lw = np.sqrt(U**2 + V**2) * 3
start_points = np.vstack((np.ones(10) * 0.1, np.linspace(1, 3, 10))).T
###ax.streamplot(X, Y, U, V, density=.8, color='k', linewidth=1.)
strm = ax.streamplot(xcart,
ycart,
U,
V,
start_points=[[4, 2]],
color='k',
linewidth=1.)
for path in strm.lines.get_paths():
path.vertices
def CreateFig(dt_output=0.1):
from tables import open_file
archive = open_file('dambreak.h5','r')
import dambreak
dambreak.outputStepping.dt_output=dt_output
dambreak.outputStepping.nDTout=None
dambreak.outputStepping.setOutputStepping()
dambreak.myTpFlowProblem.initializeAll()
import matplotlib.tri as mtri
from matplotlib import pyplot as plt
import numpy as np
domain = dambreak.domain
domain.L = dambreak.tank_dim
domain.x = (0.,0.,0.)
nodes = archive.get_node("/nodesSpatial_Domain0")
x=nodes[:,0]
y=nodes[:,1]
elements = archive.get_node("/elementsSpatial_Domain0")
triang = mtri.Triangulation(x, y, elements)
xg = np.linspace(0, domain.L[0], 20)
yg = np.linspace(0, domain.L[1], 20)
xi, yi = np.meshgrid(xg,yg)
plt.figure()
for it,t in enumerate(dambreak.myTpFlowProblem.so.tnList[:]):
phi = archive.get_node("/phi_t{0:d}".format(it))
vof = archive.get_node("/vof_t{0:d}".format(it))
wvof = np.ones(vof.shape,'d')
wvof -= vof
u = archive.get_node("/u_t{0:d}".format(it))
v = archive.get_node("/v_t{0:d}".format(it))
plt.clf()
plt.xlabel(r'z[m]')
plt.ylabel(r'x[m]')
colors = ['w','b', 'g','r','c','m','y','k']*(max(domain.segmentFlags)//8 + 1)
plt.xlim(domain.x[0]-0.1*domain.L[0],domain.x[0]+domain.L[0]+0.1*domain.L[0])
for si,s in enumerate(domain.segments):
plt.plot([domain.vertices[s[0]][0],
domain.vertices[s[1]][0]],
[domain.vertices[s[0]][1],
domain.vertices[s[1]][1]],
color=colors[domain.segmentFlags[si]-1],
linewidth=2,
marker='o')
plt.tricontourf(x,y,elements,wvof*np.sqrt(u[:]**2 + v[:]**2))
plt.tricontour(x,y,elements,phi,[0], linewidths=4)
u_interp_lin = mtri.LinearTriInterpolator(triang, u[:])
v_interp_lin = mtri.LinearTriInterpolator(triang, v[:])
u_lin = u_interp_lin(xi, yi)
v_lin = v_interp_lin(xi, yi)
plt.streamplot(xg, yg, u_lin, v_lin,color='k')
plt.title('T={0:2.2f}'.format(t))
plt.axis('equal')
plt.xlim((0,domain.L[0]))
plt.savefig('phi{0:04d}.png'.format(it))
def extract(var,triangles,sol):
s = sol[var][1:]
unit = sol[var][0]
mask = triangles.mask
triangles.set_mask(mask=None)
if(unit=='cm^{-3}' and var != 'Net_Doping'):
f = np.vectorize(mtri.LinearTriInterpolator(triangles,np.log(s)))
def g(x,y):
return np.exp(f(x,y))
return s,g
f = mtri.LinearTriInterpolator(triangles,s)
triangles.set_mask(mask=mask)
return np.array(s),np.vectorize(f)
def CreateFig():
from tables import openFile
archive = openFile('linear_waves.h5','r')
import linear_waves
import linear_waves_so
import matplotlib.tri as mtri
from matplotlib import pyplot as plt
import numpy as np
domain = linear_waves.domain
nodes = archive.getNode("/nodesSpatial_Domain0")
x=nodes[:,0]
y=nodes[:,1]
elements = archive.getNode("/elementsSpatial_Domain0")
triang = mtri.Triangulation(x, y, elements)
domain.L=linear_waves.tank_dim
domain.x=[0.,0.]
xg = np.linspace(0, domain.L[0], 20)
yg = np.linspace(0, domain.L[1], 20)
xi, yi = np.meshgrid(xg,yg)
plt.figure()
for it,t in enumerate(linear_waves_so.tnList[:]):
phi = archive.getNode("/phi_t"+`it`)
vof = archive.getNode("/vof_t"+`it`)
wvof = np.ones(vof.shape,'d')
wvof -= vof
u = archive.getNode("/u_t"+`it`)
v = archive.getNode("/v_t"+`it`)
plt.clf()
plt.xlabel(r'z[m]')
plt.ylabel(r'x[m]')
colors = ['b','g','r','c','m','y','k','w']
plt.xlim(domain.x[0]-0.1*domain.L[0],domain.x[0]+domain.L[0]+0.1*domain.L[0])
for si,s in enumerate(domain.segments):
plt.plot([domain.vertices[s[0]][0],
domain.vertices[s[1]][0]],
[domain.vertices[s[0]][1],
domain.vertices[s[1]][1]],
color=colors[domain.segmentFlags[si]-1],
linewidth=2,
marker='o')
plt.tricontourf(x,y,elements,wvof*np.sqrt(u[:]**2 + v[:]**2))
plt.tricontour(x,y,elements,phi,[0], linewidth=4)
u_interp_lin = mtri.LinearTriInterpolator(triang, u[:])
v_interp_lin = mtri.LinearTriInterpolator(triang, v[:])
u_lin = u_interp_lin(xi, yi)
v_lin = v_interp_lin(xi, yi)
plt.streamplot(xg, yg, u_lin, v_lin,color='k')
plt.title('T=%2.2f' % (t,))
plt.xlim((0,domain.L[0]))
plt.ylim(0,domain.L[1])
plt.savefig('phi%4.4d.png' % (it,))
def setup(ds, whichgrids=None):
'''Set up for using ll2xe().
Set up Delaunay triangulation by calculating triangulation and functions for
calculating grid coords from lon/lat pairs and save into and return ds object.
Create a separate triangulation setup for each grid since otherwise it impacts
the performance, especially at edges. Can input keyword whichgrids to only
calculate for particular grids — this is intended for testing purposes to save time.
Usage is demonstrated in ll2xe().
'''
tris = {}
# Set up Delaunay triangulation of grid space in lon/lat coordinates
if whichgrids is None:
whichgrids = ['rho', 'u', 'v', 'psi']
for whichgrid in whichgrids:
lonkey = 'lon_' + whichgrid
latkey = 'lat_' + whichgrid
# Triangulation for curvilinear space to grid space
# Have to use SciPy's Triangulation to be more robust.
# http://matveichev.blogspot.com/2014/02/matplotlibs-tricontour-interesting.html
lon = ds[lonkey].values.flatten()
lat = ds[latkey].values.flatten()
pts = np.column_stack((lon, lat))
tess = Delaunay(pts)
tri = mtri.Triangulation(lon, lat, tess.simplices.copy())
# For the triangulation, need to preprocess the mask to get rid of potential
# flat triangles at the boundaries.
# http://matplotlib.org/1.3.1/api/tri_api.html#matplotlib.tri.TriAnalyzer
mask = mtri.TriAnalyzer(tri).get_flat_tri_mask(0.01, rescale=False)
tri.set_mask(mask)
# Next set up the grid (or index) space grids: integer arrays that are the
# shape of the horizontal model grid.
J, I = ds[lonkey].shape
X, Y = np.meshgrid(np.arange(I), np.arange(J))
# these are the functions for interpolating X and Y (the grid arrays) onto
# lon/lat coordinates. That is, the functions for calculating grid space coords
# corresponding to input lon/lat coordinates.
fx = mtri.LinearTriInterpolator(tri, X.flatten())
fy = mtri.LinearTriInterpolator(tri, Y.flatten())
tris[whichgrid] = {'name': whichgrid, 'tri': tri, 'fx': fx, 'fy': fy}
return tris
def get_data_on_vertical_segment(self, var_name, record, point):
"""
Extract values for each plane of a 2d points in telemac-3d result file
for the given variable
@param point (numpy.array) Point of extraction
@param varname (string) Name of variable for which to extract data
@param record (int) Number of desired record
@returns (numpy.array)
"""
if self.get_mesh_dimension() != 3:
raise TelemacException("Action possible only on 3d mesh")
if len(point) != 2:
raise TelemacException('Warning the extraction point '\
'must be 2d')
nplan = self.nplan
res = np.zeros(nplan)
for plan in range(self.nplan):
values = self.get_data_on_horizontal_plane(\
var_name, record, plan)
data_interp = mtri.LinearTriInterpolator(self.tri, values)
res[plan] = data_interp(point[0], point[1])
return res
def visualize_wafer(mini_wafer_map):
# Interpolation 실행
data = mini_wafer_map
x = data['x'].tolist()
y = data['y'].tolist()
value = data['value'].tolist()
xx = np.array(x)
yy = np.array(y)
zz = np.array(value)
npts = len(xx) # 현재 PT 개수 (490개)
ngridx, ngridy = 300,300 # 보간하고자 하는 PT 개수
# Create grid values first.
xi = np.linspace(-137, 137, ngridx)
yi = np.linspace(-137, 137, ngridy)
# Linearly interpolate the data (x, y) on a grid defined by (xi, yi).
triang = tri.Triangulation(xx, yy)
interpolator = tri.LinearTriInterpolator(triang, zz) # LinearTriInterpolator
Xi, Yi = np.meshgrid(xi, yi)
zi = interpolator(Xi, Yi)
fig = plt.figure(figsize = (10,10))
ax = plt.axes(projection='3d')
ax.axes.set_zlim3d(bottom=40000, top=50000)
contour = ax.contour3D(Xi, Yi, zi,levels = 100, cmap='jet')
ax.view_init(35, 50) # 보는 각도 변경
fig.colorbar(contour, shrink=0.5, aspect=5)
fig.savefig("3d graph.png")
def interpolate(self, z, x, y, kind='linear'):
"""
Interpolate data in 'z' on current grid onto points 'x' and 'y'
kind = 'linear', 'cubic', 'barycentric' (default), 'nearest'
"""
if kind == 'linear':
self.build_tri_voronoi()
F = tri.LinearTriInterpolator(self._triv, z)
return F(x, y)
elif kind == 'cubic':
self.build_tri_voronoi()
F = tri.CubicTriInterpolator(self._triv, z)
return F(x, y)
elif kind == 'barycentric':
self.build_tri_voronoi()
xyin = np.vstack([self.xv, self.yv]).T
xyout = np.vstack([x, y]).T
F = BarycentricInterp(xyin, xyout)
return F(z)
elif kind == 'nearest':
if isinstance(x, float):
dist, idx = self.find_nearest([x, y])
return z[idx]
elif isinstance(x, np.ndarray):
sz = x.shape
xy = np.array([x.ravel(), y.ravel()]).T
dist, idx = self.find_nearest(xy)
return z[idx].reshape(sz)
def PlotADCP(ax,atd,depths,V,levels=levels,levels2=levels2,cmap=cmap,norm=norm):
"""
Still unfinished with flexibility of reg and filt
TODO adapt to filtered and regular data
Returns km
levels can be
"""
X = []
Z = []
for i in range(len(atd)):
for j in range(len(depths)):
X.append(atd[i])
Z.append(depths[j])
X = np.array(X)
Z = np.array(Z)
Vf = V.flatten()
# Regular grid
xi = np.linspace(min(atd),max(atd), len(atd))
zi = np.linspace(min(depths), max(depths), len(depths))
# Perform linear interpolation of the data (x,y)
# on a grid defined by (xi,yi)
triang = tri.Triangulation(X, Z)
interpolator = tri.LinearTriInterpolator(triang, Vf)
Xi, Zi = np.meshgrid(xi, zi)
Vi = interpolator(Xi, Zi)
ax.contourf(Xi,Zi,Vi,levels=levels,cmap=cmap,norm=norm)
cont = ax.contour(Xi,Zi,Vi,levels = levels2,linewidths=0.5,colors='black',linestyles='dashed')
ax.clabel(cont,cont.levels,fmt='%1.2f',fontsize=8, inline=1,colors='k')
lvl0 = [0]
ax.contour(Xi,Zi,Vi,levels=lvl0,colors='black',linewidths=2)
def test_triinterp_colinear():
# Tests interpolating inside a triangulation with horizontal colinear
# points (refer also to the tests :func:`test_trifinder` ).
#
# These are not valid triangulations, but we try to deal with the
# simplest violations (i. e. those handled by default TriFinder).
#
# Note that the LinearTriInterpolator and the CubicTriInterpolator with
# kind='min_E' or 'geom' still pass a linear patch test.
# We also test interpolation inside a flat triangle, by forcing
# *tri_index* in a call to :meth:`_interpolate_multikeys`.
delta = 0. # If +ve, triangulation is OK, if -ve triangulation invalid,
# if zero have colinear points but should pass tests anyway.
x0 = np.array([1.5, 0, 1, 2, 3, 1.5, 1.5])
y0 = np.array([-1, 0, 0, 0, 0, delta, 1])
# We test different affine transformations of the initial figure ; to
# avoid issues related to round-off errors we only use integer
# coefficients (otherwise the Triangulation might become invalid even with
# delta == 0).
transformations = [[1, 0], [0, 1], [1, 1], [1, 2], [-2, -1], [-2, 1]]
for transformation in transformations:
x_rot = transformation[0] * x0 + transformation[1] * y0
y_rot = -transformation[1] * x0 + transformation[0] * y0
(x, y) = (x_rot, y_rot)
z = 1.23 * x - 4.79 * y
triangles = [[0, 2, 1], [0, 3, 2], [0, 4, 3], [1, 2, 5], [2, 3, 5],
[3, 4, 5], [1, 5, 6], [4, 6, 5]]
triang = mtri.Triangulation(x, y, triangles)
xs = np.linspace(np.min(triang.x), np.max(triang.x), 20)
ys = np.linspace(np.min(triang.y), np.max(triang.y), 20)
xs, ys = np.meshgrid(xs, ys)
xs = xs.ravel()
ys = ys.ravel()
mask_out = (triang.get_trifinder()(xs, ys) == -1)
zs_target = np.ma.array(1.23 * xs - 4.79 * ys, mask=mask_out)
linear_interp = mtri.LinearTriInterpolator(triang, z)
cubic_min_E = mtri.CubicTriInterpolator(triang, z)
cubic_geom = mtri.CubicTriInterpolator(triang, z, kind='geom')
for interp in (linear_interp, cubic_min_E, cubic_geom):
zs = interp(xs, ys)
assert_array_almost_equal(zs_target, zs)
# Testing interpolation inside the flat triangle number 4: [2, 3, 5]
# by imposing *tri_index* in a call to :meth:`_interpolate_multikeys`
itri = 4
pt1 = triang.triangles[itri, 0]
pt2 = triang.triangles[itri, 1]
xs = np.linspace(triang.x[pt1], triang.x[pt2], 10)
ys = np.linspace(triang.y[pt1], triang.y[pt2], 10)
zs_target = 1.23 * xs - 4.79 * ys
for interp in (linear_interp, cubic_min_E, cubic_geom):
zs, = interp._interpolate_multikeys(xs,
ys,
tri_index=itri *
np.ones(10, dtype=np.int32))
assert_array_almost_equal(zs_target, zs)
def interpolate_mesh_on_points(self, points, values):
"""
Interpolate mesh on points given value
@param points (list) List og points for which to interpolate
@param values (np.darray) values for each mesh points
@param method (string) Interpolation methof to use
"""
if self.interp_method == "scipy.LinearND":
grid_pt = np.column_stack(
(self.meshx[:self.npoin2], self.meshy[:self.npoin2]))
data_interp = interpolate.LinearNDInterpolator(grid_pt, values)
pts = np.asarray([(pt[0], pt[1]) for pt in points])
res = data_interp(pts)
elif self.interp_method == "matplotlib.LinearTri":
data_interp = mtri.LinearTriInterpolator(self.tri, values)
pt_x = [pt[0] for pt in points]
pt_y = [pt[1] for pt in points]
res = data_interp(pt_x, pt_y)
else:
raise TelemacException(\
"Unknown interpolation method: {}\n"
"Avaialable methods: matplotlib.LinearTri, scipy.LinearND"\
.format(self.interp_method))
return res
def add_bands_surface_plot(axes3d: Axes3D,
kpoints: numpy.ndarray,
eigenvalues: numpy.ndarray,
axis: int,
layer: int,
resolution: int,
band_indices: Union[List[int], range,
numpy.ndarray],
offset: Union[List[float], numpy.ndarray] = None):
x, y, zs = get_x_y_zs(kpoints, eigenvalues, axis, layer)
if offset is not None:
x += offset[0]
y += offset[1]
zs += offset[2]
triang = tri.Triangulation(x, y)
x_linspace = numpy.linspace(min(x), max(x), resolution)
y_linspace = numpy.linspace(min(y), max(y), resolution)
for b in band_indices:
interpolator = tri.LinearTriInterpolator(triang, zs[:, b])
x_meshgrid, y_meshgrid = numpy.meshgrid(x_linspace, y_linspace)
z_mesggrid = interpolator(x_meshgrid, y_meshgrid)
axes3d.plot_surface(x_meshgrid,
y_meshgrid,
z_mesggrid,
cmap=pyplot.get_cmap("terrain"),
vmin=numpy.min(z_mesggrid),
vmax=numpy.max(z_mesggrid))
def add_bands_wireframe_plot(axes3d: Axes3D,
kpoints: numpy.ndarray,
eigenvalues: numpy.ndarray,
axis: int,
layer: int,
resolution: int,
band_indices: Union[List[int], range,
numpy.ndarray],
offset: Union[List[float], numpy.ndarray] = None):
x, y, zs = get_x_y_zs(kpoints, eigenvalues, axis, layer)
if offset is not None:
x += offset[0]
y += offset[1]
zs += offset[2]
triang = tri.Triangulation(x, y)
x_linspace = numpy.linspace(min(x), max(x), resolution)
y_linspace = numpy.linspace(min(y), max(y), resolution)
b_range = max(band_indices) - min(band_indices) if len(
band_indices) > 1 else 1
for b in band_indices:
interpolator = tri.LinearTriInterpolator(triang, zs[:, b])
x_meshgrid, y_meshgrid = numpy.meshgrid(x_linspace, y_linspace)
z_mesggrid = interpolator(x_meshgrid, y_meshgrid)
color = (max(band_indices) - b) / b_range / 1.5
axes3d.plot_wireframe(x_meshgrid,
y_meshgrid,
z_mesggrid,
colors=(color, color, color))
def interpolate_2D_soln_to_points(physics, x, var, xpoints): ''' This function interpolates a variable to an arbitrary set of points. 2D only. Inputs: ------- physics: physics object x: xy-coordinates at which variable is already evaluated [num_x, 2] var: values of variable evaluated at x [num_x, 1] xpoints: xy-coordinates to interpolate variable to [num_pts, 2] Outputs: -------- var_points: values of variable interpolated to xpoints [num_pts, 2] x: xy-coordinates at which variable is already evaluated (duplicates removed and reshaped) var: values of variable evaluated at x (duplicates removed and reshaped) ''' if physics.NDIMS != 2: raise ValueError tris, utri = triangulate(physics, x, var) interpolator = tri.LinearTriInterpolator(tris, utri) var_points = interpolator(xpoints[:,0], xpoints[:,1]) return var_points
def contour(xy, z):
xi, yi = np.meshgrid(np.linspace(-1, 1, 101), np.linspace(-1, 1, 101))
triang = tri.Triangulation(xy[:, 0], xy[:, 1])
interp_lin = tri.LinearTriInterpolator(triang, z.ravel())
zi = interp_lin(xi, yi)
plt.contourf(xi, yi, zi, cmap=plt.cm.seismic)
plt.colorbar()
def get_switchline():
r1s, r2s, phis = [], [], []
r0s = np.linspace(0.2 * r, 8 * r, 66)
for r0 in r0s:
r1l, r1u = (r0 - r) / 2, (r0 + r) / 2
for r1 in np.linspace(r1l + 0.06, r1u - 0.06, 66):
r2 = r0 - r1
if abs((r1**2 + r2**2 - r**2) / (2 * r1 * r2)) < 1:
r1s.append(r1)
r2s.append(r2)
phis.append(get_phi_max(r1, r2)[0])
r1s = np.asarray(r1s)
r2s = np.asarray(r2s)
phis = np.asarray(phis)
xi, yi = np.linspace(1., 10., 50), np.linspace(1., 10., 50)
triang = tri.Triangulation(r1s, r2s)
interpolator = tri.LinearTriInterpolator(triang, phis)
Xi, Yi = np.meshgrid(xi, yi)
zi = interpolator(Xi, Yi)
fig, ax = plt.subplots()
cs = ax.contour(xi, yi, zi, levels=14, linewidths=2, colors='r')
line = []
for p in cs.collections[1].get_paths()[0].vertices:
if p[0] > r1_min and p[1] > r2_min:
line.append(p)
with open('switch.csv', 'a') as f:
f.write(','.join(list(map(str, p))) + '\n')
plt.close()
return np.asarray(line)
def process_fenics_function(mesh,fenics_function, x_axis=np.linspace(0,1,100), y_axis=np.linspace(0,1,100)\
,to_plot=True):
"""
Method in order to convert fenics functions into np arrays, in order to be able to deal with objects of arbitrary dimension
the outputs will be masked Fenics Functions. This will only apply to 2D functions that need to be interpolated.
This is build on top of the matplotlib.tri module and is effective at interpolating from non-uniform meshs.
Args:
param1: mesh that the fenics function is defined on
param2: fenics function that needs to be converted into a
param3: x_axis (np.array) needs to be a 1-D array which represents the units of the x-axis
param4: y_axis (np.array) needs to be a 1-D array which represents the units of the y-axis
param5: to_plot (bool) determines if the image of the interpolated function should be plotted
Returns:
Masked Numpy Array with the required eigenfunction
"""
V = FunctionSpace(mesh, 'CG', 1)
fenics_function.set_allow_extrapolation(True)
fenics_function = interpolate(fenics_function, V)
C = fenics_function.compute_vertex_values(mesh)
xv, yv = np.meshgrid(x_axis, y_axis)
test = tri.LinearTriInterpolator(mesh2triang(mesh), C)(xv, yv)
if to_plot:
plt.imshow(test, cmap='seismic', origin="lower")
plt.show()
return test
def plot_tricon(x, y, z):
ngridx = 41
ngridy = 41
xi = np.linspace(-10, 10, ngridx)
yi = np.linspace(-10, 10, ngridy)
triang = tri.Triangulation(x, y)
interpolator = tri.LinearTriInterpolator(triang, z)
Xi, Yi = np.meshgrid(xi, yi)
zi = interpolator(Xi, Yi)
plt.figure()
ax1 = plt.subplot(111)
ax1.contour(xi, yi, zi, levels=14, linewidths=0.5, colors='k')
cntr1 = ax1.contourf(xi, yi, zi, levels=14, cmap="RdBu_r")
plt.colorbar(cntr1, ax=ax1)
# ax1.plot(x, y, 'ko', ms=3)
ax1.set(xlim=(-10, 10), ylim=(-10, 10))
ax1.set_title('grad and contour')
plt.savefig('testgradcont.pdf')
plt.close()
plt.figure()
ax2 = plt.subplot(111)
ax2.tricontour(x, y, z, levels=14, linewidths=0.5, colors='k')
cntr2 = ax2.tricontourf(x, y, z, levels=14, cmap="RdBu_r")
plt.colorbar(cntr2, ax=ax2)
# ax2.plot(x, y, 'ko', ms=3)
ax2.set(xlim=(-10, 10), ylim=(-10, 10))
ax2.set_title('tricontour')
plt.savefig('testtricont.pdf')
plt.close()
return
def plot_cross_section(function_space,
parameter, mean, cov,
x_axis_limits, cross_section_y,
title,
filepath,
y_axis_limits):
#=== Convert array to dolfin function ===#
parameter_fe = convert_array_to_dolfin_function(function_space, parameter)
mean_fe = convert_array_to_dolfin_function(function_space, mean)
cov_fe = convert_array_to_dolfin_function(function_space, cov)
#=== Extract mesh and triangulate ===#
mesh = parameter_fe.function_space().mesh()
coords = mesh.coordinates()
elements = mesh.cells()
triangulation = tri.Triangulation(coords[:, 0], coords[:, 1], elements)
#=== Linear Interpolators ===#
interp_parameter = tri.LinearTriInterpolator(triangulation, parameter.flatten())
interp_mean = tri.LinearTriInterpolator(triangulation, mean.flatten())
interp_cov = tri.LinearTriInterpolator(triangulation, cov.flatten())
#=== Interpolate values of cross section ===#
x = np.linspace(x_axis_limits[0], x_axis_limits[1], 100, endpoint=True)
parameter_cross = np.zeros(len(x))
mean_cross = np.zeros(len(x))
std_cross = np.zeros(len(x))
for i in range(0,len(x)):
parameter_cross[i] = interp_parameter(x[i], cross_section_y)
mean_cross[i] = interp_mean(x[i], cross_section_y)
std_cross[i] = np.exp(interp_cov(x[i], cross_section_y)/2)
#=== Plotting ===#
plt.plot(x, parameter_cross, 'r-', label='True Parameter')
plt.plot(x, mean_cross, 'k-', label='Posterior Mean')
plt.fill_between(x, mean_cross - 3*std_cross, mean_cross + 3*std_cross)
plt.xlim(x_axis_limits)
plt.ylim(y_axis_limits)
plt.title(title)
plt.legend(loc="upper left")
plt.xlabel('x-coordinate')
plt.ylabel('Parameter Value')
#=== Save Figure ===#
plt.savefig(filepath, dpi=100, bbox_inches = 'tight', pad_inches = 0)
plt.close()
def interpolate_data_on_sphere(sampling,
data,
overlap=np.pi * 0.25,
refine=False):
"""Linear interpolator for data on a spherical surface. The interpolator
exploits that the data on the sphere is periodic with regard to the
elevation and azimuth angle. The data is periodically extended to a
specified overlap angle before interpolation.
Parameters
----------
sampling : Coordinates
The coordinates at which the data is sampled.
data : ndarray, double
The sampled data points.
Returns
-------
interp : LinearTriInterpolator
The interpolator object.
"""
lats = sampling.latitude
lons = sampling.longitude
mask = lons > np.pi - overlap
lons = np.concatenate((lons, lons[mask] - np.pi * 2))
lats = np.concatenate((lats, lats[mask]))
data = np.concatenate((data, data[mask]))
mask = lons < -np.pi + overlap
lons = np.concatenate((lons, lons[mask] + np.pi * 2))
lats = np.concatenate((lats, lats[mask]))
data = np.concatenate((data, data[mask]))
tri = mtri.Triangulation(lons, lats)
if refine:
refiner = mtri.UniformTriRefiner(tri)
tri, data = refiner.refine_field(
data,
triinterpolator=mtri.LinearTriInterpolator(tri, data),
subdiv=3)
interpolator = mtri.LinearTriInterpolator(tri, data)
return interpolator
def interpolate_on_grid(tri,
data,
grid=None,
grid_xlim=None,
grid_ylim=None,
grid_resolution=(500, 500)):
"""
Interpolation on regular grid (matplotlib.mtri.LinearTriInterpolator)
@param tri (matplotlib.tri.Triangulation) triangular mesh
@param data (list(numpy.array) or numpy.array) list of scalar
data or scalar data
@param grid(tuple) x and y of interpolation grid
@param grid_xlim (list(float)) grid limit in x
@param grid_ylim (list(float)) grid limit in y
@param grid_resolution (list(float)) number of grid point on x and y
(default: (500, 500))
@return: interpolated data(list(numpy.array) or numpy.array)
and grid (tuple)
"""
if grid is None:
if grid_xlim is None:
grid_xlim = [np.min(tri.x), np.max(tri.x)]
if grid_ylim is None:
grid_ylim = [np.min(tri.y), np.max(tri.y)]
if grid is None:
m_xi, m_yi = np.meshgrid(np.linspace(grid_xlim[0],
grid_xlim[1],
grid_resolution[0]),
np.linspace(grid_ylim[0],
grid_ylim[1],
grid_resolution[1]))
else:
m_xi, m_yi = grid
# Interpolate data x,y on cartesian grid
if isinstance(data, list):
data_x_i = []
for data_x in data:
data_x_interp = mtri.LinearTriInterpolator(tri, data_x)
data_x_i.append(data_x_interp(m_xi, m_yi))
else:
data_x_interp = mtri.LinearTriInterpolator(tri, data)
data_x_i = data_x_interp(m_xi, m_yi)
return data_x_i, (m_xi, m_yi)
def triangulate_rho(X):
se = X['se']
rho = X['rho']
pval = X['pval']
Hc = X['Hc']
Hb = X['Hb']
dH = X['dH']
#PERFORM GRIDDING AND INTERPOLATION FOR FORC PLOT
X['Hc1'], X['Hc2'], X['Hb1'], X['Hb2'] = ut.measurement_limts(X)
Hc1 = 0 - 3 * dH
Hc2 = X['Hc2']
Hb1 = X['Hb1'] - X['Hc2']
Hb2 = X['Hb2']
#create grid for interpolation
Nx = np.ceil((Hc2 - Hc1) / dH) + 1 #number of points along x
Ny = np.ceil((Hb2 - Hb1) / dH) + 1 #number of points along y
xi = np.linspace(Hc1, Hc2, int(Nx))
yi = np.linspace(Hb1, Hb2, int(Ny))
#perform triangluation and interpolation
triang = tri.Triangulation(Hc, Hb)
interpolator = tri.LinearTriInterpolator(triang, rho)
Xi, Yi = np.meshgrid(xi, yi)
Zi = interpolator(Xi, Yi)
interpolator1 = tri.LinearTriInterpolator(triang, se)
SEi = interpolator1(Xi, Yi)
interpolator2 = tri.LinearTriInterpolator(triang, pval * len(pval))
Pi = interpolator2(Xi, Yi)
X['Hc1'] = Hc1
X['Xi'] = Xi
X['Yi'] = Yi
X['Zi'] = Zi
X['SEi'] = SEi
X['Pi'] = Pi
X['SEint'] = interpolator1
X['Zint'] = interpolator
X['Pint'] = interpolator2
return X
def plot_streamlines(nodes, elems, vals, title=None, clabel=None,
save=None, show=True, num_intp=200, density=0.8):
""" Plots streamlines with contour in the background.
Values given at nodes. """
fig = Figure(title=title, subplots=True, clabel=clabel,
save=save, show=show)
vals_norm = np.sqrt(vals[:, 0]**2 + vals[:, 1]**2) + 1e-10
# vals_norm_max = np.max(vals_norm)
fig.colorbar_ax = fig.ax.tricontourf(nodes[:, 0], nodes[:, 1], elems,
vals_norm)
Lx = nodes[:, 0].max()-nodes[:, 0].min()
Ly = nodes[:, 1].max()-nodes[:, 1].min()
dx = max(Lx, Ly)/num_intp
Nx = int(Lx/dx)
Ny = int(Ly/dx)
x_i, y_i = np.meshgrid(
np.linspace(dx+nodes[:, 0].min(),
nodes[:, 0].max()-dx, Nx),
np.linspace(dx+nodes[:, 1].min(),
nodes[:, 1].max()-dx, Ny))
triang = mtri.Triangulation(nodes[:, 0], nodes[:, 1], elems)
ux_interp = mtri.LinearTriInterpolator(triang, vals[:, 0])
uy_interp = mtri.LinearTriInterpolator(triang, vals[:, 1])
ux_i = ux_interp(x_i, y_i)
uy_i = uy_interp(x_i, y_i)
ux_i = np.array(ux_i.filled(0.))
uy_i = np.array(uy_i.filled(0.))
u_norm = np.sqrt(ux_i**2 + uy_i**2)
lw = np.zeros_like(ux_i)
lw[:] += 5*u_norm/(u_norm.max() + 1e-10)
mask = np.zeros(ux_i.shape, dtype=bool)
ux_i_2 = np.ma.array(ux_i, mask=mask)
fig.ax.streamplot(x_i, y_i,
ux_i_2, uy_i,
color="k",
density=density,
linewidth=lw)
def phi_at_gauss_nodes(self, triang, phi_prev, g_nodes):
num_groups = np.shape(phi_prev)[0]
num_nodes = np.shape(g_nodes)[0]
phi_vals = np.zeros((num_groups, num_nodes))
for g in range(num_groups):
interp = tri.LinearTriInterpolator(triang, phi_prev[g])
for i in range(num_nodes):
phi_vals[g, i] = interp(g_nodes[i, 0], g_nodes[i, 1])
return phi_vals
def __interpolate_flowfront(Xi, Yi, ignore_list, current_index, triang, values):
ones = np.ones_like(values)
filling_perc = np.sum(values) / np.sum(ones)
if filling_perc >= 1.0:
ignore_list.append(int(str(current_index).replace("state", "0")))
interpolator = tri.LinearTriInterpolator(triang, values)
# the PAM-RTM uses a triangle grid for filling states. Interpolate values over triangle grid with matplotlib
zi = interpolator(Xi, Yi)
return zi
def plot_contour_interpolate(self, vec_x, vec_y, vec_z, contour_resolution, contour_resolution_y=None, flush=True):
""" create a 2D contour plot
:param vec_x:
:param vec_y:
:param contour_resolution:
:param flush:
:return:
"""
# check for vec x and vec y for non-contour case
if vec_x.min() == vec_x.max() or vec_y.min() == vec_y.max():
# TODO - 20180906 - Propagate this situation
return False
# Create grid values first.
ngridx = contour_resolution
if contour_resolution_y is None:
ngridy = contour_resolution
else:
ngridy = contour_resolution_y
xi = np.linspace(vec_x.min(), vec_x.max(), ngridx)
yi = np.linspace(vec_y.min(), vec_y.max(), ngridy)
# Perform linear interpolation of the data (x,y)
# on a grid defined by (xi,yi)
try:
triang = tri.Triangulation(vec_x, vec_y)
except RuntimeError as run_err:
print('[ERROR] vec X: {}'.format(vec_x))
print(vec_y)
raise run_err
interpolator = tri.LinearTriInterpolator(triang, vec_z)
Xi, Yi = np.meshgrid(xi, yi)
zi = interpolator(Xi, Yi)
# self.main_canvas.plot_contour(xi, yi, zi, flush=False)
# self. .plot_scatter(vec_x, vec_y, flush=True)
self._xi = xi
self._yi = yi
self._zmatrix = zi
self._is_setup = True
contour_plot = self.main_canvas.add_contour_plot(xi, yi, zi)
print('[DB...BAT] Contour plot: {} of type {}'.format(contour_plot, type(contour_plot)))
# self.ui.widget.main_canvas.add_scatter(vec_x, vec_y)
# self.ui.widget.main_canvas._flush()
if flush:
self.main_canvas._flush()
# self.ui.widget.main_canvas.add_contour_plot(xi, yi, zi)
# self.ui.widget.main_canvas.add_scatter(vec_x, vec_y)
# self.ui.widget.main_canvas._flush()
return
def generate_offset_map(source, target):
anchor_pts = [[0, 0], [0, 256], [256, 0], [256, 256], [0, 128], [128, 0],
[256, 128], [128, 256], [0, 64], [0, 192], [256, 64],
[256, 192], [64, 0], [192, 0], [64, 256], [192, 256]]
anchor_pts = np.asarray(anchor_pts) / 256
xi, yi = np.meshgrid(np.linspace(0, 1, 256), np.linspace(0, 1, 256))
_source = np.concatenate([source, anchor_pts], axis=0).astype(np.float32)
_target = np.concatenate([target, anchor_pts], axis=0).astype(np.float32)
_offset = _source - _target
# interp2d
_triang = mtri.Triangulation(_target[:, 0], _target[:, 1])
_interpx = mtri.LinearTriInterpolator(_triang, _offset[:, 0])
_interpy = mtri.LinearTriInterpolator(_triang, _offset[:, 1])
_offsetmapx = _interpx(xi, yi)
_offsetmapy = _interpy(xi, yi)
offsetmap = np.stack([_offsetmapy, _offsetmapx, _offsetmapx * 0], axis=2)
return offsetmap
def interpTri(triVerts, triInd):
from matplotlib import pyplot as plt
import matplotlib.pyplot as plt
import matplotlib.tri as mtri
import numpy as np
x = triVerts[:, 0]
y = triVerts[:, 1]
triang = mtri.Triangulation(triVerts[:, 0], triVerts[:, 1], triInd)
# Interpolate to regularly-spaced quad grid.
z = np.cos(1.5 * x) * np.cos(1.5 * y)
xi, yi = np.meshgrid(np.linspace(0, 3, 20), np.linspace(0, 3, 20))
interp_lin = mtri.LinearTriInterpolator(triang, z)
zi_lin = interp_lin(xi, yi)
interp_cubic_geom = mtri.CubicTriInterpolator(triang, z, kind='geom')
zi_cubic_geom = interp_cubic_geom(xi, yi)
interp_cubic_min_E = mtri.CubicTriInterpolator(triang, z, kind='min_E')
zi_cubic_min_E = interp_cubic_min_E(xi, yi)
# Set up the figure
fig, axs = plt.subplots(nrows=2, ncols=2)
axs = axs.flatten()
# Plot the triangulation.
axs[0].tricontourf(triang, z)
axs[0].triplot(triang, 'ko-')
axs[0].set_title('Triangular grid')
# Plot linear interpolation to quad grid.
axs[1].contourf(xi, yi, zi_lin)
axs[1].plot(xi, yi, 'k-', lw=0.5, alpha=0.5)
axs[1].plot(xi.T, yi.T, 'k-', lw=0.5, alpha=0.5)
axs[1].set_title("Linear interpolation")
# Plot cubic interpolation to quad grid, kind=geom
axs[2].contourf(xi, yi, zi_cubic_geom)
axs[2].plot(xi, yi, 'k-', lw=0.5, alpha=0.5)
axs[2].plot(xi.T, yi.T, 'k-', lw=0.5, alpha=0.5)
axs[2].set_title("Cubic interpolation,\nkind='geom'")
# Plot cubic interpolation to quad grid, kind=min_E
axs[3].contourf(xi, yi, zi_cubic_min_E)
axs[3].plot(xi, yi, 'k-', lw=0.5, alpha=0.5)
axs[3].plot(xi.T, yi.T, 'k-', lw=0.5, alpha=0.5)
axs[3].set_title("Cubic interpolation,\nkind='min_E'")
fig.tight_layout()
plt.show()
