def fit(self, x, y):
t0 = time.time()
assert set(y.flatten()) == set(
[0, 1]), "y data (target data) needs to have only 0s and 1s"
# determine the clusters
self.clus = sk.cluster.MiniBatchKMeans(n_clusters=self.n_clusters)
self.clus.fit(x)
# determine the nearest neighbor for each data point
nns = sk.neighbors.NearestNeighbors(n_neighbors=self.n_neighbors)
nns.fit(x)
neighbor_dist, neighbor_idx = nns.kneighbors(
self.clus.cluster_centers_, n_neighbors=self.n_neighbors)
# compute the cluster means
self.cluster_x = self.clus.cluster_centers_
self.cluster_y = array(
map(lambda i: nanmean(y[neighbor_idx[i, :]]),
xrange(shape(self.cluster_x)[0])))
# make the interpolator
if self.interpolator == 'linear':
self.iterpol = interpolate.LinearNDInterpolator(self.cluster_x,
self.cluster_y,
fill_value=nan)
else:
self.iterpol = interpolate.CloughTocher2DInterpolator(
self.cluster_x, self.cluster_y, fill_value=nan)
self.nnb_iterpol = interpolate.NearestNDInterpolator(
self.cluster_x, self.cluster_y)
print "fit elapsed time: %.02f minutes" % ((time.time() - t0) / 60.)
def initInterpolation(self, nsamples=1):
self.interpolators = []
self.nsamples = nsamples
for i in range(nsamples):
temp = zip(*self.gridpoints(
sample=(nsamples != 1), flag='x', extendToBorder=True))
self.interpolators.append(
interpolate.CloughTocher2DInterpolator(list(temp[0]),
temp[1],
fill_value=0.))
# polynomial interpolation
nneighbor = 2
for k in self.data:
kk = np.asarray(k)
kmin = np.maximum(kk - np.full(self.dim, nneighbor, dtype=int),
np.zeros(self.dim)).astype(int)
kmax = np.minimum(kk + np.full(self.dim, nneighbor, dtype=int),
self.nbin - 1).astype(int)
degree = kmax - kmin
self.deg[k] = degree
xx = self.x(k)
dat = [
np.append(
self.x(x + kmin),
self.data[tuple(x +
kmin)].gety(sample=(nsamples != 1)))
for x in np.ndindex(*(degree + 1))
]
x, y, z = np.asarray(zip(*dat))
self.pol[k, i] = self.polyfit2d(x, y, z, orders=degree)
def __init__(self, xin, xout, **keywords):
xin = np.asarray(xin)
xout = np.asarray(xout)
if xin.shape[-1] != 2:
raise ValueError('The shape of the object plane coordinates should'
' be (npoints,ndims), where ndims is only impleme'
'nted for 2.')
if xin.shape != xout.shape:
raise ValueError('The object and image coordinates do not have the'
' same shape.')
keywords['dtype'] = float
Operator.__init__(self, **keywords)
self.interp0 = interp.CloughTocher2DInterpolator(xin, xout[..., 0])
self.interp1 = interp.CloughTocher2DInterpolator(xin, xout[..., 1])
self.set_rule('I', lambda s: DistortionOperator(xout, xin))
def build(self,knot_vals):
"""Build Spline for the passed knot values
@param [float] knot_vals Knot values on the mesh of self.knots_xx etc.
"""
#Check if logsline
if self.logspline:
if np.any(knot_vals<=0.):
print "ERROR build: At least one knot member is ~<0, cannot apply log10"
return False
else:
knot_vals = np.log10(knot_vals)
#Check/correct if passed shape does not match
if not np.array_equal(self.knots_shape, knot_vals.shape):
#print "WARNING: passed knot array does not have the right shape"
#print self.knots_shape, knot_vals.shape
knot_vals = knot_vals.reshape(self.knots_shape)
if self.built and np.array_equal(knot_vals, self.knot_vals):
return False
else:
self.knot_vals = knot_vals
#Add boundary knots"
bknot_points = []
bvals_vals = []
for name in self.bknots:
#~ print "Adding boundary", name
bknot_points.append(self.bknots[name]["points"])
bvals_vals.append(self.bknots[name]["vals"])
#~ print np.array(bknot_points)[0],len(np.array(bknot_points)[0])
#~ print self.knot_points,len(self.knot_points)
#~ print np.array(bvals_vals).flatten()
#~ print self.knot_vals.flatten()
if len(bknot_points)>0:
spline_points = np.concatenate([self.knot_points,np.array(bknot_points)[0]])
spline_vals = np.concatenate([self.knot_vals.flatten(),np.array(bvals_vals).flatten()])
else:
spline_points = self.knot_points
spline_vals = self.knot_vals.flatten()
#~ print spline_points,len(spline_points)
#~ print spline_vals,len(spline_vals)
if self.cloughtocher:
self.spline2d = interp.CloughTocher2DInterpolator(spline_points,spline_vals,tol=0.1,maxiter=100,rescale=True) #
else:
pointsplit = np.hsplit(spline_points,2)
#print "Build:"
#print np.squeeze(pointsplit[0]),len(np.squeeze(pointsplit[0]))
#print np.squeeze(pointsplit[1]),len(np.squeeze(pointsplit[1]))
#print np.squeeze(spline_vals),len(np.squeeze(spline_vals))
self.spline2d = interp.interp2d(np.squeeze(pointsplit[0]), np.squeeze(pointsplit[1]),\
np.squeeze(spline_vals), kind='cubic',\
copy=False, bounds_error= False) # Interpolator from np
self.built = True
return True
def get_maps_from_file(path):
x = np.genfromtxt(path, delimiter=',')
zx = x[1:, 0]
zy = x[1:, 1]
xy = np.zeros((len(zx), 2))
xy[:, 0] = x[1:, 2]
xy[:, 1] = x[1:, 4]
assert (not np.isnan(xy.any()))
assert (not np.isnan(zy.any()))
assert (not np.isnan(zx.any()))
xy[:, 0] = xy[:, 0] / x[0, 0]
xy[:, 1] = xy[:, 1] / x[0, 1]
mapx = interpolate.CloughTocher2DInterpolator(xy, zx)
mapy = interpolate.CloughTocher2DInterpolator(xy, zy)
return mapx, mapy
def create_cmaps(self, rot=0.):
points = np.array([[0, 0], [1, 0], [0, 0.5], [1, 0.5], [0, 1], [1, 1]])
hue = (points[:, 1] * 1.5 + 3) / 6. + rot
sat = np.array([1., 1., 1. / 3, 1. / 3, 1., 1.])
val = points[:, 0]
hfunc = interpolate.LinearNDInterpolator(points, hue)
sfunc = interpolate.CloughTocher2DInterpolator(points, sat)
vfunc = interpolate.LinearNDInterpolator(points, val)
return hfunc, sfunc, vfunc
def _cubic_interpolator(self, x, y):
if self._dim == 1:
ival = interpolate.interp1d(self._points[self._nanmask].flatten(),
y[self._nanmask].flatten(),
kind="cubic")(x)[:, np.newaxis]
else:
ival = interpolate.CloughTocher2DInterpolator(
self._triangulation, y[self._nanmask])(x)
return np.squeeze(ival)
def interpolate(self, shape=None):
self.interpolator = interp.CloughTocher2DInterpolator(
(self.anchors[:, 1], self.anchors[:, 0]),
self.coarse_fit[0, ...].reshape((self.coarse_len**2, 1)))
patch = self.interpolator(np.array(self.fine_ind))
if shape is None:
self.patch = patch.reshape(self.fine_shape)
else:
self.patch = patch.reshape(shape)
def _interpolate_missing_data(data, mask, method='cubic'):
"""
Interpolate missing data as identified by the ``mask`` keyword.
Parameters
----------
data : 2D `~numpy.ndarray`
An array containing the 2D image.
mask : 2D bool `~numpy.ndarray`
A 2D booleen mask array with the same shape as the input
``data``, where a `True` value indicates the corresponding
element of ``data`` is masked. The masked data points are
those that will be interpolated.
method : {'cubic', 'nearest'}, optional
The method of used to interpolate the missing data:
* ``'cubic'``: Masked data are interpolated using 2D cubic
splines. This is the default.
* ``'nearest'``: Masked data are interpolated using
nearest-neighbor interpolation.
Returns
-------
data_interp : 2D `~numpy.ndarray`
The interpolated 2D image.
"""
from scipy import interpolate
data_interp = np.array(data, copy=True)
if len(data_interp.shape) != 2:
raise ValueError('data must be a 2D array.')
if mask.shape != data.shape:
raise ValueError('mask and data must have the same shape.')
y, x = np.indices(data_interp.shape)
xy = np.dstack((x[~mask].ravel(), y[~mask].ravel()))[0]
z = data_interp[~mask].ravel()
if method == 'nearest':
interpol = interpolate.NearestNDInterpolator(xy, z)
elif method == 'cubic':
interpol = interpolate.CloughTocher2DInterpolator(xy, z)
else:
raise ValueError('Unsupported interpolation method.')
xy_missing = np.dstack((x[mask].ravel(), y[mask].ravel()))[0]
data_interp[mask] = interpol(xy_missing)
return data_interp
def add_transformation(self, model):
if model.is_affine():
new_model_matrix = model.get_matrix()
# Need to add the transformation either to the pre_non_affine or the post_non_affine
if self.non_affine_transform is None:
cur_transformation = self.pre_non_affine_transform
else:
cur_transformation = self.post_non_affine_transform
# Compute the new transformation (multiply from the left)
new_transformation = np.dot(new_model_matrix, np.vstack((cur_transformation, [0., 0., 1.])))[:2]
if self.non_affine_transform is None:
self.pre_non_affine_transform = new_transformation
else:
self.post_non_affine_transform = new_transformation
# Apply the model to each of the surrounding polygon locations
self.surrounding_polygon = model.apply_special(self.surrounding_polygon)
else:
# Non-affine transformation
self.non_affine_transform = model
# TODO - need to see if this returns a sufficient bounding box for the reverse transformation
# Find the new surrounding polygon locations
# using a forward transformation from the boundaries of the source image to the destination
boundary1 = np.array([[float(p), 0.] for p in np.arange(self.width)])
boundary2 = np.array([[float(p), float(self.height - 1)] for p in np.arange(self.width)])
boundary3 = np.array([[0., float(p)] for p in np.arange(self.height)])
boundary4 = np.array([[float(self.width - 1), float(p)] for p in np.arange(self.height)])
boundaries = np.concatenate((boundary1, boundary2, boundary3, boundary4))
boundaries = np.dot(self.pre_non_affine_transform[:2, :2], boundaries.T).T + self.pre_non_affine_transform[:, 2].reshape((1, 2))
src_points, dest_points = model.get_point_map()
cubic_interpolator = spint.CloughTocher2DInterpolator(src_points, dest_points)
self.surrounding_polygon = cubic_interpolator(boundaries)
# Find the new surrounding polygon locations (using the destination points of the non affine transformation)
#dest_points = model.get_point_map()[1]
#hull = ConvexHull(dest_points)
#self.surrounding_polygon = dest_points[hull.vertices]
# Update bbox and shape according to the new borders
self.bbox, self.shape = compute_bbox_and_shape(self.surrounding_polygon)
# Remove any rendering
self.already_rendered = False
self.img = None
def test_interpolation(mesh):
from scipy import interpolate
x, y = mesh.x, mesh.y
Z = np.exp(-x**2 - y**2)
# We ensure interpolation points are within convex hull
xi = np.random.uniform(0.1, 0.9, 10)
yi = np.random.uniform(0.1, 0.9, 10)
# Stripy
zn1 = mesh.interpolate_nearest(xi, yi, Z)
zl1, err = mesh.interpolate_linear(xi, yi, Z)
zc1, err = mesh.interpolate_cubic(xi, yi, Z)
# cKDTree
tree = interpolate.NearestNDInterpolator((x, y), Z)
zn2 = tree(xi, yi)
# Qhull
tri = interpolate.LinearNDInterpolator((x, y), Z, 0.0)
zl2 = tri((xi, yi))
# Clough Tocher
cti = interpolate.CloughTocher2DInterpolator(np.column_stack([x,y]),\
Z, tol=1e-10, maxiter=20)
zc2 = cti((xi, yi))
zc2[np.isnan(zc2)] = 0.0
# Spline
spl = interpolate.SmoothBivariateSpline(x, y, Z)
zc3 = spl.ev(xi, yi)
# Radial basis function
rbf = interpolate.Rbf(x, y, Z)
zc4 = rbf(xi, yi)
print("squared residual in interpolation\n \
- nearest neighbour = {}\n \
- linear = {}\n \
- cubic (clough-tocher) = {}\n \
- cubic (spline) = {}\n \
- cubic (rbf) = {}" .format(((zn1 - zn2)**2).max(), \
((zl1 - zl2)**2).max(), \
((zc1 - zc2)**2).max(), \
((zc1 - zc3)**2).max(), \
((zc1 - zc4)**2).max(),) )
def test_derivative(mesh):
from scipy import interpolate
# Create a field to test derivatives
x, y = mesh.x, mesh.y
Z = np.exp(-x**2 - y**2)
Zx = -2 * x * Z
Zy = -2 * y * Z
gradZ = np.hypot(Zx, Zy)
# Stripy
t = clock()
Zx1, Zy1 = mesh.gradient(Z, nit=10, tol=1e-10)
t1 = clock() - t
gradZ1 = np.hypot(Zx1, Zy1)
# Spline
spl = interpolate.SmoothBivariateSpline(x, y, Z)
t = clock()
Zx2 = spl.ev(x, y, dx=1)
Zy2 = spl.ev(x, y, dy=1)
t2 = clock() - t
gradZ2 = np.hypot(Zx2, Zy2)
# Clough Tocher
# This one is most similar to what is used in stripy
t = clock()
cti = interpolate.CloughTocher2DInterpolator(np.column_stack([x,y]),\
Z, tol=1e-10, maxiter=20)
t3 = clock() - t
Zx3 = cti.grad[:, :, 0].ravel()
Zy3 = cti.grad[:, :, 1].ravel()
gradZ3 = np.hypot(Zx3, Zy3)
res1 = ((gradZ1 - gradZ)**2).max()
res2 = ((gradZ2 - gradZ)**2).max()
res3 = ((gradZ3 - gradZ)**2).max()
print("squared error in first derivative\n \
- stripy = {} took {}s\n \
- spline = {} took {}s\n \
- cloughtocher = {} took {}s".format(res1, t1, res2, t2, res3, t3))
def Interpolate(videosFilePath, videoNames, pupilCenter, calibPointXY,
startFrame, endFrame):
pupilCenterCalib = pupilCenter[startFrame:endFrame]
#interpoleFuncX = interp(pupilCenterCalib[:,0], calibPointXY[:,1])
#interpoleFuncY = interp1d(pupilCenterCalib[:,0], calibPointXY[:,1])
#eyeFocusX = interpoleFuncX(pupilCenter[:,0])
#eyeFocusY = interpoleFuncX(pupilCenter[:,1])
interpolator = interp.CloughTocher2DInterpolator(
pupilCenter[startFrame:endFrame, :], calibPointXY)
#eyeFocusCoords = (eyeFocusX,eyeFocusY)
eyeFocusCoords = interpolator(pupilCenter)
worldVidCap = cv2.VideoCapture(videosFilePath + '/' + videoNames[0] +
'_f_c.mp4')
frame_count = int(worldVidCap.get(cv2.CAP_PROP_FRAME_COUNT))
vidWidth = worldVidCap.get(cv2.CAP_PROP_FRAME_WIDTH) #Get video height
vidHeight = worldVidCap.get(cv2.CAP_PROP_FRAME_HEIGHT) #Get video width
vidLength = range(frame_count)
outputVid = cv2.VideoWriter(videosFilePath + '/EyeFocusOnWorld.mp4', -1,
120, (int(vidWidth), int(vidHeight)))
for jj in range(len(eyeFocusCoords)):
if math.isnan(eyeFocusCoords[jj, 0]):
success, image = worldVidCap.read()
outputVid.write(image)
else:
success, image = worldVidCap.read()
cv2.circle(
image,
(int(eyeFocusCoords[jj, 0]), int(eyeFocusCoords[jj, 1])),
radius=10,
color=[0, 255, 0],
thickness=-1)
outputVid.write(image)
cv2.imshow('', image)
cv2.waitKey(200)
np.save(videosFilePath + '/EyeFocusWorld.npy', eyeFocusCoords)
return eyeFocusCoords
def buildInterpolator2D(obs_arr, cosmo_params, method='Rbf'):
'''Build an interpolator:
input:
obs_arr = (points, Nbin), where # of points = # of models
cosmo_params = (points, Nparams), currently Nparams is hard-coded
to be 3 (om,w,si8)
output:
spline_interps
Usage:
spline_interps[ibin](im, wm, sm)
'''
m, s = cosmo_params.T
spline_interps = list()
for ibin in range(obs_arr.shape[-1]):
model = obs_arr[:, ibin]
if method == 'Rbf':
iinterp = interpolate.Rbf(m, s, model) #
elif method == 'linear':
iinterp = interpolate.LinearNDInterpolator(cosmo_params, model) #
elif method == 'clough':
iinterp = interpolate.CloughTocher2DInterpolator(
cosmo_params, model) #
#iinterp = interpolate.Rbf(m, s, model)
spline_interps.append(iinterp)
#return spline_interps
def interp_cosmo(params):
'''Interpolate the powspec for certain param.
Params: list of 3 parameters = (om, w, si8)
Method: "multiquadric" for spline (default), and "GP" for Gaussian process.
'''
mm, sm = params
gen_ps = lambda ibin: spline_interps[ibin](mm, sm)
ps_interp = array(map(gen_ps, range(obs_arr.shape[-1])))
ps_interp = ps_interp.reshape(-1, 1).squeeze()
return ps_interp
return interp_cosmo
def interpf(x, z, method=None, extrap=False, arrays=False):
'''interpolate to find f, where z = f(*x)
Input:
x: an array of shape (npts, dim) or (npts,)
z: an array of shape (npts,)
method: string for kind of interpolator
extrap: if True, extrapolate a bounding box (can reduce # of nans)
arrays: if True, z = f(*x) is a numpy array; otherwise don't use arrays
Output:
interpolated function f, where z = f(*x)
NOTE:
if scipy is not installed, will use np.interp for 1D (non-rbf),
or mystic's rbf otherwise. default method is 'nearest' for
1D and 'linear' otherwise. method can be one of ('rbf','linear','cubic',
'nearest','inverse','gaussian','multiquadric','quintic','thin_plate').
NOTE:
if extrap is True, extrapolate using interpf with method='thin_plate'
(or 'rbf' if scipy is not found). Alternately, any one of ('rbf',
'linear','cubic','nearest','inverse','gaussian','multiquadric',
'quintic','thin_plate') can be used. If extrap is a cost function
z = f(x), then directly use it in the extrapolation.
''' #XXX: return f(*x) or f(x)?
if arrays:
_f, _fx = _to_array, _array
else:
_f, _fx = _to_nonarray, _nonarray
x,z = extrapolate(x,z,method=extrap)
x,z = _unique(x,z,sort=True)
# avoid nan as first value #XXX: better choice than 'nearest'?
if method is None: method = 'nearest' if x.ndim is 1 else 'linear'
methods = dict(rbf=0, linear=1, nearest=2, cubic=3)
functions = {0:'multiquadric', 1:'linear', 2:'nearest', 3:'cubic'}
# also: ['thin_plate','inverse','gaussian','quintic']
kind = methods[method] if method in methods else None
function = functions[kind] if (not kind is None) else method
if kind is None: kind = 0 #XXX: or raise KeyError ?
try:
import scipy.interpolate as si
except ImportError:
if not kind is 0: # non-rbf
if x.ndim is 1: # is 1D, so use np.interp
import numpy as np
return lambda xn: _fx(np.interp(xn, xp=x, fp=z))
kind = 0 # otherwise, utilize mystic's rbf
si = _rbf
if kind is 0: # 'rbf'
import numpy as np
return _f(si.Rbf(*np.vstack((x.T, z)), function=function, smooth=0))
elif x.ndim is 1:
return _f(si.interp1d(x, z, fill_value='extrapolate', bounds_error=False, kind=method))
elif kind is 1: # 'linear'
return _f(si.LinearNDInterpolator(x, z, rescale=False))
elif kind is 2: # 'nearest'
return _f(si.NearestNDInterpolator(x, z, rescale=False))
#elif x.ndim is 1: # 'cubic'
# return lambda xn: _fx(si.spline(x, z, xn))
return _f(si.CloughTocher2DInterpolator(x, z, rescale=False))
def __init__(self, coords, values, neighbors=3, dist_transform=2, **kwargs):
super().__init__(coords, values, neighbors=neighbors, dist_transform=dist_transform)
self.ct_interpolator = interpolate.CloughTocher2DInterpolator(self.tri, self.values, **kwargs)
def __call__(self, Zin):
F = interpolate.CloughTocher2DInterpolator(self.XY, Zin)
return F(self.XYout)
x = np.array(-500.* np.cos(u) * (5.3 - np.sin(u) + (1. + 0.138 * l) * np.cos(v)))
y = np.array(750. * np.sin(u) * (5.5 - 2. * np.sin(u) + (0.9 + 0.114*l) * np.cos(v)))
z = np.array(2500. * np.sin(u) + (663. + 114. * l) * np.sin(v - 0.13 * (np.pi-u)))
return x,y,z
du = (1.01*np.pi-(-0.016*np.pi))/max_u*spatial_resolution
dv = (1.425*np.pi-(-0.23*np.pi))/max_v*spatial_resolution
u = np.arange(-0.016*np.pi, 1.01*np.pi, du)
v = np.arange(-0.23*np.pi, 1.425*np.pi, dv)
u, v = np.meshgrid(u, v, indexing='ij')
# for the middle of the granule cell layer:
l = -1.
s = surface (u, v, l)
X = np.vstack((s[0].ravel(),s[1].ravel(),s[2].ravel())).T
del s, u, v, l
n_points = X.shape[0]
n_neighbors = 30
n_components = 2
Y = manifold.LocallyLinearEmbedding(n_neighbors, n_components,
eigen_solver='auto',
method='modified').fit_transform(X)
ip_surface = interpolate.CloughTocher2DInterpolator(Y, X)
d = 1e-5
#free energy landscape
k=1
T=1
x1 = np.load(args.landscape)
z = np.loadtxt(args.number)
sum_z = np.sum(z)
z = z/sum_z
g = -k*T*np.log(z)
x2 = x1[0:,:] # start from volume 0 to end
if args.interpolate=='linear':
Hfunc = interpolate.LinearNDInterpolator(x2, g)
elif args.interpolate=='cubic':
Hfunc = interpolate.CloughTocher2DInterpolator(x2, g)
grid_z = Hfunc(grid_x, grid_y)
# Main loop
for nstep in range(nstepmax):
# calculation of the x and y-components of the force, dVx and dVy respectively
dVx=(Hfunc(xi+d,yi)-Hfunc(xi-d,yi))/(2*d)
dVy=(Hfunc(xi,yi+d)-Hfunc(xi,yi-d))/(2*d)
print("dV: ", np.mean(np.sqrt(dVx**2+dVy**2)))
x0 = xi
y0 = yi
# string steps:
def __init__(self, config):
# Shot data is mode-dependent
mode = config["mode"]
if mode not in config:
raise ValueError(
"parameters for mode '%s' missing from config file" % mode)
config_mode = config[mode]
# Generate shot data
if "shot" in config_mode:
shot = config_mode["shot"]
aspect_ratio = config["aspect_ratio"]
flux_ref = config_mode["flux"]["ref"]
# TODO save and reload instead of always generating
generateShotData(shot, aspect_ratio, flux_ref)
# Load or pre-compute magnetic fields, ohmic power and magnetic energy
filename = hashname(config)
try: # Load pre-computed data set if it exists
with h5py.File(filename, "r") as file:
alpha = file["alpha"][:]
lmbda0 = file["lambda_0"][:]
flux = file["flux"][:]
B_phi = file["B_phi"][:]
B_theta = file["B_theta"][:]
P_ohm = file["P_ohm"][:]
U_mag = file["U_mag"][:]
Ip = file["Ip"][:]
F = file["F"][:]
except: # Otherwise, pre-compute and save the results
with h5py.File(filename, "w") as file:
alpha, lmbda0, flux, B_phi, B_theta, P_ohm, U_mag, Ip, F = self.preCalc(
config)
file.create_dataset("alpha", data=alpha)
file.create_dataset("lambda_0", data=lmbda0)
file.create_dataset("flux", data=flux)
file.create_dataset("B_phi", data=B_phi)
file.create_dataset("B_theta", data=B_theta)
file.create_dataset("P_ohm", data=P_ohm)
file.create_dataset("U_mag", data=U_mag)
file.create_dataset("Ip", data=Ip)
file.create_dataset("F", data=F)
# Make splines for magnetic fields, ohmic power and magnetic energy
self.B_phi = sp.RectBivariateSpline(alpha, lmbda0, B_phi)
self.B_theta = sp.RectBivariateSpline(alpha, lmbda0, B_theta)
self.P_ohm = sp.RectBivariateSpline(alpha, lmbda0, P_ohm)
self.U_mag = sp.RectBivariateSpline(alpha, lmbda0, U_mag)
# One more spline
fixed_alpha = 4.0 # FIXME: using hardcoded fixed alpha for now
fixed_B_theta = sp.interp1d(alpha, B_theta, axis=0)(fixed_alpha)
self.B_theta_to_lmbda0 = sp.CubicSpline(fixed_B_theta,
lmbda0,
bc_type="natural")
# "translation" interpolators
index_alpha = np.nonzero(
alpha == fixed_alpha)[0][0] # FIXME: at least interpolate
fixed_F = F[index_alpha, :, :]
fixed_Ip = Ip[index_alpha, :, :]
points = np.empty((fixed_F.size, 2))
lmbda0_values = np.empty(fixed_F.size)
flux_values = np.empty(fixed_F.size)
for (i, l0) in enumerate(lmbda0):
for (j, fl) in enumerate(flux):
k = i * flux.size + j
points[k, :] = [fixed_F[i, j], fixed_Ip[i, j]]
lmbda0_values[k] = l0
flux_values[k] = fl
self.lmbda0 = sp.CloughTocher2DInterpolator(points,
lmbda0_values,
rescale=True)
self.flux = sp.CloughTocher2DInterpolator(points,
flux_values,
rescale=True)
def piper(arrays, plottitle, use_color, fig=None, **kwargs):
"""Create a Piper plot:
Args:
arrays (ndarray, or see below): n x 8 ndarray with columns corresponding
to Ca Mg Na K HCO3 CO3 Cl SO4 data. See below for a different format
for this argument if you want to plot different subsets of data with
different marker styles.
plottitle (str): title of Piper plot
use_color (bool): use background use_coloring of Piper plot
fig (Figure): matplotlib Figure to use, one will be created if None
If you would like to plot different sets of data e.g. from different aquifers
with different marker styles, you can pass a list of tuples as the first
arguments. The first item of each tuple should be an n x 8 ndarray, as usual.
The second item should be a dictionary of keyword arguments to ``plt.scatter``.
Any keyword arguments for ``plt.scatter`` that are in common to all the
subsets can be passed to the ``piper()`` function directly. By default the
markers are plotted with: ``plt.scatter(..., marker=".", color="k", alpha=1)``.
Returns a dictionary with:
if use_color = False:
cat: [nx3] meq% of cations, order: Ca Mg Na+K
an: [nx3] meq% of anions, order: HCO3+CO3 SO4 Cl
if use_color = True:
cat: [nx3] RGB triple cations
an: [nx3] RGB triple anions
diamond: [nx3] RGB triple central diamond
"""
kwargs["marker"] = kwargs.get("marker", ".")
kwargs["alpha"] = kwargs.get("alpha", 1)
kwargs["facecolor"] = kwargs.get("facecolor", "k")
try:
shp = arrays.shape
if shp[1] == 8:
arrays = [(arrays, {})]
except:
pass
if fig is None:
fig = plt.figure()
# Basic shape of piper plot
offset = 0.05
offsety = offset * np.tan(np.pi / 3)
h = 0.5 * np.tan(np.pi / 3)
ltriangle_x = np.array([0, 0.5, 1, 0])
ltriangle_y = np.array([0, h, 0, 0])
rtriangle_x = ltriangle_x + 2 * offset + 1
rtriangle_y = ltriangle_y
diamond_x = np.array([0.5, 1, 1.5, 1, 0.5]) + offset
diamond_y = h * (np.array([1, 2, 1, 0, 1])) + (offset * np.tan(np.pi / 3))
ax = fig.add_subplot(111,
aspect='equal',
frameon=False,
xticks=[],
yticks=[])
ax.plot(ltriangle_x, ltriangle_y, '-k')
ax.plot(rtriangle_x, rtriangle_y, '-k')
ax.plot(diamond_x, diamond_y, '-k')
# labels and title
plt.title(plottitle)
plt.text(-offset,
-offset,
u'$Ca^{2+}$',
horizontalalignment='left',
verticalalignment='center')
plt.text(0.5,
h + offset,
u'$Mg^{2+}$',
horizontalalignment='center',
verticalalignment='center')
plt.text(1 + offset,
-offset,
u'$Na^+ + K^+$',
horizontalalignment='right',
verticalalignment='center')
plt.text(1 + offset,
-offset,
u'$HCO_3^- + CO_3^{2-}$',
horizontalalignment='left',
verticalalignment='center')
plt.text(1.5 + 2 * offset,
h + offset,
u'$SO_4^{2-}$',
horizontalalignment='center',
verticalalignment='center')
plt.text(2 + 3 * offset,
-offset,
u'$Cl^-$',
horizontalalignment='right',
verticalalignment='center')
# Convert chemistry into plot coordinates
gmol = np.array([
40.078, 24.305, 22.989768, 39.0983, 61.01714, 60.0092, 35.4527, 96.0636
])
eqmol = np.array([2., 2., 1., 1., 1., 2., 1., 2.])
for dat_piper, plt_kws in arrays:
n = dat_piper.shape[0]
meqL = (dat_piper / gmol) * eqmol
sumcat = np.sum(meqL[:, 0:4], axis=1)
suman = np.sum(meqL[:, 4:8], axis=1)
cat = np.zeros((n, 3))
an = np.zeros((n, 3))
cat[:, 0] = meqL[:, 0] / sumcat # Ca
cat[:, 1] = meqL[:, 1] / sumcat # Mg
cat[:, 2] = (meqL[:, 2] + meqL[:, 3]) / sumcat # Na+K
an[:, 0] = (meqL[:, 4] + meqL[:, 5]) / suman # HCO3 + CO3
an[:, 2] = meqL[:, 6] / suman # Cl
an[:, 1] = meqL[:, 7] / suman # SO4
# Convert into cartesian coordinates
cat_x = 0.5 * (2 * cat[:, 2] + cat[:, 1])
cat_y = h * cat[:, 1]
an_x = 1 + 2 * offset + 0.5 * (2 * an[:, 2] + an[:, 1])
an_y = h * an[:, 1]
d_x = an_y / (4 * h) + 0.5 * an_x - cat_y / (4 * h) + 0.5 * cat_x
d_y = 0.5 * an_y + h * an_x + 0.5 * cat_y - h * cat_x
# plot data
kws = dict(kwargs)
kws.update(plt_kws)
plt.scatter(cat_x, cat_y, **kws)
plt.scatter(an_x, an_y,
**{k: v
for k, v in kws.items() if not k == "label"})
plt.scatter(d_x, d_y,
**{k: v
for k, v in kws.items() if not k == "label"})
# use_color coding Piper plot
if use_color == False:
# add density use_color bar if alphalevel < 1
if kwargs.get("alpha", 1) < 1.0:
ax1 = fig.add_axes([0.75, 0.4, 0.01, 0.2])
cmap = plt.cm.gray_r
norm = mpl.use_colors.Normalize(vmin=0, vmax=1 / kwargs["alpha"])
cb1 = mpl.use_colorbar.use_colorbarBase(ax1,
cmap=cmap,
norm=norm,
orientation='vertical')
cb1.set_label('Dot Density')
return (dict(cat=cat, an=an))
else:
# create empty grids to interpolate to
x0 = 0.5
y0 = x0 * np.tan(np.pi / 6)
X = np.reshape(np.repeat(np.linspace(0, 2 + 2 * offset, 1000), 1000),
(1000, 1000), 'F')
Y = np.reshape(np.repeat(np.linspace(0, 2 * h + offsety, 1000), 1000),
(1000, 1000), 'C')
H = np.nan * np.zeros_like(X)
S = np.nan * np.zeros_like(X)
V = np.nan * np.ones_like(X)
A = np.nan * np.ones_like(X)
# create masks for cation, anion triangle and upper and lower diamond
ind_cat = np.logical_or(np.logical_and(X < 0.5, Y < 2 * h * X),
np.logical_and(X > 0.5, Y < (2 * h * (1 - X))))
ind_an = np.logical_or(
np.logical_and(X < 1.5 + (2 * offset),
Y < 2 * h * (X - 1 - 2 * offset)),
np.logical_and(X > 1.5 + (2 * offset), Y <
(2 * h * (1 - (X - 1 - 2 * offset)))))
ind_ld = np.logical_and(
np.logical_or(
np.logical_and(X < 1.0 + offset,
Y > -2 * h * X + 2 * h * (1 + 2 * offset)),
np.logical_and(X > 1.0 + offset, Y > 2 * h * X - 2 * h)),
Y < h + offsety)
ind_ud = np.logical_and(
np.logical_or(
np.logical_and(X < 1.0 + offset, Y < 2 * h * X),
np.logical_and(X > 1.0 + offset,
Y < -2 * h * X + 4 * h * (1 + offset))),
Y > h + offsety)
ind_d = np.logical_or(ind_ld == 1, ind_ud == 1)
# Hue: convert x,y to polar coordinates
# (angle between 0,0 to x0,y0 and x,y to x0,y0)
H[ind_cat] = np.pi + np.arctan2(Y[ind_cat] - y0, X[ind_cat] - x0)
H[ind_cat] = np.mod(H[ind_cat] - np.pi / 6, 2 * np.pi)
H[ind_an] = np.pi + np.arctan2(Y[ind_an] - y0, X[ind_an] -
(x0 + 1 + (2 * offset)))
H[ind_an] = np.mod(H[ind_an] - np.pi / 6, 2 * np.pi)
H[ind_d] = np.pi + np.arctan2(Y[ind_d] - (h + offsety), X[ind_d] -
(1 + offset))
# Saturation: 1 at edge of triangle, 0 in the centre,
# Clough Tocher interpolation, square root to reduce central white region
xy_cat = np.array([[0.0, 0.0], [x0, h], [1.0, 0.0], [x0, y0]])
xy_an = np.array([[1 + (2 * offset), 0.0], [x0 + 1 + (2 * offset), h],
[2 + (2 * offset), 0.0], [x0 + 1 + (2 * offset),
y0]])
xy_d = np.array([[x0 + offset, h + offsety],
[1 + offset, 2 * h + offsety],
[x0 + 1 + offset, h + offsety], [1 + offset, offsety],
[1 + offset, h + offsety]])
z_cat = np.array([1.0, 1.0, 1.0, 0.0])
z_an = np.array([1.0, 1.0, 1.0, 0.0])
z_d = np.array([1.0, 1.0, 1.0, 1.0, 0.0])
s_cat = interpolate.CloughTocher2DInterpolator(xy_cat, z_cat)
s_an = interpolate.CloughTocher2DInterpolator(xy_an, z_an)
s_d = interpolate.CloughTocher2DInterpolator(xy_d, z_d)
S[ind_cat] = s_cat.__call__(X[ind_cat], Y[ind_cat])
S[ind_an] = s_an.__call__(X[ind_an], Y[ind_an])
S[ind_d] = s_d.__call__(X[ind_d], Y[ind_d])
# Value: 1 everywhere
V[ind_cat] = 1.0
V[ind_an] = 1.0
V[ind_d] = 1.0
# Alpha: 1 everywhere
A[ind_cat] = 1.0
A[ind_an] = 1.0
A[ind_d] = 1.0
# convert HSV to RGB
R, G, B = hsvtorgb(H, S**0.5, V)
RGBA = np.dstack((R, G, B, A))
# visualise
plt.imshow(RGBA,
origin='lower',
aspect=1.0,
extent=(0, 2 + 2 * offset, 0, 2 * h + offsety))
# calculate RGB triples for data points
# hue
hcat = np.pi + np.arctan2(cat_y - y0, cat_x - x0)
hcat = np.mod(hcat - np.pi / 6, 2 * np.pi)
han = np.pi + np.arctan2(an_y - y0, an_x - (x0 + 1 + (2 * offset)))
han = np.mod(han - np.pi / 6, 2 * np.pi)
hd = np.pi + np.arctan2(d_y - (h + offsety), d_x - (1 + offset))
# saturation
scat = s_cat.__call__(cat_x, cat_y)**0.5
san = s_an.__call__(an_x, an_y)**0.5
sd = s_d.__call__(d_x, d_y)**0.5
# value
v = np.ones_like(hd)
# rgb
cat = np.vstack((hsvtorgb(hcat, scat, v))).T
an = np.vstack((hsvtorgb(han, san, v))).T
d = np.vstack((hsvtorgb(hd, sd, v))).T
return (dict(cat=cat, an=an, diamond=d))
#This here makes a grid for a given Re (alfa,S) and for each point sigma
for case in caseList:
# print case.alfa, case.Re
for p in zip(case.S, case.sigma):
alfa.append(float(case.alfa))
S.append(p[0])
sig.append(p[1])
p = [] #this grid (alfa,S) is stored in p, and used to find an interpolant
for pair in zip(alfa, S):
p.append([pair[0], pair[1]])
if InterType == 1:
interp = interpolate.LinearNDInterpolator(p, sig)
elif InterType == 2:
interp = interpolate.CloughTocher2DInterpolator(p, sig)
else:
raise "Unknown Interpolation type"
if with3D:
Anew = np.linspace(min(alfa), max(alfa), num=200, endpoint=True)
Snew = np.linspace(min(S), max(S), num=200, endpoint=True)
Anew, Snew = np.meshgrid(Anew, Snew)
zz = interp(Anew, Snew)
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.set_xlabel('alpha')
ax.set_ylabel('S')
ax.set_zlabel('Sigma')
plt.title('Re=' + str(caseList[0].Re))
def piper(dat_piper, plottitle, alphalevel, color):
'''
Create a Piper plot
INPUT:
dat_piper: [nx8] matrix, chemical analysis in mg/L
order: Ca Mg Na K HCO3 CO3 Cl SO4
plottitle: string with title of Piper plot
alphalevel: transparency level of points. If 1, points are opaque
color: boolean, use background coloring of Piper plot
OUTPUT:
figure with piperplot
dictionary with:
if color = False:
cat: [nx3] meq% of cations, order: Ca Mg Na+K
an: [nx3] meq% of anions, order: HCO3+CO3 SO4 Cl
if color = True:
cat: [nx3] RGB triple cations
an: [nx3] RGB triple anions
diamond: [nx3] RGB triple central diamond
'''
# Basic shape of piper plot
offset = 0.05
offsety = offset * np.tan(np.pi / 3)
h = 0.5 * np.tan(np.pi / 3)
ltriangle_x = np.array([0, 0.5, 1, 0])
ltriangle_y = np.array([0, h, 0, 0])
rtriangle_x = ltriangle_x + 2 * offset + 1
rtriangle_y = ltriangle_y
diamond_x = np.array([0.5, 1, 1.5, 1, 0.5]) + offset
diamond_y = h * (np.array([1, 2, 1, 0, 1])) + (offset * np.tan(np.pi / 3))
fig = plt.figure()
ax = fig.add_subplot(111,
aspect='equal',
frameon=False,
xticks=[],
yticks=[])
ax.plot(ltriangle_x, ltriangle_y, '-k')
ax.plot(rtriangle_x, rtriangle_y, '-k')
ax.plot(diamond_x, diamond_y, '-k')
# labels and title
plt.title(plottitle)
plt.text(-offset,
-offset,
u'$Ca^{2+}$',
horizontalalignment='left',
verticalalignment='center')
plt.text(0.5,
h + offset,
u'$Mg^{2+}$',
horizontalalignment='center',
verticalalignment='center')
plt.text(1 + offset,
-offset,
u'$Na^+ + K^+$',
horizontalalignment='right',
verticalalignment='center')
plt.text(1 + offset,
-offset,
u'$HCO_3^- + CO_3^{2-}$',
horizontalalignment='left',
verticalalignment='center')
plt.text(1.5 + 2 * offset,
h + offset,
u'$SO_4^{2-}$',
horizontalalignment='center',
verticalalignment='center')
plt.text(2 + 3 * offset,
-offset,
u'$Cl^-$',
horizontalalignment='right',
verticalalignment='center')
# Convert chemistry into plot coordinates
gmol = np.array([
40.078, 24.305, 22.989768, 39.0983, 61.01714, 60.0092, 35.4527, 96.0636
])
eqmol = np.array([2., 2., 1., 1., 1., 2., 1., 2.])
n = dat_piper.shape[0]
meqL = (dat_piper / gmol) * eqmol
sumcat = np.sum(meqL[:, 0:4], axis=1)
suman = np.sum(meqL[:, 4:8], axis=1)
cat = np.zeros((n, 3))
an = np.zeros((n, 3))
cat[:, 0] = meqL[:, 0] / sumcat # Ca
cat[:, 1] = meqL[:, 1] / sumcat # Mg
cat[:, 2] = (meqL[:, 2] + meqL[:, 3]) / sumcat # Na+K
an[:, 0] = (meqL[:, 4] + meqL[:, 5]) / suman # HCO3 + CO3
an[:, 2] = meqL[:, 6] / suman # Cl
an[:, 1] = meqL[:, 7] / suman # SO4
# Convert into cartesian coordinates
cat_x = 0.5 * (2 * cat[:, 2] + cat[:, 1])
cat_y = h * cat[:, 1]
an_x = 1 + 2 * offset + 0.5 * (2 * an[:, 2] + an[:, 1])
an_y = h * an[:, 1]
d_x = an_y / (4 * h) + 0.5 * an_x - cat_y / (4 * h) + 0.5 * cat_x
d_y = 0.5 * an_y + h * an_x + 0.5 * cat_y - h * cat_x
# plot data
plt.plot(cat_x, cat_y, '.k', alpha=alphalevel)
plt.plot(an_x, an_y, '.k', alpha=alphalevel)
plt.plot(d_x, d_y, '.k', alpha=alphalevel)
# color coding Piper plot
if color == False:
# add density color bar if alphalevel < 1
if alphalevel < 1.0:
ax1 = fig.add_axes([0.75, 0.4, 0.01, 0.2])
cmap = plt.cm.gray_r
norm = mpl.colors.Normalize(vmin=0, vmax=1 / alphalevel)
cb1 = mpl.colorbar.ColorbarBase(ax1,
cmap=cmap,
norm=norm,
orientation='vertical')
cb1.set_label('Dot Density')
return (dict(cat=cat, an=an))
else:
# create empty grids to interpolate to
x0 = 0.5
y0 = x0 * np.tan(np.pi / 6)
X = np.reshape(np.repeat(np.linspace(0, 2 + 2 * offset, 1000), 1000),
(1000, 1000), 'F')
Y = np.reshape(np.repeat(np.linspace(0, 2 * h + offsety, 1000), 1000),
(1000, 1000), 'C')
H = np.nan * np.zeros_like(X)
S = np.nan * np.zeros_like(X)
V = np.nan * np.ones_like(X)
A = np.nan * np.ones_like(X)
# create masks for cation, anion triangle and upper and lower diamond
ind_cat = np.logical_or(np.logical_and(X < 0.5, Y < 2 * h * X),
np.logical_and(X > 0.5, Y < (2 * h * (1 - X))))
ind_an = np.logical_or(
np.logical_and(X < 1.5 + (2 * offset),
Y < 2 * h * (X - 1 - 2 * offset)),
np.logical_and(X > 1.5 + (2 * offset), Y <
(2 * h * (1 - (X - 1 - 2 * offset)))))
ind_ld = np.logical_and(
np.logical_or(
np.logical_and(X < 1.0 + offset,
Y > -2 * h * X + 2 * h * (1 + 2 * offset)),
np.logical_and(X > 1.0 + offset, Y > 2 * h * X - 2 * h)),
Y < h + offsety)
ind_ud = np.logical_and(
np.logical_or(
np.logical_and(X < 1.0 + offset, Y < 2 * h * X),
np.logical_and(X > 1.0 + offset,
Y < -2 * h * X + 4 * h * (1 + offset))),
Y > h + offsety)
ind_d = np.logical_or(ind_ld == 1, ind_ud == 1)
# Hue: convert x,y to polar coordinates
# (angle between 0,0 to x0,y0 and x,y to x0,y0)
H[ind_cat] = np.pi + np.arctan2(Y[ind_cat] - y0, X[ind_cat] - x0)
H[ind_cat] = np.mod(H[ind_cat] - np.pi / 6, 2 * np.pi)
H[ind_an] = np.pi + np.arctan2(Y[ind_an] - y0, X[ind_an] -
(x0 + 1 + (2 * offset)))
H[ind_an] = np.mod(H[ind_an] - np.pi / 6, 2 * np.pi)
H[ind_d] = np.pi + np.arctan2(Y[ind_d] - (h + offsety), X[ind_d] -
(1 + offset))
# Saturation: 1 at edge of triangle, 0 in the centre,
# Clough Tocher interpolation, square root to reduce central white region
xy_cat = np.array([[0.0, 0.0], [x0, h], [1.0, 0.0], [x0, y0]])
xy_an = np.array([[1 + (2 * offset), 0.0], [x0 + 1 + (2 * offset), h],
[2 + (2 * offset), 0.0], [x0 + 1 + (2 * offset),
y0]])
xy_d = np.array([[x0 + offset, h + offsety],
[1 + offset, 2 * h + offsety],
[x0 + 1 + offset, h + offsety], [1 + offset, offsety],
[1 + offset, h + offsety]])
z_cat = np.array([1.0, 1.0, 1.0, 0.0])
z_an = np.array([1.0, 1.0, 1.0, 0.0])
z_d = np.array([1.0, 1.0, 1.0, 1.0, 0.0])
s_cat = interpolate.CloughTocher2DInterpolator(xy_cat, z_cat)
s_an = interpolate.CloughTocher2DInterpolator(xy_an, z_an)
s_d = interpolate.CloughTocher2DInterpolator(xy_d, z_d)
S[ind_cat] = s_cat.__call__(X[ind_cat], Y[ind_cat])
S[ind_an] = s_an.__call__(X[ind_an], Y[ind_an])
S[ind_d] = s_d.__call__(X[ind_d], Y[ind_d])
# Value: 1 everywhere
V[ind_cat] = 1.0
V[ind_an] = 1.0
V[ind_d] = 1.0
# Alpha: 1 everywhere
A[ind_cat] = 1.0
A[ind_an] = 1.0
A[ind_d] = 1.0
# convert HSV to RGB
R, G, B = hsvtorgb(H, S**0.5, V)
RGBA = np.dstack((R, G, B, A))
# visualise
plt.imshow(RGBA,
origin='lower',
aspect=1.0,
extent=(0, 2 + 2 * offset, 0, 2 * h + offsety))
# calculate RGB triples for data points
# hue
hcat = np.pi + np.arctan2(cat_y - y0, cat_x - x0)
hcat = np.mod(hcat - np.pi / 6, 2 * np.pi)
han = np.pi + np.arctan2(an_y - y0, an_x - (x0 + 1 + (2 * offset)))
han = np.mod(han - np.pi / 6, 2 * np.pi)
hd = np.pi + np.arctan2(d_y - (h + offsety), d_x - (1 + offset))
# saturation
scat = s_cat.__call__(cat_x, cat_y)**0.5
san = s_an.__call__(an_x, an_y)**0.5
sd = s_d.__call__(d_x, d_y)**0.5
# value
v = np.ones_like(hd)
# rgb
cat = np.vstack((hsvtorgb(hcat, scat, v))).T
an = np.vstack((hsvtorgb(han, san, v))).T
d = np.vstack((hsvtorgb(hd, sd, v))).T
return (dict(cat=cat, an=an, diamond=d))
# importar funciones de interpolación de la libreria de matemática avanzada from scipy import interpolate # Interpolación en una variable funcion = interpolate.interp1d([x1, x2, xN], [y1, y2, yN], 'zero') # Interpolación constante con Spline (Retorna valor de "y" anterior mas cercano) (Minimo 1 punto) funcion = interpolate.interp1d([x1, x2, xN], [y1, y2, yN], 'previous') # Interpolación constante (Retorna valor de "y" anterior mas cercano) (Minimo 1 punto) funcion = interpolate.interp1d([x1, x2, xN], [y1, y2, yN], 'next') # Interpolación constante (Retorna valor de "y" posterior mas cercano) (Minimo 1 punto) funcion = interpolate.interp1d([x1, x2, xN], [y1, y2, yN], 'nearest') # Interpolación del vecino más cercano (Retorna valor de "y" mas cercano) (Minimo 1 punto) funcion = interpolate.interp1d([x1, x2, xN], [y1, y2, yN], 'linear') # Interpolación lineal (Minimo 2 puntos) funcion = interpolate.interp1d([x1, x2, xN], [y1, y2, yN], 'slinear') # Interpolación lineal con Spline (Minimo 2 puntos) funcion = interpolate.interp1d([x1, x2, xN], [y1, y2, yN], 'quadratic') # Interpolación cuadratica con Spline (Minimo 3 puntos) funcion = interpolate.interp1d([x1, x2, xN], [y1, y2, yN], 'cubic') # Interpolación cubica con Spline (Minimo 4 puntos) # Interpolación multivariable x_vals = [[x11,x12,x1M],[x21,x22,x2M],[xN1,xN2,xNM]] # Valores independientes dados y_vals = [y1, y2, yN] # Valores dependientes dados malla = tuple(np.mgrid[x1_o:x1_f:x1_tam, x2_o:x2_f:x2_tam, xN_o:xN_f:xN_tam]) # Malla de valores a evaluar [x1 inicial:x1 final:n° puntos en x1, x2 inicial:x2 final:n° puntos en x2, xN inicial:xN final:n° puntos en xN] array = interpolate.griddata(x_vals, y_vals, malla, method='nearest') # Evaluación de la malla por Interpolación del vecino más cercano array = interpolate.griddata(x_vals, y_vals, malla, method='linear') # Evaluación de la malla por Interpolación lineal array = interpolate.griddata(x_vals, y_vals, malla, method='cubic') # Evaluación de la malla por Interpolación cubica funcion = interpolate.NearestNDInterpolator(x_vals, y_vals) # Interpolación del vecino más cercano (Retorna valor de "y" mas cercano) (Minimo 1 punto) funcion = interpolate.LinearNDInterpolator(x_vals, y_vals) # Interpolación lineal (Minimo 2 puntos) funcion = interpolate.CloughTocher2DInterpolator(x_vals, y_vals) # Interpolación cubica para funciones de 2 variables (Minimo 2 puntos)
def list_plot3d_tuples(v, interpolation_type, texture, **kwds):
r"""
A 3-dimensional plot of a surface defined by the list `v`
of points in 3-dimensional space.
INPUT:
- ``v`` - something that defines a set of points in 3
space, for example:
- a matrix
This will be if using an interpolation type other than 'linear', or if using
``num_points`` with 'linear'; otherwise see :func:`list_plot3d_matrix`.
- a list of 3-tuples
- a list of lists (all of the same length, under same conditions as a matrix)
- ``texture`` - (default: "automatic", a solid light blue)
OPTIONAL KEYWORDS:
- ``interpolation_type`` - 'linear', 'clough' (CloughTocher2D), 'spline'
'linear' will perform linear interpolation
The option 'clough' will interpolate by using a piecewise cubic interpolating
Bezier polynomial on each triangle, using a Clough-Tocher scheme.
The interpolant is guaranteed to be continuously differentiable.
The option 'spline' interpolates using a bivariate B-spline.
When v is a matrix the default is to use linear interpolation, when
v is a list of points the default is 'clough'.
- ``degree`` - an integer between 1 and 5, controls the degree of spline
used for spline interpolation. For data that is highly oscillatory
use higher values
- ``point_list`` - If point_list=True is passed, then if the array
is a list of lists of length three, it will be treated as an
array of points rather than a `3\times n` array.
- ``num_points`` - Number of points to sample interpolating
function in each direction. By default for an `n\times n`
array this is `n`.
- ``**kwds`` - all other arguments are passed to the
surface function
OUTPUT: a 3d plot
EXAMPLES:
All of these use this function; see :func:`list_plot3d` for other list plots::
sage: pi = float(pi)
sage: m = matrix(RDF, 6, [sin(i^2 + j^2) for i in [0,pi/5,..,pi] for j in [0,pi/5,..,pi]])
sage: list_plot3d(m, texture='yellow', interpolation_type='linear', num_points=5) # indirect doctest
Graphics3d Object
::
sage: list_plot3d(m, texture='yellow', interpolation_type='spline', frame_aspect_ratio=[1, 1, 1/3])
Graphics3d Object
::
sage: show(list_plot3d([[1, 1, 1], [1, 2, 1], [0, 1, 3], [1, 0, 4]], point_list=True))
::
sage: list_plot3d([(1, 2, 3), (0, 1, 3), (2, 1, 4), (1, 0, -2)], texture='yellow', num_points=50) # long time
Graphics3d Object
"""
from matplotlib import tri
import numpy
from random import random
from scipy import interpolate
from .plot3d import plot3d
if len(v) < 3:
raise ValueError(
"We need at least 3 points to perform the interpolation")
x = [float(p[0]) for p in v]
y = [float(p[1]) for p in v]
z = [float(p[2]) for p in v]
# If the (x,y)-coordinates lie in a one-dimensional subspace, the
# matplotlib Delaunay code segfaults. Therefore, we compute the
# correlation of the x- and y-coordinates and add small random
# noise to avoid the problem if needed.
corr_matrix = numpy.corrcoef(x, y)
if corr_matrix[0, 1] > 0.9 or corr_matrix[0, 1] < -0.9:
ep = float(.000001)
x = [float(p[0]) + random() * ep for p in v]
y = [float(p[1]) + random() * ep for p in v]
# If the list of data points has two points with the exact same
# (x,y)-coordinate but different z-coordinates, then we sometimes
# get segfaults. The following block checks for this and raises
# an exception if this is the case.
# We also remove duplicate points (which matplotlib can't handle).
# Alternatively, the code in the if block above which adds random
# error could be applied to perturb the points.
drop_list = []
nb_points = len(x)
for i in range(nb_points):
for j in range(i + 1, nb_points):
if x[i] == x[j] and y[i] == y[j]:
if z[i] != z[j]:
raise ValueError(
"Two points with same x,y coordinates and different z coordinates were given. Interpolation cannot handle this."
)
elif z[i] == z[j]:
drop_list.append(j)
x = [x[i] for i in range(nb_points) if i not in drop_list]
y = [y[i] for i in range(nb_points) if i not in drop_list]
z = [z[i] for i in range(nb_points) if i not in drop_list]
xmin = float(min(x))
xmax = float(max(x))
ymin = float(min(y))
ymax = float(max(y))
num_points = kwds['num_points'] if 'num_points' in kwds else int(
4 * numpy.sqrt(len(x)))
#arbitrary choice - assuming more or less a nxn grid of points
# x should have n^2 entries. We sample 4 times that many points.
if interpolation_type == 'linear':
T = tri.Triangulation(x, y)
f = tri.LinearTriInterpolator(T, z)
j = numpy.complex(0, 1)
from .parametric_surface import ParametricSurface
def g(x, y):
z = f(x, y)
return (x, y, z)
G = ParametricSurface(g, (list(numpy.r_[xmin:xmax:num_points * j]),
list(numpy.r_[ymin:ymax:num_points * j])),
texture=texture,
**kwds)
G._set_extra_kwds(kwds)
return G
if interpolation_type == 'clough' or interpolation_type == 'default':
points = [[x[i], y[i]] for i in range(len(x))]
j = numpy.complex(0, 1)
f = interpolate.CloughTocher2DInterpolator(points, z)
from .parametric_surface import ParametricSurface
def g(x, y):
z = f([x, y])
return (x, y, z)
G = ParametricSurface(g, (list(numpy.r_[xmin:xmax:num_points * j]),
list(numpy.r_[ymin:ymax:num_points * j])),
texture=texture,
**kwds)
G._set_extra_kwds(kwds)
return G
if interpolation_type == 'spline':
kx = kwds['kx'] if 'kx' in kwds else 3
ky = kwds['ky'] if 'ky' in kwds else 3
if 'degree' in kwds:
kx = kwds['degree']
ky = kwds['degree']
s = kwds['smoothing'] if 'smoothing' in kwds else len(x) - numpy.sqrt(
2 * len(x))
s = interpolate.bisplrep(x,
y,
z, [int(1)] * len(x),
xmin,
xmax,
ymin,
ymax,
kx=kx,
ky=ky,
s=s)
f = lambda x, y: interpolate.bisplev(x, y, s)
return plot3d(f, (xmin, xmax), (ymin, ymax),
texture=texture,
plot_points=[num_points, num_points],
**kwds)
def piper(array,
alphalevel=1,
color=True,
show=True,
save=False,
fname=None,
figsize=(4, 4)):
r"""
Create a Piper plot using the code by Peeters, (2014).
Args:
:param array: A one or two dimensional array containing in mM/L in the \
order of 'Ca', 'Mg', 'Na', 'K', 'HCO3', 'CO3', 'Cl', 'SO4'.
:param alphalevel: transparency level of points. If 1, points are opaque
:param color: boolean, use background coloring of Piper plot default True
:param show: If True shows plot else returns plot object.
:param save: Save the plot default is False
:param fname: Filename default is none
:param figsize: Figure size tuple default (8, 3)
:return: Piperplot
Code from https://github.com/inkenbrandt/Peeters_Piper/blob/master/peeter_\
piper.py:
Citation:
@article {GWAT:GWAT12118,
author = {Peeters, Luk},
title = {A Background Color Scheme for Piper Plots to Spatially Visualize \
Hydrochemical Patterns},
journal = {Groundwater},
volume = {52},
number = {1},
publisher = {Blackwell Publishing Ltd},
issn = {1745-6584},
url = {http://dx.doi.org/10.1111/gwat.12118},
doi = {10.1111/gwat.12118},
pages = {2--6},
year = {2014},
}
"""
dat_piper = array
ndims = len(dat_piper.shape)
if ndims == 1:
dat_piper = np.concatenate((dat_piper, dat_piper)).reshape(2, 8)
def hsvtorgb(H, S, V):
# conversion (from http://en.wikipedia.org/wiki/HSL_and_HSV)
C = V * S
Hs = H / (np.pi / 3)
X = C * (1 - np.abs(np.mod(Hs, 2.0 * np.ones_like(Hs)) - 1))
N = np.zeros_like(H)
# create empty RGB matrices
R = np.zeros_like(H)
B = np.zeros_like(H)
G = np.zeros_like(H)
# assign values
h = np.floor(Hs)
# h=0
R[h == 0] = C[h == 0]
G[h == 0] = X[h == 0]
B[h == 0] = N[h == 0]
# h=1
R[h == 1] = X[h == 1]
G[h == 1] = C[h == 1]
B[h == 1] = N[h == 1]
# h=2
R[h == 2] = N[h == 2]
G[h == 2] = C[h == 2]
B[h == 2] = X[h == 2]
# h=3
R[h == 3] = N[h == 3]
G[h == 3] = X[h == 3]
B[h == 3] = C[h == 3]
# h=4
R[h == 4] = X[h == 4]
G[h == 4] = N[h == 4]
B[h == 4] = C[h == 4]
# h=5
R[h == 5] = C[h == 5]
G[h == 5] = N[h == 5]
B[h == 5] = X[h == 5]
# match values
m = V - C
R = R + m
G = G + m
B = B + m
return (R, G, B)
# Basic shape of piper plot
offset = 0.15
offsety = offset * np.tan(np.pi / 3)
h = 0.5 * np.tan(np.pi / 3)
ltriangle_x = np.array([0, 0.5, 1, 0])
ltriangle_y = np.array([0, h, 0, 0])
rtriangle_x = ltriangle_x + 2 * offset + 1
rtriangle_y = ltriangle_y
diamond_x = np.array([0.5, 1, 1.5, 1, 0.5]) + offset
diamond_y = h * (np.array([1, 2, 1, 0, 1])) + (offset * np.tan(np.pi / 3))
fig = plt.figure(figsize=figsize)
ax = fig.add_subplot(111,
aspect='equal',
frameon=False,
xticks=[],
yticks=[])
ax.plot(ltriangle_x, ltriangle_y, '-k')
ax.plot(rtriangle_x, rtriangle_y, '-k')
ax.plot(diamond_x, diamond_y, '-k')
# labels and title
plt.text(-offset,
-offset,
'$Ca^{2+}$',
horizontalalignment='left',
verticalalignment='center')
plt.text(0.5,
h + offset,
'$Mg^{2+}$',
horizontalalignment='center',
verticalalignment='center')
plt.text(1 + offset,
-offset,
'$Na^+ + K^+$',
horizontalalignment='right',
verticalalignment='center')
plt.text(1 + offset,
-offset,
'$HCO_3^- + CO_3^{2-}$',
horizontalalignment='left',
verticalalignment='center')
plt.text(1.5 + 2 * offset,
h + offset,
'$SO_4^{2-}$',
horizontalalignment='center',
verticalalignment='center')
plt.text(2 + 3 * offset,
-offset,
'$Cl^-$',
horizontalalignment='right',
verticalalignment='center')
# Convert chemistry into plot coordinates
gmol = np.array([
40.078, 24.305, 22.989768, 39.0983, 61.01714, 60.0092, 35.4527, 96.0636
])
eqmol = np.array([2., 2., 1., 1., 1., 2., 1., 2.])
n = dat_piper.shape[0]
meqL = (dat_piper / gmol) * eqmol
sumcat = np.sum(meqL[:, 0:4], axis=1)
suman = np.sum(meqL[:, 4:8], axis=1)
cat = np.zeros((n, 3))
an = np.zeros((n, 3))
cat[:, 0] = meqL[:, 0] / sumcat # Ca
cat[:, 1] = meqL[:, 1] / sumcat # Mg
cat[:, 2] = (meqL[:, 2] + meqL[:, 3]) / sumcat # Na+K
an[:, 0] = (meqL[:, 4] + meqL[:, 5]) / suman # HCO3 + CO3
an[:, 2] = meqL[:, 6] / suman # Cl
an[:, 1] = meqL[:, 7] / suman # SO4
# Convert into cartesian coordinates
cat_x = 0.5 * (2 * cat[:, 2] + cat[:, 1])
cat_y = h * cat[:, 1]
an_x = 1 + 2 * offset + 0.5 * (2 * an[:, 2] + an[:, 1])
an_y = h * an[:, 1]
d_x = an_y / (4 * h) + 0.5 * an_x - cat_y / (4 * h) + 0.5 * cat_x
d_y = 0.5 * an_y + h * an_x + 0.5 * cat_y - h * cat_x
# plot data
plt.plot(cat_x, cat_y, '.k', alpha=alphalevel)
plt.plot(an_x, an_y, '.k', alpha=alphalevel)
plt.plot(d_x, d_y, '.k', alpha=alphalevel)
# color coding Piper plot
if color is False:
# add density color bar if alphalevel < 1
if alphalevel < 1.0:
ax1 = fig.add_axes([0.75, 0.4, 0.01, 0.2])
cmap = plt.cm.gray_r
norm = mpl.colors.Normalize(vmin=0, vmax=1 / alphalevel)
cb1 = mpl.colorbar.ColorbarBase(ax1,
cmap=cmap,
norm=norm,
orientation='vertical')
cb1.set_label('Dot Density')
return (dict(cat=cat, an=an))
else:
import scipy.interpolate as interpolate
# create empty grids to interpolate to
x0 = 0.5
y0 = x0 * np.tan(np.pi / 6)
X = np.reshape(np.repeat(np.linspace(0, 2 + 2 * offset, 1000), 1000),
(1000, 1000), 'F')
Y = np.reshape(np.repeat(np.linspace(0, 2 * h + offsety, 1000), 1000),
(1000, 1000), 'C')
H = np.nan * np.zeros_like(X)
S = np.nan * np.zeros_like(X)
V = np.nan * np.ones_like(X)
A = np.nan * np.ones_like(X)
# create masks for cation, anion triangle and upper and lower diamond
ind_cat = np.logical_or(np.logical_and(X < 0.5, Y < 2 * h * X),
np.logical_and(X > 0.5, Y < (2 * h * (1 - X))))
ind_an = np.logical_or(
np.logical_and(X < 1.5 + (2 * offset),
Y < 2 * h * (X - 1 - 2 * offset)),
np.logical_and(X > 1.5 + (2 * offset), Y <
(2 * h * (1 - (X - 1 - 2 * offset)))))
ind_ld = np.logical_and(
np.logical_or(
np.logical_and(X < 1.0 + offset,
Y > -2 * h * X + 2 * h * (1 + 2 * offset)),
np.logical_and(X > 1.0 + offset, Y > 2 * h * X - 2 * h)),
Y < h + offsety)
ind_ud = np.logical_and(
np.logical_or(
np.logical_and(X < 1.0 + offset, Y < 2 * h * X),
np.logical_and(X > 1.0 + offset,
Y < -2 * h * X + 4 * h * (1 + offset))),
Y > h + offsety)
ind_d = np.logical_or(ind_ld == 1, ind_ud == 1)
# Hue: convert x,y to polar coordinates
# (angle between 0,0 to x0,y0 and x,y to x0,y0)
H[ind_cat] = np.pi + np.arctan2(Y[ind_cat] - y0, X[ind_cat] - x0)
H[ind_cat] = np.mod(H[ind_cat] - np.pi / 6, 2 * np.pi)
H[ind_an] = np.pi + np.arctan2(Y[ind_an] - y0, X[ind_an] -
(x0 + 1 + (2 * offset)))
H[ind_an] = np.mod(H[ind_an] - np.pi / 6, 2 * np.pi)
H[ind_d] = np.pi + np.arctan2(Y[ind_d] - (h + offsety), X[ind_d] -
(1 + offset))
# Saturation: 1 at edge of triangle, 0 in the centre,
# Clough Tocher interpolation, square root to reduce central region
xy_cat = np.array([[0.0, 0.0], [x0, h], [1.0, 0.0], [x0, y0]])
xy_an = np.array([[1 + (2 * offset), 0.0], [x0 + 1 + (2 * offset), h],
[2 + (2 * offset), 0.0], [x0 + 1 + (2 * offset),
y0]])
xy_d = np.array([[x0 + offset, h + offsety],
[1 + offset, 2 * h + offsety],
[x0 + 1 + offset, h + offsety], [1 + offset, offsety],
[1 + offset, h + offsety]])
z_cat = np.array([1.0, 1.0, 1.0, 0.0])
z_an = np.array([1.0, 1.0, 1.0, 0.0])
z_d = np.array([1.0, 1.0, 1.0, 1.0, 0.0])
s_cat = interpolate.CloughTocher2DInterpolator(xy_cat, z_cat)
s_an = interpolate.CloughTocher2DInterpolator(xy_an, z_an)
s_d = interpolate.CloughTocher2DInterpolator(xy_d, z_d)
S[ind_cat] = s_cat.__call__(X[ind_cat], Y[ind_cat])
S[ind_an] = s_an.__call__(X[ind_an], Y[ind_an])
S[ind_d] = s_d.__call__(X[ind_d], Y[ind_d])
# Value: 1 everywhere
V[ind_cat] = 1.0
V[ind_an] = 1.0
V[ind_d] = 1.0
# Alpha: 1 everywhere
A[ind_cat] = 1.0
A[ind_an] = 1.0
A[ind_d] = 1.0
# convert HSV to RGB
R, G, B = hsvtorgb(H, S**0.5, V)
RGBA = np.dstack((R, G, B, A))
# visualise
plt.imshow(RGBA,
origin='lower',
aspect=1.0,
extent=(0, 2 + 2 * offset, 0, 2 * h + offsety))
# calculate RGB triples for data points
# hue
hcat = np.pi + np.arctan2(cat_y - y0, cat_x - x0)
hcat = np.mod(hcat - np.pi / 6, 2 * np.pi)
han = np.pi + np.arctan2(an_y - y0, an_x - (x0 + 1 + (2 * offset)))
han = np.mod(han - np.pi / 6, 2 * np.pi)
hd = np.pi + np.arctan2(d_y - (h + offsety), d_x - (1 + offset))
# saturation
scat = s_cat.__call__(cat_x, cat_y)**0.5
san = s_an.__call__(an_x, an_y)**0.5
# value
v = np.ones_like(hd)
# rgb
cat = np.vstack((hsvtorgb(hcat, scat, v))).T
an = np.vstack((hsvtorgb(han, san, v))).T
module_io.output(fig, show, save, fname)
def __init__(self, x, y, z):
super().__init__(x, y)
self.z = z
points = np.concatenate(
(np.expand_dims(x, axis=1), np.expand_dims(y, axis=1)), axis=1)
self.CTFunction = interpolate.CloughTocher2DInterpolator(points, z)
def piper(dat_piper, plottitle, alphalevel, color):
'''
Create a Piper plot
INPUT:
dat_piper: [nx8] matrix, chemical analysis in mg/L
order: Ca Mg Na K HCO3 CO3 Cl SO4
plottitle: string with title of Piper plot
alphalevel: transparency level of points. If 1, points are opaque
color: boolean, use background coloring of Piper plot
OUTPUT:
figure with piperplot
dictionary with:
if color = False:
cat: [nx3] meq% of cations, order: Ca Mg Na+K
an: [nx3] meq% of anions, order: HCO3+CO3 SO4 Cl
if color = True:
cat: [nx3] RGB triple cations
an: [nx3] RGB triple anions
diamond: [nx3] RGB triple central diamond
'''
# Basic shape of piper plot
offset = 0.05
offsety = offset * np.tan(np.pi / 3)
h = 0.5 * np.tan(np.pi / 3)
ltriangle_x = np.array([0, 0.5, 1, 0])
ltriangle_y = np.array([0, h, 0, 0])
rtriangle_x = ltriangle_x + 2 * offset + 1
rtriangle_y = ltriangle_y
diamond_x = np.array([0.5, 1, 1.5, 1, 0.5]) + offset
diamond_y = h * (np.array([1, 2, 1, 0, 1])) + (offset * np.tan(np.pi / 3))
fig = plt.figure()
ax = fig.add_subplot(111,
aspect='equal',
frameon=False,
xticks=[],
yticks=[])
ax.plot(ltriangle_x, ltriangle_y, '-k')
ax.plot(rtriangle_x, rtriangle_y, '-k')
ax.plot(diamond_x, diamond_y, '-k')
# labels and title
sns.set_context("notebook")
plt.title(plottitle)
plt.text(-offset,
-offset,
u'$Ca^{2+}$',
horizontalalignment='left',
verticalalignment='center')
plt.text(0.5,
h + offset,
u'$Mg^{2+}$',
horizontalalignment='center',
verticalalignment='center')
plt.text(1 + offset,
-offset,
u'$Na^+ + K^+$',
horizontalalignment='right',
verticalalignment='center')
plt.text(1 + offset,
-offset,
u'$HCO_3^- + CO_3^{2-}$',
horizontalalignment='left',
verticalalignment='center')
plt.text(1.5 + 2 * offset,
h + offset,
u'$SO_4^{2-}$',
horizontalalignment='center',
verticalalignment='center')
plt.text(2 + 3 * offset,
-offset,
u'$Cl^-$',
horizontalalignment='right',
verticalalignment='center')
# Convert chemistry into plot coordinates
gram_mol = {
"Ca": 40.078,
"Mg": 24.305,
"Na": 22.989768,
"K": 39.0983,
"HCO3": 61.01714,
"CO3": 60.0092,
"Cl": 35.4527,
"SO4": 96.0636
}
valence_abs = {
"Ca": 2.0,
"Mg": 2.0,
"Na": 1.0,
"K": 1.0,
"HCO3": 1.0,
"CO3": 2.0,
"Cl": 1.0,
"SO4": 2.0
}
#gmol = np.array( [40.078, 24.305, 22.989768, 39.0983, 61.01714, 60.0092, 35.4527, 96.0636] )
#eqmol = np.array( [2., 2., 1., 1., 1., 2., 1., 2. ])
#n = dat_piper.shape[0]
#gram_mol={"Ca":40.078,"Mg":24.305,"Na":22.989768, "K":39.0983,"HCO3":61.01714,"CO3":60.0092,"Cl":35.4527,"SO4":96.0636}
#valence_abs= {"Ca":2.0, "Mg":2.0, "Na":1.0, "K":1.0, "HCO3":1.0, "CO3":2.0, "Cl":1.0, "SO4":2.0}
df_dat = df[["Ca", "Mg", "Na", "K", "HCO3", "CO3", "Cl", "SO4"]]
df_meqL = pd.DataFrame() #initialize an empty dataframe
for i in gram_mol:
df_meqL[i] = (df_dat[i] / gram_mol[i]) * valence_abs[i]
df_meqL = df_meqL[[
"Ca", "Mg", "Na", "K", "HCO3", "CO3", "Cl", "SO4"
]] #reordering(check if this is necessary and or effective)
sumcat_pd = df_meqL["Ca"] + df_meqL["Mg"] + df_meqL["Na"] + df_meqL[
"K"] #sum cations
suman_pd = df_meqL["HCO3"] + df_meqL["CO3"] + df_meqL["Cl"] + df_meqL[
"SO4"] #sum anions
'''meqL = ( dat_piper / gmol ) * eqmol
sumcat_pd = np.sum( meqL[:,0:4],axis=1)
suman_pd = np.sum( meqL[:,4:8],axis=1)
cat = np.zeros( (n,3) )
an = np.zeros( (n,3) )'''
cat = pd.DataFrame() #initialize an empty dataframe
an = pd.DataFrame() #initialize an empty dataframe
cat["Ca"] = df_meqL["Ca"] / sumcat_pd # Ca as proportion
cat["Mg"] = df_meqL["Mg"] / sumcat_pd # Mg as proportion
cat["Na + K"] = (df_meqL["Na"] +
df_meqL["K"]) / sumcat_pd # Na+K as proportion
an["HCO3 + CO3"] = (df_meqL["HCO3"] +
df_meqL["CO3"]) / suman_pd # HCO3 + CO3 as proportion
an["Cl"] = df_meqL["Cl"] / suman_pd # Cl as proportion
an["SO4"] = df_meqL["SO4"] / suman_pd # SO4 as proportion
# Convert into cartesian coordinates
cat_x = 0.5 * (2 * cat["Na + K"] + cat["Mg"])
cat_y = h * cat["Mg"]
an_x = 1 + 2 * offset + 0.5 * (2 * an["Cl"] + an["SO4"])
an_y = h * an["SO4"]
d_x = an_y / (4 * h) + 0.5 * an_x - cat_y / (4 * h) + 0.5 * cat_x
d_y = 0.5 * an_y + h * an_x + 0.5 * cat_y - h * cat_x
#df_cart = pd.DataFrame()
#carts_list = carts_list{}
#carts_list= carts_list.append ("cat_x","cat_y","an_x", "an_y", "d_x", "d_x", "d_y")
df['cat_x'] = cat_x
df['cat_y'] = cat_y
df['an_x'] = an_x
df['an_y'] = an_y
df['d_x'] = d_x
df['d_y'] = d_y
print(df.head())
# plot data
if color is False:
sns.set()
sns.scatterplot('cat_x',
'cat_y',
data=df,
hue='Location',
edgecolor='none',
legend=None) #, hue='Location')
sns.scatterplot('an_x',
'an_y',
data=df,
hue='Location',
edgecolor='none',
legend=None) #, hue='Location', legend=False)
sns.scatterplot('d_x',
'd_y',
data=df,
edgecolor='none',
hue='Location') #, hue='Location', legend=False)
else:
sns.set()
sns.scatterplot('cat_x', 'cat_y', data=df, color=".2",
edgecolor='k') #, hue='Location')
sns.scatterplot('an_x', 'an_y', data=df, color=".2",
edgecolor='k') #, hue='Location', legend=False)
sns.scatterplot('d_x', 'd_y', data=df, color=".2",
edgecolor='k') #, hue='Location', legend=False)
#plt.plot( cat_x, cat_y, '.k', alpha=alphalevel )
#plt.plot( an_x, an_y, '.k', alpha=alphalevel )
#plt.plot( d_x, d_y, '.k', alpha=alphalevel )
# color coding Piper plot
if color == False:
# add density color bar if alphalevel < 1
if alphalevel < 1.0:
ax1 = fig.add_axes([0.75, 0.4, 0.01, 0.2])
cmap = plt.cm.gray_r
#cmap = df['Location']
norm = mpl.colors.Normalize(vmin=0, vmax=1 / alphalevel)
cb1 = mpl.colorbar.ColorbarBase(ax1,
cmap=cmap,
norm=norm,
orientation='vertical')
cb1.set_label('Dot Density')
return (dict(cat=cat, an=an))
#print dict(cat=cat, an=an)
else:
import scipy.interpolate as interpolate
# create empty grids to interpolate to
x0 = 0.5
y0 = x0 * np.tan(np.pi / 6)
X = np.reshape(np.repeat(np.linspace(0, 2 + 2 * offset, 1000), 1000),
(1000, 1000), 'F')
Y = np.reshape(np.repeat(np.linspace(0, 2 * h + offsety, 1000), 1000),
(1000, 1000), 'C')
H = np.nan * np.zeros_like(X)
S = np.nan * np.zeros_like(X)
V = np.nan * np.ones_like(X)
A = np.nan * np.ones_like(X)
# create masks for cation, anion triangle and upper and lower diamond
ind_cat = np.logical_or(np.logical_and(X < 0.5, Y < 2 * h * X),
np.logical_and(X > 0.5, Y < (2 * h * (1 - X))))
ind_an = np.logical_or(
np.logical_and(X < 1.5 + (2 * offset),
Y < 2 * h * (X - 1 - 2 * offset)),
np.logical_and(X > 1.5 + (2 * offset), Y <
(2 * h * (1 - (X - 1 - 2 * offset)))))
ind_ld = np.logical_and(
np.logical_or(
np.logical_and(X < 1.0 + offset,
Y > -2 * h * X + 2 * h * (1 + 2 * offset)),
np.logical_and(X > 1.0 + offset, Y > 2 * h * X - 2 * h)),
Y < h + offsety)
ind_ud = np.logical_and(
np.logical_or(
np.logical_and(X < 1.0 + offset, Y < 2 * h * X),
np.logical_and(X > 1.0 + offset,
Y < -2 * h * X + 4 * h * (1 + offset))),
Y > h + offsety)
ind_d = np.logical_or(ind_ld == 1, ind_ud == 1)
# Hue: convert x,y to polar coordinates
# (angle between 0,0 to x0,y0 and x,y to x0,y0)
H[ind_cat] = np.pi + np.arctan2(Y[ind_cat] - y0, X[ind_cat] - x0)
H[ind_cat] = np.mod(H[ind_cat] - np.pi / 6, 2 * np.pi)
H[ind_an] = np.pi + np.arctan2(Y[ind_an] - y0, X[ind_an] -
(x0 + 1 + (2 * offset)))
H[ind_an] = np.mod(H[ind_an] - np.pi / 6, 2 * np.pi)
H[ind_d] = np.pi + np.arctan2(Y[ind_d] - (h + offsety), X[ind_d] -
(1 + offset))
# Saturation: 1 at edge of triangle, 0 in the centre,
# Clough Tocher interpolation, square root to reduce central white region
xy_cat = np.array([[0.0, 0.0], [x0, h], [1.0, 0.0], [x0, y0]])
xy_an = np.array([[1 + (2 * offset), 0.0], [x0 + 1 + (2 * offset), h],
[2 + (2 * offset), 0.0], [x0 + 1 + (2 * offset),
y0]])
xy_d = np.array([[x0 + offset, h + offsety],
[1 + offset, 2 * h + offsety],
[x0 + 1 + offset, h + offsety], [1 + offset, offsety],
[1 + offset, h + offsety]])
z_cat = np.array([1.0, 1.0, 1.0, 0.0])
z_an = np.array([1.0, 1.0, 1.0, 0.0])
z_d = np.array([1.0, 1.0, 1.0, 1.0, 0.0])
s_cat = interpolate.CloughTocher2DInterpolator(xy_cat, z_cat)
s_an = interpolate.CloughTocher2DInterpolator(xy_an, z_an)
s_d = interpolate.CloughTocher2DInterpolator(xy_d, z_d)
S[ind_cat] = s_cat.__call__(X[ind_cat], Y[ind_cat])
S[ind_an] = s_an.__call__(X[ind_an], Y[ind_an])
S[ind_d] = s_d.__call__(X[ind_d], Y[ind_d])
# Value: 1 everywhere
V[ind_cat] = 1.0
V[ind_an] = 1.0
V[ind_d] = 1.0
# Alpha: 1 everywhere
A[ind_cat] = 1.0
A[ind_an] = 1.0
A[ind_d] = 1.0
# convert HSV to RGB
R, G, B = hsvtorgb(H, S**0.5, V)
RGBA = np.dstack((R, G, B, A))
# visualise
sns.set()
sns.set_context("talk")
plt.imshow(RGBA,
origin='lower',
aspect=1.0,
extent=(0, 2 + 2 * offset, 0, 2 * h + offsety))
# calculate RGB triples for data points
# hue
hcat = np.pi + np.arctan2(cat_y - y0, cat_x - x0)
hcat = np.mod(hcat - np.pi / 6, 2 * np.pi)
han = np.pi + np.arctan2(an_y - y0, an_x - (x0 + 1 + (2 * offset)))
han = np.mod(han - np.pi / 6, 2 * np.pi)
hd = np.pi + np.arctan2(d_y - (h + offsety), d_x - (1 + offset))
# saturation
scat = s_cat.__call__(cat_x, cat_y)**0.5
san = s_an.__call__(an_x, an_y)**0.5
sd = s_d.__call__(d_x, d_y)**0.5
# value
v = np.ones_like(hd)
# rgb
cat = np.vstack((hsvtorgb(hcat, scat, v))).T
an = np.vstack((hsvtorgb(han, san, v))).T
d = np.vstack((hsvtorgb(hd, sd, v))).T
return (dict(cat=cat, an=an, diamond=d))
def cExNear(x):
"""Function to compute the exact solution field."""
return cEx_near(x)
constructTime['near'] = time.clock()-t
t = time.clock()
figNum=4
cNear = contPlt.conPlot(cExNear, figNum=figNum)
plt.title('nearest ND interpolation')
plt.show()
executionTime['near'] = time.clock()-t
#%% Clough tocher 2D interpolation:
t = time.clock()
cEx_clough = interpolate.CloughTocher2DInterpolator(coord, cEx, fill_value=0.0)
def cExClough(x):
"""Function to compute the exact solution field."""
return cEx_clough(x)
constructTime['clough'] = time.clock()-t
t = time.clock()
figNum=5
cClough = contPlt.conPlot(cExClough, figNum=figNum)
plt.title('clough tocher 2D interpolation')
plt.show()
executionTime['clough'] = time.clock()-t
#%% Results:
print('\n\nExecution times for different interpolation functions in Scipy:')