def interpolate(*args, **kwargs):
r"""Interpolation convinience function.
Convenience function to interpolate different kind of data.
Currently supported interpolation schemes are:
* Interpolate mesh based data from one mesh to another
(syntactic sugar for the core based interpolate (see below))
Parameters:
args: :gimliapi:`GIMLI::Mesh`, :gimliapi:`GIMLI::Mesh`, iterable
`outData = interpolate(outMesh, inMesh, vals)`
Interpolate values based on inMesh to outMesh.
Values can be of length inMesh.cellCount() interpolated to
outMesh.cellCenters() or inMesh.nodeCount() which are interpolated tp
outMesh.positions().
Returns:
Interpolated values.
* Mesh based values to arbitrary points, based on finite element
interpolation (from gimli core).
Parameters:
args: :gimliapi:`GIMLI::Mesh`, ...
Arguments forwarded to :gimliapi:`GIMLI::interpolate`
kwargs:
Arguments forwarded to :gimliapi:`GIMLI::interpolate`
`interpolate(srcMesh, destMesh)`
All data from inMesh are interpolated to outMesh
Returns:
Interpolated values
* Interpolate along curve.
Forwarded to :py:mod:`pygimli.meshtools.interpolateAlongCurve`
Parameters:
args: curve, t
kwargs:
Arguments forwarded to
:py:mod:`pygimli.meshtools.interpolateAlongCurve`
* 1D point set :math:`u(x)` for ascending :math:`x`.
Find interpolation function :math:`I = u(x)` and
returns :math:`u_{\text{i}} = I(x_{\text{i}})`
(interpolation methods are [**linear** via matplotlib,
cubic **spline** via scipy, fit with **harmonic** functions' via pygimli])
Note, for 'linear' and 'spline' the interpolate contains all original
coordinates while 'harmonic' returns an approximate best fit.
The amount of harmonic coefficients can be specfied with the 'nc' keyword.
Parameters:
args: xi, x, u
* :math:`x_{\text{i}}` - target sample points
* :math:`x` - function sample points
* :math:`u` - function values
kwargs:
* method : string
Specify interpolation method 'linear, 'spline', 'harmonic'
* nc : int
Number of harmonic coefficients for the 'harmonic' method.
Returns:
ui: array of length xi
:math:`u_{\text{i}} = I(x_{\text{i}})`, with :math:`I = u(x)`
To use the core functions :gimliapi:`GIMLI::interpolate` start with a
mesh instance as first argument or use the appropriate keyword arguments.
TODO
* 2D parametric to points (method=['linear, 'spline', 'harmonic'])
* 2D/3D point cloud to points/grids ('Delauney', 'linear, 'spline', 'harmonic')
* Mesh to points based on nearest neighbour values (pg.core)
Examples
--------
>>> # no need to import matplotlib. pygimli's show does
>>> import numpy as np
>>> import pygimli as pg
>>> fig, ax = pg.plt.subplots(1, 1, figsize=(10, 5))
>>> u = np.array([1.0, 12.0, 3.0, -4.0, 5.0, 6.0, -1.0])
>>> xu = np.array(range(len(u)))
>>> xi = np.linspace(xu[0], xu[-1], 1000)
>>> _= ax.plot(xu, u, 'o')
>>> _= ax.plot(xi, pg.interpolate(xi, xu, u, method='linear'),
... color='blue', label='linear')
>>> _= ax.plot(xi, pg.interpolate(xi, xu, u, method='spline'),
... color='red', label='spline')
>>> _= ax.plot(xi, pg.interpolate(xi, xu, u, method='harmonic'),
... color='green', label='harmonic')
>>> _= ax.legend()
"""
pgcore = False
if 'srcMesh' in kwargs:
pgcore = True
elif len(args) > 0:
if isinstance(args[0], pg.Mesh):
if len(args) == 2 and isinstance(args[1], pg.Mesh):
return pg.core._pygimli_.interpolate(args[0], args[1],
**kwargs)
if len(args) == 3 and isinstance(args[1], pg.Mesh):
pgcore = False # (outMesh, inMesh, vals)
else:
pgcore = True
if pgcore:
if len(args) == 3: # args: outData = (inMesh, inData, outPos)
if args[1].ndim == 2: # outData = (inMesh, mat, vR3)
outMat = pg.Matrix()
pg.core._pygimli_.interpolate(args[0],
inMat=np.array(args[1]),
destPos=args[2],
outMat=outMat,
**kwargs)
return np.array(outMat)
if len(args) == 4: # args: (inMesh, inData, outPos, outData)
if args[1].ndim == 1 and args[2].ndim == 1 and args[3].ndim == 1:
return pg.core._pygimli_.interpolate(args[0],
inVec=args[1],
x=args[2],
y=args[3],
**kwargs)
if isinstance(args[1], pg.RMatrix) and \
isinstance(args[3], pg.RMatrix):
return pg.core._pygimli_.interpolate(args[0],
inMat=args[1],
destPos=args[2],
outMat=args[3],
**kwargs)
if isinstance(args[1], pg.RVector) and \
isinstance(args[3], pg.RVector):
return pg.core._pygimli_.interpolate(args[0],
inVec=args[1],
destPos=args[2],
outVec=args[3],
**kwargs)
if len(args) == 5:
if args[1].ndim == 1 and args[2].ndim == 1 and \
args[3].ndim == 1 and args[4].ndim == 1:
return pg.core._pygimli_.interpolate(args[0],
inVec=args[1],
x=args[2],
y=args[3],
z=args[4],
**kwargs)
return pg.core._pygimli_.interpolate(*args, **kwargs)
# end if pg.core:
if len(args) == 3:
if isinstance(args[0], pg.Mesh): # args: (outMesh, inMesh, data)
outMesh = args[0]
inMesh = args[1]
data = args[2]
if isinstance(data, pg.R3Vector) or isinstance(
data, pg.stdVectorRVector3):
x = pg.interpolate(outMesh, inMesh, pg.x(data))
y = pg.interpolate(outMesh, inMesh, pg.y(data))
z = pg.interpolate(outMesh, inMesh, pg.z(data))
return np.vstack([x, y, z]).T
if isinstance(data, np.ndarray):
if data.ndim == 2 and data.shape[1] == 3:
x = pg.interpolate(outMesh, inMesh, data[:, 0])
y = pg.interpolate(outMesh, inMesh, data[:, 1])
z = pg.interpolate(outMesh, inMesh, data[:, 2])
return np.vstack([x, y, z]).T
if len(data) == inMesh.cellCount():
return pg.interpolate(srcMesh=inMesh,
inVec=data,
destPos=outMesh.cellCenters())
elif len(data) == inMesh.nodeCount():
return pg.interpolate(srcMesh=inMesh,
inVec=data,
destPos=outMesh.positions())
else:
print(inMesh)
print(outMesh)
raise Exception("Don't know how to interpolate data of size",
str(len(data)))
print("data: ", data)
raise Exception("Cannot interpret data: ", str(len(data)))
else: #args: xi, x, u
xi = args[0]
x = args[1]
u = args[2]
method = kwargs.pop('method', 'linear')
if 'linear' in method:
return np.interp(xi, x, u)
if 'harmonic' in method:
coeff = kwargs.pop('nc', int(np.ceil(np.sqrt(len(x)))))
from pygimli.frameworks import harmfitNative
return harmfitNative(u, x=x, nc=coeff, xc=xi, err=None)[0]
if 'spline' in method:
if pg.optImport("scipy",
requiredFor="use interpolate splines."):
from scipy import interpolate
tck = interpolate.splrep(x, u, s=0)
return interpolate.splev(xi, tck, der=0)
else:
return xi * 0.
if len(args) == 2: # args curve, t
curve = args[0]
t = args[1]
return interpolateAlongCurve(curve, t, **kwargs)
def interpolate(*args, **kwargs):
r"""Interpolation convinience function.
Convenience function to interpolate different kind of data.
Currently supported interpolation schemes are:
* Interpolate mesh based data from one mesh to another
(syntactic sugar for the core based interpolate (see below))
Parameters:
args: :gimliapi:`GIMLI::Mesh`, :gimliapi:`GIMLI::Mesh`, iterable
`outData = interpolate(outMesh, inMesh, vals)`
Interpolate values based on inMesh to outMesh.
Values can be of length inMesh.cellCount() interpolated to
outMesh.cellCenters() or inMesh.nodeCount() which are interpolated tp
outMesh.positions().
Returns:
Interpolated values.
* Mesh based values to arbitrary points, based on finite element
interpolation (from gimli core).
Parameters:
args: :gimliapi:`GIMLI::Mesh`, ...
Arguments forwarded to :gimliapi:`GIMLI::interpolate`
kwargs:
Arguments forwarded to :gimliapi:`GIMLI::interpolate`
`interpolate(srcMesh, destMesh)`
All data from inMesh are interpolated to outMesh
Returns:
Interpolated values
* Interpolate along curve.
Forwarded to :py:mod:`pygimli.meshtools.interpolateAlongCurve`
Parameters:
args: curve, t
kwargs:
Arguments forwarded to
:py:mod:`pygimli.meshtools.interpolateAlongCurve`
* 1D point set :math:`u(x)` for ascending :math:`x`.
Find interpolation function :math:`I = u(x)` and
returns :math:`u_{\text{i}} = I(x_{\text{i}})`
(interpolation methods are [**linear** via matplotlib,
cubic **spline** via scipy, fit with **harmonic** functions' via pygimli])
Note, for 'linear' and 'spline' the interpolate contains all original
coordinates while 'harmonic' returns an approximate best fit.
The amount of harmonic coefficients can be specfied with the 'nc' keyword.
Parameters:
args: xi, x, u
* :math:`x_{\text{i}}` - target sample points
* :math:`x` - function sample points
* :math:`u` - function values
kwargs:
* method : string
Specify interpolation method 'linear, 'spline', 'harmonic'
* nc : int
Number of harmonic coefficients for the 'harmonic' method.
Returns:
ui: array of length xi
:math:`u_{\text{i}} = I(x_{\text{i}})`, with :math:`I = u(x)`
To use the core functions :gimliapi:`GIMLI::interpolate` start with a
mesh instance as first argument or use the appropriate keyword arguments.
TODO
* 2D parametric to points (method=['linear, 'spline', 'harmonic'])
* 2D/3D point cloud to points/grids ('Delauney', 'linear, 'spline', 'harmonic')
* Mesh to points based on nearest neighbour values (pg.core)
Examples
--------
>>> # no need to import matplotlib. pygimli's show does
>>> import numpy as np
>>> import pygimli as pg
>>> fig, ax = pg.plt.subplots(1, 1, figsize=(10, 5))
>>> u = np.array([1.0, 12.0, 3.0, -4.0, 5.0, 6.0, -1.0])
>>> xu = np.array(range(len(u)))
>>> xi = np.linspace(xu[0], xu[-1], 1000)
>>> _= ax.plot(xu, u, 'o')
>>> _= ax.plot(xi, pg.interpolate(xi, xu, u, method='linear'),
... color='blue', label='linear')
>>> _= ax.plot(xi, pg.interpolate(xi, xu, u, method='spline'),
... color='red', label='spline')
>>> _= ax.plot(xi, pg.interpolate(xi, xu, u, method='harmonic'),
... color='green', label='harmonic')
>>> _= ax.legend()
"""
pgcore = False
if 'srcMesh' in kwargs:
pgcore = True
elif len(args) > 0:
if isinstance(args[0], pg.Mesh):
if len(args) == 2 and isinstance(args[1], pg.Mesh):
return pg.core._pygimli_.interpolate(args[0], args[1],
**kwargs)
if len(args) == 3 and isinstance(args[1], pg.Mesh):
pgcore = False # (outMesh, inMesh, vals)
else:
pgcore = True
if pgcore:
if len(args) == 3: # args: outData = (inMesh, inData, outPos)
if args[1].ndim == 2: # outData = (inMesh, mat, vR3)
outMat = pg.Matrix()
pg.core._pygimli_.interpolate(args[0],
inMat=np.array(args[1]),
destPos=args[2],
outMat=outMat,
**kwargs)
return np.array(outMat)
if len(args) == 4: # args: (inMesh, inData, outPos, outData)
if args[1].ndim == 1 and args[2].ndim == 1 and args[3].ndim == 1:
return pg.core._pygimli_.interpolate(args[0],
inVec=args[1],
x=args[2],
y=args[3],
**kwargs)
if isinstance(args[1], pg.RMatrix) and \
isinstance(args[3], pg.RMatrix):
return pg.core._pygimli_.interpolate(args[0],
inMat=args[1],
destPos=args[2],
outMat=args[3],
**kwargs)
if isinstance(args[1], pg.RVector) and \
isinstance(args[3], pg.RVector):
return pg.core._pygimli_.interpolate(args[0],
inVec=args[1],
destPos=args[2],
outVec=args[3],
**kwargs)
if len(args) == 5:
if args[1].ndim == 1 and args[2].ndim == 1 and \
args[3].ndim == 1 and args[4].ndim == 1:
return pg.core._pygimli_.interpolate(args[0],
inVec=args[1],
x=args[2],
y=args[3],
z=args[4],
**kwargs)
return pg.core._pygimli_.interpolate(*args, **kwargs)
# end if pg.core:
if len(args) == 3:
if isinstance(args[0], pg.Mesh): # args: (outMesh, inMesh, data)
outMesh = args[0]
inMesh = args[1]
data = args[2]
if isinstance(data, pg.R3Vector) or isinstance(data, pg.stdVectorRVector3):
x = pg.interpolate(outMesh, inMesh, pg.x(data))
y = pg.interpolate(outMesh, inMesh, pg.y(data))
z = pg.interpolate(outMesh, inMesh, pg.z(data))
return np.vstack([x, y, z]).T
if isinstance(data, np.ndarray):
if data.ndim == 2 and data.shape[1] == 3:
x = pg.interpolate(outMesh, inMesh, data[:,0])
y = pg.interpolate(outMesh, inMesh, data[:,1])
z = pg.interpolate(outMesh, inMesh, data[:,2])
return np.vstack([x, y, z]).T
if len(data) == inMesh.cellCount():
return pg.interpolate(srcMesh=inMesh, inVec=data,
destPos=outMesh.cellCenters())
elif len(data) == inMesh.nodeCount():
return pg.interpolate(srcMesh=inMesh, inVec=data,
destPos=outMesh.positions())
else:
print(inMesh)
print(outMesh)
raise Exception("Don't know how to interpolate data of size",
str(len(data)))
print("data: ", data)
raise Exception("Cannot interpret data: ", str(len(data)))
else: #args: xi, x, u
xi = args[0]
x = args[1]
u = args[2]
method = kwargs.pop('method', 'linear')
if 'linear' in method:
return np.interp(xi, x, u)
if 'harmonic' in method:
coeff = kwargs.pop('nc', int(np.ceil(np.sqrt(len(x)))))
from pygimli.frameworks import harmfitNative
return harmfitNative(u, x=x, nc=coeff, xc=xi, err=None)[0]
if 'spline' in method:
if pg.optImport("scipy", requiredFor="use interpolate splines."):
from scipy import interpolate
tck = interpolate.splrep(x, u, s=0)
return interpolate.splev(xi, tck, der=0)
else:
return xi*0.
if len(args) == 2: # args curve, t
curve = args[0]
t = args[1]
return interpolateAlongCurve(curve, t, **kwargs)
