def init_1dcubic_c2(self, x=None, data=None, extrapolate=False, extrapolation_range=float('inf'),
extrapolation_type='nearest', tolerate_single_value=False):
"""Create the interpolating function and reference function."""
if x is None:
x = self.x
if data is None:
data = self.data
# reference interpolated data:
# C2 cubic interpolated data sampled on self.xsamples,
# calculated from solving manually the linear system given by the
# following constraints on the cubic splines:
#
# if P1, P2, ..., P9 are the 9 cubic polynomials defining the interpolation
# on respectively ranges [x[0], x[1]], [x[1], x[2]], ..., [x[8], x[9]]
# constraints are: Pi(x[i-1]) = data[i-1] for i in [1, 9]
# Pi(x[i]) = data[i] for i in [1, 9]
# dPi/dx(x[i]) = dPi+1/dx(x[i]) for i in [1, 8]
# d2Pi/dx2(x[i]) = d2Pi+1/dx2(x[i]) for i in [1, 8]
# d3P1/dx3(x[0]) = d3P9/dx3(x[9]) = 0
self.interp_data = np.array([ 1. , 0.909386322736, 0.744935119692, 0.506646390868, 0.198359265243,
-0.145597952285, -0.476357515 , -0.745969855864, -0.924576033965, -0.997965016288,
-0.95270426186 , -0.791113531095, -0.539928651551, -0.227988632848, 0.113003806643,
0.443108473075, 0.720913065294, 0.908991353712, 0.992221981868, 0.963237748147,
0.816761597858, 0.571723930259, 0.262672856832, -0.075536667115, -0.406637953849,
-0.692732204577, -0.895899188014, -0.989500940501, -0.970558387522, -0.839071529076],
dtype=np.float64)
# nearestly extrapolated data sampled on self.xsamples_extrapol,
# calculated from nearest edge value
self.extrap_data_nea = np.array([1., 1., -0.839071529076, -0.839071529076], dtype=np.float64)
# linearly extrapolated data sampled on self.xsamples_extrapol,
# calculated from P(x_nearest) + (x-x_nearest)*dP/dx(x_nearest)
# where x_nearest (=x[0] or x[9]) is the nearest coordinate in the
# interpolated range form x, and P (=P1 or P9) the nearest
# interpolation polynomial.
self.extrap_data_lin = np.array([1.1245722013484143, 1.0622861006742075, -0.62127107611011623, -0.40347062314376919], dtype=np.float64)
# quadraticaly extrapolated data sampled on self.xsamples_extrapol,
# calculated from P(x_nearest) + (x-x_nearest)*dP/dx(x_nearest)
# + 0.5*(x-x_nearest)**2*d2P/dx2(x_nearest)
# where x_nearest (=x[0] or x[9]) is the nearest coordinate in the
# interpolated range form x, and P (=P1 or P9) the nearest
# interpolation polynomial.
self.extrap_data_qua = np.array([0.92586065196970724, 1.0126082133295307, -0.5455512673927978, -0.10059138827449526], dtype=np.float64)
self.interp_func = interpolators1d.Interpolate1DCubic(x, data,
extrapolate=extrapolate,
extrapolation_range=extrapolation_range,
extrapolation_type=extrapolation_type,
tolerate_single_value=tolerate_single_value,
continuity_order=2)
def init_1dcubic_c1(self, x=None, data=None, extrapolate=False, extrapolation_range=float('inf'),
extrapolation_type='nearest', tolerate_single_value=False):
"""Create the interpolating function and reference function."""
if x is None:
x = self.x
if data is None:
data = self.data
# reference interpolated data:
# C1 cubic interpolated data sampled on self.xsamples,
# calculated from from solving manually the linear system given by the
# following constraints on the cubic splines:
#
# if P1, P2, ..., P9 are the 9 cubic polynomials defining the interpolation
# on respectively ranges [x[0], x[1]], [x[1], x[2]], ..., [x[8], x[9]]
# constraints are: Pi(x[i-1]) = data[i-1] for i in [1, 9]
# Pi(x[i]) = data[i] for i in [1, 9]
# dPi/dx(x[i]) = (data[i+1]-data[i-1])/(x[i+1]-x[i-1]) for i in [1, 8]
# dPi/dx(x[i-1]) = (data[i]-data[i-2])/(x[i]-x[i-2]) for i in [2, 9]
# d3P1/dx3(x[0]) = d3P9/dx3(x[9]) = 0
self.interp_data = np.array([ 1. , 0.880173125546, 0.712800602783, 0.497882431711, 0.209599324944,
-0.154300121054, -0.492023725037, -0.724305080592, -0.896927467157, -0.986541391474,
-0.954335254748, -0.777457953678, -0.513924204518, -0.234128226514, 0.094607534444,
0.447977457129, 0.725059163866, 0.885104972562, 0.967692230729, 0.955569808692,
0.819830442329, 0.554735584499, 0.240589044126, -0.05646951848 , -0.390685969507,
-0.698474405891, -0.889098560187, -0.964565305133, -0.947889628097, -0.839071529076],
dtype=np.float64)
# nearestly extrapolated data sampled on self.xsamples_extrapol,
# calculated from nearest edge value
self.extrap_data_nea = np.array([1., 1., -0.839071529076, -0.839071529076], dtype=np.float64)
# linearly extrapolated data sampled on self.xsamples_extrapol,
# calculated from P(x_nearest) + (x-x_nearest)*dP/dx(x_nearest)
# where x_nearest (=x[0] or x[9]) is the nearest coordinate in the
# interpolated range form x, and P (=P1 or P9) the nearest
# interpolation polynomial.
self.extrap_data_lin = np.array([ 1.222845396694, 1.111422698347, -0.659399929463, -0.479728329849], dtype=np.float64)
# quadraticaly extrapolated data sampled on self.xsamples_extrapol,
# calculated from P(x_nearest) + (x-x_nearest)*dP/dx(x_nearest)
# + 0.5*(x-x_nearest)**2*d2P/dx2(x_nearest)
# where x_nearest (=x[0] or x[9]) is the nearest coordinate in the
# interpolated range form x, and P (=P1 or P9) the nearest
# interpolation polynomial.
self.extrap_data_qua = np.array([ 1.094890547964, 1.079433986165, -0.597406507952, -0.231754643808], dtype=np.float64)
self.interp_func = interpolators1d.Interpolate1DCubic(x, data,
extrapolate=extrapolate,
extrapolation_range=extrapolation_range,
extrapolation_type=extrapolation_type,
tolerate_single_value=tolerate_single_value,
continuity_order=1)