##
##  here, we test / demonstrate interpolation, including
##  data that is outside the original x-range of the data.
## 
##  note that the quality of the extrapolation from the
##  different interpolation 'kind' arguments depends greatly
##  on the data -- here, on the value of tau.
##
##  For slowly varying data, all methods can extrapolate 
##  one or two steps outside the range of the original data
##  acceptably well.  Beyond that, or for quickly varying
##  data, no easy generalizations can be made about one
##  extrapolation being generally better than another. 
##

#py:
#import numpy as np
#from wxmplot.interactive import newplot, plot
#from larch.math import interp

offset = 0.127890

# tau   = 28.00
# tau   =  8.00
tau   =  2.00
# tau   =  0.75
# tau   =  0.333

x = np.linspace(40., 44., 9)


y = offset + np.sin(x/tau)

newplot(x, y, linewidth=0.5, marker='o', color='blue', 
	label='orig', show_legend=True)

# extends below data range:
xnew  = np.linspace(38.0, 42.5, 47) + 0.3333

# extends above data range:
# xnew  = linspace(48.0, 52.5, 23) + 0.3333

y0  = offset + np.sin(xnew/tau)    # predicted

y1 = interp(x, y, xnew, kind='linear')
y2 = interp(x, y, xnew, kind='quadratic')
y3 = interp(x, y, xnew, kind='cubic')


plot(xnew, y0, style='solid',  color='goldenrod', marker='square', 
           markersize=2, linewidth=2, label='true sinewave')

plot(xnew, y1, style='short dashed', color='red',   marker='+', label='linear')
plot(xnew, y2, style='solid',        color='dark green',        label='quadratic')
plot(xnew, y3, style='short dashed', color='black', marker='+', label='cubic')