#!/usr/bin/env python
"""Simple spectral interpolation routines."""
import scipy as S
import pylab as P
def spec_interp(coef_spec,factor=1,x1=1.0):
"""Interpolate a function"""
assert isinstance(factor,int) and factor > 0,\
"factor must be a positive integer"
npts = len(coef_spec)
padded_fft = S.zeros(npts*factor,'D')
padded_fft[:npts] = coef_spec
return factor*S.ifft(padded_fft).real
def spec_interp2(coef_spec,factor=1):
"""Interpolate a function"""
assert isinstance(factor,int) and factor > 0,\
"factor must be a positive integer"
npts = len(coef_spec)
padded_fft = S.empty(npts*factor,'D')
for i in range(factor):
padded_fft[i*npts:(i+1)*npts] = coef_spec
out = S.ifft(padded_fft)
return out.real
def spec_interp(coef_spec,factor=1):
"""Interpolate a function"""
assert isinstance(factor,int) and factor > 0,\
"factor must be a positive integer"
fhat = coef_spec
M = factor
N = len(fhat)
alpha = 2j*S.pi/(M*N)
out = S.empty(M*N,'D')
for m in range(M):
out[m::M] = S.ifft(fhat*S.exp(alpha*m*S.arange(N)))
return out.real
def spec_interp2(x,coef_spec,x1=1.0):
"""Interpolate a function"""
npts = len(coef_spec)
a = S.sin((1*S.pi/(x1))*x*S.arange(npts))
out = (1.0/npts)*S.dot(coef_spec.imag,a)
return out
def interpolating_func(coef_spec,x1=1.0):
"""Interpolate a function"""
npts = len(coef_spec)
a = S.exp((2j*S.pi/(x1))*x*S.arange(npts))
return (1.0/npts)*S.dot(coef_spec,a).real
if __name__=='__main__':
P.close('all')
x1 = 1.0
npts = 8
interp_factor = 7
npts_interp = npts*interp_factor
def parab(x,x1=1.0):
return ((x1**2)/4.0)-(x-(x1/2.0))**2
def sin2(x,x1=1.0):
return S.sin(2*S.pi*x)
xarr = P.frange(0,x1,npts=npts,closed=0)
yarr = parab(xarr,x1)
yarr = sin2(xarr,x1)
yspec = S.fft(yarr)
xinterp = P.frange(0,x1,npts=npts_interp,closed=0)
yinterp = spec_interp(yspec,interp_factor)
P.plot(xarr,yarr,'g+-',lw=2,label='data')
P.plot(xinterp,yinterp,'r+-',lw=1,mew=2,label='inerpolated')
## xinterp = P.frange(0,x1,npts=npts_interp+1,closed=0)
## yinterp = S.array([spec_interp(x,yspec,x1) for x in xinterp])
## P.plot(xinterp,yinterp,'b+-',lw=1,mew=2,label='inerpolated+1')
## xinterp = P.frange(0,x1,npts=npts_interp+2,closed=0)
## yinterp = S.array([spec_interp(x,yspec,x1) for x in xinterp])
## P.plot(xinterp,yinterp,'c+-',lw=1,mew=2,label='inerpolated+2')
## xinterp = P.frange(0,x1,npts=npts_interp*12,closed=1)
## yinterp = S.array([spec_interp(x,yspec,x1) for x in xinterp])
## P.plot(xinterp,yinterp,'m+-',lw=1,label='inerpolated-cont')
P.legend()
P.show()
