>>> # Cubic-spline
>>> x = arange(0,2*pi+pi/4,2*pi/8)
>>> y = sin(x)
>>> tck = interpolate.splrep(x,y,s=0)
>>> xnew = arange(0,2*pi,pi/50)
>>> ynew = interpolate.splev(xnew,tck,der=0)
>>> xplt.plot(x,y,'x',xnew,ynew,xnew,sin(xnew),x,y,'b')
>>> xplt.legend(['Linear','Cubic Spline', 'True'],['b-x','m','r'])
>>> xplt.limits(-0.05,6.33,-1.05,1.05)
>>> xplt.title('Cubic-spline interpolation')
>>> xplt.eps('interp_cubic')
>>> # Derivative of spline
>>> yder = interpolate.splev(xnew,tck,der=1)
>>> xplt.plot(xnew,yder,xnew,cos(xnew),'|')
>>> xplt.legend(['Cubic Spline', 'True'])
>>> xplt.limits(-0.05,6.33,-1.05,1.05)
>>> xplt.title('Derivative estimation from spline')
>>> xplt.eps('interp_cubic_der')
>>> # Integral of spline
>>> def integ(x,tck,constant=-1):
>>> x = asarray_1d(x)
>>> out = zeros(x.shape, x.typecode())
>>> for n in xrange(len(out)):
>>> out[n] = interpolate.splint(0,x[n],tck)
>>> out += constant
>>> return out
>>>
>>> yint = integ(xnew,tck)
>>> xplt.plot(xnew,yint,xnew,-cos(xnew),'|')
>>> xplt.legend(['Cubic Spline', 'True'])
>>> xplt.limits(-0.05,6.33,-1.05,1.05)
>>> xplt.title('Integral estimation from spline')
>>> xplt.eps('interp_cubic_int')
>>> # Roots of spline
>>> print interpolate.sproot(tck)
[ 0. 3.1416]
>>> # Parametric spline
>>> t = arange(0,1.1,.1)
>>> x = sin(2*pi*t)
>>> y = cos(2*pi*t)
>>> tck,u = interpolate.splprep([x,y],s=0)
>>> unew = arange(0,1.01,0.01)
>>> out = interpolate.splev(unew,tck)
>>> xplt.plot(x,y,'x',out[0],out[1],sin(2*pi*unew),cos(2*pi*unew),x,y,'b')
>>> xplt.legend(['Linear','Cubic Spline', 'True'],['b-x','m','r'])
>>> xplt.limits(-1.05,1.05,-1.05,1.05)
>>> xplt.title('Spline of parametrically-defined curve')
>>> xplt.eps('interp_cubic_param')
