def run_func_interpolation ( fun , N , low , high , scale = 1.e-8 ) :
Abscissas = Ostap.Math.Interpolation.Abscissas
## uniform abscissas
i0 = interpolate ( fun , Abscissas ( N , low , high , 0 ) )
## Chebyshev abscissas
i1 = interpolate ( fun , Abscissas ( N , low , high , 1 ) )
## lobatto abscissas
i2 = interpolate ( fun , Abscissas ( N , low , high , 2 ) )
## random abscissas
i3 = interpolate ( fun , [ random.uniform ( low , high ) for i in range (N ) ] )
## bernstein interpolant
i4 = interpolate_bernstein ( fun , Abscissas ( N , low , high , 2 ) , low , high )
xx = []
for i in range ( 100000 ) : xx.append ( random.uniform ( low , high ) )
xx.sort()
c0 = SE()
c1 = SE()
c2 = SE()
c3 = SE()
c4 = SE()
for x in xx :
f = fun ( x )
f0 = i0 ( x )
f1 = i1 ( x )
f2 = i2 ( x )
f3 = i3 ( x )
f4 = i4 ( x )
d0 = f0 - f
d1 = f1 - f
d2 = f2 - f
d3 = f3 - f
d4 = f4 - f
c0 += abs ( d0 ) / scale
c1 += abs ( d1 ) / scale
c2 += abs ( d2 ) / scale
c3 += abs ( d3 ) / scale
c4 += abs ( d4 ) / scale
logger.info ( 'Uniform precision: mean/max[%s] = %9.2f +- %-09.1f/%-9.1f' % ( scale , c0.mean () . value () , c0.rms () , c0.max () ) )
logger.info ( 'Chebyshev precision: mean/max[%s] = %9.2f +- %-09.1f/%-9.1f' % ( scale , c1.mean () . value () , c1.rms () , c1.max () ) )
logger.info ( 'Lobatto precision: mean/max[%s] = %9.2f +- %-09.1f/%-9.1f' % ( scale , c2.mean () . value () , c2.rms () , c2.max () ) )
logger.info ( 'Random precision: mean/max[%s] = %9.2f +- %-09.1f/%-9.1f' % ( scale , c3.mean () . value () , c3.rms () , c3.max () ) )
logger.info ( 'Bernstein precision: mean/max[%s] = %9.2f +- %-09.1f/%-9.1f' % ( scale , c4.mean () . value () , c4.rms () , c4.max () ) )
def run_grid_interpolation(tfunc, dct, N, low, high, scale=1.e-8):
Abscissas = Ostap.Math.Interpolation.Abscissas
## uniform abscissas
i0 = interpolate(dct)
## bernstein interpolant
i1 = interpolate_bernstein(dct, None, low, high)
xx = []
for i in range(100000):
xx.append(random.uniform(low, high))
xx.sort()
c0 = SE()
c1 = SE()
for x in xx:
f = tfunc(x)
f0 = i0(x)
f1 = i1(x)
d0 = f0 - f
d1 = f1 - f
c0 += abs(d0) / scale
c1 += abs(d1) / scale
logger.info('Grid precision: mean/max[%s] = %9.2f +- %-09.1f/%-9.1f' %
(scale, c0.mean().value(), c0.rms(), c0.max()))
logger.info('Bernstein precision: mean/max[%s] = %9.2f +- %-09.1f/%-9.1f' %
(scale, c1.mean().value(), c1.rms(), c1.max()))
def run_grid_interpolation ( tfunc , dct , N , low , high , scale = 1.e-8 ) :
Abscissas = Ostap.Math.Interpolation.Abscissas
data = points ( dct )
## uniform abscissas
i0 = interpolate ( data )
## bernstein interpolant
i1 = interpolate_bernstein ( data , None , low , high )
## neville interpolant
i2 = Ostap.Math.Neville ( data )
## largange interpolant
i3 = Ostap.Math.Lagrange ( data )
## newton interpolant
i4 = Ostap.Math.Newton ( data )
## bspline interpolant
degree = 3
## bs = Ostap.Math.BSpline ( low , high , len ( data ) - 1 - degree , degree )
i5 = interpolate_bspline ( data , None , degree )
xx = []
for i in range ( 100000 ) : xx.append ( random.uniform ( low , high ) )
xx.sort()
c0 = SE ()
c1 = SE ()
c2 = SE ()
c3 = SE ()
c4 = SE ()
c5 = SE ()
for x in xx :
f = tfunc ( x )
f0 = i0 ( x )
f1 = i1 ( x )
f2 = i2 ( x )
f3 = i3 ( x )
f4 = i4 ( x )
f5 = i5 ( x )
d0 = f0 - f
d1 = f1 - f
d2 = f2 - f
d3 = f3 - f
d4 = f4 - f
d5 = f5 - f
c0 += abs ( d0 ) / scale
c1 += abs ( d1 ) / scale
c2 += abs ( d2 ) / scale
c3 += abs ( d3 ) / scale
c4 += abs ( d4 ) / scale
c5 += abs ( d5 ) / scale
logger.info ( 'Grid precision: mean/max[%s] = %9.2f +- %-09.1f/%-9.1f' % ( scale , c0.mean () . value () , c0.rms () , c0.max () ) )
logger.info ( 'Bernstein precision: mean/max[%s] = %9.2f +- %-09.1f/%-9.1f' % ( scale , c1.mean () . value () , c1.rms () , c1.max () ) )
logger.info ( 'Neville precision: mean/max[%s] = %9.2f +- %-09.1f/%-9.1f' % ( scale , c2.mean () . value () , c2.rms () , c2.max () ) )
logger.info ( 'Lagrange precision: mean/max[%s] = %9.2f +- %-09.1f/%-9.1f' % ( scale , c3.mean () . value () , c3.rms () , c3.max () ) )
logger.info ( 'Newton precision: mean/max[%s] = %9.2f +- %-09.1f/%-9.1f' % ( scale , c4.mean () . value () , c4.rms () , c4.max () ) )
logger.info ( 'bSpline precision: mean/max[%s] = %9.2f +- %-09.1f/%-9.1f' % ( scale , c5.mean () . value () , c5.rms () , c5.max () ) )
import time
i5.draw()
time.sleep(5)