# test_nuderiv.py  simple test

from nuderiv import *

print "test_nuderiv.py running"
# nuderiv(order, npoints, point, x): # return c[]
# compute the coefficients to numerically compute a derivative
# of order 'order' using 'npoints' at ordinate point,
# where order>=1, npoints>=order+1, 0 <= point < npoints,
# 'c' array returned with numerator of coefficients,

order = 2
npoints = 7
point = 3
c = [0 for i in range(npoints)]     # numerator of terms returned

h=0.1 # does not need to be uniform
x=[0.0 for i in range(npoints)]   # x values
y=[0.0 for i in range(npoints)]   # y = f(x)
df=[0.0 for i in range(npoints)]  # df(x)/dx = f'(x)
ddf=[0.0 for i in range(npoints)]  # d^2f(x)/dx = f''(x)

for i in range(npoints):
  x[i] = i*h
  print "x[", i, "]=", x[i]

print " "
print "y = f(x) = x^3 + 2x^2 + 3x +4 "
for i in range(npoints):
  y[i] = x[i]*x[i]*x[i]+2.0*x[i]*x[i]+3.0*x[i]+4.0
  print "y[", i, "]=", y[i]

print " "
print "df(x)/dx = 3.0*x^2 + 4.0*x + 3.0"
for i in range(npoints):
  df[i] = 3.0*x[i]*x[i]+4.0*x[i]+3.0
  print "df[", i, "]=", df[i]


print " "
print "ddf(x)/dx = 6.0*x + 4.0"
for i in range(npoints):
  ddf[i] = 6.0*x[i]+4.0
  print "ddf[", i, "]=", ddf[i]

print " "
for point in range(npoints):
  print "c = nuderiv(", order, ",", npoints, ",", point, ", x)"
  c = nuderiv(order, npoints, point, x)
  print "c[0]=", c[0]
  print "c[1]=", c[1]
  print "c[2]=", c[2]
  print "c[3]=", c[3]
  print "c[4]=", c[4]
  print "c[5]=", c[5]
  print "c[6]=", c[6]
  print " "
  print "nuderiv f(x[npoint]) = (c[0]*f(x[0]) +...+ c[points-1]*f(x[points-1]))"
  print "check derivative at point ", point
  sum = 0.0
  for i in range(npoints):
    y[i] = x[i]*x[i]*x[i]+2.0*x[i]*x[i]+3.0*x[i]+4.0

  for i in range(npoints):
    sum = sum + c[i]*y[i]

  print "computed derivative = ", sum,  " should be =", ddf[point]
  print  " "

print " "
print "test_nuderiv.py finished"