# test_deriv.py  simple test

from deriv import deriv

print "test_deriv.py running"
# deriv(order, npoints, point): # return a[] bb
# compute the exact coefficients to numerically compute a derivative
# of order 'order' using 'npoints' at ordinate point,
# where order>=1, npoints>=order+1, 0 <= point < npoints,
# 'a' array returned with numerator of coefficients,
# 'bb' returned with denominator of h^order

order = 2
npoints = 7
# point = 3
for point in range(npoints):
  bb = 0
  a=[0 for i in range(npoints)]     # numerator of terms returned
  print "a,bb = deriv(",
  print order,
  print ",",
  print npoints,
  print ",",
  print point,
  print ")"
  #
  a,bb = deriv(order, npoints, point)
  print "bb=", bb
  print "a[0]=", a[0]
  print "a[1]=", a[1]
  print "a[2]=", a[2]
  print "a[3]=", a[3]
  print "a[4]=", a[4]
  print "a[5]=", a[5]
  print "a[6]=", a[6]
  print "  "


print "deriv f(x[npoint]) = (a[0]*f(x[0]) +...+ a[points-1]*f(x[points-1]))/"
print "                     (bb*h*h)"

h=0.1
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 "check derivative at point ",  point
  a,bb = deriv(order, npoints, 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 + a[i]*y[i]
  
  sum = sum/(bb*h*h)
  print "computed derivative = ", sum,  "  should be =", ddf[point]


print "test_deriv.py finished"