test_deriv.php deriv, rderiv, nuderiv

// deriv.php includes deriv, rderiv, nuderiv  require_once 'deriv.php';
//          order is order of derivative, 1 = first derivative, 2 = second 
//          points is number of points where value of function is known    
//          f(x0), f(x1), f(x2) ... f(x points-1)                          
//          point is the term where derivative is computed                 
//          f'(x0) = (1/bh^order)*( a(0)*f(x0) + a(1)*f(x1)                
//                   + ... + a(points-1)*f(x points-1)                     
//          uniformly spaced points x1=x0+h, x2=x1+h=x1+2*h, ...           
//                                                                         
//          rderiv returns c[0]=(1/bh^order)*a[0]  ...                     
//                                                                         
//          nuderiv works for non-uniformly spaced points                  
//                                                                         
// algorithm: use divided differences to get polynomial p(x) that          
//            approximates  f(x).  f(x)=p(x)+error term                    
//            f'(x) = p'(x) + error term'                                  
//            substitute xj = x0 + j*h                                     
//            substitute x = x0 to get  p'(x0) etc                         
test_deriv.php running 

gcd(6,9)=3 

gcd(9,6)=3 

gcd(8,2)=2 

gcd(2,8)=2 

deriv(2, 3, 1) 

array(4) {
  [0]=>
  int(1)
  [1]=>
  int(-2)
  [2]=>
  int(1)
  [3]=>
  int(1)
}
b=1 

a[0]=1 

a[1]=-2 

a[2]=1 

deriv(4, 5, 2) 

array(6) {
  [0]=>
  int(1)
  [1]=>
  int(-4)
  [2]=>
  int(6)
  [3]=>
  int(-4)
  [4]=>
  int(1)
  [5]=>
  int(1)
}
b=1 

a[0]=1 

a[1]=-4 

a[2]=6 

a[3]=-4 

a[4]=1 

rderiv(4, 5, 2, 0.1) 

c[0]=10000 

c[1]=-40000 

c[2]=60000 

c[3]=-40000 

c[4]=10000 



nuderiv(4,5,2,a) 

c[0]=10000 

c[1]=-40000.000000001 

c[2]=60000.000000001 

c[3]=-40000.000000001 

c[4]=10000 



rderiv(2,8,4,0.1) 

c[0]=0 

c[1]=1.1111111111111 

c[2]=-15 

c[3]=150 

c[4]=-272.22222222222 

c[5]=150 

c[6]=-15 

c[7]=1.1111111111111 



nuderiv(2,8,4,a) 

c[0]=9.9134922493249E-11 

c[1]=1.1111111104474 

c[2]=-14.999999998166 

c[3]=149.99999999735 

c[4]=-272.22222221969 

c[5]=149.99999999873 

c[6]=-14.999999999589 

c[7]=1.1111111110586 



nuderiv(2,10,4,a) 

c[0]=-0.14464314622575 

c[1]=2.057146969782 

c[2]=-16.200032393965 

c[3]=129.60025918762 

c[4]=-230.62546123317 

c[5]=129.60025918383 

c[6]=-16.20003239013 

c[7]=2.0571469673796 

c[8]=-0.14464314548331 

c[9]=-1.0101075531566E-10