source: issm/oecreview/Archive/19101-20495/ISSM-20188-20189.diff@ 20498

Index: ../trunk-jpl/src/m/psl/p_polynomial_prime.m
===================================================================
--- ../trunk-jpl/src/m/psl/p_polynomial_prime.m (revision 0)
+++ ../trunk-jpl/src/m/psl/p_polynomial_prime.m (revision 20189)
@@ -0,0 +1,85 @@
+function vp = p_polynomial_prime ( m, n, x )
+
+%*****************************************************************************80
+%
+%% P_POLYNOMIAL_PRIME evaluates the derivative of Legendre polynomials P(n,x).
+%
+%  Discussion:
+%
+%    P(0,X) = 1
+%    P(1,X) = X
+%    P(N,X) = ( (2*N-1)*X*P(N-1,X)-(N-1)*P(N-2,X) ) / N
+%
+%    P'(0,X) = 0
+%    P'(1,X) = 1
+%    P'(N,X) = ( (2*N-1)*(P(N-1,X)+X*P'(N-1,X)-(N-1)*P'(N-2,X) ) / N
+%
+%  Licensing:
+%
+%    This code is distributed under the GNU LGPL license. 
+%
+%  Modified:
+%
+%    13 March 2012
+%
+%  Author:
+%
+%    John Burkardt
+%
+%  Reference:
+%
+%    Milton Abramowitz, Irene Stegun,
+%    Handbook of Mathematical Functions,
+%    National Bureau of Standards, 1964,
+%    ISBN: 0-486-61272-4,
+%    LC: QA47.A34.
+%
+%    Daniel Zwillinger, editor,
+%    CRC Standard Mathematical Tables and Formulae,
+%    30th Edition,
+%    CRC Press, 1996.
+%
+%  Parameters:
+%
+%    Input, integer M, the number of evaluation points.
+%
+%    Input, integer N, the highest order polynomial to evaluate.
+%    Note that polynomials 0 through N will be evaluated.
+%
+%    Input, real X(M,1), the evaluation points.
+%
+%    Output, real VP(M,N+1), the values of the derivatives of the
+%    Legendre polynomials of order 0 through N at the point X.
+%
+  if ( n < 0 )
+    vp = [];
+    return
+  end
+
+  v = zeros ( m, n + 1 );
+  vp = zeros ( m, n + 1 );
+
+  v(1:m,1) = 1.0;
+  vp(1:m,1) = 0.0;
+
+  if ( n < 1 )
+    return
+  end
+
+  v(1:m,2) = x(1:m,1);
+  vp(1:m,2) = 1.0;
+ 
+  for i = 2 : n
+ 
+    v(1:m,i+1) = ( ( 2 * i - 1 ) * x(1:m,1) .* v(1:m,i)     ...
+                 - (     i - 1 ) *             v(1:m,i-1) ) ...
+                 / (     i     );
+ 
+    vp(1:m,i+1) = ( ( 2 * i - 1 ) * ( v(1:m,i) + x(1:m,1) .* vp(1:m,i) )   ...
+                  - (     i - 1 ) *                          vp(1:m,i-1) ) ...
+                  / (     i     );
+ 
+  end
+ 
+  return
+end