Index: /issm/trunk-jpl/src/c/shared/Numerics/legendre.cpp
===================================================================
--- /issm/trunk-jpl/src/c/shared/Numerics/legendre.cpp	(revision 19979)
+++ /issm/trunk-jpl/src/c/shared/Numerics/legendre.cpp	(revision 19979)
@@ -0,0 +1,150 @@
+/*!\file:  legendre.cpp
+ \brief compute legendre polynomial at specific x. 
+ This is inspired from the p_polynomial_value package, written by John Burkardt (see below 
+ for full documentation). 
+ Here, we apply the function differently: we assume previous two evaluations are provided, 
+ and we compute the level n evaluation: 
+
+*/
+
+/* function v = p_polynomial_value ( m, n, x ) {{{
+
+	%*****************************************************************************80
+	%
+	%% P_POLYNOMIAL_VALUE evaluates the Legendre polynomials P(n,x).
+	%
+	%  Discussion:
+	%
+	%    P(n,1) = 1.
+	%    P(n,-1) = (-1)^N.
+	%    | P(n,x) | <= 1 in [-1,1].
+	%
+	%    The N zeroes of P(n,x) are the abscissas used for Gauss-Legendre
+	%    quadrature of the integral of a function F(X) with weight function 1
+	%    over the interval [-1,1].
+	%
+	%    The Legendre polynomials are orthogonal under the inner product defined
+	%    as integration from -1 to 1:
+	%
+	%      Integral ( -1 <= X <= 1 ) P(I,X) * P(J,X) dX 
+	%        = 0 if I =/= J
+	%        = 2 / ( 2*I+1 ) if I = J.
+	%
+	%    Except for P(0,X), the integral of P(I,X) from -1 to 1 is 0.
+	%
+	%    A function F(X) defined on [-1,1] may be approximated by the series
+	%      C0*P(0,x) + C1*P(1,x) + ... + CN*P(n,x)
+	%    where
+	%      C(I) = (2*I+1)/(2) * Integral ( -1 <= X <= 1 ) F(X) P(I,x) dx.
+	%
+	%    The formula is:
+	%
+	%      P(n,x) = (1/2^N) * sum ( 0 <= M <= N/2 ) C(N,M) C(2N-2M,N) X^(N-2*M)
+	%
+	%  Differential equation:
+	%
+	%    (1-X*X) * P(n,x)'' - 2 * X * P(n,x)' + N * (N+1) = 0
+	%
+	%  First terms:
+	%
+	%    P( 0,x) =      1
+	%    P( 1,x) =      1 X
+	%    P( 2,x) = (    3 X^2 -       1)/2
+	%    P( 3,x) = (    5 X^3 -     3 X)/2
+	%    P( 4,x) = (   35 X^4 -    30 X^2 +     3)/8
+	%    P( 5,x) = (   63 X^5 -    70 X^3 +    15 X)/8
+	%    P( 6,x) = (  231 X^6 -   315 X^4 +   105 X^2 -     5)/16
+	%    P( 7,x) = (  429 X^7 -   693 X^5 +   315 X^3 -    35 X)/16
+	%    P( 8,x) = ( 6435 X^8 - 12012 X^6 +  6930 X^4 -  1260 X^2 +   35)/128
+	%    P( 9,x) = (12155 X^9 - 25740 X^7 + 18018 X^5 -  4620 X^3 +  315 X)/128
+	%    P(10,x) = (46189 X^10-109395 X^8 + 90090 X^6 - 30030 X^4 + 3465 X^2-63)/256
+	%
+	%  Recursion:
+	%
+	%    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:
+	%
+	%    10 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 V(M,1:N+1), the values of the Legendre polynomials 
+	%    of order 0 through N at the points X.
+	%
+	  if ( n < 0 )
+		v = [];
+		return
+	  end
+
+	  v = ones ( m, n + 1 );
+
+	  if ( n < 1 )
+		return
+	  end
+
+	  v(1:m,2) = x;
+
+	  for i = 2 : n
+	 
+		v(:,i+1) = ( ( 2 * i - 1 ) * x .* v(:,i)   ...
+					-  (     i - 1 ) *    v(:,i-1) ) ...
+					/  (     i     );
+	 
+	  end
+	  }}}  */ 
+
+#ifdef HAVE_CONFIG_H
+	#include <config.h>
+#else
+#error "Cannot compile with HAVE_CONFIG_H symbol! run configure first!"
+#endif
+
+#include "./types.h"
+#include "../Exceptions/exceptions.h"
+#include "./recast.h"
+
+IssmDouble legendre(IssmDouble Pn1, IssmDouble Pn2, IssmDouble x, int n){
+
+	if (n<0)_error_("legendre error message: order required should be >0");
+
+	if(n==0)return 1;
+	if(n==1)return x;
+
+	return ( (2*n-1)*x*Pn1 - (n-1)*Pn2 ) /n;
+	
+}
Index: /issm/trunk-jpl/src/c/shared/Numerics/numerics.h
===================================================================
--- /issm/trunk-jpl/src/c/shared/Numerics/numerics.h	(revision 19978)
+++ /issm/trunk-jpl/src/c/shared/Numerics/numerics.h	(revision 19979)
@@ -34,4 +34,5 @@
 void        XZvectorsToCoordinateSystem(IssmDouble *T,IssmDouble*xzvectors);
 int         cubic(IssmDouble a, IssmDouble b, IssmDouble c, IssmDouble d,IssmDouble X[3], int *num);
+IssmDouble  legendre(IssmDouble Pn1, IssmDouble Pn2, IssmDouble x, int i);
 
 int         NewtonSolveDnorm(IssmDouble* pdnorm,IssmDouble c1,IssmDouble c2,IssmDouble c3,IssmDouble n,IssmDouble dnorm);