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

Last change on this file since 20498 was 20498, checked in by Mathieu Morlighem, 9 years ago

CHG: done with Archive/19101-20495
File size: 2.2 KB

  • ../trunk-jpl/src/m/psl/p_polynomial_prime.m

     
     1function vp = p_polynomial_prime ( m, n, x )
     2
     3%*****************************************************************************80
     4%
     5%% P_POLYNOMIAL_PRIME evaluates the derivative of Legendre polynomials P(n,x).
     6%
     7%  Discussion:
     8%
     9%    P(0,X) = 1
     10%    P(1,X) = X
     11%    P(N,X) = ( (2*N-1)*X*P(N-1,X)-(N-1)*P(N-2,X) ) / N
     12%
     13%    P'(0,X) = 0
     14%    P'(1,X) = 1
     15%    P'(N,X) = ( (2*N-1)*(P(N-1,X)+X*P'(N-1,X)-(N-1)*P'(N-2,X) ) / N
     16%
     17%  Licensing:
     18%
     19%    This code is distributed under the GNU LGPL license.
     20%
     21%  Modified:
     22%
     23%    13 March 2012
     24%
     25%  Author:
     26%
     27%    John Burkardt
     28%
     29%  Reference:
     30%
     31%    Milton Abramowitz, Irene Stegun,
     32%    Handbook of Mathematical Functions,
     33%    National Bureau of Standards, 1964,
     34%    ISBN: 0-486-61272-4,
     35%    LC: QA47.A34.
     36%
     37%    Daniel Zwillinger, editor,
     38%    CRC Standard Mathematical Tables and Formulae,
     39%    30th Edition,
     40%    CRC Press, 1996.
     41%
     42%  Parameters:
     43%
     44%    Input, integer M, the number of evaluation points.
     45%
     46%    Input, integer N, the highest order polynomial to evaluate.
     47%    Note that polynomials 0 through N will be evaluated.
     48%
     49%    Input, real X(M,1), the evaluation points.
     50%
     51%    Output, real VP(M,N+1), the values of the derivatives of the
     52%    Legendre polynomials of order 0 through N at the point X.
     53%
     54  if ( n < 0 )
     55    vp = [];
     56    return
     57  end
     58
     59  v = zeros ( m, n + 1 );
     60  vp = zeros ( m, n + 1 );
     61
     62  v(1:m,1) = 1.0;
     63  vp(1:m,1) = 0.0;
     64
     65  if ( n < 1 )
     66    return
     67  end
     68
     69  v(1:m,2) = x(1:m,1);
     70  vp(1:m,2) = 1.0;
     71 
     72  for i = 2 : n
     73 
     74    v(1:m,i+1) = ( ( 2 * i - 1 ) * x(1:m,1) .* v(1:m,i)     ...
     75                 - (     i - 1 ) *             v(1:m,i-1) ) ...
     76                 / (     i     );
     77 
     78    vp(1:m,i+1) = ( ( 2 * i - 1 ) * ( v(1:m,i) + x(1:m,1) .* vp(1:m,i) )   ...
     79                  - (     i - 1 ) *                          vp(1:m,i-1) ) ...
     80                  / (     i     );
     81 
     82  end
     83 
     84  return
     85end
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