function x = maxwell_cdf_inv ( cdf, a ) %*****************************************************************************80 % %% MAXWELL_CDF_INV inverts the Maxwell CDF. % % Discussion: % % A simple bisection method is used. % % Licensing: % % This code is distributed under the GNU LGPL license. % % Modified: % % 09 October 2004 % % Author: % % John Burkardt % % Parameters: % % Input, real CDF, the value of the CDF. % % Input, real A, the parameter of the PDF. % 0 < A. % % Output, real X, the corresponding argument of the CDF. % it_max = 100; tol = 0.0001; if ( cdf <= 0.0 ) x = 0.0; return elseif ( 1.0 <= cdf ) x = r8_huge ( ); return end x1 = 0.0; cdf1 = 0.0; x2 = 1.0; while ( true ) cdf2 = maxwell_cdf ( x2, a ); if ( cdf < cdf2 ) break end x2 = 2.0 * x2; if ( 1000000.0 < x2 ) fprintf ( 1, '\n' ); fprintf ( 1, 'MAXWELL_CDF_INV - Fatal error!\n' ); fprintf ( 1, ' Initial bracketing effort fails.\n' ); error ( 'MAXWELL_CDF_INV - Fatal error!' ); end end % % Now use bisection. % it = 0; while ( true ) it = it + 1; x3 = 0.5 * ( x1 + x2 ); cdf3 = maxwell_cdf ( x3, a ); if ( abs ( cdf3 - cdf ) < tol ) x = x3; break end if ( it_max < it ) fprintf ( 1, '\n' ); fprintf ( 1, 'MAXWELL_CDF_INV - Fatal error!\n' ); fprintf ( 1, ' Iteration limit exceeded.\n' ); error ( 'MAXWELL_CDF_INV - Fatal error!' ); end if ( ( cdf3 <= cdf && cdf1 < cdf ) || ( cdf <= cdf3 && cdf <= cdf1 ) ) x1 = x3; cdf1 = cdf3; else x2 = x3; cdf2 = cdf3; end end return end