function x = semicircular_cdf_inv ( cdf, a, b ) %*****************************************************************************80 % %% SEMICIRCULAR_CDF_INV inverts the Semicircular CDF. % % Discussion: % % A simple bisection method is used on the interval [ A - B, A + B ]. % % Licensing: % % This code is distributed under the GNU LGPL license. % % Modified: % % 20 September 2004 % % Parameters: % % Input, real CDF, the value of the CDF. % % Input, real A, B, the parameters of the PDF. % 0.0 < B. % % Output, real X, the corresponding argument of the CDF. % it_max = 100; tol = 0.0001; if ( cdf <= 0.0 ) x = a - b; return elseif ( 1.0 <= cdf ) x = a + b; return end x1 = a - b; cdf1 = 0.0; x2 = a + b; cdf2 = 1.0; % % Now use bisection. % it = 0; while ( true ) it = it + 1; x3 = 0.5 * ( x1 + x2 ); cdf3 = semicircular_cdf ( x3, a, b ); if ( abs ( cdf3 - cdf ) < tol ) x = x3; break end if ( it_max < it ) fprintf ( 1, '\n' ); fprintf ( 1, 'SEMICIRCULAR_CDF_INV - Fatal error!\n' ); fprintf ( 1, ' Iteration limit exceeded.\n' ); error ( 'SEMICIRCULAR_CDF_INV - Fatal error!' ); end if ( ( cdf <= cdf3 && cdf <= cdf1 ) || ( cdf3 <= cdf && cdf1 <= cdf ) ) x1 = x3; cdf1 = cdf3; else x2 = x3; cdf2 = cdf3; end end return end