%
define main
% This module is a trapezoidal rule integration program.
% For any supplied function f(X:double_real), it takes
% double real inputs defining endpoints of the interval
% to be integrated over, a double real tolerance, and an
% integer count of sub-intervals to divide the interval
% into. It returns an array of double_real values of the
% numerical value of the definite integral over the interval,
% the number of refinement iterations made, the number of
% subintervals actually used to arrive at the final result,
% and the total number of subinterval area calculations made.
type One_Dim_D = array [ double_real ];
type Two_Dim_D = array [ One_Dim_D ];
% INSERT FUNCTION F HERE
%
%===============================================================
function f( x : double_real returns double_real )
15.0d0 * x * x * x - 6.375d0 * x * x + 11.9d0 * x - 33.999d0
end function %% f
%===============================================================
function trap_area( left_end, right_end : double_real
returns double_real )
% Calculates the area of a trapezoid
let h := right_end - left_end;
f_avg := ( f(left_end) + f(right_end) )/2.0d0
in h * f_avg
end let
end function %% trap_area
%===============================================================
function main( a, b : double_real; % Endpoints of integration
% interval
epsilon : double_real; % tolerance
initial_n : integer; % Initial number of
% subintervals
returns One_Dim_D, % values of approximation
% of definite integral
integer, % iteration counter
integer ) % number of subintervals
% finally used
for initial
N := initial_n;
Total_N := N;
Cnt := 1;
H := (b - a) / double_real(N);
Area := for i in 1, N
ai := a + double_real(i-1) * h;
bi := ai + h;
returns value of sum trap_area( ai, bi )
end for
repeat
N := old N * 2;
Total_N := old Total_N + N;
Cnt := old Cnt + 1;
H := old H / 2.0d0;
Area := for i in 1, N
ai := a + double_real(i-1) * h;
bi := ai + h;
returns value of sum trap_area( ai, bi )
end for
until abs( area - old area ) < epsilon | Cnt > 12
returns array of Area
value of Cnt
value of N
value of Total_N
end for
end function %% main
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