Numerical integration: Difference between revisions
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x 17999997.000000 18000003.000000 18000000.000000 18000000.000000 18000000.000000</pre>
=={{header|ALGOL W}}==
{{Trans|ALGOL 68}}
<lang algolw>begin % compare some numeric integration methods %
long real procedure leftRect ( long real procedure f
; long real value a, b
; integer value n
) ;
begin
long real h, sum, x;
h := (b - a) / n;
sum := 0;
x := a;
while x <= b - h do begin
sum := sum + (h * f(x));
x := x + h
end;
sum
end leftRect ;
long real procedure rightRect ( long real procedure f
; long real value a, b
; integer value n
) ;
begin
long real h, sum, x;
h := (b - a) / n;
sum := 0;
x := a + h;
while x <= b do begin
sum := sum + (h * f(x));
x := x + h
end;
sum
end rightRect ;
long real procedure midRect ( long real procedure f
; long real value a, b
; integer value n
) ;
begin
long real h, sum, x;
h := (b - a) / n;
sum := 0;
x := a;
while x <= b - h do begin
sum := sum + h * f(x + h / 2);
x := x + h
end;
sum
end midRect ;
long real procedure trapezium ( long real procedure f
; long real value a, b
; integer value n
) ;
begin
long real h, sum, x;
h := (b - a) / n;
sum := f(a) + f(b);
x := 1;
while x <= n - 1 do begin
sum := sum + 2 * f(a + x * h );
x := x + 1
end;
(b - a) / (2 * n) * sum
end trapezium ;
long real procedure simpson ( long real procedure f
; long real value a, b
; integer value n
) ;
begin
long real h, sum1, sum2, x;
integer limit;
h := (b - a) / n;
sum1 := 0;
sum2 := 0;
limit := n - 1;
for i := 0 until limit do sum1 := sum1 + f(a + h * i + h / 2);
for i := 1 until limit do sum2 := sum2 + f(a + h * i);
h / 6 * (f(a) + f(b) + 4 * sum1 + 2 * sum2)
end simpson ;
% tests the above procedures %
procedure testIntegrators1 ( string(3) value legend
; long real procedure f
; long real value lowerLimit
; long real value upperLimit
; integer value iterations
) ;
write( r_format := "A", r_w := 20, r_d := 6, s_w := 0,
, legend
, leftRect( f, lowerLimit, upperLimit, iterations )
, rightRect( f, lowerLimit, upperLimit, iterations )
, midRect( f, lowerLimit, upperLimit, iterations )
, trapezium( f, lowerLimit, upperLimit, iterations )
, simpson( f, lowerLimit, upperLimit, iterations )
);
procedure testIntegrators2 ( string(3) value legend
; long real procedure f
; long real value lowerLimit
; long real value upperLimit
; integer value iterations
) ;
write( r_format := "A", r_w := 16, r_d := 2, s_w := 0,
, legend
, leftRect( f, lowerLimit, upperLimit, iterations ), " "
, rightRect( f, lowerLimit, upperLimit, iterations ), " "
, midRect( f, lowerLimit, upperLimit, iterations ), " "
, trapezium( f, lowerLimit, upperLimit, iterations ), " "
, simpson( f, lowerLimit, upperLimit, iterations ), " "
);
begin % task test cases %
long real procedure xCubed ( long real value x ) ; x * x * x;
long real procedure oneOverX ( long real value x ) ; 1 / x;
long real procedure xValue ( long real value x ) ; x;
write( " "
, " left rect"
, " right rect"
, " mid rect"
, " trapezium"
, " simpson"
);
testIntegrators1( "x^3", xCubed, 0, 1, 100 );
testIntegrators1( "1/x", oneOverX, 1, 100, 1000 );
testIntegrators2( "x ", xValue, 0, 5000, 5000000 );
testIntegrators2( "x ", xValue, 0, 6000, 6000000 )
end
end.</lang>
=={{header|AutoHotkey}}==
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