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Ingy döt Net 2023-07-01 11:58:00 -04:00
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Task/Numerical-integration/REXX/numerical-integration.rexx Normal file
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/*REXX pgm performs numerical integration using 5 different algorithms and show results.*/
numeric digits 20 /*use twenty decimal digits precision. */
do test=1 for 4; say /*perform the 4 different test suites. */
if test==1 then do; L= 0; H= 1; i= 100; end
if test==2 then do; L= 1; H= 100; i= 1000; end
if test==3 then do; L= 0; H= 5000; i= 5000000; end
if test==4 then do; L= 0; H= 6000; i= 6000000; end
say center('test' test, 79, "═") /*display a header for the test suite. */
say ' left rectangular('L", "H', 'i") ──► " left_rect(L, H, i)
say ' midpoint rectangular('L", "H', 'i") ──► " midpoint_rect(L, H, i)
say ' right rectangular('L", "H', 'i") ──► " right_rect(L, H, i)
say ' Simpson('L", "H', 'i") ──► " Simpson(L, H, i)
say ' trapezium('L", "H', 'i") ──► " trapezium(L, H, i)
end /*test*/
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
f: parse arg y; if test>2 then return y /*choose the "as─is" function. */
if test==1 then return y**3 /* " " cube function. */
return 1/y /* " " reciprocal " */
/*──────────────────────────────────────────────────────────────────────────────────────*/
left_rect: procedure expose test; parse arg a,b,#; $= 0; h= (b-a)/#
do x=a by h for #; $= $ + f(x)
end /*x*/
return $*h/1
/*──────────────────────────────────────────────────────────────────────────────────────*/
midpoint_rect: procedure expose test; parse arg a,b,#; $= 0; h= (b-a)/#
do x=a+h/2 by h for #; $= $ + f(x)
end /*x*/
return $*h/1
/*──────────────────────────────────────────────────────────────────────────────────────*/
right_rect: procedure expose test; parse arg a,b,#; $= 0; h= (b-a)/#
do x=a+h by h for #; $= $ + f(x)
end /*x*/
return $*h/1
/*──────────────────────────────────────────────────────────────────────────────────────*/
Simpson: procedure expose test; parse arg a,b,#; h= (b-a)/#
hh= h/2; $= f(a + hh)
@= 0; do x=1 for #-1; hx=h*x + a; @= @ + f(hx)
$= $ + f(hx + hh)
end /*x*/
return h * (f(a) + f(b) + 4*$ + 2*@) / 6
/*──────────────────────────────────────────────────────────────────────────────────────*/
trapezium: procedure expose test; parse arg a,b,#; $= 0; h= (b-a)/#
do x=a by h for #; $= $ + (f(x) + f(x+h))
end /*x*/
return $*h/2