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Numerical integration: Difference between revisions

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Numerical integration (view source)

Revision as of 14:50, 16 May 2020

46 bytes removed ,  4 years ago
m
→‎{{header|REXX}}: optimized two subroutines.
m (→‎{{header|REXX}}: changed wording in the REXX section header, optimized one procedure (about 5% faster).)
m (→‎{{header|REXX}}: optimized two subroutines.)
Line 4,286:
=={{header|REXX}}==
Note:   there was virtually no difference in accuracy between   '''numeric digits 9'''   (the default)   and   '''numeric digits 20'''.
<lang rexx>/*REXX pgm performs numerical integration using 5five different algorithms and& show results.*/
numeric digits 20 /*use twenty decimal digits precision. */
 
Line 4,295:
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 midpt_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. */
Line 4,307:
return arg(1) /* " " "as─is" " */
/*──────────────────────────────────────────────────────────────────────────────────────*/
left_rect: procedure expose test; parse arg a,b,n; $= 0; h= (b-a)/n
do x=a by h for n; $= $ + f(x); end /*x*/
return $*h/1
/*──────────────────────────────────────────────────────────────────────────────────────*/
midpoint_rectmidpt_rect: procedure expose test; parse arg a,b,n; $= 0; h= (b-a)/n
do x=a+h/2 by h for n; $= $ + f(x); end /*x*/
return $*h/1
/*──────────────────────────────────────────────────────────────────────────────────────*/
right_rect: procedure expose test; parse arg a,b,n; $= 0; h= (b-a)/n
do x=a+h by h for n; $= $ + f(x); end /*x*/
return $*h/1
/*──────────────────────────────────────────────────────────────────────────────────────*/
Simpson: procedure expose test; parse arg a,b,n; h= (b-a)/n; hh= h/2
hh= h/2; $= f(a + h/2hh)
@= 0; do x=1 for n-1; hx _= h*x+a; $= $+f(a+hx_+hh); @= @+f(a+hx_); end /*x*/
 
return h * (f(a) + f(b) + 4*$ + 2*@) / 6
/*─────────--───────────────────────────────────────────────────────────────────────────*/
/*──────────────────────────────────────────────────────────────────────────────────────*/
trapezium: procedure expose test; parse arg a,b,n; $= 0; h= (b-a) / n
do x=a by h for n; $= $ + (f(x) + f(x+h)); end /*x*/
return $*h/2</lang>
{{out|output|text=&nbsp; when using the default inputs:}}
<pre>
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