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Numerical integration: Difference between revisions

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Numerical integration (view source)

Revision as of 12:57, 16 May 2020

13 bytes added ,  4 years ago
m
→‎{{header|REXX}}: changed whitespace, aligned some statements better.
(→‎{{header|Raku}}: Move some calculations out of hot loops, more efficient looping constructs, arguably less idiomatic, but less horribly slow)
m (→‎{{header|REXX}}: changed whitespace, aligned some statements better.)
Line 4,289:
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= 5000000; end
say center('test' test, 65, "─═") /*display a header for the test suite. */▼
say
▲ say center('test' test, 65, "─") /*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)
Line 4,308 ⟶ 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+h by h for n; $= $ + f(x); end end /*x*/▼
$= 0
do x=a by h for n; $=$+f(x); end /*x*/▼
return $*h/1
/*──────────────────────────────────────────────────────────────────────────────────────*/
midpoint_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 end /*x*/▼
$= 0
▲ 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*/
$= 0
▲ 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
$= f(a + h/2)
@= 0; do x=1 for n-1; $= $+f(a+h*x+h*.5); @= @+f(a+x*h); 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*/
$= 0
▲ 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>
═════════════════════════════test 1══════════════════════════════
─────────────────────────────test 1──────────────────────────────
left rectangular(0, 1, 100) ──► 0.245025
midpoint rectangular(0, 1, 100) ──► 0.2499875
Line 4,342 ⟶ 4,337:
trapezium(0, 1, 100) ──► 0.250025
 
═════════════════════════════test 2══════════════════════════════
─────────────────────────────test 2──────────────────────────────
left rectangular(1, 100, 1000) ──► 4.6549910575146761473
midpoint rectangular(1, 100, 1000) ──► 4.604762548678375185
Line 4,349 ⟶ 4,344:
trapezium(1, 100, 1000) ──► 4.605986057514676146
 
═════════════════════════════test 3══════════════════════════════
─────────────────────────────test 3──────────────────────────────
left rectangular(0, 5000, 5000000) ──► 12499997.5
midpoint rectangular(0, 5000, 5000000) ──► 12500000
Line 4,356 ⟶ 4,351:
trapezium(0, 5000, 5000000) ──► 12500000
 
═════════════════════════════test 4══════════════════════════════
─────────────────────────────test 4──────────────────────────────
left rectangular(0, 6000, 5000000) ──► 17999996.4
midpoint rectangular(0, 6000, 5000000) ──► 18000000
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