Numerical integration: Difference between revisions
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m (→{{header|REXX}}: changed wording in the REXX section header, optimized one procedure (about 5% faster).) |
m (→{{header|REXX}}: optimized two subroutines.) |
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=={{header|REXX}}== |
=={{header|REXX}}== |
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Note: there was virtually no difference in accuracy between '''numeric digits 9''' (the default) and '''numeric digits 20'''. |
Note: there was virtually no difference in accuracy between '''numeric digits 9''' (the default) and '''numeric digits 20'''. |
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<lang rexx>/*REXX pgm performs numerical integration using |
<lang rexx>/*REXX pgm performs numerical integration using five different algorithms & show results*/ |
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numeric digits 20 /*use twenty decimal digits precision. */ |
numeric digits 20 /*use twenty decimal digits precision. */ |
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if test==4 then do; L= 0; H= 6000; i= 6000000; end |
if test==4 then do; L= 0; H= 6000; i= 6000000; end |
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say center('test' test, 79, "═") /*display a header for the test suite. */ |
say center('test' test, 79, "═") /*display a header for the test suite. */ |
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say ' left rectangular('L", "H', 'i") ──► " left_rect(L, H, i) |
say ' left rectangular('L", "H', 'i") ──► " left_rect(L, H, i) |
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say ' midpoint rectangular('L", "H', 'i") ──► " |
say ' midpoint rectangular('L", "H', 'i") ──► " midpt_rect(L, H, i) |
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say ' right rectangular('L", "H', 'i") ──► " right_rect(L, H, i) |
say ' right rectangular('L", "H', 'i") ──► " right_rect(L, H, i) |
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say ' Simpson('L", "H', 'i") ──► " Simpson(L, H, i) |
say ' Simpson('L", "H', 'i") ──► " Simpson(L, H, i) |
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say ' trapezium('L", "H', 'i") ──► " trapezium(L, H, i) |
say ' trapezium('L", "H', 'i") ──► " trapezium(L, H, i) |
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end /*test*/ |
end /*test*/ |
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exit /*stick a fork in it, we're all done. */ |
exit /*stick a fork in it, we're all done. */ |
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return arg(1) /* " " "as─is" " */ |
return arg(1) /* " " "as─is" " */ |
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/*──────────────────────────────────────────────────────────────────────────────────────*/ |
/*──────────────────────────────────────────────────────────────────────────────────────*/ |
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left_rect: |
left_rect: procedure expose test; parse arg a,b,n; $= 0; h= (b-a)/n |
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do x=a by h for n; $= $ + f(x); end /*x*/ |
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return $*h/1 |
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/*──────────────────────────────────────────────────────────────────────────────────────*/ |
/*──────────────────────────────────────────────────────────────────────────────────────*/ |
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midpt_rect: procedure expose test; parse arg a,b,n; $= 0; h= (b-a)/n |
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do x=a+h/2 by h for n; $= $ + f(x); end /*x*/ |
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return $*h/1 |
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/*──────────────────────────────────────────────────────────────────────────────────────*/ |
/*──────────────────────────────────────────────────────────────────────────────────────*/ |
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right_rect: |
right_rect: procedure expose test; parse arg a,b,n; $= 0; h= (b-a)/n |
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do x=a+h by h for n; $= $ + f(x); end /*x*/ |
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return $*h/1 |
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/*──────────────────────────────────────────────────────────────────────────────────────*/ |
/*──────────────────────────────────────────────────────────────────────────────────────*/ |
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Simpson: |
Simpson: procedure expose test; parse arg a,b,n; h= (b-a)/n |
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hh= h/2; $= f(a + hh) |
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@= 0; do x=1 for n-1; _= h*x+a; $= $+f(_+hh); @= @+f(_); end /*x*/ |
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return h * (f(a) + f(b) + 4*$ + 2*@) / 6 |
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/*─────────--───────────────────────────────────────────────────────────────────────────*/ |
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/*──────────────────────────────────────────────────────────────────────────────────────*/ |
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trapezium: |
trapezium: procedure expose test; parse arg a,b,n; $= 0; h= (b-a)/n |
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do x=a by h for n; $= $ + (f(x) + f(x+h)); end /*x*/ |
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return $*h/2</lang> |
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{{out|output|text= when using the default inputs:}} |
{{out|output|text= when using the default inputs:}} |
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<pre> |
<pre> |
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