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2016 Update

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Tina Müller 2016-12-05 22:15:40 +01:00
parent 948b86eafa
commit dcf5d15da3
7965 changed files with 139854 additions and 31002 deletions
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Task/Numerical-integration/REXX/numerical-integration.rexx
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@ -1,47 +1,47 @@
/*REXX program does numerical integration using five different algorithms.*/
numeric digits 20 /*use twenty decimal digits precision. */
/*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 /*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
do test=1 for 4 /*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
say center('test' test,65,'─') /*display a header for the test suite. */
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)
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: if test==1 then return arg(1)**3
if test==2 then return 1/arg(1)
return arg(1)
/*────────────────────────────────────────────────────────────────────────────*/
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
f: if test==1 then return arg(1)**3 /*choose the cube function. */
if test==2 then return 1/arg(1) /* " " reciprocal " */
return arg(1) /* " " "as-is" " */
/*──────────────────────────────────────────────────────────────────────────────────────*/
left_rect: procedure expose test; parse arg a,b,n; h=(b-a)/n
$=0
do x=a by h for n; $=$+f(x); end /*x*/
return $*h/1 /*return the number with no trailing 0s*/
/*────────────────────────────────────────────────────────────────────────────*/
$=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; h=(b-a)/n
$=0
do x=a+h/2 by h for n; $=$+f(x); end /*x*/
return $*h/1 /*return the number with no trailing 0s*/
/*────────────────────────────────────────────────────────────────────────────*/
$=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; h=(b-a)/n
$=0
do x=a+h by h for n; $=$+f(x); end /*x*/
return $*h/1 /*return the number with no trailing 0s*/
/*────────────────────────────────────────────────────────────────────────────*/
$=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*/
$=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 /*return the number with no trailing 0s*/
/*────────────────────────────────────────────────────────────────────────────*/
trapezium: procedure expose test; parse arg a,b,n; h=(b-a)/n
$=0
do x=a by h for n; $=$+(f(x)+f(x+h)); end /*x*/
return $*h/2 /*return the number with no trailing 0s*/
return h*(f(a) + f(b) + 4*$ + 2*@) / 6
/*──────────────────────────────────────────────────────────────────────────────────────*/
trapezium: procedure expose test; parse arg a,b,n; h=(b-a)/n
$=0
do x=a by h for n; $=$+(f(x)+f(x+h)); end /*x*/
return $*h/2