Numerical integration: Difference between revisions

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=={{header|REXX}}==
=={{header|REXX}}==
Note: there was virtually no difference between   '''numeric digits 9'''   (the default) and   '''numeric digits 20'''.
Note:   there was virtually no difference between   '''numeric digits 9'''   (the default) and   '''numeric digits 20'''.
<lang rexx>/*REXX program does numerical integration using five different algorithms.*/
<lang rexx>/*REXX pgm performs numerical integration using 5 different algorithms and show results.*/
numeric digits 20 /*use twenty decimal digits precision. */
numeric digits 20 /*use twenty decimal digits precision. */


do test=1 for 4 /*perform the 4 different test suites. */
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==1 then do; L=0; H= 1; i= 100; end
if test==2 then do; L=1; H= 100; i= 1000; 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==3 then do; L=0; H=5000; i=5000000; end
if test==4 then do; L=0; H=6000; i=5000000; end
if test==4 then do; L=0; H=6000; i=5000000; end
say
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 ' left rectangular('L", "H', 'i") ──► " left_rect(L, H, i)
say ' midpoint rectangular('L", "H', 'i") ──► " midpoint_rect(L, H, i)
say ' midpoint rectangular('L", "H', 'i") ──► " midpoint_rect(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)
end /*test*/
end /*test*/
exit /*stick a fork in it, we're all done. */
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
/*────────────────────────────────────────────────────────────────────────────*/
f: if test==1 then return arg(1)**3
f: if test==1 then return arg(1)**3 /*choose the cube function. */
if test==2 then return 1/arg(1)
if test==2 then return 1/arg(1) /* " " reciprocal " */
return arg(1)
return arg(1) /* " " "as-is" " */
/*──────────────────────────────────────────────────────────────────────────────────────*/
/*────────────────────────────────────────────────────────────────────────────*/
left_rect: procedure expose test; parse arg a,b,n; h=(b-a)/n
left_rect: procedure expose test; parse arg a,b,n; h=(b-a)/n
$=0
$=0
do x=a by h for n; $=$+f(x); end /*x*/
do x=a by h for n; $=$+f(x); end /*x*/
return $*h/1 /*return the number with no trailing 0s*/
return $*h/1
/*──────────────────────────────────────────────────────────────────────────────────────*/
/*────────────────────────────────────────────────────────────────────────────*/
midpoint_rect: procedure expose test; parse arg a,b,n; h=(b-a)/n
midpoint_rect: procedure expose test; parse arg a,b,n; h=(b-a)/n
$=0
$=0
do x=a+h/2 by h for n; $=$+f(x); end /*x*/
do x=a+h/2 by h for n; $=$+f(x); end /*x*/
return $*h/1 /*return the number with no trailing 0s*/
return $*h/1
/*──────────────────────────────────────────────────────────────────────────────────────*/
/*────────────────────────────────────────────────────────────────────────────*/
right_rect: procedure expose test; parse arg a,b,n; h=(b-a)/n
right_rect: procedure expose test; parse arg a,b,n; h=(b-a)/n
$=0
$=0
do x=a+h by h for n; $=$+f(x); end /*x*/
do x=a+h by h for n; $=$+f(x); end /*x*/
return $*h/1 /*return the number with no trailing 0s*/
return $*h/1
/*──────────────────────────────────────────────────────────────────────────────────────*/
/*────────────────────────────────────────────────────────────────────────────*/
Simpson: procedure expose test; parse arg a,b,n; h=(b-a)/n
Simpson: procedure expose test; parse arg a,b,n; h=(b-a)/n
$=f(a+h/2)
$=f(a+h/2)
@=0; do x=1 for n-1; $=$+f(a+h*x+h*.5); @=@+f(a+x*h); end /*x*/
@=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*/
return h*(f(a) + f(b) + 4*$ + 2*@) / 6
/*──────────────────────────────────────────────────────────────────────────────────────*/
/*────────────────────────────────────────────────────────────────────────────*/
trapezium: procedure expose test; parse arg a,b,n; h=(b-a)/n
trapezium: procedure expose test; parse arg a,b,n; h=(b-a)/n
$=0
$=0
do x=a by h for n; $=$+(f(x)+f(x+h)); end /*x*/
do x=a by h for n; $=$+(f(x)+f(x+h)); end /*x*/
return $*h/2 /*return the number with no trailing 0s*/</lang>
return $*h/2</lang>
'''output'''
'''output'''
<pre>
<pre>
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