tasks a-s

Task/Numerical-integration/REXX/numerical-integration.rexx

@@ -0,0 +1,60 @@
+/*REXX program  numerically integrates  using  five  different methods. */
+numeric digits 20                      /*use twenty digits precision.   */
+
+      do test=1 for 4                  /*perform the test suite.        */
+      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,79,'─')   /*display a header for the test. */
+      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 '             trapezoid('L","H','i") = "       trapezoid(L,H,i)
+      end   /*test*/
+exit                                   /*stick a fork in it, we're done.*/
+/*──────────────────────────────────LEFT_RECT subroutine────────────────*/
+left_rect: procedure expose test;    parse arg a,b,n;     h=(b-a)/n
+sum=0
+                     do x=a  by h  for n
+                     sum=sum+f(x)
+                     end
+return sum*h
+/*──────────────────────────────────MIDPOINT_RECT subroutine────────────*/
+midpoint_rect: procedure expose test;  parse arg a,b,n;   h=(b-a)/n
+sum=0
+                     do x=a+h/2  by h  for n
+                     sum=sum+f(x)
+                     end
+return sum*h
+/*──────────────────────────────────RIGHT_RECT subroutine───────────────*/
+right_rect: procedure expose test;   parse arg a,b,n;     h=(b-a)/n
+sum=0
+                     do x=a+h  by h  for n
+                     sum=sum+f(x)
+                     end
+return sum*h
+/*──────────────────────────────────SIMPSON subroutine──────────────────*/
+simpson: procedure expose test;      parse arg a,b,n;            h=(b-a)/n
+sum1=f(a+h/2)
+sum2=0
+                     do x=1  to n-1
+                     sum1=sum1+f(a+h*x+h*.5)
+                     sum2=sum2+f(a+x*h)
+                     end
+
+return h*(f(a)+f(b)+4*sum1+2*sum2)/6
+/*──────────────────────────────────TRAPEZOID subroutine────────────────*/
+trapezoid: procedure expose test;    parse arg a,b,n;            h=(b-a)/n
+sum=0
+                     do x=a  to b  by h
+                     sum=sum+h*(f(x)+f(x+h))*.5
+                     end
+return sum
+/*──────────────────────────────────F subroutine────────────────────────*/
+f: procedure expose test;    parse arg z
+if test==1 then return z**3
+if test==2 then return 1/z
+                return z