Rosetta Code

Numerical integration: Difference between revisions

Page Discussion

Numerical integration (view source)

Revision as of 10:12, 7 September 2019

1,851 bytes added ,  4 years ago
→‎{{header|PL/I}}: Rewritten to incorporate all the requirements.
(→‎{{header|Common Lisp}}: Re-add task entry deleted for no apparent reason)
(→‎{{header|PL/I}}: Rewritten to incorporate all the requirements.)
Line 3,753:
 
=={{header|PL/I}}==
<lang PL/I>integrals: procedure options (main); /* 1 September 2019 */▼
<lang PL/I>
▲integrals: procedure options (main);
 
/*f: Theprocedure (x, function) to be integratedreturns */(float(18));
declare x float(18), function fixed binary;
f: procedure (x) returns (float);
declareselect x float(function);
when (1) return (3*x**2 + 2*x3);
when (2) return (1/x);
when (3) return (x);
when (4) return (x);
end;
end f;
 
declare (a, b) floatfixed decimal (10);
declare (rect_area, trap_area, Simpson) float(18);
declare (d, dx) fixed decimal float(10,218);
declare (lS1, rS2) float(18);
declare N fixed decimal (S115), S2)function fixed floatbinary;
declare k fixed decimal (7,2);
 
put (' Rectangle-left Rectangle-mid Rectangle-right' ||
l = 0; r = 5;▼
' Trapezoid Simpson');
a = 0; b = 5; /* bounds of integration */
dxdo function = 0.051 to 4;
select(function);
when (1) do; N = 100; a = 0; b = 1; end;
when (2) do; N = 1000; a = 1; b = 100; end;
when (3) do; N = 5000000; a = 0; b = 5000; end;
when (4) do; N = 6000000; a = 0; b = 6000; end;
▲ l = 0; r = 5end;
dx = (b-a)/float(N);
 
/* Rectangle method, left-side */
rect_area = 0;
do d = a0 to b by dxN-1;
rect_area = rect_area + dx*f(a + d*dx, function);
end;
put skip dataedit (rect_area) (E(25, 15));
 
/* trapezoidRectangle method, mid-point */
trap_area rect_area = 0;
do d = a0 to b by dxN-1;
trap_area rect_area = trap_arearect_area + dx*(f(d)a + f(d*dx + dx))/2, function);
end;
put skipedit data(rect_area) (trap_areaE(25, 15));
 
/* Rectangle method, right-side */
rect_area = 0;
do d = 1 to N;
rect_area = rect_area + dx*f(a + d*dx, function);
end;
put edit (rect_area) (E(25, 15));
 
/* Trapezoid method */
trap_area = 0;
do d = 0 to N-1;
trap_area = trap_area + dx*(f(a+d*dx, function) + f(a+(d+1)*dx, function))/2;
end;
put edit (trap_area) (X(1), E(25, 15));
 
/* Simpson's Rule */
S1 = f(a+dx/2, function);
S2 = 0;
do d = a1 to b by dxN-1;
S1 = S1 + f(da+d*dx+dx/2, function);
S2 = S2 + f(da+d*dx, function);
end;
Simpson = dx * (f(a, function) + f(b, function) + 4*S1 + 2*S2) / 6;▼
put edit (Simpson) (X(1), E(25, 15));
end;
▲ Simpson = dx * (f(a) + f(b) + 4*S1 + 2*S2) / 6;
put skip data (Simpson);
 
end integrals;
</lang>
<pre>
Rectangle-left Rectangle-mid Rectangle-right Trapezoid Simpson
2.450250000000000E-0001 2.499875000000000E-0001 2.550250000000000E-0001 2.500250000000000E-0001 2.500000000000000E-0001
4.654991057514676E+0000 4.604762548678375E+0000 4.556981057514676E+0000 4.605986057514676E+0000 4.605170384957142E+0000
1.249999750000000E+0007 1.250000000000000E+0007 1.250000250000000E+0007 1.250000000000000E+0007 1.250000000000000E+0007
1.799999700000000E+0007 1.800000000000000E+0007 1.800000300000000E+0007 1.800000000000000E+0007 1.800000000000000E+0007
</pre>
 
=={{header|PicoLisp}}==
Retrieved from "https://rosettacode.org/wiki/Special:MobileDiff/52552"