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Astronomical Applications Department, U.S. Naval Observatory - Sensitivity Integral (Page 9)

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Astronomical Applications Department, U.S. Naval Observatory - Sensitivity Integral
if nops(locp) > 0 then
subsop( locp=T, K );
collect( %, [T,cos,sin], factor );
K := subs( T=p, % );
else
K := collect( K, [cos,sin], factor );
fi;
debug_print( procname,
`cost of simplified new integrand:`, 1, cost(K) );
# put back into integral and the integral back
# into the remainder integral expression and we're done
debug_print(procname,`new definite integral:`,0);
subsop( 1=K, H );
subsop( locI=%, remdr );
end:
Now we begin the calculation. We'll apply this integration by parts procedure several times, until
the polynomial term of the integrand is differentiated into oblivion. Notice the huge amount of
simplification being done, as evidenced by the "cost" diagnostics.
time0 := time(): #reset print timing
_k_ := '_k_': #reset parts index
verbosity := 2: #not too verbose, please
ugh( integral );
ugh[0]: polynomial factor p:
+
+
+
+
a
0
a
1
x
a
2
x
2
a
3
x
3
a
4
x
4
ugh[0]: location of p in integrand:
[ ]
1
ugh[0]: integrating by parts...
ugh[0]: cost of evaluated part of integral:
+
+
+
+
91 additions
164 multiplications
28 divisions
26 functions
46 subscripts
ugh[0]: evaluated part of integral is stored in parts[0]
ugh[0]: new polynomial factor p:
+
+ +
2 x a
2
3 x
2
a
3
a
1
4 x
3
a
4
ugh[0]: location of p in integrand:
[ ]
1
ugh[0]: full non-sin/cos term:
+
+ +
2 x a
2
3 x
2
a
3
a
1
4 x
3
a
4
ugh[0]: cost of new integrand:
+
+
+
+
44 additions
81 multiplications
14 divisions
13 functions
4 subscripts
ugh[0]: simplifying sin/cos part of new integrand...
ugh[0]: cost of simplified new integrand:
+
+
+
+
44 additions
71 multiplications
16 divisions
13 functions
4 subscripts
ugh[0]: new definite integral:
Page 9

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