Astronomical Applications Department, U.S. Naval Observatory Sensitivity Integral  Page 34
 + 
 - 
-
 - 
 - 
 - 
 - 
1
8
a
1
x
1
8
a
0
1
8
a
3
x
3
1
8
a
2
x
2
1
8
a
4
x
4
r
 + 
 + 
3
16
x a
3
3
8
x
2
a
4
1
16
a
2
r
3
3
16
a
4
r
5
(
)
sin 2 r x
 + 
1
120
x (
)
 + 
 + 
 + 
 + 
20 a
2
x
2
60 a
0
30 a
1
x
15 a
3
x
3
12 a
4
x
4
 + 
Here is the fortran subroutine that evaluates the indefinite integration result calculated in 
section 2
.  
It evaluates the integral at frequency 
 = 
x
.  Hence, the integral from 
1
 to 
2
 is calculated by two 
calls to the subroutine and subtracting:
      
 - 
(
)
F
,
,
,
,
,
, , ,
2
a0 a1 a2 a3 a4 s r g
(
)
F
,
,
,
,
,
, , ,
1
a0 a1 a2 a3 a4 s r g
  
(
)
fortran
,
,
,
sensitivity_expr optimized
 = 
mode
double
 = 
precision
double
      doubleprecision function sensitivity_expr(x,a0,a1,a2,a3,a4,s,r,g)
      doubleprecision x
      doubleprecision a0
      doubleprecision a1
      doubleprecision a2
      doubleprecision a3
      doubleprecision a4
      doubleprecision s
      doubleprecision r
      doubleprecision g
      doubleprecision t1
      doubleprecision t10
      doubleprecision t101
      doubleprecision t104
      doubleprecision t105
      doubleprecision t109
      doubleprecision t11
      doubleprecision t110
      doubleprecision t113
      doubleprecision t114
      doubleprecision t115
      doubleprecision t116
      doubleprecision t117
      doubleprecision t118
      doubleprecision t119
      doubleprecision t12
      doubleprecision t120
      doubleprecision t121
      doubleprecision t122
      doubleprecision t123
      doubleprecision t124
      doubleprecision t125
      doubleprecision t126
      doubleprecision t127
      doubleprecision t128
      doubleprecision t129
      doubleprecision t13
      doubleprecision t130
      doubleprecision t131
Page 34