| uddf_c |
|
Table of contents
Procedure
uddf_c ( First derivative of a function, df(x)/dx )
void uddf_c ( void ( * udfunc ) ( SpiceDouble et,
SpiceDouble * value ),
SpiceDouble x,
SpiceDouble dx,
SpiceDouble * deriv )
AbstractCalculate the first derivative of a caller-specified scalar function using a three-point estimation. Required_ReadingNone. KeywordsDERIVATIVE MATH Brief_I/O
VARIABLE I/O DESCRIPTION
-------- --- --------------------------------------------------
udfunc I The routine that computes the scalar value
of interest.
x I Independent variable of `udfunc'.
dx I Interval from `x' for derivative calculation.
deriv O Approximate derivative of `udfunc' at `x'.
Detailed_Input
udfunc is an externally specified routine that returns the
value of the scalar quantity function of interest
at x.
The prototype for `udfunc' is
void ( * udfunc ) ( SpiceDouble et,
SpiceDouble * value )
where:
et an input double precision value of the independent
variable the function at which to determine the
scalar value.
value the scalar double precision value of `udfunc'
at `x'.
x is a scalar double precision value at which to determine
the derivative of `udfunc'.
For many SPICE uses, `x' will represent ephemeris time,
expressed as seconds past J2000 TDB.
dx is a scalar double precision value representing half the
interval in units of `x' separating the evaluation
values of `udfunc'; the evaluations occur at (x + dx)
and (x - dx).
`dx' may be negative but must be non-zero.
Detailed_Output
deriv is the scalar double precision approximate value of the
first derivative of `udfunc' with respect to `x'.
Functionally:
d udfunc ( y ) |
deriv = ---------------- |
dy | y=x
ParametersNone. Exceptions
1) If `dx' has a value of zero, an error is signaled by a routine
in the call tree of this routine.
Files
If the evaluation of `udfunc' requires SPICE kernel data, the
appropriate kernels must be loaded before calling this routine.
- SPK data: the calling application must load ephemeris data
for the targets, observer, and any intermediate objects in
a chain connecting the targets and observer for the time
used in the evaluation. If aberration corrections are
used, the states of target and observer relative to the
solar system barycenter must be calculable from the
available ephemeris data.
- If non-inertial reference frames are used, then PCK
files, frame kernels, C-kernels, and SCLK kernels may be
needed.
Such kernel data are normally loaded once per program run, NOT
every time this routine is called.
ParticularsThis routine provides a simple interface to numerically calculate the first derivative of a scalar quantity function, `udfunc'. `udfunc' is expected to be "well behaved" across at the evaluation interval [ x - dx, x + dx ]. This means a linear approximation to the function over the interval is sufficiently accurate to calculate the approximate derivative at `x'. The routine qderiv_c performs the differentiation using a three point estimation. See the header of the SPICE routine qderiv_c for details of the discrete derivative computation performed by this routine. Examples
The numerical results shown for this example may differ across
platforms. The results depend on the SPICE kernels used as
input, the compiler and supporting libraries, and the machine
specific arithmetic implementation.
1) Calculate the time derivative of the light time corresponding
to the apparent position of Mercury relative to the Moon at
time "JAN 1 2009."
Use the meta-kernel shown below to load the required SPICE
kernels.
KPL/MK
File name: uddf_ex1.tm
This meta-kernel is intended to support operation of SPICE
example programs. The kernels shown here should not be
assumed to contain adequate or correct versions of data
required by SPICE-based user applications.
In order for an application to use this meta-kernel, the
kernels referenced here must be present in the user's
current working directory.
The names and contents of the kernels referenced
by this meta-kernel are as follows:
File name Contents
--------- --------
de421.bsp Planetary ephemeris
naif0009.tls Leapseconds
\begindata
KERNELS_TO_LOAD = ( 'de421.bsp',
'naif0009.tls' )
\begintext
End of meta-kernel
Example code begins here.
/.
Program uddf_ex1
./
#include <stdio.h>
#include "SpiceUsr.h"
void udfunc ( SpiceDouble et, SpiceDouble * value );
int main()
{
SpiceDouble et;
SpiceDouble dt;
SpiceDouble deriv;
/.
Load leapsecond and SPK kernels. The name of the
meta kernel file shown here is fictitious; you
must supply the name of a file available
on your own computer system.
./
furnsh_c ( "uddf_ex1.tm" );
/.
Use a shift of one second off the epoch of interest.
./
dt = 1.;
/.
Convert the epoch date string to ephemeris seconds.
./
str2et_c ( "JAN 1 2009", &et );
/.
Calculate the derivative of `udfunc' at `et'.
./
uddf_c( udfunc, et, dt, &deriv );
/.
Output the calculated derivative.
./
printf( "%18.12f\n", deriv );
return ( 0 );
}
/.
A scalar quantity function that returns the light-time
between the Moon and Mercury at 'et'.
./
void udfunc ( SpiceDouble et, SpiceDouble * value )
{
SpiceDouble lt;
SpiceDouble pos[3];
/.
Evaluate the apparent position of Mercury with respect
to the Moon at 'et'.
./
spkpos_c ( "MERCURY", et, "J2000", "LT+S", "MOON", pos, < );
/.
Return the light-time value as the scalar quantity.
./
*value = lt;
return;
}
When this program was executed on a Mac/Intel/cc/64-bit
platform, the output was:
-0.000135670941
Restrictions1) The function `udfunc' must exist everywhere within [x - dx, x + dx]. Literature_ReferencesNone. Author_and_InstitutionN.J. Bachman (JPL) J. Diaz del Rio (ODC Space) E.D. Wright (JPL) Version
-CSPICE Version 1.0.1, 05-AUG-2021 (JDR)
Edited the header to comply with NAIF standard. Renamed example's
meta-kernel.
Added the -Exceptions, -Particulars and -Files sections.
-CSPICE Version 1.0.0, 31-MAR-2010 (EDW) (NJB)
Index_Entriesfirst derivative of a user-defined scalar function |
Fri Dec 31 18:41:14 2021