uddf_c |

Table of contents## Procedureuddf_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/OVARIABLE 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_Inputudfunc 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_Outputderiv 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. ## Exceptions1) If `dx' has a value of zero, an error is signaled by a routine in the call tree of this routine. ## FilesIf 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. ## ExamplesThe 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'. ./ ## 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