polyds_c |

Table of contents## Procedurepolyds_c ( Compute a Polynomial and its Derivatives ) void polyds_c ( ConstSpiceDouble * coeffs, SpiceInt deg, SpiceInt nderiv, SpiceDouble t, SpiceDouble * p ) ## AbstractCompute the value of a polynomial and its first `nderiv' derivatives at the value `t'. ## Required_ReadingNone. ## KeywordsINTERPOLATION MATH POLYNOMIAL ## Brief_I/OVARIABLE I/O DESCRIPTION -------- --- -------------------------------------------------- coeffs I Coefficients of the polynomial to be evaluated. deg I Degree of the polynomial to be evaluated. nderiv I Number of derivatives to compute. t I Point to evaluate the polynomial and derivatives p O Value of polynomial and derivatives. ## Detailed_Inputcoeffs are the coefficients of the polynomial that is to be evaluated. The first element of this array should be the constant term, the second element the linear coefficient, the third term the quadratic coefficient, and so on. The number of coefficients supplied should be one more than `deg'. f(x) = coeffs[0] + coeffs[1]*x + coeffs[2]*x^2 + coeffs[3]*x^4 + ... + coeffs[deg]*x^deg deg is the degree of the polynomial to be evaluated. `deg' should be one less than the number of coefficients supplied. nderiv is the number of derivatives to compute. If `nderiv' is zero, only the polynomial will be evaluated. If nderiv = 1, then the polynomial and its first derivative will be evaluated, and so on. If the value of `nderiv' is negative, the routine returns immediately. t is the point at which the polynomial and its derivatives should be evaluated. ## Detailed_Outputp is an array containing the value of the polynomial and its derivatives evaluated at `t'. The first element of the array contains the value of `p' at `t'. The second element of the array contains the value of the first derivative of `p' at `t' and so on. The nderiv + 1'st element of the array contains the nderiv'th derivative of `p' evaluated at `t'. ## ParametersNone. ## ExceptionsError free. 1) If `nderiv' is less than zero, the routine simply returns. 2) If the degree of the polynomial is less than 0, the routine returns the first nderiv+1 elements of `p' set to 0. ## FilesNone. ## ParticularsThis routine uses the user supplied coefficients (coeffs) to evaluate a polynomial (having these coefficients) and its derivatives at the point `t'. The zero'th derivative of the polynomial is regarded as the polynomial itself. ## 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) For the polynomial f(x) = 1 + 3*x + 0.5*x^2 + x^3 + 0.5*x^4 - x^5 + x^6 the coefficient set Degree coeffs ------ ------ 0 1 1 3 2 0.5 3 1 4 0.5 5 -1 6 1 Compute the value of the polynomial and it's first 3 derivatives at the value t = 1.0. We expect: Derivative Number t = 1 ------------------ ----- f(x) 0 6 f'(x) 1 10 f''(x) 2 23 f'''(x) 3 78 Example code begins here. /. Program polyds_ex1 ./ #include <stdio.h> #include "SpiceUsr.h" int main( ) { /. Local constants. ./ #define NDERIV 3 /. Local variables. ./ SpiceDouble p [ NDERIV + 1 ]; SpiceInt i; SpiceDouble coeffs [] = { 1., 3., 0.5, 1., 0.5, -1., 1. }; SpiceDouble t = 1.; SpiceInt deg = 6; ## Restrictions1) Depending on the coefficients the user should be careful when taking high order derivatives. As the example shows, these can get big in a hurry. In general the coefficients of the derivatives of a polynomial grow at a rate greater than N! (N factorial). ## Literature_ReferencesNone. ## Author_and_InstitutionJ. Diaz del Rio (ODC Space) W.L. Taber (JPL) E.D. Wright (JPL) ## Version-CSPICE Version 1.1.0, 04-AUG-2021 (JDR) Removed unnecessary Standard SPICE error handling calls to register/unregister this routine in the error handling subsystem; this routine is Error free. Updated the header to comply with NAIF standard. -CSPICE Version 1.0.0, 24-AUG-2015 (EDW) (WLT) ## Index_Entriescompute a polynomial and its derivatives |

Fri Dec 31 18:41:10 2021