mtxv_c |

Table of contents## Proceduremtxv_c ( Matrix transpose times vector, 3x3 ) void mtxv_c ( ConstSpiceDouble m [3][3], ConstSpiceDouble vin [3], SpiceDouble vout[3] ) ## AbstractMultiply the transpose of a 3x3 matrix on the left with a vector on the right. ## Required_ReadingNone. ## KeywordsMATRIX VECTOR ## Brief_I/OVARIABLE I/O DESCRIPTION -------- --- -------------------------------------------------- m I 3x3 double precision matrix. vin I 3-dimensional double precision vector. vout O 3-dimensional double precision vector. `vout' is the product m**t * vin. ## Detailed_Inputm is an arbitrary 3x3 double precision matrix. Typically, `m' will be a rotation matrix since then its transpose is its inverse (but this is NOT a requirement). vin is an arbitrary 3-dimensional double precision vector. ## Detailed_Outputvout is a 3-dimensional double precision vector. `vout' is the product vout = (m**t) x (vin). `vout' can overwrite `vin'. ## ParametersNone. ## ExceptionsError free. ## FilesNone. ## ParticularsThe code reflects precisely the following mathematical expression For each value of the subscript `i' from 0 to 2: 2 .----- \ vout(i) = ) m[k][i] * vin[k] / '----- k=0 Note that the reversal of the `k' and `i' subscripts in the left-hand matrix `m' is what makes `vout' the product of the TRANSPOSE of and not simply of `m' 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) Given a 3x3 matrix and a 3-vector, multiply the transpose of the matrix by the vector. Example code begins here. /. Program mtxv_ex1 ./ #include <stdio.h> #include "SpiceUsr.h" int main( ) { /. Local variables. ./ SpiceDouble vout [3]; /. Define `m' and `vin'. ./ SpiceDouble m [3][3] = { { 1.0, 1.0, 0.0}, {-1.0, 1.0, 0.0}, { 0.0, 0.0, 1.0} }; SpiceDouble vin [3] = { 5.0, 10.0, 15.0 }; /. Multiply the transpose of `m' by `vin'. ./ ## Restrictions1) The user is responsible for checking the magnitudes of the elements of m and vin so that a floating point overflow does not occur. ## Literature_ReferencesNone. ## Author_and_InstitutionJ. Diaz del Rio (ODC Space) W.M. Owen (JPL) E.D. Wright (JPL) ## Version-CSPICE Version 1.1.0, 25-AUG-2021 (JDR) Changed input argument name "m1" to "m" for consistency with other routines. Edited the header to comply with NAIF standard. Added complete code example based on the existing example. -CSPICE Version 1.0.1, 10-NOV-2006 (EDW) Added -Parameters section header. -CSPICE Version 1.0.0, 16-APR-1999 (EDW) (WMO) ## Index_Entriesmatrix_transpose times 3-dimensional vector |

Fri Dec 31 18:41:09 2021