mtxm_c |

Table of contents## Proceduremtxm_c ( Matrix transpose times matrix, 3x3 ) void mtxm_c ( ConstSpiceDouble m1 [3][3], ConstSpiceDouble m2 [3][3], SpiceDouble mout[3][3] ) ## AbstractMultiply the transpose of a 3x3 matrix and a 3x3 matrix. ## Required_ReadingNone. ## KeywordsMATRIX ## Brief_I/OVARIABLE I/O DESCRIPTION -------- --- -------------------------------------------------- m1 I 3x3 double precision matrix. m2 I 3x3 double precision matrix. mout O The produce m1 transpose times m2. ## Detailed_Inputm1 is any 3x3 double precision matrix. Typically, m1 will be a rotation matrix since then its transpose is its inverse (but this is not a requirement). m2 is any 3x3 double precision matrix. ## Detailed_Outputmout is a 3x3 double precision matrix. mout is the product t mout = m1 m2 mout may overwrite either m1 or m2. ## ParametersNone. ## ExceptionsError free. ## FilesNone. ## ParticularsThe code reflects precisely the following mathematical expression For each value of the subscripts `i' and `j' from 0 to 2: 2 __ \ mout[i][j] = /_ m1[k][i] * m2[k][j] k=0 Note that the reversal of the `k' and `i' subscripts in the left-hand matrix `m1' is what makes `mout' the product of the TRANSPOSE of `m1' and not simply of `m1' itself. Also, the intermediate results of the operation above are buffered in a temporary matrix which is later moved to the output matrix. Thus `mout' can be actually be `m1' or `m2' if desired without interfering with the computations. ## 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 two 3x3 matrices, multiply the transpose of the first matrix by the second one. Example code begins here. /. Program mtxm_ex1 ./ #include <stdio.h> #include "SpiceUsr.h" int main( ) { /. Local variables. ./ SpiceDouble mout [3][3]; SpiceInt i; /. Define `m1' and `m2'. ./ SpiceDouble m1 [3][3] = { {1.0, 2.0, 3.0}, {4.0, 5.0, 6.0}, {7.0, 8.0, 9.0} }; SpiceDouble m2 [3][3] = { { 1.0, 1.0, 0.0}, {-1.0, 1.0, 0.0}, { 0.0, 0.0, 1.0} }; /. Multiply the transpose of `m1' by `m2'. ./ ## Restrictions1) The user is responsible for checking the magnitudes of the elements of `m1' and `m2' so that a floating point overflow does not occur. (In the typical use where `m1' and `m2' are rotation matrices, this not a risk at all.) ## Literature_ReferencesNone. ## Author_and_InstitutionJ. Diaz del Rio (ODC Space) W.M. Owen (JPL) E.D. Wright (JPL) ## Version-CSPICE Version 1.0.1, 04-JUL-2021 (JDR) Edited the header to comply with NAIF standard. Added complete code example based on the existing example. -CSPICE Version 1.0.0, 16-APR-1999 (EDW) (WMO) ## Index_Entriesmatrix_transpose times matrix 3x3_case |

Fri Dec 31 18:41:09 2021