mxmtg_c |

Table of contents## Proceduremxmtg_c ( Matrix times matrix transpose, general dimension ) void mxmtg_c ( const void * m1, const void * m2, SpiceInt nr1, SpiceInt nc1c2, SpiceInt nr2, void * mout ) ## AbstractMultiply a matrix and the transpose of a matrix, both of arbitrary size. ## Required_ReadingNone. ## KeywordsMATRIX ## Brief_I/OVARIABLE I/O DESCRIPTION -------- --- -------------------------------------------------- m1 I Left-hand matrix to be multiplied. m2 I Right-hand matrix whose transpose is to be multiplied. nr1 I Row dimension of `m1' and row dimension of `mout'. nc1c2 I Column dimension of `m1' and column dimension of `m2'. nr2 I Row dimension of `m2' and column dimension of `mout'. mout O Product matrix. ## Detailed_Inputm1 is a double precision matrix of arbitrary size. m2 is a double precision matrix of arbitrary size. The number of columns in `m2' must match the number of columns in `m1'. nr1 is the number of rows in both `m1' and `mout'. nc1c2 is the number of columns in `m1' and (by necessity) the number of columns of `m2'. nr2 is the number of rows in both `m2' and the number of columns in `mout'. ## Detailed_Outputmout is the product matrix given by t mout = (m1) x (m2) where the superscript `t' denotes the transpose matrix. This is a double precision matrix of dimension nr1 x nr2. `mout' may overwrite `m1' or `m2'. ## ParametersNone. ## Exceptions1) If memory cannot be allocated to create the temporary matrix required for the execution of the routine, the error SPICE(MALLOCFAILED) is signaled. ## FilesNone. ## ParticularsThe code reflects precisely the following mathematical expression: For each value of the subscript `i' from 1 to `nr1', and `j' from 1 to `nr2': mout(i,j) = summation from k=1 to nc1c2 of ( m1(i,k) * m2(j,k) ) Notice that the order of the subscripts of `m2' are reversed from what they would be if this routine merely multiplied `m1' and `m2'. It is this transposition of subscripts that makes this routine multiply `m1' and the TRANPOSE of `m2'. ## 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 2x3 and a 3x4 matrices, multiply the first matrix by the transpose of the second one. Example code begins here. /. Program mxmtg_ex1 ./ #include <stdio.h> #include "SpiceUsr.h" int main( ) { /. Local variables. ./ SpiceDouble mout [2][4]; SpiceInt i; /. Define `m1' and `m2'. ./ SpiceDouble m1 [2][3] = { {1.0, 2.0, 3.0}, {3.0, 2.0, 1.0} }; SpiceDouble m2 [4][3] = { { 1.0, 2.0, 0.0}, { 2.0, 1.0, 2.0}, { 1.0, 2.0, 0.0}, { 2.0, 1.0, 2.0} }; /. Multiply `m1' by the transpose of `m2'. ./ ## Restrictions1) No error checking is performed to prevent numeric overflow or underflow. The user is responsible for checking the magnitudes of the elements of `m1' and `m2' so that a floating point overflow does not occur. 2) No error checking is performed to determine if the input and output matrices have, in fact, been correctly dimensioned. ## Literature_ReferencesNone. ## Author_and_InstitutionN.J. Bachman (JPL) J. Diaz del Rio (ODC Space) W.M. Owen (JPL) W.L. Taber (JPL) ## Version-CSPICE Version 1.3.0, 06-AUG-2021 (JDR) Changed the input argument names "nrow1" and "nrow2" to "nr1" and "nr2" for consistency with other routines. Updated short error message for consistency within CSPICE wrapper interface: MEMALLOCFAILED -> MALLOCFAILED. Edited the header to comply with NAIF standard. Added complete code example based on the existing example. -CSPICE Version 1.2.0, 28-AUG-2001 (NJB) Const-qualified input arrays. -CSPICE Version 1.1.0, 08-FEB-1998 (NJB) Corrected a comment describing the local macro INDEX. Made miscellaneous code format corrections. -CSPICE Version 1.0.0, 25-OCT-1997 (NJB) (WMO) (WLT) Based on SPICELIB Version 1.0.1, 10-MAR-1992 (WLT) ## Index_Entriesmatrix times matrix_transpose n-dimensional_case |

Fri Dec 31 18:41:09 2021