Procedure

   mxmg_c ( Matrix times matrix, general dimension ) 

   void mxmg_c ( const void    * m1,
                 const void    * m2,
                 SpiceInt        nr1,
                 SpiceInt        nc1r2,
                 SpiceInt        nc2,
                 void          * mout   )

Abstract

   Multiply two double precision matrices of arbitrary size.

Required_Reading

   None.

Keywords

   MATRIX

Brief_I/O

   VARIABLE  I/O  DESCRIPTION
   --------  ---  --------------------------------------------------
   m1         I   nr1   x nc1r2 double precision matrix.
   m2         I   nc1r2 x nc2   double precision matrix.
   nr1        I   Row dimension of `m1' (and also `mout').
   nc1r2      I   Column dimension of `m1' and row dimension of `m2'.
   nc2        I   Column dimension of `m2' (and also `mout').
   mout       O   nr1 x nc2 double precision matrix.

Detailed_Input

   m1          is any double precision matrix of arbitrary size.

   m2          is any double precision matrix of arbitrary size.
               The number of rows in m2 must match the number of
               columns in m1.

   nr1         is the number of rows in both `m1' and `mout'.

   nc1r2       is the number of columns in `m1' and (by necessity)
               the number of rows of `m2'.

   nc2         is the number of columns in both `m2' and `mout'.

Detailed_Output

   mout        is the product matrix defined by

                  mout = (m1) x (m2)

               `mout' is a double precision matrix of dimension
               nr1 x nc2.

               `mout' may overwrite `m1' or `m2'.

Parameters

   None.

Exceptions

   1)  If nc1r2 < 0, the elements of the matrix `mout' are set equal to
       zero.

   2)  If memory cannot be allocated to create the temporary matrix
       required for the execution of the routine, the error
       SPICE(MALLOCFAILED) is signaled.

Files

   None.

Particulars

   The code reflects precisely the following mathematical expression

   For each value of the subscript `i' from 1 to `nr1', and `j' from 1
   to `nc2':

      mout(i,j) = Summation from k=1 to nc1r2 of  m1(i,k) * m2(k,j)

Examples

   The 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 3x2 and a 2x3 matrices, multiply the first matrix by
      the second one.


      Example code begins here.


      /.
         Program mxmg_ex1
      ./
      #include <stdio.h>
      #include "SpiceUsr.h"

      int main( )
      {

         /.
         Local variables.
         ./
         SpiceDouble          mout   [3][3];

         SpiceInt             i;

         /.
         Define `m1' and `m2'.
         ./
         SpiceDouble          m1     [3][2] = { { 1.0, 4.0 },
                                                { 2.0, 5.0 },
                                                { 3.0, 6.0 }  };

         SpiceDouble          m2     [2][3] = { { 1.0, 3.0, 5.0 },
                                                { 2.0, 4.0, 6.0 } };

         /.
         Multiply `m1' by `m2'.
         ./
         mxmg_c ( m1, m2, 3, 2, 3, mout );

         printf( "M1 times M2:\n" );
         for ( i = 0; i < 3; i++ )
         {
            printf( "%10.3f %9.3f %9.3f\n",
                    mout[i][0], mout[i][1], mout[i][2] );
         }

         return ( 0 );
      }


      When this program was executed on a Mac/Intel/cc/64-bit
      platform, the output was:


      M1 times M2:
           9.000    19.000    29.000
          12.000    26.000    40.000
          15.000    33.000    51.000

Restrictions

   1)  No error checking is performed to prevent numeric overflow or
       underflow.

   2)  No error checking performed to determine if the input and
       output matrices have, in fact, been correctly dimensioned.

Literature_References

   None.

Author_and_Institution

   N.J. Bachman        (JPL)
   J. Diaz del Rio     (ODC Space)
   E.D. Wright         (JPL)

Version

   -CSPICE Version 1.2.0, 10-AUG-2021 (JDR)

       Changed the input argument names "nrow1", "ncol1" and "ncol2" to
       "nr1", "nc1r2" and "nc2" 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.

       Added entry #1 to -Exceptions section.

   -CSPICE Version 1.1.2, 16-JAN-2008 (EDW)

       Corrected typos in header titles:

       Detailed Input to -Detailed_Input
       Detailed Output to -Detailed_Output

   -CSPICE Version 1.1.1, 10-NOV-2006 (EDW)

       Added -Parameters section header.

   -CSPICE Version 1.1.0, 28-AUG-2001 (NJB)

       Const-qualified input arrays.

   -CSPICE Version 1.0.0, 16-APR-1999 (NJB)

Index_Entries

   matrix times matrix n-dimensional_case