Procedure

   mtxvg_c ( Matrix transpose times vector, general dimension ) 

   void mtxvg_c ( const void   * m1,
                  const void   * v2,
                  SpiceInt       nc1,
                  SpiceInt       nr1r2,
                  void         * vout   )

Abstract

   Multiply the transpose of a matrix and a vector of arbitrary size.

Required_Reading

   None.

Keywords

   MATRIX
   VECTOR

Brief_I/O

   VARIABLE  I/O  DESCRIPTION
   --------  ---  --------------------------------------------------
   m1         I   Left-hand matrix to be multiplied.
   v2         I   Right-hand vector to be multiplied.
   nc1        I   Column dimension of `m1' and length of `vout'.
   nr1r2      I   Row dimension of `m1' and length of `v2'.
   vout       O   Product vector `m1' transpose times `v2'.

Detailed_Input

   m1          is a double precision matrix of arbitrary size which
               forms the left-hand matrix of the multiplication.

   v2          is a double precision vector on the right of the
               multiplication.

   nc1         is the column dimension of `m1' and length of `vout'.

   nr1r2       is the row dimension of `m1' and length of `v2'.

Detailed_Output

   vout        is the double precision vector which results from
               the multiplication

                             t
                  vout = (m1)  x  v2

               where the superscript `t' denotes the transpose of a matrix.
               `vout' has length `nc1'.

               `vout' may overwrite `m1' or `v2'.

Parameters

   None.

Exceptions

   1)  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 `nc1',

      vout(i) = Summation from k=1 to nr1r2 of  ( m1(k,i) * v2(k) )

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 matrix and a 3-vector, multiply the transpose of
      the matrix by the vector.


      Example code begins here.


      /.
         Program mtxvg_ex1
      ./
      #include <stdio.h>
      #include "SpiceUsr.h"

      int main( )
      {

         /.
         Local variables.
         ./
         SpiceDouble          vout   [2];

         /.
         Define `m' and `vin'.
         ./
         SpiceDouble          m      [3][2] = { { 1.0,  2.0 },
                                                { 1.0,  3.0 },
                                                { 1.0,  4.0 } };

         SpiceDouble          vin    [3] = { 1.0, 2.0, 3.0 };

         /.
         Multiply the transpose of `m' by `vin'.
         ./
         mtxvg_c ( m, vin, 2, 3, vout );

         printf( "Transpose of M times VIN:\n" );
         printf( "%10.3f %9.3f\n", vout[0], vout[1] );

         return ( 0 );
      }


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


      Transpose of M times VIN:
           6.000    20.000

Restrictions

   1)  The user is responsible for checking the magnitudes of the
       elements of `m1' and `v2' so that a floating point overflow does
       not occur.

Literature_References

   None.

Author_and_Institution

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

Version

   -CSPICE Version 1.3.0, 06-AUG-2021 (JDR)

       Changed the input argument name "ncol1" "nc1" 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.

       Based on SPICELIB Version 1.0.1, 10-MAR-1992 (WLT)

Index_Entries

   matrix transpose times n-dimensional vector