Procedure

   void mtxmg_c ( const void  * m1,
                  const void  * m2,
                  SpiceInt      ncol1,
                  SpiceInt      nr1r2,
                  SpiceInt      ncol2,
                  void        * mout  )

Abstract

   Multiply the transpose of a matrix with another matrix,
   both of arbitrary size. (The dimensions of the matrices must be
   compatible with this multiplication.)

Required_Reading

   None.

Keywords

 
   MATRIX

Brief_I/O

   VARIABLE  I/O  DESCRIPTION
   --------  ---  --------------------------------------------------
   m1         I   nr1r2 X ncol1 double precision matrix.
   m2         I   nr1r2 X ncol2 double precision matrix.
   ncol1      I   Column dimension of m1 and row dimension of mout.
   nr1r2      I   Row dimension of m1 and m2.
   ncol2      I   Column dimension of m2 (and also mout).
   mout       O   Transpose of m1 times m2.
 

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
              rows in m1.

   ncol1      is the number of columns in m1 and the number of rows of
              mout.

   nr1r2      is the number of rows in both m1 and (by necessity) m2.

   ncol2      is the number of columns in both m2 and mout.
 

Detailed_Output

   mout       mout is the product matrix defined as the transpose of 
              m1 times m2, that is
              
                            t
                 mout = (m1)  x (m2)
                 
              where the superscript t denotes the transpose of m1.
              
              mout is a double precision matrix of dimension ncol1 x 
              ncol2.
              
              mout may overwrite m1 or m2.  Note that this capability 
              does not exist in the Fortran version of SPICELIB; in the
              Fortran version, the output must not overwrite either 
              input.

Parameters

   None.

Exceptions

   1) If dynamic allocation of memory fails, the error 
      SPICE(MEMALLOCFAILED) is signalled.

Files

   None.

Particulars

   The code reflects precisely the following mathematical expression

   For each value of the subscript i from 1 to ncol1, and j from 1
   to ncol2:

      mout(i,j) = Summation from k=1 to nr1r2 of  m1(k,i) * m2(k,j)

Examples

 
   1)  Suppose that m1 = | 1  2  3  0 |
                         | 1  1  1  1 |
 
       and that     m2 = | 1  2  3 |
                         | 0  0  0 |
 
       Then calling mtxmg_c as shown
 
          mtxmg_c ( m1, m2, 4, 2, 3, mout )
 
       will yield the following value for mout:
 
                 | 1  2  3 |
          mout = | 2  4  6 |
                 | 3  6  9 |
                 | 0  0  0 |
       

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)
   W.M. Owen          (JPL)

Version

   -CSPICE Version 1.2.2, 16-JAN-2008   (EDW)

      Corrected typos in header titles:
      
      Detailed Input to Detailed_Input
      Detailed Output to Detailed_Output
      
   -CSPICE Version 1.2.1, 10-NOV-2006   (EDW)

      Added Parameters section header. 

   -CSPICE Version 1.2.0, 28-AUG-2001 (NJB)

      Const-qualified input arrays.

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

Index_Entries

   matrix transpose times matrix n-dimensional_case

Link to routine mtxmg_c source file mtxmg_c.c