Procedure

     MTXMG ( Matrix transpose times matrix, general dimension )

     SUBROUTINE MTXMG ( M1, M2, NC1, NR1R2, NC2, 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

Declarations

     IMPLICIT NONE

     INTEGER            NC1
     INTEGER            NR1R2
     INTEGER            NC2
     DOUBLE PRECISION   M1   ( NR1R2,NC1 )
     DOUBLE PRECISION   M2   ( NR1R2,NC2 )
     DOUBLE PRECISION   MOUT ( NC1,  NC2 )

Brief_I/O

     VARIABLE  I/O  DESCRIPTION
     --------  ---  --------------------------------------------------
     M1         I   Left-hand matrix whose transpose is to be
                    multiplied.
     M2         I   Right-hand matrix to be multiplied.
     NC1        I   Column dimension of M1 and row dimension of MOUT.
     NR1R2      I   Row dimension of both M1 and M2.
     NC2        I   Column dimension of both M2 and MOUT.
     MOUT       O   Product matrix M1**T * M2.

Detailed_Input

     M1       is an double precision matrix of arbitrary dimension
              whose transpose is the left hand multiplier of a
              matrix multiplication.

     M2       is an double precision matrix of arbitrary dimension
              whose transpose is the left hand multiplier of a
              matrix multiplication.

     NC1      is the column dimension of M1 and row dimension of
              MOUT.

     NR1R2    is the row dimension of both M1 and M2.

     NC2      is the column dimension of both M2 and MOUT.

Detailed_Output

     MOUT     is a double precision matrix containing the product

                           T
                 MOUT =  M1  x  M2

              where the superscript T denotes the transpose of M1.

              MOUT must NOT overwrite either M1 or M2.

Parameters

     None.

Exceptions

     Error free.

     1)  If NR1R2 < 1, the elements of the matrix MOUT are set equal to
         zero.

Files

     None.

Particulars

     The code reflects precisely the following mathematical expression

     For each value of the subscript I from 1 to NC1, and J from 1
     to NC2:

     MOUT(I,J) = Summation from K=1 to NR1R2 of  ( M1(K,I) * M2(K,J) )

     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.

     Since this subroutine operates on matrices of arbitrary size, it
     is not possible to buffer intermediate results. Thus, MOUT
     should NOT overwrite either M1 or M2.

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 2x4 and a 2x3 matrices, multiply the transpose of the
        first matrix by the second one.


        Example code begins here.


              PROGRAM MTXMG_EX1
              IMPLICIT NONE

        C
        C     Local variables.
        C
              DOUBLE PRECISION      M1   ( 4, 2 )
              DOUBLE PRECISION      M2   ( 2, 3 )
              DOUBLE PRECISION      MOUT ( 4, 3 )

              INTEGER               I
              INTEGER               J

        C
        C     Define M1 and M2.
        C
              DATA                  M1 /  1.0D0,  1.0D0,
             .                            2.0D0,  1.0D0,
             .                            3.0D0,  1.0D0,
             .                            0.0D0,  1.0D0  /

              DATA                  M2 /  1.0D0,  0.0D0,
             .                            2.0D0,  0.0D0,
             .                            3.0D0,  0.0D0  /

        C
        C     Multiply the transpose of M1 by M2.
        C
              CALL MTXMG ( M1, M2, 4, 2, 3, MOUT )

              WRITE(*,'(A)') 'Transpose of M1 times M2:'
              DO I = 1, 4

                 WRITE(*,'(3F10.3)') ( MOUT(I,J), J=1,3)

              END DO

              END


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


        Transpose of M1 times M2:
             1.000     2.000     3.000
             2.000     4.000     6.000
             3.000     6.000     9.000
             0.000     0.000     0.000

Restrictions

     1)  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)  MOUT must not overwrite M1 or M2 or else the intermediate
         will affect the final result.

Literature_References

     None.

Author_and_Institution

     J. Diaz del Rio    (ODC Space)
     W.M. Owen          (JPL)
     W.L. Taber         (JPL)

Version

    SPICELIB Version 1.1.0, 04-JUL-2021 (JDR)

        Added IMPLICIT NONE statement.

        Edited the header to comply with NAIF standard. Removed
        unnecessary $Revisions section.

        Added complete code example based on the existing example.

        Added entry #1 to $Exceptions section.

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

        Comment section for permuted index source lines was added
        following the header.

    SPICELIB Version 1.0.0, 31-JAN-1990 (WMO)