Procedure

     MXMG ( Matrix times matrix, general dimension )

     SUBROUTINE MXMG ( M1, M2, NR1, NC1R2, NC2, MOUT )

Abstract

     Multiply two double precision matrices of arbitrary size.

Required_Reading

     None.

Keywords

     MATRIX

Declarations

     IMPLICIT NONE

     INTEGER             NR1
     INTEGER             NC1R2
     INTEGER             NC2
     DOUBLE PRECISION    M1   ( NR1,   NC1R2 )
     DOUBLE PRECISION    M2   ( NC1R2, NC2   )
     DOUBLE PRECISION    MOUT ( NR1,   NC2   )

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 a a double precision matrix of dimension
              NR1 x NC2. MOUT is the product matrix given
              by MOUT = (M1) x (M2). MOUT must not overwrite
              M1 or M2.

Parameters

     None.

Exceptions

     Error free.

     1)  If NC1R2 < 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 NC1R2 of ( M1(I,K) * M2(K,J)

     Since this subroutine operates on matrices of arbitrary size, it
     is not feasible 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 3x2 and a 2x3 matrices, multiply the first matrix by
        the second one.


        Example code begins here.


              PROGRAM MXMG_EX1
              IMPLICIT NONE

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

              INTEGER               I
              INTEGER               J

        C
        C     Define M1 and M2.
        C
              DATA                  M1 /  1.0D0,  2.0D0, 3.0D0,
             .                            4.0D0,  5.0D0, 6.0D0  /

              DATA                  M2 /  1.0D0,  2.0D0,
             .                            3.0D0,  4.0D0,
             .                            5.0D0,  6.0D0  /

        C
        C     Multiply M1 by M2.
        C
              CALL MXMG ( M1, M2, 3, 2, 3, MOUT )

              WRITE(*,'(A)') 'M1 times M2:'
              DO I = 1, 3

                 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:


        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.

     3)  MOUT should not overwrite M1 or M2.

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)

        Changed input argument names ROW1, COL1 and COL2 to NR1, NC1R2
        and NC2 for consistency with other routines.

        Added IMPLICIT NONE statement.

        Edited the header to comply with NAIF standard.
        Added complete code example based on the existing example.

    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)