CHAPTER 1

                  VECTOR / MATRIX ROUTINES





VECTOR / MATRIX ROUTINES                                                PAGE 1-2
CROSS


     1.1   SUBROUTINE CROSS 
           ---------- -----


      
                CALL CROSS  (C,A,B)
      
                CALL CROSSD (C,A,B)
      
      VERSION:  VECTOR / MATRIX ROUTINES     SAM MILLER     REL 1.0  
      
      FUNCTION:
      
        CROSS PRODUCT OF TWO 3-VECTORS 
      
        C = A X B
      
      
      LANGUAGE:  MACRO-11
      
      
      ARGUMENTS:
      
            C   = OUTPUT 3-VECTOR
            A,B = INPUT 3-VECTORS
      
      
      COMMONS:
      
        (NONE)
      
      
      GENERAL DESCRIPTION:
      
        ALL REAL ARGUMENTS.
      
      
            SINGLE PRECISION -      CROSS    FOR 3-VECTORS
      
            DOUBLE PRECISION -      CROSSD   FOR 3-VECTORS
      
      
      
      C CAN NOT OVERLAP A OR B.
      

      
      PERIPHERAL INPUT/OUTPUT:
      
        (NONE)
      
      

      LOGICAL UNIT USAGE:
      
        (NONE)


VECTOR / MATRIX ROUTINES                                                PAGE 1-3
CROSS


      
      
      EXTERNAL ROUTINES CALLED:
      
        NAM$
        $BOMB
      



VECTOR / MATRIX ROUTINES                                                PAGE 1-4
DOT


     1.2   SUBROUTINE DOT 
           ---------- ---


      
        CALL DOT  (C,A,B,N)
      
        CALL DOTD (C,A,B,N)
      
      VERSION:  VECTOR / MATRIX ROUTINES     SAM MILLER     REL 1.0  
      
      FUNCTION:
      
        DOT PRODUCT OF 2 VECTORS 
      
        C = SUM OF [A(I)*B(I)] FOR 1<=I<=N
      
      
      LANGUAGE:  MACRO-11
      
      
      ARGUMENTS:
      
        C   = OUTPUT 
        A,B = INPUT N-VECTORS
        N   = VECTOR DIMENSION
      
      
      COMMONS:
      

        (NONE)
      
      
      GENERAL DESCRIPTION:
      
        ALL REAL ARGUMENTS EXCEPT INTEGER N.
      
      
            SINGLE PRECISION -      DOT    FOR N-VECTORS
      
            DOUBLE PRECISION -      DOTD   FOR N-VECTORS
      
      
        NOTE -- SINGLE PRECISION ROUTINE MAINTAINS ACCURACY BY
        ACCUMULATING INTERMEDIATE QUANTITIES AS DOUBLE PRECISION
      
      
      PERIPHERAL INPUT/OUTPUT:
      
        (NONE)
      
      
      LOGICAL UNIT USAGE:


VECTOR / MATRIX ROUTINES                                                PAGE 1-5
DOT


      
        (NONE)
            
      EXTERNAL ROUTINES CALLED:
      
        NAM$
        $BOMB
  
    


VECTOR / MATRIX ROUTINES                                                PAGE 1-6
IDENT


     1.3   SUBROUTINE IDENT 
           ---------- -----


      
                CALL IDENT  (C,M,NRC)
      
                CALL IDENTD (C,M,NRC)
      
      VERSION:  VECTOR / MATRIX ROUTINES     SAM MILLER     REL 1.0  
      
      FUNCTION:
      
        C IS SET TO THE IDENTITY MATRIX 
      
      
      LANGUAGE:  MACRO-11
      
      
      ARGUMENTS:
      
            C   = OUTPUT MATRIX (RESULT IS STORED IN UPPER M X M SUBMATRIX)
            M   = NUMBER OF DIAGONAL ELEMENTS TO SET = 1.0
            NRC = NUMBER OF ROWS IN C
      
      
      COMMONS:
      
        (NONE)
      
      
      GENERAL DESCRIPTION:
   
   
        ALL INTEGER ARGUMENTS EXCEPT REAL C.
      
            SINGLE PRECISION -      IDENT    
      
            DOUBLE PRECISION -      IDENTD   
      
      
      
      PERIPHERAL INPUT/OUTPUT:
      
        (NONE)
      
      
      LOGICAL UNIT USAGE:
      
        (NONE)
      
      
      EXTERNAL ROUTINES CALLED:
      


VECTOR / MATRIX ROUTINES                                                PAGE 1-7
IDENT


        NAM$
        $BOMB
      



VECTOR / MATRIX ROUTINES                                                PAGE 1-8
MABT


     1.4   SUBROUTINE MABT 
           ---------- ----


      
         CALL MABT   (C,A,B,L,M,N)
      
         CALL M3ABT  (C,A,B,N)
      
         CALL MPABT  (C,A,B,L,M,N,NRA,NRB,NRC)
      
         CALL MABTD  (C,A,B,L,M,N)
      
         CALL M3ABTD (C,A,B,N)
      
         CALL MPABTD (C,A,B,L,M,N,NRA,NRB,NRC)
      
      VERSION:  VECTOR / MATRIX ROUTINES     SAM MILLER     REL 1.0  
      
      FUNCTION:
      
        MATRIX TRANSPOSE MULTIPLY - TRANSPOSE RIGHT HAND MATRIX
      
        C(L,N) = A(L,M) B(N,M)[TRANSPOSE]
      
      
      LANGUAGE:  MACRO-11
      
      
      ARGUMENTS:
      
            C   = OUTPUT MATRIX (RESULT IS STORED IN UPPER L X N SUBMATRIX)
            A,B = INPUT  MATRICES  (C = A B[TRANSPOSE])
            L,M,N = SUBMATRIX MULTIPLY SIZE 
                      C   =   A     B[T]
                    (LXN) = (LXM) (NXM)
            NRA = NUMBER OF ROWS IN A
            NRB = NUMBER OF ROWS IN B
            NRC = NUMBER OF ROWS IN C
      
      
      COMMONS:
      
        (NONE)
      
      
      GENERAL DESCRIPTION:
      
       REAL ARGUMENTS: C,A,B
       INTEGER ARGUMENTS: L,M,N,NRA,NRB,NRC
      
      
        THERE ARE 3 CALLING SEQUENCES:


VECTOR / MATRIX ROUTINES                                                PAGE 1-9
MABT


      
                 1.  PARTIAL MATRIX MULTIPLY
        
                   CALL MPABT(C,A,B,L,M,N,NRA,NRB,NRC)
      
                     C(L,N) = A(L,M) B(N,M)T
      
                     WHERE A, B, C ARE MATRICES
                     THE L X M UPPER SUBMATRIX OF A IS MULTIPLIED BY THE 
                     UPPER N X M SUBMATRIX OF B (TRANSPOSE) AND STORED IN
                     THE UPPER L X N SUBMATRIX OF C
      
      
                 2.  FULL MATRIX MULTIPLY
      
                     CALL MABT(C,A,B,L,M,N)
      
                     C(L,N) = A(L,M) B(N,M)T
      
      
                 3.  3X3 MATRIX MULTIPLY
      
                     CALL M3ABT(C,A,B,N)
      
                     C(3,N) = A(3,3) B(N,3)T
      
      
        NOTE -- SINGLE PRECISION ROUTINE MAINTAINS ACCURACY BY
        ACCUMULATING INTERMEDIATE QUANTITIES AS DOUBLE PRECISION
      
      
      PERIPHERAL INPUT/OUTPUT:
      
        (NONE)
      
      
      LOGICAL UNIT USAGE:
      
        (NONE)
      
      
      EXTERNAL ROUTINES CALLED:
      

        NAM$
        $BOMB
      


VECTOR / MATRIX ROUTINES                                               PAGE 1-10
MADD


     1.5   SUBROUTINE MADD 
           ---------- ----


      
                CALL MADD   (C,A,B,M,N)
      
                CALL M3ADD  (C,A,B)
      
                CALL MPADD  (C,A,B,M,N,NRA,NRB,NRC)
      
                CALL MADDD  (C,A,B,M,N)
      
                CALL M3ADDD (C,A,B)
      
                CALL MPADDD (C,A,B,M,N,NRA,NRB,NRC)
      
      
      VERSION:  VECTOR / MATRIX ROUTINES     SAM MILLER     REL 1.0  
      
      FUNCTION:
      
        MATRIX ADDITION 
      
        C = A + B
      
      
      LANGUAGE:  MACRO-11
      
      
      ARGUMENTS:
      
            C   = OUTPUT MATRIX (RESULT IS STORED IN UPPER M X N SUBMATRIX)
            A,B = INPUT  MATRICES
            M,N = UPPER M X N SUBMATRICES ARE SUMMED
      
      NRA = NUMBER OF ROWS IN A
            NRB = NUMBER OF ROWS IN B
            NRC = NUMBER OF ROWS IN C
      
      
      COMMONS:
      
        (NONE)
      
      
      GENERAL DESCRIPTION:
      
        REAL ARGUMENTS: C,A,B
        INTEGER ARGUMENTS: M,N,NRA,NRB,NRC
      
      
            SINGLE PRECISION -      MADD    FOR MXN MATRICES
                                    M3ADD   FOR 3X3 MATRICES


VECTOR / MATRIX ROUTINES                                               PAGE 1-11
MADD


                                    MPADD   FOR UPPER MXN SUB MATRICES
      
            DOUBLE PRECISION -      MADDD   FOR MXN MATRICES
                                    M3ADDD  FOR 3X3 MATRICES
                                    MPADDD  FOR UPPER MXN SUB MATRICES
      
      
      
      
      PERIPHERAL INPUT/OUTPUT:
      
        (NONE)
      
      
      LOGICAL UNIT USAGE:
      
        (NONE)
      
      
      EXTERNAL ROUTINES CALLED:
      
        NAM$
        $BOMB
      


VECTOR / MATRIX ROUTINES                                               PAGE 1-12
MATB

     1.6  SUBROUTINE MATB
          ---------- ----


      
             CALL MATB   (C,A,B,L,M,N)
      
             CALL M3ATB  (C,A,B,N)
      
             CALL MPATB  (C,A,B,L,M,N,NRA,NRB,NRC) 
      
             CALL MATBD  (C,A,B,L,M,N)
      
             CALL M3ATBD (C,A,B,N)
      
             CALL MPATBD (C,A,B,L,M,N,NRA,NRB,NRC) 
      
      VERSION:  VECTOR / MATRIX ROUTINES     SAM MILLER     REL 1.0  
      
      FUNCTION:
      
        MATRIX TRANSPOSE MULTIPLY - TRANSPOSE LEFT HAND MATRIX
      
        C(L,N) = A(M,L)[TRANSPOSE] B(M,N)
      
      
      LANGUAGE:  MACRO-11
      
      
      ARGUMENTS:
      
            C   = OUTPUT MATRIX (RESULT IS STORED IN UPPER L X N SUBMATRIX)
            A,B = INPUT  MATRICES  (C = A[TRANSPOSE] B)
            L,M,N = SUBMATRIX MULTIPLY SIZE
 
                      C   =   A[T]  B
                    (LXM) = (MXL) (MXN)
            NRA = NUMBER OF ROWS IN A
            NRB = NUMBER OF ROWS IN B
            NRC = NUMBER OF ROWS IN C
      
      
      COMMONS:
      
        (NONE)
      
      
      GENERAL DESCRIPTION:
      
       REAL ARGUMENTS: C,A,B
       INTEGER ARGUMENTS: L,M,N,NRA,NRB,NRC
      
      
            THERE ARE 3 CALLING SEQUENCES:


VECTOR / MATRIX ROUTINES                                           PAGE 1-13
MATB


      
                 1.  PARTIAL MATRIX MULTIPLY
      
                     CALL MPATB(C,A,B,L,M,N,NRA,NRB,NRC)
      
                     C(L,N) = A(M,L)[TRANSPOSE] B(M,N)
      
                     WHERE A, B, C ARE MATRICES
                     THE M X L UPPER SUBMATRIX OF A (TRANSPOSE) IS MULTIPLIED
                     BY THE UPPER M X N SUBMATRIX OF B AND STORED IN THE 
                     UPPER L X N SUBMATRIX OF C
      
      

                 2.  FULL MATRIX MULTIPLY
      
                     CALL MATB(C,A,B,L,M,N)
      
                     C(L,N) = A(M,L)[TRANSPOSE] B(M,N)
      
      
                 3.  3X3 MATRIX MULTIPLY
      
                     CALL M3ATB(C,A,B,N)
      
                     C(3,N) = A(3,3)[TRANSPOSE] B(3,N)
      
      
        NOTE -- SINGLE PRECISION ROUTINE MAINTAINS ACCURACY BY
        ACCUMULATING INTERMEDIATE QUANTITIES AS DOUBLE PRECISION
      
      
    
  PERIPHERAL INPUT/OUTPUT:
      
        (NONE)
      
      
      LOGICAL UNIT USAGE:
      
        (NONE)
            
      EXTERNAL ROUTINES CALLED:
      
        NAM$
        $BOMB
      


VECTOR / MATRIX ROUTINES                                               PAGE 1-14
MCLR


     1.7   SUBROUTINE MCLR 
           ---------- ----

      
                CALL MCLR   (C,M,N)
      
                CALL M3CLR  (C)
      
                CALL MPCLR  (C,M,N,NRC)
      
                CALL MCLRD  (C,M,N)
      
                CALL M3CLRD (C)
      
                CALL MPCLRD (C,M,N,NRC)
      
      
      VERSION:  VECTOR / MATRIX ROUTINES     SAM MILLER     REL 1.0  
      
      FUNCTION:
      
        CLEARS A MATRIX
      
        C = 0
      
      
      LANGUAGE:  MACRO-11
      
      
      ARGUMENTS:
      
            C   = OUTPUT MATRIX (RESULT IS STORED IN UPPER M X N SUBMATRIX)
            M,N = UPPER M X N SUBMATRX IS USED     
            NRC = NUMBER OF ROWS IN C
      
      
      COMMONS:
      
        (NONE)
      
      
      GENERAL DESCRIPTION:
      
       ALL INTEGER ARGUMENTS EXCEPT C.
      
      
            SINGLE PRECISION -      MCLR    FOR MXN MATRICES
                                    M3CLR   FOR 3X3 MATRICES
                                    MPCLR   FOR UPPER MXN SUBMATRICES
      
            DOUBLE PRECISION -      MCLRD   FOR MXN MATRICES
                                    M3CLRD  FOR 3X3 MATRICES


VECTOR / MATRIX ROUTINES                                               PAGE 1-15
MCLR


                                    MPCLRD  FOR UPPER MXN SUBMATRICES
      
              SET N=1 FOR VECTOR CLEAR.
      
      
      PERIPHERAL INPUT/OUTPUT:
      
        (NONE)
      
      
      LOGICAL UNIT USAGE:
      
        (NONE)
      
      
      EXTERNAL ROUTINES CALLED:
      
        NAM$
        $BOMB
      



VECTOR / MATRIX ROUTINES                                               PAGE 1-16
MCOM


     1.8   SUBROUTINE MCOM 
           ---------- ----


      
                CALL MCOM   (C,P,A,Q,B,M,N)
      
                CALL M3COM  (C,P,A,Q,B)
      
                CALL MPCOM  (C,P,A,Q,B,M,N,NRA,NRB,NRC)
      
                CALL MCOMD  (C,P,A,Q,B,M,N)
      
                CALL M3COMD (C,P,A,Q,B)
      
                CALL MPCOMD (C,P,A,Q,B,M,N,NRA,NRB,NRC)
      
    
  VERSION:  VECTOR / MATRIX ROUTINES     SAM MILLER     REL 1.0  
      
      FUNCTION:
      
        LINEAR COMBINATION OF TWO MATRICES 
      
        C = P*A + Q*B
      
      
      LANGUAGE:  MACRO-11
      
      
      ARGUMENTS:
      
            C   = OUTPUT MATRIX (RESULT IS STORED IN UPPER M X N SUBMATRIX)
            P,Q = SCALARS
            A,B = INPUT  MATRICES
            M,N = UPPER M X N SUBMATRICES ARE USED 
            NRA = NUMBER OF ROWS IN A
       
     NRB = NUMBER OF ROWS IN B
            NRC = NUMBER OF ROWS IN C
      
      
      COMMONS:
      
        (NONE)
      
      
      GENERAL DESCRIPTION:
      
        REAL ARGUMENTS: C,P,A,Q,B
        INTEGER ARGUMENTS: M,N,NRA,NRB,NRC
      
      
            SINGLE PRECISION -      MCOM    FOR MXN MATRICES
                                    M3COM   FOR 3X3 MATRICES


VECTOR / MATRIX ROUTINES                                               PAGE 1-17
MCOM


     
                               MPCOM   FOR UPPER MXN SUBMATRICES      
            DOUBLE PRECISION -      MCOMD   FOR MXN MATRICES
                                    M3COMD  FOR 3X3 MATRICES
                                    MPCOMD  FOR UPPER MXN SUBMATRICES
      
      
      
      PERIPHERAL INPUT/OUTPUT:
      
        (NONE)
      
      
      LOGICAL UNIT USAGE:
      
        (NONE)
      
      
      EXTERNAL ROUTINES CALLED:
      
        NAM$
        $BOMB
      


VECTOR / MATRIX ROUTINES                                               PAGE 1-18
MMOV


     1.9   SUBROUTINE MMOV 
           ---------- ----


      
                CALL MMOV   (C,A,M,N)
      
                CALL M3MOV  (C,A)
      
                CALL MPMOV  (C,A,M,N,NRA,NRC)
      
                CALL MMOVD  (C,A,M,N)
      
                CALL M3MOVD (C,A)
      
                CALL MPMOVD (C,A,M,N,NRA,NRC)
      
      VERSION:  VECTOR / MATRIX ROUTINES     S.A. MILLER     REL 1.0  
      
      FUNCTION:
      
        MOVE A MATRIX TO ANOTHER MATRIX 
      
        C = A
      
      
      LANGUAGE:  MACRO-11
      
      
      ARGUMENTS:
      
            C   = OUTPUT MATRIX (RESULT IS STORED IN UPPER M X N SUBMATRIX)
            A   = INPUT  MATRIX  
            M,N = UPPER M X N SUBMATRICES ARE USED 
            NRA = NUMBER OF ROWS IN A
            NRC = NUMBER OF ROWS IN C
      
      
      COMMONS:
      
  
      (NONE)
      
      
      GENERAL DESCRIPTION:
      
       REAL ARGUMENTS: C,A
       INTEGER ARGUMENTS: M,N,NRA,NRC
      
      
            SINGLE PRECISION -      MMOV    FOR MXN MATRICES
                                    M3MOV   FOR 3X3 MATRICES
                                    MPMOV   FOR UPPER MXN SUBMATRICES
      


VECTOR / MATRIX ROUTINES                                               PAGE 1-19
MMOV


            DOUBLE PRECISION -      MMOVD   FOR MXN
 MATRICES
                                    M3MOVD  FOR 3X3 MATRICES
                                    MPMOVD  FOR UPPER MXN SUBMATRICES
      
            C AND A MUST NOT OVERLAP.
      
      
      PERIPHERAL INPUT/OUTPUT:
      
        (NONE)
      
      
      LOGICAL UNIT USAGE:
      
        (NONE)
      
      
      EXTERNAL ROUTINES CALLED:
      
        NAM$
        $BOMB
      


VECTOR / MATRIX ROUTINES                                               PAGE 1-20
MMUL


     1.10   SUBROUTINE MMUL 
            ---------- ----

      
                CALL MMUL   (C,A,B,L,M,N)
      
                CALL M3MUL  (C,A,B,N)
      
                CALL MPMUL  (C,A,B,L,M,N,NRA,NRB,NRC)
      
                CALL MMULD  (C,A,B,L,M,N)
      
                CALL M3MULD (C,A,B,N)
      
                CALL MPMULD (C,A,B,L,M,N,NRA,NRB,NRC)
      
      VERSION:  VECTOR / MATRIX ROUTINES     SAM MILLER     REL 1.0  
      
      FUNCTION:
      
        MATRIX MULTIPLY 
      
        C(L,N) = A(L,M) B(M,N)
      
      
      
LANGUAGE:  MACRO-11
      
      
      ARGUMENTS:
      
            C   = OUTPUT MATRIX (RESULT IS STORED IN UPPER L X N SUBMATRIX)
            A,B = INPUT  MATRICES  (C = AB)
            L,M,N = MATRIX MULTIPLY SIZE 
                      C   =   A     B
                    (LXN) = (LXM) (MXN)
            NRA = NUMBER OF ROWS IN A
            NRB = NUMBER OF ROWS IN B
            NRC = NUMBER OF ROWS IN C
      
      
      COMMONS:
      
        (NONE)
      
      
      GENERAL DESCRIPTION:
      
       REAL ARGUMENTS: C,A,B
       INTEGER ARGUMENTS: L,M,N,NRA,NRB,NRC
      
      
            THERE ARE 3 CALLING SEQUENCES:


VECTOR / MATRIX ROUTINES                                               PAGE 1-21
MMUL


      
                 1.  PARTIAL MATRIX MULTIPLY
      
                     CALL MPMUL(C,A,B,L,M,N,NRA,NRB,NRC)
      
    
                 C(L,N) = A(L,M) B(M,N)
      
                     WHERE A, B, C ARE MATRICES
                     THE L X M UPPER SUBMATRIX OF A IS MULTIPLIED BY THE 
                     UPPER M X N SUBMATRIX OF B AND STORED IN THE UPPER L X N
                     SUBMATRIX OF C
      
      
                 2.  FULL MATRIX MULTIPLY
      
                     CALL MMUL(C,A,B,L,M,N)
      
                     C(L,N) = A(L,M) B(M,N)
      
      
                 3.  3X3 MATRIX 
MULTIPLY
      
                     CALL M3MUL(C,A,B,N)
      
                     C(3,N) = A(3,3) B(3,N)
      
        NOTE -- SINGLE PRECISION ROUTINE MAINTAINS ACCURACY BY
        ACCUMULATING INTERMEDIATE QUANTITIES AS DOUBLE PRECISION
      
      
      PERIPHERAL INPUT/OUTPUT:
      
        (NONE)
      
      
      LOGICAL UNIT USAGE:
      
        (NONE)
      
      
      EXTERNAL ROUTINES CALLED:
      
        NAM$
        $BOMB
      


VECTOR / MATRIX ROUTINES                                               PAGE 1-22
MSCL


     1.11   SUBROUTINE MSCL 
            ---------- ----


      
                CALL MSCL   (C,P,A,M,N)
      
                CALL M3SCL  (C,P,A)
      
                CALL MPSCL  (C,P,A,M,N,NRA,NRC)
      
                CALL MSCLD  (C,P,A,M,N)
      
                CALL M3SCLD (C,P,A)
      
                CALL MPSCLD (C,P,A,M,N,NRA,NRC)
      
      VERSION:  VECTOR / MATRIX ROUTINES     SAM MILLER     REL 1.0  
      
      FUNCTION:
      
        SCALAR MULTIPLICATION OF A MATRIX
      
        C = P A
      
      
      LANGUAGE:  MACRO-11
      
      
      ARGUMENTS:
      
            C   = OUTPUT MATRIX (RESULT IS STORED IN UPPER M X N SUBMATRIX)
            P   = SCALAR 
            A   = INPUT  MATRIX  
            M,N = UPPER M X N SUBMATRICES ARE USED 
            NRA = NUMBER OF ROWS IN A
            NRC = NUMBER OF ROWS IN C
      
      
   
   COMMONS:
      
        (NONE)
      
      
      GENERAL DESCRIPTION:
      
       REAL ARGUMENTS: C,P,A
       INTEGER ARGUMENTS: M,N,NRA,NRC
      
      
            SINGLE PRECISION -      MSCL    FOR MXN MATRICES
                                    M3SCL   FOR 3X3 MATRICES
                                    MPSCL   FOR UPPER MXN SUBMATRICES


VECTOR / MATRIX ROUTINES                                               PAGE 1-23
MSCL


      
            DOUBLE PRECISION -      MSCLD   FOR MXN MATRICES
                                    M3SCLD  FOR 3X3 MATRICES
                                    MPSCLD  FOR UPPER MXN SUBMATRICES
      
      
      PERIPHERAL INPUT/OUTPUT:
      
        (NONE)
      
      
      LOGICAL UNIT USAGE:
      
        (NONE)
      
      
      EXTERNAL ROUTINES CALLED:
      
        NAM$
        $BOMB
      


VECTOR / MATRIX ROUTINES                                               PAGE 1-24
MSUB


     
1.12   SUBROUTINE MSUB
       ---------- ----


      
                CALL MSUB   (C,A,B,M,N)
      
                CALL M3SUB  (C,A,B)
      
                CALL MPSUB  (C,A,B,M,N,NRA,NRB,NRC)
      
                CALL MSUBD  (C,A,B,M,N)
      
                CALL M3SUBD (C,A,B)
      
                CALL MPSUBD (C,A,B,M,N,NRA,NRB,NRC)
      
      VERSION:  VECTOR / MATRIX ROUTINES     SAM MILLER     REL 1.0  
      
      FUNCTION:
      
        MATRIX SUBTRACTION 
      
        C = A - B
      
      
      LANGUAGE:  MACRO-11
      

      
      ARGUMENTS:
      
            C   = OUTPUT MATRIX (RESULT IS STORED IN UPPER M X N SUBMATRIX)
            A,B = INPUT  MATRICES
            M,N = UPPER M X N SUBMATRICES ARE SUBTRACTED (A - B)
            NRA = NUMBER OF ROWS IN A
            NRB = NUMBER OF ROWS IN B
            NRC = NUMBER OF ROWS IN C
      
      
      COMMONS:
      
        (NONE)
      
      
      GENERAL DESCRIPTION:
      
       REAL ARGUMENTS: C,A,B
       INTEGER ARGUMENTS: M,N,NRA,NRB,NRC
      
      
            SINGLE PRECISION -      MSUB    FOR MXN MATRICES
                                    M3SUB   FOR 3X3 MATRICES
                                    MPSUB   FOR UPPER MXN SUBMATRICES


VECTOR / MATRIX ROUTINES                                               PAGE 1-25
MSUB


      
            DOUBLE PRECISION -      MSUBD   FOR MXN MATRICES
                           
         M3SUBD  FOR 3X3 MATRICES
                                    MPSUBD  FOR UPPER MXN SUBMATRICES
      
      
      
      PERIPHERAL INPUT/OUTPUT:
      
        (NONE)
      
      
      LOGICAL UNIT USAGE:
      
        (NONE)
      
      
      EXTERNAL ROUTINES CALLED:
      
        NAM$
        $BOMB
      


VECTOR / MATRIX ROUTINES                                               PAGE 1-26
MTRN


     1.13   SUBROUTINE MTRN 
            ---------- ----
VECTOR / MATRIX ROUTINES                                               PAGE 1-26
MTRN


     1.13   SUBROUTINE MTRN 
            ---------- ----



      
                CALL MTRN   (C,A,M,N)
      
                CALL M3TRN  (C,A)
      
                CALL MPTRN  (C,A,M,N,NRA,NRC)
      
                CALL MTRN   (C,A,M,N)
      
                CALL M3TRND (C,A)
      
                CALL MPTRND (C,A,M,N,NRA,NRC)
      
      VERSION:  VECTOR / MATRIX ROUTINES     SAM MILLER     REL 1.0  
      
      FUNCTION:
      
        MATRIX TRANSPOSE 
      
        C = A(TRANSPOSE)
      
      
      LANGUAGE:  MACRO-11
      
      
      ARGUMENTS:
      
            C   = OUTPUT MATRIX (RESULT IS STORED IN UPPER N X M SUBMATRIX)
            A   = INPUT  MATRIX  
            M,N = UPPER M X N SUBMATRX OF A IS USED
            NRA = NUMBER OF ROWS IN A
            NRC = NUMBER OF ROWS IN C
      
      
      COMMONS:
      
        (NONE)
      
      
      GENERAL DESCRIPTION:
      
       REAL ARGUMENTS: C,A
       INTEGER ARGUMENTS: M,N,NRA,NRC
      
      
            SINGLE PRECISION -      MTRN    FOR MXN MATRICES
                                    M3TRN   FOR 3X3 MATRICES
                                    MPTRN   FOR UPPER MXN SUBMATRICES
      


VECTOR / MATRIX ROUTINES                                               PAGE 1-27
MTRN


            DOUBLE PRECISION -      MTRND   FOR MXN MATRICES
                                    M3TRND  FOR 3X3 MATRICES
                                    MPTRND  FOR UPPER MXN SUBMATRICES
      
      
      
      PERIPHERAL INPUT/OUTPUT:
      
 
       (NONE)
      
      
      LOGICAL UNIT USAGE:
      
        (NONE)

      
      
      EXTERNAL ROUTINES CALLED:
      
        NAM$
        $BOMB
      


VECTOR / MATRIX ROUTINES                                               PAGE 1-28
PROD


     1.14   SUBROUTINE PROD 
            ---------- ----


      
                CALL PROD  (C,A,B,N)
      
                CALL PRODD (C,A,B,N)
      
      VERSION:  VECTOR / MATRIX ROUTINES     SAM MILLER     REL 1.0  
      
      FUNCTION:
      
        COMPONENT PRODUCT OF TWO VECTORS 
      
        C(I)=A(I)*B(I)  FOR I<=I<=N
      
      LANGUAGE:  MACRO-11
      
      
      ARGUMENTS:
      
        C   = OUTPUT VECTOR
        A,B = INPUT VECTOR
        N   = VECTOR DIMENSION
      
      
      COMMONS:
      
        (NONE)
      
      
      GENERAL DESCRIPTION:
      
        ALL REAL ARGUMENTS EXCEPT INTEGER N.
      
            SINGLE PRECISION -      PROD    FOR N-VECTORS
      
            DOUBLE PRECISION -      PRODD   FOR N-VECTORS
      
      
      
      PERIPHERAL INPUT/OUTPUT:
      
        (NONE)
      
      
      LOGICAL UNIT USAGE:
      
        (NONE)
      
      
      EXTERNAL ROUTINES CALLED:


VECTOR / MATRIX ROUTINES                                               PAGE 1-29
PROD


      
        NAM$
        $BOMB
      


VECTOR / MATRIX ROUTINES                                               PAGE 1-30
VADD


     1.15   SUBROUTINE VADD 
            ---------- ----


      
                CALL VADD   (C,A,B,N)
      
                CALL V3ADD  (C,A,B)
      
                CALL VADDD  (C,A,B,N)
      
                CALL V3ADDD (C,A,B)
      
      
      VERSION:  VECTOR / MATRIX ROUTINES     SAM MILLER     REL 1.0  
      
      FUNCTION:
      
        VECTOR ADDITION 
      
        C = A + B
      
      
      LANGUAGE:  MACRO-11
      
      
      ARGUMENTS:
      
            C   = OUTPUT VECTOR
            A,B = INPUT VECTORS
            N   = VECTOR DIMENSION
      
      
      COMMONS:
      
        (NONE)
      
      
      GENERAL DESCRIPTION:
      
       ALL REAL ARGUMENTS EXCEPT INTEGER N.
      
        SINGLE PRECISION -      VADD    FOR N-VECTORS
                                V3ADD   FOR 3-VECTORS
      
        DOUBLE PRECISION -      VADDD   FOR N-VECTORS
  
                                V3ADDD  FOR 3-VECTORS
      
      
      PERIPHERAL INPUT/OUTPUT:
     
 
        (NONE)
      


VECTOR / MATRIX ROUTINES                                               PAGE 1-31
VADD


      
      LOGICAL UNIT USAGE:
      
        (NONE)
      
      
      EXTERNAL ROUTINES CALLED:
      
        NAM$
        $BOMB
      


VECTOR / MATRIX ROUTINES                                               PAGE 1-32
VCLR


     1.16   SUBROUTINE VCLR
            ---------- ----


      
                CALL VCLR   (C,N)
      
                CALL V3CLR  (C)
      
                CALL VCLRD  (C,N)
      
                CALL V3CLRD (C)
      
      
      VERSION:  MATRIX / VECTOR ROUTINES     SAM MILLER     REL 1.0  
      
      FUNCTION:
      
        CLEARS A VECTOR
      
        C = 0
      
      
      LANGUAGE:  MACRO-11
      
      
      ARGUMENTS:
      
        C = OUTPUT VECTOR
        N = V
ECTOR DIMENSION
      
      
      COMMONS:
      
        (NONE)
      
      
      GENERAL DESCRIPTION:
      
       C IS REAL AND N IS INTEGER.
      
      
      
            SINGLE PRECISION -      VCLR    FOR N-VECTORS
                                    V3CLR   FOR 3-VECTORS
      
            DOUBLE PRECISION -      VCLRD   FOR N-VECTORS
                                    V3CLRD  FOR 3-VECTORS
      
      
      
      PERIPHERAL INPUT/OUTPUT:
      


VECTOR / MATRIX ROUTINES                                               PAGE 1-33
VCLR


        (NONE)
      
      
      LOGICAL UNIT USAGE:
      
        (NONE)
      
      
      EXTERNAL ROUTINES CALLED:
      
        NAM$
        $BOMB
      


VECTOR / MATRIX ROUTINES                                               PAGE 1-34
VCOM


     1.17   SUBROUTINE VCOM 
            ---------- ----


      
                CALL VCOM   (C,P,A,Q,B,N)
      
                CALL V3COM  (C,P,A,Q,B)
   
   
                CALL VCOMD  (C,P,A,Q,B,N)
      
                CALL V3COMD (C,P,A,Q,B)
      
      VERSION:  VECTOR / MATRIX ROUTINES     SAM MILLER     REL 1.0  
      
      FUNCTION:
      
        LINEAR COMBINATION OF TWO VECTORS 
      
        C = P*A + Q*B
      
      
      LANGUAGE:  MACRO-11
      
      
      ARGUMENTS:
      
            C   = OUTPUT VECTOR
            P,Q = SCALARS
            A,B = INPUT VECTOR
            N   = VECTOR DIMENSION
      
      
      COMMONS:
      
        (NONE)
      

      
      GENERAL DESCRIPTION:
      
        ALL REAL ARGUMENTS EXCEPT INTEGER N.
      
      
            SINGLE PRECISION -      VCOM    FOR N-VECTORS
                                    V3COM   FOR 3-VECTORS
      
            DOUBLE PRECISION -      VCOMD   FOR N-VECTORS
                                    V3COMD  FOR 3-VECTORS
      
      
      
      PERIPHERAL INPUT/OUTPUT:
    
  


VECTOR / MATRIX ROUTINES                                               PAGE 1-35
VCOM


        (NONE)
      
      
      LOGICAL UNIT USAGE:
      
        (NONE)
      
      
      EXTERNAL ROUTINES CALLED:
      
        NAM$
        $BOMB
      


VECTOR / MATRIX ROUTINES                                               PAGE 1-36
VMAG


     1.18   FUNCTION VMAG 
            -------- ----


      
                VMAG   (A,N)
      
                V3MAG  (
A)
      
                VMAGD  (A,N)
      
                V3MAGD (A)
      
      VERSION:  VECTOR / MATRIX ROUTINES     SAM MILLER     REL 1.0  
      
      FUNCTION:
      
        MAGNITUDE OF VECTOR 
      
        [ A(1)*A(1) + A(2)*A(2) + ... + A(N)*A(N) ] 1/2
      
      
      LANGUAGE:  MACRO-11
      
      
      ARGUMENTS:
      
            A   = INPUT VECTOR
            N   = VECTOR DIMENSION
      
      
      COMMONS:
      
        (NONE)
    
  
      
      GENERAL DESCRIPTION:
      
        A IS REAL AND N IS INTEGER.
      
      
            SINGLE PRECISION -      VMAG    FOR N-VECTORS
                                    V3MAG   FOR 3-VECTORS
      
            DOUBLE PRECISION -      VMAGD   FOR N-VECTORS
                                    V3MAGD  FOR 3-VECTORS
      
        NOTE -- SINGLE PRECISION ROUTINE MAINTAINS ACCURACY BY
        ACCUMULATING INTERMEDIATE QUANTITIES AS DOUBLE PRECISION
      
      
 
     PERIPHERAL INPUT/OUTPUT:
      


VECTOR / MATRIX ROUTINES                                               PAGE 1-37
VMAG


        (NONE)
      
      
      LOGICAL UNIT USAGE:
      
        (NONE)
      
      
      EXTERNAL ROUTINES CALLED:
      
        $$DSQR -  DOUBLE PRECISON SQUARE ROOT
        NAM$
        $BOMB
      


VECTOR / MATRIX ROUTINES                                               PAGE 1-38
VMOV


     1.19   SUBROUTINE VMOV 
            ---------- ----


      
                CALL VMOV  (C,A,N)
      
                CALL VMOVD (C,A,N)
      
      VERSION:  VECTOR / MATRIX ROUTINES     SAM MILLER     REL 1.0  
      
      FUNCTION:
      
        MOVE A VECTOR TO ANOTHER VECTOR 
      
        C = A
      
      
      LANGUAGE:  MACRO-11
      
      
      ARGUMENTS:
      
            C   = OUTPUT VECTOR
            N   = VECTOR DIMENSION
            A   = INPUT VECTOR
      
      
      COMMONS:

      
        (NONE)
      
      
      GENERAL DESCRIPTION:
      
        ALL REAL ARGUMENTS EXCEPT INTEGER N.
      
            SINGLE PRECISION -      VMOV    
      
            DOUBLE PRECISION -      VMOVD   
      
      
            A AND C MUST NOT OVERLAP
      
      
      PERIPHERAL INPUT/OUTPUT:
      
        (NONE)
      
      
      LOGICAL UNIT USAGE:
      
        (NONE)


VECTOR / MATRIX ROUTINES                                               PAGE 1-39
VMOV


      
      

      EXTERNAL ROUTINES CALLED:
      
        NAM$
        $BOMB
      


VECTOR / MATRIX ROUTINES                                               PAGE 1-40
VSCL


     1.20   SUBROUTINE VSCL 
            ---------- ----


      
                CALL VSCL   (C,P,A,N)
      
                CALL V3SCL  (C,P,A)
      
                CALL VSCLD  (C,P,A,N)
      
                CALL V3SCLD (C,P,A)
      
      VERSION:  VECTOR / MATRIX ROUTINES     SAM MILLER     REL 1.0  
      
      FUNCTION:
      
        SCALAR TIMES A VECTOR 
      
        C = P*A
      
      
      LANGUAGE:  MACRO-11
      
      
      ARGUMENTS:
      
            C   = OUTPUT VECTOR
            P   = SCALAR 
            A   = INPUT VECTOR
            N   = VECTOR DIMENSION
      
      
      COMMONS:
      
        (NONE)
      
      
      GENERAL DESCRIPTION:
      
        ALL REAL ARGUMENTS EXCEPT INTEGER N.
      
     
       SINGLE PRECISION -      VSCL    FOR N-VECTORS
                               V3SCL   FOR 3-VECTORS
      
            DOUBLE PRECISION -      VSCLD   FOR N-VECTORS
                                    V3SCLD  FOR 3-VECTORS
      
      
      
      
      PERIPHERAL INPUT/OUTPUT:
      



VECTOR / MATRIX ROUTINES                                               PAGE 1-41
VSCL


        (NONE)
      
      
      LOGICAL UNIT USAGE:
      
        (NONE)
      
   
   
      EXTERNAL ROUTINES CALLED:
      
        NAM$
        $BOMB
      


VECTOR / MATRIX ROUTINES                                               PAGE 1-42
VSUB


     1.21   SUBROUTINE VSUB 
            ---------- ----


      
                CALL VSUB   (C,A,B,N)
      
                CALL V3SUB  (C,A,B)
      
                CALL VSUBD  (C,A,B,N)
      
                CALL V3SUBD (C,A,B)
      
      VERSION:  VECTOR / MATRIX ROUTINES     SAM MILLER     REL 1.0
  
      
      FUNCTION:      
        VECTOR SUBTRACTION 
      
        C = A - B
      
      
      LANGUAGE:  MACRO-11
      
      
      ARGUMENTS:
      
            C   = OUTPUT VECTOR
            A,B = INPUT VECTORS
            N   = VECTOR DIMENSION
      
      
      COMMONS:
      
        (NONE)
      
      
      GENERAL DESCRIPTION:
      
        ALL REAL ARGUMENTS EXCEPT INTEGER N.
      
      
            SINGLE PRECISION -      VSUB    FOR N-VECTORS
                                    V3SUB   FOR 3-VECTORS
      
            DOUBLE PRECISION -      VSUBD   FOR N-VECTORS
                                    V3SUBD  FOR 3-VECTORS
      
      
      
      PERIPHERAL INPUT/OUTPUT:
      
        (NONE)


VECTOR / MATRIX ROUTINES                                               PAGE 1-43
VSUB


      
      
      LOGICAL UNIT USAGE:
      
        (NONE)
      
      
      EXTERNAL ROUTINES CALLED:
      
        NAM$
        $BOMB
      













                         CHAPTER 2

                           INDEX





INDEX                                               PAGE 2-2




CROSS  . . . . . . . . . . . . 1-2

DOT  . . . . . . . . . . . . . 1-4

IDENT  . . . . . . . . . . . . 1-6

MABT . . . . . . . . . . . . . 1-8
MADD . . . . . . . . . . . . . 1-10
MATB . . . . . . . . . . . . . 1-12
MCLR . . . . . . . . . . . . . 1-14
MCOM . . . . . . . . . . . . . 1-16

MMOV . . . . . . . . . . . . . 1-18
MMUL . . . . . . . . . . . . . 1-20
MSCL . . . . . . . . . . . . . 1-22
MSUB . . . . . . . . . . . . . 1-24
MTRN . . . . . . . . . . . . . 1-26

PROD . . . . . . . . . . . . . 1-28

VADD . . . . . . . . . . . . . 1-30
VCLR . . . . . . . . . . . . . 1-32
VCOM . . . . . . . . . . . . . 1-34
VMAG . . . . . . . . . . . . . 1-36
VMOV . . . . . . . . . . . . . 1-38
VSCL . . . . . . . . . . . . . 1-40
VSUB . . . . . . . . . . . . . 1-42