Procedure

     VNORM ( Vector norm, 3 dimensions )

     DOUBLE PRECISION FUNCTION VNORM ( V1 )

Abstract

     Compute the magnitude of a double precision 3-dimensional
     vector.

Required_Reading

     None.

Keywords

     VECTOR

Declarations

     IMPLICIT NONE

     DOUBLE PRECISION  V1 ( 3 )

Brief_I/O

     VARIABLE  I/O  DESCRIPTION
     --------  ---  --------------------------------------------------
     V1         I   Vector whose magnitude is to be found.

     The function returns the magnitude of V1.

Detailed_Input

     V1       is any double precision 3-dimensional vector.

Detailed_Output

     The function returns the magnitude of V1 calculated in a
     numerically stable way.

Parameters

     None.

Exceptions

     Error free.

Files

     None.

Particulars

     VNORM takes care to avoid overflow while computing the norm of the
     input vector V1. VNORM finds the component of V1 whose magnitude
     is the largest. Calling this magnitude V1MAX, the norm is computed
     using the formula:

                        ||    1         ||
        VNORM = V1MAX * || ------- * V1 ||
                        ||  V1MAX       ||

     where the notation ||X|| indicates the norm of the vector X.

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) Define a set of 3-dimensional vectors and compute the
        magnitude of each vector within.


        Example code begins here.


              PROGRAM VNORM_EX1
              IMPLICIT NONE

        C
        C     SPICELIB functions.
        C
              DOUBLE PRECISION      VNORM

        C
        C     Local parameters.
        C
              INTEGER               SETSIZ
              PARAMETER           ( SETSIZ = 3 )

        C
        C     Local variables.
        C
              DOUBLE PRECISION      V1   ( 3, SETSIZ )

              INTEGER               I
              INTEGER               J

        C
        C     Define a set of 3-dimensional vectors.
        C
              DATA                  V1  /  1.D0,   2.D0,   2.D0,
             .                             5.D0,  12.D0,   0.D0,
             .                            -5.D-17, 0.0D0, 12.D-17  /

        C
        C     Calculate the magnitude of each vector
        C
              DO I=1, SETSIZ

                 WRITE(*,'(A,3E10.2)') 'Input vector: ',
             .                         ( V1(J,I), J=1,3 )
                 WRITE(*,'(A,F24.20)') 'Magnitude   : ',
             .                         VNORM ( V1(1,I) )
                 WRITE(*,*)

              END DO

              END


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


        Input vector:   0.10E+01  0.20E+01  0.20E+01
        Magnitude   :   3.00000000000000000000

        Input vector:   0.50E+01  0.12E+02  0.00E+00
        Magnitude   :  13.00000000000000000000

        Input vector:  -0.50E-16  0.00E+00  0.12E-15
        Magnitude   :   0.00000000000000013000

Restrictions

     None.

Literature_References

     None.

Author_and_Institution

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

Version

    SPICELIB Version 1.0.2, 06-JUL-2020 (JDR)

        Added IMPLICIT NONE statement.

        Edited the header to comply with NAIF standard. Added complete
        code 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)