vhatg |
Table of contents
ProcedureVHATG ( "V-Hat", unit vector along V, general dimension ) SUBROUTINE VHATG ( V1, NDIM, VOUT ) AbstractFind the unit vector along a double precision vector of arbitrary dimension. Required_ReadingNone. KeywordsVECTOR DeclarationsIMPLICIT NONE INTEGER NDIM DOUBLE PRECISION V1 ( NDIM ) DOUBLE PRECISION VOUT ( NDIM ) Brief_I/OVARIABLE I/O DESCRIPTION -------- --- -------------------------------------------------- V1 I Vector to be normalized. NDIM I Dimension of V1 (and also VOUT). VOUT O Unit vector along V1. Detailed_InputV1 is any double precision vector of arbitrary dimension. NDIM is the dimension of V1 (and also VOUT). Detailed_OutputVOUT is the unit vector in the direction of V1: V1 VOUT = -------- ||V1|| If V1 represents the zero vector, then VOUT will also be the zero vector. ParametersNone. ExceptionsError free. FilesNone. ParticularsVHATG determines the magnitude of V1 and then divides each component of V1 by the magnitude. This process is highly stable over the whole range of multi-dimensional vectors. This routine will detect if V1 the zero vector, and will not attempt to divide by zero. ExamplesThe 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 n-dimensional vectors and find the unit vector along each of them. Example code begins here. PROGRAM VHATG_EX1 IMPLICIT NONE C C Local parameters. C INTEGER NDIM PARAMETER ( NDIM = 4 ) INTEGER SETSIZ PARAMETER ( SETSIZ = 2 ) C C Local variables. C DOUBLE PRECISION V1 ( NDIM, SETSIZ ) DOUBLE PRECISION VOUT ( NDIM ) INTEGER I INTEGER J C C Define the vector set. C DATA V1 / . 5.D0, 12.D0, 0.D0, 0.D0, . 1.D-7, 2.D-7, 2.D-7, 0.D0 / C C Calculate the unit vectors. C DO I=1, SETSIZ CALL VHATG ( V1(1,I), NDIM, VOUT ) WRITE(*,'(A,4F12.7)') 'Input vector: ', . ( V1(J,I), J=1,NDIM ) WRITE(*,'(A,4F12.7)') 'Unit vector : ', VOUT WRITE(*,*) END DO END When this program was executed on a Mac/Intel/gfortran/64-bit platform, the output was: Input vector: 5.0000000 12.0000000 0.0000000 0.0000000 Unit vector : 0.3846154 0.9230769 0.0000000 0.0000000 Input vector: 0.0000001 0.0000002 0.0000002 0.0000000 Unit vector : 0.3333333 0.6666667 0.6666667 0.0000000 Restrictions1) The relative number of cases whereby floating point overflow may occur is negligible. Thus, no error recovery or reporting scheme is incorporated into this subroutine. Literature_ReferencesNone. Author_and_InstitutionN.J. Bachman (JPL) J. Diaz del Rio (ODC Space) W.M. Owen (JPL) W.L. Taber (JPL) VersionSPICELIB Version 1.1.0, 05-JUL-2021 (JDR) Added IMPLICIT NONE statement. Edited the header to comply with NAIF standard. Added complete code example based on existing example. SPICELIB Version 1.0.2, 22-APR-2010 (NJB) Header correction: assertions that the output can overwrite the input have been removed. 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) |
Fri Dec 31 18:37:05 2021