math_utilities.f

!============================================================================
      MODULE math_utilities
!--------------------------------------------------------------------------
! 
! FUNCTION: Module containing routines necessary to compute the line-integrated
!           Faraday rotation angle and the line-integrated polarization phase shift.
!
!------------------------------------------------------------------------------
      USE stel_kinds
      USE stel_constants
      IMPLICIT NONE
 
 
      CONTAINS
!=============================================================================
      REAL(KIND=rprec) FUNCTION magnitude(vec)
!--------------------------------------------------------------------------
! FUNCTION: calculates the magnitude of 3D input vector.  
!
!---------------------------------------------------------------------------      
      USE stel_kinds
      IMPLICIT NONE
 
 
      REAL(rprec), DIMENSION(3), INTENT(IN) ::                                 &
     &            vec           ! 3D vector
 
      magnitude = sqrt( vec(1)*vec(1) + vec(2)*vec(2) + vec(3)*vec(3) )
 
      RETURN
      END FUNCTION magnitude
 
!=============================================================================
      SUBROUTINE unit_vector(v1, v1_unit)
!--------------------------------------------------------------------------
! FUNCTION: calculates the magnitude of 3D input vector.  
!
!---------------------------------------------------------------------------      
      USE stel_kinds
      IMPLICIT NONE
 
      REAL(rprec), DIMENSION(3), INTENT(IN) ::                                 &
     &            v1           ! 3D vector
 
      REAL(rprec), DIMENSION(3), INTENT(OUT) ::                                &
     &            v1_unit        ! 3D vector
 
      v1_unit = v1 / magnitude(v1)
 
      RETURN
      END SUBROUTINE unit_vector
 
 
!=============================================================================
      REAL(KIND=rprec) FUNCTION dist(v1, v2)
!--------------------------------------------------------------------------
! FUNCTION: calculates the absolute distance between 2 input vectors.  
!
!---------------------------------------------------------------------------      
      USE stel_kinds
      IMPLICIT NONE
 
      REAL(rprec), DIMENSION(3), INTENT(IN) ::                                 &
     &            v1, v2           ! 3D vectors
 
      REAL(rprec), DIMENSION(3) ::                                             &
     &            v3           ! difference vector btwn v1 & v2
 
      v3 = abs( v2 - v1 )
      dist = sqrt( v3(1)*v3(1) + v3(2)*v3(2) + v3(3)*v3(3) )
 
      RETURN
      END FUNCTION dist
 
!==================================================================================
      SUBROUTINE cross_product(A, B, C)
!----------------------------------------------------------------------------------
!  FUNCTION:  computes the cross product (C) for input CARTESIAN vectors A and B.
!
!  LOGIC:  C = A .cross. B
!
!  created by J. Shields 2/15/06
!
!--------------------------------------------------------------------------------------
      USE stel_kinds
      IMPLICIT NONE
 
!........passed variables....................................................!
      REAL(rprec), DIMENSION(3), INTENT(IN) ::  A   ! input Cartesian vector
 
      REAL(rprec), DIMENSION(3), INTENT(IN) ::  B   ! input Cartesian vector
 
      REAL(rprec), DIMENSION(3), INTENT(OUT) :: C   ! Cross product:  A .cross. B
 
      
!.................local variables...................................!
      INTEGER(iprec) :: i
      character(len=*), PARAMETER ::  subname = 'CROSS_PRODUCT'
 
 
!..................X component.....................................!
      c(1) = a(2) * b(3)  -  a(3) * b(2)  
 
!...................Y component.....................................!
      c(2) = a(3) * b(1)  -  a(1) * b(3) 
 
!...................Z component.....................................!
      c(3) = a(1) * b(2)  -  a(2) * b(1)  
 
      RETURN
      END SUBROUTINE cross_product
 
 
      END MODULE math_utilities