source: trunk/LMDZ.PLUTO/libf/muphypluto/lint_core.F90 @ 3608

! Copyright (c) Université de Reims Champagnne-Ardenne (2010-2015)
! Contributor: Jérémie Burgalat (jeremie.burgalat@univ-reims.fr)
! 
! This software is a computer program whose purpose is to compute multi-variate
! linear interpolation.
! 
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! abiding by the rules of distribution of free software.  You can  use, 
! modify and/ or redistribute the software under the terms of the CeCILL-B
! license as circulated by CEA, CNRS and INRIA at the following URL
! "http://www.cecill.info". 
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!! File:    lint_core.F90
!! Summary: Linear interpolation core function file
!! Author:  J. Burgalat
!! Date:    2010-2014

MODULE LINT_CORE
    !! Core module of the library.
    !! 
    !! This module contains a single function that performs the linear 
    !! interpolation of a single _N_-D point between \(2^{N}\) adjacents 
    !! points.
    USE LINT_PREC
    IMPLICIT NONE
  
    PRIVATE :: wp ! from LINT_PREC
  
    INTERFACE
      FUNCTION locate(value,vector) RESULT(idx)
        !! Locate the nearest default value in vector
        !!
        !! the method should search the subscript of the nearest value by default in
        !! in the input vector.
        IMPORT wp
        REAL(kind=wp), INTENT(in)               :: value   !! value to search 
        REAL(kind=wp), INTENT(in), DIMENSION(:) :: vector  !! Vector to search in
        INTEGER :: idx                                     !! Subscript of the nearest value in vector
      END FUNCTION locate
    END INTERFACE
  
  
    CONTAINS 
  
    FUNCTION lintc_(point,grid) RESULT(res)
      !! Multivariate linear interpolation core function
      !! 
      !! The method computes multivariate linear interpolation at the given __point__ using its 
      !! neighbours given in __grid__.
      !!
      !! @warning
      !! In order to get a correct result, __grid__ must be ordered so first dimensions vary first 
      !! (see [Generic method](page/index.html/#generic-method) section of main documentation).
      !!
      !! @warning 
      !! The method in its current version does not check array boundaries. This operation should be 
      !! performed in wrappers of the function !
      INTEGER, PARAMETER :: np = 2 
      REAL(kind=wp), INTENT(in), DIMENSION(:)   :: point 
        !! Coordinates of the point to compute.
        !!
        !! For __N__-D interpolation, ut should be a vector of __N__ points.
      REAL(kind=wp), INTENT(in), DIMENSION(:,:) :: grid
        !! Grid of values used for interpolation. 
        !!
        !! For __N__-D interpolation, it should be a 2D-array of \(2^{N}\) rows and \(N+1\) columns. 
        !! Each row corresponds to a point with N coordinates, the last column is reserved for the
        !! value of the point.
      REAL(kind=wp) :: res
        !! Interpolated value
      REAL(kind=wp), DIMENSION(:),ALLOCATABLE :: val
      REAL(kind=wp)                           :: cd
      INTEGER                                 :: nv,mi,ngp,cp,i,j,k
      nv = SIZE(point) ; mi = np**nv
      ALLOCATE(val(2*mi-1)) 
      val(1:mi) = grid(:,nv+1) ; val(mi+1:2*mi-1) = 0._wp
      ! Computes the QnD linear interpolation
      cp = 0
      DO i=1,nv
        cd = (point(i)-grid(1,i))/(grid(mi,i)-grid(1,i))
        k = 1 ; ngp = np**(nv-i+1) ; cp = cp + ngp
        DO j=1,ngp,np 
          val(cp+k) = val(j+cp-ngp) * (1._wp - cd) + val(j+cp-ngp+1)*cd
          k = k + 1
        ENDDO
      ENDDO
      res = val(cp+k-1) 
      DEALLOCATE(val) ! useless normally
      RETURN
    END FUNCTION lintc_
  
  END MODULE LINT_CORE