C ++********************************************************************
C                                                                      *
C    FOURING.F                                                         *
C                                                                      *
C **********************************************************************
C=* FROM: SPIDER - MODULAR IMAGE PROCESSING SYSTEM.   AUTHOR: J.FRANK  *
C=* Copyright (C) 1985-2005  Health Research Inc.                      *
C=*                                                                    *
C=* HEALTH RESEARCH INCORPORATED (HRI),                                *   
C=* ONE UNIVERSITY PLACE, RENSSELAER, NY 12144-3455.                   *
C=*                                                                    *
C=* Email:  spider@wadsworth.org                                       *
C=*                                                                    *
C=* This program is free software; you can redistribute it and/or      *
C=* modify it under the terms of the GNU General Public License as     *
C=* published by the Free Software Foundation; either version 2 of the *
C=* License, or (at your option) any later version.                    *
C=*                                                                    *
C=* This program is distributed in the hope that it will be useful,    *
C=* but WITHOUT ANY WARRANTY; without even the implied warranty of     *
C=* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU  *
C=* General Public License for more details.                           *
C=*                                                                    *
C=* You should have received a copy of the GNU General Public License  *
C=* along with this program; if not, write to the                      *
C=* Free Software Foundation, Inc.,                                    *
C=* 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.      *
C=*                                                                    *
C **********************************************************************
C                                                                      *
C                                                                      *
C                                                                      *
C  PURPOSE:                                                            *
C                                                                      *
C  PARAMETERS:
C             
C IMAGE_PROCESSING_ROUTINE                                             *
C                                                                      *
C        0         2         3         4         5         6         7 *
C23456789012345678901234567890123456789012345678901234567890123456789012
C***********************************************************************

        SUBROUTINE  FOURING(CIRC,LCIRC,NUMR,NRING,EO,MODE)

        INTEGER  NUMR(3,NRING)
        DIMENSION  CIRC(LCIRC)
        CHARACTER*1  MODE
        DOUBLE PRECISION  E,EO,QT,PI


        PI=4.0*DATAN(1.0D0)
        IF(MODE.EQ.'F')  PI=2*PI
        E=0.0
c$omp parallel do private(i,j,nsirt,qt,l),reduction(+:e)
        DO    I=1,NRING
           NSIRT=NUMR(3,I)
           QT=REAL(NUMR(1,I))*PI/REAL(NSIRT)
           DO    J=NUMR(2,I),NUMR(2,I)+NSIRT-1
              E=E+QT*DBLE(CIRC(J))*CIRC(J)
           ENDDO
        ENDDO
        EO=E
c$omp parallel do private(i,l)
        DO    I=1,NRING
           L=LOG2(NUMR(3,I))
           CALL  FFTR_Q(CIRC(NUMR(2,I)),L)
        ENDDO
        END