C++*********************************************************************
C
C $$ FMR_1.FOR
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  1D real mixed radix FFT.
C   Order of elements:
C    for N even
C  R(0), R(N/2), R(1), I(1), R(2), I(2), ....., R(N/2-1), I(N/2-1)
C
C    for N odd
C  R(0), I(N/2), R(1), I(1), R(2), I(2), ....., R(N/2-1), I(N/2-1), R(N/2) 
C
C
C IMAGE_PROCESSING_ROUTINE                                                                     
C        0         2         3         4         5         6         7 
C23456789012345678901234567890123456789012345678901234567890123456789012
C--*********************************************************************

         SUBROUTINE  FMR_1(X,N,WORK,INV)

         DIMENSION  X(N),WORK(N)
C INV CAN BE +1 (FORWARD FFT) OR -1 (INVERSE FFT)

         IF(INV)  2,2,1
1        DO    I=1,N
            WORK(I)=0.0
         ENDDO
         CALL FFTMCF(X,WORK,N,N,N,INV)
         IF(MOD(N,2))  12,12,13
12       WORK(1)=X(N/2+1)
         DO    I=N-1,3,-2
            X(I)=X((I+1)/2)
            X(I+1)=WORK((I+1)/2)
         ENDDO
         X(2)=WORK(1)
         RETURN
13       X(N)=X(N/2+1)
         DO    I=N-2,3,-2
            X(I)=X(I/2+1)
            X(I+1)=WORK(I/2+1)
         ENDDO
         X(2)=WORK(N/2+1)
         RETURN

2        IF(MOD(N,2))  22,22,23
22       WORK(N/2+1)=0.0
         DO    I=2,N/2
            WORK(I)=X(2*I)/N
            WORK(N-I+2)=-WORK(I)
         ENDDO
         WORK(1)=X(2)/N
         X(1)=X(1)/N
         DO    I=2,N/2
            X(I)=X(2*I-1)/N
         ENDDO
         DO    I=N/2+2,N
            X(I)=X(N-I+2)
         ENDDO
         X(N/2+1)=WORK(1)
         GOTO  31
23       WORK(N/2+1)=X(2)/N
         WORK(N/2+2)=-X(2)/N
         DO    I=2,N/2
            WORK(I)=X(2*I)/N
            WORK(N-I+2)=-WORK(I)
         ENDDO
         X(1)=X(1)/N
         DO    I=2,N/2+1
            X(I)=X(2*I-1)/N
         ENDDO
         DO    I=N,N/2+2,-1
            X(I)=X(N-I+2)
         ENDDO

31       WORK(1)=0.0
         CALL FFTMCF(X,WORK,N,N,N,INV)
         END