C     =================================================================
C     PROGRAM FOR COMPUTING NEAREST CORRELATION MATRIX BY DIFFERENTIAL
C     EVOLUTION METHOD OF GLOBAL OPTIMIZATION  WRITTEN BY:
C       PROF. SK MISHRA, DEPARTMENT OF ECONOMICS, NEHU, SHILLONG INDIA
C                     APRIL 2007 : AVAILABLE AT:
C                   http//www.webng.com/economics
C                                  AND
C                 http://freewebs.com/nehu_economics
C     =================================================================
      PARAMETER (MX=10)! PRESENTLY SET AT 10. ONE MAY CHANGE IT.
C      ACCORDINGLY IT HAS TO BE CHANGED IN OTHER SUBROUTINES ALSO.
      IMPLICIT DOUBLE PRECISION (A-H,O-Z)
      COMMON /RNDM/IU,IV
      COMMON /KFF/KF,NFCALL,Q
      COMMON /EIGENS/VO(MX,MX),WO(MX,MX),WEIGHT(MX,MX),PPROD,PROD,NORM
      INTEGER IU,IV
      CHARACTER *70 FTIT,INFIL,INWFIL,OUTFIL
      DIMENSION Q(MX,MX),QQ(MX,MX),V(MX,MX),W(MX,MX),P(MX),R(MX,MX)
      CALL FSELECT(KF,M,FTIT)
C     READ THE Q (INVALID CORRELATION MATRIX) FROM INPUT FILE
      WRITE(*,*)'FILE THAT STORES Q (INVALID CORRELATION MATRIX) ?'
      READ(*,*) INFIL
      OPEN(7,FILE=INFIL)
      DO I=1,M
      READ(7,*) (Q(I,J),J=1,M) ! Q IS THE INVALID CORRELATION MATRIX
      DO J=1,M
      QQ(I,J)=Q(I,J) ! Q IS STORED IN QQ TO PRESERVE THE ORIGINAL MATRIX
      ENDDO
      ENDDO
      CLOSE(7)
      WRITE(*,*)'ANY WEIGHT MATRIX ? YES (1/ NON-ZERO), NO (0)'
      READ(*,*) NW
      IF(NW.NE.0) THEN
      WRITE(*,*)'FILE IN WHICH WEIGHT MATRIX HAS BEEN STORED ?'
      READ(*,*) INWFIL
      OPEN(7, FILE=INWFIL)
      DO I=1,M
      READ(7,*)(WEIGHT(I,J),J=1,M)
      ENDDO
      CLOSE(7)
      ELSE
      DO I=1,M
      DO J=1,M
      WEIGHT(I,J)=1.D0
      ENDDO
      ENDDO
      ENDIF
      WRITE(*,*)'CHOOSE THE NORM [ABS(1),FROBENIUS(2),CHEBYSHEV(=>99)]?'
      READ(*,*) NORM
      WRITE(*,*)'CHOOSE A SMALL(SUGGESTED 0.01)GUARD DETERMINANT[>ZERO]'
      WRITE(*,*)'[THIS GUARD DOES NOT ALLOW THE RESULTING NEAREST MATRIX
     & TO BECOME NEARSINGULAR]'
      READ(*,*) PPROD
      WRITE(*,*) 'GIVE AN OUTPUT FILE NAME TO STORE RESULTS'
      READ(*,*) OUTFIL
      OPEN(11,FILE=OUTFIL)! OPENS OUTPUT FILE
C     FIND EIGENVALUES AND EIGENVECTORS OF Q MATRIX
      CALL EIGEN(Q,VO,WO,M)
C-----------------------------------------------------------------------
      WRITE(*,*)'ORIGINAL MATRIX'
      WRITE(11,*)'ORIGINAL MATRIX'
      DO I=1,M
      WRITE(*,1)(Q(I,J),J=1,M)
      WRITE(11,1)(Q(I,J),J=1,M)
      ENDDO
    1 FORMAT(15F8.4) ! OUTPUT FORMAT. ONE MAY CHANGE IT AS NEEDED.
      WRITE(*,*)'EIGENVALUES'
      WRITE(11,*)'EIGENVALUES'
      DO I=1,M
      WRITE(*,2)(WO(I,J),J=1,M)
      WRITE(11,2)(WO(I,J),J=1,M)
      ENDDO
    2 FORMAT(10F12.7)! OUTPUT FORMAT. ONE MAY CHANGE IT AS NEEDED.
C-----------------------------------------------------------------------
C     CHECK IF ANY EIGENVALUE IS NEGATIVE
      LNEG=0
      DO I=1,M
      IF(WO(I,I).LT.0) LNEG=1 ! IF ANY EIGENVALUE NEGETIVE LNEG=1
      ENDDO
      IF(LNEG.EQ.1) THEN
      CALL DE(M,P,FBEST,FTIT) ! P IS THE VECTOR OF EIGENVALUES
      ENDIF
      CALL EIGEN(QQ,V,W,M)
C-----------------------------------------------------------------------
      LNEG=0
      DO I=1,M
      IF(W(I,I).LT.0) LNEG=1
      ENDDO
      DO I=1,M
      W(I,I)=P(I)
      ENDDO
      DO  J=1,M
      DO  JJ=1,M
      R(J,JJ)=0.0
      DO  I=1,M
      R(J,JJ)=R(J,JJ)+V(J,I)*W(I,JJ)
      ENDDO
      ENDDO
      ENDDO
      DO  J=1,M
      DO  JJ=1,M
      W(J,JJ)=0.0
      DO  I=1,M
      W(J,JJ)=W(J,JJ)+R(J,I)*V(JJ,I)
      ENDDO
      ENDDO
      ENDDO
      DO  I=1,M
      DO  J=1,M
      R(I,J)=W(I,J)
      ENDDO
      R(I,I)=1.0
      ENDDO
      CALL EIGEN(R,V,W,M)
      F=0
      DO I=1,M
      DO J=1,M
      DIF=DABS(Q(I,J)-R(I,J))
      IF(NORM.LT.99) THEN
      F=F+WEIGHT(I,J)*DIF**NORM
      ELSE
      IF(DIF*WEIGHT(I,J).GT.F) F=DIF*WEIGHT(I,J)
      ENDIF
      ENDDO
      ENDDO
      IF(LNEG.NE.0) THEN
      WRITE(*,*)' '
      WRITE(*,*)'-----------------------------------------------------'
      WRITE(*,*)'ESTIMATED MATRIX ------------------------------------'
      WRITE(*,*)' '
      WRITE(11,*)' '
      WRITE(11,*)'-----------------------------------------------------'
      WRITE(11,*)'ESTIMATED MATRIX ------------------------------------'
      WRITE(11,*)' '
      DO I=1,M
      WRITE(*,3)(R(I,J),J=1,M)
      WRITE(11,3)(R(I,J),J=1,M)
      ENDDO
    3 FORMAT(12F12.8) ! OUTPUT FORMAT. ONE MAY CHANGE IT AS NEEDED.
      WRITE(*,*)' '
      WRITE(*,*)'MIN NORM WITH PENALTIES (NOT TO BE INTERPRETED)=',F
      WRITE(11,*)' '
      WRITE(11,*)'MIN NORM WITH PENALTIES (NOT TO BE INTERPRETED)=',F
      SUM=0
      DET=1.D0
      DO I=1,M
      SUM=SUM+W(I,I)
      DET=DET*W(I,I)
      ENDDO
      WRITE(*,*)' '
      WRITE(*,*)'EIGENVALUES'
      WRITE(*,2)(W(I,I),I=1,M)
      WRITE(*,*)' '
      WRITE(11,*)' '
      WRITE(11,*)'EIGENVALUES'
      WRITE(11,2)(W(I,I),I=1,M)
      WRITE(11,*)' '
      WRITE(*,*)'SUM AND PRODUCT OF EIGENVALUES=',SUM,DET
      WRITE(11,*)'SUM AND PRODUCT OF EIGENVALUES=',SUM,DET
      ENDIF
      IF(LNEG.EQ.0) THEN
      WRITE(*,*)'THE GIVEN MATRIX IS VALID (POSITIVE SEMI-DEFINITE).'
      WRITE(11,*)'THE GIVEN MATRIX IS VALID (POSITIVE SEMI-DEFINITE).'
      ELSE
      WRITE(*,*)'THE RESULT MATRIX IS VALID (POSITIVE SEMI-DEFINITE).'
      WRITE(11,*)'THE RESULT MATRIX IS VALID (POSITIVE SEMI-DEFINITE).'
      ENDIF
      CLOSE(11)
      END
C     -----------------------------------------------------------------
      SUBROUTINE FUNC(X,M,F)
C     FINDING THE NEAREST CORRELATION MATRIX BY DIFFERENTIAL
C     EVOLUTION METHOD OF GLOBAL OPTIMIZATION  WRITTEN BY
C     PROF. SK MISHRA, DEPARTMENT OF ECONOMICS, NEHU, SHILLONG INDIA
      PARAMETER (MX=10)! PRESENTLY SET AT 10. ONE MAY CHANGE IT.
C      ACCORDINGLY IT HAS TO BE CHANGED IN MAIN/OTHER SUBROUTINES ALSO.
C      THIS SUBROUTINE IS MEANT FOR USE BY GLOBAL OPTIMIZATION PROGRAM
      IMPLICIT DOUBLE PRECISION (A-H,O-Z)
      COMMON /RNDM/IU,IV
      COMMON /KFF/KF,NFCALL,Q
      COMMON /EIGENS/VO(MX,MX),WO(MX,MX),WEIGHT(MX,MX),PPROD,PROD,NORM
      INTEGER IU,IV
      DIMENSION X(*),Q(MX,MX),W(MX,MX),V(MX,MX),R(MX,MX)
      NFCALL=NFCALL+1 ! INCREMENT TO NUMBER OF FUNCTION CALLS
C     KF IS THE CODE OF THE TEST FUNCTION
C     -----------------------------------------------------------------
      LNEG=0
      DO I=1,M
      IF(WO(I,I).LT.0) LNEG=1
      ENDDO
      IF(LNEG.EQ.1) THEN
      SUM=0
      PROD=1.D0
      DO I=1,M
      IF(X(I).LT.0) THEN
      CALL RANDOM(RAND)
      X(I)=RAND
      ENDIF
      SUM=SUM+X(I)
      PROD=PROD*X(I)
      ENDDO
      DO I=1,M
      X(I)=X(I)*M/SUM
      ENDDO
      DO I=1,M
      W(I,I)=X(I)
      ENDDO

      DO  J=1,M
      DO  JJ=1,M
      R(J,JJ)=0.0
      DO  I=1,M
      R(J,JJ)=R(J,JJ)+VO(J,I)*W(I,JJ)
      ENDDO
      ENDDO
      ENDDO
      DO  J=1,M
      DO  JJ=1,M
      W(J,JJ)=0.0
      DO  I=1,M
      W(J,JJ)=W(J,JJ)+R(J,I)*VO(JJ,I)
      ENDDO
      ENDDO
      ENDDO
      DO  I=1,M
      DO  J=1,M
      R(I,J)=W(I,J)
      ENDDO
      R(I,I)=1.0
      ENDDO

      CALL EIGEN(R,V,W,M)
      PF=0
      SUM=0
      DO I=1,M
      SUM=SUM+W(I,I)
      IF(W(I,I).LT.0) PF=PF+100+(100*(1-W(I,I)))**2
      ENDDO
      F=0
      DO I=1,M
      F=F+100*(1.D0-R(I,I))**2
      ENDDO
      FN=0.0
      FX=0
      DO I=1,M-1
      DO J=I+1,M
      DIF=DABS(Q(I,J)-R(I,J))
      WDIF=DIF*WEIGHT(I,J)
      IF(WDIF.GT.FX) FX=WDIF
      IF(NORM.LT.99)FN=FN+WEIGHT(I,J)*DIF**NORM
      ENDDO
      ENDDO
      FNN=2*FN
      FN=0
      DO I=1,M
      DIF=DABS(Q(I,I)-R(I,I))
      WDIF=DIF*WEIGHT(I,I)
      IF(WDIF.GT.FX) FX=WDIF
      IF(NORM.LT.99)FN=FN+WEIGHT(I,I)*DIF**NORM
      ENDDO

         IF(NORM.LT.99) THEN
         F=F+FNN+FN+PF+DABS(SUM-M)*100
         ELSE
         F=F+FX+PF+DABS(SUM-M)*100
         ENDIF
      ENDIF
      IF(PROD.LT.PPROD) F=F+(1000*(PPROD-PROD))**2

      RETURN
      END
C     -----------------------------------------------------------------
      SUBROUTINE DE(M,A,FBEST,FTIT)
C     PROGRAM: "DIFFERENTIAL EVOLUTION ALGORITHM" OF GLOBAL OPTIMIZATION
C     THIS METHOD WAS PROPOSED BY R. STORN AND K. PRICE IN 1995. REF --
C     "DIFFERENTIAL EVOLUTION - A SIMPLE AND EFFICIENT ADAPTIVE SCHEME
C     FOR GLOBAL OPTIMIZATION OVER CONTINUOUS SPACES" : TECHNICAL REPORT
C     INTERNATIONAL COMPUTER SCIENCE INSTITUTE, BERKLEY, 1995.
C     PROGRAM BY PROF SK MISHRA, DEPT OF ECONOMICS,NEHU,SHILLONG(INDIA)
C     -----------------------------------------------------------------
C     PROGRAM DE :  DIFFERENTIAL EVOLUTION OPTIMIZER
      IMPLICIT DOUBLE PRECISION (A-H, O-Z) ! TYPE DECLARATION
C     -----------------------------------------------------------------
      PARAMETER (MX=10)! PRESENTLY SET AT 10. ONE MAY CHANGE IT.
C      ACCORDINGLY IT HAS TO BE CHANGED IN MAIN/OTHER SUBROUTINES ALSO.
C     -----------------------------------------------------------------
      PARAMETER(NMAX=1000,MMAX=100) ! MAXIMUM DIMENSION PARAMETERS
      PARAMETER(RX1=0, RX2=0) ! CROSSOVER SCHEME (NCROSS<=0, 1, =>2)
      PARAMETER(IPRINT=500,EPS=1.D-08)!FOR WATCHING INTERMEDIATE RESULTS
C     IT PRINTS THE INTERMEDIATE RESULTS AFTER EACH IPRINT ITERATION AND
C     EPS DETERMINES ACCURACY FOR TERMINATION. IF EPS= 0, ALL ITERATIONS
C     WOULD BE UNDERGONE EVEN IF NO IMPROVEMENT IN RESULTS IS THERE.
C     ULTIMATELY "DID NOT CONVERGE" IS REOPORTED.
      COMMON /RNDM/IU,IV ! RANDOM NUMBER GENERATION (IU = 4-DIGIT SEED)
C     INTEGER IU,IV      ! FOR RANDOM NUMBER GENERATION
      COMMON /KFF/KF,NFCALL,Q ! FUNCTION CODE AND NO. OF FUNCTION CALLS
      COMMON /EIGENS/VO(MX,MX),WO(MX,MX),WEIGHT(MX,MX),PPROD,PROD,NORM
      CHARACTER *70 FTIT ! TITLE OF THE FUNCTION
C     -----------------------------------------------------------------
C     THE PROGRAM REQUIRES INPUTS FROM THE USER ON THE FOLLOWING ------
C     (1) FUNCTION CODE (KF), (2) NO. OF VARIABLES IN THE FUNCTION (M);
C     (3) N=POPULATION SIZE (SUGGESTED 10 TIMES OF NO. OF VARIABLES, M,
C         FOR SMALLER PROBLEMS N=100 WORKS VERY WELL);
C     (4) PCROS = PROB. OF CROSS-OVER (SUGGESTED : ABOUT 0.85 TO .99);
C     (5) FACT = SCALE (SUGGESTED 0.5 TO .95 OR SO);
C     (6) ITER = MAXIMUM NUMBER OF ITERATIONS PERMITTED (5000 OR MORE)
C     (7) RANDOM NUMBER SEED (4 DIGITS INTEGER)
C     ----------------------------------------------------------------
      DIMENSION X(NMAX,MMAX),Y(NMAX,MMAX),A(MMAX),FV(NMAX),Q(MX,MX)
      DIMENSION IR(3)
C     ----------------------------------------------------------------
C     ------- SELECT THE FUNCTION TO MINIMIZE AND ITS DIMENSION -------
C     SPECIFY OTHER PARAMETERS ---------------------------------------
      WRITE(*,*)'POPULATION SIZE [N] AND NO. OF ITERATIONS [ITER] ?'
      WRITE(*,*)'SUGGESTED: MAX(100, 10.M); ITER 10000 OR SO'
      READ(*,*) N,ITER
      WRITE(*,*)'CROSSOVER PROBABILITY [PCROS] AND SCALE [FACT] ?'
      WRITE(*,*)'SUGGESTED: PCROS ABOUT 0.9; FACT=.5 OR LARGER BUT <=1'
      READ(*,*) PCROS,FACT
      WRITE(*,*)'RANDOM NUMBER SEED ?'
      WRITE(*,*)'A FOUR-DIGIT POSITIVE ODD INTEGER, SAY, 1171'
      READ(*,*) IU

      NFCALL=0 ! INITIALIZE COUNTER FOR FUNCTION CALLS
      GBEST=1.D30 ! TO BE USED FOR TERMINATION CRITERION
C     INITIALIZATION : GENERATE X(N,M) RANDOMLY
      DO I=1,N
      DO J=1,M
      CALL RANDOM(RAND)
      X(I,J)=RAND*M
C     RANDOM NUMBERS BETWEEN -RRANGE AND +RRANGE (BOTH EXCLUSIVE)
      ENDDO
      ENDDO
      WRITE(*,*)'COMPUTING --- PLEASE WAIT '
      IPCOUNT=0
      DO 100 ITR=1,ITER  ! ITERATION BEGINS
C     ===================== RANDOMIZATION OF NCROSS ===================
C     RANDOMIZES NCROSS
      NCROSS=0
      CALL RANDOM(RAND)
      IF(RAND.GT.RX1) NCROSS=1
      IF(RAND.GT.RX2) NCROSS=2
C     ------------------------------------------------------------------
C     EVALUATE ALL X FOR THE GIVEN FUNCTION
      DO I=1,N
      DO J=1,M
      A(J)=X(I,J)
      ENDDO
      CALL FUNC(A,M,F)
C     STORE FUNCTION VALUES IN FV VECTOR
      FV(I)=F
      ENDDO
C     ----------------------------------------------------------------
C     FIND THE FITTEST (BEST) INDIVIDUAL AT THIS ITERATION
                FBEST=FV(1)
                KB=1
                DO IB=2,N
                     IF(FV(IB).LT.FBEST) THEN
                     FBEST=FV(IB)
                     KB=IB
                     ENDIF
                ENDDO
C     BEST FITNESS VALUE = FBEST : INDIVIDUAL X(KB)
C     -----------------------------------------------------------------
C     GENERATE OFFSPRINGS
      DO I=1,N    ! I LOOP BEGINS
C     INITIALIZE CHILDREN IDENTICAL TO PARENTS; THEY WILL CHANGE LATER
           DO J=1,M
           Y(I,J)=X(I,J)
           ENDDO
C     SELECT RANDOMLY THREE OTHER INDIVIDUALS
   20     DO IRI=1,3  ! IRI LOOP BEGINS
          IR(IRI)=0

          CALL RANDOM(RAND)
           IRJ=INT(RAND*N)+1
C     CHECK THAT THESE THREE INDIVIDUALS ARE DISTICT AND OTHER THAN I
           IF(IRI.EQ.1.AND.IRJ.NE.I) THEN
           IR(IRI)=IRJ
           ENDIF
           IF(IRI.EQ.2.AND.IRJ.NE.I.AND.IRJ.NE.IR(1)) THEN
           IR(IRI)=IRJ
           ENDIF
       IF(IRI.EQ.3.AND.IRJ.NE.I.AND.IRJ.NE.IR(1).AND.IRJ.NE.IR(2)) THEN
            IR(IRI)=IRJ
            ENDIF
            ENDDO   ! IRI LOOP ENDS
C     CHECK IF ALL THE THREE IR ARE POSITIVE (INTEGERS)
          DO IX=1,3
          IF(IR(IX).LE.0) THEN
          GOTO 20  ! IF NOT THEN REGENERATE
          ENDIF
          ENDDO
C     THREE RANDOMLY CHOSEN INDIVIDUALS DIFFERENT FROM I AND DIFFERENT
C     FROM EACH OTHER ARE IR(1),IR(2) AND IR(3)
C     ----------------------------------------------------------------
C      NO CROSS OVER, ONLY REPLACEMENT THAT IS PROBABILISTIC
          IF(NCROSS.LE.0) THEN
          DO J=1,M
          CALL RANDOM(RAND)
          IF(RAND.LE.PCROS) THEN ! REPLACE IF RAND < PCROS
          A(J)=X(IR(1),J)+(X(IR(2),J)-X(IR(3),J))*FACT ! CANDIDATE
          ENDIF
          ENDDO
          ENDIF

C     -----------------------------------------------------------------
C     CROSSOVER SCHEME (EXPONENTIAL) SUGGESTED BY KENNETH PRICE IN HIS
C     PERSONAL LETTER TO THE AUTHOR (DATED SEPTEMBER 29, 2006)
      IF(NCROSS.EQ.1) THEN
        CALL RANDOM(RAND)
    1   JR=INT(RAND*M)+1
        J=JR
    2   A(J)=X(IR(1),J)+(X(IR(2),J)-X(IR(3),J))*FACT !CANDIDATE
    3   J=J+1
        IF(J.GT.M) J=1
    4   IF(J.EQ.JR) GOTO 10
    5   CALL RANDOM(RAND)
        IF(PCROS.LE.RAND) GOTO 2
    6   A(J)=X(I,J) ! CANDIDATE
    7   J=J+1
        IF(J.GT.M) J=1
    8   IF (J.EQ.JR) GOTO 10
    9   GOTO 6
   10   CONTINUE
      ENDIF
C     -----------------------------------------------------------------
C     THE SCHEME SUGGESTED BY KENNETH PRICE IN HIS PERSONAL LETTER TO
C     THE AUTHOR (DATED OCTOBER 19, 2006)
      IF(NCROSS.GE.2) THEN
          CALL RANDOM(RAND)
          IF(RAND.LE.PCROS) THEN
             CALL NORMAL(RN)
             DO J=1,M
C              CALL NORMAL(RN)
             A(J)=X(I,J)+(X(IR(1),J)+X(IR(2),J)-2*X(I,J))*RN ! CANDIDATE
             ENDDO
           ELSE
             DO J=1,M
             A(J)=X(I,J)+(X(IR(1),J)- X(IR(2),J))! FACT ASSUMED AS 1.
             ENDDO
           ENDIF
      ENDIF

C     -----------------------------------------------------------------
          CALL FUNC(A,M,F) ! EVALUATE THE OFFSPRING
          IF(F.LT.FV(I)) THEN ! IF BETTER, REPLACE PARENTS BY THE CHILD
          FV(I)=F
          DO J=1,M
          Y(I,J)=A(J)
          ENDDO
          ENDIF
      ENDDO   ! I LOOP ENDS
      DO I=1,N
      DO J=1,M
      X(I,J)=Y(I,J) ! NEW GENERATION IS A MIX OF BETTER PARENTS AND
C                     BETTER CHILDREN
      ENDDO
      ENDDO
      IPCOUNT=IPCOUNT+1
      IF(IPCOUNT.EQ.IPRINT) THEN
      DO J=1,M
      A(J)=X(KB,J)
      ENDDO
      WRITE(*,*)(X(KB,J),J=1,M),'  FBEST UPTO NOW = ',FBEST
      WRITE(*,*)'TOTAL NUMBER OF FUNCTION CALLS =',NFCALL
           IF(DABS(FBEST-GBEST).LT.EPS) THEN
           WRITE(*,*) FTIT
           WRITE(*,*)'COMPUTATION OVER'
           RETURN
           ELSE
           GBEST=FBEST
           ENDIF
      IPCOUNT=0
      ENDIF
C     ----------------------------------------------------------------
  100 ENDDO   ! ITERATION ENDS : GO FOR NEXT ITERATION, IF APPLICABLE
C     ----------------------------------------------------------------
      WRITE(*,*)'DID NOT CONVERGE. REDUCE EPS OR RAISE ITER OR DO BOTH'
      WRITE(*,*)'INCREASE N, PCROS, OR SCALE FACTOR (FACT)'
      RETURN
      END
C     -----------------------------------------------------------------
      SUBROUTINE NORMAL(R)
C     PROGRAM TO GENERATE N(0,1) FROM RECTANGULAR RANDOM NUMBERS
C     IT USES VARIATE TRANSFORMATION FOR THIS PURPOSE.
C     -----------------------------------------------------------------
C     IF U1 AND U2 ARE UNIFORMLY DISTRIBUTED RANDOM NUMBERS (0,1),
C     THEN X=[(-2*LN(U1))**.5]*(COS(2*PI*U2) IS N(0,1)
C     PI = 4*ARCTAN(1.0)= 3.1415926535897932384626433832795
C     2*PI = 6.283185307179586476925286766559
C     -----------------------------------------------------------------
      IMPLICIT DOUBLE PRECISION (A-H,O-Z)
      COMMON /RNDM/IU,IV
C     -----------------------------------------------------------------
      CALL RANDOM(RAND) ! INVOKES RANDOM TO GENERATE UNIFORM RAND [0, 1]
      U1=RAND ! U1 IS UNIFORMLY DISTRIBUTED [0, 1]
      CALL RANDOM(RAND) ! INVOKES RANDOM TO GENERATE UNIFORM RAND [0, 1]
      U2=RAND ! U1 IS UNIFORMLY DISTRIBUTED [0, 1]
      R=DSQRT(-2.D0*DLOG(U1))
C      R=R*DCOS(U2*6.283185307179586476925286766559D00)
      R=R*DCOS(U2*6.28318530718D00)
      RETURN
      END
C     ------------------------------------------------------------------
C     RANDOM NUMBER GENERATOR (UNIFORM BETWEEN 0 AND 1 - BOTH EXCLUSIVE)
      SUBROUTINE RANDOM(RAND)
       IMPLICIT DOUBLE PRECISION  (A-H, O-Z)
       COMMON /RNDM/IU,IV
       IV=IU*65539
       IF(IV.LT.0) THEN
       IV=IV+2147483647+1
       ENDIF
       RAND=IV
       IU=IV
       RAND=RAND*0.4656613E-09
       RETURN
       END
C     -----------------------------------------------------------------
      SUBROUTINE FSELECT(KF,M,FTIT)
C     THE PROGRAM REQUIRES INPUTS FROM THE USER ON THE FOLLOWING ------
C     (1) FUNCTION CODE (KF), (2) NO. OF VARIABLES IN THE FUNCTION (M);
      CHARACTER *70 TIT(1),FTIT
      WRITE(*,*)'----------------------------------------------------'
      DATA TIT(1)/'NEAREST CORRELATION MATRIX PROBLEM'/
C     -----------------------------------------------------------------
      KF=1
      WRITE(*,*)'      THE NEAREST CORRELATION MATRIX PROBLEM'
      WRITE(*,*)'THE METHOD AND PROGRAM DEVELOPED BY PROF. SK MISHRA'
      WRITE(*,*)' DEPT. OF ECONOMICS, NORTH-EASTERN HILL UNIVERSITY'
      WRITE(*,*)'                SHILLONG (INDIA)'
      WRITE(*,*)'----------------------------------------------------'
      WRITE(*,*)' '
      WRITE(*,*)'PLEASE FEED THE INFORMATION AS ASKED FOR'
      WRITE(*,*)' '
      WRITE(*,*)'DIMENSION OF THE INVALID CORRELATION MATRIX [M] ?'
      READ(*,*) M
      FTIT=TIT(KF) ! STORE THE NAME OF THE CHOSEN FUNCTION IN FTIT
      RETURN
      END
C ----------------------------------------------------
      SUBROUTINE EIGEN(A,V,W,N)
      PARAMETER (MX=10)! PRESENTLY SET AT 10. ONE MAY CHANGE IT.
C      ACCORDINGLY IT HAS TO BE CHANGED IN MAIN/OTHER SUBROUTINES ALSO.
C     KRISHNAMURTHY, EV AND SK SEN (1976). "COMPUTER-BASED NUMERICAL
C     ALGORITHMS", AFFILIATED EAST-WEST PRESS, NEW DELHI.
C     COMPUTES EIGENVALUES AND VECTORS OF A REAL SYMMETRIX MATRIX
      DOUBLE PRECISION A(MX,MX),V(MX,MX),W(MX,MX),P(MX)
      DOUBLE PRECISION PMAX,EPLN,TAN,SIN,COS,AI,TT,TA,TB
      DIMENSION MM(MX)
C ------------ INITIALISATION -------------------------
      DO 50 I=1,N
      DO 51 J=1,N
      V(I,J)=0.0
51    W(I,J)=A(I,J)
      P(I)=0.0
50    CONTINUE
      PMAX=0
      EPLN=0
      TAN=0
      SIN=0
      COS=0
      AI=0
      TT=0
      NN=1
      EPLN=1.0D-99
C ------------------------------------------------------
      IF(NN.NE.0) THEN
      DO 3 I=1,N
      DO 3 J=1,N
      V(I,J)=0.0
      IF(I.EQ.J) V(I,J)=1.0
3     CONTINUE
      ENDIF
2     NR=0
5     MI=N-1
      DO 6 I=1,MI
      P(I)=0.0
      MJ=I+1
      DO 6 J=MJ,N
      IF(P(I).GT.DABS(A(I,J))) GO TO 6
      P(I)=DABS(A(I,J))
      MM(I)=J
6      CONTINUE
7       DO 8 I=1,MI
        IF(I.LE.1) GOTO 10
        IF(PMAX.GT.P(I)) GOTO 8
10       PMAX=P(I)
         IP=I
         JP=MM(I)
8     CONTINUE
      IF (PMAX.LE.EPLN) THEN
      GO TO 12
      ENDIF
      NR=NR+1
13    TA=2.0*A(IP,JP)
      TB=(DABS(A(IP,IP)-A(JP,JP))+
     &DSQRT((A(IP,IP)-A(JP,JP))**2+4.0*A(IP,JP)**2))
      TAN=TA/TB
      IF(A(IP,IP).LT.A(JP,JP)) TAN=-TAN
14    COS=1.0/DSQRT(1.0+TAN**2)
      SIN=TAN*COS
      AI=A(IP,IP)
      A(IP,IP)=(COS**2)*(AI+TAN*(2.0*A(IP,JP)+TAN*A(JP,JP)))
      A(JP,JP)=(COS**2)*(A(JP,JP)-TAN*(2.0*A(IP,JP)-TAN*AI))
      A(IP,JP)=0.0
      IF(A(IP,IP).GE.A(JP,JP)) GO TO 15
      TT=A(IP,IP)
      A(IP,IP)=A(JP,JP)
      A(JP,JP)=TT
      IF(SIN.GE.0) GO TO 16
      TT=COS
      GO TO 17
16    TT=-COS
17    COS=DABS(SIN)
      SIN=TT
15    DO 18 I=1,MI
      IF(I-IP) 19, 18, 20
20    IF(I.EQ.JP)GO TO 18
19    IF(MM(I).EQ.IP) GO TO 21
      IF(MM(I).NE.JP) GO TO 18
21    K=MM(I)
      TT=A(I,K)
      A(I,K)=0.0
      MJ=I+1
      P(I)=0.0
      DO 22 J=MJ,N
      IF(P(I).GT.DABS(A(I,J))) GO TO 22
      P(I)=DABS(A(I,J))
      MM(I)=J
22    CONTINUE
      A(I,K)=TT
18    CONTINUE
      P(IP)=0.0
      P(JP)=0.0
      DO 23 I=1,N
      IF(I-IP) 24, 23, 25
24    TT=A(I,IP)
      A(I,IP)=COS*TT+SIN*A(I,JP)
      IF(P(I).GE.DABS(A(I,IP))) GO TO 26
      P(I)=DABS(A(I,IP))
      MM(I)=IP
26    A(I,JP)=-SIN*TT+COS*A(I,JP)
      IF(P(I).GE.DABS(A(I,JP))) GO TO 23
30    P(I)=DABS(A(I,JP))
      MM(I)=JP
      GO TO 23
25    IF(I.LT.JP) GO TO 27
      IF(I.GT.JP) GO TO 28
      IF(I.EQ.JP) GO TO 23
27    TT=A(IP,I)
      A(IP,I)=COS*TT+SIN*A(I,JP)
      IF(P(IP).GE.DABS(A(IP,I))) GO TO 29
      P(IP)=DABS(A(IP,I))
      MM(IP)=I
29    A(I,JP)=-TT*SIN+COS*A(I,JP)
      IF(P(I).GE.DABS(A(I,JP))) GO TO 23
      GO TO 30
28    TT=A(IP,I)
      A(IP,I)=TT*COS+SIN*A(JP,I)
      IF(P(IP).GE.DABS(A(IP,I))) GO TO 31
      P(IP)=DABS(A(IP,I))
      MM(IP)=I
31    A(JP,I)=-TT*SIN+COS*A(JP,I)
      IF(P(JP).GE.DABS(A(JP,I))) GO TO 23
      P(JP)=DABS(A(JP,I))
      MM(JP)=I
23    CONTINUE
      IF(NN.EQ.0) GOTO 7
      DO 32 I=1,N
      TT=V(I,IP)
      V(I,IP)=TT*COS+SIN*V(I,JP)
      V(I,JP)=-TT*SIN+COS*V(I,JP)
32    CONTINUE
      GO TO 7
12    DO I=1,N
      DO J=1,N
      TEMP=A(I,J)
      A(I,J)=W(I,J)
      W(I,J)=TEMP
      ENDDO
      ENDDO
      DO I=1,N
      DO J=1,N
      IF(I.NE.J) W(I,J)=0.0
      ENDDO
      ENDDO
C     NOW A STORES THE ORIGINAL MATRIX, W(I,I) STORES WIGENVALUES AND
C     V STORES EIGENVECTORS
      RETURN
      END