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|
*DECK BIVALL
SUBROUTINE BIVALL (MAXPTS,IHEX,NH,NTH,ITAB)
*
*-----------------------------------------------------------------------
*
*Purpose:
* Unfold any hexagonal geometry to produce a complete domain.
*
*Copyright:
* Copyright (C) 2002 Ecole Polytechnique de Montreal
* This library is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version
*
*Author(s): A. Benaboud
*
*Parameters: input
* MAXPTS maximum number of hexagons.
* IHEX type of symmetry:
* =1: S30; =2: SA60; =3: SB60; =4: S90; =5: R120;
* =6: R180; =7: SA180; =8: SB180; =9: COMPLETE.
* NH total number of hexagons in the partial hexagonal geometry.
*
*Parameters: output
* NTH total number of hexagons in the complete geometry.
* ITAB correspondance table.
*
*-----------------------------------------------------------------------
*
*----
* SUBROUTINE ARGUMENTS
*----
INTEGER MAXPTS,IHEX,NH,NTH,ITAB(MAXPTS)
*----
* LOCAL VARIABLES
*----
LOGICAL LPAIR
CHARACTER TEXT4*4
INTEGER NP(7)
INTEGER, DIMENSION(:), ALLOCATABLE :: J1,J2,J3,K1,K2,K3,K4
*
NC=0
IF((IHEX.EQ.1).OR.(IHEX.EQ.10)) THEN
VI = 2.* SQRT(REAL(NH)) - 1.
VP = SQRT(REAL(4*NH+1)) - 1.
IF(AINT(VI).EQ.VI) THEN
NC = INT(VI)
ELSE IF(AINT(VP).EQ.VP) THEN
NC = INT(VP)
ELSE
CALL XABORT('BIVALL: INVALID NUMBER OF HEXAGONS (1).')
ENDIF
ELSE IF((IHEX.EQ.2).OR.(IHEX.EQ.11)) THEN
VA = (SQRT(REAL(8*NH+1)) - 1.)/2.
IF(AINT(VA).EQ.VA) THEN
NC = INT(VA)
ELSE
CALL XABORT('BIVALL: INVALID NUMBER OF HEXAGONS (2).')
ENDIF
ELSE IF(IHEX.EQ.3) THEN
VI = SQRT(REAL(2*NH-1))
VP = SQRT(REAL(2*NH))
IF(AINT(VI).EQ.VI) THEN
NC = INT(VI)
ELSE IF(AINT(VP).EQ.VP) THEN
NC = INT(VP)
ELSE
CALL XABORT('BIVALL: INVALID NUMBER OF HEXAGONS (3).')
ENDIF
ELSE IF(IHEX.EQ.4) THEN
VI = SQRT(REAL((4*NH-1)/3))
VP = SQRT(REAL(4*NH/3))
IF(AINT(VI).EQ.VI) THEN
NC = INT(VI)
ELSE IF(AINT(VP).EQ.VP) THEN
NC = INT(VP)
ELSE
CALL XABORT('BIVALL: INVALID NUMBER OF HEXAGONS (4).')
ENDIF
ELSE IF(IHEX.EQ.5) THEN
VA = (SQRT(REAL(4*(NH-1)+1)) + 1.)/2.
IF(AINT(VA).EQ.VA) THEN
NC = INT(VA)
ELSE
CALL XABORT('BIVALL: INVALID NUMBER OF HEXAGONS (5).')
ENDIF
ELSE IF(IHEX.EQ.6) THEN
VA = (SQRT(REAL(8*(NH-1)/3+1)) + 1)/2
IF(AINT(VA).EQ.VA) THEN
NC = INT(VA)
ELSE
CALL XABORT('BIVALL: INVALID NUMBER OF HEXAGONS (6).')
ENDIF
ELSE IF(IHEX.EQ.7) THEN
VA = (SQRT(REAL(24*NH+1)) + 1.)/6.
IF(AINT(VA).EQ.VA) THEN
NC = INT(VA)
ELSE
CALL XABORT('BIVALL: INVALID NUMBER OF HEXAGONS (7).')
ENDIF
ELSE IF(IHEX.EQ.8) THEN
VI = (1.+SQRT(REAL(3*(2*NH-1)+1)))/3.
VP = (1.+SQRT(REAL(6*NH+1)))/3.
IF(AINT(VI).EQ.VI) THEN
NC = INT(VI)
ELSE IF(AINT(VP).EQ.VP) THEN
NC = INT(VP)
ELSE
CALL XABORT('BIVALL: INVALID NUMBER OF HEXAGONS (8).')
ENDIF
ELSE IF(IHEX.EQ.9) THEN
VA = (SQRT(REAL((4*NH-1)/3)) + 1.)/2.
IF(AINT(VA).EQ.VA) THEN
NC = INT(VA)
ELSE
CALL XABORT('BIVALL: INVALID NUMBER OF HEXAGONS (9).')
ENDIF
ELSE
WRITE(TEXT4,'(I4)') IHEX
CALL XABORT('BIVALL: INVALID TYPE OF SYMMETRY (IHEX='//TEXT4//
1 ').')
ENDIF
NTH = 1 + 3 * NC * (NC - 1)
IF(NTH.GT.MAXPTS) CALL XABORT('BIVALL: MAXPTS OVERFLOW.')
ITAB(1) = 1
ALLOCATE(J1(NC+2),J2(NC+2),J3(NC+2),K1(NC+2),K2(NC+2),K3(NC+2),
1 K4(NC+2))
J1(1) = 1
J2(1) = 1
J3(1) = 1
K1(1) = 1
K2(1) = 1
K3(1) = 1
DO 10 L = 2,NC+1
J1(L) = (L-1)*6
J3(L) = 1+3*L*(L-1)
J2(L) = 1+J3(L-1)
10 CONTINUE
*
IF((IHEX.EQ.1).OR.(IHEX.EQ.10)) THEN
IL=0
DO 20 L = 1,NC+1,2
K1(L) = 1 + IL
K1(L+1) = 1 + IL
IL = IL+1
20 CONTINUE
DO 30 L = 2,NC+1
K2(L) = K2(L-1) + K1(L-1)
30 CONTINUE
IL=0
DO 40 L = 1,NC+1,2
K3(L) = K2(L) + IL
K3(L+1) = K2(L+1) + IL
IL = IL+1
40 CONTINUE
ELSE IF((IHEX.EQ.2).OR.(IHEX.EQ.11)) THEN
K1(2) = 2
DO 50 L = 2,NC+1
K2(L) = K2(L-1) + L
K1(L+1) = K1(L) + L
50 CONTINUE
ELSE IF(IHEX.EQ.3) THEN
K1(2) = 2
DO 60 L = 1,NC+1
K1(L+1) = K1(L) + L
60 CONTINUE
IL=0
DO 70 L = 1,NC+1,2
K4(L) = 1 + IL
K4(L+1) = 1 + IL
IL = IL + 2
70 CONTINUE
DO 80 L = 2,NC+1
K2(L) = K2(L-1) + K4(L-1)
K3(L) = K3(L-1) + K4(L)
80 CONTINUE
ELSE IF(IHEX.EQ.4) THEN
IL=0
DO 90 L = 1,NC+1,2
K4(L) = L + IL
K4(L+1) = L + IL + 1
IL = IL + 1
90 CONTINUE
DO 100 L = 2,NC+1
K1(L) = K1(L-1) + K4(L-1)
K3(L) = K3(L-1) + K4(L)
100 CONTINUE
IL=0
DO 110 L = 1,NC+1,2
K2(L) = K1(L) + IL
K2(L+1) = K1(L+1) + IL
IL = IL+1
110 CONTINUE
ELSE IF(IHEX.EQ.5) THEN
DO 120 L = 2,NC+1
K2(L) = 2 * (L-1)
K1(L) = K1(L-1) + K2(L)
120 CONTINUE
ELSE IF(IHEX.EQ.6) THEN
DO 130 L = 2,NC+1
K2(L) = 3 * (L-1)
K1(L) = K1(L-1) + K2(L)
130 CONTINUE
ELSE IF(IHEX.EQ.7) THEN
DO 140 L = 2,NC+1
K2(L) = 3 + K2(L-1)
K1(L) = K1(L-1) + K2(L)
140 CONTINUE
ELSE IF(IHEX.EQ.8) THEN
IL = 1
IF = 1
DO 150 L = 2,NC+1,2
K2(L) = 3 * (L-1)
K2(L+1) = 3 * L + 1
150 CONTINUE
DO 160 L = 2,NC+1
IL = IL + K2(L)
IF = IF + K2(L-1)
K1(L) = (IF + IL) / 2
160 CONTINUE
ENDIF
*
DO 300 N = 2,NTH
I=0
J=0
DO 170 I0 = 2,NC
IF((N.GE.J2(I0)).AND.(N.LE.J3(I0))) THEN
I=I0
GO TO 180
ENDIF
170 CONTINUE
IF(I.EQ.0) CALL XABORT('BIVALL: ALGORITHM FAILURE(1).')
180 DO 190 K = 1,6
NP(K) = J2(I) + (K - 1) * (I - 1)
190 CONTINUE
NP(7) = J3(I)
COURS2 = REAL(I)/2.
LPAIR = (AINT(COURS2).EQ.COURS2)
*
IF((IHEX.EQ.1).OR.(IHEX.EQ.10)) THEN
IF(N.LE.7) THEN
ITAB(N) = 2
GO TO 300
ENDIF
DO 200 L = 1,6
IF((N.GE.NP(L)).AND.(N.LT.NP(L+1))) J = L
200 CONTINUE
IF(N.EQ.NP(7)) J = 6
IF(J.EQ.0) CALL XABORT('BIVALL: ALGORITHM FAILURE(2).')
IC = 0
IF(J.EQ.6) IC = 1
N12 = (NP(J) + NP(J+1)+IC)/2
N13 = N12 + 1
IF(N.EQ.NP(J)) THEN
ITAB(N) = K3(I)
ELSE IF(N.EQ.NP(7)) THEN
ITAB(N) = K3(I) - 1
ELSE IF((N.GT.NP(J)).AND.(N.LT.N12)) THEN
ITAB(N) = K3(I) - (N - NP(J))
ELSE IF((N.EQ.N12).OR.((N.EQ.N13).AND.LPAIR)) THEN
ITAB(N) = K2(I)
ELSE IF((N.EQ.N13).AND.(.NOT.LPAIR)) THEN
ITAB(N) = K3(I) - (NP(J+1) + IC - N)
ELSE IF((N.GT.N13).AND.(N.LT.NP(J+1))) THEN
ITAB(N) = K3(I) - (NP(J+1) + IC - N)
ENDIF
*
ELSE IF((IHEX.EQ.2).OR.(IHEX.EQ.11)) THEN
DO 210 L = 1,6,2
IF((N.GE.NP(L)).AND.(N.LT.NP(L+2))) J = L
210 CONTINUE
IF(N.EQ.NP(7)) J = 5
IF(J.EQ.0) CALL XABORT('BIVALL: ALGORITHM FAILURE(3).')
IF(N.EQ.NP(J)) THEN
ITAB(N) = K2(I)
ELSE IF(N.EQ.NP(7)) THEN
ITAB(N) = K2(I) - 1
ELSE IF((N.GT.NP(J)).AND.(N.LT.NP(J+1))) THEN
ITAB(N) = K2(I) - (N - NP(J))
ELSE IF(N.EQ.NP(J+1)) THEN
ITAB(N) = K1(I)
ELSE IF((N.GT.NP(J+1)).AND.(N.LT.NP(J+2))) THEN
ITAB(N) = K1(I) + (N - NP(J+1))
ENDIF
*
ELSE IF(IHEX.EQ.3) THEN
IF(N.LE.7) THEN
ITAB(N) = 2
GO TO 300
ENDIF
DO 220 L = 1,6,2
IF((N.GE.NP(L)).AND.(N.LT.NP(L+2))) J = L
220 CONTINUE
IF(N.EQ.NP(7)) J = 5
IF(J.EQ.0) CALL XABORT('BIVALL: ALGORITHM FAILURE(4).')
IC = 0
IF(J.EQ.5) IC = 1
N12 = (NP(J) + NP(J+1))/2
N13 = N12 + 1
N14 = (NP(J+1) + NP(J+2)+IC)/2
N15 = N14 + 1
IF((N.EQ.NP(J)).OR.(N.EQ.NP(J+1))) THEN
ITAB(N) = K1(I)
ELSE IF(N.EQ.NP(7)) THEN
ITAB(N) = K1(I) - 1
ELSE IF((N.GT.NP(J)).AND.(N.LT.N12)) THEN
ITAB(N) = K1(I) + (N - NP(J))
ELSE IF((N.EQ.N12).OR.((N.EQ.N13).AND.LPAIR)) THEN
ITAB(N) = K3(I)
ELSE IF((N.EQ.N13).AND.(.NOT.LPAIR)) THEN
ITAB(N) = K3(I) - 1
ELSE IF((N.GT.N13).AND.(N.LT.NP(J+1))) THEN
ITAB(N) = K1(I) + (NP(J+1) - N)
ELSE IF((N.GT.NP(J+1)).AND.(N.LT.N14)) THEN
ITAB(N) = K1(I) - (N - NP(J+1))
ELSE IF((N.EQ.N14).OR.((N.EQ.N15).AND.LPAIR)) THEN
ITAB(N) = K2(I)
ELSE IF((N.EQ.N15).AND.(.NOT.LPAIR)) THEN
ITAB(N) = K2(I) + 1
ELSE IF((N.GT.N15).AND.(N.LT.NP(J+2))) THEN
ITAB(N) = K1(I) - (NP(J+2) + IC - N)
ENDIF
*
ELSE IF(IHEX.EQ.4) THEN
IF(N.EQ.7) THEN
ITAB(N) = 2
GO TO 300
ENDIF
DO 230 L = 1,6,3
IF((N.GE.NP(L)).AND.(N.LT.NP(L+3))) J = L
230 CONTINUE
IF(N.EQ.NP(7)) J = 4
IF(J.EQ.0) CALL XABORT('BIVALL: ALGORITHM FAILURE(5).')
IC = 0
IF(J.EQ.4) IC = 1
N12 = (NP(J+2) + NP(J+3)+IC)/2
N13 = N12 + 1
IF((N.EQ.NP(J)).OR.(N.EQ.NP(J+2))) THEN
ITAB(N) = K2(I)
ELSE IF(N.EQ.NP(7)) THEN
ITAB(N) = K2(I) - 1
ELSE IF((N.GT.NP(J)).AND.(N.LT.NP(J+1))) THEN
ITAB(N) = K2(I) + (N - NP(J))
ELSE IF(N.EQ.NP(J+1)) THEN
ITAB(N) = K3(I)
ELSE IF((N.GT.NP(J+1)).AND.(N.LE.N12).AND.(N.NE.NP(J+2))) THEN
ITAB(N) = K2(I) - (N - NP(J+2))
ELSE IF((N.EQ.N13).AND.(.NOT.LPAIR)) THEN
ITAB(N) = K2(I) - (NP(J+3) + IC - N)
ELSE IF((N.EQ.N13).AND.LPAIR) THEN
ITAB(N) = K1(I)
ELSE IF((N.GT.N13).AND.(N.LT.NP(J+3))) THEN
ITAB(N) = K2(I) - (NP(J+3) + IC - N)
ENDIF
*
ELSE IF(IHEX.EQ.5) THEN
IF(N.EQ.7) THEN
ITAB(N) = 3
GO TO 300
ELSE IF((N.EQ.11).OR.(N.EQ.15).OR.(N.EQ.19)) THEN
ITAB(N) = 4
GO TO 300
ENDIF
DO 240 L = 1,6,2
IF((N.GE.NP(L)).AND.(N.LT.NP(L+2))) J = L
240 CONTINUE
IF(N.EQ.NP(7)) J = 5
IF(J.EQ.0) CALL XABORT('BIVALL: ALGORITHM FAILURE(6).')
IC = 0
IF(J.EQ.5) IC = 1
IF((N.GE.NP(J)).AND.(N.LE.NP(J+1))) THEN
ITAB(N) = K1(I) - (NP(J+1) - N)
ELSE IF((N.GT.NP(J+1)).AND.(N.LE.NP(J+2)+IC)) THEN
ITAB(N) = K1(I) -(2*(NP(J+2)+IC)-NP(J+1)- N)
ENDIF
*
ELSE IF(IHEX.EQ.6) THEN
DO 250 L = 1,6,3
IF((N.GE.NP(L)).AND.(N.LT.NP(L+3))) J = L
250 CONTINUE
IF(N.EQ.NP(7)) J = 4
IF(J.EQ.0) CALL XABORT('BIVALL: ALGORITHM FAILURE(7).')
IC = 0
IF(J.EQ.4) IC = 1
IF((N.GE.NP(J)).AND.(N.LE.NP(J+1))) THEN
ITAB(N) = K1(I) - (NP(J+1) - N)
ELSE IF((N.GT.NP(J+1)).AND.(N.LE.NP(J+2))) THEN
ITAB(N) = K1(I) - 2*(NP(J+2)-NP(J+1))-(NP(J+2)-N)
ELSE IF((N.GT.NP(J+2)).AND.(N.LE.NP(J+3)+IC)) THEN
ITAB(N) = K1(I)-(2*(NP(J+3)+IC)-NP(J+2)-N)
ENDIF
*
ELSE IF(IHEX.EQ.7) THEN
IF((N.GE.NP(1)).AND.(N.LE.NP(2))) THEN
ITAB(N) = K1(I) - (NP(2) - N)
ELSE IF((N.GT.NP(2)).AND.(N.LE.NP(3))) THEN
ITAB(N) = K1(I) - (NP(3) - NP(2)) + (NP(3) - N)
ELSE IF((N.GT.NP(3)).AND.(N.LE.NP(4))) THEN
ITAB(N) = K1(I) - (NP(4) - NP(2)) + (NP(4) - N)
ELSE IF((N.GT.NP(4)).AND.(N.LE.NP(5))) THEN
ITAB(N) = K1(I) - (NP(5) - NP(2)) + (NP(5) - N)
ELSE IF((N.GT.NP(5)).AND.(N.LE.NP(6))) THEN
ITAB(N) = K1(I) - (NP(4) - NP(2)) - (NP(6) - N)
ELSE IF((N.GT.NP(6)).AND.(N.LE.NP(7)+1)) THEN
ITAB(N) = K1(I) - (NP(3) - NP(2)) - (NP(7) + 1 - N)
ENDIF
*
ELSE IF(IHEX.EQ.8) THEN
N12 = (NP(3) + NP(4)) / 2
N13 = (NP(6) + NP(7) + 1) / 2
IF((N.GE.NP(1)).AND.(N.LE.N12)) THEN
ITAB(N) = K1(I) - (NP(2) - N)
ELSE IF((N.GT.N12).AND.(N.LE.N13)) THEN
ITAB(N) = K1(I) + (NP(5) - N)
ELSE IF((N.GT.N13).AND.(N.LE.NP(7)+1)) THEN
ITAB(N) = K1(I) - (NP(6) - NP(5)) - (NP(7) + 1 - N)
ENDIF
*
ELSE IF(IHEX.EQ.9) THEN
ITAB(N) = N
ENDIF
300 CONTINUE
DEALLOCATE(K4,K3,K2,K1,J3,J2,J1)
RETURN
END
|
