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Location: MD/arcos/fish90/src/genbunal.f90
d6faa5ffcedf
46.1 KiB
text/x-fortran
install arcos
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! file genbun.f
!
! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
! . .
! . copyright (c) 2004 by UCAR .
! . .
! . UNIVERSITY CORPORATION for ATMOSPHERIC RESEARCH .
! . .
! . all rights reserved .
! . .
! . .
! . FISHPACK version 5.0 .
! . .
! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
!
! * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
! * *
! * F I S H P A C K *
! * *
! * *
! * A PACKAGE OF FORTRAN SUBPROGRAMS FOR THE SOLUTION OF *
! * *
! * SEPARABLE ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS *
! * *
! * (Version 5.0 , JUNE 2004) *
! * *
! * BY *
! * *
! * JOHN ADAMS, PAUL SWARZTRAUBER AND ROLAND SWEET *
! * *
! * OF *
! * *
! * THE NATIONAL CENTER FOR ATMOSPHERIC RESEARCH *
! * *
! * BOULDER, COLORADO (80307) U.S.A. *
! * *
! * WHICH IS SPONSORED BY *
! * *
! * THE NATIONAL SCIENCE FOUNDATION *
! * *
! * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
!
! SUBROUTINE GENBUN (NPEROD,N,MPEROD,M,A,B,C,IDIMY,Y,IERROR)
!
!
! DIMENSION OF A(M),B(M),C(M),Y(IDIMY,N)
! ARGUMENTS
!
! LATEST REVISION JUNE 2004
!
! PURPOSE THE NAME OF THIS PACKAGE IS A MNEMONIC FOR THE
! GENERALIZED BUNEMAN ALGORITHM.
!
! IT SOLVES THE REAL LINEAR SYSTEM OF EQUATIONS
!
! A(I)*X(I-1,J) + B(I)*X(I,J) + C(I)*X(I+1,J)
! + X(I,J-1) - 2.*X(I,J) + X(I,J+1) = Y(I,J)
!
! FOR I = 1,2,...,M AND J = 1,2,...,N.
!
! INDICES I+1 AND I-1 ARE EVALUATED MODULO M,
! I.E., X(0,J) = X(M,J) AND X(M+1,J) = X(1,J),
! AND X(I,0) MAY EQUAL 0, X(I,2), OR X(I,N),
! AND X(I,N+1) MAY EQUAL 0, X(I,N-1), OR X(I,1)
! DEPENDING ON AN INPUT PARAMETER.
!
! USAGE CALL GENBUN (NPEROD,N,MPEROD,M,A,B,C,IDIMY,Y,
! IERROR)
!
! ARGUMENTS
!
! ON INPUT NPEROD
!
! INDICATES THE VALUES THAT X(I,0) AND
! X(I,N+1) ARE ASSUMED TO HAVE.
!
! = 0 IF X(I,0) = X(I,N) AND X(I,N+1) =
! X(I,1).
! = 1 IF X(I,0) = X(I,N+1) = 0 .
! = 2 IF X(I,0) = 0 AND X(I,N+1) = X(I,N-1).
! = 3 IF X(I,0) = X(I,2) AND X(I,N+1) =
! X(I,N-1).
! = 4 IF X(I,0) = X(I,2) AND X(I,N+1) = 0.
!
! N
! THE NUMBER OF UNKNOWNS IN THE J-DIRECTION.
! N MUST BE GREATER THAN 2.
!
! MPEROD
! = 0 IF A(1) AND C(M) ARE NOT ZERO
! = 1 IF A(1) = C(M) = 0
!
! M
! THE NUMBER OF UNKNOWNS IN THE I-DIRECTION.
! N MUST BE GREATER THAN 2.
!
! A,B,C
! ONE-DIMENSIONAL ARRAYS OF LENGTH M THAT
! SPECIFY THE COEFFICIENTS IN THE LINEAR
! EQUATIONS GIVEN ABOVE. IF MPEROD = 0
! THE ARRAY ELEMENTS MUST NOT DEPEND UPON
! THE INDEX I, BUT MUST BE CONSTANT.
! SPECIFICALLY, THE SUBROUTINE CHECKS THE
! FOLLOWING CONDITION .
!
! A(I) = C(1)
! C(I) = C(1)
! B(I) = B(1)
!
! FOR I=1,2,...,M.
!
! IDIMY
! THE ROW (OR FIRST) DIMENSION OF THE
! TWO-DIMENSIONAL ARRAY Y AS IT APPEARS
! IN THE PROGRAM CALLING GENBUN.
! THIS PARAMETER IS USED TO SPECIFY THE
! VARIABLE DIMENSION OF Y.
! IDIMY MUST BE AT LEAST M.
!
! Y
! A TWO-DIMENSIONAL COMPLEX ARRAY THAT
! SPECIFIES THE VALUES OF THE RIGHT SIDE
! OF THE LINEAR SYSTEM OF EQUATIONS GIVEN
! ABOVE.
! Y MUST BE DIMENSIONED AT LEAST M*N.
!
!
! ON OUTPUT Y
!
! CONTAINS THE SOLUTION X.
!
! IERROR
! AN ERROR FLAG WHICH INDICATES INVALID
! INPUT PARAMETERS EXCEPT FOR NUMBER
! ZERO, A SOLUTION IS NOT ATTEMPTED.
!
! = 0 NO ERROR.
! = 1 M .LE. 2 .
! = 2 N .LE. 2
! = 3 IDIMY .LT. M
! = 4 NPEROD .LT. 0 OR NPEROD .GT. 4
! = 5 MPEROD .LT. 0 OR MPEROD .GT. 1
! = 6 A(I) .NE. C(1) OR C(I) .NE. C(1) OR
! B(I) .NE. B(1) FOR
! SOME I=1,2,...,M.
! = 7 A(1) .NE. 0 OR C(M) .NE. 0 AND
! MPEROD = 1
! = 20 If the dynamic allocation of real and
! complex work space required for solution
! fails (for example if N,M are too large
! for your computer)
!
!
! SPECIAL CONDITONS NONE
!
! I/O NONE
!
! PRECISION SINGLE
!
! REQUIRED FILES comf.f,gnbnaux.f,fish.f
! FILES
!
! LANGUAGE FORTRAN 90
!
! HISTORY WRITTEN IN 1979 BY ROLAND SWEET OF NCAR'S
! SCIENTIFIC COMPUTING DIVISION. MADE AVAILABLE
! ON NCAR'S PUBLIC LIBRARIES IN JANUARY, 1980.
! Revised in June 2004 by John Adams using
! Fortran 90 dynamically allocated work space.
!
! ALGORITHM THE LINEAR SYSTEM IS SOLVED BY A CYCLIC
! REDUCTION ALGORITHM DESCRIBED IN THE
! REFERENCE.
!
! PORTABILITY FORTRAN 90 --
! THE MACHINE DEPENDENT CONSTANT PI IS
! DEFINED IN FUNCTION PIMACH.
!
! REFERENCES SWEET, R., "A CYCLIC REDUCTION ALGORITHM FOR
! SOLVING BLOCK TRIDIAGONAL SYSTEMS OF ARBITRARY
! DIMENSIONS," SIAM J. ON NUMER. ANAL., 14 (1977)
! PP. 706-720.
!
! ACCURACY THIS TEST WAS PERFORMED ON a platform with
! 64 bit floating point arithmetic.
! A UNIFORM RANDOM NUMBER GENERATOR WAS USED
! TO CREATE A SOLUTION ARRAY X FOR THE SYSTEM
! GIVEN IN THE 'PURPOSE' DESCRIPTION ABOVE
! WITH
! A(I) = C(I) = -0.5*B(I) = 1, I=1,2,...,M
!
! AND, WHEN MPEROD = 1
!
! A(1) = C(M) = 0
! A(M) = C(1) = 2.
!
! THE SOLUTION X WAS SUBSTITUTED INTO THE
! GIVEN SYSTEM AND, USING DOUBLE PRECISION
! A RIGHT SIDE Y WAS COMPUTED.
! USING THIS ARRAY Y, SUBROUTINE GENBUN
! WAS CALLED TO PRODUCE APPROXIMATE
! SOLUTION Z. THEN RELATIVE ERROR
! E = MAX(ABS(Z(I,J)-X(I,J)))/
! MAX(ABS(X(I,J)))
! WAS COMPUTED, WHERE THE TWO MAXIMA ARE TAKEN
! OVER I=1,2,...,M AND J=1,...,N.
!
! THE VALUE OF E IS GIVEN IN THE TABLE
! BELOW FOR SOME TYPICAL VALUES OF M AND N.
!
! M (=N) MPEROD NPEROD E
! ------ ------ ------ ------
!
! 31 0 0 6.E-14
! 31 1 1 4.E-13
! 31 1 3 3.E-13
! 32 0 0 9.E-14
! 32 1 1 3.E-13
! 32 1 3 1.E-13
! 33 0 0 9.E-14
! 33 1 1 4.E-13
! 33 1 3 1.E-13
! 63 0 0 1.E-13
! 63 1 1 1.E-12
! 63 1 3 2.E-13
! 64 0 0 1.E-13
! 64 1 1 1.E-12
! 64 1 3 6.E-13
! 65 0 0 2.E-13
! 65 1 1 1.E-12
! 65 1 3 4.E-13
! * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
SUBROUTINE GENBUN(NPEROD, N, MPEROD, M, A, B, C, IDIMY, Y, IERROR)
USE fish
implicit none
DOUBLE PRECISION, PARAMETER :: ZERO = 0.0D0, HALF = 0.5D0, &
ONE = 1.0D0, TWO = 2.0D0, &
FOUR = 4.0D0
TYPE(fishworkspace) :: w
!-----------------------------------------------
! D u m m y A r g u m e n t s
!-----------------------------------------------
INTEGER, INTENT(IN) :: NPEROD, N, MPEROD, M, IDIMY
INTEGER, INTENT(OUT) :: IERROR
DOUBLE PRECISION, DIMENSION(:) :: A, B, C
DOUBLE PRECISION, INTENT(INOUT) :: Y(IDIMY,*)
!-----------------------------------------------
! L o c a l V a r i a b l e s
!-----------------------------------------------
INTEGER :: IRWK, ICWK
!-----------------------------------------------
write(*,*) 'fish90: genbun'
IERROR = 0
! check input arguments
IF (M <= 2) then
ierror = 1
return
end if
IF (N <= 2) then
ierror = 2
return
end if
IF (IDIMY < M) then
ierror = 3
return
end if
IF (NPEROD<0 .OR. NPEROD>4) then
ierror = 4
return
end if
IF (MPEROD<0 .OR. MPEROD>1) then
ierror = 5
return
end if
! compute and allocate real work space for genbun
CALL GEN_SPACE (N, M, IRWK)
ICWK = 0
CALL ALLOCATFISH (IRWK, ICWK, W, IERROR)
! return if allocation failed (e.g., if n,m are too large)
IF (IERROR == 20) THEN
write(*,*) 'error call ALLOCATFISH'
RETURN
END IF
call genbunn(NPEROD,N,MPEROD,M,A,B,C,IDIMY,Y,IERROR,w%rew,IRWK)
! release allocated work space
CALL FISHFIN (W,IERROR)
IF (IERROR == 20) THEN
write(*,*) 'error call FISHFIN'
RETURN
END IF
!
END SUBROUTINE GENBUN
SUBROUTINE GENBUNN(NPEROD,N,MPEROD,M,vecA,vecB,vecC,IDIMY,matY, &
IERROR,vecW,IW)
implicit none
DOUBLE PRECISION, PARAMETER :: ZERO = 0.0D0, HALF = 0.5D0, &
ONE = 1.0D0, TWO = 2.0D0, &
FOUR = 4.0D0
!-----------------------------------------------
! D u m m y A r g u m e n t s
!-----------------------------------------------
INTEGER, INTENT(IN) :: NPEROD, N, MPEROD, M, IDIMY,IW
INTEGER, INTENT(INOUT) :: IERROR
DOUBLE PRECISION, DIMENSION(M), INTENT(IN) :: vecA, vecB, vecC
DOUBLE PRECISION, DIMENSION(IW), INTENT(OUT) :: vecW
DOUBLE PRECISION, DIMENSION(IDIMY,N),INTENT(INOUT) :: matY
!-----------------------------------------------
! L o c a l V a r i a b l e s
!-----------------------------------------------
INTEGER :: I, MP1, IWBA, IWBB, IWBC, IWB2, IWB3, IWW1, IWW2, IWW3, &
IWD, IWTCOS, IWP, IW2, K, J, MP, NP, &
IPSTOR, IREV, MH, MHM1, MODD, NBY2, MSKIP
DOUBLE PRECISION :: A1
!-----------------------------------------------
IF (MPEROD /= 1) THEN
DO I = 2, M
IF (vecA(I) /= vecC(1)) GO TO 103
IF (vecC(I) /= vecC(1)) GO TO 103
IF (vecB(I) /= vecB(1)) GO TO 103
END DO
GO TO 104
ENDIF
IF (vecA(1)/=ZERO .OR. vecC(M)/=ZERO) IERROR = 7
GO TO 104
103 CONTINUE
IERROR = 6
104 CONTINUE
IF (IERROR /= 0) RETURN
MP1 = M + 1
IWBA = MP1
IWBB = IWBA + M
IWBC = IWBB + M
IWB2 = IWBC + M
IWB3 = IWB2 + M
IWW1 = IWB3 + M
IWW2 = IWW1 + M
IWW3 = IWW2 + M
IWD = IWW3 + M
IWTCOS = IWD + M
IWP = IWTCOS + 4*N
vecW(IWBA:M-1+IWBA) = -vecA(:M)
vecW(IWBC:M-1+IWBC) = -vecC(:M)
vecW(IWBB:M-1+IWBB) = TWO - vecB(:M)
matY(:M,:N) = -matY(:M,:N)
MP = MPEROD + 1
NP = NPEROD + 1
GO TO (114,107) MP
107 CONTINUE
GO TO (108,109,110,111,123) NP
108 CONTINUE
IW2 = IW - IWP + 1
CALL POISP2 (M, N, vecW(IWBA:IWBA+M-1), vecW(IWBB:IWBB+M-1), &
vecW(IWBC:IWBC+M-1), matY, IDIMY, &
vecW(1:M), vecW(IWB2:IWB2+M-1), vecW(IWB3:IWB3+M-1), &
vecW(IWW1:IWW1+M-1), vecW(IWW2:IWW2+M-1), &
vecW(IWW3:IWW3+M-1), vecW(IWD:IWD+M-1), &
vecW(IWTCOS:IWTCOS+4*N-1), vecW(IWP:),IW2)
GO TO 112
109 CONTINUE
IW2 = IW - IWP + 1
CALL POISD2 (M, N, 1, vecW(IWBA:IWBA+M-1), vecW(IWBB:IWBB+M-1), &
vecW(IWBC::IWBC+M-1), matY, IDIMY, &
vecW(1:M), vecW(IWW1:IWW1+M-1), vecW(IWD:IWD+M-1), &
vecW(IWTCOS:IWTCOS+4*N-1), vecW(IWP:), IW2)
GO TO 112
110 CONTINUE
IW2 = IW - IWP + 1
CALL POISN2 (M, N, 1, 2, vecW(IWBA:IWBA+M-1), vecW(IWBB:IWBB+M-1), &
vecW(IWBC:IWBC+M-1), matY, IDIMY, vecW(1:M), &
vecW(IWB2:IWB2+M-1), vecW(IWB3:IWB3+M-1), &
vecW(IWW1:IWW1+M-1), vecW(IWW2:IWW2+M-1), &
vecW(IWW3::IWW3+M-1), vecW(IWD:IWD+M-1), &
vecW(IWTCOS:IWTCOS+4*N-1),vecW(IWP:),IW2)
GO TO 112
111 CONTINUE
IW2 = IW - IWP + 1
CALL POISN2 (M, N, 1, 1, vecW(IWBA:IWBA+M-1), vecW(IWBB:IWBB+M-1), &
vecW(IWBC::IWBC+M-1), matY, IDIMY, vecW(1:M), &
vecW(IWB2:IWW1+M-1), vecW(IWB3:IWB3+M-1), &
vecW(IWW1:IWW1+M-1), vecW(IWW2:IWW2+M-1), &
vecW(IWW3::IWW3+M-1), vecW(IWD:IWD+M-1), &
vecW(IWTCOS:IWTCOS+4*N-1),vecW(IWP:),IW2)
112 CONTINUE
IPSTOR = vecW(IWW1)
IREV = 2
IF (NPEROD == 4) GO TO 124
113 CONTINUE
GO TO (127,133) MP
114 CONTINUE
MH = (M + 1)/2
MHM1 = MH - 1
MODD = 1
IF (MH*2 == M) MODD = 2
DO J = 1, N
vecW(:MHM1) = matY(MH-1:MH-MHM1:(-1),J) - matY(MH+1:MHM1+MH,J)
vecW(MH+1:MHM1+MH) = matY(MH-1:MH-MHM1:(-1),J) + matY(MH+1:MHM1+MH,J)
vecW(MH) = TWO*matY(MH,J)
GO TO (117,116) MODD
116 CONTINUE
vecW(M) = TWO*matY(M,J)
117 CONTINUE
matY(:M,J) = vecW(:M)
END DO
K = IWBC + MHM1 - 1
I = IWBA + MHM1
vecW(K) = ZERO
vecW(I) = ZERO
vecW(K+1) = TWO*vecW(K+1)
SELECT CASE (MODD)
CASE DEFAULT
K = IWBB + MHM1 - 1
vecW(K) = vecW(K) - vecW(I-1)
vecW(IWBC-1) = vecW(IWBC-1) + vecW(IWBB-1)
CASE (2)
vecW(IWBB-1) = vecW(K+1)
END SELECT
GO TO 107
!
! REVERSE COLUMNS WHEN NPEROD = 4.
!
123 CONTINUE
IREV = 1
NBY2 = N/2
124 CONTINUE
DO J = 1, NBY2
MSKIP = N + 1 - J
DO I = 1, M
A1 = matY(I,J)
matY(I,J) = matY(I,MSKIP)
matY(I,MSKIP) = A1
END DO
END DO
GO TO (110,113) IREV
127 CONTINUE
DO J = 1, N
vecW(MH-1:MH-MHM1:(-1)) = HALF*(matY(MH+1:MHM1+MH,J)+matY(:MHM1,J))
vecW(MH+1:MHM1+MH) = HALF*(matY(MH+1:MHM1+MH,J)-matY(:MHM1,J))
vecW(MH) = HALF*matY(MH,J)
GO TO (130,129) MODD
129 CONTINUE
vecW(M) = HALF*matY(M,J)
130 CONTINUE
matY(:M,J) = vecW(:M)
END DO
133 CONTINUE
vecW(1) = IPSTOR + IWP - 1
RETURN
END SUBROUTINE GENBUNN
SUBROUTINE POISD2(MR,NR,ISTAG,vecBA,vecBB,vecBC,matY,IDIMY, &
vecB,vecW,vecD,TCOS,vecP,IDIMP)
implicit none
DOUBLE PRECISION, PARAMETER :: ZERO = 0.0D0, HALF = 0.5D0, &
ONE = 1.0D0, TWO = 2.0D0, &
FOUR = 4.0D0
!-----------------------------------------------
! D u m m y A r g u m e n t s
!-----------------------------------------------
INTEGER, INTENT(IN) :: MR, NR, ISTAG, IDIMY,IDIMP
DOUBLE PRECISION, DIMENSION(MR), INTENT(IN) :: vecBA, vecBB, &
vecBC
DOUBLE PRECISION, DIMENSION(IDIMY,NR),INTENT(INOUT) :: matY
DOUBLE PRECISION, DIMENSION(MR), INTENT(INOUT) :: vecB, vecD, vecW
DOUBLE PRECISION, DIMENSION(4*NR), INTENT(INOUT) :: TCOS
DOUBLE PRECISION, DIMENSION(IDIMP), INTENT(INOUT) :: vecP
!-----------------------------------------------
! L o c a l V a r i a b l e s
!-----------------------------------------------
INTEGER :: M, N, JSH, IP, IPSTOR, KR, IRREG, JSTSAV, I, LR, NUN, &
JST, JSP, L, NODD, J, JM1, JP1, JM2, JP2, JM3, JP3, &
NODDPR, KRPI, IDEG, JDEG
DOUBLE PRECISION :: FI, T
!-----------------------------------------------
!
! SUBROUTINE TO SOLVE POISSON'S EQUATION FOR DIRICHLET BOUNDARY
! CONDITIONS.
!
! ISTAG = 1 IF THE LAST DIAGONAL BLOCK IS THE MATRIX A.
! ISTAG = 2 IF THE LAST DIAGONAL BLOCK IS THE MATRIX A+I.
!
M = MR
N = NR
JSH = 0
FI = ONE/FLOAT(ISTAG)
IP = -M
IPSTOR = 0
SELECT CASE (ISTAG)
CASE DEFAULT
KR = 0
IRREG = 1
IF (N > 1) GO TO 106
TCOS(1) = ZERO
CASE (2)
KR = 1
JSTSAV = 1
IRREG = 2
IF (N > 1) GO TO 106
TCOS(1) = -ONE
END SELECT
vecB(:M) = matY(:M,1)
CALL TRIX (1, 0, M, vecBA, vecBB, vecBC, vecB, TCOS, 4*NR, vecD, vecW)
matY(:M,1) = vecB(:M)
GO TO 183
106 CONTINUE
LR = 0
vecP(:M) = ZERO
NUN = N
JST = 1
JSP = N
!
! IRREG = 1 WHEN NO IRREGULARITIES HAVE OCCURRED, OTHERWISE IT IS 2.
!
108 CONTINUE
L = 2*JST
NODD = 2 - 2*((NUN + 1)/2) + NUN
!
! NODD = 1 WHEN NUN IS ODD, OTHERWISE IT IS 2.
!
SELECT CASE (NODD)
CASE DEFAULT
JSP = JSP - L
CASE (1)
JSP = JSP - JST
IF (IRREG /= 1) JSP = JSP - L
END SELECT
CALL COSGEN (JST, 1, HALF, ZERO, TCOS, 4*NR)
IF (L <= JSP) THEN
DO J = L, JSP, L
JM1 = J - JSH
JP1 = J + JSH
JM2 = J - JST
JP2 = J + JST
JM3 = JM2 - JSH
JP3 = JP2 + JSH
IF (JST == 1) THEN
vecB(:M) = TWO*matY(:M,J)
matY(:M,J) = matY(:M,JM2) + matY(:M,JP2)
ELSE
DO I = 1, M
T = matY(I,J) - matY(I,JM1) - matY(I,JP1) + matY(I,JM2) + &
matY(I,JP2)
vecB(I) = T + matY(I,J) - matY(I,JM3) - matY(I,JP3)
matY(I,J) = T
END DO
ENDIF
CALL TRIX (JST, 0, M, vecBA, vecBB, vecBC, vecB, TCOS, 4*NR, vecD, vecW)
matY(:M,J) = matY(:M,J) + vecB(:M)
END DO
ENDIF
!
! REDUCTION FOR LAST UNKNOWN
!
SELECT CASE (NODD)
CASE DEFAULT
GO TO (152,120) IRREG
!
! ODD NUMBER OF UNKNOWNS
!
120 CONTINUE
JSP = JSP + L
J = JSP
JM1 = J - JSH
JP1 = J + JSH
JM2 = J - JST
JP2 = J + JST
JM3 = JM2 - JSH
GO TO (123,121) ISTAG
121 CONTINUE
IF (JST /= 1) GO TO 123
vecB(:M) = matY(:M,J)
matY(:M,J) = ZERO
GO TO 130
123 CONTINUE
SELECT CASE (NODDPR)
CASE DEFAULT
vecB(:M) = HALF*(matY(:M,JM2)-matY(:M,JM1)-matY(:M,JM3)) + &
vecP(IP+1:M+IP)+ matY(:M,J)
CASE (2)
vecB(:M) = HALF*(matY(:M,JM2)-matY(:M,JM1)-matY(:M,JM3)) + &
matY(:M,JP2) - matY(:M,JP1) + matY(:M,J)
END SELECT
matY(:M,J) = HALF*(matY(:M,J)-matY(:M,JM1)-matY(:M,JP1))
130 CONTINUE
CALL TRIX (JST, 0, M, vecBA, vecBB, vecBC, vecB, TCOS, 4*NR, vecD, vecW)
IP = IP + M
IPSTOR = MAX0(IPSTOR,IP + M)
vecP(IP+1:M+IP) = matY(:M,J) + vecB(:M)
vecB(:M) = matY(:M,JP2) + vecP(IP+1:M+IP)
IF (LR == 0) THEN
DO I = 1, JST
KRPI = KR + I
TCOS(KRPI) = TCOS(I)
END DO
ELSE
CALL COSGEN (LR, JSTSAV, ZERO, FI, TCOS(JST+1), 4*NR-JST)
CALL MERGE (TCOS, 0, JST, JST, LR, KR, 4*NR)
ENDIF
CALL COSGEN (KR, JSTSAV, ZERO, FI, TCOS, 4*NR)
CALL TRIX (KR, KR, M, vecBA, vecBB, vecBC, vecB, TCOS, 4*NR, vecD, vecW)
matY(:M,J) = matY(:M,JM2) + vecB(:M) + vecP(IP+1:M+IP)
LR = KR
KR = KR + L
!
! EVEN NUMBER OF UNKNOWNS
!
CASE (2)
JSP = JSP + L
J = JSP
JM1 = J - JSH
JP1 = J + JSH
JM2 = J - JST
JP2 = J + JST
JM3 = JM2 - JSH
SELECT CASE (IRREG)
CASE DEFAULT
JSTSAV = JST
IDEG = JST
KR = L
CASE (2)
CALL COSGEN (KR, JSTSAV, ZERO, FI, TCOS, 4*NR)
CALL COSGEN (LR, JSTSAV, ZERO, FI, TCOS(KR+1), 4*NR-KR)
IDEG = KR
KR = KR + JST
END SELECT
IF (JST == 1) THEN
IRREG = 2
vecB(:M) = matY(:M,J)
matY(:M,J) = matY(:M,JM2)
ELSE
vecB(:M) = matY(:M,J) + HALF*(matY(:M,JM2)-matY(:M,JM1)- &
matY(:M,JM3))
SELECT CASE (IRREG)
CASE DEFAULT
matY(:M,J) = matY(:M,JM2) + HALF*(matY(:M,J)- &
matY(:M,JM1)-matY(:M,JP1))
IRREG = 2
CASE (2)
SELECT CASE (NODDPR)
CASE DEFAULT
matY(:M,J) = matY(:M,JM2) + vecP(IP+1:M+IP)
IP = IP - M
CASE (2)
matY(:M,J) = matY(:M,JM2) + matY(:M,J) - matY(:M,JM1)
END SELECT
END SELECT
ENDIF
CALL TRIX (IDEG, LR, M, vecBA, vecBB, vecBC, vecB, TCOS, 4*NR, vecD, vecW)
matY(:M,J) = matY(:M,J) + vecB(:M)
END SELECT
152 CONTINUE
NUN = NUN/2
NODDPR = NODD
JSH = JST
JST = 2*JST
IF (NUN >= 2) GO TO 108
!
! START SOLUTION.
!
J = JSP
vecB(:M) = matY(:M,J)
SELECT CASE (IRREG)
CASE DEFAULT
CALL COSGEN (JST, 1, HALF, ZERO, TCOS, 4*NR)
IDEG = JST
CASE (2)
KR = LR + JST
CALL COSGEN (KR, JSTSAV, ZERO, FI, TCOS, 4*NR)
CALL COSGEN (LR, JSTSAV, ZERO, FI, TCOS(KR+1), 4*NR-KR)
IDEG = KR
END SELECT
CALL TRIX (IDEG, LR, M, vecBA, vecBB, vecBC, vecB, TCOS, 4*NR, vecD, vecW)
JM1 = J - JSH
JP1 = J + JSH
SELECT CASE (IRREG)
CASE DEFAULT
matY(:M,J) = HALF*(matY(:M,J)-matY(:M,JM1)-matY(:M,JP1)) + vecB(:M)
CASE (2)
SELECT CASE (NODDPR)
CASE DEFAULT
matY(:M,J) = vecP(IP+1:M+IP) + vecB(:M)
IP = IP - M
CASE (2)
matY(:M,J) = matY(:M,J) - matY(:M,JM1) + vecB(:M)
END SELECT
END SELECT
164 CONTINUE
JST = JST/2
JSH = JST/2
NUN = 2*NUN
IF (NUN > N) GO TO 183
DO J = JST, N, L
JM1 = J - JSH
JP1 = J + JSH
JM2 = J - JST
JP2 = J + JST
IF (J <= JST) THEN
vecB(:M) = matY(:M,J) + matY(:M,JP2)
ELSE
IF (JP2 <= N) GO TO 168
vecB(:M) = matY(:M,J) + matY(:M,JM2)
IF (JST < JSTSAV) IRREG = 1
GO TO (170,171) IRREG
168 CONTINUE
vecB(:M) = matY(:M,J) + matY(:M,JM2) + matY(:M,JP2)
ENDIF
170 CONTINUE
CALL COSGEN (JST, 1, HALF, ZERO, TCOS, 4*NR)
IDEG = JST
JDEG = 0
GO TO 172
171 CONTINUE
IF (J + L > N) LR = LR - JST
KR = JST + LR
CALL COSGEN (KR, JSTSAV, ZERO, FI, TCOS, 4*NR)
CALL COSGEN (LR, JSTSAV, ZERO, FI, TCOS(KR+1), 4*NR-KR)
IDEG = KR
JDEG = LR
172 CONTINUE
CALL TRIX (IDEG, JDEG, M, vecBA, vecBB, vecBC, vecB, TCOS, 4*NR, vecD, vecW)
IF (JST <= 1) THEN
matY(:M,J) = vecB(:M)
ELSE
IF (JP2 > N) GO TO 177
175 CONTINUE
matY(:M,J) = HALF*(matY(:M,J)-matY(:M,JM1)-matY(:M,JP1)) + vecB(:M)
CYCLE
177 CONTINUE
GO TO (175,178) IRREG
178 CONTINUE
IF (J + JSH <= N) THEN
matY(:M,J) = vecB(:M) + vecP(IP+1:M+IP)
IP = IP - M
ELSE
matY(:M,J) = vecB(:M) + matY(:M,J) - matY(:M,JM1)
ENDIF
ENDIF
END DO
L = L/2
GO TO 164
183 CONTINUE
vecW(1) = IPSTOR
RETURN
END SUBROUTINE POISD2
SUBROUTINE POISN2(M, N, ISTAG, MIXBND, vecA, vecBB, vecC, &
matQ, IDIMQ, vecB, vecB2,vecB3, &
vecW, vecW2, vecW3, vecD, TCOS, vecP, IDIMP)
implicit none
DOUBLE PRECISION, PARAMETER :: ZERO = 0.0D0, HALF = 0.5D0, &
ONE = 1.0D0, TWO = 2.0D0, &
FOUR = 4.0D0
!-----------------------------------------------
! D u m m y A r g u m e n t s
!-----------------------------------------------
INTEGER, INTENT(IN) :: M, N, ISTAG, MIXBND, IDIMQ,IDIMP
DOUBLE PRECISION, DIMENSION(M), INTENT(IN) :: vecA, vecBB, vecC
DOUBLE PRECISION, DIMENSION(IDIMQ,N), INTENT(INOUT) :: matQ
DOUBLE PRECISION, DIMENSION(M),INTENT(INOUT) :: vecB, vecB2, vecB3, &
vecD, vecW, vecW2, vecW3
DOUBLE PRECISION, DIMENSION(IDIMP),INTENT(INOUT) :: vecP
DOUBLE PRECISION, DIMENSION(4*N),INTENT(INOUT) :: TCOS
!-----------------------------------------------
! L o c a l V a r i a b l e s
!-----------------------------------------------
INTEGER, DIMENSION(4) :: K
INTEGER :: K1, K2, K3, K4, MR, IP, IPSTOR, I2R, JR, NR, NLAST, &
KR, LR, I, NROD, JSTART, JSTOP, I2RBY2, &
J, JP1, JP2, JP3, JM1,JM2, JM3, NRODPR, II, I1, I2, &
JR2, NLASTP, JSTEP
DOUBLE PRECISION :: FISTAG, FNUM, FDEN, FI, T
!-----------------------------------------------
!
! SUBROUTINE TO SOLVE POISSON'S EQUATION WITH NEUMANN BOUNDARY
! CONDITIONS.
!
! ISTAG = 1 IF THE LAST DIAGONAL BLOCK IS A.
! ISTAG = 2 IF THE LAST DIAGONAL BLOCK IS A-I.
! MIXBND = 1 IF HAVE NEUMANN BOUNDARY CONDITIONS AT BOTH BOUNDARIES.
! MIXBND = 2 IF HAVE NEUMANN BOUNDARY CONDITIONS AT BOTTOM AND
! DIRICHLET CONDITION AT TOP. (FOR THIS CASE, MUST HAVE ISTAG = 1.)
!
EQUIVALENCE (K(1), K1), (K(2), K2), (K(3), K3), (K(4), K4)
FISTAG = 3 - ISTAG
FNUM = ONE/FLOAT(ISTAG)
FDEN = HALF*FLOAT(ISTAG - 1)
MR = M
IP = -MR
IPSTOR = 0
I2R = 1
JR = 2
NR = N
NLAST = N
KR = 1
LR = 0
GO TO (101,103) ISTAG
101 CONTINUE
matQ(:MR,N) = HALF*matQ(:MR,N)
GO TO (103,104) MIXBND
103 CONTINUE
IF (N <= 3) GO TO 155
104 CONTINUE
JR = 2*I2R
NROD = 1
IF ((NR/2)*2 == NR) NROD = 0
SELECT CASE (MIXBND)
CASE DEFAULT
JSTART = 1
CASE (2)
JSTART = JR
NROD = 1 - NROD
END SELECT
JSTOP = NLAST - JR
IF (NROD == 0) JSTOP = JSTOP - I2R
CALL COSGEN (I2R, 1, HALF, ZERO, TCOS, 4*NR)
I2RBY2 = I2R/2
IF (JSTOP < JSTART) THEN
J = JR
ELSE
DO J = JSTART, JSTOP, JR
JP1 = J + I2RBY2
JP2 = J + I2R
JP3 = JP2 + I2RBY2
JM1 = J - I2RBY2
JM2 = J - I2R
JM3 = JM2 - I2RBY2
IF (J == 1) THEN
JM1 = JP1
JM2 = JP2
JM3 = JP3
ENDIF
IF (I2R == 1) THEN
IF (J == 1) JM2 = JP2
vecB(:MR) = TWO*matQ(:MR,J)
matQ(:MR,J) = matQ(:MR,JM2) + matQ(:MR,JP2)
ELSE
DO I = 1, MR
FI = matQ(I,J)
matQ(I,J)=matQ(I,J)-matQ(I,JM1)-matQ(I,JP1)+ &
matQ(I,JM2)+matQ(I,JP2)
vecB(I) = FI + matQ(I,J) - matQ(I,JM3) - matQ(I,JP3)
END DO
ENDIF
CALL TRIX (I2R, 0, MR, vecA, vecBB, vecC, vecB, TCOS, 4*NR, vecD, vecW)
matQ(:MR,J) = matQ(:MR,J) + vecB(:MR)
!
! END OF REDUCTION FOR REGULAR UNKNOWNS.
!
END DO
!
! BEGIN SPECIAL REDUCTION FOR LAST UNKNOWN.
!
J = JSTOP + JR
ENDIF
NLAST = J
JM1 = J - I2RBY2
JM2 = J - I2R
JM3 = JM2 - I2RBY2
IF (NROD /= 0) THEN
!
! ODD NUMBER OF UNKNOWNS
!
IF (I2R == 1) THEN
vecB(:MR) = FISTAG*matQ(:MR,J)
matQ(:MR,J) = matQ(:MR,JM2)
ELSE
vecB(:MR) = matQ(:MR,J) + HALF*(matQ(:MR,JM2)- &
matQ(:MR,JM1)-matQ(:MR,JM3))
IF (NRODPR == 0) THEN
matQ(:MR,J) = matQ(:MR,JM2) + vecP(IP+1:MR+IP)
IP = IP - MR
ELSE
matQ(:MR,J) = matQ(:MR,J) - matQ(:MR,JM1) + matQ(:MR,JM2)
ENDIF
IF (LR /= 0) THEN
CALL COSGEN (LR, 1, HALF, FDEN, TCOS(KR+1), 4*NR-KR)
ELSE
vecB(:MR) = FISTAG*vecB(:MR)
ENDIF
ENDIF
CALL COSGEN (KR, 1, HALF, FDEN, TCOS, 4*NR)
CALL TRIX (KR, LR, MR, vecA, vecBB, vecC, vecB, TCOS, 4*NR, vecD, vecW)
matQ(:MR,J) = matQ(:MR,J) + vecB(:MR)
KR = KR + I2R
ELSE
JP1 = J + I2RBY2
JP2 = J + I2R
IF (I2R == 1) THEN
vecB(:MR) = matQ(:MR,J)
CALL TRIX (1, 0, MR, vecA, vecBB, vecC, vecB, TCOS, 4*NR, vecD, vecW)
IP = 0
IPSTOR = MR
SELECT CASE (ISTAG)
CASE DEFAULT
vecP(:MR) = vecB(:MR)
vecB(:MR) = vecB(:MR) + matQ(:MR,N)
TCOS(1) = ONE
TCOS(2) = ZERO
CALL TRIX (1, 1, MR, vecA, vecBB, vecC, vecB, TCOS, 4*NR, vecD, vecW)
matQ(:MR,J) = matQ(:MR,JM2) + vecP(:MR) + vecB(:MR)
GO TO 150
CASE (1)
vecP(:MR) = vecB(:MR)
matQ(:MR,J) = matQ(:MR,JM2) + TWO*matQ(:MR,JP2) + 3.*vecB(:MR)
GO TO 150
END SELECT
ENDIF
vecB(:MR) = matQ(:MR,J) + HALF*(matQ(:MR,JM2)- &
matQ(:MR,JM1)-matQ(:MR,JM3))
IF (NRODPR == 0) THEN
vecB(:MR) = vecB(:MR) + vecP(IP+1:MR+IP)
ELSE
vecB(:MR) = vecB(:MR) + matQ(:MR,JP2) - matQ(:MR,JP1)
ENDIF
CALL TRIX (I2R, 0, MR, vecA, vecBB, vecC, vecB, TCOS, 4*NR, vecD, vecW)
IP = IP + MR
IPSTOR = MAX0(IPSTOR,IP + MR)
vecP(IP+1:MR+IP) = vecB(:MR) + HALF*(matQ(:MR,J)- &
matQ(:MR,JM1)-matQ(:MR,JP1))
vecB(:MR) = vecP(IP+1:MR+IP) + matQ(:MR,JP2)
IF (LR /= 0) THEN
CALL COSGEN (LR, 1, HALF, FDEN, TCOS(I2R+1), 4*NR-I2R)
CALL MERGE (TCOS, 0, I2R, I2R, LR, KR, 4*NR)
ELSE
DO I = 1, I2R
II = KR + I
TCOS(II) = TCOS(I)
END DO
ENDIF
CALL COSGEN (KR, 1, HALF, FDEN, TCOS, 4*NR)
IF (LR == 0) THEN
GO TO (146,145) ISTAG
ENDIF
145 CONTINUE
CALL TRIX (KR, KR, MR, vecA, vecBB, vecC, vecB, TCOS, 4*NR, vecD, vecW)
GO TO 148
146 CONTINUE
vecB(:MR) = FISTAG*vecB(:MR)
148 CONTINUE
matQ(:MR,J) = matQ(:MR,JM2) + vecP(IP+1:MR+IP) + vecB(:MR)
150 CONTINUE
LR = KR
KR = KR + JR
ENDIF
SELECT CASE (MIXBND)
CASE DEFAULT
NR = (NLAST - 1)/JR + 1
IF (NR <= 3) GO TO 155
CASE (2)
NR = NLAST/JR
IF (NR <= 1) GO TO 192
END SELECT
I2R = JR
NRODPR = NROD
GO TO 104
155 CONTINUE
J = 1 + JR
JM1 = J - I2R
JP1 = J + I2R
JM2 = NLAST - I2R
IF (NR /= 2) THEN
IF (LR /= 0) GO TO 170
IF (N == 3) THEN
!
! CASE N = 3.
!
GO TO (156,168) ISTAG
156 CONTINUE
vecB(:MR) = matQ(:MR,2)
TCOS(1) = ZERO
CALL TRIX (1, 0, MR, vecA, vecBB, vecC, vecB, TCOS, 4*NR, vecD, vecW)
matQ(:MR,2) = vecB(:MR)
vecB(:MR) = 4.*vecB(:MR) + matQ(:MR,1) + TWO*matQ(:MR,3)
TCOS(1) = -TWO
TCOS(2) = TWO
I1 = 2
I2 = 0
CALL TRIX (I1, I2, MR, vecA, vecBB, vecC, vecB, TCOS, 4*NR, vecD, vecW)
matQ(:MR,2) = matQ(:MR,2) + vecB(:MR)
vecB(:MR) = matQ(:MR,1) + TWO*matQ(:MR,2)
TCOS(1) = ZERO
CALL TRIX (1, 0, MR, vecA, vecBB, vecC, vecB, TCOS, 4*NR, vecD, vecW)
matQ(:MR,1) = vecB(:MR)
JR = 1
I2R = 0
GO TO 194
ENDIF
!
! CASE N = 2**P+1
!
GO TO (162,170) ISTAG
162 CONTINUE
vecB(:MR) = matQ(:MR,J) + HALF*matQ(:MR,1) - &
matQ(:MR,JM1) + matQ(:MR,NLAST) - matQ(:MR,JM2)
CALL COSGEN (JR, 1, HALF, ZERO, TCOS, 4*NR)
CALL TRIX (JR, 0, MR, vecA, vecBB, vecC, vecB, TCOS, 4*NR, vecD, vecW)
matQ(:MR,J) = HALF*(matQ(:MR,J)-matQ(:MR,JM1)-matQ(:MR,JP1)) + vecB(:MR)
vecB(:MR) = matQ(:MR,1) + TWO*matQ(:MR,NLAST) + 4.*matQ(:MR,J)
JR2 = 2*JR
CALL COSGEN (JR, 1, ZERO, ZERO, TCOS, 4*NR)
TCOS(JR+1:JR*2) = -TCOS(JR:1:(-1))
CALL TRIX (JR2, 0, MR, vecA, vecBB, vecC, vecB, TCOS, 4*NR, vecD, vecW)
matQ(:MR,J) = matQ(:MR,J) + vecB(:MR)
vecB(:MR) = matQ(:MR,1) + TWO*matQ(:MR,J)
CALL COSGEN (JR, 1, HALF, ZERO, TCOS, 4*NR)
CALL TRIX (JR, 0, MR, vecA, vecBB, vecC, vecB, TCOS, 4*NR, vecD, vecW)
matQ(:MR,1) = HALF*matQ(:MR,1) - matQ(:MR,JM1) + vecB(:MR)
GO TO 194
!
! CASE OF GENERAL N WITH NR = 3 .
!
168 CONTINUE
vecB(:MR) = matQ(:MR,2)
matQ(:MR,2) = ZERO
vecB2(:MR) = matQ(:MR,3)
vecB3(:MR) = matQ(:MR,1)
JR = 1
I2R = 0
J = 2
GO TO 177
170 CONTINUE
vecB(:MR) = HALF*matQ(:MR,1) - matQ(:MR,JM1) + matQ(:MR,J)
IF (NROD == 0) THEN
vecB(:MR) = vecB(:MR) + vecP(IP+1:MR+IP)
ELSE
vecB(:MR) = vecB(:MR) + matQ(:MR,NLAST) - matQ(:MR,JM2)
ENDIF
DO I = 1, MR
T = HALF*(matQ(I,J)-matQ(I,JM1)-matQ(I,JP1))
matQ(I,J) = T
vecB2(I) = matQ(I,NLAST) + T
vecB3(I) = matQ(I,1) + TWO*T
END DO
177 CONTINUE
K1 = KR + 2*JR - 1
K2 = KR + JR
TCOS(K1+1) = -TWO
K4 = K1 + 3 - ISTAG
CALL COSGEN (K2 + ISTAG - 2, 1, ZERO, FNUM, TCOS(K4), 4*NR-K4+1)
K4 = K1 + K2 + 1
CALL COSGEN (JR - 1, 1, ZERO, ONE, TCOS(K4), 4*NR-K4+1)
CALL MERGE (TCOS, K1, K2, K1 + K2, JR - 1, 0, 4*NR)
K3 = K1 + K2 + LR
CALL COSGEN (JR, 1, HALF, ZERO, TCOS(K3+1), 4*NR-K3)
K4 = K3 + JR + 1
CALL COSGEN (KR, 1, HALF, FDEN, TCOS(K4), 4*NR-K4+1)
CALL MERGE (TCOS, K3, JR, K3 + JR, KR, K1, 4*NR)
IF (LR /= 0) THEN
CALL COSGEN (LR, 1, HALF, FDEN, TCOS(K4), 4*NR-K4+1)
CALL MERGE (TCOS, K3, JR, K3 + JR, LR, K3 - LR, 4*NR)
CALL COSGEN (KR, 1, HALF, FDEN, TCOS(K4), 4*NR-K4+1)
ENDIF
K3 = KR
K4 = KR
CALL TRI3 (MR, vecA, vecBB, vecC, K, vecB, vecB2, vecB3, &
TCOS, 4*NR, vecD, vecW, vecW2, vecW3)
vecB(:MR) = vecB(:MR) + vecB2(:MR) + vecB3(:MR)
TCOS(1) = TWO
CALL TRIX (1, 0, MR, vecA, vecBB, vecC, vecB, TCOS, 4*NR, vecD, vecW)
matQ(:MR,J) = matQ(:MR,J) + vecB(:MR)
vecB(:MR) = matQ(:MR,1) + TWO*matQ(:MR,J)
CALL COSGEN (JR, 1, HALF, ZERO, TCOS, 4*NR)
CALL TRIX (JR, 0, MR, vecA, vecBB, vecC, vecB, TCOS, 4*NR, vecD, vecW)
IF (JR == 1) THEN
matQ(:MR,1) = vecB(:MR)
GO TO 194
ENDIF
matQ(:MR,1) = HALF*matQ(:MR,1) - matQ(:MR,JM1) + vecB(:MR)
GO TO 194
ENDIF
IF (N == 2) THEN
!
! CASE N = 2
!
vecB(:MR) = matQ(:MR,1)
TCOS(1) = ZERO
CALL TRIX (1, 0, MR, vecA, vecBB, vecC, vecB, TCOS, 4*NR, vecD, vecW)
matQ(:MR,1) = vecB(:MR)
vecB(:MR) = TWO*(matQ(:MR,2)+vecB(:MR))*FISTAG
TCOS(1) = -FISTAG
TCOS(2) = TWO
CALL TRIX (2, 0, MR, vecA, vecBB, vecC, vecB, TCOS, 4*NR, vecD, vecW)
matQ(:MR,1) = matQ(:MR,1) + vecB(:MR)
JR = 1
I2R = 0
GO TO 194
ENDIF
vecB3(:MR) = ZERO
vecB(:MR) = matQ(:MR,1) + TWO*vecP(IP+1:MR+IP)
matQ(:MR,1) = HALF*matQ(:MR,1) - matQ(:MR,JM1)
vecB2(:MR) = TWO*(matQ(:MR,1)+matQ(:MR,NLAST))
K1 = KR + JR - 1
TCOS(K1+1) = -TWO
K4 = K1 + 3 - ISTAG
CALL COSGEN (KR + ISTAG - 2, 1, ZERO, FNUM, TCOS(K4), 4*NR-K4+1)
K4 = K1 + KR + 1
CALL COSGEN (JR - 1, 1, ZERO, ONE, TCOS(K4), 4*NR-K4+1)
CALL MERGE (TCOS, K1, KR, K1 + KR, JR - 1, 0, 4*NR)
CALL COSGEN (KR, 1, HALF, FDEN, TCOS(K1+1), 4*NR-K1)
K2 = KR
K4 = K1 + K2 + 1
CALL COSGEN (LR, 1, HALF, FDEN, TCOS(K4), 4*NR-K4+1)
K3 = LR
K4 = 0
CALL TRI3 (MR, vecA, vecBB, vecC, K, vecB, vecB2, vecB3, TCOS, &
4*NR, vecD, vecW, vecW2, vecW3)
vecB(:MR) = vecB(:MR) + vecB2(:MR)
TCOS(1) = TWO
CALL TRIX (1, 0, MR, vecA, vecBB, vecC, vecB, TCOS, 4*NR, vecD, vecW)
matQ(:MR,1) = matQ(:MR,1) + vecB(:MR)
GO TO 194
192 CONTINUE
vecB(:MR) = matQ(:MR,NLAST)
GO TO 196
194 CONTINUE
J = NLAST - JR
vecB(:MR) = matQ(:MR,NLAST) + matQ(:MR,J)
196 CONTINUE
JM2 = NLAST - I2R
IF (JR == 1) THEN
matQ(:MR,NLAST) = ZERO
ELSE
IF (NROD == 0) THEN
matQ(:MR,NLAST) = vecP(IP+1:MR+IP)
IP = IP - MR
ELSE
matQ(:MR,NLAST) = matQ(:MR,NLAST) - matQ(:MR,JM2)
ENDIF
ENDIF
CALL COSGEN (KR, 1, HALF, FDEN, TCOS, 4*NR)
CALL COSGEN (LR, 1, HALF, FDEN, TCOS(KR+1), 4*NR-KR)
IF (LR == 0) THEN
vecB(:MR) = FISTAG*vecB(:MR)
ENDIF
CALL TRIX (KR, LR, MR, vecA, vecBB, vecC, vecB, TCOS, 4*NR, vecD, vecW)
matQ(:MR,NLAST) = matQ(:MR,NLAST) + vecB(:MR)
NLASTP = NLAST
206 CONTINUE
JSTEP = JR
JR = I2R
I2R = I2R/2
IF (JR == 0) GO TO 222
SELECT CASE (MIXBND)
CASE DEFAULT
JSTART = 1 + JR
CASE (2)
JSTART = JR
END SELECT
KR = KR - JR
IF (NLAST + JR <= N) THEN
KR = KR - JR
NLAST = NLAST + JR
JSTOP = NLAST - JSTEP
ELSE
JSTOP = NLAST - JR
ENDIF
LR = KR - JR
CALL COSGEN (JR, 1, HALF, ZERO, TCOS, 4*NR)
DO J = JSTART, JSTOP, JSTEP
JM2 = J - JR
JP2 = J + JR
IF (J == JR) THEN
vecB(:MR) = matQ(:MR,J) + matQ(:MR,JP2)
ELSE
vecB(:MR) = matQ(:MR,J) + matQ(:MR,JM2) + matQ(:MR,JP2)
ENDIF
IF (JR == 1) THEN
matQ(:MR,J) = ZERO
ELSE
JM1 = J - I2R
JP1 = J + I2R
matQ(:MR,J) = HALF*(matQ(:MR,J)-matQ(:MR,JM1)-matQ(:MR,JP1))
ENDIF
CALL TRIX (JR, 0, MR, vecA, vecBB, vecC, vecB, TCOS, 4*NR, vecD, vecW)
matQ(:MR,J) = matQ(:MR,J) + vecB(:MR)
END DO
NROD = 1
IF (NLAST + I2R <= N) NROD = 0
IF (NLASTP /= NLAST) GO TO 194
GO TO 206
222 CONTINUE
vecW(1) = IPSTOR
RETURN
END SUBROUTINE POISN2
SUBROUTINE POISP2(M, N, vecA, vecBB, vecC, matQ, IDIMQ, &
vecB, vecB2, vecB3, vecW, vecW2, vecW3, &
vecD, TCOS, vecP, IP)
implicit none
DOUBLE PRECISION, PARAMETER :: ZERO = 0.0D0, HALF = 0.5D0, &
ONE = 1.0D0, TWO = 2.0D0, &
FOUR = 4.0D0
!-----------------------------------------------
! D u m m y A r g u m e n t s
!-----------------------------------------------
INTEGER, INTENT(IN) :: M, N, IDIMQ, IP
DOUBLE PRECISION, DIMENSION(M), INTENT(IN) :: vecA, vecBB, vecC
DOUBLE PRECISION, DIMENSION(4*N), INTENT(INOUT) :: TCOS
DOUBLE PRECISION, DIMENSION(IDIMQ,N), INTENT(INOUT) :: matQ
DOUBLE PRECISION, DIMENSION(IP),INTENT(INOUT) :: vecP
DOUBLE PRECISION, DIMENSION(M),INTENT(INOUT) :: vecB, vecB2, vecB3, &
vecD, vecW, vecW2, vecW3
!-----------------------------------------------
! L o c a l V a r i a b l e s
!-----------------------------------------------
INTEGER :: MR, NR, NRM1, J, NRMJ, NRPJ, I, IPSTOR, LH
DOUBLE PRECISION :: S, T
!-----------------------------------------------
!
! SUBROUTINE TO SOLVE POISSON EQUATION WITH PERIODIC BOUNDARY
! CONDITIONS.
!
MR = M
NR = (N + 1)/2
NRM1 = NR - 1
IF (2*NR == N) THEN
!
! EVEN NUMBER OF UNKNOWNS
!
DO J = 1, NRM1
NRMJ = NR - J
NRPJ = NR + J
DO I = 1, MR
S = matQ(I,NRMJ) - matQ(I,NRPJ)
T = matQ(I,NRMJ) + matQ(I,NRPJ)
matQ(I,NRMJ) = S
matQ(I,NRPJ) = T
END DO
END DO
matQ(:MR,NR) = TWO*matQ(:MR,NR)
matQ(:MR,N) = TWO*matQ(:MR,N)
CALL POISD2 (MR, NRM1, 1, vecA, vecBB, vecC, matQ, IDIMQ, &
vecB, vecW, vecD, TCOS, vecP, IP)
IPSTOR = vecW(1)
CALL POISN2 (MR, NR + 1, 1, 1, vecA, vecBB, vecC, matQ(:,NR:), &
IDIMQ, vecB, vecB2, vecB3, vecW, vecW2, vecW3, vecD, &
TCOS, vecP, IP)
IPSTOR = MAX0(IPSTOR,INT(vecW(1)))
DO J = 1, NRM1
NRMJ = NR - J
NRPJ = NR + J
DO I = 1, MR
S = HALF*(matQ(I,NRPJ)+matQ(I,NRMJ))
T = HALF*(matQ(I,NRPJ)-matQ(I,NRMJ))
matQ(I,NRMJ) = S
matQ(I,NRPJ) = T
END DO
END DO
matQ(:MR,NR) = HALF*matQ(:MR,NR)
matQ(:MR,N) = HALF*matQ(:MR,N)
ELSE
DO J = 1, NRM1
NRPJ = N + 1 - J
DO I = 1, MR
S = matQ(I,J) - matQ(I,NRPJ)
T = matQ(I,J) + matQ(I,NRPJ)
matQ(I,J) = S
matQ(I,NRPJ) = T
END DO
END DO
matQ(:MR,NR) = TWO*matQ(:MR,NR)
LH = NRM1/2
DO J = 1, LH
NRMJ = NR - J
DO I = 1, MR
S = matQ(I,J)
matQ(I,J) = matQ(I,NRMJ)
matQ(I,NRMJ) = S
END DO
END DO
CALL POISD2 (MR, NRM1, 2, vecA, vecBB, vecC, matQ, IDIMQ, &
vecB, vecW, vecD, TCOS, vecP, IP)
IPSTOR = vecW(1)
CALL POISN2 (MR, NR, 2, 1, vecA, vecBB, vecC, matQ(:,NR:), IDIMQ, &
vecB, vecB2, vecB3, vecW, vecW2, vecW3, vecD, TCOS, &
vecP, IP)
IPSTOR = MAX0(IPSTOR,INT(vecW(1)))
DO J = 1, NRM1
NRPJ = NR + J
DO I = 1, MR
S = HALF*(matQ(I,NRPJ)+matQ(I,J))
T = HALF*(matQ(I,NRPJ)-matQ(I,J))
matQ(I,NRPJ) = T
matQ(I,J) = S
END DO
END DO
matQ(:MR,NR) = HALF*matQ(:MR,NR)
DO J = 1, LH
NRMJ = NR - J
DO I = 1, MR
S = matQ(I,J)
matQ(I,J) = matQ(I,NRMJ)
matQ(I,NRMJ) = S
END DO
END DO
ENDIF
vecW(1) = IPSTOR
!
! REVISION HISTORY---
!
! SEPTEMBER 1973 VERSION 1
! APRIL 1976 VERSION 2
! JANUARY 1978 VERSION 3
! DECEMBER 1979 VERSION 3.1
! FEBRUARY 1985 DOCUMENTATION UPGRADE
! NOVEMBER 1988 VERSION 3.2, FORTRAN 77 CHANGES
! June 2004 Version 5.0, Fortran 90 changes
!-----------------------------------------------------------------------
END SUBROUTINE POISP2
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