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Location: MD/arcos/fish90/src/gnbnaux.f90
d6faa5ffcedf
13.9 KiB
text/x-fortran
install arcos
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! file gnbnaux.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 *
! * *
! * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
!
!
! PACKAGE GNBNAUX
!
! LATEST REVISION June 2004
!
! PURPOSE TO PROVIDE AUXILIARY ROUTINES FOR FISHPACK
! ENTRIES GENBUN AND POISTG.
!
! USAGE THERE ARE NO USER ENTRIES IN THIS PACKAGE.
! THE ROUTINES IN THIS PACKAGE ARE NOT INTENDED
! TO BE CALLED BY USERS, BUT RATHER BY ROUTINES
! IN PACKAGES GENBUN AND POISTG.
!
! SPECIAL CONDITIONS NONE
!
! I/O NONE
!
! PRECISION SINGLE
!
!
! 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 by John Adams in June 2004 incorporating
! Fortran 90 features
!
! PORTABILITY FORTRAN 90
! ********************************************************************
SUBROUTINE COSGEN(N, IJUMP, FNUM, FDEN, vecA, IA)
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) :: N, IJUMP, IA
DOUBLE PRECISION, INTENT(IN) :: FNUM, FDEN
DOUBLE PRECISION, DIMENSION(IA),INTENT(OUT) :: vecA
!-----------------------------------------------
! L o c a l V a r i a b l e s
!-----------------------------------------------
INTEGER :: K3, K4, K, K1, K5, I, K2, NP1
DOUBLE PRECISION :: PI, PIBYN, X, Y
!-----------------------------------------------
!
!
! THIS SUBROUTINE COMPUTES REQUIRED COSINE VALUES IN ASCENDING
! ORDER. WHEN IJUMP .GT. 1 THE ROUTINE COMPUTES VALUES
!
! 2*COS(J*PI/L) , J=1,2,...,L AND J .NE. 0(MOD N/IJUMP+1)
!
! WHERE L = IJUMP*(N/IJUMP+1).
!
!
! WHEN IJUMP = 1 IT COMPUTES
!
! 2*COS((J-FNUM)*PI/(N+FDEN)) , J=1, 2, ... ,N
!
! WHERE
! FNUM = 0.5, FDEN = 0.0, FOR REGULAR REDUCTION VALUES
! FNUM = 0.0, FDEN = 1.0, FOR B-R AND C-R WHEN ISTAG = 1
! FNUM = 0.0, FDEN = 0.5, FOR B-R AND C-R WHEN ISTAG = 2
! FNUM = 0.5, FDEN = 0.5, FOR B-R AND C-R WHEN ISTAG = 2
! IN POISN2 ONLY.
!
!
PI = 4.0*ATAN(1.0)
IF (N /= 0) THEN
IF (IJUMP /= 1) THEN
K3 = N/IJUMP + 1
K4 = K3 - 1
PIBYN = PI/FLOAT(N + IJUMP)
DO K = 1, IJUMP
K1 = (K - 1)*K3
K5 = (K - 1)*K4
DO I = 1, K4
X = K1 + I
K2 = K5 + I
vecA(K2) = -2.*COS(X*PIBYN)
END DO
END DO
ELSE
NP1 = N + 1
Y = PI/(FLOAT(N) + FDEN)
DO I = 1, N
X = FLOAT(NP1 - I) - FNUM
vecA(I) = 2.*COS(X*Y)
END DO
ENDIF
ENDIF
!
END SUBROUTINE COSGEN
SUBROUTINE MERGE(TCOS, I1, M1, I2, M2, I3, itcos)
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) :: I1, M1, I2, M2, I3, ITCOS
DOUBLE PRECISION, DIMENSION(ITCOS), INTENT(INOUT) :: TCOS
!-----------------------------------------------
! L o c a l V a r i a b l e s
!-----------------------------------------------
INTEGER :: J11, J3, J1, J2, J, L, K, M
DOUBLE PRECISION :: X, Y
!-----------------------------------------------
!
! THIS SUBROUTINE MERGES TWO ASCENDING STRINGS OF NUMBERS IN THE
! ARRAY TCOS. THE FIRST STRING IS OF LENGTH M1 AND STARTS AT
! TCOS(I1+1). THE SECOND STRING IS OF LENGTH M2 AND STARTS AT
! TCOS(I2+1). THE MERGED STRING GOES INTO TCOS(I3+1).
!
!
J1 = 1
J2 = 1
J = I3
IF (M1 == 0) GO TO 107
IF (M2 == 0) GO TO 104
101 CONTINUE
J11 = J1
J3 = MAX(M1,J11)
DO J1 = J11, J3
J = J + 1
L = J1 + I1
X = TCOS(L)
L = J2 + I2
Y = TCOS(L)
IF (X - Y > 0.) GO TO 103
TCOS(J) = X
END DO
GO TO 106
103 CONTINUE
TCOS(J) = Y
J2 = J2 + 1
IF (J2 <= M2) GO TO 101
IF (J1 > M1) GO TO 109
104 CONTINUE
K = J - J1 + 1
DO J = J1, M1
M = K + J
L = J + I1
TCOS(M) = TCOS(L)
END DO
GO TO 109
106 CONTINUE
IF (J2 > M2) GO TO 109
107 CONTINUE
K = J - J2 + 1
DO J = J2, M2
M = K + J
L = J + I2
TCOS(M) = TCOS(L)
END DO
109 CONTINUE
!
END SUBROUTINE MERGE
SUBROUTINE TRIX(IDEGBR, IDEGCR, M, vecA, vecB, vecC, vecY, TCOS, ITCOS, &
vecD, vecW)
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) :: IDEGBR, IDEGCR, M, ITCOS
DOUBLE PRECISION, DIMENSION(M), INTENT(IN) :: vecA, vecB, vecC
DOUBLE PRECISION, DIMENSION(ITCOS), INTENT(IN) :: TCOS
DOUBLE PRECISION, DIMENSION(M), INTENT(INOUT) :: vecY, vecD, vecW
!-----------------------------------------------
! L o c a l V a r i a b l e s
!-----------------------------------------------
INTEGER :: MM1, IFB, IFC, L, LINT, K, I, IP
DOUBLE PRECISION :: X, XX, Z
!-----------------------------------------------
!
! SUBROUTINE TO SOLVE A SYSTEM OF LINEAR EQUATIONS WHERE THE
! COEFFICIENT MATRIX IS A RATIONAL FUNCTION IN THE MATRIX GIVEN BY
! TRIDIAGONAL ( . . . , vecA(I), vecB(I), vecC(I), . . . ).
!
MM1 = M - 1
IFB = IDEGBR + 1
IFC = IDEGCR + 1
L = IFB/IFC
LINT = 1
DO K = 1, IDEGBR
X = TCOS(K)
IF (K == L) THEN
I = IDEGBR + LINT
XX = X - TCOS(I)
vecW(:M) = vecY(:M)
vecY(:M) = XX*vecY(:M)
ENDIF
Z = 1./(vecB(1)-X)
vecD(1) = vecC(1)*Z
vecY(1) = vecY(1)*Z
DO I = 2, MM1
Z = 1./(vecB(I)-X-vecA(I)*vecD(I-1))
vecD(I) = vecC(I)*Z
vecY(I) = (vecY(I)-vecA(I)*vecY(I-1))*Z
END DO
Z = vecB(M) - X - vecA(M)*vecD(MM1)
IF (Z == 0.) THEN
vecY(M) = 0.
ELSE
vecY(M) = (vecY(M)-vecA(M)*vecY(MM1))/Z
ENDIF
DO IP = 1, MM1
vecY(M-IP) = vecY(M-IP) - vecD(M-IP)*vecY(M+1-IP)
END DO
IF (K /= L) CYCLE
vecY(:M) = vecY(:M) + vecW(:M)
LINT = LINT + 1
L = (LINT*IFB)/IFC
END DO
!
END SUBROUTINE TRIX
SUBROUTINE TRI3(M, vecA, vecB, vecC, ivecK, vecY1, vecY2, vecY3, TCOS, &
ITCOS, vecD, vecW1, vecW2, vecW3)
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,ITCOS
INTEGER, DIMENSION(4),INTENT(IN) :: ivecK
DOUBLE PRECISION, DIMENSION(M), INTENT(IN) :: vecA, vecB, vecC
DOUBLE PRECISION, DIMENSION(ITCOS), INTENT(IN) :: TCOS
DOUBLE PRECISION, DIMENSION(M), INTENT(INOUT) :: vecY1, vecY2, vecY3, &
vecD, vecW1, vecW2, vecW3
!-----------------------------------------------
! L o c a l V a r i a b l e s
!-----------------------------------------------
INTEGER :: MM1, K1, K2, K3, K4, IF1, IF2, IF3, IF4, K2K3K4, &
L1, L2, L3, LINT1, LINT2, LINT3, KINT1, KINT2, KINT3, &
N, I, IP
DOUBLE PRECISION :: X, Z, XX
!-----------------------------------------------
!
! SUBROUTINE TO SOLVE THREE LINEAR SYSTEMS WHOSE COMMON COEFFICIENT
! MATRIX IS A RATIONAL FUNCTION IN THE MATRIX GIVEN BY
!
! TRIDIAGONAL (...,vecA(I),vecB(I),vecC(I),...)
!
MM1 = M - 1
K1 = ivecK(1)
K2 = ivecK(2)
K3 = ivecK(3)
K4 = ivecK(4)
IF1 = K1 + 1
IF2 = K2 + 1
IF3 = K3 + 1
IF4 = K4 + 1
K2K3K4 = K2 + K3 + K4
IF (K2K3K4 /= 0) THEN
L1 = IF1/IF2
L2 = IF1/IF3
L3 = IF1/IF4
LINT1 = 1
LINT2 = 1
LINT3 = 1
KINT1 = K1
KINT2 = KINT1 + K2
KINT3 = KINT2 + K3
ELSE
write(*,*) 'warning tri3: l1,l2,l3,kint1,kint2,kint3 uninitialized'
stop 'stop in tri3: l1,l2,l3,kint1,kint2,kint3 uninitialized'
ENDIF
DO N = 1, K1
X = TCOS(N)
IF (K2K3K4 /= 0) THEN
IF (N == L1) THEN
vecW1(:M) = vecY1(:M)
ENDIF
IF (N == L2) THEN
vecW2(:M) = vecY2(:M)
ENDIF
IF (N == L3) THEN
vecW3(:M) = vecY3(:M)
ENDIF
ENDIF
Z = 1./(vecB(1)-X)
vecD(1) = vecC(1)*Z
vecY1(1) = vecY1(1)*Z
vecY2(1) = vecY2(1)*Z
vecY3(1) = vecY3(1)*Z
DO I = 2, M
Z = 1./(vecB(I)-X-vecA(I)*vecD(I-1))
vecD(I) = vecC(I)*Z
vecY1(I) = (vecY1(I)-vecA(I)*vecY1(I-1))*Z
vecY2(I) = (vecY2(I)-vecA(I)*vecY2(I-1))*Z
vecY3(I) = (vecY3(I)-vecA(I)*vecY3(I-1))*Z
END DO
DO IP = 1, MM1
vecY1(M-IP) = vecY1(M-IP) - vecD(M-IP)*vecY1(M+1-IP)
vecY2(M-IP) = vecY2(M-IP) - vecD(M-IP)*vecY2(M+1-IP)
vecY3(M-IP) = vecY3(M-IP) - vecD(M-IP)*vecY3(M+1-IP)
END DO
IF (K2K3K4 == 0) CYCLE
IF (N == L1) THEN
I = LINT1 + KINT1
XX = X - TCOS(I)
vecY1(:M) = XX*vecY1(:M) + vecW1(:M)
LINT1 = LINT1 + 1
L1 = (LINT1*IF1)/IF2
ENDIF
IF (N == L2) THEN
I = LINT2 + KINT2
XX = X - TCOS(I)
vecY2(:M) = XX*vecY2(:M) + vecW2(:M)
LINT2 = LINT2 + 1
L2 = (LINT2*IF1)/IF3
ENDIF
IF (N /= L3) CYCLE
I = LINT3 + KINT3
XX = X - TCOS(I)
vecY3(:M) = XX*vecY3(:M) + vecW3(:M)
LINT3 = LINT3 + 1
L3 = (LINT3*IF1)/IF4
END DO
RETURN
!
! REVISION HISTORY---
!
! SEPTEMBER 1973 VERSION 1
! APRIL 1976 VERSION 2
! JANUARY 1978 VERSION 3
! DECEMBER 1979 VERSION 3.1
! OCTOBER 1980 CHANGED SEVERAL DIVIDES OF FLOATING INTEGERS
! TO INTEGER DIVIDES TO ACCOMODATE CRAY-1 ARITHMETIC.
! FEBRUARY 1985 DOCUMENTATION UPGRADE
! NOVEMBER 1988 VERSION 3.2, FORTRAN 77 CHANGES
!-----------------------------------------------------------------------
END SUBROUTINE TRI3
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