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264 lines
9 KiB
Fortran
264 lines
9 KiB
Fortran
*DECK BLKTRI
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SUBROUTINE BLKTRI (IFLG, NP, N, AN, BN, CN, MP, M, AM, BM, CM,
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+ IDIMY, Y, IERROR, W)
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C***BEGIN PROLOGUE BLKTRI
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C***PURPOSE Solve a block tridiagonal system of linear equations
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C (usually resulting from the discretization of separable
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C two-dimensional elliptic equations).
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C***LIBRARY SLATEC (FISHPACK)
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C***CATEGORY I2B4B
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C***TYPE SINGLE PRECISION (BLKTRI-S, CBLKTR-C)
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C***KEYWORDS ELLIPTIC PDE, FISHPACK, TRIDIAGONAL LINEAR SYSTEM
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C***AUTHOR Adams, J., (NCAR)
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C Swarztrauber, P. N., (NCAR)
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C Sweet, R., (NCAR)
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C***DESCRIPTION
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C
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C Subroutine BLKTRI Solves a System of Linear Equations of the Form
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C
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C AN(J)*X(I,J-1) + AM(I)*X(I-1,J) + (BN(J)+BM(I))*X(I,J)
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C
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C + CN(J)*X(I,J+1) + CM(I)*X(I+1,J) = Y(I,J)
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C
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C for I = 1,2,...,M and J = 1,2,...,N.
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C
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C I+1 and I-1 are evaluated modulo M and J+1 and J-1 modulo N, i.e.,
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C
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C X(I,0) = X(I,N), X(I,N+1) = X(I,1),
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C X(0,J) = X(M,J), X(M+1,J) = X(1,J).
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C
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C These equations usually result from the discretization of
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C separable elliptic equations. Boundary conditions may be
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C Dirichlet, Neumann, or Periodic.
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C
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C
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C * * * * * * * * * * ON INPUT * * * * * * * * * *
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C
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C IFLG
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C = 0 Initialization only. Certain quantities that depend on NP,
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C N, AN, BN, and CN are computed and stored in the work
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C array W.
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C = 1 The quantities that were computed in the initialization are
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C used to obtain the solution X(I,J).
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C
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C NOTE A call with IFLG=0 takes approximately one half the time
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C as a call with IFLG = 1 . However, the
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C initialization does not have to be repeated unless NP, N,
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C AN, BN, or CN change.
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C
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C NP
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C = 0 If AN(1) and CN(N) are not zero, which corresponds to
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C periodic boundary conditions.
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C = 1 If AN(1) and CN(N) are zero.
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C
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C N
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C The number of unknowns in the J-direction. N must be greater
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C than 4. The operation count is proportional to MNlog2(N), hence
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C N should be selected less than or equal to M.
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C
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C AN,BN,CN
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C One-dimensional arrays of length N that specify the coefficients
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C in the linear equations given above.
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C
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C MP
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C = 0 If AM(1) and CM(M) are not zero, which corresponds to
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C periodic boundary conditions.
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C = 1 If AM(1) = CM(M) = 0 .
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C
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C M
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C The number of unknowns in the I-direction. M must be greater
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C than 4.
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C
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C AM,BM,CM
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C One-dimensional arrays of length M that specify the coefficients
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C in the linear equations given above.
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C
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C IDIMY
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C The row (or first) dimension of the two-dimensional array Y as
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C it appears in the program calling BLKTRI. This parameter is
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C used to specify the variable dimension of Y. IDIMY must be at
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C least M.
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C
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C Y
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C A two-dimensional array that specifies the values of the right
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C side of the linear system of equations given above. Y must be
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C dimensioned at least M*N.
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C
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C W
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C A one-dimensional array that must be provided by the user for
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C work space.
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C If NP=1 define K=INT(log2(N))+1 and set L=2**(K+1) then
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C W must have dimension (K-2)*L+K+5+MAX(2N,6M)
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C
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C If NP=0 define K=INT(log2(N-1))+1 and set L=2**(K+1) then
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C W must have dimension (K-2)*L+K+5+2N+MAX(2N,6M)
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C
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C **IMPORTANT** For purposes of checking, the required dimension
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C of W is computed by BLKTRI and stored in W(1)
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C in floating point format.
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C
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C * * * * * * * * * * On Output * * * * * * * * * *
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C
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C Y
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C Contains the solution X.
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C
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C IERROR
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C An error flag that indicates invalid input parameters. Except
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C for number zero, a solution is not attempted.
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C
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C = 0 No error.
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C = 1 M is less than 5.
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C = 2 N is less than 5.
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C = 3 IDIMY is less than M.
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C = 4 BLKTRI failed while computing results that depend on the
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C coefficient arrays AN, BN, CN. Check these arrays.
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C = 5 AN(J)*CN(J-1) is less than 0 for some J. Possible reasons
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C for this condition are
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C 1. The arrays AN and CN are not correct.
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C 2. Too large a grid spacing was used in the discretization
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C of the elliptic equation.
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C 3. The linear equations resulted from a partial
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C differential equation which was not elliptic.
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C
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C W
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C Contains intermediate values that must not be destroyed if
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C BLKTRI will be called again with IFLG=1. W(1) contains the
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C number of locations required by W in floating point format.
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C
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C *Long Description:
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C
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C * * * * * * * Program Specifications * * * * * * * * * * * *
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C
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C Dimension of AN(N),BN(N),CN(N),AM(M),BM(M),CM(M),Y(IDIMY,N)
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C Arguments W(See argument list)
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C
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C Latest June 1979
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C Revision
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C
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C Required BLKTRI,BLKTRI,PROD,PRODP,CPROD,CPRODP,COMPB,INDXA,
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C Subprograms INDXB,INDXC,PPADD,PSGF,PPSGF,PPSPF,BSRH,TEVLS,
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C R1MACH
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C
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C Special The Algorithm may fail if ABS(BM(I)+BN(J)) is less
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C Conditions than ABS(AM(I))+ABS(AN(J))+ABS(CM(I))+ABS(CN(J))
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C for some I and J. The Algorithm will also fail if
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C AN(J)*CN(J-1) is less than zero for some J.
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C See the description of the output parameter IERROR.
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C
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C Common CBLKT
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C Blocks
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C
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C I/O None
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C
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C Precision Single
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C
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C Specialist Paul Swarztrauber
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C
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C Language FORTRAN
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C
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C History Version 1 September 1973
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C Version 2 April 1976
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C Version 3 June 1979
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C
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C Algorithm Generalized Cyclic Reduction (See Reference below)
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C
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C Space
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C Required Control Data 7600
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C
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C Portability American National Standards Institute Fortran.
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C The machine accuracy is set using function R1MACH.
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C
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C Required None
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C Resident
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C Routines
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C
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C References Swarztrauber,P. and R. Sweet, 'Efficient FORTRAN
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C Subprograms For The Solution Of Elliptic Equations'
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C NCAR TN/IA-109, July, 1975, 138 PP.
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C
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C Swarztrauber P. ,'A Direct Method For The Discrete
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C Solution Of Separable Elliptic Equations', S.I.A.M.
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C J. Numer. Anal.,11(1974) PP. 1136-1150.
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C
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C***REFERENCES P. N. Swarztrauber and R. Sweet, Efficient Fortran
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C subprograms for the solution of elliptic equations,
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C NCAR TN/IA-109, July 1975, 138 pp.
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C P. N. Swarztrauber, A direct method for the discrete
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C solution of separable elliptic equations, SIAM Journal
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C on Numerical Analysis 11, (1974), pp. 1136-1150.
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C***ROUTINES CALLED BLKTR1, COMPB, CPROD, CPRODP, PROD, PRODP
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C***COMMON BLOCKS CBLKT
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C***REVISION HISTORY (YYMMDD)
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C 801001 DATE WRITTEN
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C 890531 Changed all specific intrinsics to generic. (WRB)
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C 890531 REVISION DATE from Version 3.2
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C 891214 Prologue converted to Version 4.0 format. (BAB)
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C 920501 Reformatted the REFERENCES section. (WRB)
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C***END PROLOGUE BLKTRI
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C
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DIMENSION AN(*) ,BN(*) ,CN(*) ,AM(*) ,
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1 BM(*) ,CM(*) ,Y(IDIMY,*) ,W(*)
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EXTERNAL PROD ,PRODP ,CPROD ,CPRODP
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COMMON /CBLKT/ NPP ,K ,EPS ,CNV ,
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1 NM ,NCMPLX ,IK
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C***FIRST EXECUTABLE STATEMENT BLKTRI
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NM = N
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IERROR = 0
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IF (M-5) 101,102,102
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101 IERROR = 1
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GO TO 119
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102 IF (NM-3) 103,104,104
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103 IERROR = 2
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GO TO 119
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104 IF (IDIMY-M) 105,106,106
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105 IERROR = 3
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GO TO 119
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106 NH = N
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NPP = NP
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IF (NPP) 107,108,107
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107 NH = NH+1
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108 IK = 2
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K = 1
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109 IK = IK+IK
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K = K+1
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IF (NH-IK) 110,110,109
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110 NL = IK
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IK = IK+IK
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NL = NL-1
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IWAH = (K-2)*IK+K+6
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IF (NPP) 111,112,111
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C
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C DIVIDE W INTO WORKING SUB ARRAYS
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C
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111 IW1 = IWAH
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IWBH = IW1+NM
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W(1) = IW1-1+MAX(2*NM,6*M)
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GO TO 113
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112 IWBH = IWAH+NM+NM
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IW1 = IWBH
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W(1) = IW1-1+MAX(2*NM,6*M)
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NM = NM-1
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C
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C SUBROUTINE COMP B COMPUTES THE ROOTS OF THE B POLYNOMIALS
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C
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113 IF (IERROR) 119,114,119
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114 IW2 = IW1+M
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IW3 = IW2+M
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IWD = IW3+M
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IWW = IWD+M
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IWU = IWW+M
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IF (IFLG) 116,115,116
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115 CALL COMPB (NL,IERROR,AN,BN,CN,W(2),W(IWAH),W(IWBH))
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GO TO 119
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116 IF (MP) 117,118,117
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C
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C SUBROUTINE BLKTR1 SOLVES THE LINEAR SYSTEM
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C
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117 CALL BLKTR1 (NL,AN,BN,CN,M,AM,BM,CM,IDIMY,Y,W(2),W(IW1),W(IW2),
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1 W(IW3),W(IWD),W(IWW),W(IWU),PROD,CPROD)
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GO TO 119
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118 CALL BLKTR1 (NL,AN,BN,CN,M,AM,BM,CM,IDIMY,Y,W(2),W(IW1),W(IW2),
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1 W(IW3),W(IWD),W(IWW),W(IWU),PRODP,CPRODP)
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119 CONTINUE
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RETURN
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END
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