*DECK HW3CRT
SUBROUTINE HW3CRT (XS, XF, L, LBDCND, BDXS, BDXF, YS, YF, M,
+ MBDCND, BDYS, BDYF, ZS, ZF, N, NBDCND, BDZS, BDZF, ELMBDA,
+ LDIMF, MDIMF, F, PERTRB, IERROR, W)
C***BEGIN PROLOGUE HW3CRT
C***PURPOSE Solve the standard seven-point finite difference
C approximation to the Helmholtz equation in Cartesian
C coordinates.
C***LIBRARY SLATEC (FISHPACK)
C***CATEGORY I2B1A1A
C***TYPE SINGLE PRECISION (HW3CRT-S)
C***KEYWORDS CARTESIAN, ELLIPTIC, FISHPACK, HELMHOLTZ, PDE
C***AUTHOR Adams, J., (NCAR)
C Swarztrauber, P. N., (NCAR)
C Sweet, R., (NCAR)
C***DESCRIPTION
C
C Subroutine HW3CRT solves the standard seven-point finite
C difference approximation to the Helmholtz equation in Cartesian
C coordinates:
C
C (d/dX)(dU/dX) + (d/dY)(dU/dY) + (d/dZ)(dU/dZ)
C
C + LAMBDA*U = F(X,Y,Z) .
C
C * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
C
C
C * * * * * * * * Parameter Description * * * * * * * * * *
C
C
C * * * * * * On Input * * * * * *
C
C XS,XF
C The range of X, i.e. XS .LE. X .LE. XF .
C XS must be less than XF.
C
C L
C The number of panels into which the interval (XS,XF) is
C subdivided. Hence, there will be L+1 grid points in the
C X-direction given by X(I) = XS+(I-1)DX for I=1,2,...,L+1,
C where DX = (XF-XS)/L is the panel width. L must be at
C least 5 .
C
C LBDCND
C Indicates the type of boundary conditions at X = XS and X = XF.
C
C = 0 If the solution is periodic in X, i.e.
C U(L+I,J,K) = U(I,J,K).
C = 1 If the solution is specified at X = XS and X = XF.
C = 2 If the solution is specified at X = XS and the derivative
C of the solution with respect to X is specified at X = XF.
C = 3 If the derivative of the solution with respect to X is
C specified at X = XS and X = XF.
C = 4 If the derivative of the solution with respect to X is
C specified at X = XS and the solution is specified at X=XF.
C
C BDXS
C A two-dimensional array that specifies the values of the
C derivative of the solution with respect to X at X = XS.
C when LBDCND = 3 or 4,
C
C BDXS(J,K) = (d/dX)U(XS,Y(J),Z(K)), J=1,2,...,M+1,
C K=1,2,...,N+1.
C
C When LBDCND has any other value, BDXS is a dummy variable.
C BDXS must be dimensioned at least (M+1)*(N+1).
C
C BDXF
C A two-dimensional array that specifies the values of the
C derivative of the solution with respect to X at X = XF.
C When LBDCND = 2 or 3,
C
C BDXF(J,K) = (d/dX)U(XF,Y(J),Z(K)), J=1,2,...,M+1,
C K=1,2,...,N+1.
C
C When LBDCND has any other value, BDXF is a dummy variable.
C BDXF must be dimensioned at least (M+1)*(N+1).
C
C YS,YF
C The range of Y, i.e. YS .LE. Y .LE. YF.
C YS must be less than YF.
C
C M
C The number of panels into which the interval (YS,YF) is
C subdivided. Hence, there will be M+1 grid points in the
C Y-direction given by Y(J) = YS+(J-1)DY for J=1,2,...,M+1,
C where DY = (YF-YS)/M is the panel width. M must be at
C least 5 .
C
C MBDCND
C Indicates the type of boundary conditions at Y = YS and Y = YF.
C
C = 0 If the solution is periodic in Y, i.e.
C U(I,M+J,K) = U(I,J,K).
C = 1 If the solution is specified at Y = YS and Y = YF.
C = 2 If the solution is specified at Y = YS and the derivative
C of the solution with respect to Y is specified at Y = YF.
C = 3 If the derivative of the solution with respect to Y is
C specified at Y = YS and Y = YF.
C = 4 If the derivative of the solution with respect to Y is
C specified at Y = YS and the solution is specified at Y=YF.
C
C BDYS
C A two-dimensional array that specifies the values of the
C derivative of the solution with respect to Y at Y = YS.
C When MBDCND = 3 or 4,
C
C BDYS(I,K) = (d/dY)U(X(I),YS,Z(K)), I=1,2,...,L+1,
C K=1,2,...,N+1.
C
C When MBDCND has any other value, BDYS is a dummy variable.
C BDYS must be dimensioned at least (L+1)*(N+1).
C
C BDYF
C A two-dimensional array that specifies the values of the
C derivative of the solution with respect to Y at Y = YF.
C When MBDCND = 2 or 3,
C
C BDYF(I,K) = (d/dY)U(X(I),YF,Z(K)), I=1,2,...,L+1,
C K=1,2,...,N+1.
C
C When MBDCND has any other value, BDYF is a dummy variable.
C BDYF must be dimensioned at least (L+1)*(N+1).
C
C ZS,ZF
C The range of Z, i.e. ZS .LE. Z .LE. ZF.
C ZS must be less than ZF.
C
C N
C The number of panels into which the interval (ZS,ZF) is
C subdivided. Hence, there will be N+1 grid points in the
C Z-direction given by Z(K) = ZS+(K-1)DZ for K=1,2,...,N+1,
C where DZ = (ZF-ZS)/N is the panel width. N must be at least 5.
C
C NBDCND
C Indicates the type of boundary conditions at Z = ZS and Z = ZF.
C
C = 0 If the solution is periodic in Z, i.e.
C U(I,J,N+K) = U(I,J,K).
C = 1 If the solution is specified at Z = ZS and Z = ZF.
C = 2 If the solution is specified at Z = ZS and the derivative
C of the solution with respect to Z is specified at Z = ZF.
C = 3 If the derivative of the solution with respect to Z is
C specified at Z = ZS and Z = ZF.
C = 4 If the derivative of the solution with respect to Z is
C specified at Z = ZS and the solution is specified at Z=ZF.
C
C BDZS
C A two-dimensional array that specifies the values of the
C derivative of the solution with respect to Z at Z = ZS.
C When NBDCND = 3 or 4,
C
C BDZS(I,J) = (d/dZ)U(X(I),Y(J),ZS), I=1,2,...,L+1,
C J=1,2,...,M+1.
C
C When NBDCND has any other value, BDZS is a dummy variable.
C BDZS must be dimensioned at least (L+1)*(M+1).
C
C BDZF
C A two-dimensional array that specifies the values of the
C derivative of the solution with respect to Z at Z = ZF.
C When NBDCND = 2 or 3,
C
C BDZF(I,J) = (d/dZ)U(X(I),Y(J),ZF), I=1,2,...,L+1,
C J=1,2,...,M+1.
C
C When NBDCND has any other value, BDZF is a dummy variable.
C BDZF must be dimensioned at least (L+1)*(M+1).
C
C ELMBDA
C The constant LAMBDA in the Helmholtz equation. If
C LAMBDA .GT. 0, a solution may not exist. However, HW3CRT will
C attempt to find a solution.
C
C F
C A three-dimensional array that specifies the values of the
C right side of the Helmholtz equation and boundary values (if
C any). For I=2,3,...,L, J=2,3,...,M, and K=2,3,...,N
C
C F(I,J,K) = F(X(I),Y(J),Z(K)).
C
C On the boundaries F is defined by
C
C LBDCND F(1,J,K) F(L+1,J,K)
C ------ --------------- ---------------
C
C 0 F(XS,Y(J),Z(K)) F(XS,Y(J),Z(K))
C 1 U(XS,Y(J),Z(K)) U(XF,Y(J),Z(K))
C 2 U(XS,Y(J),Z(K)) F(XF,Y(J),Z(K)) J=1,2,...,M+1
C 3 F(XS,Y(J),Z(K)) F(XF,Y(J),Z(K)) K=1,2,...,N+1
C 4 F(XS,Y(J),Z(K)) U(XF,Y(J),Z(K))
C
C MBDCND F(I,1,K) F(I,M+1,K)
C ------ --------------- ---------------
C
C 0 F(X(I),YS,Z(K)) F(X(I),YS,Z(K))
C 1 U(X(I),YS,Z(K)) U(X(I),YF,Z(K))
C 2 U(X(I),YS,Z(K)) F(X(I),YF,Z(K)) I=1,2,...,L+1
C 3 F(X(I),YS,Z(K)) F(X(I),YF,Z(K)) K=1,2,...,N+1
C 4 F(X(I),YS,Z(K)) U(X(I),YF,Z(K))
C
C NBDCND F(I,J,1) F(I,J,N+1)
C ------ --------------- ---------------
C
C 0 F(X(I),Y(J),ZS) F(X(I),Y(J),ZS)
C 1 U(X(I),Y(J),ZS) U(X(I),Y(J),ZF)
C 2 U(X(I),Y(J),ZS) F(X(I),Y(J),ZF) I=1,2,...,L+1
C 3 F(X(I),Y(J),ZS) F(X(I),Y(J),ZF) J=1,2,...,M+1
C 4 F(X(I),Y(J),ZS) U(X(I),Y(J),ZF)
C
C F must be dimensioned at least (L+1)*(M+1)*(N+1).
C
C NOTE:
C
C If the table calls for both the solution U and the right side F
C on a boundary, then the solution must be specified.
C
C LDIMF
C The row (or first) dimension of the arrays F,BDYS,BDYF,BDZS,
C and BDZF as it appears in the program calling HW3CRT. this
C parameter is used to specify the variable dimension of these
C arrays. LDIMF must be at least L+1.
C
C MDIMF
C The column (or second) dimension of the array F and the row (or
C first) dimension of the arrays BDXS and BDXF as it appears in
C the program calling HW3CRT. This parameter is used to specify
C the variable dimension of these arrays.
C MDIMF must be at least M+1.
C
C W
C A one-dimensional array that must be provided by the user for
C work space. The length of W must be at least 30 + L + M + 5*N
C + MAX(L,M,N) + 7*(INT((L+1)/2) + INT((M+1)/2))
C
C
C * * * * * * On Output * * * * * *
C
C F
C Contains the solution U(I,J,K) of the finite difference
C approximation for the grid point (X(I),Y(J),Z(K)) for
C I=1,2,...,L+1, J=1,2,...,M+1, and K=1,2,...,N+1.
C
C PERTRB
C If a combination of periodic or derivative boundary conditions
C is specified for a Poisson equation (LAMBDA = 0), a solution
C may not exist. PERTRB is a constant, calculated and subtracted
C from F, which ensures that a solution exists. PWSCRT then
C computes this solution, which is a least squares solution to
C the original approximation. This solution is not unique and is
C unnormalized. The value of PERTRB should be small compared to
C the right side F. Otherwise, a solution is obtained to an
C essentially different problem. This comparison should always
C be made to insure that a meaningful solution has been obtained.
C
C IERROR
C An error flag that indicates invalid input parameters. Except
C for numbers 0 and 12, a solution is not attempted.
C
C = 0 No error
C = 1 XS .GE. XF
C = 2 L .LT. 5
C = 3 LBDCND .LT. 0 .OR. LBDCND .GT. 4
C = 4 YS .GE. YF
C = 5 M .LT. 5
C = 6 MBDCND .LT. 0 .OR. MBDCND .GT. 4
C = 7 ZS .GE. ZF
C = 8 N .LT. 5
C = 9 NBDCND .LT. 0 .OR. NBDCND .GT. 4
C = 10 LDIMF .LT. L+1
C = 11 MDIMF .LT. M+1
C = 12 LAMBDA .GT. 0
C
C Since this is the only means of indicating a possibly incorrect
C call to HW3CRT, the user should test IERROR after the call.
C
C *Long Description:
C
C * * * * * * * Program Specifications * * * * * * * * * * * *
C
C Dimension of BDXS(MDIMF,N+1),BDXF(MDIMF,N+1),BDYS(LDIMF,N+1),
C Arguments BDYF(LDIMF,N+1),BDZS(LDIMF,M+1),BDZF(LDIMF,M+1),
C F(LDIMF,MDIMF,N+1),W(see argument list)
C
C Latest December 1, 1978
C Revision
C
C Subprograms HW3CRT,POIS3D,POS3D1,TRIDQ,RFFTI,RFFTF,RFFTF1,
C Required RFFTB,RFFTB1,COSTI,COST,SINTI,SINT,COSQI,COSQF,
C COSQF1,COSQB,COSQB1,SINQI,SINQF,SINQB,CFFTI,
C CFFTI1,CFFTB,CFFTB1,PASSB2,PASSB3,PASSB4,PASSB,
C CFFTF,CFFTF1,PASSF1,PASSF2,PASSF3,PASSF4,PASSF,
C PIMACH
C
C Special NONE
C Conditions
C
C Common NONE
C Blocks
C
C I/O NONE
C
C Precision Single
C
C Specialist Roland Sweet
C
C Language FORTRAN
C
C History Written by Roland Sweet at NCAR in July 1977
C
C Algorithm This subroutine defines the finite difference
C equations, incorporates boundary data, and
C adjusts the right side of singular systems and
C then calls POIS3D to solve the system.
C
C Space 7862(decimal) = 17300(octal) locations on the
C Required NCAR Control Data 7600
C
C Timing and The execution time T on the NCAR Control Data
C Accuracy 7600 for subroutine HW3CRT is roughly proportional
C to L*M*N*(log2(L)+log2(M)+5), but also depends on
C input parameters LBDCND and MBDCND. Some typical
C values are listed in the table below.
C The solution process employed results in a loss
C of no more than three significant digits for L,M
C and N as large as 32. More detailed information
C about accuracy can be found in the documentation
C for subroutine POIS3D which is the routine that
C actually solves the finite difference equations.
C
C
C L(=M=N) LBDCND(=MBDCND=NBDCND) T(MSECS)
C ------- ---------------------- --------
C
C 16 0 300
C 16 1 302
C 16 3 348
C 32 0 1925
C 32 1 1929
C 32 3 2109
C
C Portability American National Standards Institute FORTRAN.
C The machine dependent constant PI is defined in
C function PIMACH.
C
C Required COS,SIN,ATAN
C Resident
C Routines
C
C Reference NONE
C
C * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
C
C***REFERENCES (NONE)
C***ROUTINES CALLED POIS3D
C***REVISION HISTORY (YYMMDD)
C 801001 DATE WRITTEN
C 890531 Changed all specific intrinsics to generic. (WRB)
C 890531 REVISION DATE from Version 3.2
C 891214 Prologue converted to Version 4.0 format. (BAB)
C***END PROLOGUE HW3CRT
C
C
DIMENSION BDXS(MDIMF,*) ,BDXF(MDIMF,*) ,
1 BDYS(LDIMF,*) ,BDYF(LDIMF,*) ,
2 BDZS(LDIMF,*) ,BDZF(LDIMF,*) ,
3 F(LDIMF,MDIMF,*) ,W(*)
C***FIRST EXECUTABLE STATEMENT HW3CRT
IERROR = 0
IF (XF .LE. XS) IERROR = 1
IF (L .LT. 5) IERROR = 2
IF (LBDCND.LT.0 .OR. LBDCND.GT.4) IERROR = 3
IF (YF .LE. YS) IERROR = 4
IF (M .LT. 5) IERROR = 5
IF (MBDCND.LT.0 .OR. MBDCND.GT.4) IERROR = 6
IF (ZF .LE. ZS) IERROR = 7
IF (N .LT. 5) IERROR = 8
IF (NBDCND.LT.0 .OR. NBDCND.GT.4) IERROR = 9
IF (LDIMF .LT. L+1) IERROR = 10
IF (MDIMF .LT. M+1) IERROR = 11
IF (IERROR .NE. 0) GO TO 188
DY = (YF-YS)/M
TWBYDY = 2./DY
C2 = 1./(DY**2)
MSTART = 1
MSTOP = M
MP1 = M+1
MP = MBDCND+1
GO TO (104,101,101,102,102),MP
101 MSTART = 2
102 GO TO (104,104,103,103,104),MP
103 MSTOP = MP1
104 MUNK = MSTOP-MSTART+1
DZ = (ZF-ZS)/N
TWBYDZ = 2./DZ
NP = NBDCND+1
C3 = 1./(DZ**2)
NP1 = N+1
NSTART = 1
NSTOP = N
GO TO (108,105,105,106,106),NP
105 NSTART = 2
106 GO TO (108,108,107,107,108),NP
107 NSTOP = NP1
108 NUNK = NSTOP-NSTART+1
LP1 = L+1
DX = (XF-XS)/L
C1 = 1./(DX**2)
TWBYDX = 2./DX
LP = LBDCND+1
LSTART = 1
LSTOP = L
C
C ENTER BOUNDARY DATA FOR X-BOUNDARIES.
C
GO TO (122,109,109,112,112),LP
109 LSTART = 2
DO 111 J=MSTART,MSTOP
DO 110 K=NSTART,NSTOP
F(2,J,K) = F(2,J,K)-C1*F(1,J,K)
110 CONTINUE
111 CONTINUE
GO TO 115
112 DO 114 J=MSTART,MSTOP
DO 113 K=NSTART,NSTOP
F(1,J,K) = F(1,J,K)+TWBYDX*BDXS(J,K)
113 CONTINUE
114 CONTINUE
115 GO TO (122,116,119,119,116),LP
116 DO 118 J=MSTART,MSTOP
DO 117 K=NSTART,NSTOP
F(L,J,K) = F(L,J,K)-C1*F(LP1,J,K)
117 CONTINUE
118 CONTINUE
GO TO 122
119 LSTOP = LP1
DO 121 J=MSTART,MSTOP
DO 120 K=NSTART,NSTOP
F(LP1,J,K) = F(LP1,J,K)-TWBYDX*BDXF(J,K)
120 CONTINUE
121 CONTINUE
122 LUNK = LSTOP-LSTART+1
C
C ENTER BOUNDARY DATA FOR Y-BOUNDARIES.
C
GO TO (136,123,123,126,126),MP
123 DO 125 I=LSTART,LSTOP
DO 124 K=NSTART,NSTOP
F(I,2,K) = F(I,2,K)-C2*F(I,1,K)
124 CONTINUE
125 CONTINUE
GO TO 129
126 DO 128 I=LSTART,LSTOP
DO 127 K=NSTART,NSTOP
F(I,1,K) = F(I,1,K)+TWBYDY*BDYS(I,K)
127 CONTINUE
128 CONTINUE
129 GO TO (136,130,133,133,130),MP
130 DO 132 I=LSTART,LSTOP
DO 131 K=NSTART,NSTOP
F(I,M,K) = F(I,M,K)-C2*F(I,MP1,K)
131 CONTINUE
132 CONTINUE
GO TO 136
133 DO 135 I=LSTART,LSTOP
DO 134 K=NSTART,NSTOP
F(I,MP1,K) = F(I,MP1,K)-TWBYDY*BDYF(I,K)
134 CONTINUE
135 CONTINUE
136 CONTINUE
C
C ENTER BOUNDARY DATA FOR Z-BOUNDARIES.
C
GO TO (150,137,137,140,140),NP
137 DO 139 I=LSTART,LSTOP
DO 138 J=MSTART,MSTOP
F(I,J,2) = F(I,J,2)-C3*F(I,J,1)
138 CONTINUE
139 CONTINUE
GO TO 143
140 DO 142 I=LSTART,LSTOP
DO 141 J=MSTART,MSTOP
F(I,J,1) = F(I,J,1)+TWBYDZ*BDZS(I,J)
141 CONTINUE
142 CONTINUE
143 GO TO (150,144,147,147,144),NP
144 DO 146 I=LSTART,LSTOP
DO 145 J=MSTART,MSTOP
F(I,J,N) = F(I,J,N)-C3*F(I,J,NP1)
145 CONTINUE
146 CONTINUE
GO TO 150
147 DO 149 I=LSTART,LSTOP
DO 148 J=MSTART,MSTOP
F(I,J,NP1) = F(I,J,NP1)-TWBYDZ*BDZF(I,J)
148 CONTINUE
149 CONTINUE
C
C DEFINE A,B,C COEFFICIENTS IN W-ARRAY.
C
150 CONTINUE
IWB = NUNK+1
IWC = IWB+NUNK
IWW = IWC+NUNK
DO 151 K=1,NUNK
I = IWC+K-1
W(K) = C3
W(I) = C3
I = IWB+K-1
W(I) = -2.*C3+ELMBDA
151 CONTINUE
GO TO (155,155,153,152,152),NP
152 W(IWC) = 2.*C3
153 GO TO (155,155,154,154,155),NP
154 W(IWB-1) = 2.*C3
155 CONTINUE
PERTRB = 0.
C
C FOR SINGULAR PROBLEMS ADJUST DATA TO INSURE A SOLUTION WILL EXIST.
C
GO TO (156,172,172,156,172),LP
156 GO TO (157,172,172,157,172),MP
157 GO TO (158,172,172,158,172),NP
158 IF (ELMBDA) 172,160,159
159 IERROR = 12
GO TO 172
160 CONTINUE
MSTPM1 = MSTOP-1
LSTPM1 = LSTOP-1
NSTPM1 = NSTOP-1
XLP = (2+LP)/3
YLP = (2+MP)/3
ZLP = (2+NP)/3
S1 = 0.
DO 164 K=2,NSTPM1
DO 162 J=2,MSTPM1
DO 161 I=2,LSTPM1
S1 = S1+F(I,J,K)
161 CONTINUE
S1 = S1+(F(1,J,K)+F(LSTOP,J,K))/XLP
162 CONTINUE
S2 = 0.
DO 163 I=2,LSTPM1
S2 = S2+F(I,1,K)+F(I,MSTOP,K)
163 CONTINUE
S2 = (S2+(F(1,1,K)+F(1,MSTOP,K)+F(LSTOP,1,K)+F(LSTOP,MSTOP,K))/
1 XLP)/YLP
S1 = S1+S2
164 CONTINUE
S = (F(1,1,1)+F(LSTOP,1,1)+F(1,1,NSTOP)+F(LSTOP,1,NSTOP)+
1 F(1,MSTOP,1)+F(LSTOP,MSTOP,1)+F(1,MSTOP,NSTOP)+
2 F(LSTOP,MSTOP,NSTOP))/(XLP*YLP)
DO 166 J=2,MSTPM1
DO 165 I=2,LSTPM1
S = S+F(I,J,1)+F(I,J,NSTOP)
165 CONTINUE
166 CONTINUE
S2 = 0.
DO 167 I=2,LSTPM1
S2 = S2+F(I,1,1)+F(I,1,NSTOP)+F(I,MSTOP,1)+F(I,MSTOP,NSTOP)
167 CONTINUE
S = S2/YLP+S
S2 = 0.
DO 168 J=2,MSTPM1
S2 = S2+F(1,J,1)+F(1,J,NSTOP)+F(LSTOP,J,1)+F(LSTOP,J,NSTOP)
168 CONTINUE
S = S2/XLP+S
PERTRB = (S/ZLP+S1)/((LUNK+1.-XLP)*(MUNK+1.-YLP)*
1 (NUNK+1.-ZLP))
DO 171 I=1,LUNK
DO 170 J=1,MUNK
DO 169 K=1,NUNK
F(I,J,K) = F(I,J,K)-PERTRB
169 CONTINUE
170 CONTINUE
171 CONTINUE
172 CONTINUE
NPEROD = 0
IF (NBDCND .EQ. 0) GO TO 173
NPEROD = 1
W(1) = 0.
W(IWW-1) = 0.
173 CONTINUE
CALL POIS3D (LBDCND,LUNK,C1,MBDCND,MUNK,C2,NPEROD,NUNK,W,W(IWB),
1 W(IWC),LDIMF,MDIMF,F(LSTART,MSTART,NSTART),IR,W(IWW))
C
C FILL IN SIDES FOR PERIODIC BOUNDARY CONDITIONS.
C
IF (LP .NE. 1) GO TO 180
IF (MP .NE. 1) GO TO 175
DO 174 K=NSTART,NSTOP
F(1,MP1,K) = F(1,1,K)
174 CONTINUE
MSTOP = MP1
175 IF (NP .NE. 1) GO TO 177
DO 176 J=MSTART,MSTOP
F(1,J,NP1) = F(1,J,1)
176 CONTINUE
NSTOP = NP1
177 DO 179 J=MSTART,MSTOP
DO 178 K=NSTART,NSTOP
F(LP1,J,K) = F(1,J,K)
178 CONTINUE
179 CONTINUE
180 CONTINUE
IF (MP .NE. 1) GO TO 185
IF (NP .NE. 1) GO TO 182
DO 181 I=LSTART,LSTOP
F(I,1,NP1) = F(I,1,1)
181 CONTINUE
NSTOP = NP1
182 DO 184 I=LSTART,LSTOP
DO 183 K=NSTART,NSTOP
F(I,MP1,K) = F(I,1,K)
183 CONTINUE
184 CONTINUE
185 CONTINUE
IF (NP .NE. 1) GO TO 188
DO 187 I=LSTART,LSTOP
DO 186 J=MSTART,MSTOP
F(I,J,NP1) = F(I,J,1)
186 CONTINUE
187 CONTINUE
188 CONTINUE
RETURN
END