90 lines
2.6 KiB
Plaintext
90 lines
2.6 KiB
Plaintext
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/*
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**********************************************************************
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*
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* CLP(R) Version 2.0 (Example Programs Release)
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* (C) Copyright, March 1986, Monash University
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*
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**********************************************************************
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*/
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%
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% Solve the Dirichlet problem for Laplace's equation using
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% Leibman's five-point finit-differenc approximation. The goal
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% ?- go1 is a normal example, while the goal ?- go2
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% shows output constraints for a small region where the boundary conditions
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% are not specified.
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%
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laplace([H1,H2,H3|T]):-
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laplace_vec(H1,H2,H3),
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laplace([H2,H3|T]).
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laplace([_,_]).
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laplace_vec([TL,T,TR|T1],[ML,M,MR|T2],[BL,B,BR|T3]):-
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B + T + ML + MR - 4 * M = 0,
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laplace_vec([T,TR|T1],[M,MR|T2],[B,BR|T3]).
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laplace_vec([_,_],[_,_],[_,_]).
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printmat([H|T]):-
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printvec(H),
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printmat(T).
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printmat([]).
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printvec([H|T]):-
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printf("%7.2f",[H]),
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printvec(T).
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printvec([]):-
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printf("\n",[]).
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go1:-
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X = [
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[0,0,0,0,0,0,0,0,0,0,0],
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[100,_,_,_,_,_,_,_,_,_,100],
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[100,_,_,_,_,_,_,_,_,_,100],
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[100,_,_,_,_,_,_,_,_,_,100],
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[100,_,_,_,_,_,_,_,_,_,100],
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[100,_,_,_,_,_,_,_,_,_,100],
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[100,_,_,_,_,_,_,_,_,_,100],
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[100,_,_,_,_,_,_,_,_,_,100],
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[100,_,_,_,_,_,_,_,_,_,100],
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[100,_,_,_,_,_,_,_,_,_,100],
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[100,100,100,100,100,100,100,100,100,100,100]
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],
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laplace(X),
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printf("\n", []),
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printmat(X).
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% Answer:
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% 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
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% 100.00 51.11 32.52 24.56 21.11 20.12 21.11 24.56 32.52 51.11 100.00
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% 100.00 71.91 54.41 44.63 39.74 38.26 39.74 44.63 54.41 71.91 100.00
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% 100.00 82.12 68.59 59.80 54.97 53.44 54.97 59.80 68.59 82.12 100.00
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% 100.00 87.97 78.03 71.00 66.90 65.56 66.90 71.00 78.03 87.97 100.00
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% 100.00 91.71 84.58 79.28 76.07 75.00 76.07 79.28 84.58 91.71 100.00
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% 100.00 94.30 89.29 85.47 83.10 82.30 83.10 85.47 89.29 94.30 100.00
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% 100.00 96.20 92.82 90.20 88.56 88.00 88.56 90.20 92.82 96.20 100.00
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% 100.00 97.67 95.59 93.96 92.93 92.58 92.93 93.96 95.59 97.67 100.00
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% 100.00 98.89 97.90 97.12 96.63 96.46 96.63 97.12 97.90 98.89 100.00
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% 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00
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go2 :-
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laplace([
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[B11, B12, B13, B14],
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[B21, M22, M23, B24],
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[B31, M32, M33, B34],
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[B44, B42, B43, B44]
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]),
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printf("\n", []),
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dump.
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% Answer:
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% B12 = -B21 - 4*B31 + 16*M32 - 8*M33 + B34 - 4*B42 + B43
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% B13 = -B24 + B31 - 8*M32 + 16*M33 - 4*B34 + B42 - 4*B43
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% M22 = -B31 + 4*M32 - M33 - B42
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% M23 = -M32 + 4*M33 - B34 - B43
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?- printf("\n>>> Sample goals: go1/0, go2/0\n", []).
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