/* /* LME v2.3.1 */ /*zhuhail@vax.sbu.ac.uk*/ /* any comment welcome */ /* 19/6/95 */ /* This code solves linear multiple equations in Prolog. Using Gauss method, It finds the maximum (abs) element and changes the corresponding row and column to first row and column in the working matrix. */ go:- matrix(Matrix), write(Matrix),nl, linear_multi_equation(Matrix,Result), write('result = '),write(Result),nl,fail. matrix(Matrix):- Matrix= [[ 5, 0, 2], [ 1, 1,7] ]. /* matrix(Matrix):- Matrix= [[ 5, 1, 2,-3, 1], % 5*X1 + X2 + 2*X3 - 3*X4 = 1 [ 0, 0,-9, 7, 1], % - 9*X3 + 7*X4 = 1 [ 4, 9, 6,-8, 8], % 4*X1 + 9*X2 + 6*X3 - 8*X4 = 8 [ 5, 8, 1,-4, 8]]. % 5*X1 + 8*X2 + X3 - 4*X4 = 8 */ %The output is %[[5, 1, 2, -3, 1], [0, 0, -9, 7, 1], [4, 9, 6, -8, 8], [5, 8, 1, -4, 8]] %result = [1, 2, 3, 4] /* matrix(Matrix):- Matrix=[ [ 1,1,2,3,4,5,6,7,8,9,9,8,7,6,5,4,3,2,1,0,100 ] , [ 1,1,3,4,5,6,7,8,9,9,8,7,6,5,4,3,2,1,0,0,100 ] , [ 2,3,1,5,6,7,8,9,9,8,7,6,5,4,3,2,1,0,0,1,100 ] , [ 3,4,5,1,7,8,9,9,8,7,6,5,4,3,2,1,0,0,1,2,100 ] , [ 4,5,6,7,1,9,9,8,7,6,5,4,3,2,1,0,0,1,2,3,100 ] , [ 5,6,7,8,9,1,8,7,6,5,4,3,2,1,0,0,1,2,3,4,100 ] , [ 6,7,8,9,9,8,1,6,5,4,3,2,1,0,0,1,2,3,4,5,100 ] , [ 7,8,9,9,8,7,6,1,4,3,2,1,0,0,1,2,3,4,5,6,100 ] , [ 8,9,9,8,7,6,5,4,1,2,1,0,0,1,2,3,4,5,6,7,100 ] , [ 9,9,8,7,6,5,4,3,2,1,0,0,1,2,3,4,5,6,7,8,100 ] , [ 9,8,7,6,5,4,3,2,1,0,1,1,2,3,4,5,6,7,8,9,100 ] , [ 8,7,6,5,4,3,2,1,0,0,1,1,3,4,5,6,7,8,9,9,100 ] , [ 7,6,5,4,3,2,1,0,0,1,2,3,1,5,6,7,8,9,9,8,100 ] , [ 6,5,4,3,2,1,0,0,1,2,3,4,5,1,7,8,9,9,8,7,100 ] , [ 5,4,3,2,1,0,0,1,2,3,4,5,6,7,1,9,9,8,7,6,100 ] , [ 4,3,2,1,0,0,1,2,3,4,5,6,7,8,9,1,8,7,6,5,100 ] , [ 3,2,1,0,0,1,2,3,4,5,6,7,8,9,9,8,1,6,5,4,100 ] , [ 2,1,0,0,1,2,3,4,5,6,7,8,9,9,8,7,6,1,4,3,100 ] , [ 1,0,0,1,2,3,4,5,6,7,8,9,9,8,7,6,5,4,1,2,100 ] , [ 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,100 ]]. matrix(Matrix):- %representing a singular set of equations Matrix=[ [ 1 , 1 , 1 , 10 ], [ 2 , 2 , 2 , 12 ], [ 1 , 2 , 4 , 6 ]]. matrix(Matrix):- Matrix=[ [ 100,10,1,2.83 ], [ 144,12,1,4.51 ], [ 225,15,1,8.32 ]]. matrix(Matrix):- Matrix=[ [ 1,1,2,3,4,5,6,7,8,9,9,8,7,6,5,100 ], [ 1,1,3,4,5,6,7,8,9,9,8,7,6,5,4,100 ], [ 2,3,1,5,6,7,8,9,9,8,7,6,5,4,3,100 ], [ 3,4,5,1,7,8,9,9,8,7,6,5,4,3,2,100 ], [ 4,5,6,7,1,9,9,8,7,6,5,4,3,2,1,100 ], [ 5,6,7,8,9,1,8,7,6,5,4,3,2,1,0,100 ], [ 6,7,8,9,9,8,1,6,5,4,3,2,1,0,0,100 ], [ 7,8,9,9,8,7,6,1,4,3,2,1,0,0,1,100 ], [ 8,9,9,8,7,6,5,4,1,2,1,0,0,1,2,100 ], [ 9,9,8,7,6,5,4,3,2,1,0,0,1,2,3,100 ], [ 9,8,7,6,5,4,3,2,1,0,1,1,2,3,4,100 ], [ 8,7,6,5,4,3,2,1,0,0,1,1,3,4,5,100 ], [ 7,6,5,4,3,2,1,0,0,1,2,3,1,5,6,100 ], [ 6,5,4,3,2,1,0,0,1,2,3,4,5,1,7,100 ], [ 5,4,3,2,1,0,0,1,2,3,4,5,6,7,1,100 ]]. matrix(Matrix):- Matrix=[ [ 1,1,2,3,4,5,6,7,8,9,9,8,100 ], [ 1,1,3,4,5,6,7,8,9,9,8,7,100 ], [ 2,3,1,5,6,7,8,9,9,8,7,6,100 ], [ 3,4,5,1,7,8,9,9,8,7,6,5,100 ], [ 4,5,6,7,1,9,9,8,7,6,5,4,100 ], [ 5,6,7,8,9,1,8,7,6,5,4,3,100 ], [ 6,7,8,9,9,8,1,6,5,4,3,2,100 ], [ 7,8,9,9,8,7,6,1,4,3,2,1,100 ], [ 8,9,9,8,7,6,5,4,1,2,1,0,100 ], [ 9,9,8,7,6,5,4,3,2,1,0,0,100 ], [ 9,8,7,6,5,4,3,2,1,0,1,1,100 ], [ 8,7,6,5,4,3,2,1,0,0,1,1,100 ]]. matrix(Matrix):- Matrix=[ [ 0,1,2,3,4,5,6,7,8,9,100 ], [ 1,2,3,4,5,6,7,8,9,0,100 ], [ 2,3,4,5,6,7,8,9,0,1,100 ], [ 3,4,5,6,7,8,9,0,1,2,100 ], [ 4,5,6,7,8,9,0,1,2,3,100 ], [ 5,6,7,8,9,0,1,2,3,4,100 ], [ 6,7,8,9,0,1,2,3,4,5,100 ], [ 7,8,9,0,1,2,3,4,5,6,100 ], [ 8,9,0,1,2,3,4,5,6,7,100 ], [ 1,1,1,1,1,1,1,1,1,1,100 ]]. matrix(Matrix):- Matrix= [[ 0, 1, 1, -5, -4], [ 0, 0,-2, 1, 3], [ 1,-3, 3, 0,-11], [ 2, 0, 5, -3,-12]]. matrix(Matrix):- Matrix= [[ 3, 4,-1,-10], % 3*x1 + 4*x2 + -1*x3 = -10 [ 2,-3, 4, 28], % 2*x1 + -3*x2 + 4*x3 = 28 [-1, 1, 1, 2]]. %-1*x1 + x2 + x3 = 2 */ /*-------------------------------------------------------------------------*/ linear_multi_equation(Matrix,Result):- /* LME v2.3.1 */ getorder(Matrix,Index0), /* made by */ solut(Matrix,[],TriMatrix,Result1,Index0,Index), /*zhuhail@vax.sbu.ac.uk*/ backsubstitute(TriMatrix,[Result1],Result0), /* any comment welcome */ make_in_order(Result0,Index,Result). /* 19/6/95 */ solut([[H|[T|[]]]],Tem,TriMatrix,Result1,TemIndex,Index):- !, Tem=TriMatrix, Result1 is T/H, TemIndex=Index. solut(Matrix,Tem,TriMatrix,Result1,Index0,Index):- changematrix(Matrix,ChangedMatrix, Tem,ChangedTem,Index0,Index1), ChangedMatrix =[MainRow|SubMatrix], solut1(MainRow,SubMatrix,SubMatrix1), drop(SubMatrix1,ReduceMatrix), solut(ReduceMatrix,[MainRow|ChangedTem],TriMatrix,Result1,Index1,Index). solut1(_,[],N):- !, N=[]. solut1(MainRow,[Row|RT],[NewRow|NT]):- MainRow=[MainElement|_], Row=[LeftElement|_], Ratio is LeftElement/MainElement, solut2(MainElement,Ratio,MainRow,Row,NewRow), solut1(MainRow,RT,NT). solut2(_,_,[],E,N):- !, E=[], N=[]. solut2(MainElement,Ratio,[TopElement|MT],[Element|T],[NewElement|NT]):- NewElement is Element-Ratio*TopElement, solut2(MainElement,Ratio,MT,T,NT). changematrix(Matrix,ChangedMatrix,Tem,ChangedTem,Index0,Index):- maximum(Matrix,1,0,1,1,MaxRowNum,MaxColNum), change_row(Matrix,MaxRowNum,ChangedRowMatrix), change_col(ChangedRowMatrix,MaxColNum,ChangedMatrix), change_tri(Tem,MaxColNum,ChangedTem,Index0,Index). maximum([],_,_,TemRowNum,TemColNum,MaxRowNum,MaxColNum):- !, TemRowNum=MaxRowNum, TemColNum=MaxColNum. maximum([Row|MatrixT],RowNum,Max,TemRowNum,TemColNum,MaxRowNum,MaxColNum):- maximum1(Row,RowNum,1,Max,NewM,TemRowNum,TemColNum,MaxRowNum1,MaxColNum1), NextRowNum is RowNum+1, maximum(MatrixT,NextRowNum,NewM,MaxRowNum1,MaxColNum1,MaxRowNum,MaxColNum). abs(A,Abs):- A < 0, !, Abs is -A. abs(A,A). maximum1([_],_,_,Max,NewM,TemRowNum,TemColNum,MaxRowNum,MaxColNum):- !, Max=NewM, TemRowNum=MaxRowNum, TemColNum=MaxColNum. maximum1([H|T],RowNum,ColNum,Max,NewM,_,_,MaxRowNum,MaxColNum):- abs(H,AbsH), Max < AbsH, !, Max1 is AbsH, TemRowNum1 is RowNum, TemColNum1 is ColNum, NextC is ColNum+1, maximum1(T,RowNum,NextC,Max1,NewM,TemRowNum1,TemColNum1,MaxRowNum,MaxColNum). maximum1([_|T],RowNum,ColNum,Max,NewM,TemRowNum,TemColNum,MaxRowNum,MaxColNum):- NextC is ColNum+1, maximum1(T,RowNum,NextC,Max,NewM,TemRowNum,TemColNum,MaxRowNum,MaxColNum). change_row(Matrix,1,ChangedMatrix):- !, ChangedMatrix=Matrix. change_row(Matrix,MaxRowNum,ChangedMatrix):- change_row1(Matrix,1,MaxRowNum,NewMatrix,_,_,MainRow), NewMatrix=[_|T], ChangedMatrix = [MainRow|T]. change_col(Matrix,1,ChangedMatrix):- !, ChangedMatrix=Matrix. change_col(Matrix,MaxColNum,ChangedMatrix):- change_col1(Matrix,MaxColNum,ChangedMatrix). change_row1([],_,_,N,_,TemR,MainRow):- !, N=[], TemR=MainRow. change_row1([Row|MatrixT],RowNum,MaxRowNum,[_|NT],FirstRow,TemR,MainRow):- RowNum = 1, !, NextRowNum is RowNum+1, FirstRow = Row, change_row1(MatrixT,NextRowNum,MaxRowNum,NT,FirstRow,TemR,MainRow). change_row1([Row|MatrixT],RowNum,MaxRowNum,[NewRow|NT],FirstRow,TemR,MainRow):- RowNum = MaxRowNum, !, NewRow = FirstRow, TemR = Row, NextRowNum is RowNum+1, change_row1(MatrixT,NextRowNum,MaxRowNum,NT,FirstRow,TemR,MainRow). change_row1([Row|MatrixT],RowNum,MaxRowNum,[NewRow|NT],FirstRow,TemR,MainRow):- NewRow = Row, NextRowNum is RowNum+1, change_row1(MatrixT,NextRowNum,MaxRowNum,NT,FirstRow,TemR,MainRow). change_col1([],_,N):- !, N=[]. change_col1([Row|MatrixT],MaxColNum,[NewRow|NT]):- change_col2(Row,1,MaxColNum,Row1,_,_,Main), Row1 = [_|T], NewRow = [Main|T], change_col1(MatrixT,MaxColNum,NT). change_col2([Last],_,_,N,_,TemMain,Main):- !, N=[Last], TemMain=Main. change_col2([H|T],ColNum,MaxColNum,[_|NT],First,TemMain,Main):- ColNum = 1, !, NextColNum is ColNum+1, First = H, change_col2(T,NextColNum,MaxColNum,NT,First,TemMain,Main). change_col2([H|T],ColNum,MaxColNum,[NH|NT],First,TemMain,Main):- ColNum = MaxColNum, !, NH = First, TemMain = H, NextColNum is ColNum+1, change_col2(T,NextColNum,MaxColNum,NT,First,TemMain,Main). change_col2([H|T],ColNum,MaxColNum,[NH|NT],First,TemMain,Main):- NH = H, NextColNum is ColNum+1, change_col2(T,NextColNum,MaxColNum,NT,First,TemMain,Main). change_tri(Tem,1,ChangedTem,Index0,Index):- !, Tem=ChangedTem, Index0=Index. change_tri(Tem,MaxColNum,ChangedTem,Index0,Index):- ChangeNum is MaxColNum+1, change_tri1(Tem,2,ChangeNum,ChangedTem,MainNum1,ChangeNum1), MainNum2 is MainNum1-1, ChangeNum2 is ChangeNum1-1, /*for change vector*/ change_tri2(Index0,1,MainNum2,ChangeNum2,_,_,Index). change_tri1([],NextMainNum,NextChangeNum,N,MainNum1,ChangeNum1):- !, N=[], NextMainNum=MainNum1, NextChangeNum=ChangeNum1. change_tri1([Row|MatrixT],MainNum,ChangeNum,[NewRow|NT],MainNum1,ChangeNum1):- change_tri2(Row,1,MainNum,ChangeNum,_,_,NewRow), NextMainNum is MainNum+1, NextChangeNum is ChangeNum+1, change_tri1(MatrixT,NextMainNum,NextChangeNum,NT,MainNum1,ChangeNum1). change_tri2([],_,_,_,_,_,N):- !, N=[]. change_tri2([H|T],Num,MainNum,ChangeNum,MainE,ChangeE,[NH|NT]):- Num = MainNum, !, NH = ChangeE, NextNum is Num+1, MainE = H, change_tri2(T,NextNum,MainNum,ChangeNum,MainE,ChangeE,NT). change_tri2([H|T],Num,MainNum,ChangeNum,MainE,ChangeE,[NH|NT]):- Num = ChangeNum, !, NH = MainE, NextNum is Num+1, ChangeE = H, change_tri2(T,NextNum,MainNum,ChangeNum,MainE,ChangeE,NT). change_tri2([H|T],Num,MainNum,ChangeNum,MainE,ChangeE,[NH|NT]):- NH = H, NextNum is Num+1, change_tri2(T,NextNum,MainNum,ChangeNum,MainE,ChangeE,NT). drop([],R):- !, R=[]. drop([[_|ReduceRow]|T],[ReduceRow|RT]):- drop(T,RT). backsubstitute([],Tem,Result0):- !, Tem=Result0. backsubstitute([[H|RowT]|MatrixT],Tem,Result0):- multiply(RowT,Tem,0,Sum,RightElement), Result is (RightElement-Sum)/H, backsubstitute(MatrixT,[Result|Tem],Result0). multiply([H|[]],_,Tem,Sum,RightElement):- !, Sum is Tem, RightElement is H. multiply([H|T],[RH|RT],Tem,Sum,RightElement):- NewSum is Tem+H*RH, multiply(T,RT,NewSum,Sum,RightElement). make_in_order(Result0,Index,Result):- make_in_order1(Result0,Index,VectorWithNum), sort(VectorWithNum,SortVector), make_in_order2(SortVector,Result). make_in_order1([],_,R):- !, R=[]. make_in_order1([H|T],[IH|IT],[IH-H|RT]):- make_in_order1(T,IT,RT). make_in_order2([],R):- !, R=[]. make_in_order2([_-S|T],[S|RT]):- make_in_order2(T,RT). getorder([Row|_],Index0):- get1(Row,Index0,1). get1([],O,_):- !, O=[]. get1([_|T],[Num|OT],Num):- NextNum is Num+1, get1(T,OT,NextNum).