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Annotation of OpenXM_contrib/PHC/Ada/Math_Lib/Matrices/standard_integer_linear_equalities.ads, Revision 1.1

1.1     ! maekawa     1: with Standard_Integer_Vectors;           use Standard_Integer_Vectors;
        !             2: with Standard_Integer_Matrices;          use Standard_Integer_Matrices;
        !             3:
        !             4: package Standard_Integer_Linear_Equalities is
        !             5:
        !             6: -- DESCRIPTION :
        !             7: --   This package provides for incrementally solving systems of
        !             8: --   linear equalities w.r.t. linear inequalities.
        !             9:
        !            10:   procedure Triangulate ( l : in natural; m : in matrix;
        !            11:                           first,last : in natural; ineq : in out matrix );
        !            12:   procedure Triangulate ( l : in natural; m : in matrix;
        !            13:                           index : in natural; ineq : in out matrix );
        !            14:
        !            15:   -- DESCRIPTION :
        !            16:   --   Updates a matrix of inequalities, after elimination of the lth unknown.
        !            17:
        !            18:   -- ON ENTRY :
        !            19:   --   l         current unknown to be eliminated;
        !            20:   --   m         m(1..l,m'range(2)) is upper triangular;
        !            21:   --   first     indicates start in range of ineq to be updated;
        !            22:   --   last      indicates end in range of ineq to be updated;
        !            23:   --   index     indicates the inequality to be updated;
        !            24:   --   ineq      in ineq(first..last) or in ineq(index),
        !            25:   --             the first l-1 unknowns are already eliminated.
        !            26:
        !            27:   -- ON RETURN :
        !            28:   --   ineq      the updated inequalities.
        !            29:
        !            30:   procedure Triangulate ( index,start : in natural; ineq : in out matrix );
        !            31:
        !            32:   -- DESCRIPTION :
        !            33:   --   Updates the inequality ineq(index), i.e. tries to eliminate as
        !            34:   --   many unknowns in ineq(index) as possible, by making positive
        !            35:   --   combinations with inequalities in ineq(ineq'first..index-1).
        !            36:
        !            37:   -- ON ENTRY :
        !            38:   --   index     current row in ineq that has to be updated;
        !            39:   --   start     indicates in which column the first nonzero elements
        !            40:   --             have to be found;
        !            41:   --   ineq      matrix of inequalities of type <.,.> >= 0.
        !            42:
        !            43:   -- ON RETURN :
        !            44:   --   ineq      the updated matrix of inequalities.
        !            45:
        !            46: end Standard_Integer_Linear_Equalities;