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Annotation of OpenXM_contrib/PHC/Ada/Homotopy/scaling.ads, Revision 1.1

1.1     ! maekawa     1: with Standard_Floating_Numbers;          use Standard_Floating_Numbers;
        !             2: with Standard_Complex_Vectors;           use Standard_Complex_Vectors;
        !             3: with Standard_Complex_Polynomials;       use Standard_Complex_Polynomials;
        !             4: with Standard_Complex_Poly_Systems;      use Standard_Complex_Poly_Systems;
        !             5: with Standard_Complex_Solutions;         use Standard_Complex_Solutions;
        !             6:
        !             7: package Scaling is
        !             8:
        !             9: -- DESCRIPTION :
        !            10: --   This package provides routines for scaling polynomials systems.
        !            11:
        !            12:   procedure Scale ( p : in out Poly );
        !            13:   procedure Scale ( s : in out Poly_Sys );
        !            14:
        !            15:   -- DESCRIPTION :
        !            16:   --   In each polynomial the coefficients are divided by the average
        !            17:   --   coefficient of that polynomial.
        !            18:
        !            19:   procedure Scale ( s : in out Poly_Sys; bas : in natural := 2;
        !            20:                     diff : in boolean; cond : out double_float;
        !            21:                     sccff : out vector );
        !            22:
        !            23:   -- DESCRIPTION :
        !            24:   --   Equation and variable scaling of a polynomial system.
        !            25:
        !            26:   -- ON ENTRY :
        !            27:   --   s        a polynomial system;
        !            28:   --   bas      must be 2 or 10;
        !            29:   --   diff     true to reduce the difference between the coefficients,
        !            30:   --            false, otherwise.
        !            31:
        !            32:   -- ON RETURN :
        !            33:   --   s        is the scaled polynomial system by centering the coefficients
        !            34:   --            close to units and eventually by reducing the difference
        !            35:   --            between the coefficients
        !            36:   --   cond     is an estimate for condition number of the linear system
        !            37:   --            that had to be solved for scaling the polynomial system;
        !            38:   --            it is an indication how good or bad the polynomial system
        !            39:   --            was scaled.
        !            40:   --   sccff    is a vector containing the the exponents (w.r.t. basis 10) of
        !            41:   --            the factors to scale the solutions back to the original
        !            42:   --            coordinates
        !            43:
        !            44:   procedure Scale ( basis : in natural; sccff : in Vector;
        !            45:                     s : in out Solution );
        !            46:   procedure Scale ( basis : in natural; sccff : in Vector;
        !            47:                     sols : in out Solution_List );
        !            48:
        !            49:   -- DESCRIPTION :
        !            50:   --   The solution(s) is (are) scaled backwards to the original coordinates,
        !            51:   --   the vector sccff has been constructed by the procedure above.
        !            52:
        !            53: end Scaling;