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Annotation of OpenXM_contrib/PHC/Ada/Homotopy/scaling.ads, Revision 1.1.1.1

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;