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Annotation of OpenXM_contrib/PHC/Ada/Main/phcpack.ads, Revision 1.1

1.1     ! maekawa     1: with text_io;                            use text_io;
        !             2: with Standard_Complex_Numbers;           use Standard_Complex_Numbers;
        !             3: with Standard_Complex_Poly_Systems;      use Standard_Complex_Poly_Systems;
        !             4: with Standard_Complex_Solutions;         use Standard_Complex_Solutions;
        !             5:
        !             6: package PHCPACK is
        !             7:
        !             8: -- DESCRIPTION :
        !             9: --   PHC is a numerical general-purpose solver for polynomial systems by
        !            10: --   homotopy continuation.  This package collects all major features of
        !            11: --   the package as organized according to the four stages of the solver.
        !            12:
        !            13: -- 1. PRE-PROCESSING : SCALING AND REDUCTION
        !            14:
        !            15:   procedure Equation_Scaling
        !            16:                  ( file : in file_type; p : in Poly_Sys; s : out Poly_Sys );
        !            17:
        !            18:   -- DESCRIPTION : equation scaling by dividing average coefficient.
        !            19:
        !            20:   -- ON ENTRY :
        !            21:   --   file        to write results on, must be opened for output;
        !            22:   --   p           a polynomial system.
        !            23:
        !            24:   -- ON RETURN :
        !            25:   --   s           a scaled polynomial system.
        !            26:
        !            27:   procedure Linear_Reduction
        !            28:                  ( file : in file_type; p : in Poly_Sys; r : out Poly_Sys );
        !            29:
        !            30:   -- DESCRIPTION : linear reduction of the coefficient matrix of p.
        !            31:
        !            32:   -- ON ENTRY :
        !            33:   --   file        to write results on, must be opened for output;
        !            34:   --   p           a polynomial system.
        !            35:
        !            36:   -- ON RETURN :
        !            37:   --   r           a polynomial system with reduced coefficient matrix.
        !            38:
        !            39: -- 2. ROOT COUNTING AND CONSTRUCTION OF START SYSTEM
        !            40:
        !            41:   procedure Total_Degree
        !            42:                  ( file : in file_type; p : in Poly_Sys; d : out natural );
        !            43:
        !            44:   -- DESCRIPTION : computation of the total degree.
        !            45:
        !            46:   -- ON ENTRY :
        !            47:   --   file        to write results on, must be opened for output;
        !            48:   --   p           a polynomial system.
        !            49:
        !            50:   -- ON RETURN :
        !            51:   --   d           total degree of the system p.
        !            52:
        !            53:   procedure Total_Degree
        !            54:                  ( file : in file_type; p : in Poly_Sys; d : out natural;
        !            55:                    q : out Poly_Sys; qsols : out Solution_List );
        !            56:
        !            57:   -- DESCRIPTION : construction of start system based on total degree.
        !            58:
        !            59:   -- ON ENTRY :
        !            60:   --   file        to write results on, must be opened for output;
        !            61:   --   p           a polynomial system.
        !            62:
        !            63:   -- ON RETURN :
        !            64:   --   d           total degree of the system p.
        !            65:   --   q           start system with same total degree as p;
        !            66:   --   qsols       solutions of q.
        !            67:
        !            68:   procedure Implicit_Lifting
        !            69:                  ( file : in file_type; p : in Poly_Sys; mv : out natural );
        !            70:
        !            71:   -- DESCRIPTION : computation of mixed volume by implicit lifting.
        !            72:
        !            73:   procedure Implicit_Lifting
        !            74:                  ( file : in file_type; p : in Poly_Sys; mv : out natural;
        !            75:                    q : out Poly_Sys; qsols : out Solution_List );
        !            76:
        !            77:   -- DESCRIPTION : construction of start system by implicit polyhedral homotopy.
        !            78:
        !            79:   procedure Static_Lifting
        !            80:                  ( file : in file_type; p : in Poly_Sys; mv : out natural );
        !            81:
        !            82:   -- DESCRIPTION : computation of mixed volume by static lifting.
        !            83:
        !            84:   procedure Static_Lifting
        !            85:                  ( file : in file_type; p : in Poly_Sys; mv : out natural;
        !            86:                    q : out Poly_Sys; qsols : out Solution_List );
        !            87:
        !            88:   -- DESCRIPTION : construction of start system by static polyhedral homotopy.
        !            89:
        !            90: -- 3. POLYNOMIAL CONTINUATION
        !            91:
        !            92:   procedure Artificial_Parameter_Continuation
        !            93:                  ( file : in file_type; p,q : in Poly_Sys;
        !            94:                    sols : in out Solution_List;
        !            95:                    k : in natural := 2;
        !            96:                    a : in Complex_Number := Create(1.0);
        !            97:                    target : in Complex_Number := Create(1.0) );
        !            98:
        !            99:   -- DESCRIPTION : continuation with the artificial-parameter homotopy
        !           100:   --   h(x,t) = a*(1-t)^k*q(x) + t^k*p(x) = 0, for t going to the target.
        !           101:
        !           102:   -- ON ENTRY :
        !           103:   --   file        to write results on, must be opened for output;
        !           104:   --   p           target system;
        !           105:   --   q           start system;
        !           106:   --   sols        start solutions;
        !           107:   --   k           smoothing parameter to simulate small steps;
        !           108:   --   a           random complex number to ensure regularity;
        !           109:   --   target      target value for continuation parameter.
        !           110:
        !           111:   -- ON RETURN :
        !           112:   --   sols        solutions for t = target.
        !           113:
        !           114:   procedure Natural_Parameter_Continuation
        !           115:                  ( file : in file_type; h : in Poly_Sys; k : in natural;
        !           116:                    t0,t1 : in Complex_Number; sols : in out Solution_List );
        !           117:
        !           118:   -- DESCRIPTION : continuation with a natural-parameter homotopy.
        !           119:
        !           120: -- 4. POST-PROCESSING : VALIDATION
        !           121:
        !           122:   procedure Refine_Roots
        !           123:                  ( file : in file_type; p : in Poly_Sys;
        !           124:                    sols : in out Solution_List );
        !           125:
        !           126:   -- DESCRIPTION : refines the roots and puts a report on file.
        !           127:
        !           128:   -- ON ENTRY :
        !           129:   --   file        to write results on, must be opened for output;
        !           130:   --   p           a polynomial system system;
        !           131:   --   sols        approximate solutions.
        !           132:
        !           133:   -- ON RETURN :
        !           134:   --   sols        refined solutions.
        !           135:
        !           136: end PHCPACK;