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Annotation of OpenXM_contrib/PHC/Ada/Homotopy/projective_transformations.adb, Revision 1.1

1.1     ! maekawa     1: with Standard_Floating_Numbers;          use Standard_Floating_Numbers;
        !             2: with Standard_Complex_Numbers;           use Standard_Complex_Numbers;
        !             3: with Standard_Natural_Vectors;
        !             4:
        !             5: package body Projective_Transformations is
        !             6:
        !             7:   function Projective_Transformation ( p : Poly ) return Poly is
        !             8:
        !             9:     deg : integer := Degree(p);
        !            10:     htd : Degrees
        !            11:         := new Standard_Natural_Vectors.Vector(1..Number_of_Unknowns(p)+1);
        !            12:     res : Poly := Null_Poly;
        !            13:
        !            14:     procedure Embed_Term ( t : in Term; continue : out boolean ) is
        !            15:
        !            16:       ht : Term;
        !            17:       sum : natural := 0;
        !            18:
        !            19:     begin
        !            20:       ht.cf := t.cf;
        !            21:       for i in t.dg'range loop
        !            22:         sum := sum + t.dg(i);
        !            23:         htd(i) := t.dg(i);
        !            24:       end loop;
        !            25:       htd(htd'last) := deg-sum;
        !            26:       ht.dg := htd;
        !            27:       Add(res,ht);
        !            28:       continue := true;
        !            29:     end Embed_Term;
        !            30:     procedure Embed_Terms is new Visiting_Iterator(Embed_Term);
        !            31:
        !            32:   begin
        !            33:     Embed_Terms(p);
        !            34:     Clear(htd);
        !            35:     return res;
        !            36:   end Projective_Transformation;
        !            37:
        !            38:   procedure Projective_Transformation ( p : in out Poly ) is
        !            39:
        !            40:     res : Poly := Projective_Transformation(p);
        !            41:
        !            42:   begin
        !            43:     Copy(res,p); Clear(res);
        !            44:   end Projective_Transformation;
        !            45:
        !            46:   function Projective_Transformation ( p : Poly_Sys ) return Poly_Sys is
        !            47:
        !            48:     res : Poly_Sys(p'range);
        !            49:
        !            50:   begin
        !            51:     for k in p'range loop
        !            52:       res(k) := Projective_Transformation(p(k));
        !            53:     end loop;
        !            54:     return res;
        !            55:   end Projective_Transformation;
        !            56:
        !            57:   procedure Projective_Transformation ( p : in out Poly_Sys ) is
        !            58:   begin
        !            59:     for k in p'range loop
        !            60:       Projective_Transformation(p(k));
        !            61:     end loop;
        !            62:   end Projective_Transformation;
        !            63:
        !            64:   function Projective_Transformation ( s : Solution ) return Solution is
        !            65:
        !            66:     n : natural := s.n;
        !            67:     r : Solution(n+1);
        !            68:
        !            69:   begin
        !            70:     r.v(1..n) := s.v(1..n);
        !            71:     r.v(n+1) := Create(1.0);
        !            72:     r.t := s.t;
        !            73:     r.m := s.m;
        !            74:     r.err := s.err;
        !            75:     r.rco := s.rco;
        !            76:     r.res := s.res;
        !            77:     return r;
        !            78:   end Projective_Transformation;
        !            79:
        !            80:   function Projective_Transformation
        !            81:              ( sols : Solution_List ) return Solution_List is
        !            82:
        !            83:     res,res_last : Solution_List;
        !            84:     tmp : Solution_List := sols;
        !            85:     ls : Link_to_Solution;
        !            86:
        !            87:   begin
        !            88:        while not Is_Null(tmp) loop
        !            89:       ls := Head_Of(tmp);
        !            90:       Append(res,res_last,Projective_Transformation(ls.all));
        !            91:       tmp := Tail_Of(tmp);
        !            92:     end loop;
        !            93:     return res;
        !            94:   end Projective_Transformation;
        !            95:
        !            96:   procedure Projective_Transformation ( sols : in out Solution_List ) is
        !            97:   begin
        !            98:     if Is_Null(sols)
        !            99:      then null;
        !           100:      else declare
        !           101:             temp : Solution_List := sols;
        !           102:             n : natural := Head_Of(sols).n;
        !           103:             l : Link_To_Solution;
        !           104:             s : Solution(n);
        !           105:             s2 : Solution(n+1);
        !           106:           begin
        !           107:             while not Is_Null(temp) loop
        !           108:               l := Head_Of(temp);
        !           109:               s := l.all;
        !           110:               s2 := Projective_Transformation(s);
        !           111:               Clear(l);
        !           112:               l := new Solution'(s2);
        !           113:               Set_Head(temp,l);
        !           114:               temp := Tail_Of(temp);
        !           115:             end loop;
        !           116:           end;
        !           117:     end if;
        !           118:   end Projective_Transformation;
        !           119:
        !           120:   function Affine_Transformation ( s : Solution ) return Solution is
        !           121:
        !           122:     n : natural := s.n;
        !           123:     r : Solution(n-1);
        !           124:     absvn : double_float := AbsVal(s.v(n));
        !           125:
        !           126:   begin
        !           127:     for i in 1..(n-1) loop
        !           128:       if absvn + Create(1.0) = Create(1.0)
        !           129:        then r.v(i) := Create(10.0**10);
        !           130:        else r.v(i) := s.v(i) / s.v(n);
        !           131:       end if;
        !           132:      end loop;
        !           133:      r.t := s.t;
        !           134:      r.m := s.m;
        !           135:      r.err := s.err;
        !           136:      r.rco := s.rco;
        !           137:      r.res := s.res;
        !           138:      return r;
        !           139:   exception
        !           140:     when numeric_error => r.v(1..(n-1)) := (1..(n-1) => Create(10.0**10));
        !           141:                           return r;
        !           142:   end Affine_Transformation;
        !           143:
        !           144:   procedure Affine_Transformation ( sols : in out Solution_List ) is
        !           145:   begin
        !           146:     if Is_Null(sols)
        !           147:      then null;
        !           148:      else declare
        !           149:             n : natural := Head_Of(sols).n;
        !           150:             s1 : Solution(n);
        !           151:             s2 : Solution(n-1);
        !           152:             temp : Solution_List := sols;
        !           153:             l : Link_To_Solution;
        !           154:           begin
        !           155:             while not Is_Null(temp) loop
        !           156:               l := Head_Of(temp);
        !           157:               s1 := l.all;
        !           158:               s2 := Affine_Transformation(s1);
        !           159:               Clear(l);
        !           160:               l := new Solution'(s2);
        !           161:               Set_Head(temp,l);
        !           162:               temp := Tail_Of(temp);
        !           163:             end loop;
        !           164:           end;
        !           165:     end if;
        !           166:   end Affine_Transformation;
        !           167:
        !           168: end Projective_Transformations;