Annotation of OpenXM_contrib/PHC/Ada/Main/black_box_root_counting.adb, Revision 1.1
1.1 ! maekawa 1: with integer_io; use integer_io;
! 2: with Timing_Package; use Timing_Package;
! 3: with Communications_with_User; use Communications_with_User;
! 4: with Standard_Integer_Vectors; use Standard_Integer_Vectors;
! 5: with Standard_Complex_Poly_Systems; use Standard_Complex_Poly_Systems;
! 6: with Standard_Complex_Poly_Systems_io; use Standard_Complex_Poly_Systems_io;
! 7: with Arrays_of_Integer_Vector_Lists; use Arrays_of_Integer_Vector_Lists;
! 8: with Standard_Complex_Solutions_io; use Standard_Complex_Solutions_io;
! 9: with Total_Degree_Start_Systems; use Total_Degree_Start_Systems;
! 10: with Partitions_of_Sets_Of_Unknowns; use Partitions_of_Sets_of_Unknowns;
! 11: with Partitions_of_Sets_Of_Unknowns_io; use Partitions_of_Sets_of_Unknowns_io;
! 12: with m_Homogeneous_Bezout_Numbers; use m_Homogeneous_Bezout_Numbers;
! 13: with m_Homogeneous_Start_Systems; use m_Homogeneous_Start_Systems;
! 14: with Set_Structure,Set_Structure_io;
! 15: with Degree_Sets_Tables; use Degree_Sets_Tables;
! 16: with Random_Product_System;
! 17: with Random_Product_Start_Systems; use Random_Product_Start_Systems;
! 18: with Integer_Mixed_Subdivisions; use Integer_Mixed_Subdivisions;
! 19: with Black_Mixed_Volume_Computations; use Black_Mixed_Volume_Computations;
! 20:
! 21: procedure Black_Box_Root_Counting
! 22: ( file : in file_type;
! 23: p : in out Poly_Sys; rc : out natural;
! 24: q : out Poly_Sys; qsols : out Solution_List;
! 25: rocotime,hocotime : out duration ) is
! 26:
! 27: function Set_Structure_Bound ( p : Poly_Sys ) return natural is
! 28: begin
! 29: Random_Product_Start_Systems.Build_Set_Structure(p);
! 30: return Permanent(Degree_Sets_Tables.Create);
! 31: end Set_Structure_Bound;
! 32:
! 33: procedure Count_Roots
! 34: ( file : in file_type; p : in out Poly_Sys;
! 35: tode,mhbz,setb,mivo : out natural;
! 36: zz : out Partition; nz : out natural;
! 37: lifsup : out Link_to_Array_of_Lists;
! 38: mix : out Link_to_Vector; mixsub : out Mixed_Subdivision ) is
! 39:
! 40: -- DESCRIPTION :
! 41: -- Computes four different root counts for the system p.
! 42:
! 43: -- ON ENTRY :
! 44: -- file output file;
! 45: -- p a polynomial system.
! 46:
! 47: -- ON RETURN :
! 48: -- tode total degree;
! 49: -- mhbz m-homogeneous Bezout number;
! 50: -- setb bound based on set structure;
! 51: -- mivo mixed volume;
! 52: -- zz partition used to compute mhbz;
! 53: -- nz number of sets in partition zz;
! 54: -- lifsup lifted supports of the system;
! 55: -- mix type of mixture;
! 56: -- mixsub mixed subdivision used to compute mivo.
! 57:
! 58: timer : timing_widget;
! 59: n : constant natural := p'length;
! 60: d,bz,m,bs,mv : natural;
! 61: z : Partition(1..n);
! 62:
! 63: begin
! 64: tstart(timer);
! 65: d := Total_Degree(p);
! 66: PB(p,bz,m,z);
! 67: bs := Set_Structure_Bound(p);
! 68: Black_Box_Mixed_Volume_Computation(p,mix,lifsup,mixsub,mv);
! 69: tstop(timer);
! 70: new_line(file);
! 71: put_line(file,"ROOT COUNTS :");
! 72: new_line(file);
! 73: put(file,"total degree : ");
! 74: put(file,d,1); new_line(file);
! 75: put(file,m,1); put(file,"-homogeneous Bezout number : ");
! 76: put(file,bz,1); new_line(file);
! 77: put(file," with partition : "); put(file,z(1..m)); new_line(file);
! 78: put(file,"general linear-product Bezout number : ");
! 79: put(file,bs,1); new_line(file);
! 80: put_line(file," based on the set structure :");
! 81: Set_Structure_io.put(file);
! 82: put(file,"mixed volume : "); put(file,mv,1); new_line(file);
! 83: new_line(file);
! 84: print_times(file,timer,"Root Counting");
! 85: tode := d; mhbz := bz; setb := bs; mivo := mv;
! 86: zz := z; nz := m;
! 87: rocotime := Elapsed_User_Time(timer);
! 88: end Count_Roots;
! 89:
! 90: function Is_Minimum ( a,b,c,x : natural ) return boolean is
! 91:
! 92: -- DESCRIPTION :
! 93: -- Returns true if x <= a, x <= b, and x <= c.
! 94:
! 95: begin
! 96: return (x <= a) and (x <= b) and (x <= c);
! 97: end Is_Minimum;
! 98:
! 99: procedure Construct_Start_System
! 100: ( file : in file_type; p : in out Poly_Sys;
! 101: d,bz,bs,mv : in natural; z : in Partition;
! 102: mix : in Vector; lifted : in Array_of_Lists;
! 103: mixsub : in Mixed_Subdivision; roco : out natural;
! 104: qq : in out Poly_Sys; qqsols : in out Solution_List ) is
! 105:
! 106: -- DESCRIPTION :
! 107: -- Constructs a start system for the minimal root count and least
! 108: -- amount of work.
! 109:
! 110: -- ON ENTRY :
! 111: -- file output file;
! 112: -- p polynomial system;
! 113: -- d total degree;
! 114: -- bz m-homogeneous Bezout number;
! 115: -- bs Bezout number based on set structure;
! 116: -- mv mixed volume;
! 117: -- z partition that corresponds with bz;
! 118: -- mix type of mixture of the supports;
! 119: -- mixsub mixed subdivision used to computed mv.
! 120:
! 121: -- ON RETURN :
! 122: -- roco minimum(d,bz,bs,mv);
! 123: -- qq start system;
! 124: -- qqsols solutions of qq.
! 125:
! 126: timer : timing_widget;
! 127: n : constant natural := p'length;
! 128: nl : natural;
! 129:
! 130: begin
! 131: new_line(file);
! 132: tstart(timer);
! 133: if Is_Minimum(bz,bs,mv,d)
! 134: then put_line(file,"START SYSTEM BASED ON TOTAL DEGREE :");
! 135: roco := d;
! 136: Start_System(p,qq,qqsols);
! 137: elsif Is_Minimum(d,bs,mv,bz)
! 138: then put(file,z'length,1);
! 139: put_line(file,"-HOMOGENEOUS START SYSTEM :");
! 140: roco := bz;
! 141: m_Homogeneous_Start_System(p,z,qq,qqsols);
! 142: elsif Is_Minimum(d,bz,mv,bs)
! 143: then put_line(file,"LINEAR-PRODUCT START SYSTEM : ");
! 144: roco := bs;
! 145: Random_Product_System.Init(n);
! 146: Build_Random_Product_System(n);
! 147: qq := Random_Product_System.Polynomial_System;
! 148: Random_Product_System.Solve(qqsols,nl);
! 149: Set_Structure.Clear;
! 150: Random_Product_System.Clear;
! 151: else put_line(file,"RANDOM COEFFICIENT START SYSTEM :");
! 152: roco := mv;
! 153: Black_Box_Polyhedral_Continuation
! 154: (p,mix,lifted,mixsub,qq,qqsols);
! 155: end if;
! 156: tstop(timer);
! 157: new_line(file);
! 158: put_line(file,qq);
! 159: new_line(file);
! 160: put_line(file,"START SOLUTIONS : ");
! 161: new_line(file);
! 162: put(file,Length_Of(qqsols),Head_Of(qqsols).n,qqsols);
! 163: new_line(file);
! 164: print_times(file,timer,"Construction of Start System");
! 165: hocotime := Elapsed_User_Time(timer);
! 166: end Construct_Start_System;
! 167:
! 168: procedure Main is
! 169:
! 170: d,bz,bs,mv : natural;
! 171: z : partition(p'range);
! 172: nz : natural;
! 173: mix : Standard_Integer_Vectors.Link_to_Vector;
! 174: mixsub : Mixed_Subdivision;
! 175: lifsup : Link_to_Array_of_Lists;
! 176: qq : Poly_Sys(p'range);
! 177: qqsols : Solution_List;
! 178:
! 179: begin
! 180: Count_Roots(file,p,d,bz,bs,mv,z,nz,lifsup,mix,mixsub);
! 181: Construct_Start_System
! 182: (file,p,d,bz,bs,mv,z(1..nz),mix.all,lifsup.all,mixsub,rc,qq,qqsols);
! 183: q := qq; qsols := qqsols;
! 184: Clear(z);
! 185: Clear(mix);
! 186: Deep_Clear(lifsup);
! 187: Deep_Clear(mixsub);
! 188: end Main;
! 189:
! 190: begin
! 191: Main;
! 192: end Black_Box_Root_Counting;
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