Annotation of OpenXM_contrib/PHC/Ada/Homotopy/drivers_for_homotopy_creation.adb, Revision 1.1
1.1 ! maekawa 1: with integer_io; use integer_io;
! 2: with Communications_with_User; use Communications_with_User;
! 3: with Standard_Floating_Numbers; use Standard_Floating_Numbers;
! 4: with Standard_Complex_Numbers_io; use Standard_Complex_Numbers_io;
! 5: with Standard_Random_Numbers; use Standard_Random_Numbers;
! 6: with Numbers_io; use Numbers_io;
! 7: with Standard_Complex_Polynomials; use Standard_Complex_Polynomials;
! 8: with Homotopy;
! 9: with Projective_Transformations; use Projective_Transformations;
! 10: with Homogenization; use Homogenization;
! 11:
! 12: package body Drivers_for_Homotopy_Creation is
! 13:
! 14: procedure Info_on_Power is
! 15:
! 16: i : array(1..6) of string(1..65);
! 17:
! 18: begin
! 19: i(1):=" The homotopy parameter k determines the power of the";
! 20: i(2):="continuation parameter t. Taking k>1 has as effect that at the";
! 21: i(3):="beginning and at the end of the continuation, changes in t do not";
! 22: i(4):="change the homotopy as much as with a homotopy that is linear in";
! 23: i(5):="t so that paths are better to follow. The default value k=2 is";
! 24: i(6):="recommended. ";
! 25: for j in i'range loop
! 26: put_line(i(j));
! 27: end loop;
! 28: end Info_on_Power;
! 29:
! 30: procedure Info_on_Constant is
! 31:
! 32: i : array(1..3) of string(1..65);
! 33:
! 34: begin
! 35: i(1):=" The homotopy parameter a ensures the regularity of the solution";
! 36: i(2):="paths, i.e.: by choosing a random complex number for a, all paths";
! 37: i(3):="are regular and do not diverge for t<1. ";
! 38: for j in i'range loop
! 39: put_line(i(j));
! 40: end loop;
! 41: end Info_on_Constant;
! 42:
! 43: procedure Info_on_Target is
! 44:
! 45: i : array(1..7) of string(1..65);
! 46:
! 47: begin
! 48: i(1):=" The target value for the continuation parameter t is by default";
! 49: i(2):="1. To create stepping stones in the continuation stage, it is";
! 50: i(3):="possible to let the continuation stop at t<1, for instance at t =";
! 51: i(4):="0.9 or even at a complex value for t. The solutions at t<1 will";
! 52: i(5):="serve at start solutions to take up the continuation in a later";
! 53: i(6):="stage. In this stage, the same homotopy parameters k and a must";
! 54: i(7):="be used. ";
! 55: for j in i'range loop
! 56: put_line(i(j));
! 57: end loop;
! 58: end Info_on_Target;
! 59:
! 60: procedure Info_on_Exit is
! 61:
! 62: i : constant string
! 63: :="By typing 0, the current settings are used in the homotopy.";
! 64:
! 65: begin
! 66: put_line(i);
! 67: end Info_on_Exit;
! 68:
! 69: procedure Info_on_Projective_Transformation is
! 70:
! 71: i : array(1..5) of string(1..65);
! 72:
! 73: begin
! 74: i(1):=" A projective transformation of the homotopy and start solutions";
! 75: i(2):="makes the equations in the polynomials homogeneous and adds an a";
! 76: i(3):="random hyperplane. The vectors of the start solutions are";
! 77: i(4):="extended with an additional unknown. For solutions at infinity,";
! 78: i(5):="this additional unknown equals zero. ";
! 79: for j in i'range loop
! 80: put_line(i(j));
! 81: end loop;
! 82: end Info_on_Projective_Transformation;
! 83:
! 84: procedure Read_Complex ( x : in out Complex_Number ) is
! 85:
! 86: -- DESCRIPTION :
! 87: -- User friendly reading of a complex number.
! 88:
! 89: re,im : double_float;
! 90:
! 91: begin
! 92: put(" Give a real number for real part : "); Read_Double_Float(re);
! 93: put(" Give a real number for imaginary part : "); Read_Double_Float(im);
! 94: x := Create(re,im);
! 95: end Read_Complex;
! 96:
! 97: procedure Default_Homotopy_Settings
! 98: ( k : out positive; a,t : out Complex_Number ) is
! 99: begin
! 100: k := 2;
! 101: a := Random1;
! 102: t := Create(1.0);
! 103: end Default_Homotopy_Settings;
! 104:
! 105: procedure Default_Homotopy_Settings
! 106: ( k : out positive; a,t : out Complex_Number;
! 107: proj : out boolean ) is
! 108: begin
! 109: Default_Homotopy_Settings(k,a,t);
! 110: proj := false;
! 111: end Default_Homotopy_Settings;
! 112:
! 113: procedure Menu_for_Homotopy_Settings
! 114: ( file : in file_type; k : in out positive;
! 115: a,t : in out Complex_Number; proj : in out boolean ) is
! 116:
! 117: ans : character;
! 118: choice : string(1..2) := " ";
! 119:
! 120: begin
! 121: new_line;
! 122: put_line
! 123: ("Homotopy is H(x,t) = a*(1-t)^k * Q(x) + t^k * P(x) = 0, t in [0,1],");
! 124: put_line
! 125: (" with Q(x) = 0 a start system, and P(x) = 0 the target system.");
! 126: loop
! 127: new_line;
! 128: put_line("MENU with settings for homotopy :");
! 129: put(" relaxation constant k : "); put(k,2); new_line;
! 130: put(" regularity constant a : "); put(a); new_line;
! 131: put(" target value for t : "); put(t); new_line;
! 132: put(" projective transformation : ");
! 133: if proj then put("yes"); else put("no"); end if; new_line;
! 134: put("Type k, a, t, or p to change, preceded by i for info."
! 135: & " Type 0 to exit : ");
! 136: Ask_Alternative(choice,"katp0",'i');
! 137: exit when choice(1) = '0';
! 138: case choice(1) is
! 139: when 'k' =>
! 140: put("Give a value (1,2, or 3) for the relaxation constant k : ");
! 141: Read_Positive(k);
! 142: when 'a' =>
! 143: put_line("Reading a complex value for the regularity constant a.");
! 144: loop
! 145: Read_Complex(a);
! 146: exit when AbsVal(a) /= 0.0;
! 147: put_line("The value 0 for a is not allowed! Try again.");
! 148: end loop;
! 149: when 't' =>
! 150: put_line("Reading the (complex) target value for t.");
! 151: Read_Complex(t);
! 152: when 'p' =>
! 153: put("Do you want a projective transformation? ");
! 154: Ask_Yes_or_No(ans); proj := (ans ='y');
! 155: when 'i' =>
! 156: new_line;
! 157: case choice(2) is
! 158: when 'k' => Info_on_Power;
! 159: when 'a' => Info_on_Constant;
! 160: when 't' => Info_on_Target;
! 161: when 'p' => Info_on_Projective_Transformation;
! 162: when '0' => Info_on_Exit;
! 163: when others => null;
! 164: end case;
! 165: when others => null;
! 166: end case;
! 167: end loop;
! 168: new_line(file);
! 169: put_line(file,"HOMOTOPY PARAMETERS :");
! 170: put(file," k : "); put(file,k,2); new_line(file);
! 171: put(file," a : "); put(file,a); new_line(file);
! 172: put(file," t : "); put(file,t); new_line(file);
! 173: if proj
! 174: then put_line(file," projective transformation");
! 175: else put_line(file," no projective transformation");
! 176: end if;
! 177: end Menu_for_Homotopy_Settings;
! 178:
! 179: procedure Menu_for_Homotopy_Settings
! 180: ( file : in file_type; k : in out positive;
! 181: a,t : in out Complex_Number ) is
! 182:
! 183: choice : string(1..2) := " ";
! 184:
! 185: begin
! 186: new_line;
! 187: put_line
! 188: ("Homotopy is H(x,t) = a*(1-t)^k * Q(x) + t^k * P(x) = 0, t in [0,1],");
! 189: put_line
! 190: (" with Q(x) = 0 a start system, and P(x) = 0 the target system.");
! 191: loop
! 192: new_line;
! 193: put_line("MENU with settings for homotopy :");
! 194: put(" relaxation constant k : "); put(k,2); new_line;
! 195: put(" regularity constant a : "); put(a); new_line;
! 196: put(" target value for t : "); put(t); new_line;
! 197: put("Type k, a, or t to change, preceded by i for info."
! 198: & " Type 0 to exit : ");
! 199: Ask_Alternative(choice,"kat0",'i');
! 200: exit when choice(1) = '0';
! 201: case choice(1) is
! 202: when 'k' =>
! 203: put("Give a value (1,2, or 3) for the relaxation constant k : ");
! 204: Read_Positive(k);
! 205: when 'a' =>
! 206: put_line("Reading a complex value for the regularity constant a.");
! 207: loop
! 208: Read_Complex(a);
! 209: exit when AbsVal(a) /= 0.0;
! 210: put_line("The value 0 for a is not allowed! Try again.");
! 211: end loop;
! 212: when 't' =>
! 213: put_line("Reading the (complex) target value for t.");
! 214: Read_Complex(t);
! 215: when 'i' =>
! 216: new_line;
! 217: case choice(2) is
! 218: when 'k' => Info_on_Power;
! 219: when 'a' => Info_on_Constant;
! 220: when 't' => Info_on_Target;
! 221: when '0' => Info_on_Exit;
! 222: when others => null;
! 223: end case;
! 224: when others => null;
! 225: end case;
! 226: end loop;
! 227: new_line(file);
! 228: put_line(file,"HOMOTOPY PARAMETERS :");
! 229: put(file," k : "); put(file,k,2); new_line(file);
! 230: put(file," a : "); put(file,a); new_line(file);
! 231: put(file," t : "); put(file,t); new_line(file);
! 232: end Menu_for_Homotopy_Settings;
! 233:
! 234: procedure Driver_for_Homotopy_Construction
! 235: ( file : in file_type; p,q : in out Poly_Sys;
! 236: qsols : in out Solution_List; target : out Complex_Number ) is
! 237:
! 238: k : positive;
! 239: a,t : Complex_Number;
! 240: prt : boolean;
! 241:
! 242: begin
! 243: Default_Homotopy_Settings(k,a,t,prt);
! 244: Menu_for_Homotopy_Settings(file,k,a,t,prt);
! 245: target := t;
! 246: if prt
! 247: then Projective_Transformation(p);
! 248: Projective_Transformation(q);
! 249: Projective_Transformation(qsols);
! 250: declare
! 251: pp,sysp : Poly_Sys(p'first..p'last+1);
! 252: begin
! 253: pp := Add_Random_Hyperplanes(p,1,true);
! 254: sysp := Add_Standard_Hyperplanes(q,1);
! 255: Homotopy.Create(pp,sysp,k,a);
! 256: Clear(pp); Clear(sysp);
! 257: end;
! 258: else Homotopy.Create(p,q,k,a);
! 259: end if;
! 260: end Driver_for_Homotopy_Construction;
! 261:
! 262: end Drivers_for_Homotopy_Creation;
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