Annotation of OpenXM_contrib/PHC/Ada/Math_Lib/Polynomials/ts_poly.adb, Revision 1.1
1.1 ! maekawa 1: with text_io,integer_io; use text_io,integer_io;
! 2: with Symbol_Table;
! 3: with Standard_Floating_Numbers; use Standard_Floating_Numbers;
! 4: with Standard_Complex_Numbers; use Standard_Complex_Numbers;
! 5: with Standard_Complex_Numbers_io; use Standard_Complex_Numbers_io;
! 6: with Standard_Complex_Vectors; use Standard_Complex_Vectors;
! 7: with Standard_Complex_Vectors_io; use Standard_Complex_Vectors_io;
! 8: with Standard_Random_Vectors; use Standard_Random_Vectors;
! 9: with Standard_Complex_Polynomials; use Standard_Complex_Polynomials;
! 10: with Standard_Complex_Polynomials_io; use Standard_Complex_Polynomials_io;
! 11: with Standard_Complex_Poly_Vectors; use Standard_Complex_Poly_Vectors;
! 12: with Standard_Complex_Poly_Vectors_io; use Standard_Complex_Poly_Vectors_io;
! 13: with Standard_Complex_Poly_Matrices; use Standard_Complex_Poly_Matrices;
! 14: with Standard_Complex_Poly_Matrices_io; use Standard_Complex_Poly_Matrices_io;
! 15: with Standard_Complex_Poly_Functions; use Standard_Complex_Poly_Functions;
! 16: with Standard_Complex_Poly_Systems; use Standard_Complex_Poly_Systems;
! 17: with Standard_Complex_Poly_Systems_io; use Standard_Complex_Poly_Systems_io;
! 18: with Standard_Complex_Poly_SysFun; use Standard_Complex_Poly_SysFun;
! 19: with Standard_Complex_Laur_Polys; use Standard_Complex_Laur_Polys;
! 20: with Standard_Complex_Laur_Functions; use Standard_Complex_Laur_Functions;
! 21: with Standard_Poly_Laur_Convertors; use Standard_Poly_Laur_Convertors;
! 22: with Standard_to_Multprec_Convertors; use Standard_to_Multprec_Convertors;
! 23: with Multprec_Complex_Numbers; use Multprec_Complex_Numbers;
! 24: with Multprec_Complex_Numbers_io; use Multprec_Complex_Numbers_io;
! 25: with Multprec_Complex_Vectors; use Multprec_Complex_Vectors;
! 26: with Multprec_Complex_Vectors_io; use Multprec_Complex_Vectors_io;
! 27: with Multprec_Complex_Vector_Tools; use Multprec_Complex_Vector_Tools;
! 28: with Multprec_Complex_Polynomials; use Multprec_Complex_Polynomials;
! 29: with Multprec_Complex_Polynomials_io; use Multprec_Complex_Polynomials_io;
! 30: with Multprec_Complex_Poly_Functions; use Multprec_Complex_Poly_Functions;
! 31: with Multprec_Complex_Poly_Systems; use Multprec_Complex_Poly_Systems;
! 32: with Multprec_Complex_Poly_SysFun; use Multprec_Complex_Poly_SysFun;
! 33:
! 34: procedure ts_poly is
! 35:
! 36: -- DESCRIPTION :
! 37: -- This routine provides basic testing routines for complex polynomials.
! 38:
! 39: procedure Test_io is
! 40:
! 41: -- DESCRIPTION :
! 42: -- Tests the input/output of a polynomial in several variables
! 43: -- and with complex coefficients.
! 44:
! 45: n,m : natural;
! 46: p : Standard_Complex_Polynomials.Poly;
! 47:
! 48: begin
! 49: new_line;
! 50: put_line("Interactive testing of input/output of complex polynomials.");
! 51: new_line;
! 52: put("Give the number of variables : "); get(n);
! 53: Symbol_Table.Init(n);
! 54: put_line("Give a polynomial (terminate with ;) : "); get(p);
! 55: m := Number_of_Unknowns(p);
! 56: put("the number of unknowns : "); put(m,1); new_line;
! 57: put("the number of terms : "); put(Number_of_Terms(p),1); new_line;
! 58: put("the degree of p : "); put(Degree(p),1);
! 59: put(" max degrees : ");
! 60: for i in 1..m loop
! 61: put(Degree(p,i),1); put(" ");
! 62: end loop;
! 63: new_line;
! 64: put_line("Your polynomial : "); put(p); new_line;
! 65: Symbol_Table.Clear;
! 66: Clear(p);
! 67: end Test_io;
! 68:
! 69: procedure Test_Vector_io is
! 70:
! 71: n : natural;
! 72:
! 73: begin
! 74: new_line;
! 75: put_line("Interactive testing of i/o of vectors of complex polynomials.");
! 76: new_line;
! 77: put("Give the dimension of the vector : "); get(n);
! 78: Symbol_Table.Init(n);
! 79: declare
! 80: p : Standard_Complex_Poly_Vectors.Vector(1..n);
! 81: begin
! 82: put("Give "); put(n,1); put(" polynomials in "); put(n,1);
! 83: put_line(" variables : "); get(p);
! 84: put_line("Your polynomials : "); put_line(p);
! 85: end;
! 86: end Test_Vector_io;
! 87:
! 88: procedure Test_Matrix_io is
! 89:
! 90: n : natural;
! 91:
! 92: begin
! 93: new_line;
! 94: put_line("Interactive testing of i/o of matrices of complex polynomials.");
! 95: new_line;
! 96: put("Give the dimension of the matrix : "); get(n);
! 97: Symbol_Table.Init(n);
! 98: declare
! 99: p : Matrix(1..n,1..n);
! 100: begin
! 101: put("Give "); put(n,1); put("x"); put(n,1);
! 102: put(" polynomial matrix in "); put(n,1);
! 103: put_line(" variables : "); get(p);
! 104: put_line("Your polynomial matrix : "); put(p);
! 105: end;
! 106: end Test_Matrix_io;
! 107:
! 108: procedure Test_Standard_Eval
! 109: ( p : in Standard_Complex_Polynomials.Poly;
! 110: e : in Standard_Complex_Poly_Functions.Eval_Poly;
! 111: x : in Standard_Complex_Vectors.Vector;
! 112: output_of_results : in boolean; bug : out boolean ) is
! 113:
! 114: -- DESCRIPTION :
! 115: -- Evaluates the polynomial twice and compares the results.
! 116:
! 117: y1 : Standard_Complex_Numbers.Complex_Number := Eval(p,x);
! 118: y2 : Standard_Complex_Numbers.Complex_Number := Eval(e,x);
! 119: tol : constant double_float := 10.0**(-12);
! 120:
! 121: begin
! 122: if AbsVal(y1-y2) < tol
! 123: then put_line("Test on evaluation is successful."); bug := false;
! 124: else put_line("Different results! Bug detected."); bug := true;
! 125: end if;
! 126: if output_of_results or bug
! 127: then put("p(x) : "); put(y1); new_line;
! 128: put("e(x) : "); put(y2); new_line;
! 129: end if;
! 130: end Test_Standard_Eval;
! 131:
! 132: procedure Test_Standard_Laurent_Eval
! 133: ( p : in Standard_Complex_Laur_Polys.Poly;
! 134: e : in Standard_Complex_Laur_Functions.Eval_Poly;
! 135: x : in Standard_Complex_Vectors.Vector;
! 136: output_of_results : in boolean; bug : out boolean ) is
! 137:
! 138: -- DESCRIPTION :
! 139: -- Evaluates the polynomial twice and compares the results.
! 140:
! 141: y1 : Standard_Complex_Numbers.Complex_Number := Eval(p,x);
! 142: y2 : Standard_Complex_Numbers.Complex_Number := Eval(e,x);
! 143: tol : constant double_float := 10.0**(-12);
! 144:
! 145: begin
! 146: if AbsVal(y1-y2) < tol
! 147: then put_line("Test on evaluation is successful."); bug := false;
! 148: else put_line("Different results! Bug detected."); bug := true;
! 149: end if;
! 150: if output_of_results or bug
! 151: then put("p(x) : "); put(y1); new_line;
! 152: put("e(x) : "); put(y2); new_line;
! 153: end if;
! 154: end Test_Standard_Laurent_Eval;
! 155:
! 156: procedure Interactive_Standard_Eval is
! 157:
! 158: -- DESCRIPTION :
! 159: -- Tests the evaluation of a polynomial in several variables
! 160: -- and with standard complex coefficients.
! 161:
! 162: n : natural;
! 163: p : Standard_Complex_Polynomials.Poly;
! 164: e : Standard_Complex_Poly_Functions.Eval_Poly;
! 165: bug : boolean;
! 166: ans : character;
! 167:
! 168: begin
! 169: new_line;
! 170: put_line("Interactive evaluation of standard complex polynomials.");
! 171: new_line;
! 172: put("Give the number of variables : "); get(n);
! 173: Symbol_Table.Init(n);
! 174: put_line("Give a polynomial (terminate with ;) : "); get(p);
! 175: put_line("Your polynomial p : "); put(p); new_line;
! 176: e := Create(p);
! 177: loop
! 178: declare
! 179: x : Standard_Complex_Vectors.Vector(1..n);
! 180: begin
! 181: put("Give "); put(n,1); put_line(" complex numbers : "); get(x);
! 182: Test_Standard_Eval(p,e,x,true,bug);
! 183: end;
! 184: put("Do you wish to evaluate at other points (y/n) ? "); get(ans);
! 185: exit when (ans /= 'y');
! 186: end loop;
! 187: Symbol_Table.Clear;
! 188: Clear(p); Clear(e);
! 189: end Interactive_Standard_Eval;
! 190:
! 191: procedure Interactive_Standard_Laurent_Eval is
! 192:
! 193: -- DESCRIPTION :
! 194: -- Tests the evaluation of a polynomial in several variables
! 195: -- and with standard complex coefficients.
! 196:
! 197: n : natural;
! 198: p : Standard_Complex_Polynomials.Poly;
! 199: lp : Standard_Complex_Laur_Polys.Poly;
! 200: elp : Standard_Complex_Laur_Functions.Eval_Poly;
! 201: bug : boolean;
! 202: ans : character;
! 203:
! 204: begin
! 205: new_line;
! 206: put_line("Interactive evaluation of standard complex Laurent polynomials.");
! 207: new_line;
! 208: put("Give the number of variables : "); get(n);
! 209: Symbol_Table.Init(n);
! 210: put_line("Give a polynomial (terminate with ;) : "); get(p);
! 211: put_line("Your polynomial p : "); put(p); new_line;
! 212: lp := Polynomial_to_Laurent_Polynomial(p);
! 213: elp := Create(lp);
! 214: loop
! 215: declare
! 216: x : Standard_Complex_Vectors.Vector(1..n);
! 217: begin
! 218: put("Give "); put(n,1); put_line(" complex numbers : "); get(x);
! 219: Test_Standard_Laurent_Eval(lp,elp,x,true,bug);
! 220: end;
! 221: put("Do you wish to evaluate at other points (y/n) ? "); get(ans);
! 222: exit when (ans /= 'y');
! 223: end loop;
! 224: Symbol_Table.Clear;
! 225: Clear(p); Clear(lp); Clear(elp);
! 226: end Interactive_Standard_Laurent_Eval;
! 227:
! 228: procedure Random_Standard_Eval is
! 229:
! 230: -- DESCRIPTION :
! 231: -- Tests the evaluation of a polynomial in several variables
! 232: -- and with standard complex coefficients.
! 233:
! 234: n,nb : natural;
! 235: p : Standard_Complex_Polynomials.Poly;
! 236: e : Standard_Complex_Poly_Functions.Eval_Poly;
! 237: bug : boolean;
! 238:
! 239: begin
! 240: new_line;
! 241: put_line("Random evaluation of standard complex polynomials.");
! 242: new_line;
! 243: put("Give the number of variables : "); get(n);
! 244: Symbol_Table.Init(n);
! 245: put_line("Give a polynomial (terminate with ;) : "); get(p);
! 246: put_line("Your polynomial p : "); put(p); new_line;
! 247: e := Create(p);
! 248: put("Give the number of samples : "); get(nb);
! 249: for i in 1..nb loop
! 250: declare
! 251: x : constant Standard_Complex_Vectors.Vector := Random_Vector(1,n);
! 252: begin
! 253: Test_Standard_Eval(p,e,x,false,bug);
! 254: end;
! 255: exit when bug;
! 256: end loop;
! 257: Symbol_Table.Clear;
! 258: Clear(p); Clear(e);
! 259: end Random_Standard_Eval;
! 260:
! 261: procedure Random_Standard_Laurent_Eval is
! 262:
! 263: -- DESCRIPTION :
! 264: -- Tests the evaluation of a Laurent polynomial in several variables
! 265: -- and with standard complex coefficients.
! 266:
! 267: n,nb : natural;
! 268: p : Standard_Complex_Polynomials.Poly;
! 269: lp : Standard_Complex_Laur_Polys.Poly;
! 270: elp : Standard_Complex_Laur_Functions.Eval_Poly;
! 271: bug : boolean;
! 272:
! 273: begin
! 274: new_line;
! 275: put_line("Random evaluation of standard complex Laurent polynomials.");
! 276: new_line;
! 277: put("Give the number of variables : "); get(n);
! 278: Symbol_Table.Init(n);
! 279: put_line("Give a polynomial (terminate with ;) : "); get(p);
! 280: put_line("Your polynomial p : "); put(p); new_line;
! 281: lp := Polynomial_to_Laurent_Polynomial(p);
! 282: elp := Create(lp);
! 283: put("Give the number of samples : "); get(nb);
! 284: for i in 1..nb loop
! 285: declare
! 286: x : constant Standard_Complex_Vectors.Vector := Random_Vector(1,n);
! 287: begin
! 288: Test_Standard_Laurent_Eval(lp,elp,x,false,bug);
! 289: end;
! 290: exit when bug;
! 291: end loop;
! 292: Symbol_Table.Clear;
! 293: Clear(p); Clear(lp); Clear(elp);
! 294: end Random_Standard_Laurent_Eval;
! 295:
! 296: procedure Test_Multprec_Eval is
! 297:
! 298: -- DESCRIPTION :
! 299: -- Tests the evaluation of a polynomial in several variables
! 300: -- and with multi-precision complex coefficients.
! 301:
! 302: ans : character;
! 303: n : natural;
! 304: p : Standard_Complex_Polynomials.Poly;
! 305: mp : Multprec_Complex_Polynomials.Poly;
! 306: ep : Multprec_Complex_Poly_Functions.Eval_Poly;
! 307:
! 308: begin
! 309: new_line;
! 310: put_line("Testing the evaluation of multi-precision complex polynomials.");
! 311: new_line;
! 312: put("Give the number of variables : "); get(n);
! 313: Symbol_Table.Init(n);
! 314: put_line("Give a polynomial (terminate with ;) : "); get(p);
! 315: put_line("Your polynomial p : "); put(p); new_line;
! 316: mp := Convert(p);
! 317: ep := Create(mp);
! 318: declare
! 319: x : Multprec_Complex_Vectors.Vector(1..n);
! 320: sz : natural;
! 321: y1,y2 : Multprec_Complex_Numbers.Complex_Number;
! 322: begin
! 323: put("Give "); put(n,1); put_line(" complex numbers : "); get(x);
! 324: loop
! 325: put("Give the size of the numbers : "); get(sz);
! 326: Set_Size(x,sz);
! 327: y1 := Eval(mp,x); put("p(x) : "); put(y1); new_line;
! 328: y2 := Eval(ep,x); put("e(x) : "); put(y2); new_line;
! 329: if Equal(y1,y2)
! 330: then put_line("Test on evaluation is successful.");
! 331: else put_line("Different results! Bug detected.");
! 332: end if;
! 333: put("Do you want to evaluate for other precisions ? (y/n) ");
! 334: get(ans);
! 335: exit when ans /= 'y';
! 336: end loop;
! 337: end;
! 338: Symbol_Table.Clear;
! 339: Clear(p); Clear(mp); Clear(ep);
! 340: end Test_Multprec_Eval;
! 341:
! 342: procedure Test_Standard_Diff is
! 343:
! 344: -- DESCRIPTION :
! 345: -- Test on the differentiation of standard complex polynomials.
! 346:
! 347: n,m : natural;
! 348: p,dp : Standard_Complex_Polynomials.Poly;
! 349:
! 350: begin
! 351: new_line;
! 352: put_line("Test on differentiation of standard complex polynomials.");
! 353: new_line;
! 354: put("Give the number of variables : "); get(n);
! 355: Symbol_Table.Init(n);
! 356: put_line("Give a polynomial (terminate with ;) : "); get(p);
! 357: m := Number_of_Unknowns(p);
! 358: put("Your polynomial p : "); put(p); new_line;
! 359: put("The number of unknowns : "); put(m,1); new_line;
! 360: for i in 1..m loop
! 361: dp := Diff(p,i);
! 362: put("Diff(p,"); put(i,1); put(") : ");
! 363: put(dp); new_line;
! 364: Clear(dp);
! 365: end loop;
! 366: Symbol_Table.Clear;
! 367: Clear(p);
! 368: end Test_Standard_Diff;
! 369:
! 370: procedure Test_Multprec_Diff is
! 371:
! 372: -- DESCRIPTION :
! 373: -- Test on the differentiation of multi-precision complex polynomials.
! 374:
! 375: n,m : natural;
! 376: p : Standard_Complex_Polynomials.Poly;
! 377: mp,dp : Multprec_Complex_Polynomials.Poly;
! 378:
! 379: begin
! 380: new_line;
! 381: put_line("Test on differentiation of multi-precision complex polynomials.");
! 382: new_line;
! 383: put("Give the number of variables : "); get(n);
! 384: Symbol_Table.Init(n);
! 385: put_line("Give a polynomial (terminate with ;) : "); get(p);
! 386: m := Number_of_Unknowns(p);
! 387: put("Your polynomial p : "); put(p); new_line;
! 388: mp := Convert(p);
! 389: put("As multi-precision poly : "); put(mp); new_line;
! 390: put("The number of unknowns : "); put(m,1); new_line;
! 391: for i in 1..m loop
! 392: dp := Diff(mp,i);
! 393: put("Diff(p,"); put(i,1); put(") : ");
! 394: put(dp); new_line;
! 395: Clear(dp);
! 396: end loop;
! 397: Symbol_Table.Clear;
! 398: Clear(p); Clear(mp);
! 399: end Test_Multprec_Diff;
! 400:
! 401: procedure Test_System_io is
! 402:
! 403: lp : Standard_Complex_Poly_Systems.Link_to_Poly_Sys;
! 404: n : natural;
! 405:
! 406: begin
! 407: new_line;
! 408: put_line("Interactive testing on input/output of polynomial systems.");
! 409: new_line;
! 410: put("Give the dimension : "); get(n);
! 411: Symbol_Table.Init(n);
! 412: put("Give "); put(n,1); put_line(" polynomials : ");
! 413: declare
! 414: p : Standard_Complex_Poly_Systems.Poly_Sys(1..n);
! 415: begin
! 416: get(p);
! 417: put_line("The system : "); put(p);
! 418: end;
! 419: Symbol_Table.Clear;
! 420: get(lp);
! 421: put_line("The system : "); put(lp.all);
! 422: end Test_System_io;
! 423:
! 424: procedure Test_Eval_Standard_System is
! 425:
! 426: lp : Standard_Complex_Poly_Systems.Link_to_Poly_Sys;
! 427:
! 428: begin
! 429: new_line;
! 430: put_line("Testing the evaluation of standard polynomial systems.");
! 431: new_line;
! 432: get(lp);
! 433: put_line("The system : "); put(lp.all);
! 434: declare
! 435: n : constant natural := lp'last;
! 436: x,y1,y2,y3 : Standard_Complex_Vectors.Vector(1..n);
! 437: ep : Standard_Complex_Poly_SysFun.Eval_Poly_Sys(1..n) := Create(lp.all);
! 438:
! 439: function Evaluate ( x : Standard_Complex_Vectors.Vector )
! 440: return Standard_Complex_Vectors.Vector is
! 441: begin
! 442: return Eval(ep,x);
! 443: end Evaluate;
! 444: begin
! 445: put("Give "); put(n,1); put_line(" complex numbers :"); get(x);
! 446: y1 := Eval(lp.all,x);
! 447: y2 := Eval(ep,x);
! 448: y3 := Evaluate(x);
! 449: put("p(x) : "); put(y1); new_line;
! 450: put("e(x) : "); put(y2); new_line;
! 451: put("E(x) : "); put(y2); new_line;
! 452: if Equal(y1,y2) and Equal(y2,y3)
! 453: then put_line("Test on evaluation of system is successful.");
! 454: else put_line("Different evaluations! Bug detected.");
! 455: end if;
! 456: end;
! 457: end Test_Eval_Standard_System;
! 458:
! 459: procedure Test_Eval_Multprec_System is
! 460:
! 461: lp : Standard_Complex_Poly_Systems.Link_to_Poly_Sys;
! 462:
! 463: begin
! 464: new_line;
! 465: put_line("Testing the evaluation of multi-precision polynomial systems.");
! 466: new_line;
! 467: get(lp);
! 468: put_line("The system : "); put(lp.all);
! 469: declare
! 470: n : constant natural := lp'last;
! 471: x,y1,y2 : Multprec_Complex_Vectors.Vector(1..n);
! 472: mp : Multprec_Complex_Poly_Systems.Poly_Sys(1..n) := Convert(lp.all);
! 473: ep : Multprec_Complex_Poly_SysFun.Eval_Poly_Sys(1..n) := Create(mp);
! 474: begin
! 475: put("Give "); put(n,1); put_line(" complex numbers :"); get(x);
! 476: y1 := Eval(mp,x);
! 477: y2 := Eval(ep,x);
! 478: put("p(x) : "); put(y1); new_line;
! 479: put("e(x) : "); put(y2); new_line;
! 480: if Equal(y1,y2)
! 481: then put_line("Test on evaluation of system is successful.");
! 482: else put_line("Different evaluations! Bug detected.");
! 483: end if;
! 484: end;
! 485: end Test_Eval_Multprec_System;
! 486:
! 487: procedure Main is
! 488:
! 489: ans : character;
! 490:
! 491: begin
! 492: new_line;
! 493: put_line("Interactive testing of the operations on complex polynomials.");
! 494: loop
! 495: new_line;
! 496: put_line("Choose one of the following : ");
! 497: put_line(" 0. Exit this program. ");
! 498: put_line(" 1. i/o of standard complex polynomials. ");
! 499: put_line(" 2. i/o of vectors of standard complex polynomials. ");
! 500: put_line(" 3. i/o of matrices of standard complex polynomials. ");
! 501: put_line(" 4. Interactive evaluation of standard complex polynomials.");
! 502: put_line(" 5. Interactive evaluation of standard Laurent polynomials.");
! 503: put_line(" 6. Random evaluation of standard complex polynomials. ");
! 504: put_line(" 7. Random evaluation of standard Laurent polynomials. ");
! 505: put_line(" 8. Evaluation of multi-precision complex polynomials. ");
! 506: put_line(" 9. Differentiation of standard complex polynomials. ");
! 507: put_line(" A. Differentiation of multi-precision complex polynomials.");
! 508: put_line(" B. i/o of systems of standard complex polynomials. ");
! 509: put_line(" C. Evaluation of systems of standard complex polynomials. ");
! 510: put_line(" D. Evaluation of systems of multprec complex polynomials. ");
! 511: put("Type 0,1,2,3,4,5,6,7,8,9,A,B,C or D to select : "); get(ans);
! 512: exit when (ans = '0');
! 513: case ans is
! 514: when '1' => Test_io;
! 515: when '2' => Test_Vector_io;
! 516: when '3' => Test_Matrix_io;
! 517: when '4' => Interactive_Standard_Eval;
! 518: when '5' => Interactive_Standard_Laurent_Eval;
! 519: when '6' => Random_Standard_Eval;
! 520: when '7' => Random_Standard_Laurent_Eval;
! 521: when '8' => Test_Multprec_Eval;
! 522: when '9' => Test_Standard_Diff;
! 523: when 'A' => Test_Multprec_Diff;
! 524: when 'B' => Test_System_io;
! 525: when 'C' => Test_Eval_Standard_System;
! 526: when 'D' => Test_Eval_Multprec_System;
! 527: when others => null;
! 528: end case;
! 529: end loop;
! 530: end Main;
! 531:
! 532: begin
! 533: Main;
! 534: end ts_poly;
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