Annotation of OpenXM_contrib/PHC/Ada/Continuation/correctors.ads, Revision 1.1
1.1 ! maekawa 1: with text_io; use text_io;
! 2: with Standard_Floating_Numbers; use Standard_Floating_Numbers;
! 3: with Standard_Complex_Numbers; use Standard_Complex_Numbers;
! 4: with Standard_Complex_Vectors; use Standard_Complex_Vectors;
! 5: with Standard_Complex_Matrices; use Standard_Complex_Matrices;
! 6: with Standard_Complex_Solutions; use Standard_Complex_Solutions;
! 7: with Continuation_Data; use Continuation_Data;
! 8:
! 9: package Correctors is
! 10:
! 11: -- DESCRIPTION :
! 12: -- This package contains implementations for the corrector
! 13: -- in an increment-and-fix continuation.
! 14: --
! 15: -- The following options can be made :
! 16: -- (Affine,Projective)
! 17: -- An affine corrector works in affine space, while a projective
! 18: -- corrector is a projective-perpendicular corrector: it works in
! 19: -- projective space and corrects in a perpendicular way.
! 20: -- (Single,Multiple)
! 21: -- A single corrector only deals with one path at a time.
! 22: -- A multiple corrector corrects more than one path when it is called.
! 23: -- (Loose,Severe)
! 24: -- A loose corrector will stop when either one of the following
! 25: -- conditions is satisfied:
! 26: -- 1. One of the desired accuracies has been met.
! 27: -- 2. The maximum number of iterations is reached.
! 28: -- 3. The Jacobian matrix is singular.
! 29: -- In addition to these stopping criteria, a severe corrector checks
! 30: -- the convergence during the iterations and stops when it notices
! 31: -- divergence is noticed. A loose correctors allows divergence.
! 32: -- (Normal,Conditioned)
! 33: -- A normal corrector does not compute an estimate for the inverse of
! 34: -- the condition number of the Jacobian matrix. This additional work
! 35: -- is done by a conditioned corrector.
! 36: -- (Silent,Reporting)
! 37: -- A silent corrector does not produce any output on file.
! 38: -- A reporting corrector allows to put intermediate results on file.
! 39: --
! 40: -- Based on these options, the following 32 different correctors
! 41: -- are provided :
! 42: --
! 43: -- Affine_Single_Loose_Normal_Silent_Corrector
! 44: -- Affine_Single_Loose_Normal_Reporting_Corrector
! 45: -- Affine_Single_Loose_Conditioned_Silent_Corrector
! 46: -- Affine_Single_Loose_Conditioned_Reporting_Corrector
! 47: -- Affine_Single_Severe_Normal_Silent_Corrector
! 48: -- Affine_Single_Severe_Normal_Reporting_Corrector
! 49: -- Affine_Single_Severe_Conditioned_Silent_Corrector
! 50: -- Affine_Single_Severe_Conditioned_Reporting_Corrector
! 51: -- Affine_Multiple_Loose_Normal_Silent_Corrector
! 52: -- Affine_Multiple_Loose_Normal_Reporting_Corrector
! 53: -- Affine_Multiple_Loose_Conditioned_Silent_Corrector
! 54: -- Affine_Multiple_Loose_Conditioned_Reporting_Corrector
! 55: -- Affine_Multiple_Severe_Normal_Silent_Corrector
! 56: -- Affine_Multiple_Severe_Normal_Reporting_Corrector
! 57: -- Affine_Multiple_Severe_Conditioned_Silent_Corrector
! 58: -- Affine_Multiple_Severe_Conditioned_Reporting_Corrector
! 59: -- Projective_Single_Loose_Normal_Silent_Corrector
! 60: -- Projective_Single_Loose_Normal_Reporting_Corrector
! 61: -- Projective_Single_Loose_Conditioned_Silent_Corrector
! 62: -- Projective_Single_Loose_Conditioned_Reporting_Corrector
! 63: -- Projective_Single_Severe_Normal_Silent_Corrector
! 64: -- Projective_Single_Severe_Normal_Reporting_Corrector
! 65: -- Projective_Single_Severe_Conditioned_Silent_Corrector
! 66: -- Projective_Single_Severe_Conditioned_Reporting_Corrector
! 67: -- Projective_Multiple_Loose_Normal_Silent_Corrector
! 68: -- Projective_Multiple_Loose_Normal_Reporting_Corrector
! 69: -- Projective_Multiple_Loose_Conditioned_Silent_Corrector
! 70: -- Projective_Multiple_Loose_Conditioned_Reporting_Corrector
! 71: -- Projective_Multiple_Severe_Normal_Silent_Corrector
! 72: -- Projective_Multiple_Severe_Normal_Reporting_Corrector
! 73: -- Projective_Multiple_Severe_Conditioned_Silent_Corrector
! 74: -- Projective_Multiple_Severe_Conditioned_Reporting_Corrector
! 75: --
! 76: -- All these procedures have the following generic parameters:
! 77: -- a norm function, polynomial vector and Jacobian matrix function.
! 78: -- Note that the projective correctors require a homogeneous polynomial
! 79: -- vector function.
! 80:
! 81: generic
! 82: with function Norm ( x : Vector ) return double_float;
! 83: with function H ( x : Vector; t : Complex_Number ) return Vector;
! 84: with function dH ( x : Vector; t : Complex_Number ) return Matrix;
! 85: procedure Affine_Single_Loose_Normal_Silent_Corrector
! 86: ( s : in out Solu_Info; c : in Corr_Pars );
! 87:
! 88: generic
! 89: with function Norm ( x : Vector ) return double_float;
! 90: with function H ( x : Vector; t : Complex_Number ) return Vector;
! 91: with function dH ( x : Vector; t : Complex_Number ) return Matrix;
! 92: procedure Affine_Single_Loose_Normal_Reporting_Corrector
! 93: ( file : in file_type; s : in out Solu_Info; c : in Corr_Pars );
! 94:
! 95: generic
! 96: with function Norm ( x : Vector ) return double_float;
! 97: with function H ( x : Vector; t : Complex_Number ) return Vector;
! 98: with function dH ( x : Vector; t : Complex_Number ) return Matrix;
! 99: procedure Affine_Single_Loose_Conditioned_Silent_Corrector
! 100: ( s : in out Solu_Info; c : in Corr_Pars );
! 101:
! 102: generic
! 103: with function Norm ( x : Vector ) return double_float;
! 104: with function H ( x : Vector; t : Complex_Number ) return Vector;
! 105: with function dH ( x : Vector; t : Complex_Number ) return Matrix;
! 106: procedure Affine_Single_Loose_Conditioned_Reporting_Corrector
! 107: ( file : in file_type; s : in out Solu_Info; c : in Corr_Pars );
! 108:
! 109: generic
! 110: with function Norm ( x : Vector ) return double_float;
! 111: with function H ( x : Vector; t : Complex_Number ) return Vector;
! 112: with function dH ( x : Vector; t : Complex_Number ) return Matrix;
! 113: procedure Affine_Single_Severe_Normal_Silent_Corrector
! 114: ( s : in out Solu_Info; c : in Corr_Pars );
! 115:
! 116: generic
! 117: with function Norm ( x : Vector ) return double_float;
! 118: with function H ( x : Vector; t : Complex_Number ) return Vector;
! 119: with function dH ( x : Vector; t : Complex_Number ) return Matrix;
! 120: procedure Affine_Single_Severe_Normal_Reporting_Corrector
! 121: ( file : in file_type; s : in out Solu_Info; c : in Corr_Pars );
! 122:
! 123: generic
! 124: with function Norm ( x : Vector ) return double_float;
! 125: with function H ( x : Vector; t : Complex_Number ) return Vector;
! 126: with function dH ( x : Vector; t : Complex_Number ) return Matrix;
! 127: procedure Affine_Single_Severe_Conditioned_Silent_Corrector
! 128: ( s : in out Solu_Info; c : in Corr_Pars );
! 129:
! 130: generic
! 131: with function Norm ( x : Vector ) return double_float;
! 132: with function H ( x : Vector; t : Complex_Number ) return Vector;
! 133: with function dH ( x : Vector; t : Complex_Number ) return Matrix;
! 134: procedure Affine_Single_Severe_Conditioned_Reporting_Corrector
! 135: ( file : in file_type; s : in out Solu_Info; c : in Corr_Pars );
! 136:
! 137: generic
! 138: with function Norm ( x : Vector ) return double_float;
! 139: with function H ( x : Vector; t : Complex_Number ) return Vector;
! 140: with function dH ( x : Vector; t : Complex_Number ) return Matrix;
! 141: procedure Affine_Multiple_Loose_Normal_Silent_Corrector
! 142: ( s : in out Solu_Info_Array;
! 143: pivot : in out natural; dist_sols : in double_float;
! 144: c : in Corr_Pars; fail : out boolean );
! 145:
! 146: generic
! 147: with function Norm ( x : Vector ) return double_float;
! 148: with function H ( x : Vector; t : Complex_Number ) return Vector;
! 149: with function dH ( x : Vector; t : Complex_Number ) return Matrix;
! 150: procedure Affine_Multiple_Loose_Normal_Reporting_Corrector
! 151: ( file : in file_type; s : in out Solu_Info_Array;
! 152: pivot : in out natural; dist_sols : in double_float;
! 153: c : in Corr_Pars; fail : out boolean );
! 154:
! 155: generic
! 156: with function Norm ( x : Vector ) return double_float;
! 157: with function H ( x : Vector; t : Complex_Number ) return Vector;
! 158: with function dH ( x : Vector; t : Complex_Number ) return Matrix;
! 159: procedure Affine_Multiple_Loose_Conditioned_Silent_Corrector
! 160: ( s : in out Solu_Info_Array;
! 161: pivot : in out natural; dist_sols : in double_float;
! 162: c : in Corr_Pars; fail : out boolean );
! 163:
! 164: generic
! 165: with function Norm ( x : Vector ) return double_float;
! 166: with function H ( x : Vector; t : Complex_Number ) return Vector;
! 167: with function dH ( x : Vector; t : Complex_Number ) return Matrix;
! 168: procedure Affine_Multiple_Loose_Conditioned_Reporting_Corrector
! 169: ( file : in file_type; s : in out Solu_Info_Array;
! 170: pivot : in out natural; dist_sols : in double_float;
! 171: c : in Corr_Pars; fail : out boolean );
! 172:
! 173: generic
! 174: with function Norm ( x : Vector ) return double_float;
! 175: with function H ( x : Vector; t : Complex_Number ) return Vector;
! 176: with function dH ( x : Vector; t : Complex_Number ) return Matrix;
! 177: procedure Affine_Multiple_Severe_Normal_Silent_Corrector
! 178: ( s : in out Solu_Info_Array;
! 179: pivot : in out natural; dist_sols : in double_float;
! 180: c : in Corr_Pars; fail : out boolean );
! 181:
! 182: generic
! 183: with function Norm ( x : Vector ) return double_float;
! 184: with function H ( x : Vector; t : Complex_Number ) return Vector;
! 185: with function dH ( x : Vector; t : Complex_Number ) return Matrix;
! 186: procedure Affine_Multiple_Severe_Normal_Reporting_Corrector
! 187: ( file : in file_type; s : in out Solu_Info_Array;
! 188: pivot : in out natural; dist_sols : in double_float;
! 189: c : in Corr_Pars; fail : out boolean );
! 190:
! 191: generic
! 192: with function Norm ( x : Vector ) return double_float;
! 193: with function H ( x : Vector; t : Complex_Number ) return Vector;
! 194: with function dH ( x : Vector; t : Complex_Number ) return Matrix;
! 195: procedure Affine_Multiple_Severe_Conditioned_Silent_Corrector
! 196: ( s : in out Solu_Info_Array;
! 197: pivot : in out natural; dist_sols : in double_float;
! 198: c : in Corr_Pars; fail : out boolean );
! 199:
! 200: generic
! 201: with function Norm ( x : Vector ) return double_float;
! 202: with function H ( x : Vector; t : Complex_Number ) return Vector;
! 203: with function dH ( x : Vector; t : Complex_Number ) return Matrix;
! 204: procedure Affine_Multiple_Severe_Conditioned_Reporting_Corrector
! 205: ( file : in file_type; s : in out Solu_Info_Array;
! 206: pivot : in out natural; dist_sols : in double_float;
! 207: c : in Corr_Pars; fail : out boolean );
! 208:
! 209: generic
! 210: with function Norm ( x : Vector ) return double_float;
! 211: with function H ( x : Vector; t : Complex_Number ) return Vector;
! 212: with function dH ( x : Vector; t : Complex_Number ) return Matrix;
! 213: procedure Projective_Single_Loose_Normal_Silent_Corrector
! 214: ( s : in out Solu_Info; c : in Corr_Pars );
! 215:
! 216: generic
! 217: with function Norm ( x : Vector ) return double_float;
! 218: with function H ( x : Vector; t : Complex_Number ) return Vector;
! 219: with function dH ( x : Vector; t : Complex_Number ) return Matrix;
! 220: procedure Projective_Single_Loose_Normal_Reporting_Corrector
! 221: ( file : in file_type; s : in out Solu_Info; c : in Corr_Pars );
! 222:
! 223: generic
! 224: with function Norm ( x : Vector ) return double_float;
! 225: with function H ( x : Vector; t : Complex_Number ) return Vector;
! 226: with function dH ( x : Vector; t : Complex_Number ) return Matrix;
! 227: procedure Projective_Single_Loose_Conditioned_Silent_Corrector
! 228: ( s : in out Solu_Info; c : in Corr_Pars );
! 229:
! 230: generic
! 231: with function Norm ( x : Vector ) return double_float;
! 232: with function H ( x : Vector; t : Complex_Number ) return Vector;
! 233: with function dH ( x : Vector; t : Complex_Number ) return Matrix;
! 234: procedure Projective_Single_Loose_Conditioned_Reporting_Corrector
! 235: ( file : in file_type; s : in out Solu_Info; c : in Corr_Pars );
! 236:
! 237: generic
! 238: with function Norm ( x : Vector ) return double_float;
! 239: with function H ( x : Vector; t : Complex_Number ) return Vector;
! 240: with function dH ( x : Vector; t : Complex_Number ) return Matrix;
! 241: procedure Projective_Single_Severe_Normal_Silent_Corrector
! 242: ( s : in out Solu_Info; c : in Corr_Pars );
! 243:
! 244: generic
! 245: with function Norm ( x : Vector ) return double_float;
! 246: with function H ( x : Vector; t : Complex_Number ) return Vector;
! 247: with function dH ( x : Vector; t : Complex_Number ) return Matrix;
! 248: procedure Projective_Single_Severe_Normal_Reporting_Corrector
! 249: ( file : in file_type; s : in out Solu_Info; c : in Corr_Pars );
! 250:
! 251: generic
! 252: with function Norm ( x : Vector ) return double_float;
! 253: with function H ( x : Vector; t : Complex_Number ) return Vector;
! 254: with function dH ( x : Vector; t : Complex_Number ) return Matrix;
! 255: procedure Projective_Single_Severe_Conditioned_Silent_Corrector
! 256: ( s : in out Solu_Info; c : in Corr_Pars );
! 257:
! 258: generic
! 259: with function Norm ( x : Vector ) return double_float;
! 260: with function H ( x : Vector; t : Complex_Number ) return Vector;
! 261: with function dH ( x : Vector; t : Complex_Number ) return Matrix;
! 262: procedure Projective_Single_Severe_Conditioned_Reporting_Corrector
! 263: ( file : in file_type; s : in out Solu_Info; c : in Corr_Pars );
! 264:
! 265: generic
! 266: with function Norm ( x : Vector ) return double_float;
! 267: with function H ( x : Vector; t : Complex_Number ) return Vector;
! 268: with function dH ( x : Vector; t : Complex_Number ) return Matrix;
! 269: procedure Projective_Multiple_Loose_Normal_Silent_Corrector
! 270: ( s : in out Solu_Info_Array;
! 271: pivot : in out natural; dist_sols : in double_float;
! 272: c : in Corr_Pars; fail : out boolean );
! 273:
! 274: generic
! 275: with function Norm ( x : Vector ) return double_float;
! 276: with function H ( x : Vector; t : Complex_Number ) return Vector;
! 277: with function dH ( x : Vector; t : Complex_Number ) return Matrix;
! 278: procedure Projective_Multiple_Loose_Normal_Reporting_Corrector
! 279: ( file : in file_type; s : in out Solu_Info_Array;
! 280: pivot : in out natural; dist_sols : in double_float;
! 281: c : in Corr_Pars; fail : out boolean );
! 282:
! 283: generic
! 284: with function Norm ( x : Vector ) return double_float;
! 285: with function H ( x : Vector; t : Complex_Number ) return Vector;
! 286: with function dH ( x : Vector; t : Complex_Number ) return Matrix;
! 287: procedure Projective_Multiple_Loose_Conditioned_Silent_Corrector
! 288: ( s : in out Solu_Info_Array;
! 289: pivot : in out natural; dist_sols : in double_float;
! 290: c : in Corr_Pars; fail : out boolean );
! 291:
! 292: generic
! 293: with function Norm ( x : Vector ) return double_float;
! 294: with function H ( x : Vector; t : Complex_Number ) return Vector;
! 295: with function dH ( x : Vector; t : Complex_Number ) return Matrix;
! 296: procedure Projective_Multiple_Loose_Conditioned_Reporting_Corrector
! 297: ( file : in file_type; s : in out Solu_Info_Array;
! 298: pivot : in out natural; dist_sols : in double_float;
! 299: c : in Corr_Pars; fail : out boolean );
! 300:
! 301: generic
! 302: with function Norm ( x : Vector ) return double_float;
! 303: with function H ( x : Vector; t : Complex_Number ) return Vector;
! 304: with function dH ( x : Vector; t : Complex_Number ) return Matrix;
! 305: procedure Projective_Multiple_Severe_Normal_Silent_Corrector
! 306: ( s : in out Solu_Info_Array;
! 307: pivot : in out natural; dist_sols : in double_float;
! 308: c : in Corr_Pars; fail : out boolean );
! 309:
! 310: generic
! 311: with function Norm ( x : Vector ) return double_float;
! 312: with function H ( x : Vector; t : Complex_Number ) return Vector;
! 313: with function dH ( x : Vector; t : Complex_Number ) return Matrix;
! 314: procedure Projective_Multiple_Severe_Normal_Reporting_Corrector
! 315: ( file : in file_type; s : in out Solu_Info_Array;
! 316: pivot : in out natural; dist_sols : in double_float;
! 317: c : in Corr_Pars; fail : out boolean );
! 318:
! 319: generic
! 320: with function Norm ( x : Vector ) return double_float;
! 321: with function H ( x : Vector; t : Complex_Number ) return Vector;
! 322: with function dH ( x : Vector; t : Complex_Number ) return Matrix;
! 323: procedure Projective_Multiple_Severe_Conditioned_Silent_Corrector
! 324: ( s : in out Solu_Info_Array;
! 325: pivot : in out natural; dist_sols : in double_float;
! 326: c : in Corr_Pars; fail : out boolean );
! 327:
! 328: generic
! 329: with function Norm ( x : Vector ) return double_float;
! 330: with function H ( x : Vector; t : Complex_Number ) return Vector;
! 331: with function dH ( x : Vector; t : Complex_Number ) return Matrix;
! 332: procedure Projective_Multiple_Severe_Conditioned_Reporting_Corrector
! 333: ( file : in file_type; s : in out Solu_Info_Array;
! 334: pivot : in out natural; dist_sols : in double_float;
! 335: c : in Corr_Pars; fail : out boolean );
! 336:
! 337: -- DESCRIPTION :
! 338: -- The predicted solutions of the system H(x,t)=0 are corrected.
! 339: -- With a multiple corrector, the correction starts at s(pivot).
! 340:
! 341: -- ON ENTRY :
! 342: -- file to write intermediate results on;
! 343: -- s are the predicted values for the solutions;
! 344: -- pivot is the index in the array where the correction
! 345: -- process must start;
! 346: -- dist_sols two solutions x1 and x2 are different
! 347: -- if for some k in 1..n : | x1(k) - x2(k) | > dist_sols;
! 348: -- c the corrector parameters.
! 349:
! 350: -- ON RETURN :
! 351: -- s the computed solutions;
! 352: -- pivot if fail then pivot is the index in the array where
! 353: -- a difficulty occured; otherwise it is the same pivot as
! 354: -- on entry;
! 355: -- fail is false if all solutions are computed with the desired
! 356: -- precision eps, within the maximum number of allowed
! 357: -- iterations, and if all solutions are different.
! 358:
! 359: end Correctors;
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