Annotation of OpenXM_contrib/PHC/Ada/Continuation/path_trackers.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_Floating_Vectors;
! 5: with Standard_Complex_Vectors; use Standard_Complex_Vectors;
! 6: with Standard_Complex_Matrices; use Standard_Complex_Matrices;
! 7: with Standard_Complex_Solutions; use Standard_Complex_Solutions;
! 8: with Continuation_Data; use Continuation_Data;
! 9:
! 10: package Path_Trackers is
! 11:
! 12: -- DESCRIPTION :
! 13: -- This package offers some routines for tracking solution paths,
! 14: -- using an increment-and-fix predictor-corrector method.
! 15:
! 16: -- The following options can be made :
! 17: -- (Linear,Circular)
! 18: -- A linear path tracker takes t from a starting to a target value.
! 19: -- For computing winding numbers, a circular path tracker is needed.
! 20: -- (Single,Multiple)
! 21: -- A single path tracker only deals with one path at a time.
! 22: -- A multiple path tracker follows more than one path when it is called.
! 23: -- (Normal,Conditioned)
! 24: -- A normal path tracker does not compute an estimate for the inverse of
! 25: -- the condition number of the Jacobian matrix. This additional work
! 26: -- is done by a conditioned path tracker.
! 27: -- (Silent,Reporting)
! 28: -- A silent path tracker does not produce any output on file.
! 29: -- A reporting path tracker allows to put intermediate results on file.
! 30:
! 31: -- By combining these options, the following path trackers are provided:
! 32:
! 33: -- Linear_Single_Normal_Silent_Continue
! 34: -- Linear_Single_Normal_Reporting_Continue
! 35: -- Linear_Single_Conditioned_Silent_Continue
! 36: -- Linear_Single_Conditioned_Reporting_Continue
! 37: -- Linear_Multiple_Normal_Silent_Continue
! 38: -- Linear_Multiple_Normal_Reporting_Continue
! 39: -- Linear_Multiple_Conditioned_Silent_Continue
! 40: -- Linear_Multiple_Conditioned_Reporting_Continue
! 41: -- Circular_Single_Normal_Reporting_Continue
! 42: -- Circular_Single_Conditioned_Reporting_Continue
! 43:
! 44: -- LINEAR PATH FOLLOWING FOR ONE PATH :
! 45:
! 46: generic
! 47:
! 48: with function Norm ( x : Vector ) return double_float;
! 49: with function H ( x : Vector; t : Complex_Number ) return Vector;
! 50: with function dH ( x : Vector; t : Complex_Number ) return Vector;
! 51: with function dH ( x : Vector; t : Complex_Number ) return Matrix;
! 52:
! 53: procedure Linear_Single_Normal_Silent_Continue
! 54: ( s : in out Solu_Info; target : in Complex_Number;
! 55: tol : in double_float; proj : in boolean;
! 56: p : in Pred_Pars; c : in Corr_Pars );
! 57:
! 58: generic
! 59:
! 60: with function Norm ( x : Vector ) return double_float;
! 61: with function H ( x : Vector; t : Complex_Number ) return Vector;
! 62: with function dH ( x : Vector; t : Complex_Number ) return Vector;
! 63: with function dH ( x : Vector; t : Complex_Number ) return Matrix;
! 64:
! 65: procedure Linear_Single_Normal_Reporting_Continue
! 66: ( file : in file_type; s : in out Solu_Info;
! 67: target : in Complex_Number; tol : in double_float;
! 68: proj : in boolean; p : in Pred_Pars; c : in Corr_Pars );
! 69:
! 70: generic
! 71:
! 72: with function Norm ( x : Vector ) return double_float;
! 73: with function H ( x : Vector; t : Complex_Number ) return Vector;
! 74: with function dH ( x : Vector; t : Complex_Number ) return Vector;
! 75: with function dH ( x : Vector; t : Complex_Number ) return Matrix;
! 76:
! 77: procedure Linear_Single_Conditioned_Silent_Continue
! 78: ( s : in out Solu_Info; target : in Complex_Number;
! 79: tol : in double_float; proj : in boolean;
! 80: rtoric : in natural;
! 81: v : in out Standard_Floating_Vectors.Link_to_Vector;
! 82: errorv : in out double_float;
! 83: p : in Pred_Pars; c : in Corr_Pars );
! 84:
! 85: generic
! 86:
! 87: with function Norm ( x : Vector) return double_float;
! 88: with function H ( x : Vector; t : Complex_Number ) return Vector;
! 89: with function dH ( x : Vector; t : Complex_Number ) return Vector;
! 90: with function dH ( x : Vector; t : Complex_Number ) return Matrix;
! 91:
! 92: procedure Linear_Single_Conditioned_Reporting_Continue
! 93: ( file : in file_type; s : in out Solu_Info;
! 94: target : in Complex_Number; tol : in double_float;
! 95: proj : in boolean; rtoric : in natural;
! 96: v : in out Standard_Floating_Vectors.Link_to_Vector;
! 97: errorv : in out double_float;
! 98: p : in Pred_Pars; c : in Corr_Pars );
! 99:
! 100: -- DESCRIPTION :
! 101: -- This routine follows a path of solutions of the system
! 102: -- H(x,t) = 0, with t : t ---> target.
! 103: -- An increment-and-fix path-following technique is applied.
! 104:
! 105: -- ON ENTRY :
! 106: -- file to write intermediate results on;
! 107: -- s start solution and initial value of t;
! 108: -- target target value of the continuation parameter;
! 109: -- tol tolerance to decide when two double_floats are the same;
! 110: -- proj when perpendicular-projective corrector has to be used;
! 111: -- rtoric order of extrapolation for computation of path directions;
! 112: -- v direction of toric compactificiation, null when (rtoric = 0);
! 113: -- errorv error on the current direction;
! 114: -- p parameters for the predictor;
! 115: -- c parameters for the corrector.
! 116:
! 117: -- ON RETURN :
! 118: -- s the computed solution of H(x,t) = 0;
! 119: -- v direction of the compactification, when rtoric > 0;
! 120: -- errorv difference with previously computed direction.
! 121:
! 122: -- LINEAR PATH FOLLOWING FOR A NUMBER OF PATHS :
! 123:
! 124: generic
! 125:
! 126: with function Norm ( x : Vector ) return double_float;
! 127: with function H ( x : Vector; t : Complex_Number ) return Vector;
! 128: with function dH ( x : Vector; t : Complex_Number ) return Vector;
! 129: with function dH ( x : Vector; t : Complex_Number ) return Matrix;
! 130:
! 131: procedure Linear_Multiple_Normal_Silent_Continue
! 132: ( s : in out Solu_Info_Array;
! 133: target : in Complex_Number; tol,dist_sols : in double_float;
! 134: proj : in boolean; p : in Pred_Pars; c : in Corr_Pars );
! 135:
! 136: generic
! 137:
! 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 Vector;
! 141: with function dH ( x : Vector; t : Complex_Number ) return Matrix;
! 142:
! 143: procedure Linear_Multiple_Normal_Reporting_Continue
! 144: ( file : in file_type; s : in out Solu_Info_Array;
! 145: target : in Complex_Number; tol,dist_sols : in double_float;
! 146: proj : in boolean; p : in Pred_Pars; c : in Corr_Pars );
! 147:
! 148: generic
! 149:
! 150: with function Norm ( x : Vector ) return double_float;
! 151: with function H ( x : Vector; t : Complex_Number ) return Vector;
! 152: with function dH ( x : Vector; t : Complex_Number ) return Vector;
! 153: with function dH ( x : Vector; t : Complex_Number ) return Matrix;
! 154:
! 155: procedure Linear_Multiple_Conditioned_Silent_Continue
! 156: ( s : in out Solu_Info_Array;
! 157: target : in Complex_Number; tol,dist_sols : in double_float;
! 158: proj : in boolean; p : in Pred_Pars; c : in Corr_Pars );
! 159:
! 160: generic
! 161:
! 162: with function Norm ( x : Vector ) return double_float;
! 163: with function H ( x : Vector; t : Complex_Number ) return Vector;
! 164: with function dH ( x : Vector; t : Complex_Number ) return Vector;
! 165: with function dH ( x : Vector; t : Complex_Number ) return Matrix;
! 166:
! 167: procedure Linear_Multiple_Conditioned_Reporting_Continue
! 168: ( file : in file_type; s : in out Solu_Info_Array;
! 169: target : in Complex_Number; tol,dist_sols : in double_float;
! 170: proj : in boolean; p : in Pred_Pars; c : in Corr_Pars );
! 171:
! 172: -- DESCRIPTION :
! 173: -- This routine follows simultaneously a number of paths in order
! 174: -- to avoid clustering of solutions.
! 175:
! 176: -- ON ENTRY :
! 177: -- file to write intermediate results on;
! 178: -- s array of start solutions, all for the same t;
! 179: -- target target value of the continuation parameters;
! 180: -- tol tolerance to decide when two double_floats are the same;
! 181: -- dist_sols distance to be kept between the solutions;
! 182: -- proj indicates whether perpendicular-projective corrector has
! 183: -- to be used or not;
! 184: -- p parameters for the predictor;
! 185: -- c parameters for the corrector.
! 186:
! 187: -- ON RETURN :
! 188: -- s the computed solutions of H(x,t) = 0.
! 189:
! 190: -- CIRCULAR PATH FOLLOWING FOR ONE PATH :
! 191:
! 192: generic
! 193:
! 194: with function Norm ( x : Vector ) return double_float;
! 195: with function H ( x : Vector; t : Complex_Number ) return Vector;
! 196: with function dH ( x : Vector; t : Complex_Number ) return Vector;
! 197: with function dH ( x : Vector; t : Complex_Number ) return Matrix;
! 198:
! 199: procedure Circular_Single_Normal_Reporting_Continue
! 200: ( file : in file_type; s : in out Solu_Info;
! 201: target : in Complex_Number; tol,epslop : in double_float;
! 202: wc : out natural; max_wc : in natural;
! 203: sum,all_sum : out Vector;
! 204: proj : in boolean; p : in Pred_Pars; c : in Corr_Pars );
! 205:
! 206: generic
! 207:
! 208: with function Norm ( x : Vector ) return double_float;
! 209: with function H ( x : Vector; t : Complex_Number ) return Vector;
! 210: with function dH ( x : Vector; t : Complex_Number ) return Vector;
! 211: with function dH ( x : Vector; t : Complex_Number ) return Matrix;
! 212:
! 213: procedure Circular_Single_Conditioned_Reporting_Continue
! 214: ( file : in file_type; s : in out Solu_Info;
! 215: target : in Complex_Number; tol,epslop : in double_float;
! 216: wc : out natural; max_wc : in natural;
! 217: sum,all_sum : out Vector;
! 218: proj : in boolean; p : in Pred_Pars; c : in Corr_Pars );
! 219:
! 220:
! 221: -- DESCRIPTION :
! 222: -- This routine follows a path of solutions of the system
! 223: -- H(x,t) = 0, with t circuling around the target.
! 224: -- An increment-and-fix path-following technique is applied.
! 225:
! 226: -- ON ENTRY :
! 227: -- file to write intermediate results on;
! 228: -- s array of start solutions, all for the same t;
! 229: -- target target value of the continuation parameters;
! 230: -- tol tolerance to decide when two floats are the same;
! 231: -- epslop tolerance to decide when w(0) = w(2*PI*wc);
! 232: -- max_wc maximum bound for winding number;
! 233: -- proj indicates whether perpendicular-projective corrector has
! 234: -- to be used or not;
! 235: -- p parameters for the predictor;
! 236: -- c parameters for the corrector.
! 237:
! 238: -- ON RETURN :
! 239: -- s the computed solution of H(x,t) = 0;
! 240: -- wc estimated cycle number;
! 241: -- sum is the trapezium sum over the equidistant points;
! 242: -- all_sum is the trapezium sum over all the points.
! 243:
! 244: end Path_Trackers;
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