Annotation of OpenXM_contrib/PHC/Ada/Continuation/predictors.ads, Revision 1.1
1.1 ! maekawa 1: with Standard_Floating_Numbers; use Standard_Floating_Numbers;
! 2: with Standard_Complex_Numbers; use Standard_Complex_Numbers;
! 3: with Standard_Complex_Vectors; use Standard_Complex_Vectors;
! 4: with Standard_Complex_Matrices; use Standard_Complex_Matrices;
! 5: with Standard_Complex_Solutions; use Standard_Complex_Solutions;
! 6: with Continuation_Data; use Continuation_Data;
! 7:
! 8: package Predictors is
! 9:
! 10: -- DESCRIPTION :
! 11: -- This package contains several implementations for the predictor
! 12: -- in an increment-and-fix continuation.
! 13:
! 14: -- The predictor provides a prediction both for the continuation parameter t
! 15: -- and for the solution(s) x.
! 16:
! 17: -- For the continuation paramter t the following options can be made :
! 18: -- Real : linear prediction, simply adds the step size;
! 19: -- Complex : can make predictions in complex space;
! 20: -- Circular : to perform a circular sample, for winding numbers;
! 21: -- Geometric : distances to target form geometric series.
! 22:
! 23: -- For the solution vector x the following options are provided :
! 24: -- Secant : linear extrapolation using differences;
! 25: -- Tangent : linear extrapolation using the first derivatives;
! 26: -- Hermite : third-order extrapolation using first derivatives.
! 27: -- Furthermore, these predictors for x can be applied
! 28: -- for one solution (Single) or for an array of solutions (Multiple).
! 29:
! 30: -- By combining these options, the following 13 predictors are provided :
! 31:
! 32: -- Secant_Single_Real_Predictor
! 33: -- Secant_Single_Complex_Predictor
! 34: -- Secant_Multiple_Real_Predictor
! 35: -- Secant_Multiple_Complex_Predictor
! 36: -- Tangent_Single_Real_Predictor
! 37: -- Tangent_Single_Complex_Predictor
! 38: -- Tangent_Multiple_Real_Predictor
! 39: -- Tangent_Multiple_Complex_Predictor
! 40:
! 41: -- Secant_Circular_Predictor
! 42: -- Secant_Geometric_Predictor
! 43: -- Tangent_Circular_Predictor
! 44: -- Tangent_Geometric_Predictor
! 45:
! 46: -- Hermite_Single_Real_Predictor
! 47:
! 48: -- The order in which these predictors are listed depends on their mutual
! 49: -- resemblances of the specified parameters.
! 50:
! 51: procedure Secant_Single_Real_Predictor
! 52: ( x : in out Vector; prev_x : in Vector;
! 53: t : in out Complex_Number; prev_t,target : in Complex_Number;
! 54: h,tol : in double_float; pow : in positive := 1 );
! 55:
! 56: procedure Secant_Multiple_Real_Predictor
! 57: ( x : in out Solution_Array; prev_x : in Solution_Array;
! 58: t : in out Complex_Number; prev_t,target : in Complex_Number;
! 59: h,tol,dist_x : in double_float; pow : in positive := 1 );
! 60:
! 61: -- DESCRIPTION :
! 62: -- Secant predictor for x and a linear predictor for t.
! 63:
! 64: -- ON ENTRY :
! 65: -- x the current approximation(s) for t;
! 66: -- prev_x the approximation(s) for a previous t;
! 67: -- t the current value of the continuation parameter;
! 68: -- prev_t is the previous value for t;
! 69: -- target is the target value for t;
! 70: -- h is the step size;
! 71: -- tol tolerance to decide when t = target;
! 72: -- dist_x for all i /= j : |x(i)(k) - x(j)(k)| > d, for k in 1..n;
! 73: -- pow power of t in the homotopy towards 1.
! 74:
! 75: -- ON RETURN :
! 76: -- x the predicted approximation(s);
! 77: -- t the predicted value of the continuation parameter.
! 78:
! 79: procedure Secant_Single_Complex_Predictor
! 80: ( x : in out Vector; prev_x : in Vector;
! 81: t : in out Complex_Number; prev_t,target : in Complex_Number;
! 82: h,tol,dist_t : in double_float; trial : in natural );
! 83:
! 84: procedure Secant_Multiple_Complex_Predictor
! 85: ( x : in out Solution_Array; prev_x : in Solution_Array;
! 86: t : in out Complex_Number; prev_t,target : in Complex_Number;
! 87: h,tol,dist_x,dist_t : in double_float;
! 88: trial : in natural);
! 89:
! 90: -- DESCRIPTION :
! 91: -- Secant predictor for x and complex predictor for t.
! 92:
! 93: -- ON ENTRY :
! 94: -- x the current approximation(s) for t;
! 95: -- prev_x the approximation(s) for a previous t;
! 96: -- t the current value of the continuation parameter;
! 97: -- prev_t is the previous value for t;
! 98: -- target is the target value for t;
! 99: -- h is the step size;
! 100: -- tol tolerance to decide when two numbers are equal;
! 101: -- dist_x for all i /= j : |x(i)(k) - x(j)(k)| > d, for k in 1..n;
! 102: -- dist_t t must keep a distance to the target;
! 103: -- trial indicates the number of trials for starting out of
! 104: -- the previous value for t.
! 105:
! 106: -- ON RETURN :
! 107: -- x the predicted approximation(s);
! 108: -- t the predicted value of the continuation parameter.
! 109:
! 110: procedure Secant_Circular_Predictor
! 111: ( x : in out Vector; prev_x : in Vector;
! 112: t : in out Complex_Number; theta : in out double_float;
! 113: prev_t,t0_min_target,target : in Complex_Number;
! 114: h,tol : in double_float );
! 115:
! 116: -- DESCRIPTION :
! 117: -- Secant predictor for x and circular predictor for t, around target.
! 118:
! 119: -- NOTE : This is the link between t and theta :
! 120: -- t = target + t0_min_target * ( cos(theta) + i sin(theta) )
! 121:
! 122: -- ON ENTRY :
! 123: -- x,prev_x,t,prev_t,target as before;
! 124: -- theta the angle for t.
! 125: -- t0_min_target is t0-target, where t0 is the start point;
! 126: -- h is step size for theta !!
! 127:
! 128: -- ON RETURN :
! 129: -- x the predicted approximation;
! 130: -- t the predicted value of the continuation parameter;
! 131: -- theta the predicted angle.
! 132:
! 133: procedure Secant_Geometric_Predictor
! 134: ( x : in out Vector; prev_x : in Vector;
! 135: t : in out Complex_Number; prev_t,target : in Complex_Number;
! 136: h,tol : in double_float );
! 137:
! 138: -- DESCRIPTION :
! 139: -- Secant predictor for x and a geometric predictor for t.
! 140:
! 141: -- ON ENTRY :
! 142: -- x the current approximation(s) for t;
! 143: -- prev_x the approximation(s) for a previous t;
! 144: -- t the current value of the continuation parameter;
! 145: -- prev_t is the previous value for t;
! 146: -- target is the target value for t;
! 147: -- h ratio between two consecutive distance to target, 0<h<1;
! 148: -- tol tolerance to decide when t = target;
! 149:
! 150: -- ON RETURN :
! 151: -- x the predicted approximation;
! 152: -- t the predicted value of the continuation parameter.
! 153:
! 154: generic
! 155:
! 156: with function Norm ( x : Vector ) return double_float;
! 157: with function dH ( x : Vector; t : Complex_Number ) return Vector;
! 158: -- returns the derivatives of H(x,t) w.r.t. t in (x,t)
! 159: with function dH ( x : Vector; t : Complex_Number ) return Matrix;
! 160: -- returns the Jacobian matrix of H(x,t) at (x,t)
! 161:
! 162: procedure Tangent_Single_Real_Predictor
! 163: ( x : in out Vector; t : in out Complex_Number;
! 164: target : in Complex_Number; h,tol : in double_float;
! 165: pow : in positive := 1 );
! 166:
! 167: generic
! 168:
! 169: with function Norm ( x : Vector ) return double_float;
! 170: with function dH ( x : Vector; t : Complex_Number ) return Vector;
! 171: -- returns the derivatives of H(x,t) w.r.t. t in (x,t)
! 172: with function dH ( x : Vector; t : Complex_Number ) return Matrix;
! 173: -- returns the Jacobian matrix of H(x,t) at (x,t)
! 174:
! 175: procedure Tangent_Multiple_Real_Predictor
! 176: ( x : in out Solution_Array; t : in out Complex_Number;
! 177: target : in Complex_Number; h,tol,dist_x : in double_float;
! 178: nsys : in out natural; pow : in positive := 1 );
! 179:
! 180: -- DESCRIPTION :
! 181: -- Tangent predictor for x and a linear predictor for t.
! 182:
! 183: -- ON ENTRY :
! 184: -- x current approximation for the solution;
! 185: -- t current value of the continuation parameter;
! 186: -- target target value for the continuation parameter;
! 187: -- h steplength;
! 188: -- tol tolerance to decide when t = target;
! 189: -- dist_x for all i /= j : |x(i)(k) - x(j)(k)| > dist_x, for k in 1..n;
! 190: -- nsys must be initally equal to zero, used for counting;
! 191: -- pow power of t in the homotopy.
! 192:
! 193: -- ON RETURN :
! 194: -- x predicted approximation for the solution;
! 195: -- t new value of the continuation parameter;
! 196: -- nsys the number of linear systems solved.
! 197:
! 198: generic
! 199:
! 200: with function Norm ( x : Vector ) return double_float;
! 201: with function dH ( x : Vector; t : Complex_Number ) return Vector;
! 202: -- returns the derivatives of H(x,t) w.r.t. t in (x,t)
! 203: with function dH ( x : Vector; t : Complex_Number ) return Matrix;
! 204: -- returns the Jacobian matrix of H(x,t) at (x,t)
! 205:
! 206: procedure Tangent_Single_Complex_Predictor
! 207: ( x : in out Vector; t : in out Complex_Number;
! 208: target : in Complex_Number;
! 209: h,tol,dist_t : in double_float; trial : in natural );
! 210:
! 211: generic
! 212:
! 213: with function Norm ( x : Vector) return double_float;
! 214: with function dH ( x : Vector; t : Complex_Number ) return Vector;
! 215: -- returns the derivatives of H(x,t) w.r.t. t in (x,t)
! 216: with function dH ( x : Vector; t : Complex_Number ) return Matrix;
! 217: -- returns the Jacobian matrix of H(x,t) at (x,t)
! 218:
! 219: procedure Tangent_Multiple_Complex_Predictor
! 220: ( x : in out Solution_Array; t : in out Complex_Number;
! 221: target : in Complex_Number;
! 222: h,tol,dist_x,dist_t : in double_float;
! 223: trial : in natural; nsys : in out natural );
! 224:
! 225: -- DESCRIPTION :
! 226: -- Tangent predictor for x and a complex predictor for t.
! 227:
! 228: -- ON ENTRY :
! 229: -- x current approximation for the solution;
! 230: -- t current value of the continuation parameter;
! 231: -- target target value for the continuation parameter;
! 232: -- h steplength;
! 233: -- tol tolerance to decide when two numbers are equal;
! 234: -- dist_x for all i /= j : |x(i)(k) - x(j)(k)| > d, for k in 1..n;
! 235: -- dist_t t must keep distance to the target;
! 236: -- trial indicates the number of trials for starting out of
! 237: -- the previous value for t;
! 238: -- nsys must be initially equal to zero.
! 239:
! 240: -- ON RETURN :
! 241: -- x predicted approximation for the solution;
! 242: -- t new value of the continuation parameter;
! 243: -- nsys the number of linear systems solved.
! 244:
! 245: generic
! 246:
! 247: with function Norm ( x : Vector) return double_float;
! 248: with function dH ( x : Vector; t : Complex_Number ) return Vector;
! 249: -- returns the derivatives of H(x,t) w.r.t. t in (x,t)
! 250: with function dH ( x : Vector; t : Complex_Number ) return Matrix;
! 251: -- returns the Jacobian matrix of H(x,t) at (x,t)
! 252:
! 253: procedure Tangent_Circular_Predictor
! 254: ( x : in out Vector; t : in out Complex_Number;
! 255: theta : in out double_float;
! 256: t0_min_target,target : in Complex_Number;
! 257: h,tol : in double_float );
! 258:
! 259: -- DESCRIPTION :
! 260: -- This is a tangent predictor for x and a circular predictor for t
! 261: -- For information on the parameters, see Secant_Circular_Predictor.
! 262:
! 263: generic
! 264:
! 265: with function Norm ( x : Vector) return double_float;
! 266: with function dH ( x : Vector; t : Complex_Number ) return Vector;
! 267: -- returns the derivatives of H(x,t) w.r.t. t in (x,t)
! 268: with function dH ( x : Vector; t : Complex_Number ) return Matrix;
! 269: -- returns the Jacobian matrix of H(x,t) at (x,t)
! 270:
! 271: procedure Tangent_Geometric_Predictor
! 272: ( x : in out Vector; t : in out Complex_Number;
! 273: target : in Complex_Number; h,tol : in double_float );
! 274:
! 275: -- DESCRIPTION :
! 276: -- Tangent predictor for x and a geometric predictor for t.
! 277: -- For information on the parameters, see Secant_Geometric_Predictor.
! 278:
! 279: generic
! 280:
! 281: with function Norm ( x : Vector) return double_float;
! 282: with function dH ( x : Vector; t : Complex_Number ) return Vector;
! 283: -- returns the derivatives of H(x,t) w.r.t. t in (x,t)
! 284: with function dH ( x : Vector; t : Complex_Number ) return Matrix;
! 285: -- returns the Jacobian matrix of H(x,t) at (x,t)
! 286:
! 287: procedure Hermite_Single_Real_Predictor
! 288: ( x : in out Vector; prev_x : in Vector;
! 289: t : in out Complex_Number; prev_t,target : in Complex_Number;
! 290: v : in out Vector; prev_v : in Vector;
! 291: h,tol : in double_float; pow : in positive := 1 );
! 292:
! 293: -- DESCRIPTION :
! 294: -- Third-order extrapolation based on previous values of the solution
! 295: -- paths along with corresponding first derivatives.
! 296:
! 297: -- ON ENTRY :
! 298: -- x current approximation for the solution;
! 299: -- prev_x previous approximation of the solution at prev_t;
! 300: -- t current value of the continuation parameter;
! 301: -- prev_t previous value of the continuation parameter;
! 302: -- target target value for the continuation parameter;
! 303: -- v will be used at work space;
! 304: -- prev_v direction of the path at prev_t;
! 305: -- h steplength;
! 306: -- tol tolerance to decide when t = target;
! 307: -- dist_x for all i /= j : |x(i)(k) - x(j)(k)| > dist_x, for k in 1..n;
! 308: -- pow power of t in the homotopy.
! 309:
! 310: -- ON RETURN :
! 311: -- x predicted approximation for the solution;
! 312: -- t new value of the continuation parameter;
! 313: -- v direction of the path computed for value of t on entry.
! 314:
! 315: end Predictors;
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