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Annotation of OpenXM_contrib/PHC/Ada/Continuation/directions_of_solution_paths.ads, Revision 1.1.1.1

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;
                      6: with Standard_Floating_VecVecs;          use Standard_Floating_VecVecs;
                      7:
                      8: package Directions_of_Solution_Paths is
                      9:
                     10: -- DESCRIPTION :
                     11: --   This package provides some routines to estimate numerically the direction
                     12: --   of a solution path diverging to a solution of a face system.
                     13:
                     14:   procedure Affine_Update_Direction
                     15:                 ( t,prev_t,target : in Complex_Number;
                     16:                   x,prevx : in Standard_Complex_Vectors.Vector;
                     17:                   prevdls,prevstep : in out double_float;
                     18:                   prevdiff,v : in out Standard_Floating_Vectors.Vector );
                     19:
                     20:   -- DESCRIPTION :
                     21:   --   Computes an approximation of the direction of the path.
                     22:   --   When prevdls /= 0.0, a second-order extrapolation will be applied.
                     23:
                     24:   -- ON ENTRY :
                     25:   --   t          current value of continuation parameter;
                     26:   --   prev_t     previous value of continuation parameter;
                     27:   --   target     target value of continuation parameter;
                     28:   --   x          current solution vector;
                     29:   --   prevx      solution vector for previous value of continuation parameter;
                     30:   --   prevdls    previous difference of the logs of distances to target;
                     31:   --   prevstep   previous step size;
                     32:   --   prevdiff   previous difference of the logs of the solution vectors;
                     33:   --   v          current approximate direction of the path.
                     34:
                     35:   procedure Projective_Update_Direction
                     36:                 ( t,prev_t,target : in Complex_Number;
                     37:                   x,prevx : in Standard_Complex_Vectors.Vector;
                     38:                   prevdls,prevstep : in out double_float;
                     39:                   prevdiff,v : in out Standard_Floating_Vectors.Vector );
                     40:
                     41:   -- DESCRIPTION :
                     42:   --   Does the same as the other procedure, under the assumption that the
                     43:   --   solution vector lies in projective space.
                     44:
                     45:   -- REQUIRED :
                     46:   --   The homogenization variable is the last element of the solution vector.
                     47:
                     48:   procedure Affine_Update_Direction
                     49:                 ( r,m,estm,cntm : in out natural; thresm : in natural;
                     50:                   er : in out integer; t,target : in Complex_Number;
                     51:                   x : in Standard_Complex_Vectors.Vector;
                     52:                   dt,s,logs : in out Standard_Floating_Vectors.Vector;
                     53:                   logx,wvl0,wvl1,wvltmp : in out VecVec;
                     54:                   v,diferr : in out Standard_Floating_Vectors.Vector;
                     55:                   error : in out double_float );
                     56:
                     57:   procedure Affine_Update_Direction
                     58:                 ( file : in file_type;
                     59:                   r,m,estm,cntm : in out natural; thresm : in natural;
                     60:                   er : in out integer; t,target : in Complex_Number;
                     61:                   x : in Standard_Complex_Vectors.Vector;
                     62:                   dt,s,logs : in out Standard_Floating_Vectors.Vector;
                     63:                   logx,wvl0,wvl1,wvltmp : in out VecVec;
                     64:                   v,diferr : in out Standard_Floating_Vectors.Vector;
                     65:                   error : in out double_float );
                     66:
                     67:   -- DESCRIPTION :
                     68:   --   Higher-order extrapolation method that produces direction with error of
                     69:   --   order (t-target)^r, when the solution path converges to regular solution
                     70:   --   in affine space.
                     71:
                     72:   -- REQUIRED : s'range = logs'range = logx'range = 0..max,
                     73:   --   wvl'range = 1..max, logx(i)'range = wvl'range(i) = 1..n,
                     74:   --   diferr'range = 0..max, max >= 1, equals maximal order of extrapolator.
                     75:
                     76:   -- ON ENTRY :
                     77:   --   file       to write intermediate data, if not submitted, no output;
                     78:   --   r          last meaningful entry in logx and logs;
                     79:   --   m          current value for multiplicity;
                     80:   --   estm       current estimate for multiplicity;
                     81:   --   cntm       number of consecutive times estm has been guessed;
                     82:   --   thresm     threshold for changing the m to estm;
                     83:   --   er         order of extrapolator on the errors;
                     84:   --   t          current value of continuation parameter;
                     85:   --   target     target value of continuation parameter;
                     86:   --   x          current solution for t;
                     87:   --   dt         consecutive distances of t-values to target value;
                     88:   --   s          consecutive s-values, with proper value for m;
                     89:   --   logs       logarithms of previous values (target - t);
                     90:   --   logx       logarithms of previous solution vectors;
                     91:   --   wvl0       previous consecutive estimates for direction;
                     92:   --   wvl1       current consecutive estimates for direction;
                     93:   --   wvltmp     work space for updating wvl0 and wvl1.
                     94:
                     95:   -- ON RETURN :
                     96:   --   r          if r < logs'last, then r will be raised by one,
                     97:   --              otherwise r remains unchanged;
                     98:   --   s          updated distance vector;
                     99:   --   logs       updated vector of logarithms of distances to target;
                    100:   --   logx       updated vector of solution vectors;
                    101:   --   wvl0       updated previous consecutive estimates, equals wvl1;
                    102:   --   wvl1       updated current consecutive estimates for direction;
                    103:   --   v          estimated direction of path;
                    104:   --   diferr     norms of consecutive differences of estimates for v;
                    105:   --   error      norm of errorv;
                    106:
                    107:   procedure Projective_Update_Direction
                    108:                 ( r,m,estm,cntm : in out natural; thresm : in natural;
                    109:                   er : in out integer; t,target : in Complex_Number;
                    110:                   x : in Standard_Complex_Vectors.Vector;
                    111:                   dt,s,logs : in out Standard_Floating_Vectors.Vector;
                    112:                   logx : in out VecVec;
                    113:                   prevv,v : in out Standard_Floating_Vectors.Vector;
                    114:                   error : in out double_float );
                    115:
                    116:   procedure Projective_Update_Direction
                    117:                 ( file : in file_type;
                    118:                   r,m,estm,cntm : in out natural; thresm : in natural;
                    119:                   er : in out integer; t,target : in Complex_Number;
                    120:                   x : in Standard_Complex_Vectors.Vector;
                    121:                   dt,s,logs : in out Standard_Floating_Vectors.Vector;
                    122:                   logx : in out VecVec;
                    123:                   prevv,v : in out Standard_Floating_Vectors.Vector;
                    124:                   error : in out double_float );
                    125:
                    126:   -- DESCRIPTION :
                    127:   --   Higher-order extrapolation method that produces direction with error of
                    128:   --   order (t-target)^r, when the solution path converges to regular solution
                    129:   --   in affine space.
                    130:
                    131:   -- REQUIRED :
                    132:   --   x(x'last) contains value of variable introduced to homogenize the system.
                    133:
                    134: end Directions_of_Solution_Paths;