File: [local] / OpenXM_contrib / PHC / Ada / Continuation / directions_of_solution_paths.ads (download)
Revision 1.1.1.1 (vendor branch), Sun Oct 29 17:45:22 2000 UTC (23 years, 8 months ago) by maekawa
Branch: PHC, MAIN
CVS Tags: v2, maekawa-ipv6, RELEASE_1_2_3, RELEASE_1_2_2_KNOPPIX_b, RELEASE_1_2_2_KNOPPIX, RELEASE_1_2_2, RELEASE_1_2_1, HEAD Changes since 1.1: +0 -0
lines
Import the second public release of PHCpack.
OKed by Jan Verschelde.
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with text_io; use text_io;
with Standard_Floating_Numbers; use Standard_Floating_Numbers;
with Standard_Complex_Numbers; use Standard_Complex_Numbers;
with Standard_Floating_Vectors;
with Standard_Complex_Vectors;
with Standard_Floating_VecVecs; use Standard_Floating_VecVecs;
package Directions_of_Solution_Paths is
-- DESCRIPTION :
-- This package provides some routines to estimate numerically the direction
-- of a solution path diverging to a solution of a face system.
procedure Affine_Update_Direction
( t,prev_t,target : in Complex_Number;
x,prevx : in Standard_Complex_Vectors.Vector;
prevdls,prevstep : in out double_float;
prevdiff,v : in out Standard_Floating_Vectors.Vector );
-- DESCRIPTION :
-- Computes an approximation of the direction of the path.
-- When prevdls /= 0.0, a second-order extrapolation will be applied.
-- ON ENTRY :
-- t current value of continuation parameter;
-- prev_t previous value of continuation parameter;
-- target target value of continuation parameter;
-- x current solution vector;
-- prevx solution vector for previous value of continuation parameter;
-- prevdls previous difference of the logs of distances to target;
-- prevstep previous step size;
-- prevdiff previous difference of the logs of the solution vectors;
-- v current approximate direction of the path.
procedure Projective_Update_Direction
( t,prev_t,target : in Complex_Number;
x,prevx : in Standard_Complex_Vectors.Vector;
prevdls,prevstep : in out double_float;
prevdiff,v : in out Standard_Floating_Vectors.Vector );
-- DESCRIPTION :
-- Does the same as the other procedure, under the assumption that the
-- solution vector lies in projective space.
-- REQUIRED :
-- The homogenization variable is the last element of the solution vector.
procedure Affine_Update_Direction
( r,m,estm,cntm : in out natural; thresm : in natural;
er : in out integer; t,target : in Complex_Number;
x : in Standard_Complex_Vectors.Vector;
dt,s,logs : in out Standard_Floating_Vectors.Vector;
logx,wvl0,wvl1,wvltmp : in out VecVec;
v,diferr : in out Standard_Floating_Vectors.Vector;
error : in out double_float );
procedure Affine_Update_Direction
( file : in file_type;
r,m,estm,cntm : in out natural; thresm : in natural;
er : in out integer; t,target : in Complex_Number;
x : in Standard_Complex_Vectors.Vector;
dt,s,logs : in out Standard_Floating_Vectors.Vector;
logx,wvl0,wvl1,wvltmp : in out VecVec;
v,diferr : in out Standard_Floating_Vectors.Vector;
error : in out double_float );
-- DESCRIPTION :
-- Higher-order extrapolation method that produces direction with error of
-- order (t-target)^r, when the solution path converges to regular solution
-- in affine space.
-- REQUIRED : s'range = logs'range = logx'range = 0..max,
-- wvl'range = 1..max, logx(i)'range = wvl'range(i) = 1..n,
-- diferr'range = 0..max, max >= 1, equals maximal order of extrapolator.
-- ON ENTRY :
-- file to write intermediate data, if not submitted, no output;
-- r last meaningful entry in logx and logs;
-- m current value for multiplicity;
-- estm current estimate for multiplicity;
-- cntm number of consecutive times estm has been guessed;
-- thresm threshold for changing the m to estm;
-- er order of extrapolator on the errors;
-- t current value of continuation parameter;
-- target target value of continuation parameter;
-- x current solution for t;
-- dt consecutive distances of t-values to target value;
-- s consecutive s-values, with proper value for m;
-- logs logarithms of previous values (target - t);
-- logx logarithms of previous solution vectors;
-- wvl0 previous consecutive estimates for direction;
-- wvl1 current consecutive estimates for direction;
-- wvltmp work space for updating wvl0 and wvl1.
-- ON RETURN :
-- r if r < logs'last, then r will be raised by one,
-- otherwise r remains unchanged;
-- s updated distance vector;
-- logs updated vector of logarithms of distances to target;
-- logx updated vector of solution vectors;
-- wvl0 updated previous consecutive estimates, equals wvl1;
-- wvl1 updated current consecutive estimates for direction;
-- v estimated direction of path;
-- diferr norms of consecutive differences of estimates for v;
-- error norm of errorv;
procedure Projective_Update_Direction
( r,m,estm,cntm : in out natural; thresm : in natural;
er : in out integer; t,target : in Complex_Number;
x : in Standard_Complex_Vectors.Vector;
dt,s,logs : in out Standard_Floating_Vectors.Vector;
logx : in out VecVec;
prevv,v : in out Standard_Floating_Vectors.Vector;
error : in out double_float );
procedure Projective_Update_Direction
( file : in file_type;
r,m,estm,cntm : in out natural; thresm : in natural;
er : in out integer; t,target : in Complex_Number;
x : in Standard_Complex_Vectors.Vector;
dt,s,logs : in out Standard_Floating_Vectors.Vector;
logx : in out VecVec;
prevv,v : in out Standard_Floating_Vectors.Vector;
error : in out double_float );
-- DESCRIPTION :
-- Higher-order extrapolation method that produces direction with error of
-- order (t-target)^r, when the solution path converges to regular solution
-- in affine space.
-- REQUIRED :
-- x(x'last) contains value of variable introduced to homogenize the system.
end Directions_of_Solution_Paths;