Home > manopt > core > getSqrtPrecon.m

getSqrtPrecon

PURPOSE ^

Applies the square root of the Hessian preconditioner at x along d.

SYNOPSIS ^

function sqrtPd = getSqrtPrecon(problem, x, d, storedb, key)

DESCRIPTION ^

 Applies the square root of the Hessian preconditioner at x along d.

 function sqrtPd = getSqrtPrecon(problem, x, d)
 function sqrtPd = getSqrtPrecon(problem, x, d, storedb)
 function sqrtPd = getSqrtPrecon(problem, x, d, storedb, key)

 Returns as sqrtPd the result of applying the square root of the Hessian
 preconditioner to the tangent vector d at point x. The preconditioner is
 supposed to be a symmetric, positive definite approximation of the
 inverse of the Hessian. Its square root must thus be symmetric and
 positive definite itself.
 
 If no square root of preconditioner is available, sqrtPd = d (identity).
 Note that this may be incompatible with the preconditioner, if that one
 is supplied in the problem description. Always check with canGetPrecon
 and canGetSqrtPrecon.

 storedb is a StoreDB object, key is the StoreDB key to point x.

 See also: getPrecon canGetPrecon canGetSqrtPrecon getHessian

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 function sqrtPd = getSqrtPrecon(problem, x, d, storedb, key)
0002 % Applies the square root of the Hessian preconditioner at x along d.
0003 %
0004 % function sqrtPd = getSqrtPrecon(problem, x, d)
0005 % function sqrtPd = getSqrtPrecon(problem, x, d, storedb)
0006 % function sqrtPd = getSqrtPrecon(problem, x, d, storedb, key)
0007 %
0008 % Returns as sqrtPd the result of applying the square root of the Hessian
0009 % preconditioner to the tangent vector d at point x. The preconditioner is
0010 % supposed to be a symmetric, positive definite approximation of the
0011 % inverse of the Hessian. Its square root must thus be symmetric and
0012 % positive definite itself.
0013 %
0014 % If no square root of preconditioner is available, sqrtPd = d (identity).
0015 % Note that this may be incompatible with the preconditioner, if that one
0016 % is supplied in the problem description. Always check with canGetPrecon
0017 % and canGetSqrtPrecon.
0018 %
0019 % storedb is a StoreDB object, key is the StoreDB key to point x.
0020 %
0021 % See also: getPrecon canGetPrecon canGetSqrtPrecon getHessian
0022 
0023 % This file is part of Manopt: www.manopt.org.
0024 % Original author: Nicolas Boumal, April 3, 2015.
0025 % Contributors:
0026 % Change log:
0027 
0028     % Allow omission of the key, and even of storedb.
0029     if ~exist('key', 'var')
0030         if ~exist('storedb', 'var')
0031             storedb = StoreDB();
0032         end
0033         key = storedb.getNewKey();
0034     end
0035 
0036     
0037     if isfield(problem, 'sqrtprecon')
0038     %% Apply sqrtprecon for the square root of the preconditioner
0039     
0040         % Check whether this function wants to deal with storedb or not.
0041         switch nargin(problem.sqrtprecon)
0042             case 2
0043                 sqrtPd = problem.sqrtprecon(x, d);
0044             case 3
0045                 % Obtain, pass along, and save the store for x.
0046                 store = storedb.getWithShared(key);
0047                 [sqrtPd, store] = problem.sqrtprecon(x, d, store);
0048                 storedb.setWithShared(store, key);
0049             case 4
0050                 % Pass along the whole storedb (by reference), with key.
0051                 sqrtPd = problem.sqrtprecon(x, d, storedb, key);
0052             otherwise
0053                 up = MException('manopt:getSqrtPrecon:badsqrtprecon', ...
0054                     'sqrtprecon should accept 2, 3 or 4 inputs.');
0055                 throw(up);
0056         end
0057         
0058     else
0059     %% No preconditioner square root provided, so just use the identity.
0060     
0061         sqrtPd = d;
0062         
0063     end
0064     
0065 end

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