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.

## CROSS-REFERENCE INFORMATION This function calls: This function is called by:
• getPrecon Applies the preconditioner for the Hessian of the cost at x along d.
• hessianspectrum Returns the eigenvalues of the (preconditioned) Hessian at x.

## 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 %
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
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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