Checks whether a square root of preconditioner was specified in problem. function candoit = canGetSqrtPrecon(problem) Returns true if the problem structure allows for applying the square root of a preconditioner to tangent vectors at a given point. The square root of the preconditioner at x must be a symmetric, positive definite operator Q such that applying Q twice (Q o Q) amounts to applying the preconditioner once. If both a preconditioner and a square root of preconditioner are provided, it is the user's responsibility to ensure their compatibility. Similarly to getPrecon, if the present function returns false, calls to getSqrtPrecon will still work: they will act as the identity. Note that this may be incompatible with the preconditioner if it is given. Thus, always check by calling canGetSqrtPrecon first. See also: canGetPrecon getSqrtPrecon getPrecon

- canGetPrecon Checks whether a preconditioner was specified in the problem description.
- getPrecon Applies the preconditioner for the Hessian of the cost at x along d.
- hessianspectrum Returns the eigenvalues of the (preconditioned) Hessian at x.

0001 function candoit = canGetSqrtPrecon(problem) 0002 % Checks whether a square root of preconditioner was specified in problem. 0003 % 0004 % function candoit = canGetSqrtPrecon(problem) 0005 % 0006 % Returns true if the problem structure allows for applying the square root 0007 % of a preconditioner to tangent vectors at a given point. The square root 0008 % of the preconditioner at x must be a symmetric, positive definite 0009 % operator Q such that applying Q twice (Q o Q) amounts to applying the 0010 % preconditioner once. If both a preconditioner and a square root of 0011 % preconditioner are provided, it is the user's responsibility to ensure 0012 % their compatibility. 0013 % 0014 % Similarly to getPrecon, if the present function returns false, calls to 0015 % getSqrtPrecon will still work: they will act as the identity. Note that 0016 % this may be incompatible with the preconditioner if it is given. Thus, 0017 % always check by calling canGetSqrtPrecon first. 0018 % 0019 % See also: canGetPrecon getSqrtPrecon getPrecon 0020 0021 % This file is part of Manopt: www.manopt.org. 0022 % Original author: Nicolas Boumal, April 3, 2015. 0023 % Contributors: 0024 % Change log: 0025 0026 candoit = isfield(problem, 'sqrtprecon'); 0027 0028 end

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