- StoreDB
- getApproxGradient Computes an approximation of the gradient of the cost function at x.
- getApproxHessian Computes an approximation of the Hessian of the cost fun. at x along d.
- getCost Computes the cost function at x.
- getCostGrad Computes the cost function and the gradient at x in one call if possible.
- getDirectionalDerivative Computes the directional derivative of the cost function at x along d.
- getEuclideanGradient Computes the Euclidean gradient of the cost function at x.
- getGradient Computes the gradient of the cost function at x.
- getGradientFD Computes an approx. of the gradient w/ finite differences of the cost.
- getHessian Computes the Hessian of the cost function at x along d.
- getHessianFD Computes an approx. of the Hessian w/ finite differences of the gradient.
- getLinesearch Returns a hint for line-search algorithms.
- getPartialEuclideanGradient Computes the Euclidean gradient of a subset of terms in cost function.
- getPartialGradient Computes the gradient of a subset of terms in the cost function at x.
- getPrecon Applies the preconditioner for the Hessian of the cost at x along d.
- getSqrtPrecon Applies the square root of the Hessian preconditioner at x along d.
- conjugategradient Conjugate gradient minimization algorithm for Manopt.
- approxgradientFD Gradient approx. fnctn handle based on finite differences of the cost.
- approxhessianFD Hessian approx. fnctn handle based on finite differences of the gradient.
- linesearch Standard line-search algorithm (step size selection) for descent methods.
- linesearch_adaptive Adaptive line search algorithm (step size selection) for descent methods.
- linesearch_decrease Backtracking line-search aiming merely for a decrease in cost value.
- linesearch_hint Armijo line-search based on the line-search hint in the problem structure.
- neldermead Nelder Mead optimization algorithm for derivative-free minimization.
- preconhessiansolve Preconditioner based on the inverse Hessian, by solving linear systems.
- pso Particle swarm optimization (PSO) for derivative-free minimization.
- steepestdescent Steepest descent (gradient descent) minimization algorithm for Manopt.
- trustregions Riemannian trust-regions solver for optimization on manifolds.
- checkdiff Checks the consistency of the cost function and directional derivatives.
- checkgradient Checks the consistency of the cost function and the gradient.
- checkhessian Checks the consistency of the cost function and the Hessian.
- hessianextreme Compute an extreme eigenvector / eigenvalue of the Hessian of a problem.
- hessianmatrix Computes a matrix which represents the Hessian in some tangent basis.
- hessianspectrum Returns the eigenvalues of the (preconditioned) Hessian at x.
- plotprofile Plot the cost function along a geodesic or a retraction path.
- surfprofile Plot the cost function as a surface over a 2-dimensional subspace.

- function storedb = StoreDB(storedepth)
- function store = get(storedb, key)
- function store = getWithShared(storedb, key)
- function key = set(storedb, store, key)
- function key = setWithShared(storedb, store, key)
- function key = getNewKey(storedb)
- function purge(storedb)

0001 classdef StoreDB < handle_light 0002 % The StoreDB class is a handle class to manage caching in Manopt. 0003 % 0004 % To create an object, call: storedb = StoreDB(); 0005 % Alternatively, call: storedb = StoreDB(storedepth); to instruct 0006 % the database to keep at most storedepth store's in its history. 0007 % (Note that clean up only happens when purge() is called). 0008 % 0009 % The storedb object is passed by reference: when it is passed to a 0010 % function as an input, and that function modifies it, the original 0011 % object is modified. 0012 0013 % This file is part of Manopt: www.manopt.org. 0014 % Original author: Nicolas Boumal, April 3, 2015. 0015 % Contributors: 0016 % Change log: 0017 0018 % TODO : protect get/setWithShared calls: limit to one, and forbid access 0019 % to shared memory while it has not been returned. 0020 % Do think of the applyStatsFun case : calls a getWithShared, does 0021 % not need a setWithShared. I think for statsfun there should be a 0022 % method "forfeitWithShared". 0023 0024 properties(Access = public) 0025 0026 % This memory is meant to be shared at all times. Users can modify 0027 % this at will. It is the same for all points x. 0028 shared = struct(); 0029 0030 % This memory is used by the toolbox for, e.g., automatic caching 0031 % and book keeping. Users should not overwrite this. It is the 0032 % same for all points x. 0033 internal = struct(); 0034 0035 % When calling purge(), only a certain number of stores will be 0036 % kept in 'history'. This parameter fixes that number. The most 0037 % recently modified stores are kept. Set to inf to keep all stores. 0038 storedepth = inf; 0039 0040 end 0041 0042 properties(Access = private) 0043 0044 % This structure holds separate memories for individual points. 0045 % Use get and set to interact with this. The field name 'shared' is 0046 % reserved, for use with get/setWithShared. 0047 history = struct(); 0048 0049 % This internal counter is used to obtain unique key's for points. 0050 counter = uint32(0); 0051 0052 % This internal counter is used to time calls to 'set', and hence 0053 % keep track of which stores in 'history' were last updated. 0054 timer = uint32(0); 0055 0056 end 0057 0058 0059 methods(Access = public) 0060 0061 % Constructor 0062 function storedb = StoreDB(storedepth) 0063 if nargin >= 1 0064 storedb.storedepth = storedepth; 0065 end 0066 end 0067 0068 % Return the store associated to a given key. 0069 % If the key is unknown, returns an empty structure. 0070 function store = get(storedb, key) 0071 if isfield(storedb.history, key) 0072 store = storedb.history.(key); 0073 else 0074 store = struct(); 0075 end 0076 end 0077 0078 % Same as get, but adds the shared memory in store.shared. 0079 function store = getWithShared(storedb, key) 0080 store = storedb.get(key); 0081 store.shared = storedb.shared; 0082 end 0083 0084 % Save the given store at the given key. If no key is provided, a 0085 % new key is generated for this store (i.e., it is assumed this 0086 % store pertains to a new point). The key is returned in all cases. 0087 % A field 'lastset__' is added/updated in the store structure, 0088 % keeping track of the last time that store was modified. 0089 function key = set(storedb, store, key) 0090 if nargin < 3 0091 key = getNewKey(storedb); 0092 end 0093 store.lastset__ = storedb.timer; 0094 storedb.timer = storedb.timer + 1; 0095 storedb.history.(key) = store; 0096 end 0097 0098 % Same as set, but extracts the shared memory and saves it. 0099 % The stored store will still have a 'shared' field, but it will be 0100 % empty. 0101 function key = setWithShared(storedb, store, key) 0102 storedb.shared = store.shared; 0103 store.shared = []; 0104 key = storedb.set(store, key); 0105 end 0106 0107 % Generate a unique key and return it. This should be called 0108 % everytime a new point is generated / stored. Keys are valid field 0109 % names for structures. 0110 function key = getNewKey(storedb) 0111 key = sprintf('z%d', storedb.counter); 0112 storedb.counter = storedb.counter + 1; 0113 end 0114 0115 % Clear entries in storedb.history to limit memory usage. 0116 function purge(storedb) 0117 0118 if isinf(storedb.storedepth) 0119 return; 0120 end 0121 0122 if storedb.storedepth <= 0 0123 storedb.history = struct(); 0124 return; 0125 end 0126 0127 % Get list of field names (keys). 0128 keys = fieldnames(storedb.history); 0129 nkeys = length(keys); 0130 0131 % If we need to remove some of the elements in the database, 0132 if nkeys > storedb.storedepth 0133 0134 % Get the last-set counter of each element: 0135 % a higher number means it was modified more recently. 0136 lastset = zeros(nkeys, 1, 'uint32'); 0137 for i = 1 : nkeys 0138 lastset(i) = storedb.history.(keys{i}).lastset__; 0139 end 0140 0141 % Sort the counters and determine the threshold above which 0142 % the field needs to be removed. 0143 sortlastset = sort(lastset, 1, 'descend'); 0144 minlastset = sortlastset(storedb.storedepth); 0145 0146 % Remove all fields that are too old. 0147 storedb.history = rmfield(storedb.history, ... 0148 keys(lastset < minlastset)); 0149 end 0150 0151 end % end of purge() 0152 0153 end 0154 0155 end

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