bounds函数matlab

在MATLAB中，bounds函数用于计算给定数组的最小和最大值。它的语法如下：

[bmin, bmax] = bounds(A)

其中，A是输入数组，bmin是A的最小值，bmax是A的最大值。

例如，我们有一个数组A = [2, 5, 1, 9, 4]，我们可以使用bounds函数来计算最小和最大值：

[Amin, Amax] = bounds(A)

输出将是Amin = 1，Amax = 9。

相关问题

贝叶斯优化函数matlab代码

以下是一个使用贝叶斯优化的示例函数的Matlab代码：

function [xopt,fopt] = bayesopt_fun(f,x0,lb,ub,opts)
% BAYESOPT_FUN: Bayesian optimization of a function
%   [XOPT,FOPT] = BAYESOPT_FUN(F,X0,LB,UB,OPTS) finds the minimum of a
%   function F using Bayesian optimization. X0 is the initial guess,
%   LB and UB are the lower and upper bounds of the variables, and OPTS
%   is an options structure created using BAYESOPT_OPTIONS. The function
%   F should take a vector of variables as input and return a scalar
%   output.
%
%   Example usage:
%   f = @(x) sin(3*x) + x.^2 - 0.7*x;
%   opts = bayesopt_options('AcquisitionFunctionName','expected-improvement-plus');
%   [xopt,fopt] = bayesopt_fun(f,0,0,1,opts);
%
%   See also BAYESOPT_OPTIONS.

% Check inputs
narginchk(4,5);
if nargin < 5, opts = bayesopt_options(); end
assert(isa(f,'function_handle'),'F must be a function handle');
assert(isvector(x0) && isnumeric(x0),'X0 must be a numeric vector');
assert(isvector(lb) && isnumeric(lb),'LB must be a numeric vector');
assert(isvector(ub) && isnumeric(ub),'UB must be a numeric vector');
assert(all(size(x0)==size(lb)) && all(size(x0)==size(ub)), ...
    'X0, LB, and UB must have the same size');
opts = bayesopt_options(opts); % ensure opts has all fields

% Initialize
X = x0(:); % column vector
Y = f(X);
n = numel(X);
Xbest = X;
Ybest = Y;
fmin = min(Y);
fmax = max(Y);

% Loop over iterations
for i = 1:opts.MaxIterations
    % Train surrogate model
    model = fitrgp(X,Y,'Basis','linear','FitMethod','exact', ...
        'PredictMethod','exact','Standardize',true, ...
        'KernelFunction',opts.KernelFunction,'KernelParameters',opts.KernelParameters);
    
    % Find next point to evaluate
    if strcmp(opts.AcquisitionFunctionName,'expected-improvement-plus')
        % Use expected improvement with small positive improvement threshold
        impThreshold = 0.01*(fmax-fmin);
        acqFcn = @(x) expected_improvement_plus(x,model,fmin,impThreshold);
    else
        % Use acquisition function specified in options
        acqFcn = str2func(opts.AcquisitionFunctionName);
    end
    xnext = bayesopt_acq(acqFcn,model,lb,ub,opts.AcquisitionSamples);
    
    % Evaluate function at next point
    ynext = f(xnext);
    
    % Update data
    X = [X; xnext(:)];
    Y = [Y; ynext];
    if ynext < Ybest
        Xbest = xnext;
        Ybest = ynext;
    end
    fmin = min(Y);
    fmax = max(Y);
    
    % Check stopping criterion
    if i >= opts.MaxIterations || (i > 1 && abs(Y(end)-Y(end-1))/Ybest <= opts.TolFun)
        break;
    end
end

% Return best point found
xopt = Xbest;
fopt = Ybest;
end

function EI = expected_improvement_plus(X,model,fmin,impThreshold)
% EXPECTED_IMPROVEMENT_PLUS: Expected improvement with small positive improvement threshold
%   EI = EXPECTED_IMPROVEMENT_PLUS(X,MODEL,FMIN,IMPTHRESHOLD) computes
%   the expected improvement (EI) of a surrogate model at the point X.
%   The input MODEL is a regression model, FMIN is the current minimum
%   value of the function being modeled, and IMPTHRESHOLD is a small
%   positive improvement threshold.
%
%   The expected improvement is defined as:
%   EI = E[max(FMIN - Y, 0)]
%   where Y is the predicted value of the surrogate model at X.
%   The expected value is taken over the posterior distribution of Y.
%
%   However, if the predicted value Y is within IMPTHRESHOLD of FMIN,
%   then EI is set to IMPTHRESHOLD instead. This is done to encourage
%   exploration of the search space, even if the expected improvement
%   is very small.
%
%   See also BAYESOPT_ACQ.

% Check inputs
narginchk(4,4);

% Compute predicted value and variance at X
[Y,~,sigma] = predict(model,X);

% Compute expected improvement
z = (fmin - Y - impThreshold)/sigma;
EI = (fmin - Y - impThreshold)*normcdf(z) + sigma*normpdf(z);
EI(sigma==0) = 0; % avoid division by zero

% Check if improvement is small
if Y >= fmin - impThreshold
    EI = impThreshold;
end
end

function opts = bayesopt_options(varargin)
% BAYESOPT_OPTIONS: Create options structure for Bayesian optimization
%   OPTS = BAYESOPT_OPTIONS() creates an options structure with default
%   values for all parameters.
%
%   OPTS = BAYESOPT_OPTIONS(P1,V1,P2,V2,...) creates an options structure
%   with parameter names and values specified in pairs. Any unspecified
%   parameters will take on their default values.
%
%   OPTS = BAYESOPT_OPTIONS(OLDOPTS,P1,V1,P2,V2,...) creates a copy of
%   the OLDOPTS structure, with any parameters specified in pairs
%   overwriting the corresponding values.
%
%   Available parameters:
%     MaxIterations - Maximum number of iterations (default 100)
%     TolFun - Tolerance on function value improvement (default 1e-6)
%     KernelFunction - Name of kernel function for Gaussian process
%                      regression (default 'squaredexponential')
%     KernelParameters - Parameters of kernel function (default [])
%     AcquisitionFunctionName - Name of acquisition function for deciding
%                               which point to evaluate next (default
%                               'expected-improvement-plus')
%     AcquisitionSamples - Number of samples to use when evaluating the
%                          acquisition function (default 1000)
%
%   See also BAYESOPT_FUN, BAYESOPT_ACQ.

% Define default options
opts = struct('MaxIterations',100,'TolFun',1e-6, ...
    'KernelFunction','squaredexponential','KernelParameters',[], ...
    'AcquisitionFunctionName','expected-improvement-plus','AcquisitionSamples',1000);

% Overwrite default options with user-specified options
if nargin > 0
    if isstruct(varargin{1})
        % Copy old options structure and overwrite fields with new values
        oldopts = varargin{1};
        for i = 2:2:nargin
            fieldname = validatestring(varargin{i},fieldnames(opts));
            oldopts.(fieldname) = varargin{i+1};
        end
        opts = oldopts;
    else
        % Overwrite fields of default options with new values
        for i = 1:2:nargin
            fieldname = validatestring(varargin{i},fieldnames(opts));
            opts.(fieldname) = varargin{i+1};
        end
    end
end
end

function xnext = bayesopt_acq(acqFcn,model,lb,ub,nSamples)
% BAYESOPT_ACQ: Find next point to evaluate using an acquisition function
%   XNEXT = BAYESOPT_ACQ(ACQFCN,MODEL,LB,UB,NSAMPLES) finds the next point
%   to evaluate using the acquisition function ACQFCN and the regression
%   model MODEL. LB and UB are the lower and upper bounds of the variables,
%   and NSAMPLES is the number of random samples to use when maximizing
%   the acquisition function.
%
%   The input ACQFCN should be a function handle that takes a regression
%   model and a set of input points as inputs, and returns a vector of
%   acquisition function values. The set of input points is a matrix with
%   one row per point and one column per variable.
%
%   The output XNEXT is a vector containing the next point to evaluate.
%
%   See also BAYESOPT_FUN, EXPECTED_IMPROVEMENT_PLUS.

% Check inputs
narginchk(4,5);
assert(isa(acqFcn,'function_handle'),'ACQFCN must be a function handle');
assert(isa(model,'RegressionGP'),'MODEL must be a regressionGP object');
assert(isvector(lb) && isnumeric(lb),'LB must be a numeric vector');
assert(isvector(ub) && isnumeric(ub),'UB must be a numeric vector');
assert(all(size(lb)==size(ub)),'LB and UB must have the same size');
if nargin < 5, nSamples = 1000; end

% Generate random samples
X = bsxfun(@plus,lb,bsxfun(@times,rand(nSamples,numel(lb)),ub-lb));

% Evaluate acquisition function
acq = acqFcn(model,X);

% Find maximum of acquisition function
[~,imax] = max(acq);
xnext = X(imax,:);
end

该示例代码实现了一个使用贝叶斯优化的函数优化器。该优化器使用高斯过程回归模型来近似目标函数，并使用期望改进加上（EI+）作为获取函数。您可以将此代码用作自己的优化问题的起点，并根据需要进行修改。

matlab中bounds

在Matlab中，bounds可以指定优化问题中变量的上下限范围。这对于某些优化问题至关重要，例如需要满足特定约束条件的问题，或者需要确保变量在合理范围内的问题。您可以使用Matlab中的optimoptions函数来设置变量的上下限，具体示例代码如下：

options = optimoptions('fmincon','Algorithm','interior-point','Display','iter-detailed');
lb = [-10;-10];  % lower bounds
ub = [10;10];     % upper bounds
[x,fval] = fmincon(@objfun,x0,[],[],[],[],lb,ub,@confun,options);

上述代码中，lb和ub分别表示变量的下限和上限，x0是变量的初始值，objfun是优化目标函数，confun是约束函数。