You are an expert in writing code in many different languages. Your goal is to perform code completion for the following code, keeping in mind the rest of the code and the file meta data.
    Metadata details:
    filename: GridSearch.m
    path of file: ./repos/FaceVerification/BLUFR
    
    the code of the file until where you have to start completion: function [pcaDims, lambda] = GridSearch(trainX, trainY, testX, testY)
%% [pcaDims, lambda] = GridSearch(trainX, trainY, testX, testY)
%
% This function demostrates how to use the development set to learn the
% optimal parameters.
%
% Inputs:
%   trainX, trainY: training data and class labels.
%   testX, testY: test data and class labels.
% Outputs:
%   pcaDims: the optimal PCA dimensions.
%   lambda: the optimal ridge regression parameter.

    
function [pcaDims, lambda] = GridSearch(trainX, trainY, testX, testY)
%% [pcaDims, lambda] = GridSearch(trainX, trainY, testX, testY)
%
% This function demostrates how to use the development set to learn the
% optimal parameters.
%
% Inputs:
%   trainX, trainY: training data and class labels.
%   testX, testY: test data and class labels.
% Outputs:
%   pcaDims: the optimal PCA dimensions.
%   lambda: the optimal ridge regression parameter.
% 
% Version: 1.0
% Date: 2014-07-22
%
% Author: Shengcai Liao
% Institute: National Laboratory of Pattern Recognition,
%   Institute of Automation, Chinese Academy of Sciences
% Email: scliao@nlpr.ia.ac.cn

candiPcaDims = 100:100:500; % candidate parameter values for the pca dimensions.
candiLambda = 10.^(-4:0); % candidate parameter values for the ridge regression.
veriFarPoints = [0, kron(10.^(-8:-1), 1:9), 1]; % FAR points for verification performance evaluation

fprintf('Learn parameters on the development set...\n');

%% Learn a PCA subspace.
W = PCA(trainX);

%% Transform both the training and test data into the learned PCA subspace.
trainX = trainX * W; 
testX = testX * W;

%% Select classes which have at least two images.
hst = hist(trainY, 1 : max(trainY));
classIndex = find(hst >= 2);
[sampleIndex, trainY] = ismember(trainY, classIndex); % class labels are continuously relabeled starting from 1
trainY = trainY(sampleIndex);
trainX = trainX(sampleIndex,:);
numTrainSamples = length(trainY);

%% Construct the discriminant response matrix
Y = zeros(numTrainSamples, length(classIndex));
Y( sub2ind(size(Y), 1 : numTrainSamples, trainY') ) = 1;

%% Pre-compute the working variables for the ridge regression.
R = trainX' * trainX;
Z = trainX' * Y;

numPara1 = length(candiPcaDims);
numPara2 = length(candiLambda);
auc = zeros(numPara1, numPara2);

%% Learn the optimal parameters by grid search
for i = 1 : numPara1
    d = candiPcaDims(i);
    
    for j = 1 : numPara2  
        % Learn a linear subspace by ridge regression. You can replace this with
        % your own supervised learning algorithm here.
        W = (R(1:d, 1:d) + candiLambda(j) * numTrainSamples * eye(d)) \ Z(1:d,:);
    
        % Transform the test data into the learned subspace.
        X = testX(:, 1:d) * W;

        % Normlize each row to unit length. If you do not have this function,
        % do it manually.
        X = normr(X);

        % Compute the cosine similarity score between the test samples.
        score = X * X';

        % Evaluate the verification performance.
        VR = EvalROC(score, testY, [], veriFarPoints);

        % Average the verification rates as the AUC performance
        auc(i,j) = mean(VR);
    end