Octave: function doesn't return expected value? - syntax

Question

This code is a programming assignment for Andrew Ng's machine learning course.
The function is expecting a row vector [J grad]. The code computes J (albeit wrongly, but that's not the issue here), and I put in a dummy value for grad (because I haven't written the code to compute it yet). When I run the code, it only outputs ans as a scalar with the value of J. Where did grad go?
function [J grad] = nnCostFunction(nn_params, ...
input_layer_size, ...
hidden_layer_size, ...
num_labels, ...
X, y, lambda)
%NNCOSTFUNCTION Implements the neural network cost function for a two layer
%neural network which performs classification
% [J grad] = NNCOSTFUNCTON(nn_params, hidden_layer_size, num_labels, ...
% X, y, lambda) computes the cost and gradient of the neural network. The
% parameters for the neural network are "unrolled" into the vector
% nn_params and need to be converted back into the weight matrices.
%
% The returned parameter grad should be a "unrolled" vector of the
% partial derivatives of the neural network.
%
% Reshape nn_params back into the parameters Theta1 and Theta2, the weight matrices
% for our 2 layer neural network
Theta1 = reshape(nn_params(1:hidden_layer_size * (input_layer_size + 1)), ...
hidden_layer_size, (input_layer_size + 1));
Theta2 = reshape(nn_params((1 + (hidden_layer_size * (input_layer_size + 1))):end), ...
num_labels, (hidden_layer_size + 1));
% Setup some useful variables
m = size(X, 1);
% You need to return the following variables correctly
J = 0;
Theta1_grad = zeros(size(Theta1));
Theta2_grad = zeros(size(Theta2));
% ====================== YOUR CODE HERE ======================
% Instructions: You should complete the code by working through the
% following parts.
%
% Part 1: Feedforward the neural network and return the cost in the
% variable J. After implementing Part 1, you can verify that your
% cost function computation is correct by verifying the cost
% computed in ex4.m
%
% Part 2: Implement the backpropagation algorithm to compute the gradients
% Theta1_grad and Theta2_grad. You should return the partial derivatives of
% the cost function with respect to Theta1 and Theta2 in Theta1_grad and
% Theta2_grad, respectively. After implementing Part 2, you can check
% that your implementation is correct by running checkNNGradients
%
% Note: The vector y passed into the function is a vector of labels
% containing values from 1..K. You need to map this vector into a
% binary vector of 1's and 0's to be used with the neural network
% cost function.
%
% Hint: We recommend implementing backpropagation using a for-loop
% over the training examples if you are implementing it for the
% first time.
%
% Part 3: Implement regularization with the cost function and gradients.
%
% Hint: You can implement this around the code for
% backpropagation. That is, you can compute the gradients for
% the regularization separately and then add them to Theta1_grad
% and Theta2_grad from Part 2.
%
% PART 1
a1 = [ones(m,1) X]; % set a1 to equal X and add column of 1's
z2 = a1 * Theta1'; % matrix times matrix [5000*401 * 401*25 = 5000*25]
a2 = [ones(m,1),sigmoid(z2)]; % sigmoid function on matrix [5000*26]
z3 = a2 * Theta2'; % matrix times matrix [5000*26 * 26*10 = 5000 * 10]
hox = sigmoid(z3); % sigmoid function on matrix [5000*10]
for k = 1:num_labels
yk = y == k; % using the correct column vector y each loop
J = J + sum(-yk.*log(hox(:,k)) - (1-yk).*log(1-hox(:,k)));
end
J = 1/m * J;
% -------------------------------------------------------------
% =========================================================================
% Unroll gradients
% grad = [Theta1_grad(:) ; Theta2_grad(:)];
grad = 6.6735;
end

Answer 1

You have specified in your function declaration that the function can simultaneously return more than one output value:
function [J grad] = nnCostFunction(nn_params, ... % etc
You can capture both outputs if you 'request' them by assigning to a matrix of variables instead of a single variable:
[a, b] = nnCostFunction(input1, input2, etc)
If you don't do this, you're essentially 'requesting' only the first of the returned variables:
a = nnCostFunction(input1, input2, etc) % output 'b' is discarded.
If you don't specify a variable to assign to at all, octave by default assigns to the 'default' variable ans. So it's essentially equivalent to doing
ans = nnCostFunction(input1, input2, etc) % output 'b' is discarded.
See the documentation for the find function (i.e. type help find in your octave terminal) to see an example of such a function.
PS. If you only wanted the second output and did not want to 'waste' a variable name for the first one, you can do this by specifying ~ as the first output, e.g.:
[~, b] = nnCostFunction(input1, input2, etc) % output 'a' is discarded