generate some 'random' test data and test (input_layer_size = 3; hidden_layer_size = 5; num_labels = 3; m = 5;)

coursera-stanford-machine-learning-class-week5-complete-backpropagation-and-check-Neural-network-gradients.m

% Octave console output
Initializing Neural Network Parameters ...

Checking Backpropagation... 
  -9.2783e-03  -9.2783e-03
   8.8991e-03   8.8991e-03
  -8.3601e-03  -8.3601e-03
   7.6281e-03   7.6281e-03
  -6.7480e-03  -6.7480e-03
  -3.0498e-06  -3.0498e-06
   1.4287e-05   1.4287e-05
  -2.5938e-05  -2.5938e-05
   3.6988e-05   3.6988e-05
  -4.6876e-05  -4.6876e-05
  -1.7506e-04  -1.7506e-04
   2.3315e-04   2.3315e-04
  -2.8747e-04  -2.8747e-04
   3.3532e-04   3.3532e-04
  -3.7622e-04  -3.7622e-04
  -9.6266e-05  -9.6266e-05
   1.1798e-04   1.1798e-04
  -1.3715e-04  -1.3715e-04
   1.5325e-04   1.5325e-04
  -1.6656e-04  -1.6656e-04
   3.1454e-01   3.1454e-01
   1.1106e-01   1.1106e-01
   9.7401e-02   9.7401e-02
   1.6409e-01   1.6409e-01
   5.7574e-02   5.7574e-02
   5.0458e-02   5.0458e-02
   1.6457e-01   1.6457e-01
   5.7787e-02   5.7787e-02
   5.0753e-02   5.0753e-02
   1.5834e-01   1.5834e-01
   5.5924e-02   5.5924e-02
   4.9162e-02   4.9162e-02
   1.5113e-01   1.5113e-01
   5.3697e-02   5.3697e-02
   4.7146e-02   4.7146e-02
   1.4957e-01   1.4957e-01
   5.3154e-02   5.3154e-02
   4.6560e-02   4.6560e-02
The above two columns you get should be very similar.
(Left-Your Numerical Gradient, Right-Analytical Gradient)

If your backpropagation implementation is correct, then 
the relative difference will be small (less than 1e-9). 

Relative Difference: 2.48422e-11