IDX file format

The IDX file format is a simple format for vectors and multidimensional matrices of various numerical types.

The basic format according to http://yann.lecun.com/exdb/mnist/ is:

`magic number
` `size in dimension 1
` `size in dimension 2
` `size in dimension 3
` `....
` `size in dimension N
` `data
`

The magic number is four bytes long. The first 2 bytes are always 0.

The third byte codes the type of the data:

`0x08: unsigned byte
` `0x09: signed byte
` `0x0B: short (2 bytes)
` `0x0C: int (4 bytes)
` `0x0D: float (4 bytes)
` `0x0E: double (8 bytes)
`

The fourth byte codes the number of dimensions of the vector/matrix: 1 for vectors, 2 for matrices....

The sizes in each dimension are 4-byte integers (big-endian, like in most non-Intel processors).

The data is stored like in a C array, i.e. the index in the last dimension changes the fastest.

## Behaviour

If the storage format indicates that there are more than 2 dimensions, the resulting Matrix accumulates dimensions 2 and higher in the columns. For example, with three dimensions of size n1, n2 and n3, respectively, the resulting Matrix object will have n1 rows and n2×n3 columns.

## Example

The training and testing data of the MNIST database of handwritten digits at http://yann.lecun.com/exdb/mnist/ is stored in compressed IDX formatted files.

Reading the uncompressed file train-images-idx3-ubyte available at http://yann.lecun.com/exdb/mnist/ with 60000 images of 28×28 pixel data, will result in a new Matrix object with 60000 rows and 784 (=28×28) columns. Each cell will contain a number in the interval from 0 to 255.

Reading the uncompressed file train-labels-idx1-ubyte with 60000 labels will result in a new Matrix object with 1 row and 60000 columns. Each cell will contain a number in the interval from 0 to 9.