eric-haibin-lin commented on a change in pull request #7656: CSRNDArray Tutorial URL: https://github.com/apache/incubator-mxnet/pull/7656#discussion_r135961277
########## File path: docs/tutorials/sparse/csr.md ########## @@ -0,0 +1,258 @@ +# CSRNDArray - NDArray in Compressed Sparse Row Storage Format + +Many real world datasets deal with high dimensional sparse feature vectors. For instance, +in a recommendation system, the number of categories and users is in the order of millions, +while most users only made a few purchases, leading to feature vectors with high sparsity +(i.e. most of the elements are zeros). + +Storing and manipulating such large sparse matrices in the default dense structure results +in wasted memory and processing on the zeros. +To take advantage of the sparse structure of the matrix, the ``CSRNDArray`` in MXNet +stores the matrix in [compressed sparse row(CSR)](https://en.wikipedia.org/wiki/Sparse_matrix#Compressed_sparse_row_.28CSR.2C_CRS_or_Yale_format.29) format +and uses specialized algorithms in operators. +The format is designed for 2D matrices with a large number of columns, +and each row is sparse(i.e. with only a few nonzeros). +For matrices of high sparsity (e.g. ~1% non-zeros), the advantage of ``CSRNDArray`` over +the existing ``NDArray`` is that + +- memory consumption is reduced significantly +- certain operations (e.g. matrix-vector multiplication) are much faster + +Meanwhile, ``CSRNDArray`` inherits competitive features from ``NDArray`` such as +lazy evaluation and automatic parallelization, which are not available in the +scientific computing python package [SciPy](https://www.scipy.org/). + +Apart from often queried attributes such as **ndarray.shape**, **ndarray.dtype** and **ndarray.context**, +you?ll also want to query **ndarray.stype**: the storage type of the NDArray. For a usual dense NDArray, +the value of stype is **"default"**. For an CSRNDArray, the value of stype is **"csr"**. + +## Prerequisites + +To complete this tutorial, we need: + +- MXNet. See the instructions for your operating system in [Setup and Installation](http://mxnet.io/get_started/install.html) +- [Jupyter](http://jupyter.org/) + ``` + pip install jupyter + ``` +- Scipy - A section of this tutorial uses Scipy package in python. If you don't have Scipy, +the example in that section will be ignored. +- GPUs - A section of this tutorial uses GPUs. If you don't have GPUs on your +machine, simply set the variable gpu_device (set in the GPUs section of this +tutorial) to mx.cpu(). + +## Compressed Sparse Row Format + +A CSRNDArray represents a 2D matrix as three separate 1D arrays: **data**, +**indptr** and **indices**, where the column indices for +row ``i`` are stored in ``indices[indptr[i]:indptr[i+1]]`` in ascending order, +and their corresponding values are stored in ``data[indptr[i]:indptr[i+1]]``. + +For example, the CSR representation for matrix +``` +[[7, 0, 8, 0] + [0, 0, 0, 0] + [0, 9, 0, 0]] +``` +is: +``` +[7, 8, 9] # data +[0, 2, 1] # indices +[0, 2, 2, 3] # indptr +``` + +Note that in MXNet, the column indices for a given row are always sorted in ascending order, +and duplicated column entries for the same row are not allowed. + +## Array Creation + +There are a few different ways to create a `CSRNDArray`. + +* We can create a CSRNDArray with data, indices and indptr by using the `csr_matrix` function: + +```python +import mxnet as mx +import numpy as np +# create a CSRNDArray with python lists +shape = (3, 4) +data_list = [7, 8, 9] +indptr_list = [0, 2, 2, 3] +indices_list = [0, 2, 1] +a = mx.nd.sparse.csr_matrix(data_list, indptr_list, indices_list, shape) +# create a CSRNDArray with numpy arrays +data_np = np.array([7, 8, 9]) +indptr_np = np.array([0, 2, 2, 3]) +indices_np = np.array([0, 2, 1]) +b = mx.nd.sparse.csr_matrix(data_np, indptr_np, indices_np, shape) +{'a':a, 'b':b} +``` + +* We can also create an MXNet CSRNDArray from a `scipy.sparse.csr.csr_matrix` object by using the `array` function: + +```python +try: + import scipy.sparse as spsp + # generate a csr matrix in scipy + c = spsp.csr.csr_matrix((data_np, indices_np, indptr_np), shape=shape) + # create a CSRNDArray from a scipy csr object + d = mx.nd.sparse.array(c) Review comment: This feature is included in #7638. Probably it's still too early to review this since #7638 is not merged in ... Sorry about that ---------------------------------------------------------------- This is an automated message from the Apache Git Service. To respond to the message, please log on GitHub and use the URL above to go to the specific comment. For queries about this service, please contact Infrastructure at: us...@infra.apache.org With regards, Apache Git Services
