# Matrix Utilities¶

We have some matrix-related utilities, since matrices are used so heavily in recommendation algorithms.

## Building Ratings Matrices¶

lenskit.matrix.sparse_ratings(ratings, scipy=False)

Convert a rating table to a sparse matrix of ratings.

Parameters: ratings (pandas.DataFrame) – a data table of (user, item, rating) triples. scipy – if True, return a SciPy matrix instead of CSR. a named tuple containing the sparse matrix, user index, and item index. RatingMatrix
class lenskit.matrix.RatingMatrix

A rating matrix with associated indices.

matrix

The rating matrix, with users on rows and items on columns.

Type: CSR or scipy.sparse.csr_matrix
users

mapping from user IDs to row numbers.

Type: pandas.Index
items

mapping from item IDs to column numbers.

Type: pandas.Index

## Compressed Sparse Row Matrices¶

We use CSR-format sparse matrices in quite a few places. Since SciPy’s sparse matrices are not directly usable from Numba, we have implemented a Numba-compiled CSR representation that can be used from accelerated algorithm implementations.

class lenskit.matrix.CSR(nrows=None, ncols=None, nnz=None, ptrs=None, inds=None, vals=None, N=None)

Simple compressed sparse row matrix. This is like scipy.sparse.csr_matrix, with a couple of useful differences:

• It is backed by a Numba jitclass, so it can be directly used from Numba-optimized functions.
• The value array is optional, for cases in which only the matrix structure is required.
• The value array, if present, is always double-precision.

You generally don’t want to create this class yourself with the constructor. Instead, use one of its class methods.

If you need to pass an instance off to a Numba-compiled function, use N:

_some_numba_fun(csr.N)


We use the indirection between this and the Numba jitclass so that the main CSR implementation can be pickled, and so that we can have class and instance methods that are not compatible with jitclass but which are useful from interpreted code.

N

the Numba jitclass backing (has the same attributes and most methods).

Type: _CSR
nrows

the number of rows.

Type: int
ncols

the number of columns.

Type: int
nnz

the number of entries.

Type: int
rowptrs

the row pointers.

Type: numpy.ndarray
colinds

the column indices.

Type: numpy.ndarray
values

the values

Type: numpy.ndarray
classmethod from_coo(rows, cols, vals, shape=None)

Create a CSR matrix from data in COO format.

Parameters: rows (array-like) – the row indices. cols (array-like) – the column indices. vals (array-like) – the data values; can be None. shape (tuple) – the array shape, or None to infer from row & column indices.
classmethod from_scipy(mat, copy=True)

Convert a scipy sparse matrix to an internal CSR.

Parameters: mat (scipy.sparse.spmatrix) – a SciPy sparse matrix. copy (bool) – if False, reuse the SciPy storage if possible. a CSR matrix. CSR
row(row)

Return a row of this matrix as a dense ndarray.

Parameters: row (int) – the row index. the row, with 0s in the place of missing values. numpy.ndarray
row_cs(row)

Get the column indcies for the stored values of a row.

row_extent(row)

Get the extent of a row in the underlying column index and value arrays.

Parameters: row (int) – the row index. (s, e), where the row occupies positions $$[s, e)$$ in the CSR data. tuple
row_nnzs()

Get a vector of the number of nonzero entries in each row.

Note

This method is not available from Numba.

Returns: the number of nonzero entries in each row. numpy.ndarray
row_vs(row)

Get the stored values of a row.

rowinds() → numpy.ndarray

Get the row indices from this array. Combined with colinds and values, this can form a COO-format sparse matrix.

Note

This method is not available from Numba.

sort_values()

Sort CSR rows in nonincreasing order by value.

Note

This method is not available from Numba.

to_scipy()

Convert a CSR matrix to a SciPy scipy.sparse.csr_matrix.

Parameters: self (CSR) – A CSR matrix. A SciPy sparse matrix with the same data. scipy.sparse.csr_matrix
transpose(values=True)

Transpose a CSR matrix.

Note

This method is not available from Numba.

Parameters: values (bool) – whether to include the values in the transpose. the transpose of this matrix (or, equivalently, this matrix in CSC format). CSR
class lenskit.matrix._CSR(nrows, ncols, nnz, ptrs, inds, vals)

Internal implementation class for CSR. If you work with CSRs from Numba, you will use this.