# Compressed Sparse Row Format (CSR)¶

• row oriented
• three NumPy arrays: indices, indptr, data
• indices is array of column indices
• data is array of corresponding nonzero values
• indptr points to row starts in indices and data
• length is n_row + 1, last item = number of values = length of both indices and data
• nonzero values of the i-th row are data[indptr[i]:indptr[i+1]] with column indices indices[indptr[i]:indptr[i+1]]
• item (i, j) can be accessed as data[indptr[i]+k], where k is position of j in indices[indptr[i]:indptr[i+1]]
• subclass of _cs_matrix (common CSR/CSC functionality)
• subclass of _data_matrix (sparse matrix classes with .data attribute)
• fast matrix vector products and other arithmetics (sparsetools)

• constructor accepts:
• dense matrix (array)
• sparse matrix
• shape tuple (create empty matrix)
• (data, ij) tuple
• (data, indices, indptr) tuple
• efficient row slicing, row-oriented operations

• slow column slicing, expensive changes to the sparsity structure

• use:
• actual computations (most linear solvers support this format)

## Examples¶

• create empty CSR matrix:

```>>> mtx = sps.csr_matrix((3, 4), dtype=np.int8)
>>> mtx.todense()
matrix([[0, 0, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 0]], dtype=int8)
```
• create using (data, ij) tuple:

```>>> row = np.array([0, 0, 1, 2, 2, 2])
>>> col = np.array([0, 2, 2, 0, 1, 2])
>>> data = np.array([1, 2, 3, 4, 5, 6])
>>> mtx = sps.csr_matrix((data, (row, col)), shape=(3, 3))
>>> mtx
<3x3 sparse matrix of type '<type 'numpy.int32'>'
with 6 stored elements in Compressed Sparse Row format>
>>> mtx.todense()
matrix([[1, 0, 2],
[0, 0, 3],
[4, 5, 6]])
>>> mtx.data
array([1, 2, 3, 4, 5, 6])
>>> mtx.indices
array([0, 2, 2, 0, 1, 2])
>>> mtx.indptr
array([0, 2, 3, 6])
```
• create using (data, indices, indptr) tuple:

```>>> data = np.array([1, 2, 3, 4, 5, 6])
>>> indices = np.array([0, 2, 2, 0, 1, 2])
>>> indptr = np.array([0, 2, 3, 6])
>>> mtx = sps.csr_matrix((data, indices, indptr), shape=(3, 3))
>>> mtx.todense()
matrix([[1, 0, 2],
[0, 0, 3],
[4, 5, 6]])
```