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A SciPy CSR matrix stores a sparse two-dimensional array row by row: one array holds the nonzero values, another holds their column positions, and a third marks each row’s boundaries. This layout makes CSR a strong choice for row-based work and matrix-vector multiplication, but a poor fit for frequent column slicing or changes to which entries are stored.
What is a CSR matrix?
CSR means Compressed Sparse Row. It stores a matrix without allocating a value for every position: each row’s stored values and column indices occupy a contiguous segment of arrays. This is useful when most positions are zero and your computations can operate on the stored entries.
In SciPy, scipy.sparse.csr_matrix is the matrix-class interface for this format. The sparse overview also documents sparse arrays; the distinction matters because a sparse array is an array interface, while a sparse matrix follows matrix-specific behavior. See SciPy’s CSR matrix reference and sparse arrays overview.
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How CSR’s three arrays work
A CSR object’s core representation consists of data, indices, and indptr:
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datacontains the stored values.indicescontains the column index for each stored value.indptrmarks the start and end positions of each row’s segment in the first two arrays.
For row i, its column indices are indices[indptr[i]:indptr[i+1]], and the matching values are data[indptr[i]:indptr[i+1]]. The pair at a given position in indices and data identifies a stored matrix entry. The final value in indptr marks the end of the stored entries.
For example, if indptr is [0, 2, 3], row 0 uses entries 0 and 1, while row 1 uses entry 2. The number of stored entries is available as nnz. It counts explicitly stored zeros too, so it is not necessarily the count of mathematically nonzero values.
How to create a CSR matrix
Choose a constructor based on the data you already have. The following examples use the matrix interface named in the title.
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Convert a dense array or another sparse object
import numpy as np
from scipy.sparse import csr_matrix
dense = np.array([[0, 4, 0], [2, 0, 5]])
A = csr_matrix(dense)You can also pass another sparse matrix or sparse array to csr_matrix to convert it to CSR.
Build from coordinate triples
When your input is a list of row positions, column positions, and values, use the coordinate constructor. Specify the shape when trailing rows or columns may have no stored entries.
from scipy.sparse import csr_matrix
row = [0, 0, 1]
col = [0, 2, 1]
data = [3, 4, 5]
A = csr_matrix((data, (row, col)), shape=(2, 3))The corresponding entries are placed at (row[k], col[k]) with value data[k]. If the same coordinate appears more than once, SciPy sums those values; for example, duplicate values 1 and 8 at (0, 0) produce 9.
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Construct directly from CSR arrays
If you already have row-compressed storage, pass the three arrays in CSR order:
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values = [3, 4, 5]
column_indices = [0, 2, 1]
row_pointers = [0, 2, 3]
A = csr_matrix((values, column_indices, row_pointers), shape=(2, 3))The shape is optional for this form; when omitted, SciPy infers dimensions from the index arrays. Providing it explicitly makes the intended dimensions clear, especially when the last rows or columns contain no stored entries.
Create an empty matrix
from scipy.sparse import csr_matrix
A = csr_matrix((4, 6), dtype=float)This creates a 4-by-6 matrix with no stored entries.
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Building data efficiently
For data supplied as coordinate and value arrays, SciPy recommends COO as a construction format. DOK and LIL are also useful when constructing data or changing the sparsity structure. Convert to CSR when the structure is ready for row-oriented computation.
For incremental row-by-row construction, append each row’s column indices and values, then record the cumulative number of entries in indptr after every row. Each new pointer marks where the next row begins; the last pointer marks the total number of stored entries. This is the bookkeeping that turns accumulated row data into valid CSR storage.
Conversions among CSR, CSC, and COO are documented as linear-time. See SciPy’s sparse format overview for construction-format guidance and conversion details.
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What CSR is good at—and where it struggles
Pick a sparse format around the operations you perform most often, not just the way your input arrives.
| Format | Best fit | Trade-off |
|---|---|---|
| CSR | Row slicing, sparse arithmetic, and matrix-vector products | Column slicing is slow; changing the sparsity structure is expensive |
| CSC | Column slicing and column-oriented workloads | Row slicing is slow |
| COO | Construction from coordinate and value arrays | Convert to an operation-oriented format when appropriate |
| LIL or DOK | Building a matrix or changing which entries are stored | Choose another format for workloads better served by row- or column-compressed storage |
CSR supports sparse arithmetic, including addition, subtraction, multiplication, division, and matrix power. For a column-oriented workload, SciPy identifies CSC as the natural alternative: it provides efficient column slicing, while row slicing is slow. The CSC matrix reference describes that trade-off.
Use sparse operations deliberately
For matrix-vector multiplication, use the @ operator:
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Account for SciPy’s sparse API transition
SciPy’s csr_matrix reference warns that the project is shifting from a sparse matrix interface to a sparse array interface and expects to deprecate the matrix interface in the next few releases. The documentation does not establish a specific deprecation date. When maintaining code, consult SciPy’s current migration guidance and check how downstream libraries handle sparse arrays before changing an established matrix-based workflow.
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