---
title: IndexedMatrix (latest version)
description: API reference for qiskit_noise_learning.math.IndexedMatrix in the latest version of qiskit-noise-learning
source: https://quantum.cloud.ibm.com/docs/en/api/qiskit-noise-learning/generated/math-indexed-matrix
---

# qiskit\_noise\_learning.math.IndexedMatrix

*class* `qiskit_noise_learning.math.IndexedMatrix(row_index_map: Mapping[RowIndex, int] | None = None, column_index_map: Mapping[ColumnIndex, int] | None = None, data: ndarray[float] | None = None)`

[GitHub](https://github.com/Qiskit/qiskit-noise-learning/tree/stable/0.1/qiskit_noise_learning/math/indexed_matrix.py)

Bases: [`Generic`](https://docs.python.org/3/library/typing.html#typing.Generic)\[`RowIndex`, `ColumnIndex`]

A matrix with float entries and arbitrary row and column index data.

**Parameters**

- **row\_index\_map** – A mapping from row indices to the integer row axes of `data`.
- **column\_index\_map** – A mapping from column indices to the integer column axes of `data`.
- **data** – The array for the given row and column indices.

**Raises**

[**ValueError**](https://docs.python.org/3/library/exceptions.html#ValueError) – If the shape of `data` is inconsistent with the values of `row_index_map` or `column_index_map`.

### \_\_init\_\_

`__init__(row_index_map: Mapping[RowIndex, int] | None = None, column_index_map: Mapping[ColumnIndex, int] | None = None, data: ndarray[float] | None = None)`

## Methods

|                                                                                                                                                                                 |                                                                                                                                                                               |
| ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
| [`__init__`](#qiskit_noise_learning.math.IndexedMatrix.__init__ "qiskit_noise_learning.math.IndexedMatrix.__init__")(\[row\_index\_map, column\_index\_map, data])              |                                                                                                                                                                               |
| [`add_rows`](#qiskit_noise_learning.math.IndexedMatrix.add_rows "qiskit_noise_learning.math.IndexedMatrix.add_rows")(row\_indices, rows\[, tol])                                | Add rows to the matrix.                                                                                                                                                       |
| [`copy`](#qiskit_noise_learning.math.IndexedMatrix.copy "qiskit_noise_learning.math.IndexedMatrix.copy")()                                                                      | Return a copy of self.                                                                                                                                                        |
| [`from_index_lists`](#qiskit_noise_learning.math.IndexedMatrix.from_index_lists "qiskit_noise_learning.math.IndexedMatrix.from_index_lists")(row\_indices, ...)                 | Construct from ordered lists of row and column indices.                                                                                                                       |
| [`from_rows`](#qiskit_noise_learning.math.IndexedMatrix.from_rows "qiskit_noise_learning.math.IndexedMatrix.from_rows")(row\_indices, rows\[, tol])                             | Construct from row indices and their sparse [`IndexedVector`](/docs/api/qiskit-noise-learning/generated/math-indexed-vector "qiskit_noise_learning.math.IndexedVector") rows. |
| [`linearly_independent_rows`](#qiskit_noise_learning.math.IndexedMatrix.linearly_independent_rows "qiskit_noise_learning.math.IndexedMatrix.linearly_independent_rows")(\[tol]) | Return a submatrix containing a maximal set of linearly independent rows.                                                                                                     |

## Attributes

|                                                                                                                                              |                                                                              |
| -------------------------------------------------------------------------------------------------------------------------------------------- | ---------------------------------------------------------------------------- |
| [`column_index_map`](#qiskit_noise_learning.math.IndexedMatrix.column_index_map "qiskit_noise_learning.math.IndexedMatrix.column_index_map") | Dictionary mapping column indices to the column axis integer of `self.data`. |
| [`data`](#qiskit_noise_learning.math.IndexedMatrix.data "qiskit_noise_learning.math.IndexedMatrix.data")                                     | The numerical data.                                                          |
| [`rank`](#qiskit_noise_learning.math.IndexedMatrix.rank "qiskit_noise_learning.math.IndexedMatrix.rank")                                     | The rank of the matrix.                                                      |
| [`row_index_map`](#qiskit_noise_learning.math.IndexedMatrix.row_index_map "qiskit_noise_learning.math.IndexedMatrix.row_index_map")          | Dictionary mapping row indices to the row axis integer of `self.data`.       |
| [`shape`](#qiskit_noise_learning.math.IndexedMatrix.shape "qiskit_noise_learning.math.IndexedMatrix.shape")                                  | The shape of the matrix.                                                     |

### from\_index\_lists

*classmethod* `from_index_lists(row_indices: Sequence[RowIndex], column_indices: Sequence[ColumnIndex], data: ndarray[float]) → Self`

Construct from ordered lists of row and column indices.

**Parameters**

- **row\_indices** – The list of row indices for the row axes of `data`.
- **column\_indices** – The list of column indices for the column axes of `data`.
- **data** – The data matrix.

**Returns**

An [`IndexedMatrix`](#qiskit_noise_learning.math.IndexedMatrix "qiskit_noise_learning.math.IndexedMatrix") whose row and column index maps are built from `row_indices` and `column_indices`.

### from\_rows

*classmethod* `from_rows(row_indices: Sequence[RowIndex], rows: Sequence[IndexedVector[ColumnIndex]], tol: float = 1e-08) → Self`

Construct from row indices and their sparse [`IndexedVector`](/docs/api/qiskit-noise-learning/generated/math-indexed-vector "qiskit_noise_learning.math.IndexedVector") rows.

**Parameters**

- **row\_indices** – The index for each row.
- **rows** – The sparse rows, as [`IndexedVector`](/docs/api/qiskit-noise-learning/generated/math-indexed-vector "qiskit_noise_learning.math.IndexedVector") instances.
- **tol** – Tolerance below which row values are treated as `0.0`.

**Returns**

An [`IndexedMatrix`](#qiskit_noise_learning.math.IndexedMatrix "qiskit_noise_learning.math.IndexedMatrix") containing the (non-zero) rows.

### row\_index\_map

Type: [`dict`](https://docs.python.org/3/library/stdtypes.html#dict)\[`RowIndex`, [`int`](https://docs.python.org/3/library/functions.html#int)]

Dictionary mapping row indices to the row axis integer of `self.data`.

### column\_index\_map

Type: [`dict`](https://docs.python.org/3/library/stdtypes.html#dict)\[`ColumnIndex`, [`int`](https://docs.python.org/3/library/functions.html#int)]

Dictionary mapping column indices to the column axis integer of `self.data`.

### data

Type: [`ndarray`](https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray)\[[`float`](https://docs.python.org/3/library/functions.html#float)]

The numerical data.

### shape

Type: [`tuple`](https://docs.python.org/3/library/stdtypes.html#tuple)\[[`int`](https://docs.python.org/3/library/functions.html#int), [`int`](https://docs.python.org/3/library/functions.html#int)]

The shape of the matrix.

### rank

Type: [`int`](https://docs.python.org/3/library/functions.html#int)

The rank of the matrix.

### add\_rows

`add_rows(row_indices: list[RowIndex], rows: list[IndexedVector[ColumnIndex]], tol=1e-08)`

Add rows to the matrix.

**Parameters**

- **row\_indices** – A list of indices for the rows.
- **rows** – The list of rows.
- **tol** – Tolerance below which values in `rows` are assumed to be `0.0`.

**Raises**

- [**ValueError**](https://docs.python.org/3/library/exceptions.html#ValueError) – If any row index is duplicated in `row_indices` or is already present in this instance.
- [**ValueError**](https://docs.python.org/3/library/exceptions.html#ValueError) – If the number of row indices does not match the number of rows.

### linearly\_independent\_rows

`linearly_independent_rows(tol=1e-08) → Self`

Return a submatrix containing a maximal set of linearly independent rows.

Rows are processed in order (according to the indices in `self.row_index_map`): a row is kept if and only if it is linearly independent of all preceding kept rows. This guarantees earlier rows are always preferred.

**Parameters**

**tol** – The tolerance for determining linear independence based on the norm of the component of a row orthogonal to the span of preceding kept rows.

### copy

`copy() → Self`

Return a copy of self.