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```{code-cell}
:tags: [hide-input]

import numpy as np
import scipy as sp
```

# Coordinate Format (COO)

- also known as the 'ijv' or 'triplet' format
  - three NumPy arrays: `row`, `col`, `data`.
  - attribute `coords` is the tuple `(row, col)`
  - `data[i]` is value at `(row[i], col[i])` position
  - permits duplicate entries
  - subclass of {class}`_data_matrix` (sparse matrix classes with
    `.data` attribute)
- fast format for constructing sparse arrays
- constructor accepts:
  - dense array/matrix
  - sparse array/matrix
  - shape tuple (create empty matrix)
  - `(data, coords)` tuple
- very fast conversion to and from CSR/CSC formats
- fast matrix \* vector (sparsetools)
- fast and easy item-wise operations
  - manipulate data array directly (fast NumPy machinery)
- no slicing, no arithmetic (directly, converts to CSR)
- use:
  - facilitates fast conversion among sparse formats

  - when converting to other format (usually CSR or CSC), duplicate
    entries are summed together

  - facilitates efficient construction of finite element matrices

## Examples

### Create empty COO array:

```{code-cell}
mtx = sp.sparse.coo_array((3, 4), dtype=np.int8)
mtx.toarray()
```

### Create using `(data, ij)` tuple:

```{code-cell}
row = np.array([0, 3, 1, 0])
col = np.array([0, 3, 1, 2])
data = np.array([4, 5, 7, 9])
mtx = sp.sparse.coo_array((data, (row, col)), shape=(4, 4))
mtx
```

```{code-cell}
mtx.toarray()
```

**Note**: duplicate entries are summed together:

```{code-cell}
row = np.array([0, 0, 1, 3, 1, 0, 0])
col = np.array([0, 2, 1, 3, 1, 0, 0])
data = np.array([1, 1, 1, 1, 1, 1, 1])
mtx = sp.sparse.coo_array((data, (row, col)), shape=(4, 4))
mtx.toarray()
```

**Note**: no slicing...:

```{code-cell}
:tags: [raises-exception]

mtx[2, 3]
```