COO format (Coordinate) in SciPy - Step-by-Step Execution

Concept Flow - COO format (Coordinate)

Start with sparse matrix data

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Extract row indices, col indices, values

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Store as three arrays: rows, cols, data

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Use COO format to represent sparse matrix

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Perform operations or convert to dense if needed

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End

COO format stores a sparse matrix by keeping three arrays: row positions, column positions, and values of non-zero elements.

Execution Sample

SciPy

from scipy.sparse import coo_matrix
row = [0, 1, 2]
col = [1, 2, 0]
data = [4, 5, 6]
sparse = coo_matrix((data, (row, col)), shape=(3, 3))
print(sparse.toarray())

Creates a 3x3 sparse matrix in COO format and prints its dense form.

Execution Table

Step	Action	Row array	Col array	Data array	Matrix shape	Result
1	Define row indices	[0, 1, 2]
2	Define col indices		[1, 2, 0]
3	Define data values			[4, 5, 6]
4	Create COO matrix	[0, 1, 2]	[1, 2, 0]	[4, 5, 6]	(3, 3)	Sparse COO matrix created
5	Convert to dense array					[[0 4 0] [0 0 5] [6 0 0]]

💡 All non-zero elements stored in COO format; dense matrix printed.

Variable Tracker

Variable	Start	After Step 1	After Step 2	After Step 3	After Step 4	After Step 5
row	[]	[0, 1, 2]	[0, 1, 2]	[0, 1, 2]	[0, 1, 2]	[0, 1, 2]
col	[]	[]	[1, 2, 0]	[1, 2, 0]	[1, 2, 0]	[1, 2, 0]
data	[]	[]	[]	[4, 5, 6]	[4, 5, 6]	[4, 5, 6]
sparse	None	None	None	None	COO matrix object	COO matrix object
dense_array	None	None	None	None	None	[[0 4 0] [0 0 5] [6 0 0]]

Key Moments - 3 Insights

Why do we need three arrays (row, col, data) to represent the sparse matrix?

Because COO format stores only non-zero elements, we need to know their positions (row and col) and their values (data). This is shown in execution_table rows 1-4.

What happens if we convert the COO matrix to a dense array?

The sparse matrix is expanded to a full 2D array with zeros where no data exists, as shown in execution_table row 5.

Can COO format handle duplicate entries at the same position?

COO format can store duplicates, but they are summed or handled when converting or performing operations. This is not shown here but is important to know.

Visual Quiz - 3 Questions

Look at the execution_table at Step 4, what are the values of the row and col arrays?

A [1, 2, 0] and [0, 1, 2]

B [0, 1, 2] and [1, 2, 0]

C [4, 5, 6] and [0, 1, 2]

D [0, 1, 2] and [4, 5, 6]

💡 Hint

Check the 'Row array' and 'Col array' columns in execution_table row with Step 4.

At which step does the sparse matrix get converted to a dense array?

A Step 5

B Step 4

C Step 3

D Step 2

💡 Hint

Look at the 'Action' column in execution_table for conversion to dense.

If the data array was [7, 8, 9] instead of [4, 5, 6], what would be the value at position (2,0) in the dense matrix?

A 6

B 7

C 9

D 0

💡 Hint

Refer to variable_tracker for 'data' values and their corresponding positions in row and col arrays.

Concept Snapshot

COO format stores sparse matrices using three arrays:
- row indices
- column indices
- data values
Only non-zero elements are stored.
Use scipy.sparse.coo_matrix((data, (row, col)), shape) to create.
Convert to dense with .toarray() for full matrix view.

Full Transcript

COO format is a way to store sparse matrices by keeping track of only the non-zero elements. It uses three arrays: one for row positions, one for column positions, and one for the values. In the example, we define these arrays and create a COO matrix with scipy. Then we convert it to a dense array to see the full matrix. This method saves memory when many elements are zero. The execution table shows each step, and the variable tracker shows how data changes. Key moments clarify why three arrays are needed and what happens when converting to dense. The quiz tests understanding of these steps.