Python program to Convert a Matrix to Sparse Matrix

Converting a matrix to a sparse matrix involves storing only non-zero elements along with their row and column indices to save memory.

Using a Dictionary

Converting a matrix to a sparse matrix using a dictionary involves storing only the non-zero elements of the matrix, with their row and column indices as keys and the corresponding values as dictionary values.

m = [
    [1, 0, 0, 0],
    [0, 0, 3, 0],
    [0, 0, 0, 4]
]

sparse_matrix = {}
for i in range(len(m)):
    for j in range(len(m[i])):
        if m[i][j] != 0:
            sparse_matrix[(i, j)] = m[i][j]

print(sparse_matrix)

{(0, 0): 1, (1, 2): 3, (2, 3): 4}

Explanation:

• The program iterates through each element of the matrix and stores non-zero elements in a dictionary, where the key is a tuple of indices (i, j) and the value is the element.
• This reduces memory usage by only storing non-zero values.

Using a List of Tuples

Converting a matrix to a sparse matrix using a list of tuples involves storing the non-zero elements as tuples where each tuple contains the row index, column index and the value. This method is efficient for representing sparse matrices while maintaining the order of the elements.

m = [
    [1, 0, 0, 0],
    [0, 0, 3, 0],
    [0, 0, 0, 4]
]

sparse_matrix = []
for i in range(len(m)):
    for j in range(len(m[i])):
        if m[i][j] != 0:
            sparse_matrix.append((i, j, m[i][j]))

print(sparse_matrix)

[(0, 0, 1), (1, 2, 3), (2, 3, 4)]

Explanation:

• The program creates a list of tuples, each containing the row index, column index, and non-zero value of the matrix.
• This format allows easy tracking of positions and values for sparse matrices.