Added rank of matrix in linear algebra

linear_algebra/src/rank_of_matrix.py

@@ -0,0 +1,89 @@
+"""
+Calculate the rank of a matrix.
+
+See: https://en.wikipedia.org/wiki/Rank_(linear_algebra)
+"""
+
+
+def rank_of_matrix(matrix: list[list[int | float]]) -> int:
+ """
+ Finds the rank of a matrix.
+ Args:
+ matrix: The matrix as a list of lists.
+ Returns:
+ The rank of the matrix.
+ Example:
+ >>> matrix1 = [[1, 2, 3],
+ ... [4, 5, 6],
+ ... [7, 8, 9]]
+ >>> rank_of_matrix(matrix1)
+ 2
+ >>> matrix2 = [[1, 0, 0],
+ ... [0, 1, 0],
+ ... [0, 0, 0]]
+ >>> rank_of_matrix(matrix2)
+ 2
+ >>> matrix3 = [[1, 2, 3, 4],
+ ... [5, 6, 7, 8],
+ ... [9, 10, 11, 12]]
+ >>> rank_of_matrix(matrix3)
+ 2
+ >>> rank_of_matrix([[2,3,-1,-1],
+ ... [1,-1,-2,4],
+ ... [3,1,3,-2],
+ ... [6,3,0,-7]])
+ 4
+ >>> rank_of_matrix([[2,1,-3,-6],
+ ... [3,-3,1,2],
+ ... [1,1,1,2]])
+ 3
+ >>> rank_of_matrix([[2,-1,0],
+ ... [1,3,4],
+ ... [4,1,-3]])
+ 3
+ >>> rank_of_matrix([[3,2,1],
+ ... [-6,-4,-2]])
+ 1
+ >>> rank_of_matrix([[],[]])
+ 0
+ >>> rank_of_matrix([[1]])
+ 1
+ >>> rank_of_matrix([[]])
+ 0
+ """
+
+ rows = len(matrix)
+ columns = len(matrix[0])
+ rank = min(rows, columns)
+
+ for row in range(rank):
+ # Check if diagonal element is not zero
+ if matrix[row][row] != 0:
+ # Eliminate all the elements below the diagonal
+ for col in range(row + 1, rows):
+ multiplier = matrix[col][row] / matrix[row][row]
+ for i in range(row, columns):
+ matrix[col][i] -= multiplier * matrix[row][i]
+ else:
+ # Find a non-zero diagonal element to swap rows
+ reduce = True
+ for i in range(row + 1, rows):
+ if matrix[i][row] != 0:
+ matrix[row], matrix[i] = matrix[i], matrix[row]
+ reduce = False
+ break
+ if reduce:
+ rank -= 1
+ for i in range(rows):
+ matrix[i][row] = matrix[i][rank]
+
+ # Reduce the row pointer by one to stay on the same row
+ row -= 1
+
+ return rank
+
+
+if __name__ == "__main__":
+ import doctest
+
+ doctest.testmod()