From e871540e37b834673f9e6650b8e2281d7d36a8c3 Mon Sep 17 00:00:00 2001 From: Rudransh Bhardwaj <115872354+rudransh61@users.noreply.github.com> Date: Wed, 31 May 2023 20:33:02 +0530 Subject: [PATCH] Added rank of matrix in linear algebra (#8687) * Added rank of matrix in linear algebra * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * Corrected name of function * Corrected Rank_of_Matrix.py * Completed rank_of_matrix.py * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * delete to rename Rank_of_Matrix.py * created rank_of_matrix * added more doctests in rank_of_matrix.py * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * fixed some issues in rank_of_matrix.py * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * added moreeee doctestsss in rank_of_mtrix.py and fixed some bugss * Update linear_algebra/src/rank_of_matrix.py Co-authored-by: Christian Clauss * Update linear_algebra/src/rank_of_matrix.py Co-authored-by: Christian Clauss * Update linear_algebra/src/rank_of_matrix.py Co-authored-by: Christian Clauss * Update rank_of_matrix.py * Update linear_algebra/src/rank_of_matrix.py Co-authored-by: Caeden Perelli-Harris --------- Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com> Co-authored-by: Christian Clauss Co-authored-by: Caeden Perelli-Harris --- linear_algebra/src/rank_of_matrix.py | 89 ++++++++++++++++++++++++++++ 1 file changed, 89 insertions(+) create mode 100644 linear_algebra/src/rank_of_matrix.py diff --git a/linear_algebra/src/rank_of_matrix.py b/linear_algebra/src/rank_of_matrix.py new file mode 100644 index 000000000..7ff3c1699 --- /dev/null +++ b/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()