{'fraction_non_alphanumeric': 0.023752969121140142, 'fraction_numerical': 0.0023752969121140144, 'mean_word_length': 5.0285714285714285, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
An implicit QR algorithm for symmetric semiseparable matrices

The QR algorithm is one of the classical methods to compute the eigendecomposition of a matrix. If it is applied on a dense n × n matrix, this algorithm requires O(n3) operations per iteration step. To reduce this complexity for a symmetric matrix to O(n), the original matrix is first reduced to tridiagonal form using orthogonal similarity transformations.