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# scipy.sparse.tril

`scipy.sparse.``tril`(A, k=0, format=None)

  Return the lower triangular portion of a matrix in sparse format

  Returns the elements on or below the k-th diagonal of the matrix A.
    - k = 0 corresponds to the main diagonal
    - k > 0 is above the main diagonal
    - k < 0 is below the main diagonal

  Parameters: | A : dense or sparse matrix Matrix whose lower trianglar portion is desired. k : integer The top-most diagonal of the lower triangle. format : string Sparse format of the result, e.g. format=”csr”, etc.
  Returns: | L : sparse matrix Lower triangular portion of A in sparse format.

  See also

  `triu`
    upper triangle in sparse format

  Examples

      >>> from scipy.sparse import csr_matrix, tril
      >>> A = csr_matrix([[1, 2, 0, 0, 3], [4, 5, 0, 6, 7], [0, 0, 8, 9, 0]],
      ...                dtype='int32')
      >>> A.toarray()
      array([[1, 2, 0, 0, 3],
             [4, 5, 0, 6, 7],
             [0, 0, 8, 9, 0]])
      >>> tril(A).toarray()
      array([[1, 0, 0, 0, 0],
             [4, 5, 0, 0, 0],
             [0, 0, 8, 0, 0]])
      >>> tril(A).nnz
      4
      >>> tril(A, k=1).toarray()
      array([[1, 2, 0, 0, 0],
             [4, 5, 0, 0, 0],
             [0, 0, 8, 9, 0]])
      >>> tril(A, k=-1).toarray()
      array([[0, 0, 0, 0, 0],
             [4, 0, 0, 0, 0],
             [0, 0, 0, 0, 0]])
      >>> tril(A, format='csc')
      <3x5 sparse matrix of type '<type 'numpy.int32'>'
              with 4 stored elements in Compressed Sparse Column format>