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# scipy.sparse.tril

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

  Return the lower triangular portion of a sparse array or matrix

  Returns the elements on or below the k-th diagonal of 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 array or matrix

      Matrix whose lower trianglar portion is desired.

    k integer optional

      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_array, tril
      >>> A = csr_array([[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 array of type '<class 'numpy.int32'>'
              with 4 stored elements in Compressed Sparse Column format>