class_docstr: Help lazily evaluate a matrix exponential.
  
  The idea is to not do more work than we need for high expm precision,
  so we lazily compute matrix powers and store or precompute
  other properties of the matrix.
class_docstr_tok: ["Help","lazily","evaluate","a","matrix","exponential",".","The","idea","is","to","not","do","more","work","than","we","need","for","high","expm","precision",",","so","we","lazily","compute","matrix","powers","and","store","or","precompute","other","properties","of","the","matrix","."]
code: def pade5(self):
      b = (30240.0, 15120.0, 3360.0, 420.0, 30.0, 1.0)
      U = _smart_matrix_product(
          self.A,
          b[5] * self.A4 + b[3] * self.A2 + b[1] * self.ident,
          structure=self.structure,
      )
      V = b[4] * self.A4 + b[2] * self.A2 + b[0] * self.ident
      return U, V
  
imports: import numpy
  import scipy.special
  from scipy._lib._util import float_factorial
  from scipy.linalg.basic import solve, solve_triangular
  from scipy.sparse.base import isspmatrix
  from scipy.sparse.linalg import spsolve
  from scipy.sparse.sputils import is_pydata_spmatrix
  import scipy.sparse
  import scipy.sparse.linalg
  from scipy.sparse.linalg.interface import LinearOperator
  from ._expm_multiply import _ident_like, _exact_1_norm
label_desc: Use image node_id 16 for calling the _ExpmPadeHelper obj's underlying member method code with example usage: obj.pade5() and returns: U,  V