class_docstr: Implementation of reduced HCT triangular element with explicit shape
  functions.
  
  Computes z, dz, d2z and the element stiffness matrix for bending energy:
  E(f) = integral( (d2z/dx2 + d2z/dy2)**2 dA)
  
  *** Reference for the shape functions: ***
  [1] Basis functions for general Hsieh-Clough-Tocher _triangles, complete or
      reduced.
      Michel Bernadou, Kamal Hassan
      International Journal for Numerical Methods in Engineering.
      17(5):784 - 789.  2.01
  
  *** Element description: ***
  9 dofs: z and dz given at 3 apex
  C1 (conform)
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docstr: Parameters
  ----------
  *alpha* is a (N x 3 x 1) array (array of column-matrices) of
  barycentric coordinates
  *J* is a (N x 2 x 2) array of jacobian matrices (jacobian matrix at
  triangle first apex)
  *ecc* is a (N x 3 x 1) array (array of column-matrices) of triangle
  eccentricities
  *dofs* is a (N x 1 x 9) arrays (arrays of row-matrices) of computed
  degrees of freedom.
  
  Returns
  -------
  Returns the values of interpolated function 2nd-derivatives
  [d2z/dx2, d2z/dy2, d2z/dxdy] in global coordinates at locations alpha,
  as a column-matrices of shape (N x 3 x 1).
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code: def get_function_hessians(self, alpha, J, ecc, dofs):
      """
      Parameters
      ----------
      *alpha* is a (N x 3 x 1) array (array of column-matrices) of
      barycentric coordinates
      *J* is a (N x 2 x 2) array of jacobian matrices (jacobian matrix at
      triangle first apex)
      *ecc* is a (N x 3 x 1) array (array of column-matrices) of triangle
      eccentricities
      *dofs* is a (N x 1 x 9) arrays (arrays of row-matrices) of computed
      degrees of freedom.
  
      Returns
      -------
      Returns the values of interpolated function 2nd-derivatives
      [d2z/dx2, d2z/dy2, d2z/dxdy] in global coordinates at locations alpha,
      as a column-matrices of shape (N x 3 x 1).
      """
      d2sdksi2 = self.get_d2Sidksij2(alpha, ecc)
      d2fdksi2 = dofs @ d2sdksi2
      H_rot = self.get_Hrot_from_J(J)
      d2fdx2 = d2fdksi2 @ H_rot
      return _transpose_vectorized(d2fdx2)
  
imports: import numpy
  from matplotlib import _api
  from matplotlib.tri import Triangulation
  from matplotlib.tri._trifinder import TriFinder
  from matplotlib.tri._tritools import TriAnalyzer
label_desc: Use image node_id 3 for calling the _ReducedHCT_Element obj's underlying member method code with example usage: obj.get_function_hessians(alpha, J, ecc, dofs) and returns: _transpose_vectorized