code: def get_direction_and_spacings(affine, dim):
      """Extracts the rotational and spacing components from a matrix
  
      Extracts the rotational and spacing (voxel dimensions) components from a
      matrix. An image gradient represents the local variation of the image's
      gray values per voxel. Since we are iterating on the physical space, we
      need to compute the gradients as variation per millimeter, so we need to
      divide each gradient's component by the voxel size along the corresponding
      axis, that's what the spacings are used for. Since the image's gradients
      are oriented along the grid axes, we also need to re-orient the gradients
      to be given in physical space coordinates.
  
      Parameters
      ----------
      affine : array, shape (k, k), k = 3, 4
          the matrix transforming grid coordinates to physical space.
  
      Returns
      -------
      direction : array, shape (k-1, k-1)
          the rotational component of the input matrix
      spacings : array, shape (k-1,)
          the scaling component (voxel size) of the matrix
  
      """
      if affine is None:
          return np.eye(dim), np.ones(dim)
      dim = affine.shape[1] - 1
      # Temporary hack: get the zooms by building a nifti image
      affine4x4 = np.eye(4)
      empty_volume = np.zeros((0, 0, 0))
      affine4x4[:dim, :dim] = affine[:dim, :dim]
      affine4x4[:dim, 3] = affine[:dim, dim - 1]
      nib_nifti = nib.Nifti1Image(empty_volume, affine4x4)
      scalings = np.asarray(nib_nifti.header.get_zooms())
      scalings = np.asarray(scalings[:dim], dtype=np.float64)
      A = affine[:dim, :dim]
      return A.dot(np.diag(1.0 / scalings)), scalings
  
imports: import logging
  import abc
  import numpy
  import numpy.linalg
  import nibabel
  from nibabel.streamlines import ArraySequence
  from dipy.align import vector_fields
  from dipy.align import floating
  from dipy.align import VerbosityLevels
  from dipy.align import Bunch
  from dipy.align.scalespace import ScaleSpace
label_desc: Use image node_id 2 for calling a global function with example usage: get_direction_and_spacings(affine, dim) and returns: A,  scalings, np,  np