code: def corr_clipped(corr, threshold=1e-15):
      """
      Find a near correlation matrix that is positive semi-definite
  
      This function clips the eigenvalues, replacing eigenvalues smaller than
      the threshold by the threshold. The new matrix is normalized, so that the
      diagonal elements are one.
      Compared to corr_nearest, the distance between the original correlation
      matrix and the positive definite correlation matrix is larger, however,
      it is much faster since it only computes eigenvalues once.
  
      Parameters
      ----------
      corr : ndarray, (k, k)
          initial correlation matrix
      threshold : float
          clipping threshold for smallest eigenvalue, see Notes
  
      Returns
      -------
      corr_new : ndarray, (optional)
          corrected correlation matrix
  
  
      Notes
      -----
      The smallest eigenvalue of the corrected correlation matrix is
      approximately equal to the ``threshold``. In examples, the
      smallest eigenvalue can be by a factor of 10 smaller than the threshold,
      e.g. threshold 1e-8 can result in smallest eigenvalue in the range
      between 1e-9 and 1e-8.
      If the threshold=0, then the smallest eigenvalue of the correlation matrix
      might be negative, but zero within a numerical error, for example in the
      range of -1e-16.
  
      Assumes input correlation matrix is symmetric. The diagonal elements of
      returned correlation matrix is set to ones.
  
      If the correlation matrix is already positive semi-definite given the
      threshold, then the original correlation matrix is returned.
  
      ``cov_clipped`` is 40 or more times faster than ``cov_nearest`` in simple
      example, but has a slightly larger approximation error.
  
      See Also
      --------
      corr_nearest
      cov_nearest
  
      """
      x_new, clipped = clip_evals(corr, value=threshold)
      if not clipped:
          return corr
  
      # cov2corr
      x_std = np.sqrt(np.diag(x_new))
      x_new = x_new / x_std / x_std[:, None]
      return x_new
  
imports: import numpy
  import scipy.sparse
  from scipy.sparse.linalg import svds
  from scipy.optimize import fminbound
  import warnings
  from statsmodels.tools.tools import Bunch
  from statsmodels.tools.sm_exceptions import IterationLimitWarning, iteration_limit_doc
label_desc: Use image node_id 3 for calling a global function with example usage: corr_clipped(corr, threshold) and returns: x_new, corr