code: def pos_def(ws, alpha=0.001, eps=1e-20):
      """Diagonal modification.
  
      This method takes a complex Hermitian matrix represented by its upper
      triangular part and adds the value of its trace multiplied by alpha
      to the real part of its diagonal. The output will have the format:
      (*,2,C+P)
  
      Arguments
      ---------
      ws : tensor
          An input matrix. The tensor must have the following format:
          (*,2,C+P)
  
      alpha : float
          A coefficient to multiply the trace. The default value is 0.001.
  
      eps : float
          A small value to increase the real part of the diagonal. The
          default value is 1e-20.
      """
  
      # Extracting data
      D = ws.dim()
      P = ws.shape[D - 1]
      C = int(round(((1 + 8 * P) ** 0.5 - 1) / 2))
  
      # Finding the indices of the diagonal
      ids_triu = torch.triu_indices(C, C)
      ids_diag = torch.eq(ids_triu[0, :], ids_triu[1, :])
  
      # Computing the trace
      trace = torch.sum(ws[..., 0, ids_diag], D - 2)
      trace = trace.view(trace.shape + (1,))
      trace = trace.repeat((1,) * (D - 2) + (C,))
  
      # Adding the trace multiplied by alpha to the diagonal
      ws_pf = ws.clone()
      ws_pf[..., 0, ids_diag] += alpha * trace + eps
  
      return ws_pf
  
file_path: speechbrain/speechbrain/processing/decomposition.py
imports: import torch
label_desc: Use image node_id 7 for calling a global function with example usage: pos_def(ws, alpha, eps) and returns: ws_pf