text: # This file is part of QuTiP: Quantum Toolbox in Python.
  #
  #    Copyright (c) 2011 and later, Paul D. Nation.
  #    All rights reserved.
  #
  #    Redistribution and use in source and binary forms, with or without
  #    modification, are permitted provided that the following conditions are
  #    met:
  #
  #    1. Redistributions of source code must retain the above copyright notice,
  #       this list of conditions and the following disclaimer.
  #
  #    2. Redistributions in binary form must reproduce the above copyright
  #       notice, this list of conditions and the following disclaimer in the
  #       documentation and/or other materials provided with the distribution.
  #
  #    3. Neither the name of the QuTiP: Quantum Toolbox in Python nor the names
  #       of its contributors may be used to endorse or promote products derived
  #       from this software without specific prior written permission.
  #
  #    THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
  #    "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
  #    LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
  #    PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
  #    HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
  #    SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
  #    LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
  #    DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
  #    THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
  #    (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
  #    OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
  ###############################################################################
  import numpy as np
  import scipy.sparse as sp
  import ctypes
  from ctypes import POINTER,c_int,c_char,c_double, byref
  from numpy import ctypeslib
  import qutip.settings as qset
  zcsrgemv = qset.mkl_lib.mkl_cspblas_zcsrgemv
  
  def mkl_spmv(A, x):
       """
       sparse csr_spmv using MKL
       """
       (m,n) = A.shape
  
       # Pointers to data of the matrix
       data    = A.data.ctypes.data_as(ctypeslib.ndpointer(np.complex128, ndim=1, flags='C'))
       indptr  = A.indptr.ctypes.data_as(POINTER(c_int))
       indices = A.indices.ctypes.data_as(POINTER(c_int))
  
       # Allocate output, using same conventions as input
       if x.ndim == 1:
          y = np.empty(m,dtype=np.complex,order='C')
       elif x.ndim==2 and x.shape[1]==1:
          y = np.empty((m,1),dtype=np.complex,order='C')
       else:
          raise Exception('Input vector must be 1D row or 2D column vector')
       
       np_x = x.ctypes.data_as(ctypeslib.ndpointer(np.complex128, ndim=1, flags='C'))
       np_y = y.ctypes.data_as(ctypeslib.ndpointer(np.complex128, ndim=1, flags='C'))
       # now call MKL. This returns the answer in np_y, which points to y
       zcsrgemv(byref(c_char(bytes(b'N'))), byref(c_int(m)), data ,indptr, indices, np_x, np_y ) 
       return y
  