code: def gen_simps_mult(N, dtype, even="avg"):
      """
      Generate multiplication array for composite Simpson's rule.
  
      Generates an array whose dot product with some array of equal
      length is equivalent to the definite integral of the latter
      computed using composite Simpson's rule.
  
      If there are an even number of samples, N, then there are an odd
      number of intervals (N-1), but Simpson's rule requires an even number
      of intervals. The parameter 'even' controls how this is handled.
  
      Parameters
      ----------
      N : int
          Length of array.
      dtype : float type
          Floating point type to use when generating the array.
      even : str {'avg', 'first', 'last'}, optional
          'avg' : Average two results:1) use the first N-2 intervals with
                    a trapezoidal rule on the last interval and 2) use the last
                    N-2 intervals with a trapezoidal rule on the first interval.
          'first' : Use Simpson's rule for the first N-2 intervals with
                  a trapezoidal rule on the last interval.
          'last' : Use Simpson's rule for the last N-2 intervals with a
                 trapezoidal rule on the first interval.
  
      Returns
      -------
      result : pycuda.gpuarray.GPUArray
          Generated array.
      """
  
      if dtype not in [
          np.float32,
          np.float64,
          np.complex64,
          np.complex128,
      ]:
          raise ValueError("unrecognized type")
  
      ctype = tools.dtype_to_ctype(dtype)
      x_gpu = gpuarray.zeros(N, dtype)
  
      if N % 2:
          func = elementwise.ElementwiseKernel(
              "{ctype} *x".format(ctype=ctype),
              "x[i] = (i%2 == 0) ? ((i != 0 && i != {M}) ? 2. : 1.) : 4.".format(
                  M=N - 1
              ),
          )
          x_gpu.fill(1.0)
          func(x_gpu)
          return x_gpu / 3.0
      else:
          if even not in ["avg", "last", "first"]:
              raise ValueError(
                  "Parameter 'even' must be "
                  "'avg', 'last', or 'first'."
              )
          basic_simps = gen_simps_mult(N - 1, dtype)
  
          if even in ["avg", "first"]:
              x_gpu[:-1] += basic_simps
              x_gpu[-2:] += 0.5  # trapz on last interval
          if even in ["avg", "last"]:
              x_gpu[1:] += basic_simps
              x_gpu[:2] += 0.5  # trapz on first interval
          if even == "avg":
              x_gpu /= 2.0
          return x_gpu
  
file_path: scikit-cuda/skcuda/integrate.py
imports: from string import Template
  from pycuda.tools import context_dependent_memoize
  from pycuda.compiler import SourceModule
  import pycuda.elementwise
  import pycuda.gpuarray
  import pycuda.tools
  import numpy
  from .misc import init, shutdown
  from .None import cublas
  from .None import misc
label_desc: Use image node_id 3 for calling a global function with example usage: gen_simps_mult(N, dtype, even) and returns: unknown, x_gpu