code: def det(a, overwrite_a=False, check_finite=True):
      """
      Compute the determinant of a matrix
  
      The determinant is a scalar that is a function of the associated square
      matrix coefficients. The determinant value is zero for singular matrices.
  
      Parameters
      ----------
      a : (..., M, M) array_like
          Input array to compute determinants for.
      overwrite_a : bool, optional
          Allow overwriting data in a (may enhance performance).
      check_finite : bool, optional
          Whether to check that the input matrix contains only finite numbers.
          Disabling may give a performance gain, but may result in problems
          (crashes, non-termination) if the inputs do contain infinities or NaNs.
  
      Returns
      -------
      det : (...) float or complex
          Determinant of `a`. For stacked arrays, a scalar is returned for each
          (m, m) slice in the last two dimensions of the input. For example, an
          input of shape (p, q, m, m) will produce a result of shape (p, q). If
          all dimensions are 1 a scalar is returned regardless of ndim.
  
      Notes
      -----
      The determinant is computed by performing an LU factorization of the
      input with LAPACK routine 'getrf', and then calculating the product of
      diagonal entries of the U factor.
  
      Even the input array is single precision (float32 or complex64), the result
      will be returned in double precision (float64 or complex128) to prevent
      overflows.
  
      Examples
      --------
      >>> import numpy as np
      >>> from scipy import linalg
      >>> a = np.array([[1,2,3], [4,5,6], [7,8,9]])  # A singular matrix
      >>> linalg.det(a)
      0.0
      >>> b = np.array([[0,2,3], [4,5,6], [7,8,9]])
      >>> linalg.det(b)
      3.0
      >>> # An array with the shape (3, 2, 2, 2)
      >>> c = np.array([[[[1., 2.], [3., 4.]],
      ...                [[5., 6.], [7., 8.]]],
      ...               [[[9., 10.], [11., 12.]],
      ...                [[13., 14.], [15., 16.]]],
      ...               [[[17., 18.], [19., 20.]],
      ...                [[21., 22.], [23., 24.]]]])
      >>> linalg.det(c)  # The resulting shape is (3, 2)
      array([[-2., -2.],
             [-2., -2.],
             [-2., -2.]])
      >>> linalg.det(c[0, 0])  # Confirm the (0, 0) slice, [[1, 2], [3, 4]]
      -2.0
      """
      # The goal is to end up with a writable contiguous array to pass to Cython
  
      # First we check and make arrays.
      a1 = np.asarray_chkfinite(a) if check_finite else np.asarray(a)
      if a1.ndim < 2:
          raise ValueError(
              "The input array must be at least two-dimensional."
          )
      if a1.shape[-1] != a1.shape[-2]:
          raise ValueError(
              "Last 2 dimensions of the array must be square"
              f" but received shape {a1.shape}."
          )
  
      # Also check if dtype is LAPACK compatible
      if a1.dtype.char not in "fdFD":
          dtype_char = lapack_cast_dict[a1.dtype.char]
          if not dtype_char:  # No casting possible
              raise TypeError(
                  f'The dtype "{a1.dtype.name}" cannot be cast '
                  "to float(32, 64) or complex(64, 128)."
              )
  
          a1 = a1.astype(dtype_char[0])  # makes a copy, free to scratch
          overwrite_a = True
  
      # Empty array has determinant 1 because math.
      if min(*a1.shape) == 0:
          if a1.ndim == 2:
              return np.float64(1.0)
          else:
              return np.ones(shape=a1.shape[:-2], dtype=np.float64)
  
      # Scalar case
      if a1.shape[-2:] == (1, 1):
          # Either ndarray with spurious singletons or a single element
          if max(*a1.shape) > 1:
              temp = np.squeeze(a1)
              if a1.dtype.char in "dD":
                  return temp
              else:
                  return (
                      temp.astype("d")
                      if a1.dtype.char == "f"
                      else temp.astype("D")
                  )
          else:
              return (
                  np.float64(a1.item())
                  if a1.dtype.char in "fd"
                  else np.complex128(a1.item())
              )
  
      # Then check overwrite permission
      if not _datacopied(a1, a):  # "a"  still alive through "a1"
          if not overwrite_a:
              # Data belongs to "a" so make a copy
              a1 = a1.copy(order="C")
          #  else: Do nothing we'll use "a" if possible
      # else:  a1 has its own data thus free to scratch
  
      # Then layout checks, might happen that overwrite is allowed but original
      # array was read-only or non-C-contiguous.
      if not (a1.flags["C_CONTIGUOUS"] and a1.flags["WRITEABLE"]):
          a1 = a1.copy(order="C")
  
      if a1.ndim == 2:
          det = find_det_from_lu(a1)
          # Convert float, complex to to NumPy scalars
          return (
              np.float64(det)
              if np.isrealobj(det)
              else np.complex128(det)
          )
  
      # loop over the stacked array, and avoid overflows for single precision
      # Cf. np.linalg.det(np.diag([1e+38, 1e+38]).astype(np.float32))
      dtype_char = a1.dtype.char
      if dtype_char in "fF":
          dtype_char = "d" if dtype_char.islower() else "D"
  
      det = np.empty(a1.shape[:-2], dtype=dtype_char)
      for ind in product(*[range(x) for x in a1.shape[:-2]]):
          det[ind] = find_det_from_lu(a1[ind])
      return det
  
imports: from warnings import warn
  from itertools import product
  import numpy
  from numpy import atleast_1d, atleast_2d
  from .lapack import get_lapack_funcs, _compute_lwork
  from ._misc import LinAlgError, _datacopied, LinAlgWarning
  from ._decomp import _asarray_validated
  from .None import _decomp, _decomp_svd
  from ._solve_toeplitz import levinson
  from ._cythonized_array_utils import find_det_from_lu
  from scipy._lib.deprecation import _NoValue, _deprecate_positional_args
label_desc: Use image node_id 10 for calling a global function with example usage: det(a, overwrite_a, check_finite) and returns: det, unknown, np, np, unknown, temp, unknown