code: def solve(
      a,
      b,
      lower=False,
      overwrite_a=False,
      overwrite_b=False,
      check_finite=True,
      assume_a="gen",
      transposed=False,
  ):
      """
      Solves the linear equation set ``a @ x == b`` for the unknown ``x``
      for square `a` matrix.
  
      If the data matrix is known to be a particular type then supplying the
      corresponding string to ``assume_a`` key chooses the dedicated solver.
      The available options are
  
      ===================  ========
       generic matrix       'gen'
       symmetric            'sym'
       hermitian            'her'
       positive definite    'pos'
      ===================  ========
  
      If omitted, ``'gen'`` is the default structure.
  
      The datatype of the arrays define which solver is called regardless
      of the values. In other words, even when the complex array entries have
      precisely zero imaginary parts, the complex solver will be called based
      on the data type of the array.
  
      Parameters
      ----------
      a : (N, N) array_like
          Square input data
      b : (N, NRHS) array_like
          Input data for the right hand side.
      lower : bool, default: False
          Ignored if ``assume_a == 'gen'`` (the default). If True, the
          calculation uses only the data in the lower triangle of `a`;
          entries above the diagonal are ignored. If False (default), the
          calculation uses only the data in the upper triangle of `a`; entries
          below the diagonal are ignored.
      overwrite_a : bool, default: False
          Allow overwriting data in `a` (may enhance performance).
      overwrite_b : bool, default: False
          Allow overwriting data in `b` (may enhance performance).
      check_finite : bool, default: True
          Whether to check that the input matrices contain 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.
      assume_a : str, {'gen', 'sym', 'her', 'pos'}
          Valid entries are explained above.
      transposed : bool, default: False
          If True, solve ``a.T @ x == b``. Raises `NotImplementedError`
          for complex `a`.
  
      Returns
      -------
      x : (N, NRHS) ndarray
          The solution array.
  
      Raises
      ------
      ValueError
          If size mismatches detected or input a is not square.
      LinAlgError
          If the matrix is singular.
      LinAlgWarning
          If an ill-conditioned input a is detected.
      NotImplementedError
          If transposed is True and input a is a complex matrix.
  
      Notes
      -----
      If the input b matrix is a 1-D array with N elements, when supplied
      together with an NxN input a, it is assumed as a valid column vector
      despite the apparent size mismatch. This is compatible with the
      numpy.dot() behavior and the returned result is still 1-D array.
  
      The generic, symmetric, Hermitian and positive definite solutions are
      obtained via calling ?GESV, ?SYSV, ?HESV, and ?POSV routines of
      LAPACK respectively.
  
      Examples
      --------
      Given `a` and `b`, solve for `x`:
  
      >>> import numpy as np
      >>> a = np.array([[3, 2, 0], [1, -1, 0], [0, 5, 1]])
      >>> b = np.array([2, 4, -1])
      >>> from scipy import linalg
      >>> x = linalg.solve(a, b)
      >>> x
      array([ 2., -2.,  9.])
      >>> np.dot(a, x) == b
      array([ True,  True,  True], dtype=bool)
  
      """
      # Flags for 1-D or N-D right-hand side
      b_is_1D = False
  
      a1 = atleast_2d(_asarray_validated(a, check_finite=check_finite))
      b1 = atleast_1d(_asarray_validated(b, check_finite=check_finite))
      n = a1.shape[0]
  
      overwrite_a = overwrite_a or _datacopied(a1, a)
      overwrite_b = overwrite_b or _datacopied(b1, b)
  
      if a1.shape[0] != a1.shape[1]:
          raise ValueError("Input a needs to be a square matrix.")
  
      if n != b1.shape[0]:
          # Last chance to catch 1x1 scalar a and 1-D b arrays
          if not (n == 1 and b1.size != 0):
              raise ValueError(
                  "Input b has to have same number of rows as "
                  "input a"
              )
  
      # accommodate empty arrays
      if b1.size == 0:
          return np.asfortranarray(b1.copy())
  
      # regularize 1-D b arrays to 2D
      if b1.ndim == 1:
          if n == 1:
              b1 = b1[None, :]
          else:
              b1 = b1[:, None]
          b_is_1D = True
  
      if assume_a not in ("gen", "sym", "her", "pos"):
          raise ValueError(
              f"{assume_a} is not a recognized matrix structure"
          )
  
      # for a real matrix, describe it as "symmetric", not "hermitian"
      # (lapack doesn't know what to do with real hermitian matrices)
      if assume_a == "her" and not np.iscomplexobj(a1):
          assume_a = "sym"
  
      # Get the correct lamch function.
      # The LAMCH functions only exists for S and D
      # So for complex values we have to convert to real/double.
      if a1.dtype.char in "fF":  # single precision
          lamch = get_lapack_funcs("lamch", dtype="f")
      else:
          lamch = get_lapack_funcs("lamch", dtype="d")
  
      # Currently we do not have the other forms of the norm calculators
      #   lansy, lanpo, lanhe.
      # However, in any case they only reduce computations slightly...
      lange = get_lapack_funcs("lange", (a1,))
  
      # Since the I-norm and 1-norm are the same for symmetric matrices
      # we can collect them all in this one call
      # Note however, that when issuing 'gen' and form!='none', then
      # the I-norm should be used
      if transposed:
          trans = 1
          norm = "I"
          if np.iscomplexobj(a1):
              raise NotImplementedError(
                  "scipy.linalg.solve can currently "
                  "not solve a^T x = b or a^H x = b "
                  "for complex matrices."
              )
      else:
          trans = 0
          norm = "1"
  
      anorm = lange(norm, a1)
  
      # Generalized case 'gesv'
      if assume_a == "gen":
          gecon, getrf, getrs = get_lapack_funcs(
              ("gecon", "getrf", "getrs"), (a1, b1)
          )
          lu, ipvt, info = getrf(a1, overwrite_a=overwrite_a)
          _solve_check(n, info)
          x, info = getrs(
              lu, ipvt, b1, trans=trans, overwrite_b=overwrite_b
          )
          _solve_check(n, info)
          rcond, info = gecon(lu, anorm, norm=norm)
      # Hermitian case 'hesv'
      elif assume_a == "her":
          hecon, hesv, hesv_lw = get_lapack_funcs(
              ("hecon", "hesv", "hesv_lwork"), (a1, b1)
          )
          lwork = _compute_lwork(hesv_lw, n, lower)
          lu, ipvt, x, info = hesv(
              a1,
              b1,
              lwork=lwork,
              lower=lower,
              overwrite_a=overwrite_a,
              overwrite_b=overwrite_b,
          )
          _solve_check(n, info)
          rcond, info = hecon(lu, ipvt, anorm)
      # Symmetric case 'sysv'
      elif assume_a == "sym":
          sycon, sysv, sysv_lw = get_lapack_funcs(
              ("sycon", "sysv", "sysv_lwork"), (a1, b1)
          )
          lwork = _compute_lwork(sysv_lw, n, lower)
          lu, ipvt, x, info = sysv(
              a1,
              b1,
              lwork=lwork,
              lower=lower,
              overwrite_a=overwrite_a,
              overwrite_b=overwrite_b,
          )
          _solve_check(n, info)
          rcond, info = sycon(lu, ipvt, anorm)
      # Positive definite case 'posv'
      else:
          pocon, posv = get_lapack_funcs(("pocon", "posv"), (a1, b1))
          lu, x, info = posv(
              a1,
              b1,
              lower=lower,
              overwrite_a=overwrite_a,
              overwrite_b=overwrite_b,
          )
          _solve_check(n, info)
          rcond, info = pocon(lu, anorm)
  
      _solve_check(n, info, lamch, rcond)
  
      if b_is_1D:
          x = x.ravel()
  
      return x
  
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 2 for calling a global function with example usage: solve(a, b, lower, overwrite_a, overwrite_b, check_finite, assume_a, transposed) and returns: x, np