prompt: You will be provided with a partial code base and an issue statement explaining a problem to resolve.
  <issue>
  Error in fermi-hubbard example
  Hello, there.
  
  It seems that the definition of create and annihilation operators are defined reversely in fermi-hubbard model, and results are wrong. [link](https://github.com/netket/netket/blob/26372e3527ae12861cc7953c24654614e8679d87/Examples/Fermions/fermi_hubbard.py#L25C1-L26)
  
  </issue>
  <code>
  [start of Examples/Fermions/fermi_hubbard.py]
  1 import netket as nk
  2 import numpy as np
  3 import matplotlib.pyplot as plt
  4 import json
  5 
  6 from netket import experimental as nkx
  7 
  8 L = 2  # take a 2x2 lattice
  9 D = 2
  10 t = 1  # tunneling/hopping
  11 U = 0.01  # coulomb
  12 
  13 # create the graph our fermions can hop on
  14 g = nk.graph.Hypercube(length=L, n_dim=D, pbc=True)
  15 n_sites = g.n_nodes
  16 
  17 # create a hilbert space with 2 up and 2 down spins
  18 hi = nkx.hilbert.SpinOrbitalFermions(n_sites, s=1 / 2, n_fermions=(2, 2))
  19 
  20 
  21 # create an operator representing fermi hubbard interactions
  22 # -t (i^ j + h.c.) + U (i^ i j^ j)
  23 # we will create a helper function to abbreviate the creation, destruction and number operators
  24 # each operator has a site and spin projection (sz) in order to find the right position in the hilbert space samples
  25 def c(site, sz):
  26     return nkx.operator.fermion.create(hi, site, sz=sz)
  27 
  28 
  29 def cdag(site, sz):
  30     return nkx.operator.fermion.destroy(hi, site, sz=sz)
  31 
  32 
  33 def nc(site, sz):
  34     return nkx.operator.fermion.number(hi, site, sz=sz)
  35 
  36 
  37 up = +1 / 2
  38 down = -1 / 2
  39 ham = 0.0
  40 for sz in (up, down):
  41     for u, v in g.edges():
  42         ham += -t * cdag(u, sz) * c(v, sz) - t * cdag(v, sz) * c(u, sz)
  43 for u in g.nodes():
  44     ham += U * nc(u, up) * nc(u, down)
  45 
  46 print("Hamiltonian =", ham.operator_string())
  47 
  48 # metropolis exchange moves fermions around according to a graph
  49 # the physical graph has LxL vertices, but the computational basis defined by the
  50 # hilbert space contains (2s+1)*L*L occupation numbers
  51 # by taking a disjoint copy of the lattice, we can
  52 # move the fermions around independently for both spins
  53 # and therefore conserve the number of fermions with up and down spin
  54 
  55 # g.n_nodes == L*L --> disj_graph == 2*L*L
  56 disj_graph = nk.graph.disjoint_union(g, g)
  57 sa = nk.sampler.MetropolisExchange(hi, graph=disj_graph, n_chains=16)
  58 
  59 # since the hilbert basis is a set of occupation numbers, we can take a general RBM
  60 # we take complex parameters, since it learns sign structures more easily, and for even fermion number, the wave function might be complex
  61 ma = nk.models.RBM(alpha=1, param_dtype=complex, use_visible_bias=False)
  62 vs = nk.vqs.MCState(sa, ma, n_discard_per_chain=100, n_samples=512)
  63 
  64 # we will use sgd with Stochastic Reconfiguration
  65 opt = nk.optimizer.Sgd(learning_rate=0.01)
  66 sr = nk.optimizer.SR(diag_shift=0.1)
  67 
  68 gs = nk.driver.VMC(ham, opt, variational_state=vs, preconditioner=sr)
  69 
  70 # now run the optimization
  71 # first step will take longer in order to compile
  72 exp_name = "fermions_test"
  73 gs.run(500, out=exp_name)
  74 
  75 ############## plot #################
  76 
  77 ed_energies = np.linalg.eigvalsh(ham.to_dense())
  78 
  79 with open(f"{exp_name}.log", "r") as f:
  80     data = json.load(f)
  81 
  82 x = data["Energy"]["iters"]
  83 y = data["Energy"]["Mean"]["real"]
  84 
  85 # plot the energy levels
  86 plt.axhline(ed_energies[0], color="red", label="E0")
  87 for e in ed_energies[1:]:
  88     plt.axhline(e, color="black")
  89 plt.plot(x, y, color="red", label="VMC")
  90 plt.xlabel("step")
  91 plt.ylabel("E")
  92 plt.show()
  93
  [end of Examples/Fermions/fermi_hubbard.py]
  </code>
  
  I need you to solve this issue by generating a single patch file that I can apply directly to this repository using git apply. Please respond with a single patch file in the following format.
  <patch>
  diff --git a/file.py b/file.py
  --- a/file.py
  +++ b/file.py
  @@ -1,27 +1,35 @@
   def euclidean(a, b):
  -    while b:
  -        a, b = b, a % b
  -    return a
  +    if b == 0:
  +        return a
  +    return euclidean(b, a % b)
   
   
   def bresenham(x0, y0, x1, y1):
       points = []
       dx = abs(x1 - x0)
       dy = abs(y1 - y0)
  -    sx = 1 if x0 < x1 else -1
  -    sy = 1 if y0 < y1 else -1
  -    err = dx - dy
  +    x, y = x0, y0
  +    sx = -1 if x0 > x1 else 1
  +    sy = -1 if y0 > y1 else 1
   
  -    while True:
  -        points.append((x0, y0))
  -        if x0 == x1 and y0 == y1:
  -            break
  -        e2 = 2 * err
  -        if e2 > -dy:
  -            err -= dy
  -            x0 += sx
  -        if e2 < dx:
  -            err += dx
  -            y0 += sy
  +    if dx > dy:
  +        err = dx / 2.0
  +        while x != x1:
  +            points.append((x, y))
  +            err -= dy
  +            if err < 0:
  +                y += sy
  +                err += dx
  +            x += sx
  +    else:
  +        err = dy / 2.0
  +        while y != y1:
  +            points.append((x, y))
  +            err -= dx
  +            if err < 0:
  +                x += sx
  +                err += dy
  +            y += sy
  +
  +    points.append((x, y))
       return points
  
  </patch>
golden_diff: diff --git a/Examples/Fermions/fermi_hubbard.py b/Examples/Fermions/fermi_hubbard.py
  --- a/Examples/Fermions/fermi_hubbard.py
  +++ b/Examples/Fermions/fermi_hubbard.py
  @@ -23,11 +23,11 @@
   # we will create a helper function to abbreviate the creation, destruction and number operators
   # each operator has a site and spin projection (sz) in order to find the right position in the hilbert space samples
   def c(site, sz):
  -    return nkx.operator.fermion.create(hi, site, sz=sz)
  +    return nkx.operator.fermion.destroy(hi, site, sz=sz)
   
   
   def cdag(site, sz):
  -    return nkx.operator.fermion.destroy(hi, site, sz=sz)
  +    return nkx.operator.fermion.create(hi, site, sz=sz)
   
   
   def nc(site, sz):
  
verification_info: {"golden_diff": "diff --git a/Examples/Fermions/fermi_hubbard.py b/Examples/Fermions/fermi_hubbard.py\n--- a/Examples/Fermions/fermi_hubbard.py\n+++ b/Examples/Fermions/fermi_hubbard.py\n@@ -23,11 +23,11 @@\n # we will create a helper function to abbreviate the creation, destruction and number operators\n # each operator has a site and spin projection (sz) in order to find the right position in the hilbert space samples\n def c(site, sz):\n-    return nkx.operator.fermion.create(hi, site, sz=sz)\n+    return nkx.operator.fermion.destroy(hi, site, sz=sz)\n \n \n def cdag(site, sz):\n-    return nkx.operator.fermion.destroy(hi, site, sz=sz)\n+    return nkx.operator.fermion.create(hi, site, sz=sz)\n \n \n def nc(site, sz):\n", "issue": "Error in fermi-hubbard example\nHello, there.\r\n\r\nIt seems that the definition of create and annihilation operators are defined reversely in fermi-hubbard model, and results are wrong. [link](https://github.com/netket/netket/blob/26372e3527ae12861cc7953c24654614e8679d87/Examples/Fermions/fermi_hubbard.py#L25C1-L26)\n", "before_files": [{"content": "import netket as nk\nimport numpy as np\nimport matplotlib.pyplot as plt\nimport json\n\nfrom netket import experimental as nkx\n\nL = 2  # take a 2x2 lattice\nD = 2\nt = 1  # tunneling/hopping\nU = 0.01  # coulomb\n\n# create the graph our fermions can hop on\ng = nk.graph.Hypercube(length=L, n_dim=D, pbc=True)\nn_sites = g.n_nodes\n\n# create a hilbert space with 2 up and 2 down spins\nhi = nkx.hilbert.SpinOrbitalFermions(n_sites, s=1 / 2, n_fermions=(2, 2))\n\n\n# create an operator representing fermi hubbard interactions\n# -t (i^ j + h.c.) + U (i^ i j^ j)\n# we will create a helper function to abbreviate the creation, destruction and number operators\n# each operator has a site and spin projection (sz) in order to find the right position in the hilbert space samples\ndef c(site, sz):\n    return nkx.operator.fermion.create(hi, site, sz=sz)\n\n\ndef cdag(site, sz):\n    return nkx.operator.fermion.destroy(hi, site, sz=sz)\n\n\ndef nc(site, sz):\n    return nkx.operator.fermion.number(hi, site, sz=sz)\n\n\nup = +1 / 2\ndown = -1 / 2\nham = 0.0\nfor sz in (up, down):\n    for u, v in g.edges():\n        ham += -t * cdag(u, sz) * c(v, sz) - t * cdag(v, sz) * c(u, sz)\nfor u in g.nodes():\n    ham += U * nc(u, up) * nc(u, down)\n\nprint(\"Hamiltonian =\", ham.operator_string())\n\n# metropolis exchange moves fermions around according to a graph\n# the physical graph has LxL vertices, but the computational basis defined by the\n# hilbert space contains (2s+1)*L*L occupation numbers\n# by taking a disjoint copy of the lattice, we can\n# move the fermions around independently for both spins\n# and therefore conserve the number of fermions with up and down spin\n\n# g.n_nodes == L*L --> disj_graph == 2*L*L\ndisj_graph = nk.graph.disjoint_union(g, g)\nsa = nk.sampler.MetropolisExchange(hi, graph=disj_graph, n_chains=16)\n\n# since the hilbert basis is a set of occupation numbers, we can take a general RBM\n# we take complex parameters, since it learns sign structures more easily, and for even fermion number, the wave function might be complex\nma = nk.models.RBM(alpha=1, param_dtype=complex, use_visible_bias=False)\nvs = nk.vqs.MCState(sa, ma, n_discard_per_chain=100, n_samples=512)\n\n# we will use sgd with Stochastic Reconfiguration\nopt = nk.optimizer.Sgd(learning_rate=0.01)\nsr = nk.optimizer.SR(diag_shift=0.1)\n\ngs = nk.driver.VMC(ham, opt, variational_state=vs, preconditioner=sr)\n\n# now run the optimization\n# first step will take longer in order to compile\nexp_name = \"fermions_test\"\ngs.run(500, out=exp_name)\n\n############## plot #################\n\ned_energies = np.linalg.eigvalsh(ham.to_dense())\n\nwith open(f\"{exp_name}.log\", \"r\") as f:\n    data = json.load(f)\n\nx = data[\"Energy\"][\"iters\"]\ny = data[\"Energy\"][\"Mean\"][\"real\"]\n\n# plot the energy levels\nplt.axhline(ed_energies[0], color=\"red\", label=\"E0\")\nfor e in ed_energies[1:]:\n    plt.axhline(e, color=\"black\")\nplt.plot(x, y, color=\"red\", label=\"VMC\")\nplt.xlabel(\"step\")\nplt.ylabel(\"E\")\nplt.show()\n", "path": "Examples/Fermions/fermi_hubbard.py"}]}