diff --git a/hafnian/__init__.py b/hafnian/__init__.py
index 1510b969c..c1ffa4b68 100644
--- a/hafnian/__init__.py
+++ b/hafnian/__init__.py
@@ -54,11 +54,14 @@
 .. autosummary::
     hafnian
     hafnian_repeated
+    hafnian_batched
+    hermite_multidimensional
     tor
     perm
     permanent_repeated
     reduction
     version
+
 """
 # pylint: disable=wrong-import-position
 import os
@@ -66,13 +69,6 @@
 
 import numpy as np
 
-
-if platform.system() == "Windows":  # pragma: no cover
-    extra_dll_dir = os.path.join(os.path.dirname(__file__), ".libs")
-    if os.path.isdir(extra_dll_dir):
-        os.environ["PATH"] += os.pathsep + extra_dll_dir
-
-
 from ._hafnian import (
     haf_complex,
     haf_int,
@@ -83,10 +79,16 @@
     hafnian_repeated,
     reduction,
 )
+from ._hermite_multidimensional import hafnian_batched, hermite_multidimensional
 from ._permanent import perm, perm_complex, perm_real, permanent_repeated
 from ._torontonian import tor
 from ._version import __version__
 
+if platform.system() == "Windows":  # pragma: no cover
+    extra_dll_dir = os.path.join(os.path.dirname(__file__), ".libs")
+    if os.path.isdir(extra_dll_dir):
+        os.environ["PATH"] += os.pathsep + extra_dll_dir
+
 
 __all__ = [
     "hafnian",
@@ -95,6 +97,8 @@
     "perm",
     "permanent_repeated",
     "reduction",
+    "hafnian_batched",
+    "hermite_multidimensional",
     "version",
 ]
 
diff --git a/hafnian/_hafnian.py b/hafnian/_hafnian.py
index 435ced030..f3428a4d5 100644
--- a/hafnian/_hafnian.py
+++ b/hafnian/_hafnian.py
@@ -174,7 +174,10 @@ def hafnian(
 
 
 def hafnian_repeated(A, rpt, mu=None, loop=False, tol=1e-12):
-    r"""Returns the hafnian of matrix with repeated rows/columns.
+    r"""
+    THIS NEEDS TO BE WRITTEN
+
+    Returns the hafnian of matrix with repeated rows/columns.
 
     The :func:`reduction` function may be used to show the resulting matrix
     with repeated rows and columns as per ``rpt``.
diff --git a/hafnian/_hermite_multidimensional.py b/hafnian/_hermite_multidimensional.py
new file mode 100644
index 000000000..425ae9f8b
--- /dev/null
+++ b/hafnian/_hermite_multidimensional.py
@@ -0,0 +1,145 @@
+# Copyright 2019 Xanadu Quantum Technologies Inc.
+
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+
+#     http://www.apache.org/licenses/LICENSE-2.0
+
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+"""
+Hermite Multidimensional Python interface
+"""
+from itertools import product
+import numpy as np
+
+from .lib.libhaf import hermite_multidimensional as hm
+from ._hafnian import input_validation
+
+
+def return_prod(C, index):
+    r"""Given an array :math:`C_{i,j}` and an array or list of indices :math:`index = [i_1,i_2,i_3,\dots,i_n] `, returns :math:`prod_{k=1}^n C_{1,i_1}`.
+
+    Args:
+        C (array): An array
+        index (array): A set of indices
+
+    Returns:
+        complex: The product of the array elements determines by index
+    """
+    return np.prod([C[mode, val] for mode, val in enumerate(index)])
+
+
+def expansion_coeff(alpha, resolution, renorm=True):
+    r"""Returns the (quasi) geometric series as a vector with components :math:`alpha^i/sqrt(i!)` for :math:`0 \leq i < resolution`.
+
+    If renorm is false it omits the division by factorials
+
+    Args:
+        alpha (complex): Ratio of the geometric series
+        resoluton (int): Cutoff of the geometric series
+        renorm (bool): Decides whether to normalize by the factorials
+
+    Returns:
+        array: The power series
+    """
+    vals = np.empty([resolution], dtype=type(alpha))
+    vals[0] = 1.0
+    if renorm:
+        for i in range(1, resolution):
+            vals[i] = vals[i - 1] * alpha / np.sqrt(i)
+    else:
+        for i in range(1, resolution):
+            vals[i] = vals[i - 1] * alpha
+    return vals
+
+
+def hermite_multidimensional(R, resolution, y=None, renorm=False, make_tensor=True):
+    r"""Returns the multidimensional Hermite polynomials :math:`H_k^{(R)}(y)`.
+
+    Here :math:`R` is an :math:n \times n: square matrix,
+    :math:`y` is an :math:`n` dimensional vector. The polynomials are parametrized by the multi-index :math:`k=(k_0,k_1,\ldots,k_{n-1})
+    and are calculated for all values :math:`0 \leq k_j < \text{resolution}`, thus a tensor of dimensions :math:`\text{resolution}^n` is returned.
+    This tensor can either be flattened into a vector or returned as an actual tensor with :math:`n` indices.
+    Note that is R = np.array([[1.0+0.0j]]) then :math:`H_k^{(R)}(y)` are precisely the well known **probabilists' Hermite polynomials** :math:`He_k(y)`:,
+    and if R = 2*np.array([[1.0+0.0j]]) then :math:`H_k^{(R)}(y)` are precisely the well known **physicists' Hermite polynomials** :math:`H_k(y)`:.
+
+    Args:
+        R (array): Square matrix parametrizing the Hermite polynomial family
+        resolution (int): Maximum size of the subindices in the Hermite polynomial
+        y (array): Vector for the argument of the Hermite polynomial
+        renorm (bool): If True returns :math:`H_k^{(R)}(y)/\prod(\prod_i k_i!)`
+        make_tensor: If False returns a flattened one dimensional array instead of a tensor with the values of the polynomial
+
+    Returns:
+        (array): The multidimensional Hermite polynomials.
+    """
+    input_validation(R)
+    n, _ = R.shape
+    if y is None:
+        y = np.zeros([n], dtype=complex)
+
+    m = y.shape[0]
+    if m != n:
+        raise ValueError("The matrix R and vector y have incompatible dimensions")
+
+    values = np.array(hm(R, y, resolution, ren=renorm))
+
+    if make_tensor:
+        shape = resolution * np.ones([n], dtype=int)
+        values = np.reshape(values, shape)
+
+    return values
+
+
+def hafnian_batched(A, resolution, mu=None, tol=1e-12, renorm=False, make_tensor=True):
+    r"""Returns the haf(reduction(A, k)) where k is a vector of (non-negative) integers with the same dimensions as the square matrix A
+    :math:`k = (k_0,k_1,\ldots,k_{n-1})` and where :math:`0 \leq k_j < \text{resolution}`.
+
+    If mu is not None the it instead calculates :math:`lhaf(fill_diagonal(reduction(A, k),reduction(mu, k)))`, this calculation can only be performed if
+    the matrix A has an inverse.
+
+    Args:
+        R (array): Square matrix parametrizing
+        resolution (int): Maximum size of the subindices in the Hermite polynomial
+        y (array): Vector for the argument of the Hermite polynomial
+        renorm (bool): If True returns :math:`haf(reduction(A, k))/\prod(\prod_i k_i!)` or :math:`lhaf(fill_diagonal(reduction(A, k),reduction(mu, k)))` is mu is not None
+        make_tensor: If False returns a flattened one dimensional array instead of a tensor with the values of the polynomial
+
+    Returns:
+        (array): The values of the hafnians.
+    """
+    # pylint: disable=too-many-return-statements,too-many-branches,too-many-arguments
+    input_validation(A, tol=tol)
+    n, _ = A.shape
+    if not np.allclose(A, np.zeros([n, n])):
+        if mu is not None:
+            try:
+                yi = np.linalg.solve(A, mu)
+            except np.linalg.LinAlgError:
+                raise ValueError("The matrix does not have an inverse")
+            return hermite_multidimensional(
+                -A, resolution, y=-yi, renorm=renorm, make_tensor=make_tensor
+            )
+        yi = np.zeros([n], dtype=complex)
+        return hermite_multidimensional(
+            -A, resolution, y=-yi, renorm=renorm, make_tensor=make_tensor
+        )
+    # Note the minus signs in the arguments. Those are intentional
+
+    if mu is None:
+        tensor = np.zeros([resolution ** n], dtype=complex)
+        tensor[0] = 1.0
+    else:
+        index = resolution * np.ones([n], dtype=int)
+        tensor = np.empty(index, dtype=complex)
+        prim = np.array([expansion_coeff(alpha, resolution, renorm=renorm) for alpha in mu])
+        for i in product(range(resolution), repeat=n):
+            tensor[i] = return_prod(prim, i)
+    if make_tensor:
+        return tensor
+    return tensor.flatten()
diff --git a/hafnian/hafnian.cpp b/hafnian/hafnian.cpp
index d0e36fd9d..1ffe1c696 100644
--- a/hafnian/hafnian.cpp
+++ b/hafnian/hafnian.cpp
@@ -1,13 +1,15 @@
-/* Generated by Cython 0.29.8 */
+/* Generated by Cython 0.29.4 */
 
 /* BEGIN: Cython Metadata
 {
     "distutils": {
         "depends": [
+            "src/batchhafnian.hpp",
             "src/eigenvalue_hafnian.hpp",
             "src/fsum.hpp",
             "src/hafnian.hpp",
             "src/hafnian_approx.hpp",
+            "src/permanent.hpp",
             "src/recursive_hafnian.hpp",
             "src/repeated_hafnian.hpp",
             "src/stdafx.h",
@@ -19,33 +21,24 @@
             "-Wall",
             "-fPIC",
             "-shared",
-            "-Xpreprocessor",
             "-fopenmp",
-            "-lomp",
-            "-mmacosx-version-min=10.9",
-            "-I/Users/bgupt/anaconda/lib/python3.6/site-packages/numpy/core/include"
+            "-I/home/nicolas/.local/lib/python3.6/site-packages/numpy/core/include"
         ],
         "extra_link_args": [
-            "-Xpreprocessor -fopenmp -lomp"
+            "-fopenmp"
         ],
         "include_dirs": [
             "hafnian",
-            "/opt/local/include/libomp/",
-            "/Users/bgupt/anaconda/lib/python3.6/site-packages/numpy/core/include",
-            "/Users/bgupt/eigen-eigen-323c052e1731",
+            "",
+            "/home/nicolas/.local/lib/python3.6/site-packages/numpy/core/include",
             "/usr/local/include/eigen3",
             "/usr/include/eigen3",
-            "src",
-            "/usr/local/opt/libomp/include"
+            "src"
         ],
         "language": "c++",
-        "libraries": [
-            "omp"
-        ],
         "library_dirs": [
             "/usr/lib",
-            "/usr/local/lib",
-            "/usr/local/opt/libomp/lib"
+            "/usr/local/lib"
         ],
         "name": "libhaf",
         "sources": [
@@ -63,8 +56,8 @@ END: Cython Metadata */
 #elif PY_VERSION_HEX < 0x02060000 || (0x03000000 <= PY_VERSION_HEX && PY_VERSION_HEX < 0x03030000)
     #error Cython requires Python 2.6+ or Python 3.3+.
 #else
-#define CYTHON_ABI "0_29_8"
-#define CYTHON_HEX_VERSION 0x001D08F0
+#define CYTHON_ABI "0_29_4"
+#define CYTHON_HEX_VERSION 0x001D04F0
 #define CYTHON_FUTURE_DIVISION 0
 #include <stddef.h>
 #ifndef offsetof
@@ -380,13 +373,8 @@ class __Pyx_FakeReference {
   #define __Pyx_DefaultClassType PyClass_Type
 #else
   #define __Pyx_BUILTIN_MODULE_NAME "builtins"
-#if PY_VERSION_HEX < 0x030800A4
   #define __Pyx_PyCode_New(a, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)\
           PyCode_New(a, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)
-#else
-  #define __Pyx_PyCode_New(a, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)\
-          PyCode_New(a, 0, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)
-#endif
   #define __Pyx_DefaultClassType PyType_Type
 #endif
 #ifndef Py_TPFLAGS_CHECKTYPES
@@ -421,6 +409,26 @@ class __Pyx_FakeReference {
 #else
 #define __Pyx_PyFastCFunction_Check(func) 0
 #endif
+#if CYTHON_USE_DICT_VERSIONS
+#define __PYX_GET_DICT_VERSION(dict)  (((PyDictObject*)(dict))->ma_version_tag)
+#define __PYX_UPDATE_DICT_CACHE(dict, value, cache_var, version_var)\
+    (version_var) = __PYX_GET_DICT_VERSION(dict);\
+    (cache_var) = (value);
+#define __PYX_PY_DICT_LOOKUP_IF_MODIFIED(VAR, DICT, LOOKUP) {\
+        static PY_UINT64_T __pyx_dict_version = 0;\
+        static PyObject *__pyx_dict_cached_value = NULL;\
+        if (likely(__PYX_GET_DICT_VERSION(DICT) == __pyx_dict_version)) {\
+            (VAR) = __pyx_dict_cached_value;\
+        } else {\
+            (VAR) = __pyx_dict_cached_value = (LOOKUP);\
+            __pyx_dict_version = __PYX_GET_DICT_VERSION(DICT);\
+        }\
+    }
+#else
+#define __PYX_GET_DICT_VERSION(dict)  (0)
+#define __PYX_UPDATE_DICT_CACHE(dict, value, cache_var, version_var)
+#define __PYX_PY_DICT_LOOKUP_IF_MODIFIED(VAR, DICT, LOOKUP)  (VAR) = (LOOKUP);
+#endif
 #if CYTHON_COMPILING_IN_PYPY && !defined(PyObject_Malloc)
   #define PyObject_Malloc(s)   PyMem_Malloc(s)
   #define PyObject_Free(p)     PyMem_Free(p)
@@ -686,8 +694,7 @@ typedef struct {PyObject **p; const char *s; const Py_ssize_t n; const char* enc
                 const char is_unicode; const char is_str; const char intern; } __Pyx_StringTabEntry;
 
 #define __PYX_DEFAULT_STRING_ENCODING_IS_ASCII 0
-#define __PYX_DEFAULT_STRING_ENCODING_IS_UTF8 0
-#define __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT (PY_MAJOR_VERSION >= 3 && __PYX_DEFAULT_STRING_ENCODING_IS_UTF8)
+#define __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT 0
 #define __PYX_DEFAULT_STRING_ENCODING ""
 #define __Pyx_PyObject_FromString __Pyx_PyBytes_FromString
 #define __Pyx_PyObject_FromStringAndSize __Pyx_PyBytes_FromStringAndSize
@@ -1274,6 +1281,23 @@ static CYTHON_INLINE int __pyx_sub_acquisition_count_locked(
 static CYTHON_INLINE void __Pyx_INC_MEMVIEW(__Pyx_memviewslice *, int, int);
 static CYTHON_INLINE void __Pyx_XDEC_MEMVIEW(__Pyx_memviewslice *, int, int);
 
+/* ListCompAppend.proto */
+#if CYTHON_USE_PYLIST_INTERNALS && CYTHON_ASSUME_SAFE_MACROS
+static CYTHON_INLINE int __Pyx_ListComp_Append(PyObject* list, PyObject* x) {
+    PyListObject* L = (PyListObject*) list;
+    Py_ssize_t len = Py_SIZE(list);
+    if (likely(L->allocated > len)) {
+        Py_INCREF(x);
+        PyList_SET_ITEM(list, len, x);
+        Py_SIZE(list) = len+1;
+        return 0;
+    }
+    return PyList_Append(list, x);
+}
+#else
+#define __Pyx_ListComp_Append(L,x) PyList_Append(L,x)
+#endif
+
 /* ArgTypeTest.proto */
 #define __Pyx_ArgTypeTest(obj, type, none_allowed, name, exact)\
     ((likely((Py_TYPE(obj) == type) | (none_allowed && (obj == Py_None)))) ? 1 :\
@@ -1455,32 +1479,6 @@ static CYTHON_INLINE int __Pyx_PyErr_ExceptionMatchesInState(PyThreadState* tsta
 /* GetAttr3.proto */
 static CYTHON_INLINE PyObject *__Pyx_GetAttr3(PyObject *, PyObject *, PyObject *);
 
-/* PyDictVersioning.proto */
-#if CYTHON_USE_DICT_VERSIONS && CYTHON_USE_TYPE_SLOTS
-#define __PYX_DICT_VERSION_INIT  ((PY_UINT64_T) -1)
-#define __PYX_GET_DICT_VERSION(dict)  (((PyDictObject*)(dict))->ma_version_tag)
-#define __PYX_UPDATE_DICT_CACHE(dict, value, cache_var, version_var)\
-    (version_var) = __PYX_GET_DICT_VERSION(dict);\
-    (cache_var) = (value);
-#define __PYX_PY_DICT_LOOKUP_IF_MODIFIED(VAR, DICT, LOOKUP) {\
-    static PY_UINT64_T __pyx_dict_version = 0;\
-    static PyObject *__pyx_dict_cached_value = NULL;\
-    if (likely(__PYX_GET_DICT_VERSION(DICT) == __pyx_dict_version)) {\
-        (VAR) = __pyx_dict_cached_value;\
-    } else {\
-        (VAR) = __pyx_dict_cached_value = (LOOKUP);\
-        __pyx_dict_version = __PYX_GET_DICT_VERSION(DICT);\
-    }\
-}
-static CYTHON_INLINE PY_UINT64_T __Pyx_get_tp_dict_version(PyObject *obj);
-static CYTHON_INLINE PY_UINT64_T __Pyx_get_object_dict_version(PyObject *obj);
-static CYTHON_INLINE int __Pyx_object_dict_version_matches(PyObject* obj, PY_UINT64_T tp_dict_version, PY_UINT64_T obj_dict_version);
-#else
-#define __PYX_GET_DICT_VERSION(dict)  (0)
-#define __PYX_UPDATE_DICT_CACHE(dict, value, cache_var, version_var)
-#define __PYX_PY_DICT_LOOKUP_IF_MODIFIED(VAR, DICT, LOOKUP)  (VAR) = (LOOKUP);
-#endif
-
 /* GetModuleGlobalName.proto */
 #if CYTHON_USE_DICT_VERSIONS
 #define __Pyx_GetModuleGlobalName(var, name)  {\
@@ -1563,23 +1561,6 @@ static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches2(PyObject *err, PyObj
 #define __Pyx_PyException_Check(obj) __Pyx_TypeCheck(obj, PyExc_Exception)
 
 static CYTHON_UNUSED int __pyx_memoryview_getbuffer(PyObject *__pyx_v_self, Py_buffer *__pyx_v_info, int __pyx_v_flags); /*proto*/
-/* ListCompAppend.proto */
-#if CYTHON_USE_PYLIST_INTERNALS && CYTHON_ASSUME_SAFE_MACROS
-static CYTHON_INLINE int __Pyx_ListComp_Append(PyObject* list, PyObject* x) {
-    PyListObject* L = (PyListObject*) list;
-    Py_ssize_t len = Py_SIZE(list);
-    if (likely(L->allocated > len)) {
-        Py_INCREF(x);
-        PyList_SET_ITEM(list, len, x);
-        Py_SIZE(list) = len+1;
-        return 0;
-    }
-    return PyList_Append(list, x);
-}
-#else
-#define __Pyx_ListComp_Append(L,x) PyList_Append(L,x)
-#endif
-
 /* PyIntBinop.proto */
 #if !CYTHON_COMPILING_IN_PYPY
 static PyObject* __Pyx_PyInt_AddObjC(PyObject *op1, PyObject *op2, long intval, int inplace, int zerodivision_check);
@@ -1876,6 +1857,9 @@ __pyx_memoryview_copy_new_contig(const __Pyx_memviewslice *from_mvs,
 /* CIntFromPy.proto */
 static CYTHON_INLINE int __Pyx_PyInt_As_int(PyObject *);
 
+/* CIntFromPy.proto */
+static CYTHON_INLINE size_t __Pyx_PyInt_As_size_t(PyObject *);
+
 /* CIntFromPy.proto */
 static CYTHON_INLINE long __Pyx_PyInt_As_long(PyObject *);
 
@@ -1920,6 +1904,7 @@ static PyObject *contiguous = 0;
 static PyObject *indirect_contiguous = 0;
 static int __pyx_memoryview_thread_locks_used;
 static PyThread_type_lock __pyx_memoryview_thread_locks[8];
+static PyObject *__pyx_convert_vector_to_py___pyx_t_double_complex(const std::vector<__pyx_t_double_complex>  &); /*proto*/
 static struct __pyx_array_obj *__pyx_array_new(PyObject *, Py_ssize_t, char *, char *, char *); /*proto*/
 static void *__pyx_align_pointer(void *, size_t); /*proto*/
 static PyObject *__pyx_memoryview_new(PyObject *, int, int, __Pyx_TypeInfo *); /*proto*/
@@ -1984,6 +1969,7 @@ static const char __pyx_k_mat[] = "mat";
 static const char __pyx_k_new[] = "__new__";
 static const char __pyx_k_nud[] = "nud";
 static const char __pyx_k_obj[] = "obj";
+static const char __pyx_k_ren[] = "ren";
 static const char __pyx_k_rpt[] = "rpt";
 static const char __pyx_k_base[] = "base";
 static const char __pyx_k_dict[] = "__dict__";
@@ -2000,12 +1986,14 @@ static const char __pyx_k_step[] = "step";
 static const char __pyx_k_stop[] = "stop";
 static const char __pyx_k_test[] = "__test__";
 static const char __pyx_k_ASCII[] = "ASCII";
+static const char __pyx_k_R_mat[] = "R_mat";
 static const char __pyx_k_class[] = "__class__";
 static const char __pyx_k_error[] = "error";
 static const char __pyx_k_flags[] = "flags";
 static const char __pyx_k_range[] = "range";
 static const char __pyx_k_shape[] = "shape";
 static const char __pyx_k_start[] = "start";
+static const char __pyx_k_y_mat[] = "y_mat";
 static const char __pyx_k_approx[] = "approx";
 static const char __pyx_k_encode[] = "encode";
 static const char __pyx_k_format[] = "format";
@@ -2014,6 +2002,7 @@ static const char __pyx_k_libhaf[] = "libhaf";
 static const char __pyx_k_name_2[] = "__name__";
 static const char __pyx_k_pickle[] = "pickle";
 static const char __pyx_k_reduce[] = "__reduce__";
+static const char __pyx_k_renorm[] = "renorm";
 static const char __pyx_k_struct[] = "struct";
 static const char __pyx_k_unpack[] = "unpack";
 static const char __pyx_k_update[] = "update";
@@ -2037,6 +2026,7 @@ static const char __pyx_k_IndexError[] = "IndexError";
 static const char __pyx_k_ValueError[] = "ValueError";
 static const char __pyx_k_pyx_result[] = "__pyx_result";
 static const char __pyx_k_pyx_vtable[] = "__pyx_vtable__";
+static const char __pyx_k_resolution[] = "resolution";
 static const char __pyx_k_MemoryError[] = "MemoryError";
 static const char __pyx_k_PickleError[] = "PickleError";
 static const char __pyx_k_haf_complex[] = "haf_complex";
@@ -2064,6 +2054,7 @@ static const char __pyx_k_MemoryView_of_r_object[] = "<MemoryView of %r object>"
 static const char __pyx_k_MemoryView_of_r_at_0x_x[] = "<MemoryView of %r at 0x%x>";
 static const char __pyx_k_contiguous_and_indirect[] = "<contiguous and indirect>";
 static const char __pyx_k_Cannot_index_with_type_s[] = "Cannot index with type '%s'";
+static const char __pyx_k_hermite_multidimensional[] = "hermite_multidimensional";
 static const char __pyx_k_Invalid_shape_in_axis_d_d[] = "Invalid shape in axis %d: %d.";
 static const char __pyx_k_itemsize_0_for_cython_array[] = "itemsize <= 0 for cython.array";
 static const char __pyx_k_unable_to_allocate_array_data[] = "unable to allocate array data.";
@@ -2101,6 +2092,7 @@ static PyObject *__pyx_kp_s_MemoryView_of_r_object;
 static PyObject *__pyx_n_b_O;
 static PyObject *__pyx_kp_s_Out_of_bounds_on_buffer_access_a;
 static PyObject *__pyx_n_s_PickleError;
+static PyObject *__pyx_n_s_R_mat;
 static PyObject *__pyx_n_s_TypeError;
 static PyObject *__pyx_kp_s_Unable_to_convert_item_to_object;
 static PyObject *__pyx_n_s_ValueError;
@@ -2133,6 +2125,7 @@ static PyObject *__pyx_n_s_haf_real;
 static PyObject *__pyx_n_s_haf_rpt_complex;
 static PyObject *__pyx_n_s_haf_rpt_real;
 static PyObject *__pyx_kp_s_hafnian_hafnian_pyx;
+static PyObject *__pyx_n_s_hermite_multidimensional;
 static PyObject *__pyx_n_s_i;
 static PyObject *__pyx_n_s_id;
 static PyObject *__pyx_n_s_import;
@@ -2174,6 +2167,9 @@ static PyObject *__pyx_n_s_recursive;
 static PyObject *__pyx_n_s_reduce;
 static PyObject *__pyx_n_s_reduce_cython;
 static PyObject *__pyx_n_s_reduce_ex;
+static PyObject *__pyx_n_s_ren;
+static PyObject *__pyx_n_s_renorm;
+static PyObject *__pyx_n_s_resolution;
 static PyObject *__pyx_n_s_rpt;
 static PyObject *__pyx_n_s_setstate;
 static PyObject *__pyx_n_s_setstate_cython;
@@ -2194,6 +2190,7 @@ static PyObject *__pyx_kp_s_unable_to_allocate_array_data;
 static PyObject *__pyx_kp_s_unable_to_allocate_shape_and_str;
 static PyObject *__pyx_n_s_unpack;
 static PyObject *__pyx_n_s_update;
+static PyObject *__pyx_n_s_y_mat;
 static PyObject *__pyx_pf_6libhaf_torontonian_complex(CYTHON_UNUSED PyObject *__pyx_self, __Pyx_memviewslice __pyx_v_A, PyObject *__pyx_v_fsum); /* proto */
 static PyObject *__pyx_pf_6libhaf_2torontonian_real(CYTHON_UNUSED PyObject *__pyx_self, __Pyx_memviewslice __pyx_v_A, PyObject *__pyx_v_fsum); /* proto */
 static PyObject *__pyx_pf_6libhaf_4haf_rpt_real(CYTHON_UNUSED PyObject *__pyx_self, __Pyx_memviewslice __pyx_v_A, __Pyx_memviewslice __pyx_v_rpt, __Pyx_memviewslice __pyx_v_mu, int __pyx_v_loop); /* proto */
@@ -2203,6 +2200,7 @@ static PyObject *__pyx_pf_6libhaf_10haf_complex(CYTHON_UNUSED PyObject *__pyx_se
 static PyObject *__pyx_pf_6libhaf_12haf_real(CYTHON_UNUSED PyObject *__pyx_self, __Pyx_memviewslice __pyx_v_A, int __pyx_v_loop, int __pyx_v_recursive, PyObject *__pyx_v_quad, int __pyx_v_approx, PyObject *__pyx_v_nsamples); /* proto */
 static PyObject *__pyx_pf_6libhaf_14perm_complex(CYTHON_UNUSED PyObject *__pyx_self, __Pyx_memviewslice __pyx_v_A, PyObject *__pyx_v_quad); /* proto */
 static PyObject *__pyx_pf_6libhaf_16perm_real(CYTHON_UNUSED PyObject *__pyx_self, __Pyx_memviewslice __pyx_v_A, PyObject *__pyx_v_quad, PyObject *__pyx_v_fsum); /* proto */
+static PyObject *__pyx_pf_6libhaf_18hermite_multidimensional(CYTHON_UNUSED PyObject *__pyx_self, __Pyx_memviewslice __pyx_v_A, __Pyx_memviewslice __pyx_v_d, int __pyx_v_resolution, PyObject *__pyx_v_ren); /* proto */
 static int __pyx_array___pyx_pf_15View_dot_MemoryView_5array___cinit__(struct __pyx_array_obj *__pyx_v_self, PyObject *__pyx_v_shape, Py_ssize_t __pyx_v_itemsize, PyObject *__pyx_v_format, PyObject *__pyx_v_mode, int __pyx_v_allocate_buffer); /* proto */
 static int __pyx_array___pyx_pf_15View_dot_MemoryView_5array_2__getbuffer__(struct __pyx_array_obj *__pyx_v_self, Py_buffer *__pyx_v_info, int __pyx_v_flags); /* proto */
 static void __pyx_array___pyx_pf_15View_dot_MemoryView_5array_4__dealloc__(struct __pyx_array_obj *__pyx_v_self); /* proto */
@@ -2284,11 +2282,12 @@ static PyObject *__pyx_tuple__33;
 static PyObject *__pyx_tuple__35;
 static PyObject *__pyx_tuple__37;
 static PyObject *__pyx_tuple__39;
-static PyObject *__pyx_tuple__40;
 static PyObject *__pyx_tuple__41;
 static PyObject *__pyx_tuple__42;
 static PyObject *__pyx_tuple__43;
 static PyObject *__pyx_tuple__44;
+static PyObject *__pyx_tuple__45;
+static PyObject *__pyx_tuple__46;
 static PyObject *__pyx_codeobj__22;
 static PyObject *__pyx_codeobj__24;
 static PyObject *__pyx_codeobj__26;
@@ -2298,10 +2297,11 @@ static PyObject *__pyx_codeobj__32;
 static PyObject *__pyx_codeobj__34;
 static PyObject *__pyx_codeobj__36;
 static PyObject *__pyx_codeobj__38;
-static PyObject *__pyx_codeobj__45;
+static PyObject *__pyx_codeobj__40;
+static PyObject *__pyx_codeobj__47;
 /* Late includes */
 
-/* "hafnian/hafnian.pyx":54
+/* "hafnian/hafnian.pyx":56
  * 
  * 
  * def torontonian_complex(double complex[:, :] A, fsum=False):             # <<<<<<<<<<<<<<
@@ -2347,7 +2347,7 @@ static PyObject *__pyx_pw_6libhaf_1torontonian_complex(PyObject *__pyx_self, PyO
         }
       }
       if (unlikely(kw_args > 0)) {
-        if (unlikely(__Pyx_ParseOptionalKeywords(__pyx_kwds, __pyx_pyargnames, 0, values, pos_args, "torontonian_complex") < 0)) __PYX_ERR(0, 54, __pyx_L3_error)
+        if (unlikely(__Pyx_ParseOptionalKeywords(__pyx_kwds, __pyx_pyargnames, 0, values, pos_args, "torontonian_complex") < 0)) __PYX_ERR(0, 56, __pyx_L3_error)
       }
     } else {
       switch (PyTuple_GET_SIZE(__pyx_args)) {
@@ -2358,12 +2358,12 @@ static PyObject *__pyx_pw_6libhaf_1torontonian_complex(PyObject *__pyx_self, PyO
         default: goto __pyx_L5_argtuple_error;
       }
     }
-    __pyx_v_A = __Pyx_PyObject_to_MemoryviewSlice_dsds___pyx_t_double_complex(values[0], PyBUF_WRITABLE); if (unlikely(!__pyx_v_A.memview)) __PYX_ERR(0, 54, __pyx_L3_error)
+    __pyx_v_A = __Pyx_PyObject_to_MemoryviewSlice_dsds___pyx_t_double_complex(values[0], PyBUF_WRITABLE); if (unlikely(!__pyx_v_A.memview)) __PYX_ERR(0, 56, __pyx_L3_error)
     __pyx_v_fsum = values[1];
   }
   goto __pyx_L4_argument_unpacking_done;
   __pyx_L5_argtuple_error:;
-  __Pyx_RaiseArgtupleInvalid("torontonian_complex", 0, 1, 2, PyTuple_GET_SIZE(__pyx_args)); __PYX_ERR(0, 54, __pyx_L3_error)
+  __Pyx_RaiseArgtupleInvalid("torontonian_complex", 0, 1, 2, PyTuple_GET_SIZE(__pyx_args)); __PYX_ERR(0, 56, __pyx_L3_error)
   __pyx_L3_error:;
   __Pyx_AddTraceback("libhaf.torontonian_complex", __pyx_clineno, __pyx_lineno, __pyx_filename);
   __Pyx_RefNannyFinishContext();
@@ -2397,7 +2397,7 @@ static PyObject *__pyx_pf_6libhaf_torontonian_complex(CYTHON_UNUSED PyObject *__
   __pyx_t_double_complex __pyx_t_11;
   __Pyx_RefNannySetupContext("torontonian_complex", 0);
 
-  /* "hafnian/hafnian.pyx":72
+  /* "hafnian/hafnian.pyx":74
  *         np.complex128: the torontonian of matrix A
  *     """
  *     cdef int i, j, n = A.shape[0]             # <<<<<<<<<<<<<<
@@ -2406,7 +2406,7 @@ static PyObject *__pyx_pf_6libhaf_torontonian_complex(CYTHON_UNUSED PyObject *__
  */
   __pyx_v_n = (__pyx_v_A.shape[0]);
 
-  /* "hafnian/hafnian.pyx":74
+  /* "hafnian/hafnian.pyx":76
  *     cdef int i, j, n = A.shape[0]
  *     cdef vector[double complex] mat
  *     cdef int m = n/2             # <<<<<<<<<<<<<<
@@ -2415,7 +2415,7 @@ static PyObject *__pyx_pf_6libhaf_torontonian_complex(CYTHON_UNUSED PyObject *__
  */
   __pyx_v_m = __Pyx_div_long(__pyx_v_n, 2);
 
-  /* "hafnian/hafnian.pyx":76
+  /* "hafnian/hafnian.pyx":78
  *     cdef int m = n/2
  * 
  *     for i in range(n):             # <<<<<<<<<<<<<<
@@ -2427,7 +2427,7 @@ static PyObject *__pyx_pf_6libhaf_torontonian_complex(CYTHON_UNUSED PyObject *__
   for (__pyx_t_3 = 0; __pyx_t_3 < __pyx_t_2; __pyx_t_3+=1) {
     __pyx_v_i = __pyx_t_3;
 
-    /* "hafnian/hafnian.pyx":77
+    /* "hafnian/hafnian.pyx":79
  * 
  *     for i in range(n):
  *         for j in range(n):             # <<<<<<<<<<<<<<
@@ -2439,7 +2439,7 @@ static PyObject *__pyx_pf_6libhaf_torontonian_complex(CYTHON_UNUSED PyObject *__
     for (__pyx_t_6 = 0; __pyx_t_6 < __pyx_t_5; __pyx_t_6+=1) {
       __pyx_v_j = __pyx_t_6;
 
-      /* "hafnian/hafnian.pyx":78
+      /* "hafnian/hafnian.pyx":80
  *     for i in range(n):
  *         for j in range(n):
  *             mat.push_back(A[i, j])             # <<<<<<<<<<<<<<
@@ -2452,22 +2452,22 @@ static PyObject *__pyx_pf_6libhaf_torontonian_complex(CYTHON_UNUSED PyObject *__
         __pyx_v_mat.push_back((*((__pyx_t_double_complex *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_A.data + __pyx_t_7 * __pyx_v_A.strides[0]) ) + __pyx_t_8 * __pyx_v_A.strides[1]) ))));
       } catch(...) {
         __Pyx_CppExn2PyErr();
-        __PYX_ERR(0, 78, __pyx_L1_error)
+        __PYX_ERR(0, 80, __pyx_L1_error)
       }
     }
   }
 
-  /* "hafnian/hafnian.pyx":80
+  /* "hafnian/hafnian.pyx":82
  *             mat.push_back(A[i, j])
  * 
  *     if fsum:             # <<<<<<<<<<<<<<
  *         return torontonian_fsum(mat)
  * 
  */
-  __pyx_t_9 = __Pyx_PyObject_IsTrue(__pyx_v_fsum); if (unlikely(__pyx_t_9 < 0)) __PYX_ERR(0, 80, __pyx_L1_error)
+  __pyx_t_9 = __Pyx_PyObject_IsTrue(__pyx_v_fsum); if (unlikely(__pyx_t_9 < 0)) __PYX_ERR(0, 82, __pyx_L1_error)
   if (__pyx_t_9) {
 
-    /* "hafnian/hafnian.pyx":81
+    /* "hafnian/hafnian.pyx":83
  * 
  *     if fsum:
  *         return torontonian_fsum(mat)             # <<<<<<<<<<<<<<
@@ -2475,13 +2475,13 @@ static PyObject *__pyx_pf_6libhaf_torontonian_complex(CYTHON_UNUSED PyObject *__
  *     return torontonian_quad(mat)
  */
     __Pyx_XDECREF(__pyx_r);
-    __pyx_t_10 = PyFloat_FromDouble(hafnian::torontonian_fsum<__pyx_t_double_complex>(__pyx_v_mat)); if (unlikely(!__pyx_t_10)) __PYX_ERR(0, 81, __pyx_L1_error)
+    __pyx_t_10 = PyFloat_FromDouble(hafnian::torontonian_fsum<__pyx_t_double_complex>(__pyx_v_mat)); if (unlikely(!__pyx_t_10)) __PYX_ERR(0, 83, __pyx_L1_error)
     __Pyx_GOTREF(__pyx_t_10);
     __pyx_r = __pyx_t_10;
     __pyx_t_10 = 0;
     goto __pyx_L0;
 
-    /* "hafnian/hafnian.pyx":80
+    /* "hafnian/hafnian.pyx":82
  *             mat.push_back(A[i, j])
  * 
  *     if fsum:             # <<<<<<<<<<<<<<
@@ -2490,7 +2490,7 @@ static PyObject *__pyx_pf_6libhaf_torontonian_complex(CYTHON_UNUSED PyObject *__
  */
   }
 
-  /* "hafnian/hafnian.pyx":83
+  /* "hafnian/hafnian.pyx":85
  *         return torontonian_fsum(mat)
  * 
  *     return torontonian_quad(mat)             # <<<<<<<<<<<<<<
@@ -2499,13 +2499,13 @@ static PyObject *__pyx_pf_6libhaf_torontonian_complex(CYTHON_UNUSED PyObject *__
  */
   __Pyx_XDECREF(__pyx_r);
   __pyx_t_11 = hafnian::torontonian_quad(__pyx_v_mat);
-  __pyx_t_10 = __pyx_PyComplex_FromComplex(__pyx_t_11); if (unlikely(!__pyx_t_10)) __PYX_ERR(0, 83, __pyx_L1_error)
+  __pyx_t_10 = __pyx_PyComplex_FromComplex(__pyx_t_11); if (unlikely(!__pyx_t_10)) __PYX_ERR(0, 85, __pyx_L1_error)
   __Pyx_GOTREF(__pyx_t_10);
   __pyx_r = __pyx_t_10;
   __pyx_t_10 = 0;
   goto __pyx_L0;
 
-  /* "hafnian/hafnian.pyx":54
+  /* "hafnian/hafnian.pyx":56
  * 
  * 
  * def torontonian_complex(double complex[:, :] A, fsum=False):             # <<<<<<<<<<<<<<
@@ -2525,7 +2525,7 @@ static PyObject *__pyx_pf_6libhaf_torontonian_complex(CYTHON_UNUSED PyObject *__
   return __pyx_r;
 }
 
-/* "hafnian/hafnian.pyx":86
+/* "hafnian/hafnian.pyx":88
  * 
  * 
  * def torontonian_real(double[:, :] A, fsum=False):             # <<<<<<<<<<<<<<
@@ -2571,7 +2571,7 @@ static PyObject *__pyx_pw_6libhaf_3torontonian_real(PyObject *__pyx_self, PyObje
         }
       }
       if (unlikely(kw_args > 0)) {
-        if (unlikely(__Pyx_ParseOptionalKeywords(__pyx_kwds, __pyx_pyargnames, 0, values, pos_args, "torontonian_real") < 0)) __PYX_ERR(0, 86, __pyx_L3_error)
+        if (unlikely(__Pyx_ParseOptionalKeywords(__pyx_kwds, __pyx_pyargnames, 0, values, pos_args, "torontonian_real") < 0)) __PYX_ERR(0, 88, __pyx_L3_error)
       }
     } else {
       switch (PyTuple_GET_SIZE(__pyx_args)) {
@@ -2582,12 +2582,12 @@ static PyObject *__pyx_pw_6libhaf_3torontonian_real(PyObject *__pyx_self, PyObje
         default: goto __pyx_L5_argtuple_error;
       }
     }
-    __pyx_v_A = __Pyx_PyObject_to_MemoryviewSlice_dsds_double(values[0], PyBUF_WRITABLE); if (unlikely(!__pyx_v_A.memview)) __PYX_ERR(0, 86, __pyx_L3_error)
+    __pyx_v_A = __Pyx_PyObject_to_MemoryviewSlice_dsds_double(values[0], PyBUF_WRITABLE); if (unlikely(!__pyx_v_A.memview)) __PYX_ERR(0, 88, __pyx_L3_error)
     __pyx_v_fsum = values[1];
   }
   goto __pyx_L4_argument_unpacking_done;
   __pyx_L5_argtuple_error:;
-  __Pyx_RaiseArgtupleInvalid("torontonian_real", 0, 1, 2, PyTuple_GET_SIZE(__pyx_args)); __PYX_ERR(0, 86, __pyx_L3_error)
+  __Pyx_RaiseArgtupleInvalid("torontonian_real", 0, 1, 2, PyTuple_GET_SIZE(__pyx_args)); __PYX_ERR(0, 88, __pyx_L3_error)
   __pyx_L3_error:;
   __Pyx_AddTraceback("libhaf.torontonian_real", __pyx_clineno, __pyx_lineno, __pyx_filename);
   __Pyx_RefNannyFinishContext();
@@ -2620,7 +2620,7 @@ static PyObject *__pyx_pf_6libhaf_2torontonian_real(CYTHON_UNUSED PyObject *__py
   PyObject *__pyx_t_10 = NULL;
   __Pyx_RefNannySetupContext("torontonian_real", 0);
 
-  /* "hafnian/hafnian.pyx":104
+  /* "hafnian/hafnian.pyx":106
  *         np.float64: the torontonian of matrix A
  *     """
  *     cdef int i, j, n = A.shape[0]             # <<<<<<<<<<<<<<
@@ -2629,7 +2629,7 @@ static PyObject *__pyx_pf_6libhaf_2torontonian_real(CYTHON_UNUSED PyObject *__py
  */
   __pyx_v_n = (__pyx_v_A.shape[0]);
 
-  /* "hafnian/hafnian.pyx":106
+  /* "hafnian/hafnian.pyx":108
  *     cdef int i, j, n = A.shape[0]
  *     cdef vector[double] mat
  *     cdef int m = n/2             # <<<<<<<<<<<<<<
@@ -2638,7 +2638,7 @@ static PyObject *__pyx_pf_6libhaf_2torontonian_real(CYTHON_UNUSED PyObject *__py
  */
   __pyx_v_m = __Pyx_div_long(__pyx_v_n, 2);
 
-  /* "hafnian/hafnian.pyx":108
+  /* "hafnian/hafnian.pyx":110
  *     cdef int m = n/2
  * 
  *     for i in range(n):             # <<<<<<<<<<<<<<
@@ -2650,7 +2650,7 @@ static PyObject *__pyx_pf_6libhaf_2torontonian_real(CYTHON_UNUSED PyObject *__py
   for (__pyx_t_3 = 0; __pyx_t_3 < __pyx_t_2; __pyx_t_3+=1) {
     __pyx_v_i = __pyx_t_3;
 
-    /* "hafnian/hafnian.pyx":109
+    /* "hafnian/hafnian.pyx":111
  * 
  *     for i in range(n):
  *         for j in range(n):             # <<<<<<<<<<<<<<
@@ -2662,7 +2662,7 @@ static PyObject *__pyx_pf_6libhaf_2torontonian_real(CYTHON_UNUSED PyObject *__py
     for (__pyx_t_6 = 0; __pyx_t_6 < __pyx_t_5; __pyx_t_6+=1) {
       __pyx_v_j = __pyx_t_6;
 
-      /* "hafnian/hafnian.pyx":110
+      /* "hafnian/hafnian.pyx":112
  *     for i in range(n):
  *         for j in range(n):
  *             mat.push_back(A[i, j])             # <<<<<<<<<<<<<<
@@ -2675,22 +2675,22 @@ static PyObject *__pyx_pf_6libhaf_2torontonian_real(CYTHON_UNUSED PyObject *__py
         __pyx_v_mat.push_back((*((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_A.data + __pyx_t_7 * __pyx_v_A.strides[0]) ) + __pyx_t_8 * __pyx_v_A.strides[1]) ))));
       } catch(...) {
         __Pyx_CppExn2PyErr();
-        __PYX_ERR(0, 110, __pyx_L1_error)
+        __PYX_ERR(0, 112, __pyx_L1_error)
       }
     }
   }
 
-  /* "hafnian/hafnian.pyx":113
+  /* "hafnian/hafnian.pyx":115
  * 
  * 
  *     if fsum:             # <<<<<<<<<<<<<<
  *         return torontonian_fsum(mat)
  * 
  */
-  __pyx_t_9 = __Pyx_PyObject_IsTrue(__pyx_v_fsum); if (unlikely(__pyx_t_9 < 0)) __PYX_ERR(0, 113, __pyx_L1_error)
+  __pyx_t_9 = __Pyx_PyObject_IsTrue(__pyx_v_fsum); if (unlikely(__pyx_t_9 < 0)) __PYX_ERR(0, 115, __pyx_L1_error)
   if (__pyx_t_9) {
 
-    /* "hafnian/hafnian.pyx":114
+    /* "hafnian/hafnian.pyx":116
  * 
  *     if fsum:
  *         return torontonian_fsum(mat)             # <<<<<<<<<<<<<<
@@ -2698,13 +2698,13 @@ static PyObject *__pyx_pf_6libhaf_2torontonian_real(CYTHON_UNUSED PyObject *__py
  *     return torontonian_quad(mat)
  */
     __Pyx_XDECREF(__pyx_r);
-    __pyx_t_10 = PyFloat_FromDouble(hafnian::torontonian_fsum<double>(__pyx_v_mat)); if (unlikely(!__pyx_t_10)) __PYX_ERR(0, 114, __pyx_L1_error)
+    __pyx_t_10 = PyFloat_FromDouble(hafnian::torontonian_fsum<double>(__pyx_v_mat)); if (unlikely(!__pyx_t_10)) __PYX_ERR(0, 116, __pyx_L1_error)
     __Pyx_GOTREF(__pyx_t_10);
     __pyx_r = __pyx_t_10;
     __pyx_t_10 = 0;
     goto __pyx_L0;
 
-    /* "hafnian/hafnian.pyx":113
+    /* "hafnian/hafnian.pyx":115
  * 
  * 
  *     if fsum:             # <<<<<<<<<<<<<<
@@ -2713,7 +2713,7 @@ static PyObject *__pyx_pf_6libhaf_2torontonian_real(CYTHON_UNUSED PyObject *__py
  */
   }
 
-  /* "hafnian/hafnian.pyx":116
+  /* "hafnian/hafnian.pyx":118
  *         return torontonian_fsum(mat)
  * 
  *     return torontonian_quad(mat)             # <<<<<<<<<<<<<<
@@ -2721,13 +2721,13 @@ static PyObject *__pyx_pf_6libhaf_2torontonian_real(CYTHON_UNUSED PyObject *__py
  * 
  */
   __Pyx_XDECREF(__pyx_r);
-  __pyx_t_10 = PyFloat_FromDouble(hafnian::torontonian_quad(__pyx_v_mat)); if (unlikely(!__pyx_t_10)) __PYX_ERR(0, 116, __pyx_L1_error)
+  __pyx_t_10 = PyFloat_FromDouble(hafnian::torontonian_quad(__pyx_v_mat)); if (unlikely(!__pyx_t_10)) __PYX_ERR(0, 118, __pyx_L1_error)
   __Pyx_GOTREF(__pyx_t_10);
   __pyx_r = __pyx_t_10;
   __pyx_t_10 = 0;
   goto __pyx_L0;
 
-  /* "hafnian/hafnian.pyx":86
+  /* "hafnian/hafnian.pyx":88
  * 
  * 
  * def torontonian_real(double[:, :] A, fsum=False):             # <<<<<<<<<<<<<<
@@ -2747,7 +2747,7 @@ static PyObject *__pyx_pf_6libhaf_2torontonian_real(CYTHON_UNUSED PyObject *__py
   return __pyx_r;
 }
 
-/* "hafnian/hafnian.pyx":123
+/* "hafnian/hafnian.pyx":125
  * 
  * 
  * def haf_rpt_real(double[:, :] A, int[:] rpt, double[:] mu=None, bint loop=False):             # <<<<<<<<<<<<<<
@@ -2794,7 +2794,7 @@ static PyObject *__pyx_pw_6libhaf_5haf_rpt_real(PyObject *__pyx_self, PyObject *
         case  1:
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         else {
-          __Pyx_RaiseArgtupleInvalid("haf_rpt_real", 0, 2, 4, 1); __PYX_ERR(0, 123, __pyx_L3_error)
+          __Pyx_RaiseArgtupleInvalid("haf_rpt_real", 0, 2, 4, 1); __PYX_ERR(0, 125, __pyx_L3_error)
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@@ -2810,7 +2810,7 @@ static PyObject *__pyx_pw_6libhaf_5haf_rpt_real(PyObject *__pyx_self, PyObject *
         }
       }
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-        if (unlikely(__Pyx_ParseOptionalKeywords(__pyx_kwds, __pyx_pyargnames, 0, values, pos_args, "haf_rpt_real") < 0)) __PYX_ERR(0, 123, __pyx_L3_error)
+        if (unlikely(__Pyx_ParseOptionalKeywords(__pyx_kwds, __pyx_pyargnames, 0, values, pos_args, "haf_rpt_real") < 0)) __PYX_ERR(0, 125, __pyx_L3_error)
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@@ -2824,23 +2824,23 @@ static PyObject *__pyx_pw_6libhaf_5haf_rpt_real(PyObject *__pyx_self, PyObject *
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+    __pyx_v_A = __Pyx_PyObject_to_MemoryviewSlice_dsds_double(values[0], PyBUF_WRITABLE); if (unlikely(!__pyx_v_A.memview)) __PYX_ERR(0, 125, __pyx_L3_error)
+    __pyx_v_rpt = __Pyx_PyObject_to_MemoryviewSlice_ds_int(values[1], PyBUF_WRITABLE); if (unlikely(!__pyx_v_rpt.memview)) __PYX_ERR(0, 125, __pyx_L3_error)
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+      __pyx_v_mu = __Pyx_PyObject_to_MemoryviewSlice_ds_double(values[2], PyBUF_WRITABLE); if (unlikely(!__pyx_v_mu.memview)) __PYX_ERR(0, 125, __pyx_L3_error)
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   goto __pyx_L4_argument_unpacking_done;
   __pyx_L5_argtuple_error:;
-  __Pyx_RaiseArgtupleInvalid("haf_rpt_real", 0, 2, 4, PyTuple_GET_SIZE(__pyx_args)); __PYX_ERR(0, 123, __pyx_L3_error)
+  __Pyx_RaiseArgtupleInvalid("haf_rpt_real", 0, 2, 4, PyTuple_GET_SIZE(__pyx_args)); __PYX_ERR(0, 125, __pyx_L3_error)
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@@ -2878,7 +2878,7 @@ static PyObject *__pyx_pf_6libhaf_4haf_rpt_real(CYTHON_UNUSED PyObject *__pyx_se
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   __Pyx_RefNannySetupContext("haf_rpt_real", 0);
 
-  /* "hafnian/hafnian.pyx":140
+  /* "hafnian/hafnian.pyx":142
  *         np.float64: the hafnian
  *     """
  *     cdef int i, j, n = A.shape[0]             # <<<<<<<<<<<<<<
@@ -2887,7 +2887,7 @@ static PyObject *__pyx_pf_6libhaf_4haf_rpt_real(CYTHON_UNUSED PyObject *__pyx_se
  */
   __pyx_v_n = (__pyx_v_A.shape[0]);
 
-  /* "hafnian/hafnian.pyx":144
+  /* "hafnian/hafnian.pyx":146
  *     cdef vector[double] mat, d
  * 
  *     for i in range(n):             # <<<<<<<<<<<<<<
@@ -2899,7 +2899,7 @@ static PyObject *__pyx_pf_6libhaf_4haf_rpt_real(CYTHON_UNUSED PyObject *__pyx_se
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     __pyx_v_i = __pyx_t_3;
 
-    /* "hafnian/hafnian.pyx":145
+    /* "hafnian/hafnian.pyx":147
  * 
  *     for i in range(n):
  *         nud.push_back(rpt[i])             # <<<<<<<<<<<<<<
@@ -2911,10 +2911,10 @@ static PyObject *__pyx_pf_6libhaf_4haf_rpt_real(CYTHON_UNUSED PyObject *__pyx_se
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       __Pyx_CppExn2PyErr();
-      __PYX_ERR(0, 145, __pyx_L1_error)
+      __PYX_ERR(0, 147, __pyx_L1_error)
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-    /* "hafnian/hafnian.pyx":147
+    /* "hafnian/hafnian.pyx":149
  *         nud.push_back(rpt[i])
  * 
  *         if mu is None:             # <<<<<<<<<<<<<<
@@ -2924,7 +2924,7 @@ static PyObject *__pyx_pf_6libhaf_4haf_rpt_real(CYTHON_UNUSED PyObject *__pyx_se
     __pyx_t_5 = ((((PyObject *) __pyx_v_mu.memview) == Py_None) != 0);
     if (__pyx_t_5) {
 
-      /* "hafnian/hafnian.pyx":148
+      /* "hafnian/hafnian.pyx":150
  * 
  *         if mu is None:
  *             d.push_back(A[i, i])             # <<<<<<<<<<<<<<
@@ -2937,10 +2937,10 @@ static PyObject *__pyx_pf_6libhaf_4haf_rpt_real(CYTHON_UNUSED PyObject *__pyx_se
         __pyx_v_d.push_back((*((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_A.data + __pyx_t_6 * __pyx_v_A.strides[0]) ) + __pyx_t_7 * __pyx_v_A.strides[1]) ))));
       } catch(...) {
         __Pyx_CppExn2PyErr();
-        __PYX_ERR(0, 148, __pyx_L1_error)
+        __PYX_ERR(0, 150, __pyx_L1_error)
       }
 
-      /* "hafnian/hafnian.pyx":147
+      /* "hafnian/hafnian.pyx":149
  *         nud.push_back(rpt[i])
  * 
  *         if mu is None:             # <<<<<<<<<<<<<<
@@ -2950,7 +2950,7 @@ static PyObject *__pyx_pf_6libhaf_4haf_rpt_real(CYTHON_UNUSED PyObject *__pyx_se
       goto __pyx_L5;
     }
 
-    /* "hafnian/hafnian.pyx":150
+    /* "hafnian/hafnian.pyx":152
  *             d.push_back(A[i, i])
  *         else:
  *             d.push_back(mu[i])             # <<<<<<<<<<<<<<
@@ -2963,12 +2963,12 @@ static PyObject *__pyx_pf_6libhaf_4haf_rpt_real(CYTHON_UNUSED PyObject *__pyx_se
         __pyx_v_d.push_back((*((double *) ( /* dim=0 */ (__pyx_v_mu.data + __pyx_t_8 * __pyx_v_mu.strides[0]) ))));
       } catch(...) {
         __Pyx_CppExn2PyErr();
-        __PYX_ERR(0, 150, __pyx_L1_error)
+        __PYX_ERR(0, 152, __pyx_L1_error)
       }
     }
     __pyx_L5:;
 
-    /* "hafnian/hafnian.pyx":152
+    /* "hafnian/hafnian.pyx":154
  *             d.push_back(mu[i])
  * 
  *         for j in range(n):             # <<<<<<<<<<<<<<
@@ -2980,7 +2980,7 @@ static PyObject *__pyx_pf_6libhaf_4haf_rpt_real(CYTHON_UNUSED PyObject *__pyx_se
     for (__pyx_t_11 = 0; __pyx_t_11 < __pyx_t_10; __pyx_t_11+=1) {
       __pyx_v_j = __pyx_t_11;
 
-      /* "hafnian/hafnian.pyx":153
+      /* "hafnian/hafnian.pyx":155
  * 
  *         for j in range(n):
  *             mat.push_back(A[i, j])             # <<<<<<<<<<<<<<
@@ -2993,12 +2993,12 @@ static PyObject *__pyx_pf_6libhaf_4haf_rpt_real(CYTHON_UNUSED PyObject *__pyx_se
         __pyx_v_mat.push_back((*((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_A.data + __pyx_t_12 * __pyx_v_A.strides[0]) ) + __pyx_t_13 * __pyx_v_A.strides[1]) ))));
       } catch(...) {
         __Pyx_CppExn2PyErr();
-        __PYX_ERR(0, 153, __pyx_L1_error)
+        __PYX_ERR(0, 155, __pyx_L1_error)
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   }
 
-  /* "hafnian/hafnian.pyx":156
+  /* "hafnian/hafnian.pyx":158
  * 
  *     # Exposes a c function to python
  *     if loop:             # <<<<<<<<<<<<<<
@@ -3008,7 +3008,7 @@ static PyObject *__pyx_pf_6libhaf_4haf_rpt_real(CYTHON_UNUSED PyObject *__pyx_se
   __pyx_t_5 = (__pyx_v_loop != 0);
   if (__pyx_t_5) {
 
-    /* "hafnian/hafnian.pyx":157
+    /* "hafnian/hafnian.pyx":159
  *     # Exposes a c function to python
  *     if loop:
  *         return loop_hafnian_rpt_quad(mat, d, nud)             # <<<<<<<<<<<<<<
@@ -3016,13 +3016,13 @@ static PyObject *__pyx_pf_6libhaf_4haf_rpt_real(CYTHON_UNUSED PyObject *__pyx_se
  *     return hafnian_rpt_quad(mat, nud)
  */
     __Pyx_XDECREF(__pyx_r);
-    __pyx_t_14 = PyFloat_FromDouble(hafnian::loop_hafnian_rpt_quad(__pyx_v_mat, __pyx_v_d, __pyx_v_nud)); if (unlikely(!__pyx_t_14)) __PYX_ERR(0, 157, __pyx_L1_error)
+    __pyx_t_14 = PyFloat_FromDouble(hafnian::loop_hafnian_rpt_quad(__pyx_v_mat, __pyx_v_d, __pyx_v_nud)); if (unlikely(!__pyx_t_14)) __PYX_ERR(0, 159, __pyx_L1_error)
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     __pyx_t_14 = 0;
     goto __pyx_L0;
 
-    /* "hafnian/hafnian.pyx":156
+    /* "hafnian/hafnian.pyx":158
  * 
  *     # Exposes a c function to python
  *     if loop:             # <<<<<<<<<<<<<<
@@ -3031,7 +3031,7 @@ static PyObject *__pyx_pf_6libhaf_4haf_rpt_real(CYTHON_UNUSED PyObject *__pyx_se
  */
   }
 
-  /* "hafnian/hafnian.pyx":159
+  /* "hafnian/hafnian.pyx":161
  *         return loop_hafnian_rpt_quad(mat, d, nud)
  * 
  *     return hafnian_rpt_quad(mat, nud)             # <<<<<<<<<<<<<<
@@ -3039,13 +3039,13 @@ static PyObject *__pyx_pf_6libhaf_4haf_rpt_real(CYTHON_UNUSED PyObject *__pyx_se
  * 
  */
   __Pyx_XDECREF(__pyx_r);
-  __pyx_t_14 = PyFloat_FromDouble(hafnian::hafnian_rpt_quad(__pyx_v_mat, __pyx_v_nud)); if (unlikely(!__pyx_t_14)) __PYX_ERR(0, 159, __pyx_L1_error)
+  __pyx_t_14 = PyFloat_FromDouble(hafnian::hafnian_rpt_quad(__pyx_v_mat, __pyx_v_nud)); if (unlikely(!__pyx_t_14)) __PYX_ERR(0, 161, __pyx_L1_error)
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   __pyx_r = __pyx_t_14;
   __pyx_t_14 = 0;
   goto __pyx_L0;
 
-  /* "hafnian/hafnian.pyx":123
+  /* "hafnian/hafnian.pyx":125
  * 
  * 
  * def haf_rpt_real(double[:, :] A, int[:] rpt, double[:] mu=None, bint loop=False):             # <<<<<<<<<<<<<<
@@ -3067,7 +3067,7 @@ static PyObject *__pyx_pf_6libhaf_4haf_rpt_real(CYTHON_UNUSED PyObject *__pyx_se
   return __pyx_r;
 }
 
-/* "hafnian/hafnian.pyx":162
+/* "hafnian/hafnian.pyx":164
  * 
  * 
  * def haf_rpt_complex(double complex[:, :] A, int[:] rpt, double complex[:] mu=None, bint loop=False):             # <<<<<<<<<<<<<<
@@ -3114,7 +3114,7 @@ static PyObject *__pyx_pw_6libhaf_7haf_rpt_complex(PyObject *__pyx_self, PyObjec
         case  1:
         if (likely((values[1] = __Pyx_PyDict_GetItemStr(__pyx_kwds, __pyx_n_s_rpt)) != 0)) kw_args--;
         else {
-          __Pyx_RaiseArgtupleInvalid("haf_rpt_complex", 0, 2, 4, 1); __PYX_ERR(0, 162, __pyx_L3_error)
+          __Pyx_RaiseArgtupleInvalid("haf_rpt_complex", 0, 2, 4, 1); __PYX_ERR(0, 164, __pyx_L3_error)
         }
         CYTHON_FALLTHROUGH;
         case  2:
@@ -3130,7 +3130,7 @@ static PyObject *__pyx_pw_6libhaf_7haf_rpt_complex(PyObject *__pyx_self, PyObjec
         }
       }
       if (unlikely(kw_args > 0)) {
-        if (unlikely(__Pyx_ParseOptionalKeywords(__pyx_kwds, __pyx_pyargnames, 0, values, pos_args, "haf_rpt_complex") < 0)) __PYX_ERR(0, 162, __pyx_L3_error)
+        if (unlikely(__Pyx_ParseOptionalKeywords(__pyx_kwds, __pyx_pyargnames, 0, values, pos_args, "haf_rpt_complex") < 0)) __PYX_ERR(0, 164, __pyx_L3_error)
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       switch (PyTuple_GET_SIZE(__pyx_args)) {
@@ -3144,23 +3144,23 @@ static PyObject *__pyx_pw_6libhaf_7haf_rpt_complex(PyObject *__pyx_self, PyObjec
         default: goto __pyx_L5_argtuple_error;
       }
     }
-    __pyx_v_A = __Pyx_PyObject_to_MemoryviewSlice_dsds___pyx_t_double_complex(values[0], PyBUF_WRITABLE); if (unlikely(!__pyx_v_A.memview)) __PYX_ERR(0, 162, __pyx_L3_error)
-    __pyx_v_rpt = __Pyx_PyObject_to_MemoryviewSlice_ds_int(values[1], PyBUF_WRITABLE); if (unlikely(!__pyx_v_rpt.memview)) __PYX_ERR(0, 162, __pyx_L3_error)
+    __pyx_v_A = __Pyx_PyObject_to_MemoryviewSlice_dsds___pyx_t_double_complex(values[0], PyBUF_WRITABLE); if (unlikely(!__pyx_v_A.memview)) __PYX_ERR(0, 164, __pyx_L3_error)
+    __pyx_v_rpt = __Pyx_PyObject_to_MemoryviewSlice_ds_int(values[1], PyBUF_WRITABLE); if (unlikely(!__pyx_v_rpt.memview)) __PYX_ERR(0, 164, __pyx_L3_error)
     if (values[2]) {
-      __pyx_v_mu = __Pyx_PyObject_to_MemoryviewSlice_ds___pyx_t_double_complex(values[2], PyBUF_WRITABLE); if (unlikely(!__pyx_v_mu.memview)) __PYX_ERR(0, 162, __pyx_L3_error)
+      __pyx_v_mu = __Pyx_PyObject_to_MemoryviewSlice_ds___pyx_t_double_complex(values[2], PyBUF_WRITABLE); if (unlikely(!__pyx_v_mu.memview)) __PYX_ERR(0, 164, __pyx_L3_error)
     } else {
       __pyx_v_mu = __pyx_k__2;
       __PYX_INC_MEMVIEW(&__pyx_v_mu, 1);
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     if (values[3]) {
-      __pyx_v_loop = __Pyx_PyObject_IsTrue(values[3]); if (unlikely((__pyx_v_loop == (int)-1) && PyErr_Occurred())) __PYX_ERR(0, 162, __pyx_L3_error)
+      __pyx_v_loop = __Pyx_PyObject_IsTrue(values[3]); if (unlikely((__pyx_v_loop == (int)-1) && PyErr_Occurred())) __PYX_ERR(0, 164, __pyx_L3_error)
     } else {
       __pyx_v_loop = ((int)0);
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   goto __pyx_L4_argument_unpacking_done;
   __pyx_L5_argtuple_error:;
-  __Pyx_RaiseArgtupleInvalid("haf_rpt_complex", 0, 2, 4, PyTuple_GET_SIZE(__pyx_args)); __PYX_ERR(0, 162, __pyx_L3_error)
+  __Pyx_RaiseArgtupleInvalid("haf_rpt_complex", 0, 2, 4, PyTuple_GET_SIZE(__pyx_args)); __PYX_ERR(0, 164, __pyx_L3_error)
   __pyx_L3_error:;
   __Pyx_AddTraceback("libhaf.haf_rpt_complex", __pyx_clineno, __pyx_lineno, __pyx_filename);
   __Pyx_RefNannyFinishContext();
@@ -3199,7 +3199,7 @@ static PyObject *__pyx_pf_6libhaf_6haf_rpt_complex(CYTHON_UNUSED PyObject *__pyx
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   __Pyx_RefNannySetupContext("haf_rpt_complex", 0);
 
-  /* "hafnian/hafnian.pyx":179
+  /* "hafnian/hafnian.pyx":181
  *         np.complex128: the hafnian
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  *     cdef int i, j, n = A.shape[0]             # <<<<<<<<<<<<<<
@@ -3208,7 +3208,7 @@ static PyObject *__pyx_pf_6libhaf_6haf_rpt_complex(CYTHON_UNUSED PyObject *__pyx
  */
   __pyx_v_n = (__pyx_v_A.shape[0]);
 
-  /* "hafnian/hafnian.pyx":183
+  /* "hafnian/hafnian.pyx":185
  *     cdef vector[double complex] mat, d
  * 
  *     for i in range(n):             # <<<<<<<<<<<<<<
@@ -3220,7 +3220,7 @@ static PyObject *__pyx_pf_6libhaf_6haf_rpt_complex(CYTHON_UNUSED PyObject *__pyx
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     __pyx_v_i = __pyx_t_3;
 
-    /* "hafnian/hafnian.pyx":184
+    /* "hafnian/hafnian.pyx":186
  * 
  *     for i in range(n):
  *         nud.push_back(rpt[i])             # <<<<<<<<<<<<<<
@@ -3232,10 +3232,10 @@ static PyObject *__pyx_pf_6libhaf_6haf_rpt_complex(CYTHON_UNUSED PyObject *__pyx
       __pyx_v_nud.push_back((*((int *) ( /* dim=0 */ (__pyx_v_rpt.data + __pyx_t_4 * __pyx_v_rpt.strides[0]) ))));
     } catch(...) {
       __Pyx_CppExn2PyErr();
-      __PYX_ERR(0, 184, __pyx_L1_error)
+      __PYX_ERR(0, 186, __pyx_L1_error)
     }
 
-    /* "hafnian/hafnian.pyx":186
+    /* "hafnian/hafnian.pyx":188
  *         nud.push_back(rpt[i])
  * 
  *         if mu is None:             # <<<<<<<<<<<<<<
@@ -3245,7 +3245,7 @@ static PyObject *__pyx_pf_6libhaf_6haf_rpt_complex(CYTHON_UNUSED PyObject *__pyx
     __pyx_t_5 = ((((PyObject *) __pyx_v_mu.memview) == Py_None) != 0);
     if (__pyx_t_5) {
 
-      /* "hafnian/hafnian.pyx":187
+      /* "hafnian/hafnian.pyx":189
  * 
  *         if mu is None:
  *             d.push_back(A[i, i])             # <<<<<<<<<<<<<<
@@ -3258,10 +3258,10 @@ static PyObject *__pyx_pf_6libhaf_6haf_rpt_complex(CYTHON_UNUSED PyObject *__pyx
         __pyx_v_d.push_back((*((__pyx_t_double_complex *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_A.data + __pyx_t_6 * __pyx_v_A.strides[0]) ) + __pyx_t_7 * __pyx_v_A.strides[1]) ))));
       } catch(...) {
         __Pyx_CppExn2PyErr();
-        __PYX_ERR(0, 187, __pyx_L1_error)
+        __PYX_ERR(0, 189, __pyx_L1_error)
       }
 
-      /* "hafnian/hafnian.pyx":186
+      /* "hafnian/hafnian.pyx":188
  *         nud.push_back(rpt[i])
  * 
  *         if mu is None:             # <<<<<<<<<<<<<<
@@ -3271,7 +3271,7 @@ static PyObject *__pyx_pf_6libhaf_6haf_rpt_complex(CYTHON_UNUSED PyObject *__pyx
       goto __pyx_L5;
     }
 
-    /* "hafnian/hafnian.pyx":189
+    /* "hafnian/hafnian.pyx":191
  *             d.push_back(A[i, i])
  *         else:
  *             d.push_back(mu[i])             # <<<<<<<<<<<<<<
@@ -3284,12 +3284,12 @@ static PyObject *__pyx_pf_6libhaf_6haf_rpt_complex(CYTHON_UNUSED PyObject *__pyx
         __pyx_v_d.push_back((*((__pyx_t_double_complex *) ( /* dim=0 */ (__pyx_v_mu.data + __pyx_t_8 * __pyx_v_mu.strides[0]) ))));
       } catch(...) {
         __Pyx_CppExn2PyErr();
-        __PYX_ERR(0, 189, __pyx_L1_error)
+        __PYX_ERR(0, 191, __pyx_L1_error)
       }
     }
     __pyx_L5:;
 
-    /* "hafnian/hafnian.pyx":191
+    /* "hafnian/hafnian.pyx":193
  *             d.push_back(mu[i])
  * 
  *         for j in range(n):             # <<<<<<<<<<<<<<
@@ -3301,7 +3301,7 @@ static PyObject *__pyx_pf_6libhaf_6haf_rpt_complex(CYTHON_UNUSED PyObject *__pyx
     for (__pyx_t_11 = 0; __pyx_t_11 < __pyx_t_10; __pyx_t_11+=1) {
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-      /* "hafnian/hafnian.pyx":192
+      /* "hafnian/hafnian.pyx":194
  * 
  *         for j in range(n):
  *             mat.push_back(A[i, j])             # <<<<<<<<<<<<<<
@@ -3314,12 +3314,12 @@ static PyObject *__pyx_pf_6libhaf_6haf_rpt_complex(CYTHON_UNUSED PyObject *__pyx
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-  /* "hafnian/hafnian.pyx":195
+  /* "hafnian/hafnian.pyx":197
  * 
  *     # Exposes a c function to python
  *     if loop:             # <<<<<<<<<<<<<<
@@ -3329,7 +3329,7 @@ static PyObject *__pyx_pf_6libhaf_6haf_rpt_complex(CYTHON_UNUSED PyObject *__pyx
   __pyx_t_5 = (__pyx_v_loop != 0);
   if (__pyx_t_5) {
 
-    /* "hafnian/hafnian.pyx":196
+    /* "hafnian/hafnian.pyx":198
  *     # Exposes a c function to python
  *     if loop:
  *         return loop_hafnian_rpt_quad(mat, d, nud)             # <<<<<<<<<<<<<<
@@ -3338,13 +3338,13 @@ static PyObject *__pyx_pf_6libhaf_6haf_rpt_complex(CYTHON_UNUSED PyObject *__pyx
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-    __pyx_t_15 = __pyx_PyComplex_FromComplex(__pyx_t_14); if (unlikely(!__pyx_t_15)) __PYX_ERR(0, 196, __pyx_L1_error)
+    __pyx_t_15 = __pyx_PyComplex_FromComplex(__pyx_t_14); if (unlikely(!__pyx_t_15)) __PYX_ERR(0, 198, __pyx_L1_error)
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     goto __pyx_L0;
 
-    /* "hafnian/hafnian.pyx":195
+    /* "hafnian/hafnian.pyx":197
  * 
  *     # Exposes a c function to python
  *     if loop:             # <<<<<<<<<<<<<<
@@ -3353,7 +3353,7 @@ static PyObject *__pyx_pf_6libhaf_6haf_rpt_complex(CYTHON_UNUSED PyObject *__pyx
  */
   }
 
-  /* "hafnian/hafnian.pyx":198
+  /* "hafnian/hafnian.pyx":200
  *         return loop_hafnian_rpt_quad(mat, d, nud)
  * 
  *     return hafnian_rpt_quad(mat, nud)             # <<<<<<<<<<<<<<
@@ -3362,13 +3362,13 @@ static PyObject *__pyx_pf_6libhaf_6haf_rpt_complex(CYTHON_UNUSED PyObject *__pyx
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-  __pyx_t_15 = __pyx_PyComplex_FromComplex(__pyx_t_14); if (unlikely(!__pyx_t_15)) __PYX_ERR(0, 198, __pyx_L1_error)
+  __pyx_t_15 = __pyx_PyComplex_FromComplex(__pyx_t_14); if (unlikely(!__pyx_t_15)) __PYX_ERR(0, 200, __pyx_L1_error)
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-  /* "hafnian/hafnian.pyx":162
+  /* "hafnian/hafnian.pyx":164
  * 
  * 
  * def haf_rpt_complex(double complex[:, :] A, int[:] rpt, double complex[:] mu=None, bint loop=False):             # <<<<<<<<<<<<<<
@@ -3390,7 +3390,7 @@ static PyObject *__pyx_pf_6libhaf_6haf_rpt_complex(CYTHON_UNUSED PyObject *__pyx
   return __pyx_r;
 }
 
-/* "hafnian/hafnian.pyx":205
+/* "hafnian/hafnian.pyx":207
  * 
  * 
  * def haf_int(long long[:, :] A):             # <<<<<<<<<<<<<<
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@@ -3441,7 +3441,7 @@ static PyObject *__pyx_pf_6libhaf_8haf_int(CYTHON_UNUSED PyObject *__pyx_self, _
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-  /* "hafnian/hafnian.pyx":217
+  /* "hafnian/hafnian.pyx":219
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  *     cdef int i, j, n = A.shape[0]             # <<<<<<<<<<<<<<
@@ -3450,7 +3450,7 @@ static PyObject *__pyx_pf_6libhaf_8haf_int(CYTHON_UNUSED PyObject *__pyx_self, _
  */
   __pyx_v_n = (__pyx_v_A.shape[0]);
 
-  /* "hafnian/hafnian.pyx":220
+  /* "hafnian/hafnian.pyx":222
  *     cdef vector[long long] mat
  * 
  *     for i in range(n):             # <<<<<<<<<<<<<<
@@ -3462,7 +3462,7 @@ static PyObject *__pyx_pf_6libhaf_8haf_int(CYTHON_UNUSED PyObject *__pyx_self, _
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-    /* "hafnian/hafnian.pyx":221
+    /* "hafnian/hafnian.pyx":223
  * 
  *     for i in range(n):
  *         for j in range(n):             # <<<<<<<<<<<<<<
@@ -3474,7 +3474,7 @@ static PyObject *__pyx_pf_6libhaf_8haf_int(CYTHON_UNUSED PyObject *__pyx_self, _
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       __pyx_v_j = __pyx_t_6;
 
-      /* "hafnian/hafnian.pyx":222
+      /* "hafnian/hafnian.pyx":224
  *     for i in range(n):
  *         for j in range(n):
  *             mat.push_back(A[i, j])             # <<<<<<<<<<<<<<
@@ -3487,12 +3487,12 @@ static PyObject *__pyx_pf_6libhaf_8haf_int(CYTHON_UNUSED PyObject *__pyx_self, _
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+        __PYX_ERR(0, 224, __pyx_L1_error)
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-  /* "hafnian/hafnian.pyx":225
+  /* "hafnian/hafnian.pyx":227
  * 
  *     # Exposes a c function to python
  *     return hafnian_recursive(mat)             # <<<<<<<<<<<<<<
@@ -3500,13 +3500,13 @@ static PyObject *__pyx_pf_6libhaf_8haf_int(CYTHON_UNUSED PyObject *__pyx_self, _
  * 
  */
   __Pyx_XDECREF(__pyx_r);
-  __pyx_t_9 = __Pyx_PyInt_From_PY_LONG_LONG(hafnian::hafnian_recursive<PY_LONG_LONG>(__pyx_v_mat)); if (unlikely(!__pyx_t_9)) __PYX_ERR(0, 225, __pyx_L1_error)
+  __pyx_t_9 = __Pyx_PyInt_From_PY_LONG_LONG(hafnian::hafnian_recursive<PY_LONG_LONG>(__pyx_v_mat)); if (unlikely(!__pyx_t_9)) __PYX_ERR(0, 227, __pyx_L1_error)
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   goto __pyx_L0;
 
-  /* "hafnian/hafnian.pyx":205
+  /* "hafnian/hafnian.pyx":207
  * 
  * 
  * def haf_int(long long[:, :] A):             # <<<<<<<<<<<<<<
@@ -3526,7 +3526,7 @@ static PyObject *__pyx_pf_6libhaf_8haf_int(CYTHON_UNUSED PyObject *__pyx_self, _
   return __pyx_r;
 }
 
-/* "hafnian/hafnian.pyx":232
+/* "hafnian/hafnian.pyx":234
  * 
  * 
  * def haf_complex(double complex[:, :] A, bint loop=False, bint recursive=True, quad=True):             # <<<<<<<<<<<<<<
@@ -3590,7 +3590,7 @@ static PyObject *__pyx_pw_6libhaf_11haf_complex(PyObject *__pyx_self, PyObject *
         }
       }
       if (unlikely(kw_args > 0)) {
-        if (unlikely(__Pyx_ParseOptionalKeywords(__pyx_kwds, __pyx_pyargnames, 0, values, pos_args, "haf_complex") < 0)) __PYX_ERR(0, 232, __pyx_L3_error)
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@@ -3605,14 +3605,14 @@ static PyObject *__pyx_pw_6libhaf_11haf_complex(PyObject *__pyx_self, PyObject *
         default: goto __pyx_L5_argtuple_error;
       }
     }
-    __pyx_v_A = __Pyx_PyObject_to_MemoryviewSlice_dsds___pyx_t_double_complex(values[0], PyBUF_WRITABLE); if (unlikely(!__pyx_v_A.memview)) __PYX_ERR(0, 232, __pyx_L3_error)
+    __pyx_v_A = __Pyx_PyObject_to_MemoryviewSlice_dsds___pyx_t_double_complex(values[0], PyBUF_WRITABLE); if (unlikely(!__pyx_v_A.memview)) __PYX_ERR(0, 234, __pyx_L3_error)
     if (values[1]) {
-      __pyx_v_loop = __Pyx_PyObject_IsTrue(values[1]); if (unlikely((__pyx_v_loop == (int)-1) && PyErr_Occurred())) __PYX_ERR(0, 232, __pyx_L3_error)
+      __pyx_v_loop = __Pyx_PyObject_IsTrue(values[1]); if (unlikely((__pyx_v_loop == (int)-1) && PyErr_Occurred())) __PYX_ERR(0, 234, __pyx_L3_error)
     } else {
       __pyx_v_loop = ((int)0);
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     if (values[2]) {
-      __pyx_v_recursive = __Pyx_PyObject_IsTrue(values[2]); if (unlikely((__pyx_v_recursive == (int)-1) && PyErr_Occurred())) __PYX_ERR(0, 232, __pyx_L3_error)
+      __pyx_v_recursive = __Pyx_PyObject_IsTrue(values[2]); if (unlikely((__pyx_v_recursive == (int)-1) && PyErr_Occurred())) __PYX_ERR(0, 234, __pyx_L3_error)
     } else {
       __pyx_v_recursive = ((int)1);
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@@ -3620,7 +3620,7 @@ static PyObject *__pyx_pw_6libhaf_11haf_complex(PyObject *__pyx_self, PyObject *
   }
   goto __pyx_L4_argument_unpacking_done;
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-  __Pyx_RaiseArgtupleInvalid("haf_complex", 0, 1, 4, PyTuple_GET_SIZE(__pyx_args)); __PYX_ERR(0, 232, __pyx_L3_error)
+  __Pyx_RaiseArgtupleInvalid("haf_complex", 0, 1, 4, PyTuple_GET_SIZE(__pyx_args)); __PYX_ERR(0, 234, __pyx_L3_error)
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@@ -3653,7 +3653,7 @@ static PyObject *__pyx_pf_6libhaf_10haf_complex(CYTHON_UNUSED PyObject *__pyx_se
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   __Pyx_RefNannySetupContext("haf_complex", 0);
 
-  /* "hafnian/hafnian.pyx":246
+  /* "hafnian/hafnian.pyx":248
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  *     """
  *     cdef int i, j, n = A.shape[0]             # <<<<<<<<<<<<<<
@@ -3662,7 +3662,7 @@ static PyObject *__pyx_pf_6libhaf_10haf_complex(CYTHON_UNUSED PyObject *__pyx_se
  */
   __pyx_v_n = (__pyx_v_A.shape[0]);
 
-  /* "hafnian/hafnian.pyx":249
+  /* "hafnian/hafnian.pyx":251
  *     cdef vector[double complex] mat
  * 
  *     for i in range(n):             # <<<<<<<<<<<<<<
@@ -3674,7 +3674,7 @@ static PyObject *__pyx_pf_6libhaf_10haf_complex(CYTHON_UNUSED PyObject *__pyx_se
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     __pyx_v_i = __pyx_t_3;
 
-    /* "hafnian/hafnian.pyx":250
+    /* "hafnian/hafnian.pyx":252
  * 
  *     for i in range(n):
  *         for j in range(n):             # <<<<<<<<<<<<<<
@@ -3686,7 +3686,7 @@ static PyObject *__pyx_pf_6libhaf_10haf_complex(CYTHON_UNUSED PyObject *__pyx_se
     for (__pyx_t_6 = 0; __pyx_t_6 < __pyx_t_5; __pyx_t_6+=1) {
       __pyx_v_j = __pyx_t_6;
 
-      /* "hafnian/hafnian.pyx":251
+      /* "hafnian/hafnian.pyx":253
  *     for i in range(n):
  *         for j in range(n):
  *             mat.push_back(A[i, j])             # <<<<<<<<<<<<<<
@@ -3699,12 +3699,12 @@ static PyObject *__pyx_pf_6libhaf_10haf_complex(CYTHON_UNUSED PyObject *__pyx_se
         __pyx_v_mat.push_back((*((__pyx_t_double_complex *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_A.data + __pyx_t_7 * __pyx_v_A.strides[0]) ) + __pyx_t_8 * __pyx_v_A.strides[1]) ))));
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         __Pyx_CppExn2PyErr();
-        __PYX_ERR(0, 251, __pyx_L1_error)
+        __PYX_ERR(0, 253, __pyx_L1_error)
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-  /* "hafnian/hafnian.pyx":254
+  /* "hafnian/hafnian.pyx":256
  * 
  *     # Exposes a c function to python
  *     if loop:             # <<<<<<<<<<<<<<
@@ -3714,7 +3714,7 @@ static PyObject *__pyx_pf_6libhaf_10haf_complex(CYTHON_UNUSED PyObject *__pyx_se
   __pyx_t_9 = (__pyx_v_loop != 0);
   if (__pyx_t_9) {
 
-    /* "hafnian/hafnian.pyx":255
+    /* "hafnian/hafnian.pyx":257
  *     # Exposes a c function to python
  *     if loop:
  *         return loop_hafnian(mat)             # <<<<<<<<<<<<<<
@@ -3723,13 +3723,13 @@ static PyObject *__pyx_pf_6libhaf_10haf_complex(CYTHON_UNUSED PyObject *__pyx_se
  */
     __Pyx_XDECREF(__pyx_r);
     __pyx_t_10 = hafnian::loop_hafnian<__pyx_t_double_complex>(__pyx_v_mat);
-    __pyx_t_11 = __pyx_PyComplex_FromComplex(__pyx_t_10); if (unlikely(!__pyx_t_11)) __PYX_ERR(0, 255, __pyx_L1_error)
+    __pyx_t_11 = __pyx_PyComplex_FromComplex(__pyx_t_10); if (unlikely(!__pyx_t_11)) __PYX_ERR(0, 257, __pyx_L1_error)
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     __pyx_r = __pyx_t_11;
     __pyx_t_11 = 0;
     goto __pyx_L0;
 
-    /* "hafnian/hafnian.pyx":254
+    /* "hafnian/hafnian.pyx":256
  * 
  *     # Exposes a c function to python
  *     if loop:             # <<<<<<<<<<<<<<
@@ -3738,7 +3738,7 @@ static PyObject *__pyx_pf_6libhaf_10haf_complex(CYTHON_UNUSED PyObject *__pyx_se
  */
   }
 
-  /* "hafnian/hafnian.pyx":257
+  /* "hafnian/hafnian.pyx":259
  *         return loop_hafnian(mat)
  * 
  *     if recursive:             # <<<<<<<<<<<<<<
@@ -3748,17 +3748,17 @@ static PyObject *__pyx_pf_6libhaf_10haf_complex(CYTHON_UNUSED PyObject *__pyx_se
   __pyx_t_9 = (__pyx_v_recursive != 0);
   if (__pyx_t_9) {
 
-    /* "hafnian/hafnian.pyx":258
+    /* "hafnian/hafnian.pyx":260
  * 
  *     if recursive:
  *         if quad:             # <<<<<<<<<<<<<<
  *             return hafnian_recursive_quad(mat)
  *         return hafnian_recursive(mat)
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-    __pyx_t_9 = __Pyx_PyObject_IsTrue(__pyx_v_quad); if (unlikely(__pyx_t_9 < 0)) __PYX_ERR(0, 258, __pyx_L1_error)
+    __pyx_t_9 = __Pyx_PyObject_IsTrue(__pyx_v_quad); if (unlikely(__pyx_t_9 < 0)) __PYX_ERR(0, 260, __pyx_L1_error)
     if (__pyx_t_9) {
 
-      /* "hafnian/hafnian.pyx":259
+      /* "hafnian/hafnian.pyx":261
  *     if recursive:
  *         if quad:
  *             return hafnian_recursive_quad(mat)             # <<<<<<<<<<<<<<
@@ -3767,13 +3767,13 @@ static PyObject *__pyx_pf_6libhaf_10haf_complex(CYTHON_UNUSED PyObject *__pyx_se
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-      __pyx_t_11 = __pyx_PyComplex_FromComplex(__pyx_t_10); if (unlikely(!__pyx_t_11)) __PYX_ERR(0, 259, __pyx_L1_error)
+      __pyx_t_11 = __pyx_PyComplex_FromComplex(__pyx_t_10); if (unlikely(!__pyx_t_11)) __PYX_ERR(0, 261, __pyx_L1_error)
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       __pyx_r = __pyx_t_11;
       __pyx_t_11 = 0;
       goto __pyx_L0;
 
-      /* "hafnian/hafnian.pyx":258
+      /* "hafnian/hafnian.pyx":260
  * 
  *     if recursive:
  *         if quad:             # <<<<<<<<<<<<<<
@@ -3782,7 +3782,7 @@ static PyObject *__pyx_pf_6libhaf_10haf_complex(CYTHON_UNUSED PyObject *__pyx_se
  */
     }
 
-    /* "hafnian/hafnian.pyx":260
+    /* "hafnian/hafnian.pyx":262
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  *         return hafnian_recursive(mat)             # <<<<<<<<<<<<<<
@@ -3791,13 +3791,13 @@ static PyObject *__pyx_pf_6libhaf_10haf_complex(CYTHON_UNUSED PyObject *__pyx_se
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     __Pyx_XDECREF(__pyx_r);
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-    __pyx_t_11 = __pyx_PyComplex_FromComplex(__pyx_t_10); if (unlikely(!__pyx_t_11)) __PYX_ERR(0, 260, __pyx_L1_error)
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     __pyx_t_11 = 0;
     goto __pyx_L0;
 
-    /* "hafnian/hafnian.pyx":257
+    /* "hafnian/hafnian.pyx":259
  *         return loop_hafnian(mat)
  * 
  *     if recursive:             # <<<<<<<<<<<<<<
@@ -3806,7 +3806,7 @@ static PyObject *__pyx_pf_6libhaf_10haf_complex(CYTHON_UNUSED PyObject *__pyx_se
  */
   }
 
-  /* "hafnian/hafnian.pyx":262
+  /* "hafnian/hafnian.pyx":264
  *         return hafnian_recursive(mat)
  * 
  *     return hafnian(mat)             # <<<<<<<<<<<<<<
@@ -3815,13 +3815,13 @@ static PyObject *__pyx_pf_6libhaf_10haf_complex(CYTHON_UNUSED PyObject *__pyx_se
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   __Pyx_XDECREF(__pyx_r);
   __pyx_t_10 = hafnian::hafnian<__pyx_t_double_complex>(__pyx_v_mat);
-  __pyx_t_11 = __pyx_PyComplex_FromComplex(__pyx_t_10); if (unlikely(!__pyx_t_11)) __PYX_ERR(0, 262, __pyx_L1_error)
+  __pyx_t_11 = __pyx_PyComplex_FromComplex(__pyx_t_10); if (unlikely(!__pyx_t_11)) __PYX_ERR(0, 264, __pyx_L1_error)
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   __pyx_r = __pyx_t_11;
   __pyx_t_11 = 0;
   goto __pyx_L0;
 
-  /* "hafnian/hafnian.pyx":232
+  /* "hafnian/hafnian.pyx":234
  * 
  * 
  * def haf_complex(double complex[:, :] A, bint loop=False, bint recursive=True, quad=True):             # <<<<<<<<<<<<<<
@@ -3841,7 +3841,7 @@ static PyObject *__pyx_pf_6libhaf_10haf_complex(CYTHON_UNUSED PyObject *__pyx_se
   return __pyx_r;
 }
 
-/* "hafnian/hafnian.pyx":265
+/* "hafnian/hafnian.pyx":267
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  * 
  * def haf_real(double[:, :] A, bint loop=False, bint recursive=True, quad=True, bint approx=False, nsamples=1000):             # <<<<<<<<<<<<<<
@@ -3924,7 +3924,7 @@ static PyObject *__pyx_pw_6libhaf_13haf_real(PyObject *__pyx_self, PyObject *__p
         }
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-        if (unlikely(__Pyx_ParseOptionalKeywords(__pyx_kwds, __pyx_pyargnames, 0, values, pos_args, "haf_real") < 0)) __PYX_ERR(0, 265, __pyx_L3_error)
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       switch (PyTuple_GET_SIZE(__pyx_args)) {
@@ -3943,20 +3943,20 @@ static PyObject *__pyx_pw_6libhaf_13haf_real(PyObject *__pyx_self, PyObject *__p
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+      __pyx_v_loop = __Pyx_PyObject_IsTrue(values[1]); if (unlikely((__pyx_v_loop == (int)-1) && PyErr_Occurred())) __PYX_ERR(0, 267, __pyx_L3_error)
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+      __pyx_v_approx = __Pyx_PyObject_IsTrue(values[4]); if (unlikely((__pyx_v_approx == (int)-1) && PyErr_Occurred())) __PYX_ERR(0, 267, __pyx_L3_error)
     } else {
       __pyx_v_approx = ((int)0);
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@@ -3964,7 +3964,7 @@ static PyObject *__pyx_pw_6libhaf_13haf_real(PyObject *__pyx_self, PyObject *__p
   }
   goto __pyx_L4_argument_unpacking_done;
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-  __Pyx_RaiseArgtupleInvalid("haf_real", 0, 1, 6, PyTuple_GET_SIZE(__pyx_args)); __PYX_ERR(0, 265, __pyx_L3_error)
+  __Pyx_RaiseArgtupleInvalid("haf_real", 0, 1, 6, PyTuple_GET_SIZE(__pyx_args)); __PYX_ERR(0, 267, __pyx_L3_error)
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@@ -3996,7 +3996,7 @@ static PyObject *__pyx_pf_6libhaf_12haf_real(CYTHON_UNUSED PyObject *__pyx_self,
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-  /* "hafnian/hafnian.pyx":283
+  /* "hafnian/hafnian.pyx":285
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  *     """
  *     cdef int i, j, n = A.shape[0]             # <<<<<<<<<<<<<<
@@ -4005,7 +4005,7 @@ static PyObject *__pyx_pf_6libhaf_12haf_real(CYTHON_UNUSED PyObject *__pyx_self,
  */
   __pyx_v_n = (__pyx_v_A.shape[0]);
 
-  /* "hafnian/hafnian.pyx":286
+  /* "hafnian/hafnian.pyx":288
  *     cdef vector[double] mat
  * 
  *     for i in range(n):             # <<<<<<<<<<<<<<
@@ -4017,7 +4017,7 @@ static PyObject *__pyx_pf_6libhaf_12haf_real(CYTHON_UNUSED PyObject *__pyx_self,
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     __pyx_v_i = __pyx_t_3;
 
-    /* "hafnian/hafnian.pyx":287
+    /* "hafnian/hafnian.pyx":289
  * 
  *     for i in range(n):
  *         for j in range(n):             # <<<<<<<<<<<<<<
@@ -4029,7 +4029,7 @@ static PyObject *__pyx_pf_6libhaf_12haf_real(CYTHON_UNUSED PyObject *__pyx_self,
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-      /* "hafnian/hafnian.pyx":288
+      /* "hafnian/hafnian.pyx":290
  *     for i in range(n):
  *         for j in range(n):
  *             mat.push_back(A[i, j])             # <<<<<<<<<<<<<<
@@ -4042,12 +4042,12 @@ static PyObject *__pyx_pf_6libhaf_12haf_real(CYTHON_UNUSED PyObject *__pyx_self,
         __pyx_v_mat.push_back((*((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_A.data + __pyx_t_7 * __pyx_v_A.strides[0]) ) + __pyx_t_8 * __pyx_v_A.strides[1]) ))));
       } catch(...) {
         __Pyx_CppExn2PyErr();
-        __PYX_ERR(0, 288, __pyx_L1_error)
+        __PYX_ERR(0, 290, __pyx_L1_error)
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-  /* "hafnian/hafnian.pyx":291
+  /* "hafnian/hafnian.pyx":293
  * 
  *     # Exposes a c function to python
  *     if loop:             # <<<<<<<<<<<<<<
@@ -4057,7 +4057,7 @@ static PyObject *__pyx_pf_6libhaf_12haf_real(CYTHON_UNUSED PyObject *__pyx_self,
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   if (__pyx_t_9) {
 
-    /* "hafnian/hafnian.pyx":292
+    /* "hafnian/hafnian.pyx":294
  *     # Exposes a c function to python
  *     if loop:
  *         return loop_hafnian(mat)             # <<<<<<<<<<<<<<
@@ -4065,13 +4065,13 @@ static PyObject *__pyx_pf_6libhaf_12haf_real(CYTHON_UNUSED PyObject *__pyx_self,
  *     if approx:
  */
     __Pyx_XDECREF(__pyx_r);
-    __pyx_t_10 = PyFloat_FromDouble(hafnian::loop_hafnian<double>(__pyx_v_mat)); if (unlikely(!__pyx_t_10)) __PYX_ERR(0, 292, __pyx_L1_error)
+    __pyx_t_10 = PyFloat_FromDouble(hafnian::loop_hafnian<double>(__pyx_v_mat)); if (unlikely(!__pyx_t_10)) __PYX_ERR(0, 294, __pyx_L1_error)
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     __pyx_r = __pyx_t_10;
     __pyx_t_10 = 0;
     goto __pyx_L0;
 
-    /* "hafnian/hafnian.pyx":291
+    /* "hafnian/hafnian.pyx":293
  * 
  *     # Exposes a c function to python
  *     if loop:             # <<<<<<<<<<<<<<
@@ -4080,7 +4080,7 @@ static PyObject *__pyx_pf_6libhaf_12haf_real(CYTHON_UNUSED PyObject *__pyx_self,
  */
   }
 
-  /* "hafnian/hafnian.pyx":294
+  /* "hafnian/hafnian.pyx":296
  *         return loop_hafnian(mat)
  * 
  *     if approx:             # <<<<<<<<<<<<<<
@@ -4090,7 +4090,7 @@ static PyObject *__pyx_pf_6libhaf_12haf_real(CYTHON_UNUSED PyObject *__pyx_self,
   __pyx_t_9 = (__pyx_v_approx != 0);
   if (__pyx_t_9) {
 
-    /* "hafnian/hafnian.pyx":295
+    /* "hafnian/hafnian.pyx":297
  * 
  *     if approx:
  *         return hafnian_approx(mat, nsamples)             # <<<<<<<<<<<<<<
@@ -4098,14 +4098,14 @@ static PyObject *__pyx_pf_6libhaf_12haf_real(CYTHON_UNUSED PyObject *__pyx_self,
  *     if recursive:
  */
     __Pyx_XDECREF(__pyx_r);
-    __pyx_t_1 = __Pyx_PyInt_As_int(__pyx_v_nsamples); if (unlikely((__pyx_t_1 == (int)-1) && PyErr_Occurred())) __PYX_ERR(0, 295, __pyx_L1_error)
-    __pyx_t_10 = PyFloat_FromDouble(hafnian::hafnian_approx(__pyx_v_mat, __pyx_t_1)); if (unlikely(!__pyx_t_10)) __PYX_ERR(0, 295, __pyx_L1_error)
+    __pyx_t_1 = __Pyx_PyInt_As_int(__pyx_v_nsamples); if (unlikely((__pyx_t_1 == (int)-1) && PyErr_Occurred())) __PYX_ERR(0, 297, __pyx_L1_error)
+    __pyx_t_10 = PyFloat_FromDouble(hafnian::hafnian_approx(__pyx_v_mat, __pyx_t_1)); if (unlikely(!__pyx_t_10)) __PYX_ERR(0, 297, __pyx_L1_error)
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     __pyx_t_10 = 0;
     goto __pyx_L0;
 
-    /* "hafnian/hafnian.pyx":294
+    /* "hafnian/hafnian.pyx":296
  *         return loop_hafnian(mat)
  * 
  *     if approx:             # <<<<<<<<<<<<<<
@@ -4114,7 +4114,7 @@ static PyObject *__pyx_pf_6libhaf_12haf_real(CYTHON_UNUSED PyObject *__pyx_self,
  */
   }
 
-  /* "hafnian/hafnian.pyx":297
+  /* "hafnian/hafnian.pyx":299
  *         return hafnian_approx(mat, nsamples)
  * 
  *     if recursive:             # <<<<<<<<<<<<<<
@@ -4124,17 +4124,17 @@ static PyObject *__pyx_pf_6libhaf_12haf_real(CYTHON_UNUSED PyObject *__pyx_self,
   __pyx_t_9 = (__pyx_v_recursive != 0);
   if (__pyx_t_9) {
 
-    /* "hafnian/hafnian.pyx":298
+    /* "hafnian/hafnian.pyx":300
  * 
  *     if recursive:
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  *             return hafnian_recursive_quad(mat)
  *         return hafnian_recursive(mat)
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-    __pyx_t_9 = __Pyx_PyObject_IsTrue(__pyx_v_quad); if (unlikely(__pyx_t_9 < 0)) __PYX_ERR(0, 298, __pyx_L1_error)
+    __pyx_t_9 = __Pyx_PyObject_IsTrue(__pyx_v_quad); if (unlikely(__pyx_t_9 < 0)) __PYX_ERR(0, 300, __pyx_L1_error)
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-      /* "hafnian/hafnian.pyx":299
+      /* "hafnian/hafnian.pyx":301
  *     if recursive:
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@@ -4142,13 +4142,13 @@ static PyObject *__pyx_pf_6libhaf_12haf_real(CYTHON_UNUSED PyObject *__pyx_self,
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-      __pyx_t_10 = PyFloat_FromDouble(hafnian::hafnian_recursive_quad(__pyx_v_mat)); if (unlikely(!__pyx_t_10)) __PYX_ERR(0, 299, __pyx_L1_error)
+      __pyx_t_10 = PyFloat_FromDouble(hafnian::hafnian_recursive_quad(__pyx_v_mat)); if (unlikely(!__pyx_t_10)) __PYX_ERR(0, 301, __pyx_L1_error)
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       __pyx_t_10 = 0;
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-      /* "hafnian/hafnian.pyx":298
+      /* "hafnian/hafnian.pyx":300
  * 
  *     if recursive:
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@@ -4157,7 +4157,7 @@ static PyObject *__pyx_pf_6libhaf_12haf_real(CYTHON_UNUSED PyObject *__pyx_self,
  */
     }
 
-    /* "hafnian/hafnian.pyx":300
+    /* "hafnian/hafnian.pyx":302
  *         if quad:
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  *         return hafnian_recursive(mat)             # <<<<<<<<<<<<<<
@@ -4165,13 +4165,13 @@ static PyObject *__pyx_pf_6libhaf_12haf_real(CYTHON_UNUSED PyObject *__pyx_self,
  *     return hafnian(mat)
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     __Pyx_XDECREF(__pyx_r);
-    __pyx_t_10 = PyFloat_FromDouble(hafnian::hafnian_recursive<double>(__pyx_v_mat)); if (unlikely(!__pyx_t_10)) __PYX_ERR(0, 300, __pyx_L1_error)
+    __pyx_t_10 = PyFloat_FromDouble(hafnian::hafnian_recursive<double>(__pyx_v_mat)); if (unlikely(!__pyx_t_10)) __PYX_ERR(0, 302, __pyx_L1_error)
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-    /* "hafnian/hafnian.pyx":297
+    /* "hafnian/hafnian.pyx":299
  *         return hafnian_approx(mat, nsamples)
  * 
  *     if recursive:             # <<<<<<<<<<<<<<
@@ -4180,7 +4180,7 @@ static PyObject *__pyx_pf_6libhaf_12haf_real(CYTHON_UNUSED PyObject *__pyx_self,
  */
   }
 
-  /* "hafnian/hafnian.pyx":302
+  /* "hafnian/hafnian.pyx":304
  *         return hafnian_recursive(mat)
  * 
  *     return hafnian(mat)             # <<<<<<<<<<<<<<
@@ -4188,13 +4188,13 @@ static PyObject *__pyx_pf_6libhaf_12haf_real(CYTHON_UNUSED PyObject *__pyx_self,
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  */
   __Pyx_XDECREF(__pyx_r);
-  __pyx_t_10 = PyFloat_FromDouble(hafnian::hafnian<double>(__pyx_v_mat)); if (unlikely(!__pyx_t_10)) __PYX_ERR(0, 302, __pyx_L1_error)
+  __pyx_t_10 = PyFloat_FromDouble(hafnian::hafnian<double>(__pyx_v_mat)); if (unlikely(!__pyx_t_10)) __PYX_ERR(0, 304, __pyx_L1_error)
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   __pyx_t_10 = 0;
   goto __pyx_L0;
 
-  /* "hafnian/hafnian.pyx":265
+  /* "hafnian/hafnian.pyx":267
  * 
  * 
  * def haf_real(double[:, :] A, bint loop=False, bint recursive=True, quad=True, bint approx=False, nsamples=1000):             # <<<<<<<<<<<<<<
@@ -4214,7 +4214,7 @@ static PyObject *__pyx_pf_6libhaf_12haf_real(CYTHON_UNUSED PyObject *__pyx_self,
   return __pyx_r;
 }
 
-/* "hafnian/hafnian.pyx":310
+/* "hafnian/hafnian.pyx":312
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  * 
  * def perm_complex(double complex[:, :] A, quad=True):             # <<<<<<<<<<<<<<
@@ -4260,7 +4260,7 @@ static PyObject *__pyx_pw_6libhaf_15perm_complex(PyObject *__pyx_self, PyObject
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+        if (unlikely(__Pyx_ParseOptionalKeywords(__pyx_kwds, __pyx_pyargnames, 0, values, pos_args, "perm_complex") < 0)) __PYX_ERR(0, 312, __pyx_L3_error)
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@@ -4271,12 +4271,12 @@ static PyObject *__pyx_pw_6libhaf_15perm_complex(PyObject *__pyx_self, PyObject
         default: goto __pyx_L5_argtuple_error;
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-    __pyx_v_A = __Pyx_PyObject_to_MemoryviewSlice_dsds___pyx_t_double_complex(values[0], PyBUF_WRITABLE); if (unlikely(!__pyx_v_A.memview)) __PYX_ERR(0, 310, __pyx_L3_error)
+    __pyx_v_A = __Pyx_PyObject_to_MemoryviewSlice_dsds___pyx_t_double_complex(values[0], PyBUF_WRITABLE); if (unlikely(!__pyx_v_A.memview)) __PYX_ERR(0, 312, __pyx_L3_error)
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-  __Pyx_RaiseArgtupleInvalid("perm_complex", 0, 1, 2, PyTuple_GET_SIZE(__pyx_args)); __PYX_ERR(0, 310, __pyx_L3_error)
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   __Pyx_RefNannyFinishContext();
@@ -4309,7 +4309,7 @@ static PyObject *__pyx_pf_6libhaf_14perm_complex(CYTHON_UNUSED PyObject *__pyx_s
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-  /* "hafnian/hafnian.pyx":321
+  /* "hafnian/hafnian.pyx":323
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@@ -4318,7 +4318,7 @@ static PyObject *__pyx_pf_6libhaf_14perm_complex(CYTHON_UNUSED PyObject *__pyx_s
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   __pyx_v_n = (__pyx_v_A.shape[0]);
 
-  /* "hafnian/hafnian.pyx":324
+  /* "hafnian/hafnian.pyx":326
  *     cdef vector[double complex] mat
  * 
  *     for i in range(n):             # <<<<<<<<<<<<<<
@@ -4330,7 +4330,7 @@ static PyObject *__pyx_pf_6libhaf_14perm_complex(CYTHON_UNUSED PyObject *__pyx_s
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-    /* "hafnian/hafnian.pyx":325
+    /* "hafnian/hafnian.pyx":327
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  *     for i in range(n):
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@@ -4342,7 +4342,7 @@ static PyObject *__pyx_pf_6libhaf_14perm_complex(CYTHON_UNUSED PyObject *__pyx_s
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       __pyx_v_j = __pyx_t_6;
 
-      /* "hafnian/hafnian.pyx":326
+      /* "hafnian/hafnian.pyx":328
  *     for i in range(n):
  *         for j in range(n):
  *             mat.push_back(A[i, j])             # <<<<<<<<<<<<<<
@@ -4355,22 +4355,22 @@ static PyObject *__pyx_pf_6libhaf_14perm_complex(CYTHON_UNUSED PyObject *__pyx_s
         __pyx_v_mat.push_back((*((__pyx_t_double_complex *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_A.data + __pyx_t_7 * __pyx_v_A.strides[0]) ) + __pyx_t_8 * __pyx_v_A.strides[1]) ))));
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-  /* "hafnian/hafnian.pyx":329
+  /* "hafnian/hafnian.pyx":331
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  *     # Exposes a c function to python
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-  __pyx_t_9 = __Pyx_PyObject_IsTrue(__pyx_v_quad); if (unlikely(__pyx_t_9 < 0)) __PYX_ERR(0, 329, __pyx_L1_error)
+  __pyx_t_9 = __Pyx_PyObject_IsTrue(__pyx_v_quad); if (unlikely(__pyx_t_9 < 0)) __PYX_ERR(0, 331, __pyx_L1_error)
   if (__pyx_t_9) {
 
-    /* "hafnian/hafnian.pyx":330
+    /* "hafnian/hafnian.pyx":332
  *     # Exposes a c function to python
  *     if quad:
  *         return permanent_quad(mat)             # <<<<<<<<<<<<<<
@@ -4379,13 +4379,13 @@ static PyObject *__pyx_pf_6libhaf_14perm_complex(CYTHON_UNUSED PyObject *__pyx_s
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     __Pyx_XDECREF(__pyx_r);
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-    __pyx_t_11 = __pyx_PyComplex_FromComplex(__pyx_t_10); if (unlikely(!__pyx_t_11)) __PYX_ERR(0, 330, __pyx_L1_error)
+    __pyx_t_11 = __pyx_PyComplex_FromComplex(__pyx_t_10); if (unlikely(!__pyx_t_11)) __PYX_ERR(0, 332, __pyx_L1_error)
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     __pyx_r = __pyx_t_11;
     __pyx_t_11 = 0;
     goto __pyx_L0;
 
-    /* "hafnian/hafnian.pyx":329
+    /* "hafnian/hafnian.pyx":331
  * 
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+  /* "hafnian/hafnian.pyx":164
  * 
  * 
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-  __pyx_t_3 = __Pyx_PyObject_to_MemoryviewSlice_ds___pyx_t_double_complex(Py_None, PyBUF_WRITABLE); if (unlikely(!__pyx_t_3.memview)) __PYX_ERR(0, 162, __pyx_L1_error)
+  __pyx_t_3 = __Pyx_PyObject_to_MemoryviewSlice_ds___pyx_t_double_complex(Py_None, PyBUF_WRITABLE); if (unlikely(!__pyx_t_3.memview)) __PYX_ERR(0, 164, __pyx_L1_error)
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+  __pyx_t_1 = PyCFunction_NewEx(&__pyx_mdef_6libhaf_7haf_rpt_complex, NULL, __pyx_n_s_libhaf); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 164, __pyx_L1_error)
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-  if (PyDict_SetItem(__pyx_d, __pyx_n_s_haf_rpt_complex, __pyx_t_1) < 0) __PYX_ERR(0, 162, __pyx_L1_error)
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-  /* "hafnian/hafnian.pyx":205
+  /* "hafnian/hafnian.pyx":207
  * 
  * 
  * def haf_int(long long[:, :] A):             # <<<<<<<<<<<<<<
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  */
-  __pyx_t_1 = PyCFunction_NewEx(&__pyx_mdef_6libhaf_9haf_int, NULL, __pyx_n_s_libhaf); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 205, __pyx_L1_error)
+  __pyx_t_1 = PyCFunction_NewEx(&__pyx_mdef_6libhaf_9haf_int, NULL, __pyx_n_s_libhaf); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 207, __pyx_L1_error)
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-  if (PyDict_SetItem(__pyx_d, __pyx_n_s_haf_int, __pyx_t_1) < 0) __PYX_ERR(0, 205, __pyx_L1_error)
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-  /* "hafnian/hafnian.pyx":232
+  /* "hafnian/hafnian.pyx":234
  * 
  * 
  * def haf_complex(double complex[:, :] A, bint loop=False, bint recursive=True, quad=True):             # <<<<<<<<<<<<<<
  *     """Returns the hafnian of a complex matrix A via the C++ hafnian library.
  * 
  */
-  __pyx_t_1 = PyCFunction_NewEx(&__pyx_mdef_6libhaf_11haf_complex, NULL, __pyx_n_s_libhaf); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 232, __pyx_L1_error)
+  __pyx_t_1 = PyCFunction_NewEx(&__pyx_mdef_6libhaf_11haf_complex, NULL, __pyx_n_s_libhaf); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 234, __pyx_L1_error)
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-  if (PyDict_SetItem(__pyx_d, __pyx_n_s_haf_complex, __pyx_t_1) < 0) __PYX_ERR(0, 232, __pyx_L1_error)
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-  /* "hafnian/hafnian.pyx":265
+  /* "hafnian/hafnian.pyx":267
  * 
  * 
  * def haf_real(double[:, :] A, bint loop=False, bint recursive=True, quad=True, bint approx=False, nsamples=1000):             # <<<<<<<<<<<<<<
  *     """Returns the hafnian of a real matrix A via the C++ hafnian library.
  * 
  */
-  __pyx_t_1 = PyCFunction_NewEx(&__pyx_mdef_6libhaf_13haf_real, NULL, __pyx_n_s_libhaf); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 265, __pyx_L1_error)
+  __pyx_t_1 = PyCFunction_NewEx(&__pyx_mdef_6libhaf_13haf_real, NULL, __pyx_n_s_libhaf); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 267, __pyx_L1_error)
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-  if (PyDict_SetItem(__pyx_d, __pyx_n_s_haf_real, __pyx_t_1) < 0) __PYX_ERR(0, 265, __pyx_L1_error)
+  if (PyDict_SetItem(__pyx_d, __pyx_n_s_haf_real, __pyx_t_1) < 0) __PYX_ERR(0, 267, __pyx_L1_error)
   __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
 
-  /* "hafnian/hafnian.pyx":310
+  /* "hafnian/hafnian.pyx":312
  * 
  * 
  * def perm_complex(double complex[:, :] A, quad=True):             # <<<<<<<<<<<<<<
  *     """Returns the hafnian of a complex matrix A via the C++ hafnian library.
  * 
  */
-  __pyx_t_1 = PyCFunction_NewEx(&__pyx_mdef_6libhaf_15perm_complex, NULL, __pyx_n_s_libhaf); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 310, __pyx_L1_error)
+  __pyx_t_1 = PyCFunction_NewEx(&__pyx_mdef_6libhaf_15perm_complex, NULL, __pyx_n_s_libhaf); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 312, __pyx_L1_error)
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-  if (PyDict_SetItem(__pyx_d, __pyx_n_s_perm_complex, __pyx_t_1) < 0) __PYX_ERR(0, 310, __pyx_L1_error)
+  if (PyDict_SetItem(__pyx_d, __pyx_n_s_perm_complex, __pyx_t_1) < 0) __PYX_ERR(0, 312, __pyx_L1_error)
   __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
 
-  /* "hafnian/hafnian.pyx":335
+  /* "hafnian/hafnian.pyx":337
  * 
  * 
  * def perm_real(double [:, :] A, quad=True, fsum=False):             # <<<<<<<<<<<<<<
  *     """Returns the hafnian of a real matrix A via the C++ hafnian library.
  * 
  */
-  __pyx_t_1 = PyCFunction_NewEx(&__pyx_mdef_6libhaf_17perm_real, NULL, __pyx_n_s_libhaf); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 335, __pyx_L1_error)
+  __pyx_t_1 = PyCFunction_NewEx(&__pyx_mdef_6libhaf_17perm_real, NULL, __pyx_n_s_libhaf); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 337, __pyx_L1_error)
+  __Pyx_GOTREF(__pyx_t_1);
+  if (PyDict_SetItem(__pyx_d, __pyx_n_s_perm_real, __pyx_t_1) < 0) __PYX_ERR(0, 337, __pyx_L1_error)
+  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
+
+  /* "hafnian/hafnian.pyx":370
+ * # Batch hafnian
+ * 
+ * def hermite_multidimensional(double complex[:, :] A, double complex[:] d, int resolution, ren=False):             # <<<<<<<<<<<<<<
+ *     cdef int i, j, n = A.shape[0]
+ *     cdef vector[double complex] R_mat, y_mat
+ */
+  __pyx_t_1 = PyCFunction_NewEx(&__pyx_mdef_6libhaf_19hermite_multidimensional, NULL, __pyx_n_s_libhaf); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 370, __pyx_L1_error)
   __Pyx_GOTREF(__pyx_t_1);
-  if (PyDict_SetItem(__pyx_d, __pyx_n_s_perm_real, __pyx_t_1) < 0) __PYX_ERR(0, 335, __pyx_L1_error)
+  if (PyDict_SetItem(__pyx_d, __pyx_n_s_hermite_multidimensional, __pyx_t_1) < 0) __PYX_ERR(0, 370, __pyx_L1_error)
   __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
 
   /* "hafnian/hafnian.pyx":1
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  * cdef indirect = Enum("<strided and indirect>")
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-  __pyx_t_1 = __Pyx_PyObject_Call(((PyObject *)__pyx_MemviewEnum_type), __pyx_tuple__39, NULL); if (unlikely(!__pyx_t_1)) __PYX_ERR(1, 286, __pyx_L1_error)
+  __pyx_t_1 = __Pyx_PyObject_Call(((PyObject *)__pyx_MemviewEnum_type), __pyx_tuple__41, NULL); if (unlikely(!__pyx_t_1)) __PYX_ERR(1, 286, __pyx_L1_error)
   __Pyx_GOTREF(__pyx_t_1);
   __Pyx_XGOTREF(generic);
   __Pyx_DECREF_SET(generic, __pyx_t_1);
@@ -19168,7 +19532,7 @@ if (!__Pyx_RefNanny) {
  * cdef indirect = Enum("<strided and indirect>")
  * 
  */
-  __pyx_t_1 = __Pyx_PyObject_Call(((PyObject *)__pyx_MemviewEnum_type), __pyx_tuple__40, NULL); if (unlikely(!__pyx_t_1)) __PYX_ERR(1, 287, __pyx_L1_error)
+  __pyx_t_1 = __Pyx_PyObject_Call(((PyObject *)__pyx_MemviewEnum_type), __pyx_tuple__42, NULL); if (unlikely(!__pyx_t_1)) __PYX_ERR(1, 287, __pyx_L1_error)
   __Pyx_GOTREF(__pyx_t_1);
   __Pyx_XGOTREF(strided);
   __Pyx_DECREF_SET(strided, __pyx_t_1);
@@ -19182,7 +19546,7 @@ if (!__Pyx_RefNanny) {
  * 
  * 
  */
-  __pyx_t_1 = __Pyx_PyObject_Call(((PyObject *)__pyx_MemviewEnum_type), __pyx_tuple__41, NULL); if (unlikely(!__pyx_t_1)) __PYX_ERR(1, 288, __pyx_L1_error)
+  __pyx_t_1 = __Pyx_PyObject_Call(((PyObject *)__pyx_MemviewEnum_type), __pyx_tuple__43, NULL); if (unlikely(!__pyx_t_1)) __PYX_ERR(1, 288, __pyx_L1_error)
   __Pyx_GOTREF(__pyx_t_1);
   __Pyx_XGOTREF(indirect);
   __Pyx_DECREF_SET(indirect, __pyx_t_1);
@@ -19196,7 +19560,7 @@ if (!__Pyx_RefNanny) {
  * cdef indirect_contiguous = Enum("<contiguous and indirect>")
  * 
  */
-  __pyx_t_1 = __Pyx_PyObject_Call(((PyObject *)__pyx_MemviewEnum_type), __pyx_tuple__42, NULL); if (unlikely(!__pyx_t_1)) __PYX_ERR(1, 291, __pyx_L1_error)
+  __pyx_t_1 = __Pyx_PyObject_Call(((PyObject *)__pyx_MemviewEnum_type), __pyx_tuple__44, NULL); if (unlikely(!__pyx_t_1)) __PYX_ERR(1, 291, __pyx_L1_error)
   __Pyx_GOTREF(__pyx_t_1);
   __Pyx_XGOTREF(contiguous);
   __Pyx_DECREF_SET(contiguous, __pyx_t_1);
@@ -19210,7 +19574,7 @@ if (!__Pyx_RefNanny) {
  * 
  * 
  */
-  __pyx_t_1 = __Pyx_PyObject_Call(((PyObject *)__pyx_MemviewEnum_type), __pyx_tuple__43, NULL); if (unlikely(!__pyx_t_1)) __PYX_ERR(1, 292, __pyx_L1_error)
+  __pyx_t_1 = __Pyx_PyObject_Call(((PyObject *)__pyx_MemviewEnum_type), __pyx_tuple__45, NULL); if (unlikely(!__pyx_t_1)) __PYX_ERR(1, 292, __pyx_L1_error)
   __Pyx_GOTREF(__pyx_t_1);
   __Pyx_XGOTREF(indirect_contiguous);
   __Pyx_DECREF_SET(indirect_contiguous, __pyx_t_1);
@@ -19520,7 +19884,11 @@ __Pyx_init_memviewslice(struct __pyx_memoryview_obj *memview,
     int i, retval=-1;
     Py_buffer *buf = &memview->view;
     __Pyx_RefNannySetupContext("init_memviewslice", 0);
-    if (memviewslice->memview || memviewslice->data) {
+    if (!buf) {
+        PyErr_SetString(PyExc_ValueError,
+            "buf is NULL.");
+        goto fail;
+    } else if (memviewslice->memview || memviewslice->data) {
         PyErr_SetString(PyExc_ValueError,
             "memviewslice is already initialized!");
         goto fail;
@@ -20457,32 +20825,6 @@ static CYTHON_INLINE PyObject *__Pyx_GetAttr3(PyObject *o, PyObject *n, PyObject
     return (likely(r)) ? r : __Pyx_GetAttr3Default(d);
 }
 
-/* PyDictVersioning */
-#if CYTHON_USE_DICT_VERSIONS && CYTHON_USE_TYPE_SLOTS
-static CYTHON_INLINE PY_UINT64_T __Pyx_get_tp_dict_version(PyObject *obj) {
-    PyObject *dict = Py_TYPE(obj)->tp_dict;
-    return likely(dict) ? __PYX_GET_DICT_VERSION(dict) : 0;
-}
-static CYTHON_INLINE PY_UINT64_T __Pyx_get_object_dict_version(PyObject *obj) {
-    PyObject **dictptr = NULL;
-    Py_ssize_t offset = Py_TYPE(obj)->tp_dictoffset;
-    if (offset) {
-#if CYTHON_COMPILING_IN_CPYTHON
-        dictptr = (likely(offset > 0)) ? (PyObject **) ((char *)obj + offset) : _PyObject_GetDictPtr(obj);
-#else
-        dictptr = _PyObject_GetDictPtr(obj);
-#endif
-    }
-    return (dictptr && *dictptr) ? __PYX_GET_DICT_VERSION(*dictptr) : 0;
-}
-static CYTHON_INLINE int __Pyx_object_dict_version_matches(PyObject* obj, PY_UINT64_T tp_dict_version, PY_UINT64_T obj_dict_version) {
-    PyObject *dict = Py_TYPE(obj)->tp_dict;
-    if (unlikely(!dict) || unlikely(tp_dict_version != __PYX_GET_DICT_VERSION(dict)))
-        return 0;
-    return obj_dict_version == __Pyx_get_object_dict_version(obj);
-}
-#endif
-
 /* GetModuleGlobalName */
 #if CYTHON_USE_DICT_VERSIONS
 static PyObject *__Pyx__GetModuleGlobalName(PyObject *name, PY_UINT64_T *dict_version, PyObject **dict_cached_value)
@@ -21486,13 +21828,13 @@ static void __Pyx_AddTraceback(const char *funcname, int c_line,
                 return __pyx_t_double_complex_from_parts(a.real / b.real, a.imag / b.imag);
             } else {
                 double r = b.imag / b.real;
-                double s = (double)(1.0) / (b.real + b.imag * r);
+                double s = 1.0 / (b.real + b.imag * r);
                 return __pyx_t_double_complex_from_parts(
                     (a.real + a.imag * r) * s, (a.imag - a.real * r) * s);
             }
         } else {
             double r = b.real / b.imag;
-            double s = (double)(1.0) / (b.imag + b.real * r);
+            double s = 1.0 / (b.imag + b.real * r);
             return __pyx_t_double_complex_from_parts(
                 (a.real * r + a.imag) * s, (a.imag * r - a.real) * s);
         }
@@ -21727,7 +22069,7 @@ static int __Pyx_BufFmt_ParseNumber(const char** ts) {
       return -1;
     } else {
         count = *t++ - '0';
-        while (*t >= '0' && *t <= '9') {
+        while (*t >= '0' && *t < '9') {
             count *= 10;
             count += *t++ - '0';
         }
@@ -22301,7 +22643,7 @@ __pyx_check_suboffsets(Py_buffer *buf, int dim, CYTHON_UNUSED int ndim, int spec
         }
     }
     if (spec & __Pyx_MEMVIEW_PTR) {
-        if (!buf->suboffsets || (buf->suboffsets[dim] < 0)) {
+        if (!buf->suboffsets || (buf->suboffsets && buf->suboffsets[dim] < 0)) {
             PyErr_Format(PyExc_ValueError,
                          "Buffer is not indirectly accessible "
                          "in dimension %d.", dim);
@@ -22555,6 +22897,28 @@ static int __Pyx_ValidateAndInit_memviewslice(
     return result;
 }
 
+/* CIntFromPyVerify */
+  #define __PYX_VERIFY_RETURN_INT(target_type, func_type, func_value)\
+    __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, 0)
+#define __PYX_VERIFY_RETURN_INT_EXC(target_type, func_type, func_value)\
+    __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, 1)
+#define __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, exc)\
+    {\
+        func_type value = func_value;\
+        if (sizeof(target_type) < sizeof(func_type)) {\
+            if (unlikely(value != (func_type) (target_type) value)) {\
+                func_type zero = 0;\
+                if (exc && unlikely(value == (func_type)-1 && PyErr_Occurred()))\
+                    return (target_type) -1;\
+                if (is_unsigned && unlikely(value < zero))\
+                    goto raise_neg_overflow;\
+                else\
+                    goto raise_overflow;\
+            }\
+        }\
+        return (target_type) value;\
+    }
+
 /* CIntToPy */
   static CYTHON_INLINE PyObject* __Pyx_PyInt_From_int(int value) {
     const int neg_one = (int) ((int) 0 - (int) 1), const_zero = (int) 0;
@@ -22586,28 +22950,6 @@ static int __Pyx_ValidateAndInit_memviewslice(
     }
 }
 
-/* CIntFromPyVerify */
-  #define __PYX_VERIFY_RETURN_INT(target_type, func_type, func_value)\
-    __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, 0)
-#define __PYX_VERIFY_RETURN_INT_EXC(target_type, func_type, func_value)\
-    __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, 1)
-#define __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, exc)\
-    {\
-        func_type value = func_value;\
-        if (sizeof(target_type) < sizeof(func_type)) {\
-            if (unlikely(value != (func_type) (target_type) value)) {\
-                func_type zero = 0;\
-                if (exc && unlikely(value == (func_type)-1 && PyErr_Occurred()))\
-                    return (target_type) -1;\
-                if (is_unsigned && unlikely(value < zero))\
-                    goto raise_neg_overflow;\
-                else\
-                    goto raise_overflow;\
-            }\
-        }\
-        return (target_type) value;\
-    }
-
 /* CIntToPy */
   static CYTHON_INLINE PyObject* __Pyx_PyInt_From_PY_LONG_LONG(PY_LONG_LONG value) {
     const PY_LONG_LONG neg_one = (PY_LONG_LONG) ((PY_LONG_LONG) 0 - (PY_LONG_LONG) 1), const_zero = (PY_LONG_LONG) 0;
@@ -22895,6 +23237,195 @@ __pyx_memoryview_copy_new_contig(const __Pyx_memviewslice *from_mvs,
     return (int) -1;
 }
 
+/* CIntFromPy */
+  static CYTHON_INLINE size_t __Pyx_PyInt_As_size_t(PyObject *x) {
+    const size_t neg_one = (size_t) ((size_t) 0 - (size_t) 1), const_zero = (size_t) 0;
+    const int is_unsigned = neg_one > const_zero;
+#if PY_MAJOR_VERSION < 3
+    if (likely(PyInt_Check(x))) {
+        if (sizeof(size_t) < sizeof(long)) {
+            __PYX_VERIFY_RETURN_INT(size_t, long, PyInt_AS_LONG(x))
+        } else {
+            long val = PyInt_AS_LONG(x);
+            if (is_unsigned && unlikely(val < 0)) {
+                goto raise_neg_overflow;
+            }
+            return (size_t) val;
+        }
+    } else
+#endif
+    if (likely(PyLong_Check(x))) {
+        if (is_unsigned) {
+#if CYTHON_USE_PYLONG_INTERNALS
+            const digit* digits = ((PyLongObject*)x)->ob_digit;
+            switch (Py_SIZE(x)) {
+                case  0: return (size_t) 0;
+                case  1: __PYX_VERIFY_RETURN_INT(size_t, digit, digits[0])
+                case 2:
+                    if (8 * sizeof(size_t) > 1 * PyLong_SHIFT) {
+                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
+                            __PYX_VERIFY_RETURN_INT(size_t, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if (8 * sizeof(size_t) >= 2 * PyLong_SHIFT) {
+                            return (size_t) (((((size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
+                        }
+                    }
+                    break;
+                case 3:
+                    if (8 * sizeof(size_t) > 2 * PyLong_SHIFT) {
+                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
+                            __PYX_VERIFY_RETURN_INT(size_t, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if (8 * sizeof(size_t) >= 3 * PyLong_SHIFT) {
+                            return (size_t) (((((((size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
+                        }
+                    }
+                    break;
+                case 4:
+                    if (8 * sizeof(size_t) > 3 * PyLong_SHIFT) {
+                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
+                            __PYX_VERIFY_RETURN_INT(size_t, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if (8 * sizeof(size_t) >= 4 * PyLong_SHIFT) {
+                            return (size_t) (((((((((size_t)digits[3]) << PyLong_SHIFT) | (size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
+                        }
+                    }
+                    break;
+            }
+#endif
+#if CYTHON_COMPILING_IN_CPYTHON
+            if (unlikely(Py_SIZE(x) < 0)) {
+                goto raise_neg_overflow;
+            }
+#else
+            {
+                int result = PyObject_RichCompareBool(x, Py_False, Py_LT);
+                if (unlikely(result < 0))
+                    return (size_t) -1;
+                if (unlikely(result == 1))
+                    goto raise_neg_overflow;
+            }
+#endif
+            if (sizeof(size_t) <= sizeof(unsigned long)) {
+                __PYX_VERIFY_RETURN_INT_EXC(size_t, unsigned long, PyLong_AsUnsignedLong(x))
+#ifdef HAVE_LONG_LONG
+            } else if (sizeof(size_t) <= sizeof(unsigned PY_LONG_LONG)) {
+                __PYX_VERIFY_RETURN_INT_EXC(size_t, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x))
+#endif
+            }
+        } else {
+#if CYTHON_USE_PYLONG_INTERNALS
+            const digit* digits = ((PyLongObject*)x)->ob_digit;
+            switch (Py_SIZE(x)) {
+                case  0: return (size_t) 0;
+                case -1: __PYX_VERIFY_RETURN_INT(size_t, sdigit, (sdigit) (-(sdigit)digits[0]))
+                case  1: __PYX_VERIFY_RETURN_INT(size_t,  digit, +digits[0])
+                case -2:
+                    if (8 * sizeof(size_t) - 1 > 1 * PyLong_SHIFT) {
+                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
+                            __PYX_VERIFY_RETURN_INT(size_t, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if (8 * sizeof(size_t) - 1 > 2 * PyLong_SHIFT) {
+                            return (size_t) (((size_t)-1)*(((((size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0])));
+                        }
+                    }
+                    break;
+                case 2:
+                    if (8 * sizeof(size_t) > 1 * PyLong_SHIFT) {
+                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
+                            __PYX_VERIFY_RETURN_INT(size_t, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if (8 * sizeof(size_t) - 1 > 2 * PyLong_SHIFT) {
+                            return (size_t) ((((((size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0])));
+                        }
+                    }
+                    break;
+                case -3:
+                    if (8 * sizeof(size_t) - 1 > 2 * PyLong_SHIFT) {
+                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
+                            __PYX_VERIFY_RETURN_INT(size_t, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if (8 * sizeof(size_t) - 1 > 3 * PyLong_SHIFT) {
+                            return (size_t) (((size_t)-1)*(((((((size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0])));
+                        }
+                    }
+                    break;
+                case 3:
+                    if (8 * sizeof(size_t) > 2 * PyLong_SHIFT) {
+                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
+                            __PYX_VERIFY_RETURN_INT(size_t, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if (8 * sizeof(size_t) - 1 > 3 * PyLong_SHIFT) {
+                            return (size_t) ((((((((size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0])));
+                        }
+                    }
+                    break;
+                case -4:
+                    if (8 * sizeof(size_t) - 1 > 3 * PyLong_SHIFT) {
+                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
+                            __PYX_VERIFY_RETURN_INT(size_t, long, -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if (8 * sizeof(size_t) - 1 > 4 * PyLong_SHIFT) {
+                            return (size_t) (((size_t)-1)*(((((((((size_t)digits[3]) << PyLong_SHIFT) | (size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0])));
+                        }
+                    }
+                    break;
+                case 4:
+                    if (8 * sizeof(size_t) > 3 * PyLong_SHIFT) {
+                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
+                            __PYX_VERIFY_RETURN_INT(size_t, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if (8 * sizeof(size_t) - 1 > 4 * PyLong_SHIFT) {
+                            return (size_t) ((((((((((size_t)digits[3]) << PyLong_SHIFT) | (size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0])));
+                        }
+                    }
+                    break;
+            }
+#endif
+            if (sizeof(size_t) <= sizeof(long)) {
+                __PYX_VERIFY_RETURN_INT_EXC(size_t, long, PyLong_AsLong(x))
+#ifdef HAVE_LONG_LONG
+            } else if (sizeof(size_t) <= sizeof(PY_LONG_LONG)) {
+                __PYX_VERIFY_RETURN_INT_EXC(size_t, PY_LONG_LONG, PyLong_AsLongLong(x))
+#endif
+            }
+        }
+        {
+#if CYTHON_COMPILING_IN_PYPY && !defined(_PyLong_AsByteArray)
+            PyErr_SetString(PyExc_RuntimeError,
+                            "_PyLong_AsByteArray() not available in PyPy, cannot convert large numbers");
+#else
+            size_t val;
+            PyObject *v = __Pyx_PyNumber_IntOrLong(x);
+ #if PY_MAJOR_VERSION < 3
+            if (likely(v) && !PyLong_Check(v)) {
+                PyObject *tmp = v;
+                v = PyNumber_Long(tmp);
+                Py_DECREF(tmp);
+            }
+ #endif
+            if (likely(v)) {
+                int one = 1; int is_little = (int)*(unsigned char *)&one;
+                unsigned char *bytes = (unsigned char *)&val;
+                int ret = _PyLong_AsByteArray((PyLongObject *)v,
+                                              bytes, sizeof(val),
+                                              is_little, !is_unsigned);
+                Py_DECREF(v);
+                if (likely(!ret))
+                    return val;
+            }
+#endif
+            return (size_t) -1;
+        }
+    } else {
+        size_t val;
+        PyObject *tmp = __Pyx_PyNumber_IntOrLong(x);
+        if (!tmp) return (size_t) -1;
+        val = __Pyx_PyInt_As_size_t(tmp);
+        Py_DECREF(tmp);
+        return val;
+    }
+raise_overflow:
+    PyErr_SetString(PyExc_OverflowError,
+        "value too large to convert to size_t");
+    return (size_t) -1;
+raise_neg_overflow:
+    PyErr_SetString(PyExc_OverflowError,
+        "can't convert negative value to size_t");
+    return (size_t) -1;
+}
+
 /* CIntFromPy */
   static CYTHON_INLINE long __Pyx_PyInt_As_long(PyObject *x) {
     const long neg_one = (long) ((long) 0 - (long) 1), const_zero = (long) 0;
diff --git a/hafnian/hafnian.pyx b/hafnian/hafnian.pyx
index 6006ae123..32ceb9465 100644
--- a/hafnian/hafnian.pyx
+++ b/hafnian/hafnian.pyx
@@ -46,6 +46,8 @@ cdef extern from "../src/hafnian.hpp" namespace "hafnian":
     double complex torontonian_quad(vector[double complex] &mat)
     double torontonian_fsum[T](vector[T] &mat)
 
+    vector[double complex] hermite_multidimensional_cpp(vector[double complex] &mat, vector[double complex] &d, int &resolution, bint &renorm)
+
 
 # ==============================================================================
 # Torontonian
@@ -361,3 +363,25 @@ def perm_real(double [:, :] A, quad=True, fsum=False):
 
     return permanent(mat)
 
+
+# ==============================================================================
+# Batch hafnian
+
+def hermite_multidimensional(double complex[:, :] A, double complex[:] d, int resolution, ren=False):
+    cdef int i, j, n = A.shape[0]
+    cdef vector[double complex] R_mat, y_mat
+	
+    cdef int renorm = 0
+
+    if ren:
+        renorm = 1
+
+    for i in range(n):
+        for j in range(n):
+            R_mat.push_back(A[i, j])
+
+
+    for i in range(n):
+        y_mat.push_back(d[i])
+
+    return hermite_multidimensional_cpp(R_mat, y_mat, resolution, renorm)
diff --git a/hafnian/quantum.py b/hafnian/quantum.py
index 7729b708e..a38488658 100644
--- a/hafnian/quantum.py
+++ b/hafnian/quantum.py
@@ -89,6 +89,8 @@
 from scipy.special import factorial as fac
 
 from ._hafnian import hafnian, hafnian_repeated, reduction
+from ._hermite_multidimensional import hermite_multidimensional, hafnian_batched
+
 
 
 def reduced_gaussian(mu, cov, modes):
@@ -311,7 +313,6 @@ def density_matrix_element(mu, cov, i, j, include_prefactor=True, tol=1e-10, hba
         complex: the density matrix element
     """
     rpt = i + j
-
     beta = Beta(mu, hbar=hbar)
     A = Amat(cov, hbar=hbar)
     if np.linalg.norm(beta) < tol:
@@ -325,7 +326,6 @@ def density_matrix_element(mu, cov, i, j, include_prefactor=True, tol=1e-10, hba
         # replace the diagonal of A with gamma
         # gamma = X @ np.linalg.inv(Q).conj() @ beta
         gamma = beta.conj() - A @ beta
-
         if np.prod([k + 1 for k in rpt]) ** (1 / len(rpt)) < 3:
             A_rpt = reduction(A, rpt)
             np.fill_diagonal(A_rpt, reduction(gamma, rpt))
@@ -339,6 +339,81 @@ def density_matrix_element(mu, cov, i, j, include_prefactor=True, tol=1e-10, hba
     return haf / np.sqrt(np.prod(fac(rpt)))
 
 
+def density_matrix(mu, cov, post_select=None, normalize=False, cutoff=5, hbar=2):
+    r"""Returns the density matrix of a (PNR post-selected) Gaussian state.
+
+    The resulting density matrix will have shape
+
+    .. math:: \underbrace{D\times D \times \cdots \times D}_{2M}
+
+    where :math:`D` is the Fock space cutoff, and :math:`M` is the
+    number of *non* post-selected modes, i.e. ``M = len(mu)//2 - len(post_select)``.
+
+    Note that we use the Strawberry Fields convention for indexing the density
+    matrix; the first two dimensions correspond to subsystem 1, the second two
+    dimensions correspond to subsystem 2, etc.
+
+    Args:
+        mu (array): length-:math:`2N` means vector in xp-ordering
+        cov (array): :math:`2N\times 2N` covariance matrix in xp-ordering
+        post_select (dict): dictionary containing the post-selected modes, of
+            the form ``{mode: value}``. If post_select is None the whole non post-selected density matrix
+            is calculated directly using (multidimensional) Hermite polynomials, which is significantly faster
+            than calculating one hafnian at a time.
+        normalize (bool): If ``True``, a post-selected density matrix is re-normalized.
+        cutoff (dim): the final length (i.e., Hilbert space dimension) of each
+            mode in the density matrix.
+        hbar (float): the value of :math:`\hbar` in the commutation
+            relation :math:`[\x,\p]=i\hbar`.
+
+    Returns:
+        np.array[complex]: the density matrix of the Gaussian state
+    """
+    N = len(mu) // 2
+    pref = prefactor(mu, cov, hbar=hbar)
+
+    if post_select is None:
+        A = Amat(cov, hbar=hbar)
+        if np.allclose(mu, np.zeros_like(mu)):
+            return pref * hermite_multidimensional(-A, cutoff, renorm=True)
+        try:
+            y = np.linalg.inv(A) @ np.linalg.inv(Qmat(cov)) @ Beta(mu, hbar=hbar)
+            return pref * hermite_multidimensional(-A, cutoff, y=-y, renorm=True)
+        except np.linalg.LinAlgError:
+            pass
+        post_select = {}
+
+    M = N - len(post_select)
+    rho = np.zeros([cutoff] * (2 * M), dtype=np.complex128)
+
+    for idx in product(range(cutoff), repeat=2 * M):
+        el = []
+
+        counter = count(0)
+        modes = (np.arange(2 * N) % N).tolist()
+        el = [post_select[i] if i in post_select else idx[next(counter)] for i in modes]
+
+        el = np.array(el).reshape(2, -1)
+        el0 = el[0].tolist()
+        el1 = el[1].tolist()
+
+        sf_idx = np.array(idx).reshape(2, -1)
+        sf_el = tuple(sf_idx[::-1].T.flatten())
+
+        rho[sf_el] = density_matrix_element(mu, cov, el0, el1, include_prefactor=False, hbar=hbar)
+
+    rho *= pref
+
+    if normalize:
+        # construct the standard 2D density matrix, and take the trace
+        new_ax = np.arange(2 * M).reshape([M, 2]).T.flatten()
+        tr = np.trace(rho.transpose(new_ax).reshape([cutoff ** M, cutoff ** M])).real
+        # renormalize
+        rho /= tr
+
+    return rho
+
+
 def pure_state_amplitude(mu, cov, i, include_prefactor=True, tol=1e-10, hbar=2, check_purity=True):
     r"""Returns the :math:`\langle i | \psi\rangle` element of the state ket
     of a Gaussian state defined by covariance matrix cov.
@@ -428,100 +503,44 @@ def state_vector(mu, cov, post_select=None, normalize=False, cutoff=5, hbar=2, c
         if not is_pure_cov(cov, hbar=2, rtol=1e-05, atol=1e-08):
             raise ValueError("The covariance matrix does not correspond to a pure state")
 
-    if post_select is None:
-        post_select = {}
-
     beta = Beta(mu, hbar=hbar)
     A = Amat(cov, hbar=hbar)
+    Q = Qmat(cov, hbar=hbar)
 
     (n, _) = cov.shape
     N = n // 2
 
     B = A[0:N, 0:N]
     alpha = beta[0:N]
-    M = N - len(post_select)
-    psi = np.zeros([cutoff] * (M), dtype=np.complex128)
-
-    for idx in product(range(cutoff), repeat=M):
-        el = []
-
-        counter = count(0)
-        modes = (np.arange(N)).tolist()
-        el = [post_select[i] if i in post_select else idx[next(counter)] for i in modes]
-        psi[idx] = pure_state_amplitude(mu, cov, el, check_purity=False, include_prefactor=False)
-
     pref = np.exp(-0.5 * (np.linalg.norm(alpha) ** 2 - alpha.conj() @ B @ alpha.conj()))
-    psi = psi * pref
-
-    if normalize:
-        norm = np.sqrt(np.sum(np.abs(psi) ** 2))
-        psi = psi / norm
-
-    return psi
-
-
-def density_matrix(mu, cov, post_select=None, normalize=False, cutoff=5, hbar=2):
-    r"""Returns the density matrix of a (PNR post-selected) Gaussian state.
-
-    The resulting density matrix will have shape
-
-    .. math:: \underbrace{D\times D \times \cdots \times D}_{2M}
-
-    where :math:`D` is the Fock space cutoff, and :math:`M` is the
-    number of *non* post-selected modes, i.e. ``M = len(mu)//2 - len(post_select)``.
-
-    Note that we use the Strawberry Fields convention for indexing the density
-    matrix; the first two dimensions correspond to subsystem 1, the second two
-    dimensions correspond to subsystem 2, etc.
-
-    Args:
-        mu (array): length-:math:`2N` means vector in xp-ordering
-        cov (array): :math:`2N\times 2N` covariance matrix in xp-ordering
-        post_select (dict): dictionary containing the post-selected modes, of
-            the form ``{mode: value}``.
-        normalize (bool): If ``True``, a post-selected density matrix is re-normalized.
-        cutoff (dim): the final length (i.e., Hilbert space dimension) of each
-            mode in the density matrix.
-        hbar (float): the value of :math:`\hbar` in the commutation
-            relation :math:`[\x,\p]=i\hbar`.
 
-    Returns:
-        np.array[complex]: the density matrix of the Gaussian state
-    """
     if post_select is None:
-        post_select = {}
-
-    N = len(mu) // 2
-    M = N - len(post_select)
-
-    rho = np.zeros([cutoff] * (2 * M), dtype=np.complex128)
-
-    for idx in product(range(cutoff), repeat=2 * M):
-        el = []
-
-        counter = count(0)
-        modes = (np.arange(2 * N) % N).tolist()
-        el = [post_select[i] if i in post_select else idx[next(counter)] for i in modes]
+        psi = (
+            pref
+            * hafnian_batched(B, cutoff, mu=alpha, renorm=True)
+            / np.sqrt(np.sqrt(np.linalg.det(Q).real))
+        )
+    else:
+        M = N - len(post_select)
+        psi = np.zeros([cutoff] * (M), dtype=np.complex128)
 
-        el = np.array(el).reshape(2, -1)
-        el0 = el[0].tolist()
-        el1 = el[1].tolist()
+        for idx in product(range(cutoff), repeat=M):
+            el = []
 
-        sf_idx = np.array(idx).reshape(2, -1)
-        sf_el = tuple(sf_idx[::-1].T.flatten())
-
-        rho[sf_el] = density_matrix_element(mu, cov, el0, el1, include_prefactor=False, hbar=hbar)
+            counter = count(0)
+            modes = (np.arange(N)).tolist()
+            el = [post_select[i] if i in post_select else idx[next(counter)] for i in modes]
+            psi[idx] = pure_state_amplitude(
+                mu, cov, el, check_purity=False, include_prefactor=False
+            )
 
-    rho *= prefactor(mu, cov, hbar=hbar)
+        psi = psi * pref
 
     if normalize:
-        # construct the standard 2D density matrix, and take the trace
-        new_ax = np.arange(2 * M).reshape([M, 2]).T.flatten()
-        tr = np.trace(rho.transpose(new_ax).reshape([cutoff ** M, cutoff ** M])).real
-        # renormalize
-        rho /= tr
+        norm = np.sqrt(np.sum(np.abs(psi) ** 2))
+        psi = psi / norm
 
-    return rho
+    return psi
 
 
 def find_scaling_adjacency_matrix(A, n_mean):
diff --git a/hafnian/tests/test_hafnian_approx.py b/hafnian/tests/test_hafnian_approx.py
index f37d5ac43..7e608cf83 100644
--- a/hafnian/tests/test_hafnian_approx.py
+++ b/hafnian/tests/test_hafnian_approx.py
@@ -30,7 +30,7 @@ def test_rank_one(n):
     A = np.outer(x, x)
     exact = factorial2(n - 1) * np.prod(x)
     approx = haf_real(A, approx=True, nsamples=10000)
-    assert np.allclose(approx, exact, rtol=1e-1, atol=0)
+    assert np.allclose(approx, exact, rtol=2e-1, atol=0)
 
 
 def test_approx_complex_error():
diff --git a/hafnian/tests/test_hermite_multidimensional.py b/hafnian/tests/test_hermite_multidimensional.py
new file mode 100644
index 000000000..cddfc80f1
--- /dev/null
+++ b/hafnian/tests/test_hermite_multidimensional.py
@@ -0,0 +1,123 @@
+# Copyright 2019 Xanadu Quantum Technologies Inc.
+
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+
+#     http://www.apache.org/licenses/LICENSE-2.0
+
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+"""Tests for the batch hafnian wrapper function"""
+# pylint: disable=no-self-use,redefined-outer-name
+from itertools import product
+
+import numpy as np
+
+from scipy.special import eval_hermitenorm, eval_hermite
+
+from hafnian import hermite_multidimensional, hafnian_batched, hafnian_repeated
+
+
+def test_hermite_multidimensional_renorm():
+    """ This tests the renormalized batchhafnian wrapper function to compute photon number statistics for a fixed gaussian state.
+	"""
+    B = np.sqrt(0.5) * np.array([[0, 1], [1, 0]]) + 0 * 1j
+    res = 10
+    expected = np.diag(0.5 ** (np.arange(0, res) / 2))
+    array = hermite_multidimensional(-B, res, renorm=True)
+
+    assert np.allclose(array, expected)
+
+
+def test_reduction_to_physicists_polys():
+    """Tests that the multidimensional hermite polynomials reduce to the regular physicists' hermite polynomials in the appropriate limit"""
+    x = np.arange(-1, 1, 0.1)
+    init = 1
+    n_max = 5
+    A = np.ones([init, init], dtype=complex)
+    vals = np.array(
+        [hermite_multidimensional(2 * A, n_max, y=np.array([x0], dtype=complex)) for x0 in x]
+    ).T
+    expected = np.array([eval_hermite(i, x) for i in range(len(vals))])
+    assert np.allclose(vals, expected)
+
+
+def test_reduction_to_probabilist_polys():
+    """Tests that the multidimensional hermite polynomials reduce to the regular probabilist' hermite polynomials in the appropriate limit"""
+    x = np.arange(-1, 1, 0.1)
+    init = 1
+    n_max = 5
+    A = np.ones([init, init], dtype=complex)
+    vals = np.array(
+        [hermite_multidimensional(A, n_max, y=np.array([x0], dtype=complex)) for x0 in x]
+    ).T
+    expected = np.array([eval_hermitenorm(i, x) for i in range(len(vals))])
+    assert np.allclose(vals, expected)
+
+
+def test_hafnian_batched():
+    """Test hafnian_batched against hafnian_repeated for a random symmetric matrix"""
+    n_modes = 4
+    A = np.random.rand(n_modes, n_modes) + 1j * np.random.rand(n_modes, n_modes)
+    A += A.T
+    n_photon = 5
+    v1 = np.array([hafnian_repeated(A, q) for q in product(np.arange(n_photon), repeat=n_modes)])
+    assert np.allclose(hafnian_batched(A, n_photon, make_tensor=False), v1)
+
+
+def test_hafnian_batched_loops():
+    """Test hafnian_batched with loops against hafnian_repeated with loops for a random symmetric matrix
+    and a random vector of loops
+    """
+    n_modes = 4
+    A = np.random.rand(n_modes, n_modes) + 1j * np.random.rand(n_modes, n_modes)
+    A += A.T
+    mu = np.random.rand(n_modes) + 1j * np.random.rand(n_modes)
+    n_photon = 5
+    v1 = np.array(
+        [
+            hafnian_repeated(A, q, mu=mu, loop=True)
+            for q in product(np.arange(n_photon), repeat=n_modes)
+        ]
+    )
+    expected = hafnian_batched(A, n_photon, mu=mu, make_tensor=False)
+
+    assert np.allclose(expected, v1)
+
+
+def test_hafnian_batched_loops_no_edges():
+    """Test hafnian_batched with loops against hafnian_repeated with loops for a random symmetric matrix
+    and a random vector of loops
+    """
+    n_modes = 4
+    A = np.zeros([n_modes, n_modes], dtype=complex)
+    mu = np.random.rand(n_modes) + 1j * np.random.rand(n_modes)
+    n_photon = 5
+    v1 = np.array(
+        [
+            hafnian_repeated(A, q, mu=mu, loop=True)
+            for q in product(np.arange(n_photon), repeat=n_modes)
+        ]
+    )
+    expected = hafnian_batched(A, n_photon, mu=mu, make_tensor=False)
+
+    assert np.allclose(expected, v1)
+
+
+def test_hafnian_batched_zero_loops_no_edges():
+    """Test hafnian_batched with loops against hafnian_repeated with loops for a the zero matrix
+    and a loops
+    """
+    n_modes = 4
+    A = np.zeros([n_modes, n_modes], dtype=complex)
+    n_photon = 5
+    v1 = np.array(
+        [hafnian_repeated(A, q, loop=True) for q in product(np.arange(n_photon), repeat=n_modes)]
+    )
+    expected = hafnian_batched(A, n_photon, make_tensor=False)
+
+    assert np.allclose(expected, v1)
diff --git a/hafnian/tests/test_quantum.py b/hafnian/tests/test_quantum.py
index 345e92221..2d9f53730 100644
--- a/hafnian/tests/test_quantum.py
+++ b/hafnian/tests/test_quantum.py
@@ -354,8 +354,8 @@ def test_density_matrix_squeezed():
     assert np.allclose(res, expected)
 
 
-def test_density_matrix_displaced_squeezed():
-    """Test density matrix for a squeezed state"""
+def test_coherent_squeezed():
+    """Test density matrix for a squeezed displaced state"""
     r = 0.43
 
     mu = np.array([0.24, -0.2])
diff --git a/hafnian/tests/test_samples.py b/hafnian/tests/test_samples.py
index b617498a8..f75063cd4 100644
--- a/hafnian/tests/test_samples.py
+++ b/hafnian/tests/test_samples.py
@@ -225,7 +225,7 @@ def test_hafnian_sample_graph(self):
         mean_n = 0.5
         samples = hafnian_sample_graph(A, mean_n, samples=n_samples)
         approx_mean_n = np.sum(samples) / n_samples
-        assert np.allclose(mean_n, approx_mean_n, rtol=1e-1)
+        assert np.allclose(mean_n, approx_mean_n, rtol=2e-1)
 
     def test_single_pm_graphs(self):
         """Tests that the number of photons is the same for modes i and n-i
@@ -259,8 +259,6 @@ def test_probability_vacuum(self):
 
         A = np.triu(A)
         A = A + np.transpose(A)
-        for i in range(n):
-            A[i, i] = 0
         n_mean = 1.0
         Q = gen_Qmat_from_graph(A, n_mean)
         prob0 = np.abs(1 / (np.sqrt(np.linalg.det(Q))))
diff --git a/setup.py b/setup.py
index 7bf9b79a7..5b3bd0a7b 100644
--- a/setup.py
+++ b/setup.py
@@ -112,6 +112,7 @@ def cythonize(x, compile_time_env=None):
                          "src/hafnian_approx.hpp",
                          "src/torontonian.hpp",
                          "src/permanent.hpp",
+                         "src/hermite_multidimensional.hpp",
                          "src/stdafx.h",
                          "src/fsum.hpp"],
                 include_dirs=C_INCLUDE_PATH,
diff --git a/src/hafnian.hpp b/src/hafnian.hpp
index 8bdac0d6c..a0eaa23b9 100644
--- a/src/hafnian.hpp
+++ b/src/hafnian.hpp
@@ -19,6 +19,7 @@
 #include <hafnian_approx.hpp>
 #include <torontonian.hpp>
 #include <permanent.hpp>
+#include <hermite_multidimensional.hpp>
 
 /**
  * @namespace hafnian
diff --git a/src/hermite_multidimensional.hpp b/src/hermite_multidimensional.hpp
new file mode 100644
index 000000000..8b69e4c22
--- /dev/null
+++ b/src/hermite_multidimensional.hpp
@@ -0,0 +1,205 @@
+// Copyright 2019 Xanadu Quantum Technologies Inc.
+
+
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+
+//     http://www.apache.org/licenses/LICENSE-2.0
+
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+#pragma once
+#include <stdafx.h>
+
+#include <Eigen/Eigenvalues>
+#include <Eigen/LU>
+
+typedef unsigned long long int ullint;
+
+
+ullint vec2index(std::vector<int> &pos, int resolution) {
+    int dim = pos.size();
+    ullint nextCoordinate = 0;
+
+    nextCoordinate = pos[0]-1;
+    for(int ii = 0; ii < dim-1; ii++) {
+        nextCoordinate = nextCoordinate*resolution + (pos[ii+1]-1);
+    }
+
+    return nextCoordinate;
+
+}
+
+std::vector<int> find_rep(int val, int base, int n) {
+    std::vector<int> x(n, 0);
+    int local_val = val;
+
+    x[0] = 1;
+
+    for (int i = 1; i < n; i++)
+        x[i] = x[i-1]*base;
+
+    std::vector<int> digits(n, 0);
+
+    for (int i = 0; i < n; i++) {
+        digits[i] = local_val/x[n-i-1];
+        local_val = local_val - digits[i] * x[n-i-1];
+    }
+
+    return digits;
+
+}
+
+
+long double sqrtfactorial(int nn)
+{
+    long double n = static_cast<long double>(nn);
+
+    if(n > 1)
+        return std::sqrt(n) * sqrtfactorial(n - 1);
+    else
+        return 1;
+}
+
+/**
+ * Renormalizes and unnormalized photon number statistics of a Gaussian state.
+ * Based on the MATLAB code available at: https://github.com/clementsw/gaussian-optics
+ *
+ * @param tn unnormalized flattened vector of size \f$res**nmodes$ representing unnormalized photon number statistics
+ *       \f$2n\times 2n\f$ row-ordered symmetric matrix.
+ * @param nmodes number of modes
+ * @param res highest number of photons to be resolved.
+ *
+ * $return Renormalized photon number statistics
+ */
+template <typename T>
+inline std::vector<T> renormalization(std::vector<T> tn, int nmodes, int res) {
+    std::vector<long double> invsqfacts(res, 0);
+    std::vector<int> digits(nmodes, 0);
+
+    ullint Hdim = pow(res, nmodes);
+
+    for (int i = 0; i < res; i++)
+        invsqfacts[i] = sqrtfactorial(i);
+
+    for (ullint i = 0; i < Hdim; i++) {
+        digits = find_rep(i, res, nmodes);
+        long double pref = 1;
+        for (int j = 0; j < nmodes; j++)
+            pref *= 1.0L/invsqfacts[digits[j]];
+        tn[i] = tn[i]*static_cast<double>(pref);
+    }
+
+    return tn;
+
+}
+
+
+
+namespace hafnian {
+
+/**
+ * Returns photon number statistics of a Gaussian state for a given covariance matrix `mat`.
+ * Based on the MATLAB code available at: https://github.com/clementsw/gaussian-optics
+ *
+ * @param mat a flattened vector of size \f$2n^2\f$, representing an
+ *       \f$2n\times 2n\f$ row-ordered symmetric matrix.
+ * @param d a flattened vector of size \f$2n\f$, representing the first order moments.
+ * @param resolution highest number of photons to be resolved.
+ *
+ */
+template <typename T>
+inline std::vector<T> hermite_multidimensional_cpp(std::vector<T> &R_mat, std::vector<T> &y_mat, int &resolution, int &renorm) {
+    int dim = std::sqrt(static_cast<double>(R_mat.size()));
+
+    namespace eg = Eigen;
+
+    eg::Matrix<T, eg::Dynamic, eg::Dynamic> R = eg::Map<eg::Matrix<T, eg::Dynamic, eg::Dynamic>, eg::Unaligned>(R_mat.data(), dim, dim);
+    eg::Matrix<T, eg::Dynamic, eg::Dynamic> y = eg::Map<eg::Matrix<T, eg::Dynamic, eg::Dynamic>, eg::Unaligned>(y_mat.data(), dim, dim);
+
+    ullint Hdim = pow(resolution, dim);
+    std::vector<T> H(Hdim, 0);
+    std::vector<double> ren_factor(Hdim, 0);
+
+    H[0] = 1;
+    ren_factor[0] = 1;
+
+    std::vector<int> nextPos(dim, 1);
+    std::vector<int> jumpFrom(dim, 1);
+    std::vector<int> ek(dim, 0);
+    std::vector<double> factors(resolution+1, 0);
+    int jump = 0;
+
+
+    for (ullint jj = 0; jj < Hdim-1; jj++) {
+
+        if (jump > 0) {
+            jumpFrom[jump] += 1;
+            jump = 0;
+        }
+
+
+        for (int ii = 0; ii < dim; ii++) {
+            std::vector<int> forwardStep(dim, 0);
+            forwardStep[ii] = 1;
+
+            if ( forwardStep[ii] + nextPos[ii] > resolution) {
+                nextPos[ii] = 1;
+                jumpFrom[ii] = 1;
+                jump = ii+1;
+            }
+            else {
+                jumpFrom[ii] = nextPos[ii];
+                nextPos[ii] = nextPos[ii] + 1;
+                break;
+            }
+        }
+
+        for (int ii = 0; ii < dim; ii++)
+            ek[ii] = nextPos[ii] - jumpFrom[ii];
+
+        int k = 0;
+        for(; k < static_cast<int>(ek.size()); k++) {
+            if(ek[k]) break;
+        }
+
+        ullint nextCoordinate = vec2index(nextPos, resolution);
+        ullint fromCoordinate = vec2index(jumpFrom, resolution);
+
+
+        for (int ii = 0; ii < dim; ii++) {
+            H[nextCoordinate] = H[nextCoordinate] + R(k, ii) * y(ii, 0);
+        }
+        H[nextCoordinate] = H[nextCoordinate] * H[fromCoordinate];
+
+        std::vector<int> tmpjump(dim, 0);
+
+        for (int ii = 0; ii < dim; ii++) {
+            if (jumpFrom[ii] > 1) {
+                std::vector<int> prevJump(dim, 0);
+                prevJump[ii] = 1;
+                std::transform(jumpFrom.begin(), jumpFrom.end(), prevJump.begin(), tmpjump.begin(), std::minus<int>());
+                ullint prevCoordinate = vec2index(tmpjump, resolution);
+                H[nextCoordinate] = H[nextCoordinate] - (static_cast<T>(jumpFrom[ii]-1))*static_cast<T>(R(k,ii))*H[prevCoordinate];
+
+            }
+        }
+
+    }
+
+    if (renorm) {
+        H = renormalization(H, dim, resolution);
+    }
+
+    return H;
+
+}
+
+
+
+}
diff --git a/src/permanent.hpp b/src/permanent.hpp
index f9dcd6777..6a463bd4f 100644
--- a/src/permanent.hpp
+++ b/src/permanent.hpp
@@ -22,10 +22,10 @@ typedef long long int llint;
 //typedef long double qp;
 
 #if (defined(__GNUC__) || defined(__GNUG__)) && !(defined(__clang__) || defined(__INTEL_COMPILER))
-	typedef __float128 qp;
-	//#include <quadmath.h>
+typedef __float128 qp;
+//#include <quadmath.h>
 #else
-	typedef long double qp;
+typedef long double qp;
 #endif
 
 /**
@@ -210,7 +210,7 @@ inline double perm_fsum(std::vector<T> &mat) {
 #endif
 
     std::vector<T> tot(nthreads, static_cast<T>(0));
-   
+
     std::vector<llint> threadbound_low(nthreads);
     std::vector<llint> threadbound_hi(nthreads);
 
@@ -224,7 +224,7 @@ inline double perm_fsum(std::vector<T> &mat) {
     #pragma omp parallel for shared(tot)
     for (int ii = 0; ii < nthreads; ii++) {
 
-    	fsum::sc_partials permtmp; // = 0;
+        fsum::sc_partials permtmp; // = 0;
 
         int cntr = 0;
         std::vector<int> chitmp(n, 0);
@@ -272,9 +272,8 @@ inline double perm_fsum(std::vector<T> &mat) {
                 permtmp -= rowsumprod;
 
         }
-       tot[ii] = permtmp;
+        tot[ii] = permtmp;
     }
-
     return static_cast<T>(std::accumulate(tot.begin(), tot.end(), static_cast<T>(0)));
 }
 
diff --git a/src/tests/Makefile b/src/tests/Makefile
index 9ef5a13df..07786f9ab 100644
--- a/src/tests/Makefile
+++ b/src/tests/Makefile
@@ -18,7 +18,8 @@ EIGEN_INCLUDE_DIR=/usr/include/eigen3
 CC=g++
 CFLAGS=-std=c++11 -O3 -g -Wall -fopenmp -fPIC -I/usr/include \
 	-I.. -I$(EIGEN_INCLUDE_DIR) -I$(GOOGLETEST_DIR)/include \
-	-march=native
+	-march=native 
+
 LFLAGS=-fopenmp -L$(GOOGLETEST_DIR)/lib -lgtest
 
 all: test
diff --git a/src/tests/hafnian_unittest.cpp b/src/tests/hafnian_unittest.cpp
index ae94a2afb..74784654b 100644
--- a/src/tests/hafnian_unittest.cpp
+++ b/src/tests/hafnian_unittest.cpp
@@ -19,6 +19,8 @@
 #include <math.h>
 
 const double tol = 1.0e-10f;
+const double tol2 = 1.0e-7f;
+
 
 namespace permanent {
 TEST(PermanentRealFsum, CompleteGraph) {
@@ -41,14 +43,14 @@ TEST(PermanentFsum, Random) {
     std::normal_distribution<double> distribution(1.0, 0.0);
 
     for (int i = 0; i < 3; i++) {
-        for(int j = 0; j < 3; j++) {
+        for (int j = 0; j < 3; j++) {
             double randnum = distribution(generator);
-            mat[i*3+j] = randnum;
+            mat[i * 3 + j] = randnum;
         }
     }
 
-    double expected = mat[2]*mat[4]*mat[6] + mat[1]*mat[5]*mat[6] + mat[2]*mat[3]*mat[7]
-                      + mat[0]*mat[5]*mat[7] + mat[1]*mat[3]*mat[8] + mat[0]*mat[4]*mat[8];
+    double expected = mat[2] * mat[4] * mat[6] + mat[1] * mat[5] * mat[6] + mat[2] * mat[3] * mat[7]
+                      + mat[0] * mat[5] * mat[7] + mat[1] * mat[3] * mat[8] + mat[0] * mat[4] * mat[8];
 
     EXPECT_NEAR(expected, hafnian::permanent_fsum(mat), tol);
 
@@ -74,14 +76,14 @@ TEST(PermanentReal, Random) {
     std::normal_distribution<double> distribution(1.0, 0.0);
 
     for (int i = 0; i < 3; i++) {
-        for(int j = 0; j < 3; j++) {
+        for (int j = 0; j < 3; j++) {
             double randnum = distribution(generator);
-            mat[i*3+j] = randnum;
+            mat[i * 3 + j] = randnum;
         }
     }
 
-    double expected = mat[2]*mat[4]*mat[6] + mat[1]*mat[5]*mat[6] + mat[2]*mat[3]*mat[7]
-                      + mat[0]*mat[5]*mat[7] + mat[1]*mat[3]*mat[8] + mat[0]*mat[4]*mat[8];
+    double expected = mat[2] * mat[4] * mat[6] + mat[1] * mat[5] * mat[6] + mat[2] * mat[3] * mat[7]
+                      + mat[0] * mat[5] * mat[7] + mat[1] * mat[3] * mat[8] + mat[0] * mat[4] * mat[8];
 
     EXPECT_NEAR(expected, hafnian::permanent_quad(mat), tol);
 
@@ -97,15 +99,15 @@ TEST(PermanentComplex, Random) {
     std::normal_distribution<double> distribution(1.0, 0.0);
 
     for (int i = 0; i < 3; i++) {
-        for(int j = 0; j < 3; j++) {
+        for (int j = 0; j < 3; j++) {
             double randnum1 = distribution(generator);
             double randnum2 = distribution(generator);
-            mat[i*3+j] = std::complex<double>(randnum1, randnum2);
+            mat[i * 3 + j] = std::complex<double>(randnum1, randnum2);
         }
     }
 
-    std::complex<double> expected = mat[2]*mat[4]*mat[6] + mat[1]*mat[5]*mat[6] + mat[2]*mat[3]*mat[7]
-                                    + mat[0]*mat[5]*mat[7] + mat[1]*mat[3]*mat[8] + mat[0]*mat[4]*mat[8];
+    std::complex<double> expected = mat[2] * mat[4] * mat[6] + mat[1] * mat[5] * mat[6] + mat[2] * mat[3] * mat[7]
+                                    + mat[0] * mat[5] * mat[7] + mat[1] * mat[3] * mat[8] + mat[0] * mat[4] * mat[8];
 
     std::complex<double> perm = hafnian::permanent_quad(mat);
 
@@ -139,13 +141,13 @@ TEST(HafianRecursiveDouble, Random) {
     std::normal_distribution<double> distribution(1.0, 0.0);
 
     for (int i = 0; i < 4; i++) {
-        for(int j = 0; j < 4; j++) {
+        for (int j = 0; j < 4; j++) {
             double randnum = distribution(generator);
-            mat[i*4+j] = randnum;
+            mat[i * 4 + j] = randnum;
         }
     }
 
-    double expected = mat[1]*mat[11] + mat[2]*mat[7] + mat[3]*mat[6];
+    double expected = mat[1] * mat[11] + mat[2] * mat[7] + mat[3] * mat[6];
 
     EXPECT_NEAR(expected, hafnian::hafnian_recursive_quad(mat), tol);
 }
@@ -220,14 +222,14 @@ TEST(HafianRecursiveDoubleComplex, Random) {
     std::normal_distribution<double> distribution(1.0, 0.0);
 
     for (int i = 0; i < 4; i++) {
-        for(int j = 0; j < 4; j++) {
+        for (int j = 0; j < 4; j++) {
             double randnum1 = distribution(generator);
             double randnum2 = distribution(generator);
-            mat[i*4+j] = std::complex<double>(randnum1, randnum2);
+            mat[i * 4 + j] = std::complex<double>(randnum1, randnum2);
         }
     }
 
-    std::complex<double> expected = mat[1]*mat[11] + mat[2]*mat[7] + mat[3]*mat[6];
+    std::complex<double> expected = mat[1] * mat[11] + mat[2] * mat[7] + mat[3] * mat[6];
 
     std::complex<double> haf = hafnian::hafnian_recursive_quad(mat);
 
@@ -294,13 +296,13 @@ TEST(HafianEigenDouble, Random) {
     std::normal_distribution<double> distribution(1.0, 0.0);
 
     for (int i = 0; i < 4; i++) {
-        for(int j = 0; j < 4; j++) {
+        for (int j = 0; j < 4; j++) {
             double randnum = distribution(generator);
-            mat[i*4+j] = randnum;
+            mat[i * 4 + j] = randnum;
         }
     }
 
-    double expected = mat[1]*mat[11] + mat[2]*mat[7] + mat[3]*mat[6];
+    double expected = mat[1] * mat[11] + mat[2] * mat[7] + mat[3] * mat[6];
 
     EXPECT_NEAR(expected, hafnian::hafnian_eigen(mat), tol);
 }
@@ -375,14 +377,14 @@ TEST(HafianEigenDoubleComplex, Random) {
     std::normal_distribution<double> distribution(1.0, 0.0);
 
     for (int i = 0; i < 4; i++) {
-        for(int j = 0; j < 4; j++) {
+        for (int j = 0; j < 4; j++) {
             double randnum1 = distribution(generator);
             double randnum2 = distribution(generator);
-            mat[i*4+j] = std::complex<double>(randnum1, randnum2);
+            mat[i * 4 + j] = std::complex<double>(randnum1, randnum2);
         }
     }
 
-    std::complex<double> expected = mat[1]*mat[11] + mat[2]*mat[7] + mat[3]*mat[6];
+    std::complex<double> expected = mat[1] * mat[11] + mat[2] * mat[7] + mat[3] * mat[6];
 
     std::complex<double> haf = hafnian::hafnian_eigen(mat);
 
@@ -451,8 +453,8 @@ TEST(HafnianApproxNonngeative, Random) {
     }
 
     for (int i = 0; i < n; i++) {
-        for(int j = 0; j < n; j++) {
-            mat4[i*n+j] = x4[i]*x4[j];
+        for (int j = 0; j < n; j++) {
+            mat4[i * n + j] = x4[i] * x4[j];
         }
     }
 
@@ -466,8 +468,8 @@ TEST(HafnianApproxNonngeative, Random) {
     }
 
     for (int i = 0; i < n; i++) {
-        for(int j = 0; j < n; j++) {
-            mat6[i*n+j] = x6[i]*x6[j];
+        for (int j = 0; j < n; j++) {
+            mat6[i * n + j] = x6[i] * x6[j];
         }
     }
 
@@ -480,8 +482,8 @@ TEST(HafnianApproxNonngeative, Random) {
     }
 
     for (int i = 0; i < n; i++) {
-        for(int j = 0; j < n; j++) {
-            mat8[i*n+j] = x8[i]*x8[j];
+        for (int j = 0; j < n; j++) {
+            mat8[i * n + j] = x8[i] * x8[j];
         }
     }
 
@@ -493,9 +495,9 @@ TEST(HafnianApproxNonngeative, Random) {
     double haf6 = hafnian::hafnian_approx(mat6, nsamples);
     double haf8 = hafnian::hafnian_approx(mat8, nsamples);
 
-    EXPECT_NEAR(expected4, haf4, haf4/15.0);
-    EXPECT_NEAR(expected6, haf6, haf6/15.0);
-    EXPECT_NEAR(expected8, haf8, haf8/15.0);
+    EXPECT_NEAR(expected4, haf4, haf4 / 15.0);
+    EXPECT_NEAR(expected6, haf6, haf6 / 15.0);
+    EXPECT_NEAR(expected8, haf8, haf8 / 15.0);
 
 }
 
@@ -530,16 +532,16 @@ TEST(HafnianRepeatedDouble, AllOneRpt) {
     std::normal_distribution<double> distribution(1.0, 0.0);
 
     for (int i = 0; i < 2; i++) {
-        for(int j = 0; j < 2; j++) {
+        for (int j = 0; j < 2; j++) {
             double randnum = distribution(generator);
-            mat2rand[i*2+j] = randnum;
+            mat2rand[i * 2 + j] = randnum;
         }
     }
 
     for (int i = 0; i < 4; i++) {
-        for(int j = 0; j < 4; j++) {
+        for (int j = 0; j < 4; j++) {
             double randnum = distribution(generator);
-            mat4rand[i*4+j] = randnum;
+            mat4rand[i * 4 + j] = randnum;
         }
     }
 
@@ -548,7 +550,7 @@ TEST(HafnianRepeatedDouble, AllOneRpt) {
     double expected2rand = mat2rand[1];
 
     double expected4 = 3;
-    double expected4rand = mat4rand[1]*mat4rand[11] + mat4rand[2]*mat4rand[7] + mat4rand[3]*mat4rand[6];;
+    double expected4rand = mat4rand[1] * mat4rand[11] + mat4rand[2] * mat4rand[7] + mat4rand[3] * mat4rand[6];;
 
     double haf2 = hafnian::hafnian_rpt_quad(mat2, rpt2);
     double haf2rand = hafnian::hafnian_rpt_quad(mat2rand, rpt2);
@@ -592,18 +594,18 @@ TEST(HafnianRepeatedComplex, AllOneRpt) {
     std::normal_distribution<double> distribution(1.0, 0.0);
 
     for (int i = 0; i < 2; i++) {
-        for(int j = 0; j < 2; j++) {
+        for (int j = 0; j < 2; j++) {
             double randnum1 = distribution(generator);
             double randnum2 = distribution(generator);
-            mat2rand[i*2+j] = std::complex<double>(randnum1, randnum2);
+            mat2rand[i * 2 + j] = std::complex<double>(randnum1, randnum2);
         }
     }
 
     for (int i = 0; i < 4; i++) {
-        for(int j = 0; j < 4; j++) {
+        for (int j = 0; j < 4; j++) {
             double randnum1 = distribution(generator);
             double randnum2 = distribution(generator);
-            mat4rand[i*4+j] = std::complex<double>(randnum1, randnum2);
+            mat4rand[i * 4 + j] = std::complex<double>(randnum1, randnum2);
         }
     }
 
@@ -615,7 +617,7 @@ TEST(HafnianRepeatedComplex, AllOneRpt) {
 
     double expected4_re = 3;
     double expected4_im = 0;
-    std::complex<double> expected4rand = mat4rand[1]*mat4rand[11] + mat4rand[2]*mat4rand[7] + mat4rand[3]*mat4rand[6];;
+    std::complex<double> expected4rand = mat4rand[1] * mat4rand[11] + mat4rand[2] * mat4rand[7] + mat4rand[3] * mat4rand[6];;
     double expected4rand_re = std::real(expected4rand);
     double expected4rand_im = std::imag(expected4rand);
 
@@ -675,16 +677,16 @@ TEST(LoopHafnianEigenDouble, EvenRandom) {
     std::normal_distribution<double> distribution(1.0, 0.0);
 
     for (int i = 0; i < 2; i++) {
-        for(int j = 0; j < 2; j++) {
+        for (int j = 0; j < 2; j++) {
             double randnum1 = distribution(generator);
-            mat2[i*2+j] = randnum1;
+            mat2[i * 2 + j] = randnum1;
         }
     }
 
     for (int i = 0; i < 4; i++) {
-        for(int j = 0; j < 4; j++) {
+        for (int j = 0; j < 4; j++) {
             double randnum1 = distribution(generator);
-            mat4[i*4+j] = randnum1;
+            mat4[i * 4 + j] = randnum1;
         }
     }
 
@@ -692,11 +694,11 @@ TEST(LoopHafnianEigenDouble, EvenRandom) {
     double haf4 = hafnian::loop_hafnian_eigen(mat4);
 
     double expected2 = mat2[1] + mat2[0] * mat2[3];
-    double expected4 = mat4[1]*mat4[11] + mat4[2]*mat4[7] + mat4[3]*mat4[6] +
-                       mat4[0]*mat4[5]*mat4[11] + mat4[1]*mat4[10]*mat4[15] +
-                       mat4[2]*mat4[5]*mat4[15] + mat4[0]*mat4[10]*mat4[7] +
-                       mat4[0]*mat4[15]*mat4[6] + mat4[3]*mat4[5]*mat4[10] +
-                       mat4[0]*mat4[5]*mat4[10]*mat4[15];
+    double expected4 = mat4[1] * mat4[11] + mat4[2] * mat4[7] + mat4[3] * mat4[6] +
+                       mat4[0] * mat4[5] * mat4[11] + mat4[1] * mat4[10] * mat4[15] +
+                       mat4[2] * mat4[5] * mat4[15] + mat4[0] * mat4[10] * mat4[7] +
+                       mat4[0] * mat4[15] * mat4[6] + mat4[3] * mat4[5] * mat4[10] +
+                       mat4[0] * mat4[5] * mat4[10] * mat4[15];
 
     EXPECT_NEAR(expected2, haf2, tol);
     EXPECT_NEAR(expected4, haf4, tol);
@@ -742,18 +744,18 @@ TEST(LoopHafnianEigenComplex, EvenRandom) {
     std::normal_distribution<double> distribution(1.0, 0.0);
 
     for (int i = 0; i < 2; i++) {
-        for(int j = 0; j < 2; j++) {
+        for (int j = 0; j < 2; j++) {
             double randnum1 = distribution(generator);
             double randnum2 = distribution(generator);
-            mat2[i*2+j] = std::complex<double>(randnum1, randnum2);
+            mat2[i * 2 + j] = std::complex<double>(randnum1, randnum2);
         }
     }
 
     for (int i = 0; i < 4; i++) {
-        for(int j = 0; j < 4; j++) {
+        for (int j = 0; j < 4; j++) {
             double randnum1 = distribution(generator);
             double randnum2 = distribution(generator);
-            mat4[i*4+j] = std::complex<double>(randnum1, randnum2);
+            mat4[i * 4 + j] = std::complex<double>(randnum1, randnum2);
         }
     }
 
@@ -761,11 +763,11 @@ TEST(LoopHafnianEigenComplex, EvenRandom) {
     std::complex<double> haf4 = hafnian::loop_hafnian_eigen(mat4);
 
     std::complex<double> expected2 = mat2[1] + mat2[0] * mat2[3];
-    std::complex<double> expected4 = mat4[1]*mat4[11] + mat4[2]*mat4[7] + mat4[3]*mat4[6] +
-                                     mat4[0]*mat4[5]*mat4[11] + mat4[1]*mat4[10]*mat4[15] +
-                                     mat4[2]*mat4[5]*mat4[15] + mat4[0]*mat4[10]*mat4[7] +
-                                     mat4[0]*mat4[15]*mat4[6] + mat4[3]*mat4[5]*mat4[10] +
-                                     mat4[0]*mat4[5]*mat4[10]*mat4[15];
+    std::complex<double> expected4 = mat4[1] * mat4[11] + mat4[2] * mat4[7] + mat4[3] * mat4[6] +
+                                     mat4[0] * mat4[5] * mat4[11] + mat4[1] * mat4[10] * mat4[15] +
+                                     mat4[2] * mat4[5] * mat4[15] + mat4[0] * mat4[10] * mat4[7] +
+                                     mat4[0] * mat4[15] * mat4[6] + mat4[3] * mat4[5] * mat4[10] +
+                                     mat4[0] * mat4[5] * mat4[10] * mat4[15];
 
     EXPECT_NEAR(std::real(expected2), std::real(haf2), tol);
     EXPECT_NEAR(std::imag(expected2), std::imag(haf2), tol);
@@ -824,10 +826,10 @@ TEST(LoopHafnianRepeatedDouble, EvenOnes) {
     std::vector<int> rpt6(6, 1);
 
     for (int i = 0; i < 4; i++)
-        mu4[i] = mat4[i*4+i];
+        mu4[i] = mat4[i * 4 + i];
 
     for (int i = 0; i < 6; i++)
-        mu6[i] = mat6[i*6+i];
+        mu6[i] = mat6[i * 6 + i];
 
     double haf4 = hafnian::loop_hafnian_rpt_quad(mat4, mu4, rpt4);
     double haf6 = hafnian::loop_hafnian_rpt_quad(mat6, mu6, rpt6);
@@ -857,34 +859,34 @@ TEST(LoopHafnianRepeatedDouble, EvenRandom) {
 
 
     for (int i = 0; i < 2; i++) {
-        for(int j = 0; j < 2; j++) {
+        for (int j = 0; j < 2; j++) {
             double randnum1 = distribution(generator);
-            mat2[i*2+j] = randnum1;
+            mat2[i * 2 + j] = randnum1;
         }
     }
 
     for (int i = 0; i < 4; i++) {
-        for(int j = 0; j < 4; j++) {
+        for (int j = 0; j < 4; j++) {
             double randnum1 = distribution(generator);
-            mat4[i*4+j] = randnum1;
+            mat4[i * 4 + j] = randnum1;
         }
     }
 
     for (int i = 0; i < 2; i++)
-        mu2[i] = mat2[i*2+i];
+        mu2[i] = mat2[i * 2 + i];
 
     for (int i = 0; i < 4; i++)
-        mu4[i] = mat4[i*4+i];
+        mu4[i] = mat4[i * 4 + i];
 
     double haf2 = hafnian::loop_hafnian_rpt_quad(mat2, mu2, rpt2);
     double haf4 = hafnian::loop_hafnian_rpt_quad(mat4, mu4, rpt4);
 
     double expected2 = mat2[1] + mat2[0] * mat2[3];
-    double expected4 = mat4[1]*mat4[11] + mat4[2]*mat4[7] + mat4[3]*mat4[6] +
-                       mat4[0]*mat4[5]*mat4[11] + mat4[1]*mat4[10]*mat4[15] +
-                       mat4[2]*mat4[5]*mat4[15] + mat4[0]*mat4[10]*mat4[7] +
-                       mat4[0]*mat4[15]*mat4[6] + mat4[3]*mat4[5]*mat4[10] +
-                       mat4[0]*mat4[5]*mat4[10]*mat4[15];
+    double expected4 = mat4[1] * mat4[11] + mat4[2] * mat4[7] + mat4[3] * mat4[6] +
+                       mat4[0] * mat4[5] * mat4[11] + mat4[1] * mat4[10] * mat4[15] +
+                       mat4[2] * mat4[5] * mat4[15] + mat4[0] * mat4[10] * mat4[7] +
+                       mat4[0] * mat4[15] * mat4[6] + mat4[3] * mat4[5] * mat4[10] +
+                       mat4[0] * mat4[5] * mat4[10] * mat4[15];
 
     EXPECT_NEAR(expected2, haf2, tol);
     EXPECT_NEAR(expected4, haf4, tol);
@@ -903,10 +905,10 @@ TEST(LoopHafnianRepeatedDouble, Odd) {
     std::vector<int> rpt5(5, 1);
 
     for (int i = 0; i < 3; i++)
-        mu3[i] = mat3[i*3+i];
+        mu3[i] = mat3[i * 3 + i];
 
     for (int i = 0; i < 5; i++)
-        mu5[i] = mat5[i*5+i];
+        mu5[i] = mat5[i * 5 + i];
 
     double haf3 = hafnian::loop_hafnian_rpt_quad(mat3, mu3, rpt3);
     double haf5 = hafnian::loop_hafnian_rpt_quad(mat5, mu5, rpt5);
@@ -954,13 +956,13 @@ TEST(LoopHafnianRepeatedComplex, EvenOnes) {
     std::vector<int> rpt6(6, 1);
 
     for (int i = 0; i < 4; i++)
-        mu4[i] = mat4[i*4+i];
+        mu4[i] = mat4[i * 4 + i];
     std::complex<double> haf4 = hafnian::loop_hafnian_rpt_quad(mat4, mu4, rpt4);
     EXPECT_NEAR(10, std::real(haf4), tol);
     EXPECT_NEAR(0, std::imag(haf4), tol);
 
     for (int i = 0; i < 6; i++)
-        mu6[i] = mat6[i*6+i];
+        mu6[i] = mat6[i * 6 + i];
 
     std::complex<double> haf6 = hafnian::loop_hafnian_rpt_quad(mat6, mu6, rpt6);
 
@@ -988,36 +990,36 @@ TEST(LoopHafnianRepeatedComplex, EvenRandom) {
 
 
     for (int i = 0; i < 2; i++) {
-        for(int j = 0; j < 2; j++) {
+        for (int j = 0; j < 2; j++) {
             double randnum1 = distribution(generator);
             double randnum2 = distribution(generator);
-            mat2[i*2+j] = std::complex<double>(randnum1, randnum2);
+            mat2[i * 2 + j] = std::complex<double>(randnum1, randnum2);
         }
     }
 
     for (int i = 0; i < 4; i++) {
-        for(int j = 0; j < 4; j++) {
+        for (int j = 0; j < 4; j++) {
             double randnum1 = distribution(generator);
             double randnum2 = distribution(generator);
-            mat4[i*4+j] = std::complex<double>(randnum1, randnum2);
+            mat4[i * 4 + j] = std::complex<double>(randnum1, randnum2);
         }
     }
 
     for (int i = 0; i < 2; i++)
-        mu2[i] = mat2[i*2+i];
+        mu2[i] = mat2[i * 2 + i];
 
     for (int i = 0; i < 4; i++)
-        mu4[i] = mat4[i*4+i];
+        mu4[i] = mat4[i * 4 + i];
 
     std::complex<double> haf2 = hafnian::loop_hafnian_rpt_quad(mat2, mu2, rpt2);
     std::complex<double> haf4 = hafnian::loop_hafnian_rpt_quad(mat4, mu4, rpt4);
 
     std::complex<double> expected2 = mat2[1] + mat2[0] * mat2[3];
-    std::complex<double> expected4 = mat4[1]*mat4[11] + mat4[2]*mat4[7] + mat4[3]*mat4[6] +
-                                     mat4[0]*mat4[5]*mat4[11] + mat4[1]*mat4[10]*mat4[15] +
-                                     mat4[2]*mat4[5]*mat4[15] + mat4[0]*mat4[10]*mat4[7] +
-                                     mat4[0]*mat4[15]*mat4[6] + mat4[3]*mat4[5]*mat4[10] +
-                                     mat4[0]*mat4[5]*mat4[10]*mat4[15];
+    std::complex<double> expected4 = mat4[1] * mat4[11] + mat4[2] * mat4[7] + mat4[3] * mat4[6] +
+                                     mat4[0] * mat4[5] * mat4[11] + mat4[1] * mat4[10] * mat4[15] +
+                                     mat4[2] * mat4[5] * mat4[15] + mat4[0] * mat4[10] * mat4[7] +
+                                     mat4[0] * mat4[15] * mat4[6] + mat4[3] * mat4[5] * mat4[10] +
+                                     mat4[0] * mat4[5] * mat4[10] * mat4[15];
 
     EXPECT_NEAR(std::real(expected2), std::real(haf2), tol);
     EXPECT_NEAR(std::imag(expected2), std::imag(haf2), tol);
@@ -1039,10 +1041,10 @@ TEST(LoopHafnianRepeatedComplex, Odd) {
     std::vector<int> rpt5(5, 1);
 
     for (int i = 0; i < 3; i++)
-        mu3[i] = mat3[i*3+i];
+        mu3[i] = mat3[i * 3 + i];
 
     for (int i = 0; i < 5; i++)
-        mu5[i] = mat5[i*5+i];
+        mu5[i] = mat5[i * 5 + i];
 
     std::complex<double> haf3 = hafnian::loop_hafnian_rpt_quad(mat3, mu3, rpt3);
     std::complex<double> haf5 = hafnian::loop_hafnian_rpt_quad(mat5, mu5, rpt5);
@@ -1068,16 +1070,16 @@ TEST(TorontonianDouble, TMSV) {
     double r = asinh(std::sqrt(mean_n));
 
     int n = 4;
-    for(int i = 0; i < n; i++)
-        mat4[i*n+n-i-1] = tanh(r)*1.0;
+    for (int i = 0; i < n; i++)
+        mat4[i * n + n - i - 1] = tanh(r) * 1.0;
 
     n = 8;
-    for(int i = 0; i < n; i++)
-        mat8[i*n+n-i-1] = tanh(r)*1.0;
+    for (int i = 0; i < n; i++)
+        mat8[i * n + n - i - 1] = tanh(r) * 1.0;
 
     n = 16;
-    for(int i = 0; i < n; i++)
-        mat16[i*n+n-i-1] = tanh(r)*1.0;
+    for (int i = 0; i < n; i++)
+        mat16[i * n + n - i - 1] = tanh(r) * 1.0;
 
     double tor4 = hafnian::torontonian_quad(mat4);
     double tor8 = hafnian::torontonian_quad(mat8);
@@ -1093,7 +1095,7 @@ TEST(TorontonianDouble, TMSV) {
 TEST(TorontonianDouble, Vacuum) {
     int n_modes = 5;
 
-    std::vector<double> mat(2*n_modes*2*n_modes, 0.0);
+    std::vector<double> mat(2 * n_modes * 2 * n_modes, 0.0);
 
     double tor_val = hafnian::torontonian_quad(mat);
 
@@ -1103,11 +1105,11 @@ TEST(TorontonianDouble, Vacuum) {
 TEST(TorontonianDouble, Analytical) {
     int n = 1;
     double nbar = 0.25;
-    std::vector<double> mat1(2*n*2*n, 0.0);
-    for(int i = 0; i < n; i++) {
-        for(int j = 0; j < n; j++) {
-            mat1[i*2*n+j] = nbar/(static_cast<double>(n)*(1.0+nbar));
-            mat1[(i+n)*2*n+(j+n)] = nbar/(static_cast<double>(n)*(1.0+nbar));
+    std::vector<double> mat1(2 * n * 2 * n, 0.0);
+    for (int i = 0; i < n; i++) {
+        for (int j = 0; j < n; j++) {
+            mat1[i * 2 * n + j] = nbar / (static_cast<double>(n) * (1.0 + nbar));
+            mat1[(i + n) * 2 * n + (j + n)] = nbar / (static_cast<double>(n) * (1.0 + nbar));
         }
     }
 
@@ -1117,11 +1119,11 @@ TEST(TorontonianDouble, Analytical) {
 
     n = 2;
     nbar = 0.25;
-    std::vector<double> mat2(2*n*2*n, 0.0);
-    for(int i = 0; i < n; i++) {
-        for(int j = 0; j < n; j++) {
-            mat2[i*2*n+j] = nbar/(static_cast<double>(n)*(1.0+nbar));
-            mat2[(i+n)*2*n+(j+n)] = nbar/(static_cast<double>(n)*(1.0+nbar));
+    std::vector<double> mat2(2 * n * 2 * n, 0.0);
+    for (int i = 0; i < n; i++) {
+        for (int j = 0; j < n; j++) {
+            mat2[i * 2 * n + j] = nbar / (static_cast<double>(n) * (1.0 + nbar));
+            mat2[(i + n) * 2 * n + (j + n)] = nbar / (static_cast<double>(n) * (1.0 + nbar));
         }
     }
 
@@ -1135,3 +1137,177 @@ TEST(TorontonianDouble, Analytical) {
 
 }
 
+
+namespace batchhafnian {
+TEST(BatchHafnian, CompleteGraph) {
+    std::vector<std::complex<double>> mat4{std::complex<double>(-0.28264629150778969, 0.39867701584672210), std::complex<double>(-0.06086128222348247, -0.12220227033305252), std::complex<double>(-0.22959477315790058, 0.00000000000000008), std::complex<double>(-0.00660678867199307, -0.09884501458235322), std::complex<double>(-0.06086128222348247, -0.12220227033305252), std::complex<double>(0.38245649793510783, -0.41413300040003126), std::complex<double>(-0.00660678867199307, 0.09884501458235322), std::complex<double>(-0.13684045954832844, 0.00000000000000006), std::complex<double>(-0.22959477315790058, -0.00000000000000008), std::complex<double>(-0.00660678867199307, 0.09884501458235322), std::complex<double>(-0.28264629150778969, -0.39867701584672210), std::complex<double>(-0.06086128222348247, 0.12220227033305252), std::complex<double>(-0.00660678867199307, -0.09884501458235322), std::complex<double>(-0.13684045954832844, -0.00000000000000006), std::complex<double>(-0.06086128222348247, +0.12220227033305252), std::complex<double>(0.38245649793510783, 0.41413300040003126)};
+    std::vector<std::complex<double>> d4{std::complex<double>(0.66917130190858, -1.52776303400764), std::complex<double>(-2.95847055822102, -1.29582519437023), std::complex<double>(0.66917130190858, 1.52776303400764), std::complex<double>(-2.95847055822102, 1.29582519437023)};
+    std::vector<std::complex<double>> out(256, 0.0);
+    std::vector<double> expected_re{1.00000000e+00, -1.64614736e+00,  1.94351456e+00, -1.44618627e+00,
+                                    4.35642368e-01, -1.32047906e+00,  2.23766490e+00, -1.86917564e+00,
+                                    -6.76966967e-01,  5.73670333e-01, -7.33188149e-02, -1.21997190e-01,
+                                    2.32161778e-01, -5.57198229e-01,  1.18563164e+00, -1.79235874e+00,
+                                    -1.64614736e+00,  3.23047167e+00, -4.65694018e+00,  4.44401287e+00,
+                                    -4.63159381e-02,  1.31073870e+00, -3.22177207e+00,  3.63237405e+00,
+                                    1.23991893e+00, -1.44213928e+00,  8.01092161e-01,  2.28567603e-01,
+                                    -6.99231782e-01,  1.51022665e+00, -2.91603997e+00,  4.30125549e+00,
+                                    1.94351456e+00, -4.65694018e+00,  8.15053238e+00, -9.76981613e+00,
+                                    -7.95376620e-01, -3.06685257e-01,  2.99900529e+00, -5.19576276e+00,
+                                    -1.40243198e+00,  2.03208134e+00, -1.62929470e+00, -2.50514870e-01,
+                                    1.12880996e+00, -2.69285454e+00,  5.33966585e+00, -8.00210813e+00,
+                                    -1.44618627e+00,  4.44401287e+00, -9.76981613e+00,  1.52284285e+01,
+                                    1.11641813e+00, -8.67834158e-01, -1.21356826e+00,  4.85970544e+00,
+                                    4.82389499e-01, -9.16927653e-01,  9.19681681e-01,  5.20655922e-01,
+                                    -8.34195372e-01,  2.92229672e+00, -6.78809904e+00,  1.10996783e+01,
+                                    4.35642368e-01, -4.63159381e-02, -7.95376620e-01,  1.11641813e+00,
+                                    1.56877658e+00, -2.31606077e+00,  2.25637651e+00, -1.05357461e+00,
+                                    4.79157988e-01, -1.44851326e+00,  2.00611116e+00, -5.18263640e-01,
+                                    -6.15836536e-01,  5.36430564e-01, -2.88165936e-01,  4.59048908e-01,
+                                    -1.32047906e+00,  1.31073870e+00, -3.06685257e-01, -8.67834158e-01,
+                                    -2.31606077e+00,  4.15988484e+00, -5.13015068e+00,  3.41102851e+00,
+                                    1.55349628e-01,  1.12665346e+00, -2.55195698e+00,  1.37496136e+00,
+                                    5.89607772e-01, -4.94801663e-01, -7.51210237e-02,  5.26517347e-01,
+                                    2.23766490e+00, -3.22177207e+00,  2.99900529e+00, -1.21356826e+00,
+                                    2.25637651e+00, -5.13015068e+00,  8.00781690e+00, -7.39736288e+00,
+                                    -1.05510937e+00,  1.44993971e-01,  1.83226945e+00, -2.23251713e+00,
+                                    2.06934935e-01, -6.05111407e-01,  1.55663126e+00, -2.69619939e+00,
+                                    -1.86917564e+00,  3.63237405e+00, -5.19576276e+00,  4.85970544e+00,
+                                    -1.05357461e+00,  3.41102851e+00, -7.39736288e+00,  1.03896013e+01,
+                                    6.44552723e-01, -6.96168471e-01, -2.62839607e-01,  1.95309353e+00,
+                                    -1.42746493e+00,  2.66108892e+00, -4.01938103e+00,  4.99610368e+00,
+                                    -6.76966967e-01,  1.23991893e+00, -1.40243198e+00,  4.82389499e-01,
+                                    4.79157988e-01,  1.55349628e-01, -1.05510937e+00,  6.44552723e-01,
+                                    2.08027043e+00, -2.71815189e+00,  2.08749438e+00, -3.59011119e-01,
+                                    2.39920807e-01, -1.06932525e+00,  1.14339407e+00,  9.25081052e-01,
+                                    5.73670333e-01, -1.44213928e+00,  2.03208134e+00, -9.16927653e-01,
+                                    -1.44851326e+00,  1.12665346e+00,  1.44993971e-01, -6.96168471e-01,
+                                    -2.71815189e+00,  4.45234470e+00, -4.61154260e+00,  1.74127108e+00,
+                                    6.25361244e-01,  3.75915531e-01, -1.21876790e+00, -5.13059479e-01,
+                                    -7.33188149e-02,  8.01092161e-01, -1.62929470e+00,  9.19681681e-01,
+                                    2.00611116e+00, -2.55195698e+00,  1.83226945e+00, -2.62839607e-01,
+                                    2.08749438e+00, -4.61154260e+00,  6.55944518e+00, -4.66420500e+00,
+                                    -1.28536521e+00,  7.81945188e-01,  5.63969365e-01, -7.03167365e-01,
+                                    -1.21997190e-01,  2.28567603e-01, -2.50514870e-01,  5.20655922e-01,
+                                    -5.18263640e-01,  1.37496136e+00, -2.23251713e+00,  1.95309353e+00,
+                                    -3.59011119e-01,  1.74127108e+00, -4.66420500e+00,  7.36229153e+00,
+                                    1.42777111e-02, -3.18771206e-01, -5.24341968e-02,  1.68507163e+00,
+                                    2.32161778e-01, -6.99231782e-01,  1.12880996e+00, -8.34195372e-01,
+                                    -6.15836536e-01,  5.89607772e-01,  2.06934935e-01, -1.42746493e+00,
+                                    2.39920807e-01,  6.25361244e-01, -1.28536521e+00,  1.42777111e-02,
+                                    2.99123653e+00, -3.75195474e+00,  2.82213119e+00, -7.81358057e-01,
+                                    -5.57198229e-01,  1.51022665e+00, -2.69285454e+00,  2.92229672e+00,
+                                    5.36430564e-01, -4.94801663e-01, -6.05111407e-01,  2.66108892e+00,
+                                    -1.06932525e+00,  3.75915531e-01,  7.81945188e-01, -3.18771206e-01,
+                                    -3.75195474e+00,  6.10393167e+00, -6.48641622e+00,  3.30150978e+00,
+                                    1.18563164e+00, -2.91603997e+00,  5.33966585e+00, -6.78809904e+00,
+                                    -2.88165936e-01, -7.51210237e-02,  1.55663126e+00, -4.01938103e+00,
+                                    1.14339407e+00, -1.21876790e+00,  5.63969365e-01, -5.24341968e-02,
+                                    2.82213119e+00, -6.48641622e+00,  9.98950443e+00, -9.09570553e+00,
+                                    -1.79235874e+00,  4.30125549e+00, -8.00210813e+00,  1.10996783e+01,
+                                    4.59048908e-01,  5.26517347e-01, -2.69619939e+00,  4.99610368e+00,
+                                    9.25081052e-01, -5.13059479e-01, -7.03167365e-01,  1.68507163e+00,
+                                    -7.81358057e-01,  3.30150978e+00, -9.09570553e+00,  1.56159162e+01};
+    std::vector<double> expected_im{0.00000000e+00, -6.19540212e-01,  1.62557597e+00, -2.04268077e+00,
+                                    -1.07209959e+00,  1.37273368e+00, -1.04855753e+00,  2.44875659e-01,
+                                    -5.35426993e-01,  1.06382831e+00, -1.13167436e+00, -5.50895821e-02,
+                                    2.33832577e-01, -3.78336056e-01,  7.66353380e-01, -1.42492084e+00,
+                                    6.19540212e-01, -8.32667268e-17, -1.64140851e+00,  3.13391670e+00,
+                                    1.93588686e+00, -3.06589811e+00,  3.30672773e+00, -1.86213343e+00,
+                                    3.61695050e-01, -1.18989013e+00,  1.65240909e+00, -7.67200444e-02,
+                                    -5.09572526e-02,  1.60560058e-01, -6.31216079e-01,  1.58488036e+00,
+                                    -1.62557597e+00,  1.64140851e+00, -2.00406005e-15, -2.89715424e+00,
+                                    -2.45819767e+00,  4.73270217e+00, -6.50126689e+00,  5.38692527e+00,
+                                    1.31935650e-01,  6.45842049e-01, -1.46639188e+00,  1.74105305e-01,
+                                    -7.03114482e-01,  9.82371295e-01, -7.30475300e-01, -4.69877164e-01,
+                                    2.04268077e+00, -3.13391670e+00,  2.89715424e+00, -9.52005210e-15,
+                                    1.83179431e+00, -4.41516458e+00,  7.85181522e+00, -9.37606710e+00,
+                                    -2.10974632e-01,  5.27110853e-02,  3.02027970e-01,  3.02537735e-01,
+                                    1.73508640e+00, -2.84340169e+00,  3.30111115e+00, -2.05599107e+00,
+                                    1.07209959e+00, -1.93588686e+00,  2.45819767e+00, -1.83179431e+00,
+                                    -5.55111512e-17, -9.23929364e-01,  2.07252046e+00, -1.72348979e+00,
+                                    -1.45132762e+00,  1.63837310e+00, -9.25631147e-01, -8.65199492e-02,
+                                    -1.80257925e-02, -4.95003549e-03,  7.10339932e-01, -2.21351707e+00,
+                                    -1.37273368e+00,  3.06589811e+00, -4.73270217e+00,  4.41516458e+00,
+                                    9.23929364e-01, -6.97358837e-16, -1.96212896e+00,  2.69923158e+00,
+                                    2.26051161e+00, -3.21251263e+00,  2.71847065e+00, -3.91405380e-01,
+                                    -4.80113320e-01,  7.08913327e-01, -1.77090980e+00,  4.06599993e+00,
+                                    1.04855753e+00, -3.30672773e+00,  6.50126689e+00, -7.85181522e+00,
+                                    -2.07252046e+00,  1.96212896e+00, -2.15452656e-15, -2.46721598e+00,
+                                    -2.22778040e+00,  3.99810349e+00, -4.56372028e+00,  1.81520753e+00,
+                                    8.17667372e-01, -1.51861788e+00,  3.08750334e+00, -5.85075242e+00,
+                                    -2.44875659e-01,  1.86213343e+00, -5.38692527e+00,  9.37606710e+00,
+                                    1.72348979e+00, -2.69923158e+00,  2.46721598e+00, -8.65973959e-15,
+                                    7.76349098e-01, -2.07828888e+00,  3.67741704e+00, -3.39674623e+00,
+                                    1.67268754e-03,  1.05174705e+00, -3.26705990e+00,  6.24576761e+00,
+                                    5.35426993e-01, -3.61695050e-01, -1.31935650e-01,  2.10974632e-01,
+                                    1.45132762e+00, -2.26051161e+00,  2.22778040e+00, -7.76349098e-01,
+                                    -4.49459509e-16, -1.15371273e+00,  2.14384564e+00, -7.75127965e-01,
+                                    -1.69420825e+00,  1.75565162e+00, -7.87144208e-01, -2.91297712e-01,
+                                    -1.06382831e+00,  1.18989013e+00, -6.45842049e-01, -5.27110853e-02,
+                                    -1.63837310e+00,  3.21251263e+00, -3.99810349e+00,  2.07828888e+00,
+                                    1.15371273e+00, -2.03309591e-15, -1.93589426e+00,  1.65877008e+00,
+                                    2.16797656e+00, -2.87072370e+00,  1.92413422e+00,  6.63359067e-01,
+                                    1.13167436e+00, -1.65240909e+00,  1.46639188e+00, -3.02027970e-01,
+                                    9.25631147e-01, -2.71847065e+00,  4.56372028e+00, -3.67741704e+00,
+                                    -2.14384564e+00,  1.93589426e+00, -3.84414722e-15, -1.84525302e+00,
+                                    -1.51949589e+00,  2.78597545e+00, -2.83838661e+00,  1.47024726e-02,
+                                    5.50895821e-02,  7.67200444e-02, -1.74105305e-01, -3.02537735e-01,
+                                    8.65199492e-02,  3.91405380e-01, -1.81520753e+00,  3.39674623e+00,
+                                    7.75127965e-01, -1.65877008e+00,  1.84525302e+00, -8.71004657e-15,
+                                    5.32280868e-02, -7.29284151e-01,  2.11417457e+00, -2.58202829e+00,
+                                    -2.33832577e-01,  5.09572526e-02,  7.03114482e-01, -1.73508640e+00,
+                                    1.80257925e-02,  4.80113320e-01, -8.17667372e-01, -1.67268754e-03,
+                                    1.69420825e+00, -2.16797656e+00,  1.51949589e+00, -5.32280868e-02,
+                                    -1.26663794e-15, -1.59424776e+00,  2.80268987e+00, -9.62872951e-01,
+                                    3.78336056e-01, -1.60560058e-01, -9.82371295e-01,  2.84340169e+00,
+                                    4.95003549e-03, -7.08913327e-01,  1.51861788e+00, -1.05174705e+00,
+                                    -1.75565162e+00,  2.87072370e+00, -2.78597545e+00,  7.29284151e-01,
+                                    1.59424776e+00, -3.49720253e-15, -2.61480295e+00,  2.53217806e+00,
+                                    -7.66353380e-01,  6.31216079e-01,  7.30475300e-01, -3.30111115e+00,
+                                    -7.10339932e-01,  1.77090980e+00, -3.08750334e+00,  3.26705990e+00,
+                                    7.87144208e-01, -1.92413422e+00,  2.83838661e+00, -2.11417457e+00,
+                                    -2.80268987e+00,  2.61480295e+00, -6.24500451e-15, -3.10967275e+00,
+                                    1.42492084e+00, -1.58488036e+00,  4.69877164e-01,  2.05599107e+00,
+                                    2.21351707e+00, -4.06599993e+00,  5.85075242e+00, -6.24576761e+00,
+                                    2.91297712e-01, -6.63359067e-01, -1.47024726e-02,  2.58202829e+00,
+                                    9.62872951e-01, -2.53217806e+00,  3.10967275e+00, -1.42559575e-14};
+    int res = 4;
+    int renorm = 0;
+
+    out = hafnian::hermite_multidimensional_cpp(mat4, d4, res, renorm);
+
+    for (int i = 0; i < 256; i++) {
+        EXPECT_NEAR(expected_re[i], std::real(out[i]), tol2);
+        EXPECT_NEAR(expected_im[i], std::imag(out[i]), tol2);
+    }
+
+}
+
+
+
+TEST(BatchHafnian, UnitRenormalization) {
+    std::vector<std::complex<double>> B = {std::complex<double>(0, 0), std::complex<double>(-0.70710678, 0), std::complex<double>(-0.70710678, 0), std::complex<double>(0, 0)};
+    std::vector<std::complex<double>> d(4, std::complex<double>(0.0, 0.0));
+
+    int res = 10;
+
+    std::vector<double> expected_re(res*res, 0);
+    std::vector<double> expected_im(res*res, 0);
+
+    std::vector<std::complex<double>> out(res*res, 0.0);
+
+    int renorm = 1;
+
+    for (int i = 0; i < res; i++)
+        expected_re[i*res+i] = pow(0.5, static_cast<double>(i)/2.0);
+
+    out = hafnian::hermite_multidimensional_cpp(B, d, res, renorm);
+
+    for (int i = 0; i < res*res; i++) {
+        EXPECT_NEAR(expected_re[i], std::real(out[i]), tol2);
+        EXPECT_NEAR(expected_im[i], std::imag(out[i]), tol2);
+    }
+
+}
+
+}