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    #define __Pyx_PyString_Format(a, b)  PyUnicode_Format(a, b)
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    #define __Pyx_PyBaseString_Check(obj) PyUnicode_Check(obj)
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    #define __Pyx_PyBaseString_Check(obj) (PyString_Check(obj) || PyUnicode_Check(obj))
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    #define __Pyx_PySequence_SIZE(seq)  Py_SIZE(seq)
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    #define __Pyx_PySequence_SIZE(seq)  PySequence_Size(seq)
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  #if PY_MAJOR_VERSION >= 3
    #define PyIntObject                  PyLongObject
    #define PyInt_Type                   PyLong_Type
    #define PyInt_Check(op)              PyLong_Check(op)
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    #define PyInt_FromString             PyLong_FromString
    #define PyInt_FromUnicode            PyLong_FromUnicode
    #define PyInt_FromLong               PyLong_FromLong
    #define PyInt_FromSize_t             PyLong_FromSize_t
    #define PyInt_FromSsize_t            PyLong_FromSsize_t
    #define PyInt_AsLong                 PyLong_AsLong
    #define PyInt_AS_LONG                PyLong_AS_LONG
    #define PyInt_AsSsize_t              PyLong_AsSsize_t
    #define PyInt_AsUnsignedLongMask     PyLong_AsUnsignedLongMask
    #define PyInt_AsUnsignedLongLongMask PyLong_AsUnsignedLongLongMask
    #define PyNumber_Int                 PyNumber_Long
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  #if PY_MAJOR_VERSION >= 3
    #define PyBoolObject                 PyLongObject
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  #if PY_MAJOR_VERSION >= 3 && CYTHON_COMPILING_IN_PYPY
    #ifndef PyUnicode_InternFromString
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  #if PY_VERSION_HEX < 0x030200A4
    typedef long Py_hash_t;
    #define __Pyx_PyInt_FromHash_t PyInt_FromLong
    #define __Pyx_PyInt_AsHash_t   PyInt_AsLong
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    #define __Pyx_PyInt_FromHash_t PyInt_FromSsize_t
    #define __Pyx_PyInt_AsHash_t   PyInt_AsSsize_t
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  #if PY_MAJOR_VERSION >= 3
    #define __Pyx_PyMethod_New(func, self, klass) ((self) ? PyMethod_New(func, self) : (Py_INCREF(func), func))
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    #define __Pyx_PyMethod_New(func, self, klass) PyMethod_New(func, self, klass)
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    #if PY_VERSION_HEX >= 0x030500B1
      #define __Pyx_PyAsyncMethodsStruct PyAsyncMethods
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      #define __Pyx_PyType_AsAsync(obj) ((__Pyx_PyAsyncMethodsStruct*) (Py_TYPE(obj)->tp_reserved))
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    #define __Pyx_PyType_AsAsync(obj) NULL
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  #ifndef __Pyx_PyAsyncMethodsStruct
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  #if defined(WIN32) || defined(MS_WINDOWS)
    #define _USE_MATH_DEFINES
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  #include <math.h>
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  #define __PYX_NAN() ((float) NAN)
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  static CYTHON_INLINE float __PYX_NAN() {
    float value;
    memset(&value, 0xFF, sizeof(value));
    return value;
  }
  #endif
  #if defined(__CYGWIN__) && defined(_LDBL_EQ_DBL)
  #define __Pyx_truncl trunc
  #else
  #define __Pyx_truncl truncl
  #endif
  
  
  #define __PYX_ERR(f_index, lineno, Ln_error) \
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  }
  
  #ifndef __PYX_EXTERN_C
    #ifdef __cplusplus
      #define __PYX_EXTERN_C extern "C"
    #else
      #define __PYX_EXTERN_C extern
    #endif
  #endif
  
  #define __PYX_HAVE__pysteps__motion___vet
  #define __PYX_HAVE_API__pysteps__motion___vet
  /* Early includes */
  #include <string.h>
  #include <stdio.h>
  #include "numpy/arrayobject.h"
  #include "numpy/ufuncobject.h"
  #include <math.h>
  #ifdef _OPENMP
  #include <omp.h>
  #endif /* _OPENMP */
  
  #if defined(PYREX_WITHOUT_ASSERTIONS) && !defined(CYTHON_WITHOUT_ASSERTIONS)
  #define CYTHON_WITHOUT_ASSERTIONS
  #endif
  
  typedef struct {PyObject **p; const char *s; const Py_ssize_t n; const char* encoding;
                  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 ""
  #define __Pyx_PyObject_FromString __Pyx_PyBytes_FromString
  #define __Pyx_PyObject_FromStringAndSize __Pyx_PyBytes_FromStringAndSize
  #define __Pyx_uchar_cast(c) ((unsigned char)c)
  #define __Pyx_long_cast(x) ((long)x)
  #define __Pyx_fits_Py_ssize_t(v, type, is_signed)  (\
      (sizeof(type) < sizeof(Py_ssize_t))  ||\
      (sizeof(type) > sizeof(Py_ssize_t) &&\
            likely(v < (type)PY_SSIZE_T_MAX ||\
                   v == (type)PY_SSIZE_T_MAX)  &&\
            (!is_signed || likely(v > (type)PY_SSIZE_T_MIN ||\
                                  v == (type)PY_SSIZE_T_MIN)))  ||\
      (sizeof(type) == sizeof(Py_ssize_t) &&\
            (is_signed || likely(v < (type)PY_SSIZE_T_MAX ||\
                                 v == (type)PY_SSIZE_T_MAX)))  )
  static CYTHON_INLINE int __Pyx_is_valid_index(Py_ssize_t i, Py_ssize_t limit) {
      return (size_t) i < (size_t) limit;
  }
  #if defined (__cplusplus) && __cplusplus >= 201103L
      #include <cstdlib>
      #define __Pyx_sst_abs(value) std::abs(value)
  #elif SIZEOF_INT >= SIZEOF_SIZE_T
      #define __Pyx_sst_abs(value) abs(value)
  #elif SIZEOF_LONG >= SIZEOF_SIZE_T
      #define __Pyx_sst_abs(value) labs(value)
  #elif defined (_MSC_VER)
      #define __Pyx_sst_abs(value) ((Py_ssize_t)_abs64(value))
  #elif defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L
      #define __Pyx_sst_abs(value) llabs(value)
  #elif defined (__GNUC__)
      #define __Pyx_sst_abs(value) __builtin_llabs(value)
  #else
      #define __Pyx_sst_abs(value) ((value<0) ? -value : value)
  #endif
  static CYTHON_INLINE const char* __Pyx_PyObject_AsString(PyObject*);
  static CYTHON_INLINE const char* __Pyx_PyObject_AsStringAndSize(PyObject*, Py_ssize_t* length);
  #define __Pyx_PyByteArray_FromString(s) PyByteArray_FromStringAndSize((const char*)s, strlen((const char*)s))
  #define __Pyx_PyByteArray_FromStringAndSize(s, l) PyByteArray_FromStringAndSize((const char*)s, l)
  #define __Pyx_PyBytes_FromString        PyBytes_FromString
  #define __Pyx_PyBytes_FromStringAndSize PyBytes_FromStringAndSize
  static CYTHON_INLINE PyObject* __Pyx_PyUnicode_FromString(const char*);
  #if PY_MAJOR_VERSION < 3
      #define __Pyx_PyStr_FromString        __Pyx_PyBytes_FromString
      #define __Pyx_PyStr_FromStringAndSize __Pyx_PyBytes_FromStringAndSize
  #else
      #define __Pyx_PyStr_FromString        __Pyx_PyUnicode_FromString
      #define __Pyx_PyStr_FromStringAndSize __Pyx_PyUnicode_FromStringAndSize
  #endif
  #define __Pyx_PyBytes_AsWritableString(s)     ((char*) PyBytes_AS_STRING(s))
  #define __Pyx_PyBytes_AsWritableSString(s)    ((signed char*) PyBytes_AS_STRING(s))
  #define __Pyx_PyBytes_AsWritableUString(s)    ((unsigned char*) PyBytes_AS_STRING(s))
  #define __Pyx_PyBytes_AsString(s)     ((const char*) PyBytes_AS_STRING(s))
  #define __Pyx_PyBytes_AsSString(s)    ((const signed char*) PyBytes_AS_STRING(s))
  #define __Pyx_PyBytes_AsUString(s)    ((const unsigned char*) PyBytes_AS_STRING(s))
  #define __Pyx_PyObject_AsWritableString(s)    ((char*) __Pyx_PyObject_AsString(s))
  #define __Pyx_PyObject_AsWritableSString(s)    ((signed char*) __Pyx_PyObject_AsString(s))
  #define __Pyx_PyObject_AsWritableUString(s)    ((unsigned char*) __Pyx_PyObject_AsString(s))
  #define __Pyx_PyObject_AsSString(s)    ((const signed char*) __Pyx_PyObject_AsString(s))
  #define __Pyx_PyObject_AsUString(s)    ((const unsigned char*) __Pyx_PyObject_AsString(s))
  #define __Pyx_PyObject_FromCString(s)  __Pyx_PyObject_FromString((const char*)s)
  #define __Pyx_PyBytes_FromCString(s)   __Pyx_PyBytes_FromString((const char*)s)
  #define __Pyx_PyByteArray_FromCString(s)   __Pyx_PyByteArray_FromString((const char*)s)
  #define __Pyx_PyStr_FromCString(s)     __Pyx_PyStr_FromString((const char*)s)
  #define __Pyx_PyUnicode_FromCString(s) __Pyx_PyUnicode_FromString((const char*)s)
  static CYTHON_INLINE size_t __Pyx_Py_UNICODE_strlen(const Py_UNICODE *u) {
      const Py_UNICODE *u_end = u;
      while (*u_end++) ;
      return (size_t)(u_end - u - 1);
  }
  #define __Pyx_PyUnicode_FromUnicode(u)       PyUnicode_FromUnicode(u, __Pyx_Py_UNICODE_strlen(u))
  #define __Pyx_PyUnicode_FromUnicodeAndLength PyUnicode_FromUnicode
  #define __Pyx_PyUnicode_AsUnicode            PyUnicode_AsUnicode
  #define __Pyx_NewRef(obj) (Py_INCREF(obj), obj)
  #define __Pyx_Owned_Py_None(b) __Pyx_NewRef(Py_None)
  static CYTHON_INLINE PyObject * __Pyx_PyBool_FromLong(long b);
  static CYTHON_INLINE int __Pyx_PyObject_IsTrue(PyObject*);
  static CYTHON_INLINE int __Pyx_PyObject_IsTrueAndDecref(PyObject*);
  static CYTHON_INLINE PyObject* __Pyx_PyNumber_IntOrLong(PyObject* x);
  #define __Pyx_PySequence_Tuple(obj)\
      (likely(PyTuple_CheckExact(obj)) ? __Pyx_NewRef(obj) : PySequence_Tuple(obj))
  static CYTHON_INLINE Py_ssize_t __Pyx_PyIndex_AsSsize_t(PyObject*);
  static CYTHON_INLINE PyObject * __Pyx_PyInt_FromSize_t(size_t);
  #if CYTHON_ASSUME_SAFE_MACROS
  #define __pyx_PyFloat_AsDouble(x) (PyFloat_CheckExact(x) ? PyFloat_AS_DOUBLE(x) : PyFloat_AsDouble(x))
  #else
  #define __pyx_PyFloat_AsDouble(x) PyFloat_AsDouble(x)
  #endif
  #define __pyx_PyFloat_AsFloat(x) ((float) __pyx_PyFloat_AsDouble(x))
  #if PY_MAJOR_VERSION >= 3
  #define __Pyx_PyNumber_Int(x) (PyLong_CheckExact(x) ? __Pyx_NewRef(x) : PyNumber_Long(x))
  #else
  #define __Pyx_PyNumber_Int(x) (PyInt_CheckExact(x) ? __Pyx_NewRef(x) : PyNumber_Int(x))
  #endif
  #define __Pyx_PyNumber_Float(x) (PyFloat_CheckExact(x) ? __Pyx_NewRef(x) : PyNumber_Float(x))
  #if PY_MAJOR_VERSION < 3 && __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
  static int __Pyx_sys_getdefaultencoding_not_ascii;
  static int __Pyx_init_sys_getdefaultencoding_params(void) {
      PyObject* sys;
      PyObject* default_encoding = NULL;
      PyObject* ascii_chars_u = NULL;
      PyObject* ascii_chars_b = NULL;
      const char* default_encoding_c;
      sys = PyImport_ImportModule("sys");
      if (!sys) goto bad;
      default_encoding = PyObject_CallMethod(sys, (char*) "getdefaultencoding", NULL);
      Py_DECREF(sys);
      if (!default_encoding) goto bad;
      default_encoding_c = PyBytes_AsString(default_encoding);
      if (!default_encoding_c) goto bad;
      if (strcmp(default_encoding_c, "ascii") == 0) {
          __Pyx_sys_getdefaultencoding_not_ascii = 0;
      } else {
          char ascii_chars[128];
          int c;
          for (c = 0; c < 128; c++) {
              ascii_chars[c] = c;
          }
          __Pyx_sys_getdefaultencoding_not_ascii = 1;
          ascii_chars_u = PyUnicode_DecodeASCII(ascii_chars, 128, NULL);
          if (!ascii_chars_u) goto bad;
          ascii_chars_b = PyUnicode_AsEncodedString(ascii_chars_u, default_encoding_c, NULL);
          if (!ascii_chars_b || !PyBytes_Check(ascii_chars_b) || memcmp(ascii_chars, PyBytes_AS_STRING(ascii_chars_b), 128) != 0) {
              PyErr_Format(
                  PyExc_ValueError,
                  "This module compiled with c_string_encoding=ascii, but default encoding '%.200s' is not a superset of ascii.",
                  default_encoding_c);
              goto bad;
          }
          Py_DECREF(ascii_chars_u);
          Py_DECREF(ascii_chars_b);
      }
      Py_DECREF(default_encoding);
      return 0;
  bad:
      Py_XDECREF(default_encoding);
      Py_XDECREF(ascii_chars_u);
      Py_XDECREF(ascii_chars_b);
      return -1;
  }
  #endif
  #if __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT && PY_MAJOR_VERSION >= 3
  #define __Pyx_PyUnicode_FromStringAndSize(c_str, size) PyUnicode_DecodeUTF8(c_str, size, NULL)
  #else
  #define __Pyx_PyUnicode_FromStringAndSize(c_str, size) PyUnicode_Decode(c_str, size, __PYX_DEFAULT_STRING_ENCODING, NULL)
  #if __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT
  static char* __PYX_DEFAULT_STRING_ENCODING;
  static int __Pyx_init_sys_getdefaultencoding_params(void) {
      PyObject* sys;
      PyObject* default_encoding = NULL;
      char* default_encoding_c;
      sys = PyImport_ImportModule("sys");
      if (!sys) goto bad;
      default_encoding = PyObject_CallMethod(sys, (char*) (const char*) "getdefaultencoding", NULL);
      Py_DECREF(sys);
      if (!default_encoding) goto bad;
      default_encoding_c = PyBytes_AsString(default_encoding);
      if (!default_encoding_c) goto bad;
      __PYX_DEFAULT_STRING_ENCODING = (char*) malloc(strlen(default_encoding_c) + 1);
      if (!__PYX_DEFAULT_STRING_ENCODING) goto bad;
      strcpy(__PYX_DEFAULT_STRING_ENCODING, default_encoding_c);
      Py_DECREF(default_encoding);
      return 0;
  bad:
      Py_XDECREF(default_encoding);
      return -1;
  }
  #endif
  #endif
  
  
  /* Test for GCC > 2.95 */
  #if defined(__GNUC__)     && (__GNUC__ > 2 || (__GNUC__ == 2 && (__GNUC_MINOR__ > 95)))
    #define likely(x)   __builtin_expect(!!(x), 1)
    #define unlikely(x) __builtin_expect(!!(x), 0)
  #else /* !__GNUC__ or GCC < 2.95 */
    #define likely(x)   (x)
    #define unlikely(x) (x)
  #endif /* __GNUC__ */
  static CYTHON_INLINE void __Pyx_pretend_to_initialize(void* ptr) { (void)ptr; }
  
  static PyObject *__pyx_m = NULL;
  static PyObject *__pyx_d;
  static PyObject *__pyx_b;
  static PyObject *__pyx_cython_runtime = NULL;
  static PyObject *__pyx_empty_tuple;
  static PyObject *__pyx_empty_bytes;
  static PyObject *__pyx_empty_unicode;
  static int __pyx_lineno;
  static int __pyx_clineno = 0;
  static const char * __pyx_cfilenm= __FILE__;
  static const char *__pyx_filename;
  
  /* Header.proto */
  #if !defined(CYTHON_CCOMPLEX)
    #if defined(__cplusplus)
      #define CYTHON_CCOMPLEX 1
    #elif defined(_Complex_I)
      #define CYTHON_CCOMPLEX 1
    #else
      #define CYTHON_CCOMPLEX 0
    #endif
  #endif
  #if CYTHON_CCOMPLEX
    #ifdef __cplusplus
      #include <complex>
    #else
      #include <complex.h>
    #endif
  #endif
  #if CYTHON_CCOMPLEX && !defined(__cplusplus) && defined(__sun__) && defined(__GNUC__)
    #undef _Complex_I
    #define _Complex_I 1.0fj
  #endif
  
  
  static const char *__pyx_f[] = {
    "pysteps/motion/_vet.pyx",
    "__init__.pxd",
    "type.pxd",
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  /* BufferFormatStructs.proto */
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  struct __Pyx_StructField_;
  #define __PYX_BUF_FLAGS_PACKED_STRUCT (1 << 0)
  typedef struct {
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    struct __Pyx_StructField_* fields;
    size_t size;
    size_t arraysize[8];
    int ndim;
    char typegroup;
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    int flags;
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  typedef struct __Pyx_StructField_ {
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    const char* name;
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  typedef struct {
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  typedef struct {
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    size_t fmt_offset;
    size_t new_count, enc_count;
    size_t struct_alignment;
    int is_complex;
    char enc_type;
    char new_packmode;
    char enc_packmode;
    char is_valid_array;
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  /* NoFastGil.proto */
  #define __Pyx_PyGILState_Ensure PyGILState_Ensure
  #define __Pyx_PyGILState_Release PyGILState_Release
  #define __Pyx_FastGIL_Remember()
  #define __Pyx_FastGIL_Forget()
  #define __Pyx_FastGilFuncInit()
  
  
  /* "../pysteps_env/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":776
   * # in Cython to enable them only on the right systems.
   * 
   * ctypedef npy_int8       int8_t             # <<<<<<<<<<<<<<
   * ctypedef npy_int16      int16_t
   * ctypedef npy_int32      int32_t
   */
  typedef npy_int8 __pyx_t_5numpy_int8_t;
  
  /* "../pysteps_env/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":777
   * 
   * ctypedef npy_int8       int8_t
   * ctypedef npy_int16      int16_t             # <<<<<<<<<<<<<<
   * ctypedef npy_int32      int32_t
   * ctypedef npy_int64      int64_t
   */
  typedef npy_int16 __pyx_t_5numpy_int16_t;
  
  /* "../pysteps_env/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":778
   * ctypedef npy_int8       int8_t
   * ctypedef npy_int16      int16_t
   * ctypedef npy_int32      int32_t             # <<<<<<<<<<<<<<
   * ctypedef npy_int64      int64_t
   * #ctypedef npy_int96      int96_t
   */
  typedef npy_int32 __pyx_t_5numpy_int32_t;
  
  /* "../pysteps_env/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":779
   * ctypedef npy_int16      int16_t
   * ctypedef npy_int32      int32_t
   * ctypedef npy_int64      int64_t             # <<<<<<<<<<<<<<
   * #ctypedef npy_int96      int96_t
   * #ctypedef npy_int128     int128_t
   */
  typedef npy_int64 __pyx_t_5numpy_int64_t;
  
  /* "../pysteps_env/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":783
   * #ctypedef npy_int128     int128_t
   * 
   * ctypedef npy_uint8      uint8_t             # <<<<<<<<<<<<<<
   * ctypedef npy_uint16     uint16_t
   * ctypedef npy_uint32     uint32_t
   */
  typedef npy_uint8 __pyx_t_5numpy_uint8_t;
  
  /* "../pysteps_env/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":784
   * 
   * ctypedef npy_uint8      uint8_t
   * ctypedef npy_uint16     uint16_t             # <<<<<<<<<<<<<<
   * ctypedef npy_uint32     uint32_t
   * ctypedef npy_uint64     uint64_t
   */
  typedef npy_uint16 __pyx_t_5numpy_uint16_t;
  
  /* "../pysteps_env/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":785
   * ctypedef npy_uint8      uint8_t
   * ctypedef npy_uint16     uint16_t
   * ctypedef npy_uint32     uint32_t             # <<<<<<<<<<<<<<
   * ctypedef npy_uint64     uint64_t
   * #ctypedef npy_uint96     uint96_t
   */
  typedef npy_uint32 __pyx_t_5numpy_uint32_t;
  
  /* "../pysteps_env/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":786
   * ctypedef npy_uint16     uint16_t
   * ctypedef npy_uint32     uint32_t
   * ctypedef npy_uint64     uint64_t             # <<<<<<<<<<<<<<
   * #ctypedef npy_uint96     uint96_t
   * #ctypedef npy_uint128    uint128_t
   */
  typedef npy_uint64 __pyx_t_5numpy_uint64_t;
  
  /* "../pysteps_env/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":790
   * #ctypedef npy_uint128    uint128_t
   * 
   * ctypedef npy_float32    float32_t             # <<<<<<<<<<<<<<
   * ctypedef npy_float64    float64_t
   * #ctypedef npy_float80    float80_t
   */
  typedef npy_float32 __pyx_t_5numpy_float32_t;
  
  /* "../pysteps_env/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":791
   * 
   * ctypedef npy_float32    float32_t
   * ctypedef npy_float64    float64_t             # <<<<<<<<<<<<<<
   * #ctypedef npy_float80    float80_t
   * #ctypedef npy_float128   float128_t
   */
  typedef npy_float64 __pyx_t_5numpy_float64_t;
  
  /* "../pysteps_env/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":800
   * # The int types are mapped a bit surprising --
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  /* "../pysteps_env/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":801
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   * ctypedef npy_long       int_t
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  static PyObject* __Pyx_PyInt_SubtractObjC(PyObject *op1, PyObject *op2, long intval, int inplace, int zerodivision_check);
  #else
  #define __Pyx_PyInt_SubtractObjC(op1, op2, intval, inplace, zerodivision_check)\
      (inplace ? PyNumber_InPlaceSubtract(op1, op2) : PyNumber_Subtract(op1, op2))
  #endif
  
  /* GetItemInt.proto */
  #define __Pyx_GetItemInt(o, i, type, is_signed, to_py_func, is_list, wraparound, boundscheck)\
      (__Pyx_fits_Py_ssize_t(i, type, is_signed) ?\
      __Pyx_GetItemInt_Fast(o, (Py_ssize_t)i, is_list, wraparound, boundscheck) :\
      (is_list ? (PyErr_SetString(PyExc_IndexError, "list index out of range"), (PyObject*)NULL) :\
                 __Pyx_GetItemInt_Generic(o, to_py_func(i))))
  #define __Pyx_GetItemInt_List(o, i, type, is_signed, to_py_func, is_list, wraparound, boundscheck)\
      (__Pyx_fits_Py_ssize_t(i, type, is_signed) ?\
      __Pyx_GetItemInt_List_Fast(o, (Py_ssize_t)i, wraparound, boundscheck) :\
      (PyErr_SetString(PyExc_IndexError, "list index out of range"), (PyObject*)NULL))
  static CYTHON_INLINE PyObject *__Pyx_GetItemInt_List_Fast(PyObject *o, Py_ssize_t i,
                                                                int wraparound, int boundscheck);
  #define __Pyx_GetItemInt_Tuple(o, i, type, is_signed, to_py_func, is_list, wraparound, boundscheck)\
      (__Pyx_fits_Py_ssize_t(i, type, is_signed) ?\
      __Pyx_GetItemInt_Tuple_Fast(o, (Py_ssize_t)i, wraparound, boundscheck) :\
      (PyErr_SetString(PyExc_IndexError, "tuple index out of range"), (PyObject*)NULL))
  static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Tuple_Fast(PyObject *o, Py_ssize_t i,
                                                                int wraparound, int boundscheck);
  static PyObject *__Pyx_GetItemInt_Generic(PyObject *o, PyObject* j);
  static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Fast(PyObject *o, Py_ssize_t i,
                                                       int is_list, int wraparound, int boundscheck);
  
  /* ObjectGetItem.proto */
  #if CYTHON_USE_TYPE_SLOTS
  static CYTHON_INLINE PyObject *__Pyx_PyObject_GetItem(PyObject *obj, PyObject* key);
  #else
  #define __Pyx_PyObject_GetItem(obj, key)  PyObject_GetItem(obj, key)
  #endif
  
  /* DictGetItem.proto */
  #if PY_MAJOR_VERSION >= 3 && !CYTHON_COMPILING_IN_PYPY
  static PyObject *__Pyx_PyDict_GetItem(PyObject *d, PyObject* key);
  #define __Pyx_PyObject_Dict_GetItem(obj, name)\
      (likely(PyDict_CheckExact(obj)) ?\
       __Pyx_PyDict_GetItem(obj, name) : PyObject_GetItem(obj, name))
  #else
  #define __Pyx_PyDict_GetItem(d, key) PyObject_GetItem(d, key)
  #define __Pyx_PyObject_Dict_GetItem(obj, name)  PyObject_GetItem(obj, name)
  #endif
  
  /* RaiseNoneIterError.proto */
  static CYTHON_INLINE void __Pyx_RaiseNoneNotIterableError(void);
  
  /* GetTopmostException.proto */
  #if CYTHON_USE_EXC_INFO_STACK
  static _PyErr_StackItem * __Pyx_PyErr_GetTopmostException(PyThreadState *tstate);
  #endif
  
  /* SaveResetException.proto */
  #if CYTHON_FAST_THREAD_STATE
  #define __Pyx_ExceptionSave(type, value, tb)  __Pyx__ExceptionSave(__pyx_tstate, type, value, tb)
  static CYTHON_INLINE void __Pyx__ExceptionSave(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb);
  #define __Pyx_ExceptionReset(type, value, tb)  __Pyx__ExceptionReset(__pyx_tstate, type, value, tb)
  static CYTHON_INLINE void __Pyx__ExceptionReset(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb);
  #else
  #define __Pyx_ExceptionSave(type, value, tb)   PyErr_GetExcInfo(type, value, tb)
  #define __Pyx_ExceptionReset(type, value, tb)  PyErr_SetExcInfo(type, value, tb)
  #endif
  
  /* PyErrExceptionMatches.proto */
  #if CYTHON_FAST_THREAD_STATE
  #define __Pyx_PyErr_ExceptionMatches(err) __Pyx_PyErr_ExceptionMatchesInState(__pyx_tstate, err)
  static CYTHON_INLINE int __Pyx_PyErr_ExceptionMatchesInState(PyThreadState* tstate, PyObject* err);
  #else
  #define __Pyx_PyErr_ExceptionMatches(err)  PyErr_ExceptionMatches(err)
  #endif
  
  /* GetException.proto */
  #if CYTHON_FAST_THREAD_STATE
  #define __Pyx_GetException(type, value, tb)  __Pyx__GetException(__pyx_tstate, type, value, tb)
  static int __Pyx__GetException(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb);
  #else
  static int __Pyx_GetException(PyObject **type, PyObject **value, PyObject **tb);
  #endif
  
  /* TypeImport.proto */
  #ifndef __PYX_HAVE_RT_ImportType_proto
  #define __PYX_HAVE_RT_ImportType_proto
  enum __Pyx_ImportType_CheckSize {
     __Pyx_ImportType_CheckSize_Error = 0,
     __Pyx_ImportType_CheckSize_Warn = 1,
     __Pyx_ImportType_CheckSize_Ignore = 2
  };
  static PyTypeObject *__Pyx_ImportType(PyObject* module, const char *module_name, const char *class_name, size_t size, enum __Pyx_ImportType_CheckSize check_size);
  #endif
  
  /* Import.proto */
  static PyObject *__Pyx_Import(PyObject *name, PyObject *from_list, int level);
  
  /* CLineInTraceback.proto */
  #ifdef CYTHON_CLINE_IN_TRACEBACK
  #define __Pyx_CLineForTraceback(tstate, c_line)  (((CYTHON_CLINE_IN_TRACEBACK)) ? c_line : 0)
  #else
  static int __Pyx_CLineForTraceback(PyThreadState *tstate, int c_line);
  #endif
  
  /* CodeObjectCache.proto */
  typedef struct {
      PyCodeObject* code_object;
      int code_line;
  } __Pyx_CodeObjectCacheEntry;
  struct __Pyx_CodeObjectCache {
      int count;
      int max_count;
      __Pyx_CodeObjectCacheEntry* entries;
  };
  static struct __Pyx_CodeObjectCache __pyx_code_cache = {0,0,NULL};
  static int __pyx_bisect_code_objects(__Pyx_CodeObjectCacheEntry* entries, int count, int code_line);
  static PyCodeObject *__pyx_find_code_object(int code_line);
  static void __pyx_insert_code_object(int code_line, PyCodeObject* code_object);
  
  /* AddTraceback.proto */
  static void __Pyx_AddTraceback(const char *funcname, int c_line,
                                 int py_line, const char *filename);
  
  /* BufferStructDeclare.proto */
  typedef struct {
    Py_ssize_t shape, strides, suboffsets;
  } __Pyx_Buf_DimInfo;
  typedef struct {
    size_t refcount;
    Py_buffer pybuffer;
  } __Pyx_Buffer;
  typedef struct {
    __Pyx_Buffer *rcbuffer;
    char *data;
    __Pyx_Buf_DimInfo diminfo[8];
  } __Pyx_LocalBuf_ND;
  
  #if PY_MAJOR_VERSION < 3
      static int __Pyx_GetBuffer(PyObject *obj, Py_buffer *view, int flags);
      static void __Pyx_ReleaseBuffer(Py_buffer *view);
  #else
      #define __Pyx_GetBuffer PyObject_GetBuffer
      #define __Pyx_ReleaseBuffer PyBuffer_Release
  #endif
  
  
  /* CIntToPy.proto */
  static CYTHON_INLINE PyObject* __Pyx_PyInt_From_Py_intptr_t(Py_intptr_t value);
  
  /* CIntToPy.proto */
  static CYTHON_INLINE PyObject* __Pyx_PyInt_From_long(long value);
  
  /* RealImag.proto */
  #if CYTHON_CCOMPLEX
    #ifdef __cplusplus
      #define __Pyx_CREAL(z) ((z).real())
      #define __Pyx_CIMAG(z) ((z).imag())
    #else
      #define __Pyx_CREAL(z) (__real__(z))
      #define __Pyx_CIMAG(z) (__imag__(z))
    #endif
  #else
      #define __Pyx_CREAL(z) ((z).real)
      #define __Pyx_CIMAG(z) ((z).imag)
  #endif
  #if defined(__cplusplus) && CYTHON_CCOMPLEX\
          && (defined(_WIN32) || defined(__clang__) || (defined(__GNUC__) && (__GNUC__ >= 5 || __GNUC__ == 4 && __GNUC_MINOR__ >= 4 )) || __cplusplus >= 201103)
      #define __Pyx_SET_CREAL(z,x) ((z).real(x))
      #define __Pyx_SET_CIMAG(z,y) ((z).imag(y))
  #else
      #define __Pyx_SET_CREAL(z,x) __Pyx_CREAL(z) = (x)
      #define __Pyx_SET_CIMAG(z,y) __Pyx_CIMAG(z) = (y)
  #endif
  
  /* Arithmetic.proto */
  #if CYTHON_CCOMPLEX
      #define __Pyx_c_eq_float(a, b)   ((a)==(b))
      #define __Pyx_c_sum_float(a, b)  ((a)+(b))
      #define __Pyx_c_diff_float(a, b) ((a)-(b))
      #define __Pyx_c_prod_float(a, b) ((a)*(b))
      #define __Pyx_c_quot_float(a, b) ((a)/(b))
      #define __Pyx_c_neg_float(a)     (-(a))
    #ifdef __cplusplus
      #define __Pyx_c_is_zero_float(z) ((z)==(float)0)
      #define __Pyx_c_conj_float(z)    (::std::conj(z))
      #if 1
          #define __Pyx_c_abs_float(z)     (::std::abs(z))
          #define __Pyx_c_pow_float(a, b)  (::std::pow(a, b))
      #endif
    #else
      #define __Pyx_c_is_zero_float(z) ((z)==0)
      #define __Pyx_c_conj_float(z)    (conjf(z))
      #if 1
          #define __Pyx_c_abs_float(z)     (cabsf(z))
          #define __Pyx_c_pow_float(a, b)  (cpowf(a, b))
      #endif
   #endif
  #else
      static CYTHON_INLINE int __Pyx_c_eq_float(__pyx_t_float_complex, __pyx_t_float_complex);
      static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_sum_float(__pyx_t_float_complex, __pyx_t_float_complex);
      static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_diff_float(__pyx_t_float_complex, __pyx_t_float_complex);
      static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_prod_float(__pyx_t_float_complex, __pyx_t_float_complex);
      static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_quot_float(__pyx_t_float_complex, __pyx_t_float_complex);
      static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_neg_float(__pyx_t_float_complex);
      static CYTHON_INLINE int __Pyx_c_is_zero_float(__pyx_t_float_complex);
      static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_conj_float(__pyx_t_float_complex);
      #if 1
          static CYTHON_INLINE float __Pyx_c_abs_float(__pyx_t_float_complex);
          static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_pow_float(__pyx_t_float_complex, __pyx_t_float_complex);
      #endif
  #endif
  
  /* Arithmetic.proto */
  #if CYTHON_CCOMPLEX
      #define __Pyx_c_eq_double(a, b)   ((a)==(b))
      #define __Pyx_c_sum_double(a, b)  ((a)+(b))
      #define __Pyx_c_diff_double(a, b) ((a)-(b))
      #define __Pyx_c_prod_double(a, b) ((a)*(b))
      #define __Pyx_c_quot_double(a, b) ((a)/(b))
      #define __Pyx_c_neg_double(a)     (-(a))
    #ifdef __cplusplus
      #define __Pyx_c_is_zero_double(z) ((z)==(double)0)
      #define __Pyx_c_conj_double(z)    (::std::conj(z))
      #if 1
          #define __Pyx_c_abs_double(z)     (::std::abs(z))
          #define __Pyx_c_pow_double(a, b)  (::std::pow(a, b))
      #endif
    #else
      #define __Pyx_c_is_zero_double(z) ((z)==0)
      #define __Pyx_c_conj_double(z)    (conj(z))
      #if 1
          #define __Pyx_c_abs_double(z)     (cabs(z))
          #define __Pyx_c_pow_double(a, b)  (cpow(a, b))
      #endif
   #endif
  #else
      static CYTHON_INLINE int __Pyx_c_eq_double(__pyx_t_double_complex, __pyx_t_double_complex);
      static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_sum_double(__pyx_t_double_complex, __pyx_t_double_complex);
      static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_diff_double(__pyx_t_double_complex, __pyx_t_double_complex);
      static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_prod_double(__pyx_t_double_complex, __pyx_t_double_complex);
      static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_quot_double(__pyx_t_double_complex, __pyx_t_double_complex);
      static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_neg_double(__pyx_t_double_complex);
      static CYTHON_INLINE int __Pyx_c_is_zero_double(__pyx_t_double_complex);
      static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_conj_double(__pyx_t_double_complex);
      #if 1
          static CYTHON_INLINE double __Pyx_c_abs_double(__pyx_t_double_complex);
          static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_pow_double(__pyx_t_double_complex, __pyx_t_double_complex);
      #endif
  #endif
  
  /* CIntToPy.proto */
  static CYTHON_INLINE PyObject* __Pyx_PyInt_From_int(int value);
  
  /* CIntToPy.proto */
  static CYTHON_INLINE PyObject* __Pyx_PyInt_From_enum__NPY_TYPES(enum NPY_TYPES value);
  
  /* CIntFromPy.proto */
  static CYTHON_INLINE Py_intptr_t __Pyx_PyInt_As_Py_intptr_t(PyObject *);
  
  /* CIntFromPy.proto */
  static CYTHON_INLINE int __Pyx_PyInt_As_int(PyObject *);
  
  /* CIntFromPy.proto */
  static CYTHON_INLINE long __Pyx_PyInt_As_long(PyObject *);
  
  /* FastTypeChecks.proto */
  #if CYTHON_COMPILING_IN_CPYTHON
  #define __Pyx_TypeCheck(obj, type) __Pyx_IsSubtype(Py_TYPE(obj), (PyTypeObject *)type)
  static CYTHON_INLINE int __Pyx_IsSubtype(PyTypeObject *a, PyTypeObject *b);
  static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches(PyObject *err, PyObject *type);
  static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches2(PyObject *err, PyObject *type1, PyObject *type2);
  #else
  #define __Pyx_TypeCheck(obj, type) PyObject_TypeCheck(obj, (PyTypeObject *)type)
  #define __Pyx_PyErr_GivenExceptionMatches(err, type) PyErr_GivenExceptionMatches(err, type)
  #define __Pyx_PyErr_GivenExceptionMatches2(err, type1, type2) (PyErr_GivenExceptionMatches(err, type1) || PyErr_GivenExceptionMatches(err, type2))
  #endif
  #define __Pyx_PyException_Check(obj) __Pyx_TypeCheck(obj, PyExc_Exception)
  
  /* CheckBinaryVersion.proto */
  static int __Pyx_check_binary_version(void);
  
  /* InitStrings.proto */
  static int __Pyx_InitStrings(__Pyx_StringTabEntry *t);
  
  
  /* Module declarations from 'cython' */
  
  /* Module declarations from 'cpython.buffer' */
  
  /* Module declarations from 'libc.string' */
  
  /* Module declarations from 'libc.stdio' */
  
  /* Module declarations from '__builtin__' */
  
  /* Module declarations from 'cpython.type' */
  static PyTypeObject *__pyx_ptype_7cpython_4type_type = 0;
  
  /* Module declarations from 'cpython' */
  
  /* Module declarations from 'cpython.object' */
  
  /* Module declarations from 'cpython.ref' */
  
  /* Module declarations from 'cpython.mem' */
  
  /* Module declarations from 'numpy' */
  
  /* Module declarations from 'numpy' */
  static PyTypeObject *__pyx_ptype_5numpy_dtype = 0;
  static PyTypeObject *__pyx_ptype_5numpy_flatiter = 0;
  static PyTypeObject *__pyx_ptype_5numpy_broadcast = 0;
  static PyTypeObject *__pyx_ptype_5numpy_ndarray = 0;
  static PyTypeObject *__pyx_ptype_5numpy_ufunc = 0;
  static CYTHON_INLINE char *__pyx_f_5numpy__util_dtypestring(PyArray_Descr *, char *, char *, int *); /*proto*/
  
  /* Module declarations from 'libc.math' */
  
  /* Module declarations from 'pysteps.motion._vet' */
  static CYTHON_INLINE __pyx_t_7pysteps_6motion_4_vet_float64 __pyx_f_7pysteps_6motion_4_vet_float_abs(__pyx_t_7pysteps_6motion_4_vet_float64); /*proto*/
  static CYTHON_INLINE __pyx_t_7pysteps_6motion_4_vet_intp __pyx_f_7pysteps_6motion_4_vet_int_min(__pyx_t_7pysteps_6motion_4_vet_intp, __pyx_t_7pysteps_6motion_4_vet_intp); /*proto*/
  static CYTHON_INLINE __pyx_t_7pysteps_6motion_4_vet_intp __pyx_f_7pysteps_6motion_4_vet_int_max(__pyx_t_7pysteps_6motion_4_vet_intp, __pyx_t_7pysteps_6motion_4_vet_intp); /*proto*/
  static CYTHON_INLINE __pyx_t_7pysteps_6motion_4_vet_float64 __pyx_f_7pysteps_6motion_4_vet__linear_interpolation(__pyx_t_7pysteps_6motion_4_vet_float64, __pyx_t_7pysteps_6motion_4_vet_float64, __pyx_t_7pysteps_6motion_4_vet_float64, __pyx_t_7pysteps_6motion_4_vet_float64, __pyx_t_7pysteps_6motion_4_vet_float64); /*proto*/
  static __Pyx_TypeInfo __Pyx_TypeInfo_nn___pyx_t_7pysteps_6motion_4_vet_float64 = { "float64", NULL, sizeof(__pyx_t_7pysteps_6motion_4_vet_float64), { 0 }, 0, 'R', 0, 0 };
  static __Pyx_TypeInfo __Pyx_TypeInfo_nn___pyx_t_7pysteps_6motion_4_vet_int8 = { "int8", NULL, sizeof(__pyx_t_7pysteps_6motion_4_vet_int8), { 0 }, 0, IS_UNSIGNED(__pyx_t_7pysteps_6motion_4_vet_int8) ? 'U' : 'I', IS_UNSIGNED(__pyx_t_7pysteps_6motion_4_vet_int8), 0 };
  static __Pyx_TypeInfo __Pyx_TypeInfo_nn___pyx_t_7pysteps_6motion_4_vet_intp = { "intp", NULL, sizeof(__pyx_t_7pysteps_6motion_4_vet_intp), { 0 }, 0, IS_UNSIGNED(__pyx_t_7pysteps_6motion_4_vet_intp) ? 'U' : 'I', IS_UNSIGNED(__pyx_t_7pysteps_6motion_4_vet_intp), 0 };
  #define __Pyx_MODULE_NAME "pysteps.motion._vet"
  extern int __pyx_module_is_main_pysteps__motion___vet;
  int __pyx_module_is_main_pysteps__motion___vet = 0;
  
  /* Implementation of 'pysteps.motion._vet' */
  static PyObject *__pyx_builtin_range;
  static PyObject *__pyx_builtin_ValueError;
  static PyObject *__pyx_builtin_zip;
  static PyObject *__pyx_builtin_RuntimeError;
  static PyObject *__pyx_builtin_ImportError;
  static const char __pyx_k_i[] = "i";
  static const char __pyx_k_j[] = "j";
  static const char __pyx_k_l[] = "l";
  static const char __pyx_k_m[] = "m";
  static const char __pyx_k_x[] = "x";
  static const char __pyx_k_y[] = "y";
  static const char __pyx_k_dx[] = "dx";
  static const char __pyx_k_dy[] = "dy";
  static const char __pyx_k_l0[] = "l0";
  static const char __pyx_k_l1[] = "l1";
  static const char __pyx_k_ll[] = "ll";
  static const char __pyx_k_m0[] = "m0";
  static const char __pyx_k_m1[] = "m1";
  static const char __pyx_k_mm[] = "mm";
  static const char __pyx_k_np[] = "np";
  static const char __pyx_k_nx[] = "nx";
  static const char __pyx_k_ny[] = "ny";
  static const char __pyx_k_xy[] = "xy";
  static const char __pyx_k_f00[] = "f00";
  static const char __pyx_k_f01[] = "f01";
  static const char __pyx_k_f10[] = "f10";
  static const char __pyx_k_f11[] = "f11";
  static const char __pyx_k_l_i[] = "l_i";
  static const char __pyx_k_m_j[] = "m_j";
  static const char __pyx_k_sum[] = "sum";
  static const char __pyx_k_zip[] = "zip";
  static const char __pyx_k_axis[] = "axis";
  static const char __pyx_k_full[] = "full";
  static const char __pyx_k_int8[] = "int8";
  static const char __pyx_k_intp[] = "intp";
  static const char __pyx_k_main[] = "__main__";
  static const char __pyx_k_mask[] = "mask";
  static const char __pyx_k_mean[] = "mean";
  static const char __pyx_k_name[] = "__name__";
  static const char __pyx_k_test[] = "__test__";
  static const char __pyx_k_warp[] = "_warp";
  static const char __pyx_k_dtype[] = "dtype";
  static const char __pyx_k_i_max[] = "i_max";
  static const char __pyx_k_i_min[] = "i_min";
  static const char __pyx_k_i_sec[] = "i_sec";
  static const char __pyx_k_image[] = "image";
  static const char __pyx_k_j_max[] = "j_max";
  static const char __pyx_k_j_min[] = "j_min";
  static const char __pyx_k_j_sec[] = "j_sec";
  static const char __pyx_k_numpy[] = "numpy";
  static const char __pyx_k_range[] = "range";
  static const char __pyx_k_zeros[] = "zeros";
  static const char __pyx_k_arange[] = "arange";
  static const char __pyx_k_buffer[] = "buffer";
  static const char __pyx_k_counts[] = "counts";
  static const char __pyx_k_df_dx2[] = "df_dx2";
  static const char __pyx_k_df_dy2[] = "df_dy2";
  static const char __pyx_k_import[] = "__import__";
  static const char __pyx_k_unique[] = "unique";
  static const char __pyx_k_x_ceil[] = "x_ceil";
  static const char __pyx_k_y_ceil[] = "y_ceil";
  static const char __pyx_k_df_dxdy[] = "df_dxdy";
  static const char __pyx_k_float64[] = "float64";
  static const char __pyx_k_i_shift[] = "i_shift";
  static const char __pyx_k_j_shift[] = "j_shift";
  static const char __pyx_k_reshape[] = "reshape";
  static const char __pyx_k_x_float[] = "x_float";
  static const char __pyx_k_x_floor[] = "x_floor";
  static const char __pyx_k_x_guess[] = "x_guess";
  static const char __pyx_k_y_float[] = "y_float";
  static const char __pyx_k_y_floor[] = "y_floor";
  static const char __pyx_k_y_guess[] = "y_guess";
  static const char __pyx_k_gradient[] = "gradient";
  static const char __pyx_k_new_image[] = "new_image";
  static const char __pyx_k_residuals[] = "residuals";
  static const char __pyx_k_x_max_int[] = "x_max_int";
  static const char __pyx_k_x_sectors[] = "x_sectors";
  static const char __pyx_k_y_max_int[] = "y_max_int";
  static const char __pyx_k_y_sectors[] = "y_sectors";
  static const char __pyx_k_ValueError[] = "ValueError";
  static const char __pyx_k_morph_mask[] = "morph_mask";
  static const char __pyx_k_ImportError[] = "ImportError";
  static const char __pyx_k_grad_smooth[] = "grad_smooth";
  static const char __pyx_k_input_image[] = "input_image";
  static const char __pyx_k_interp_coef[] = "interp_coef";
  static const char __pyx_k_sector_area[] = "sector_area";
  static const char __pyx_k_smooth_gain[] = "smooth_gain";
  static const char __pyx_k_x_max_float[] = "x_max_float";
  static const char __pyx_k_y_max_float[] = "y_max_float";
  static const char __pyx_k_RuntimeError[] = "RuntimeError";
  static const char __pyx_k_displacement[] = "displacement";
  static const char __pyx_k_morphed_mask[] = "morphed_mask";
  static const char __pyx_k_return_index[] = "return_index";
  static const char __pyx_k_x_image_size[] = "x_image_size";
  static const char __pyx_k_y_image_size[] = "y_image_size";
  static const char __pyx_k_cost_function[] = "_cost_function";
  static const char __pyx_k_gradient_data[] = "_gradient_data";
  static const char __pyx_k_morphed_image[] = "morphed_image";
  static const char __pyx_k_return_counts[] = "return_counts";
  static const char __pyx_k_x_sector_size[] = "x_sector_size";
  static const char __pyx_k_y_sector_size[] = "y_sector_size";
  static const char __pyx_k_grad_residuals[] = "grad_residuals";
  static const char __pyx_k_template_image[] = "template_image";
  static const char __pyx_k_gradient_values[] = "gradient_values";
  static const char __pyx_k_cline_in_traceback[] = "cline_in_traceback";
  static const char __pyx_k_smoothness_penalty[] = "smoothness_penalty";
  static const char __pyx_k_pysteps_motion__vet[] = "pysteps.motion._vet";
  static const char __pyx_k_sector_displacement[] = "sector_displacement";
  static const char __pyx_k_pysteps_motion__vet_pyx[] = "pysteps/motion/_vet.pyx";
  static const char __pyx_k_inloop_smoothness_penalty[] = "inloop_smoothness_penalty";
  static const char __pyx_k_ndarray_is_not_C_contiguous[] = "ndarray is not C contiguous";
  static const char __pyx_k_Error_computing_cost_function[] = "Error computing cost function.\n";
  static const char __pyx_k_Cython_module_for_morphing_and[] = "\nCython module for morphing and cost functions implementations used in\nin the Variation Echo Tracking Algorithm\n";
  static const char __pyx_k_The_number_of_sectors_in_x_axis[] = "The number of sectors in x axis (axis=0) don't divide the image size";
  static const char __pyx_k_The_number_of_sectors_in_y_axis[] = "The number of sectors in y axis (axis=1) don't divide the image size";
  static const char __pyx_k_numpy_core_multiarray_failed_to[] = "numpy.core.multiarray failed to import";
  static const char __pyx_k_unknown_dtype_code_in_numpy_pxd[] = "unknown dtype code in numpy.pxd (%d)";
  static const char __pyx_k_Format_string_allocated_too_shor[] = "Format string allocated too short, see comment in numpy.pxd";
  static const char __pyx_k_Non_native_byte_order_not_suppor[] = "Non-native byte order not supported";
  static const char __pyx_k_ndarray_is_not_Fortran_contiguou[] = "ndarray is not Fortran contiguous";
  static const char __pyx_k_numpy_core_umath_failed_to_impor[] = "numpy.core.umath failed to import";
  static const char __pyx_k_Format_string_allocated_too_shor_2[] = "Format string allocated too short.";
  static PyObject *__pyx_kp_u_Error_computing_cost_function;
  static PyObject *__pyx_kp_u_Format_string_allocated_too_shor;
  static PyObject *__pyx_kp_u_Format_string_allocated_too_shor_2;
  static PyObject *__pyx_n_s_ImportError;
  static PyObject *__pyx_kp_u_Non_native_byte_order_not_suppor;
  static PyObject *__pyx_n_s_RuntimeError;
  static PyObject *__pyx_kp_u_The_number_of_sectors_in_x_axis;
  static PyObject *__pyx_kp_u_The_number_of_sectors_in_y_axis;
  static PyObject *__pyx_n_s_ValueError;
  static PyObject *__pyx_n_s_arange;
  static PyObject *__pyx_n_s_axis;
  static PyObject *__pyx_n_s_buffer;
  static PyObject *__pyx_n_s_cline_in_traceback;
  static PyObject *__pyx_n_s_cost_function;
  static PyObject *__pyx_n_s_counts;
  static PyObject *__pyx_n_s_df_dx2;
  static PyObject *__pyx_n_s_df_dxdy;
  static PyObject *__pyx_n_s_df_dy2;
  static PyObject *__pyx_n_s_displacement;
  static PyObject *__pyx_n_s_dtype;
  static PyObject *__pyx_n_s_dx;
  static PyObject *__pyx_n_s_dy;
  static PyObject *__pyx_n_s_f00;
  static PyObject *__pyx_n_s_f01;
  static PyObject *__pyx_n_s_f10;
  static PyObject *__pyx_n_s_f11;
  static PyObject *__pyx_n_s_float64;
  static PyObject *__pyx_n_u_float64;
  static PyObject *__pyx_n_s_full;
  static PyObject *__pyx_n_s_grad_residuals;
  static PyObject *__pyx_n_s_grad_smooth;
  static PyObject *__pyx_n_s_gradient;
  static PyObject *__pyx_n_s_gradient_data;
  static PyObject *__pyx_n_s_gradient_values;
  static PyObject *__pyx_n_s_i;
  static PyObject *__pyx_n_s_i_max;
  static PyObject *__pyx_n_s_i_min;
  static PyObject *__pyx_n_s_i_sec;
  static PyObject *__pyx_n_s_i_shift;
  static PyObject *__pyx_n_s_image;
  static PyObject *__pyx_n_s_import;
  static PyObject *__pyx_n_s_inloop_smoothness_penalty;
  static PyObject *__pyx_n_s_input_image;
  static PyObject *__pyx_n_s_int8;
  static PyObject *__pyx_n_s_interp_coef;
  static PyObject *__pyx_n_s_intp;
  static PyObject *__pyx_n_s_j;
  static PyObject *__pyx_n_s_j_max;
  static PyObject *__pyx_n_s_j_min;
  static PyObject *__pyx_n_s_j_sec;
  static PyObject *__pyx_n_s_j_shift;
  static PyObject *__pyx_n_s_l;
  static PyObject *__pyx_n_s_l0;
  static PyObject *__pyx_n_s_l1;
  static PyObject *__pyx_n_s_l_i;
  static PyObject *__pyx_n_s_ll;
  static PyObject *__pyx_n_s_m;
  static PyObject *__pyx_n_s_m0;
  static PyObject *__pyx_n_s_m1;
  static PyObject *__pyx_n_s_m_j;
  static PyObject *__pyx_n_s_main;
  static PyObject *__pyx_n_s_mask;
  static PyObject *__pyx_n_s_mean;
  static PyObject *__pyx_n_s_mm;
  static PyObject *__pyx_n_s_morph_mask;
  static PyObject *__pyx_n_s_morphed_image;
  static PyObject *__pyx_n_s_morphed_mask;
  static PyObject *__pyx_n_s_name;
  static PyObject *__pyx_kp_u_ndarray_is_not_C_contiguous;
  static PyObject *__pyx_kp_u_ndarray_is_not_Fortran_contiguou;
  static PyObject *__pyx_n_s_new_image;
  static PyObject *__pyx_n_s_np;
  static PyObject *__pyx_n_s_numpy;
  static PyObject *__pyx_kp_u_numpy_core_multiarray_failed_to;
  static PyObject *__pyx_kp_u_numpy_core_umath_failed_to_impor;
  static PyObject *__pyx_n_s_nx;
  static PyObject *__pyx_n_s_ny;
  static PyObject *__pyx_n_s_pysteps_motion__vet;
  static PyObject *__pyx_kp_s_pysteps_motion__vet_pyx;
  static PyObject *__pyx_n_s_range;
  static PyObject *__pyx_n_s_reshape;
  static PyObject *__pyx_n_s_residuals;
  static PyObject *__pyx_n_s_return_counts;
  static PyObject *__pyx_n_s_return_index;
  static PyObject *__pyx_n_s_sector_area;
  static PyObject *__pyx_n_s_sector_displacement;
  static PyObject *__pyx_n_s_smooth_gain;
  static PyObject *__pyx_n_s_smoothness_penalty;
  static PyObject *__pyx_n_s_sum;
  static PyObject *__pyx_n_s_template_image;
  static PyObject *__pyx_n_s_test;
  static PyObject *__pyx_n_s_unique;
  static PyObject *__pyx_kp_u_unknown_dtype_code_in_numpy_pxd;
  static PyObject *__pyx_n_s_warp;
  static PyObject *__pyx_n_s_x;
  static PyObject *__pyx_n_s_x_ceil;
  static PyObject *__pyx_n_s_x_float;
  static PyObject *__pyx_n_s_x_floor;
  static PyObject *__pyx_n_s_x_guess;
  static PyObject *__pyx_n_s_x_image_size;
  static PyObject *__pyx_n_s_x_max_float;
  static PyObject *__pyx_n_s_x_max_int;
  static PyObject *__pyx_n_s_x_sector_size;
  static PyObject *__pyx_n_s_x_sectors;
  static PyObject *__pyx_n_s_xy;
  static PyObject *__pyx_n_s_y;
  static PyObject *__pyx_n_s_y_ceil;
  static PyObject *__pyx_n_s_y_float;
  static PyObject *__pyx_n_s_y_floor;
  static PyObject *__pyx_n_s_y_guess;
  static PyObject *__pyx_n_s_y_image_size;
  static PyObject *__pyx_n_s_y_max_float;
  static PyObject *__pyx_n_s_y_max_int;
  static PyObject *__pyx_n_s_y_sector_size;
  static PyObject *__pyx_n_s_y_sectors;
  static PyObject *__pyx_n_s_zeros;
  static PyObject *__pyx_n_s_zip;
  static PyObject *__pyx_pf_7pysteps_6motion_4_vet__warp(CYTHON_UNUSED PyObject *__pyx_self, PyArrayObject *__pyx_v_image, PyArrayObject *__pyx_v_mask, PyArrayObject *__pyx_v_displacement, int __pyx_v_gradient); /* proto */
  static PyObject *__pyx_pf_7pysteps_6motion_4_vet_2_cost_function(CYTHON_UNUSED PyObject *__pyx_self, PyArrayObject *__pyx_v_sector_displacement, PyArrayObject *__pyx_v_template_image, PyArrayObject *__pyx_v_input_image, PyArrayObject *__pyx_v_mask, float __pyx_v_smooth_gain, int __pyx_v_gradient); /* proto */
  static int __pyx_pf_5numpy_7ndarray___getbuffer__(PyArrayObject *__pyx_v_self, Py_buffer *__pyx_v_info, int __pyx_v_flags); /* proto */
  static void __pyx_pf_5numpy_7ndarray_2__releasebuffer__(PyArrayObject *__pyx_v_self, Py_buffer *__pyx_v_info); /* proto */
  static PyObject *__pyx_float_1_0;
  static PyObject *__pyx_int_0;
  static PyObject *__pyx_int_1;
  static PyObject *__pyx_int_2;
  static PyObject *__pyx_int_4;
  static PyObject *__pyx_tuple_;
  static PyObject *__pyx_slice__3;
  static PyObject *__pyx_tuple__2;
  static PyObject *__pyx_tuple__4;
  static PyObject *__pyx_tuple__5;
  static PyObject *__pyx_tuple__6;
  static PyObject *__pyx_tuple__7;
  static PyObject *__pyx_tuple__8;
  static PyObject *__pyx_tuple__9;
  static PyObject *__pyx_tuple__10;
  static PyObject *__pyx_tuple__11;
  static PyObject *__pyx_tuple__12;
  static PyObject *__pyx_tuple__13;
  static PyObject *__pyx_tuple__15;
  static PyObject *__pyx_codeobj__14;
  static PyObject *__pyx_codeobj__16;
  /* Late includes */
  
  /* "pysteps/motion/_vet.pyx":21
   * cimport numpy as np
   * 
   * cdef inline float64 float_abs(float64 a) nogil: return a if a > 0. else -a             # <<<<<<<<<<<<<<
   * """ Return the absolute value of a float """
   * 
   */
  
  static CYTHON_INLINE __pyx_t_7pysteps_6motion_4_vet_float64 __pyx_f_7pysteps_6motion_4_vet_float_abs(__pyx_t_7pysteps_6motion_4_vet_float64 __pyx_v_a) {
    __pyx_t_7pysteps_6motion_4_vet_float64 __pyx_r;
    __pyx_t_7pysteps_6motion_4_vet_float64 __pyx_t_1;
    if (((__pyx_v_a > 0.) != 0)) {
      __pyx_t_1 = __pyx_v_a;
    } else {
      __pyx_t_1 = (-__pyx_v_a);
    }
    __pyx_r = __pyx_t_1;
    goto __pyx_L0;
  
    /* function exit code */
    __pyx_L0:;
    return __pyx_r;
  }
  
  /* "pysteps/motion/_vet.pyx":24
   * """ Return the absolute value of a float """
   * 
   * cdef inline intp int_min(intp a, intp b) nogil: return a if a < b else b             # <<<<<<<<<<<<<<
   * 
   * cdef inline intp int_max(intp a, intp b) nogil: return a if a > b else b
   */
  
  static CYTHON_INLINE __pyx_t_7pysteps_6motion_4_vet_intp __pyx_f_7pysteps_6motion_4_vet_int_min(__pyx_t_7pysteps_6motion_4_vet_intp __pyx_v_a, __pyx_t_7pysteps_6motion_4_vet_intp __pyx_v_b) {
    __pyx_t_7pysteps_6motion_4_vet_intp __pyx_r;
    __pyx_t_7pysteps_6motion_4_vet_intp __pyx_t_1;
    if (((__pyx_v_a < __pyx_v_b) != 0)) {
      __pyx_t_1 = __pyx_v_a;
    } else {
      __pyx_t_1 = __pyx_v_b;
    }
    __pyx_r = __pyx_t_1;
    goto __pyx_L0;
  
    /* function exit code */
    __pyx_L0:;
    return __pyx_r;
  }
  
  /* "pysteps/motion/_vet.pyx":26
   * cdef inline intp int_min(intp a, intp b) nogil: return a if a < b else b
   * 
   * cdef inline intp int_max(intp a, intp b) nogil: return a if a > b else b             # <<<<<<<<<<<<<<
   * 
   * @cython.cdivision(True)
   */
  
  static CYTHON_INLINE __pyx_t_7pysteps_6motion_4_vet_intp __pyx_f_7pysteps_6motion_4_vet_int_max(__pyx_t_7pysteps_6motion_4_vet_intp __pyx_v_a, __pyx_t_7pysteps_6motion_4_vet_intp __pyx_v_b) {
    __pyx_t_7pysteps_6motion_4_vet_intp __pyx_r;
    __pyx_t_7pysteps_6motion_4_vet_intp __pyx_t_1;
    if (((__pyx_v_a > __pyx_v_b) != 0)) {
      __pyx_t_1 = __pyx_v_a;
    } else {
      __pyx_t_1 = __pyx_v_b;
    }
    __pyx_r = __pyx_t_1;
    goto __pyx_L0;
  
    /* function exit code */
    __pyx_L0:;
    return __pyx_r;
  }
  
  /* "pysteps/motion/_vet.pyx":29
   * 
   * @cython.cdivision(True)
   * cdef inline float64 _linear_interpolation(float64 x,             # <<<<<<<<<<<<<<
   *                                           float64 x1,
   *                                           float64 x2,
   */
  
  static CYTHON_INLINE __pyx_t_7pysteps_6motion_4_vet_float64 __pyx_f_7pysteps_6motion_4_vet__linear_interpolation(__pyx_t_7pysteps_6motion_4_vet_float64 __pyx_v_x, __pyx_t_7pysteps_6motion_4_vet_float64 __pyx_v_x1, __pyx_t_7pysteps_6motion_4_vet_float64 __pyx_v_x2, __pyx_t_7pysteps_6motion_4_vet_float64 __pyx_v_y1, __pyx_t_7pysteps_6motion_4_vet_float64 __pyx_v_y2) {
    __pyx_t_7pysteps_6motion_4_vet_float64 __pyx_r;
    int __pyx_t_1;
  
    /* "pysteps/motion/_vet.pyx":39
   *     """
   * 
   *     if float_abs(x1 - x2) < 1e-6:             # <<<<<<<<<<<<<<
   *         return y1
   * 
   */
    __pyx_t_1 = ((__pyx_f_7pysteps_6motion_4_vet_float_abs((__pyx_v_x1 - __pyx_v_x2)) < 1e-6) != 0);
    if (__pyx_t_1) {
  
      /* "pysteps/motion/_vet.pyx":40
   * 
   *     if float_abs(x1 - x2) < 1e-6:
   *         return y1             # <<<<<<<<<<<<<<
   * 
   *     return y1 + (x - x1) * (y2 - y1) / (x2 - x1)
   */
      __pyx_r = __pyx_v_y1;
      goto __pyx_L0;
  
      /* "pysteps/motion/_vet.pyx":39
   *     """
   * 
   *     if float_abs(x1 - x2) < 1e-6:             # <<<<<<<<<<<<<<
   *         return y1
   * 
   */
    }
  
    /* "pysteps/motion/_vet.pyx":42
   *         return y1
   * 
   *     return y1 + (x - x1) * (y2 - y1) / (x2 - x1)             # <<<<<<<<<<<<<<
   * 
   * @cython.cdivision(True)
   */
    __pyx_r = (__pyx_v_y1 + (((__pyx_v_x - __pyx_v_x1) * (__pyx_v_y2 - __pyx_v_y1)) / (__pyx_v_x2 - __pyx_v_x1)));
    goto __pyx_L0;
  
    /* "pysteps/motion/_vet.pyx":29
   * 
   * @cython.cdivision(True)
   * cdef inline float64 _linear_interpolation(float64 x,             # <<<<<<<<<<<<<<
   *                                           float64 x1,
   *                                           float64 x2,
   */
  
    /* function exit code */
    __pyx_L0:;
    return __pyx_r;
  }
  
  /* "pysteps/motion/_vet.pyx":45
   * 
   * @cython.cdivision(True)
   * cdef inline float64 _bilinear_interpolation(float64 x,             # <<<<<<<<<<<<<<
   *                                             float64 y,
   *                                             float64 x1,
   */
  
  static CYTHON_INLINE __pyx_t_7pysteps_6motion_4_vet_float64 __pyx_f_7pysteps_6motion_4_vet__bilinear_interpolation(__pyx_t_7pysteps_6motion_4_vet_float64 __pyx_v_x, __pyx_t_7pysteps_6motion_4_vet_float64 __pyx_v_y, __pyx_t_7pysteps_6motion_4_vet_float64 __pyx_v_x1, __pyx_t_7pysteps_6motion_4_vet_float64 __pyx_v_x2, __pyx_t_7pysteps_6motion_4_vet_float64 __pyx_v_y1, __pyx_t_7pysteps_6motion_4_vet_float64 __pyx_v_y2, __pyx_t_7pysteps_6motion_4_vet_float64 __pyx_v_q11, __pyx_t_7pysteps_6motion_4_vet_float64 __pyx_v_q12, __pyx_t_7pysteps_6motion_4_vet_float64 __pyx_v_q21, __pyx_t_7pysteps_6motion_4_vet_float64 __pyx_v_q22) {
    __pyx_t_7pysteps_6motion_4_vet_float64 __pyx_v_f_x_y1;
    __pyx_t_7pysteps_6motion_4_vet_float64 __pyx_v_f_x_y2;
    __pyx_t_7pysteps_6motion_4_vet_float64 __pyx_r;
  
    /* "pysteps/motion/_vet.pyx":59
   *     cdef float64 f_x_y1, f_x_y2
   * 
   *     f_x_y1 = _linear_interpolation(x, x1, x2, q11, q21)             # <<<<<<<<<<<<<<
   *     f_x_y2 = _linear_interpolation(x, x1, x2, q12, q22)
   *     return _linear_interpolation(y, y1, y2, f_x_y1, f_x_y2)
   */
    __pyx_v_f_x_y1 = __pyx_f_7pysteps_6motion_4_vet__linear_interpolation(__pyx_v_x, __pyx_v_x1, __pyx_v_x2, __pyx_v_q11, __pyx_v_q21);
  
    /* "pysteps/motion/_vet.pyx":60
   * 
   *     f_x_y1 = _linear_interpolation(x, x1, x2, q11, q21)
   *     f_x_y2 = _linear_interpolation(x, x1, x2, q12, q22)             # <<<<<<<<<<<<<<
   *     return _linear_interpolation(y, y1, y2, f_x_y1, f_x_y2)
   * 
   */
    __pyx_v_f_x_y2 = __pyx_f_7pysteps_6motion_4_vet__linear_interpolation(__pyx_v_x, __pyx_v_x1, __pyx_v_x2, __pyx_v_q12, __pyx_v_q22);
  
    /* "pysteps/motion/_vet.pyx":61
   *     f_x_y1 = _linear_interpolation(x, x1, x2, q11, q21)
   *     f_x_y2 = _linear_interpolation(x, x1, x2, q12, q22)
   *     return _linear_interpolation(y, y1, y2, f_x_y1, f_x_y2)             # <<<<<<<<<<<<<<
   * 
   * @cython.boundscheck(False)
   */
    __pyx_r = __pyx_f_7pysteps_6motion_4_vet__linear_interpolation(__pyx_v_y, __pyx_v_y1, __pyx_v_y2, __pyx_v_f_x_y1, __pyx_v_f_x_y2);
    goto __pyx_L0;
  
    /* "pysteps/motion/_vet.pyx":45
   * 
   * @cython.cdivision(True)
   * cdef inline float64 _bilinear_interpolation(float64 x,             # <<<<<<<<<<<<<<
   *                                             float64 y,
   *                                             float64 x1,
   */
  
    /* function exit code */
    __pyx_L0:;
    return __pyx_r;
  }
  
  /* "pysteps/motion/_vet.pyx":67
   * @cython.nonecheck(False)
   * @cython.cdivision(True)
   * def _warp(np.ndarray[float64, ndim=2] image,             # <<<<<<<<<<<<<<
   *           np.ndarray[int8, ndim=2] mask,
   *           np.ndarray[float64, ndim=3] displacement,
   */
  
  /* Python wrapper */
  static PyObject *__pyx_pw_7pysteps_6motion_4_vet_1_warp(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds); /*proto*/
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                                __pyx_t_20 = __pyx_v_y;
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                                /* "pysteps/motion/_vet.pyx":168
   *             y_float = (<float64> y) - displacement[1, x, y]
   * 
   *             if x_float < 0:             # <<<<<<<<<<<<<<
   *                 morphed_mask[x, y] = 1
   *                 x_float = 0
   */
                                __pyx_t_21 = ((__pyx_v_x_float < 0.0) != 0);
                                if (__pyx_t_21) {
  
                                  /* "pysteps/motion/_vet.pyx":169
   * 
   *             if x_float < 0:
   *                 morphed_mask[x, y] = 1             # <<<<<<<<<<<<<<
   *                 x_float = 0
   *                 x_floor = 0
   */
                                  __pyx_t_22 = __pyx_v_x;
                                  __pyx_t_23 = __pyx_v_y;
                                  *__Pyx_BufPtrStrided2d(__pyx_t_7pysteps_6motion_4_vet_int8 *, __pyx_pybuffernd_morphed_mask.rcbuffer->pybuffer.buf, __pyx_t_22, __pyx_pybuffernd_morphed_mask.diminfo[0].strides, __pyx_t_23, __pyx_pybuffernd_morphed_mask.diminfo[1].strides) = 1;
  
                                  /* "pysteps/motion/_vet.pyx":170
   *             if x_float < 0:
   *                 morphed_mask[x, y] = 1
   *                 x_float = 0             # <<<<<<<<<<<<<<
   *                 x_floor = 0
   *                 x_ceil = 0
   */
                                  __pyx_v_x_float = 0.0;
  
                                  /* "pysteps/motion/_vet.pyx":171
   *                 morphed_mask[x, y] = 1
   *                 x_float = 0
   *                 x_floor = 0             # <<<<<<<<<<<<<<
   *                 x_ceil = 0
   * 
   */
                                  __pyx_v_x_floor = 0;
  
                                  /* "pysteps/motion/_vet.pyx":172
   *                 x_float = 0
   *                 x_floor = 0
   *                 x_ceil = 0             # <<<<<<<<<<<<<<
   * 
   *             elif x_float > x_max_float:
   */
                                  __pyx_v_x_ceil = 0;
  
                                  /* "pysteps/motion/_vet.pyx":168
   *             y_float = (<float64> y) - displacement[1, x, y]
   * 
   *             if x_float < 0:             # <<<<<<<<<<<<<<
   *                 morphed_mask[x, y] = 1
   *                 x_float = 0
   */
                                  goto __pyx_L12;
                                }
  
                                /* "pysteps/motion/_vet.pyx":174
   *                 x_ceil = 0
   * 
   *             elif x_float > x_max_float:             # <<<<<<<<<<<<<<
   *                 morphed_mask[x, y] = 1
   *                 x_float = x_max_float
   */
                                __pyx_t_21 = ((__pyx_v_x_float > __pyx_v_x_max_float) != 0);
                                if (__pyx_t_21) {
  
                                  /* "pysteps/motion/_vet.pyx":175
   * 
   *             elif x_float > x_max_float:
   *                 morphed_mask[x, y] = 1             # <<<<<<<<<<<<<<
   *                 x_float = x_max_float
   *                 x_floor = x_max_int
   */
                                  __pyx_t_24 = __pyx_v_x;
                                  __pyx_t_25 = __pyx_v_y;
                                  *__Pyx_BufPtrStrided2d(__pyx_t_7pysteps_6motion_4_vet_int8 *, __pyx_pybuffernd_morphed_mask.rcbuffer->pybuffer.buf, __pyx_t_24, __pyx_pybuffernd_morphed_mask.diminfo[0].strides, __pyx_t_25, __pyx_pybuffernd_morphed_mask.diminfo[1].strides) = 1;
  
                                  /* "pysteps/motion/_vet.pyx":176
   *             elif x_float > x_max_float:
   *                 morphed_mask[x, y] = 1
   *                 x_float = x_max_float             # <<<<<<<<<<<<<<
   *                 x_floor = x_max_int
   *                 x_ceil = x_max_int
   */
                                  __pyx_v_x_float = __pyx_v_x_max_float;
  
                                  /* "pysteps/motion/_vet.pyx":177
   *                 morphed_mask[x, y] = 1
   *                 x_float = x_max_float
   *                 x_floor = x_max_int             # <<<<<<<<<<<<<<
   *                 x_ceil = x_max_int
   * 
   */
                                  __pyx_v_x_floor = __pyx_v_x_max_int;
  
                                  /* "pysteps/motion/_vet.pyx":178
   *                 x_float = x_max_float
   *                 x_floor = x_max_int
   *                 x_ceil = x_max_int             # <<<<<<<<<<<<<<
   * 
   *             else:
   */
                                  __pyx_v_x_ceil = __pyx_v_x_max_int;
  
                                  /* "pysteps/motion/_vet.pyx":174
   *                 x_ceil = 0
   * 
   *             elif x_float > x_max_float:             # <<<<<<<<<<<<<<
   *                 morphed_mask[x, y] = 1
   *                 x_float = x_max_float
   */
                                  goto __pyx_L12;
                                }
  
                                /* "pysteps/motion/_vet.pyx":181
   * 
   *             else:
   *                 x_floor = <intp> floor(x_float)             # <<<<<<<<<<<<<<
   *                 x_ceil = x_floor + 1
   *                 if x_ceil > x_max_int:
   */
                                /*else*/ {
                                  __pyx_v_x_floor = ((__pyx_t_7pysteps_6motion_4_vet_intp)floor(__pyx_v_x_float));
  
                                  /* "pysteps/motion/_vet.pyx":182
   *             else:
   *                 x_floor = <intp> floor(x_float)
   *                 x_ceil = x_floor + 1             # <<<<<<<<<<<<<<
   *                 if x_ceil > x_max_int:
   *                     x_ceil = x_max_int
   */
                                  __pyx_v_x_ceil = (__pyx_v_x_floor + 1);
  
                                  /* "pysteps/motion/_vet.pyx":183
   *                 x_floor = <intp> floor(x_float)
   *                 x_ceil = x_floor + 1
   *                 if x_ceil > x_max_int:             # <<<<<<<<<<<<<<
   *                     x_ceil = x_max_int
   * 
   */
                                  __pyx_t_21 = ((__pyx_v_x_ceil > __pyx_v_x_max_int) != 0);
                                  if (__pyx_t_21) {
  
                                    /* "pysteps/motion/_vet.pyx":184
   *                 x_ceil = x_floor + 1
   *                 if x_ceil > x_max_int:
   *                     x_ceil = x_max_int             # <<<<<<<<<<<<<<
   * 
   *             if y_float < 0:
   */
                                    __pyx_v_x_ceil = __pyx_v_x_max_int;
  
                                    /* "pysteps/motion/_vet.pyx":183
   *                 x_floor = <intp> floor(x_float)
   *                 x_ceil = x_floor + 1
   *                 if x_ceil > x_max_int:             # <<<<<<<<<<<<<<
   *                     x_ceil = x_max_int
   * 
   */
                                  }
                                }
                                __pyx_L12:;
  
                                /* "pysteps/motion/_vet.pyx":186
   *                     x_ceil = x_max_int
   * 
   *             if y_float < 0:             # <<<<<<<<<<<<<<
   *                 morphed_mask[x, y] = 1
   *                 y_float = 0
   */
                                __pyx_t_21 = ((__pyx_v_y_float < 0.0) != 0);
                                if (__pyx_t_21) {
  
                                  /* "pysteps/motion/_vet.pyx":187
   * 
   *             if y_float < 0:
   *                 morphed_mask[x, y] = 1             # <<<<<<<<<<<<<<
   *                 y_float = 0
   *                 y_floor = 0
   */
                                  __pyx_t_26 = __pyx_v_x;
                                  __pyx_t_27 = __pyx_v_y;
                                  *__Pyx_BufPtrStrided2d(__pyx_t_7pysteps_6motion_4_vet_int8 *, __pyx_pybuffernd_morphed_mask.rcbuffer->pybuffer.buf, __pyx_t_26, __pyx_pybuffernd_morphed_mask.diminfo[0].strides, __pyx_t_27, __pyx_pybuffernd_morphed_mask.diminfo[1].strides) = 1;
  
                                  /* "pysteps/motion/_vet.pyx":188
   *             if y_float < 0:
   *                 morphed_mask[x, y] = 1
   *                 y_float = 0             # <<<<<<<<<<<<<<
   *                 y_floor = 0
   *                 y_ceil = 0
   */
                                  __pyx_v_y_float = 0.0;
  
                                  /* "pysteps/motion/_vet.pyx":189
   *                 morphed_mask[x, y] = 1
   *                 y_float = 0
   *                 y_floor = 0             # <<<<<<<<<<<<<<
   *                 y_ceil = 0
   *             elif y_float > y_max_float:
   */
                                  __pyx_v_y_floor = 0;
  
                                  /* "pysteps/motion/_vet.pyx":190
   *                 y_float = 0
   *                 y_floor = 0
   *                 y_ceil = 0             # <<<<<<<<<<<<<<
   *             elif y_float > y_max_float:
   *                 morphed_mask[x, y] = 1
   */
                                  __pyx_v_y_ceil = 0;
  
                                  /* "pysteps/motion/_vet.pyx":186
   *                     x_ceil = x_max_int
   * 
   *             if y_float < 0:             # <<<<<<<<<<<<<<
   *                 morphed_mask[x, y] = 1
   *                 y_float = 0
   */
                                  goto __pyx_L14;
                                }
  
                                /* "pysteps/motion/_vet.pyx":191
   *                 y_floor = 0
   *                 y_ceil = 0
   *             elif y_float > y_max_float:             # <<<<<<<<<<<<<<
   *                 morphed_mask[x, y] = 1
   *                 y_float = y_max_float
   */
                                __pyx_t_21 = ((__pyx_v_y_float > __pyx_v_y_max_float) != 0);
                                if (__pyx_t_21) {
  
                                  /* "pysteps/motion/_vet.pyx":192
   *                 y_ceil = 0
   *             elif y_float > y_max_float:
   *                 morphed_mask[x, y] = 1             # <<<<<<<<<<<<<<
   *                 y_float = y_max_float
   *                 y_floor = y_max_int
   */
                                  __pyx_t_28 = __pyx_v_x;
                                  __pyx_t_29 = __pyx_v_y;
                                  *__Pyx_BufPtrStrided2d(__pyx_t_7pysteps_6motion_4_vet_int8 *, __pyx_pybuffernd_morphed_mask.rcbuffer->pybuffer.buf, __pyx_t_28, __pyx_pybuffernd_morphed_mask.diminfo[0].strides, __pyx_t_29, __pyx_pybuffernd_morphed_mask.diminfo[1].strides) = 1;
  
                                  /* "pysteps/motion/_vet.pyx":193
   *             elif y_float > y_max_float:
   *                 morphed_mask[x, y] = 1
   *                 y_float = y_max_float             # <<<<<<<<<<<<<<
   *                 y_floor = y_max_int
   *                 y_ceil = y_max_int
   */
                                  __pyx_v_y_float = __pyx_v_y_max_float;
  
                                  /* "pysteps/motion/_vet.pyx":194
   *                 morphed_mask[x, y] = 1
   *                 y_float = y_max_float
   *                 y_floor = y_max_int             # <<<<<<<<<<<<<<
   *                 y_ceil = y_max_int
   *             else:
   */
                                  __pyx_v_y_floor = __pyx_v_y_max_int;
  
                                  /* "pysteps/motion/_vet.pyx":195
   *                 y_float = y_max_float
   *                 y_floor = y_max_int
   *                 y_ceil = y_max_int             # <<<<<<<<<<<<<<
   *             else:
   *                 y_floor = <intp> floor(y_float)
   */
                                  __pyx_v_y_ceil = __pyx_v_y_max_int;
  
                                  /* "pysteps/motion/_vet.pyx":191
   *                 y_floor = 0
   *                 y_ceil = 0
   *             elif y_float > y_max_float:             # <<<<<<<<<<<<<<
   *                 morphed_mask[x, y] = 1
   *                 y_float = y_max_float
   */
                                  goto __pyx_L14;
                                }
  
                                /* "pysteps/motion/_vet.pyx":197
   *                 y_ceil = y_max_int
   *             else:
   *                 y_floor = <intp> floor(y_float)             # <<<<<<<<<<<<<<
   *                 y_ceil = y_floor + 1
   *                 if y_ceil > y_max_int:
   */
                                /*else*/ {
                                  __pyx_v_y_floor = ((__pyx_t_7pysteps_6motion_4_vet_intp)floor(__pyx_v_y_float));
  
                                  /* "pysteps/motion/_vet.pyx":198
   *             else:
   *                 y_floor = <intp> floor(y_float)
   *                 y_ceil = y_floor + 1             # <<<<<<<<<<<<<<
   *                 if y_ceil > y_max_int:
   *                     y_ceil = y_max_int
   */
                                  __pyx_v_y_ceil = (__pyx_v_y_floor + 1);
  
                                  /* "pysteps/motion/_vet.pyx":199
   *                 y_floor = <intp> floor(y_float)
   *                 y_ceil = y_floor + 1
   *                 if y_ceil > y_max_int:             # <<<<<<<<<<<<<<
   *                     y_ceil = y_max_int
   * 
   */
                                  __pyx_t_21 = ((__pyx_v_y_ceil > __pyx_v_y_max_int) != 0);
                                  if (__pyx_t_21) {
  
                                    /* "pysteps/motion/_vet.pyx":200
   *                 y_ceil = y_floor + 1
   *                 if y_ceil > y_max_int:
   *                     y_ceil = y_max_int             # <<<<<<<<<<<<<<
   * 
   *             dx = x_float - <float64> x_floor
   */
                                    __pyx_v_y_ceil = __pyx_v_y_max_int;
  
                                    /* "pysteps/motion/_vet.pyx":199
   *                 y_floor = <intp> floor(y_float)
   *                 y_ceil = y_floor + 1
   *                 if y_ceil > y_max_int:             # <<<<<<<<<<<<<<
   *                     y_ceil = y_max_int
   * 
   */
                                  }
                                }
                                __pyx_L14:;
  
                                /* "pysteps/motion/_vet.pyx":202
   *                     y_ceil = y_max_int
   * 
   *             dx = x_float - <float64> x_floor             # <<<<<<<<<<<<<<
   *             dy = y_float - <float64> y_floor
   * 
   */
                                __pyx_v_dx = (__pyx_v_x_float - ((__pyx_t_7pysteps_6motion_4_vet_float64)__pyx_v_x_floor));
  
                                /* "pysteps/motion/_vet.pyx":203
   * 
   *             dx = x_float - <float64> x_floor
   *             dy = y_float - <float64> y_floor             # <<<<<<<<<<<<<<
   * 
   *             # This assumes that the spacing between grid points=1.
   */
                                __pyx_v_dy = (__pyx_v_y_float - ((__pyx_t_7pysteps_6motion_4_vet_float64)__pyx_v_y_floor));
  
                                /* "pysteps/motion/_vet.pyx":208
   * 
   *             # Bilinear interpolation coeficients
   *             f00 = image[x_floor, y_floor]             # <<<<<<<<<<<<<<
   *             f10 = image[x_ceil, y_floor] - image[x_floor, y_floor]
   *             f01 = image[x_floor, y_ceil] - image[x_floor, y_floor]
   */
                                __pyx_t_30 = __pyx_v_x_floor;
                                __pyx_t_31 = __pyx_v_y_floor;
                                __pyx_v_f00 = (*__Pyx_BufPtrStrided2d(__pyx_t_7pysteps_6motion_4_vet_float64 *, __pyx_pybuffernd_image.rcbuffer->pybuffer.buf, __pyx_t_30, __pyx_pybuffernd_image.diminfo[0].strides, __pyx_t_31, __pyx_pybuffernd_image.diminfo[1].strides));
  
                                /* "pysteps/motion/_vet.pyx":209
   *             # Bilinear interpolation coeficients
   *             f00 = image[x_floor, y_floor]
   *             f10 = image[x_ceil, y_floor] - image[x_floor, y_floor]             # <<<<<<<<<<<<<<
   *             f01 = image[x_floor, y_ceil] - image[x_floor, y_floor]
   *             f11 = (image[x_floor, y_floor] - image[x_ceil, y_floor]
   */
                                __pyx_t_32 = __pyx_v_x_ceil;
                                __pyx_t_33 = __pyx_v_y_floor;
                                __pyx_t_34 = __pyx_v_x_floor;
                                __pyx_t_35 = __pyx_v_y_floor;
                                __pyx_v_f10 = ((*__Pyx_BufPtrStrided2d(__pyx_t_7pysteps_6motion_4_vet_float64 *, __pyx_pybuffernd_image.rcbuffer->pybuffer.buf, __pyx_t_32, __pyx_pybuffernd_image.diminfo[0].strides, __pyx_t_33, __pyx_pybuffernd_image.diminfo[1].strides)) - (*__Pyx_BufPtrStrided2d(__pyx_t_7pysteps_6motion_4_vet_float64 *, __pyx_pybuffernd_image.rcbuffer->pybuffer.buf, __pyx_t_34, __pyx_pybuffernd_image.diminfo[0].strides, __pyx_t_35, __pyx_pybuffernd_image.diminfo[1].strides)));
  
                                /* "pysteps/motion/_vet.pyx":210
   *             f00 = image[x_floor, y_floor]
   *             f10 = image[x_ceil, y_floor] - image[x_floor, y_floor]
   *             f01 = image[x_floor, y_ceil] - image[x_floor, y_floor]             # <<<<<<<<<<<<<<
   *             f11 = (image[x_floor, y_floor] - image[x_ceil, y_floor]
   *                    - image[x_floor, y_ceil] + image[x_ceil, y_ceil])
   */
                                __pyx_t_36 = __pyx_v_x_floor;
                                __pyx_t_37 = __pyx_v_y_ceil;
                                __pyx_t_38 = __pyx_v_x_floor;
                                __pyx_t_39 = __pyx_v_y_floor;
                                __pyx_v_f01 = ((*__Pyx_BufPtrStrided2d(__pyx_t_7pysteps_6motion_4_vet_float64 *, __pyx_pybuffernd_image.rcbuffer->pybuffer.buf, __pyx_t_36, __pyx_pybuffernd_image.diminfo[0].strides, __pyx_t_37, __pyx_pybuffernd_image.diminfo[1].strides)) - (*__Pyx_BufPtrStrided2d(__pyx_t_7pysteps_6motion_4_vet_float64 *, __pyx_pybuffernd_image.rcbuffer->pybuffer.buf, __pyx_t_38, __pyx_pybuffernd_image.diminfo[0].strides, __pyx_t_39, __pyx_pybuffernd_image.diminfo[1].strides)));
  
                                /* "pysteps/motion/_vet.pyx":211
   *             f10 = image[x_ceil, y_floor] - image[x_floor, y_floor]
   *             f01 = image[x_floor, y_ceil] - image[x_floor, y_floor]
   *             f11 = (image[x_floor, y_floor] - image[x_ceil, y_floor]             # <<<<<<<<<<<<<<
   *                    - image[x_floor, y_ceil] + image[x_ceil, y_ceil])
   * 
   */
                                __pyx_t_40 = __pyx_v_x_floor;
                                __pyx_t_41 = __pyx_v_y_floor;
                                __pyx_t_42 = __pyx_v_x_ceil;
                                __pyx_t_43 = __pyx_v_y_floor;
  
                                /* "pysteps/motion/_vet.pyx":212
   *             f01 = image[x_floor, y_ceil] - image[x_floor, y_floor]
   *             f11 = (image[x_floor, y_floor] - image[x_ceil, y_floor]
   *                    - image[x_floor, y_ceil] + image[x_ceil, y_ceil])             # <<<<<<<<<<<<<<
   * 
   *             # Bilinear interpolation
   */
                                __pyx_t_44 = __pyx_v_x_floor;
                                __pyx_t_45 = __pyx_v_y_ceil;
                                __pyx_t_46 = __pyx_v_x_ceil;
                                __pyx_t_47 = __pyx_v_y_ceil;
                                __pyx_v_f11 = ((((*__Pyx_BufPtrStrided2d(__pyx_t_7pysteps_6motion_4_vet_float64 *, __pyx_pybuffernd_image.rcbuffer->pybuffer.buf, __pyx_t_40, __pyx_pybuffernd_image.diminfo[0].strides, __pyx_t_41, __pyx_pybuffernd_image.diminfo[1].strides)) - (*__Pyx_BufPtrStrided2d(__pyx_t_7pysteps_6motion_4_vet_float64 *, __pyx_pybuffernd_image.rcbuffer->pybuffer.buf, __pyx_t_42, __pyx_pybuffernd_image.diminfo[0].strides, __pyx_t_43, __pyx_pybuffernd_image.diminfo[1].strides))) - (*__Pyx_BufPtrStrided2d(__pyx_t_7pysteps_6motion_4_vet_float64 *, __pyx_pybuffernd_image.rcbuffer->pybuffer.buf, __pyx_t_44, __pyx_pybuffernd_image.diminfo[0].strides, __pyx_t_45, __pyx_pybuffernd_image.diminfo[1].strides))) + (*__Pyx_BufPtrStrided2d(__pyx_t_7pysteps_6motion_4_vet_float64 *, __pyx_pybuffernd_image.rcbuffer->pybuffer.buf, __pyx_t_46, __pyx_pybuffernd_image.diminfo[0].strides, __pyx_t_47, __pyx_pybuffernd_image.diminfo[1].strides)));
  
                                /* "pysteps/motion/_vet.pyx":215
   * 
   *             # Bilinear interpolation
   *             new_image[x, y] = f00 + dx * f10 + dy * f01 + dx * dy * f11             # <<<<<<<<<<<<<<
   * 
   *             if gradient:
   */
                                __pyx_t_48 = __pyx_v_x;
                                __pyx_t_49 = __pyx_v_y;
                                *__Pyx_BufPtrStrided2d(__pyx_t_7pysteps_6motion_4_vet_float64 *, __pyx_pybuffernd_new_image.rcbuffer->pybuffer.buf, __pyx_t_48, __pyx_pybuffernd_new_image.diminfo[0].strides, __pyx_t_49, __pyx_pybuffernd_new_image.diminfo[1].strides) = (((__pyx_v_f00 + (__pyx_v_dx * __pyx_v_f10)) + (__pyx_v_dy * __pyx_v_f01)) + ((__pyx_v_dx * __pyx_v_dy) * __pyx_v_f11));
  
                                /* "pysteps/motion/_vet.pyx":217
   *             new_image[x, y] = f00 + dx * f10 + dy * f01 + dx * dy * f11
   * 
   *             if gradient:             # <<<<<<<<<<<<<<
   *                 gradient_values[0, x, y] = f10 + dy * f11
   *                 gradient_values[1, x, y] = f01 + dx * f11
   */
                                __pyx_t_21 = (__pyx_v_gradient != 0);
                                if (__pyx_t_21) {
  
                                  /* "pysteps/motion/_vet.pyx":218
   * 
   *             if gradient:
   *                 gradient_values[0, x, y] = f10 + dy * f11             # <<<<<<<<<<<<<<
   *                 gradient_values[1, x, y] = f01 + dx * f11
   * 
   */
                                  __pyx_t_50 = 0;
                                  __pyx_t_51 = __pyx_v_x;
                                  __pyx_t_52 = __pyx_v_y;
                                  *__Pyx_BufPtrStrided3d(__pyx_t_7pysteps_6motion_4_vet_float64 *, __pyx_pybuffernd_gradient_values.rcbuffer->pybuffer.buf, __pyx_t_50, __pyx_pybuffernd_gradient_values.diminfo[0].strides, __pyx_t_51, __pyx_pybuffernd_gradient_values.diminfo[1].strides, __pyx_t_52, __pyx_pybuffernd_gradient_values.diminfo[2].strides) = (__pyx_v_f10 + (__pyx_v_dy * __pyx_v_f11));
  
                                  /* "pysteps/motion/_vet.pyx":219
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  static char __pyx_doc_7pysteps_6motion_4_vet_2_cost_function[] = "\n    Variational Echo Tracking Cost function.\n    \n    This function computes the Variational Echo Tracking (VET) \n    Cost function presented  by `Laroche and Zawazdki (1995)`_ and used in the \n    McGill Algorithm for Prediction by Lagrangian Extrapolation (MAPLE) \n    described in\n    `Germann and Zawadzki (2002)`_.\n    \n    \n    .. _`Laroche and Zawazdki (1995)`:     http://dx.doi.org/10.1175/1520-0426(1995)012<0721:ROHWFS>2.0.CO;2\n    \n    .. _`Germann and Zawadzki (2002)`:     http://dx.doi.org/10.1175/1520-0493(2002)130<2859:SDOTPO>2.0.CO;2\n     \n     \n    The cost function is a the sum of the residuals of the squared image \n    differences along with a smoothness constrain.   \n        \n    This cost function implementation, supports displacement vector \n    sectorization.\n    The displacement vector represent the displacement applied to the pixels in\n    each individual sector.\n     \n    This help to reduce the number of degrees of freedom of the cost function \n    when hierarchical approaches are used to obtain the minima of \n    the cost function (from low resolution to full image resolution).\n    For example, in the MAPLE algorithm an Scaling Guess procedure is used to \n    find the displacement vectors.\n    The echo motion field is retrieved in three runs with increasing resolution.\n    The retrieval starts with (left) a uniform field, which is used as a first \n    guess to retrieve (middle) the field on a 5 \303\227 5 grid, which in turn is the \n    first guess of (right) the final minimization with a 25 \303\227 25 grid\n    \n    The shape of the sector is deduced from the image shape and the displacement\n    vector shape. \n    \n    IMPORTANT: The number of sectors in each dimension (x and y) must be a \n    factor full image size.\n         \n    The value of displaced pixels that fall outside the limits takes the \n    value of the nearest edge.\n    \n    The cost function is computed in parallel over the x axis.""\n    \n    .. _ndarray:     https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.html\n         \n    Parameters\n    ----------\n    \n    sector_displacement : ndarray_ (ndim=3)  \n        Array of displacements to apply to each sector. The dimensions are:\n        sector_displacement [ x (0) or y (1) displacement, \n                               i index of sector, j index of sector ]  \n        \n        \n    template_image : ndarray_  (ndim=2)\n        Input image array where the sector displacement is applied.\n     \n    input_image : ndarray_\n        Image array to be used as reference \n    \n    smooth_gain : float\n        Smoothness constrain gain\n\n    mask : ndarray_ (ndim=2)\n        Data mask. If is True, the data is marked as not valid and is not\n        used in the computations.\n\n    gradient : bool, optional\n        If True, the gradient of the morphing function is returned.\n\n    Returns\n    -------\n    \n    penalty or  gradient values.\n\n    penalty : float\n        Value of the cost function\n\n    gradient_values : ndarray (float64 ,ndim = 3), optional\n        If gradient keyword is True, the gradient of the function is also\n        returned.\n    \n    \n    References\n    ----------\n    \n    Laroche, S., and I. Zawadzki, 1995: \n    Retrievals of horizontal winds from single-Doppler clear-air data by methods\n    of cross-correlation and variational analysis. \n    J. Atmos. Oceanic Technol., 12, 721\342\200\223738.\n    doi: http://dx.doi.org/10.1175/1520-0426(1995)012<0721:ROHWFS>2.0.CO;2\n \n    Germann, U. and I. Zawadzki, 2002: \n    Scale-Dependence of the Predictability of Precipitation from Continental \n    Radar Images.\n    Part I: Description of the Methodology. Mon. Wea. Rev., 130, 2859\342\200\2232873,\n    doi: 10.1175/1520-0493(2002)130<2859:SDOTPO>2.0.CO;2. \n    \n    ";
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   */
                              __pyx_t_27 = __pyx_v_y_image_size;
                              __pyx_t_28 = __pyx_t_27;
                              for (__pyx_t_29 = 0; __pyx_t_29 < __pyx_t_28; __pyx_t_29+=1) {
                                __pyx_v_j = __pyx_t_29;
  
                                /* "pysteps/motion/_vet.pyx":428
   * 
   *         for j in range(y_image_size):
   *             m0 = int_min((j - j_shift) // y_sector_size, y_sectors - 2)             # <<<<<<<<<<<<<<
   *             m0 = int_max(m0, 0)
   *             m1 = m0 + 1
   */
                                __pyx_v_m0 = __pyx_f_7pysteps_6motion_4_vet_int_min(((__pyx_v_j - __pyx_v_j_shift) / __pyx_v_y_sector_size), (__pyx_v_y_sectors - 2));
  
                                /* "pysteps/motion/_vet.pyx":429
   *         for j in range(y_image_size):
   *             m0 = int_min((j - j_shift) // y_sector_size, y_sectors - 2)
   *             m0 = int_max(m0, 0)             # <<<<<<<<<<<<<<
   *             m1 = m0 + 1
   * 
   */
                                __pyx_v_m0 = __pyx_f_7pysteps_6motion_4_vet_int_max(__pyx_v_m0, 0);
  
                                /* "pysteps/motion/_vet.pyx":430
   *             m0 = int_min((j - j_shift) // y_sector_size, y_sectors - 2)
   *             m0 = int_max(m0, 0)
   *             m1 = m0 + 1             # <<<<<<<<<<<<<<
   * 
   *             m_j[j] = m0
   */
                                __pyx_v_m1 = (__pyx_v_m0 + 1);
  
                                /* "pysteps/motion/_vet.pyx":432
   *             m1 = m0 + 1
   * 
   *             m_j[j] = m0             # <<<<<<<<<<<<<<
   * 
   *             sector_area = (x_guess[l1] - x_guess[l0]) * (y_guess[m1] - y_guess[m0])
   */
                                __pyx_t_30 = __pyx_v_j;
                                *__Pyx_BufPtrStrided1d(__pyx_t_7pysteps_6motion_4_vet_intp *, __pyx_pybuffernd_m_j.rcbuffer->pybuffer.buf, __pyx_t_30, __pyx_pybuffernd_m_j.diminfo[0].strides) = __pyx_v_m0;
  
                                /* "pysteps/motion/_vet.pyx":434
   *             m_j[j] = m0
   * 
   *             sector_area = (x_guess[l1] - x_guess[l0]) * (y_guess[m1] - y_guess[m0])             # <<<<<<<<<<<<<<
   * 
   *             interp_coef[0, i, j] = (x_guess[l1] * y_guess[m1]
   */
                                __pyx_t_31 = __pyx_v_l1;
                                __pyx_t_32 = __pyx_v_l0;
                                __pyx_t_33 = __pyx_v_m1;
                                __pyx_t_34 = __pyx_v_m0;
                                __pyx_v_sector_area = (((*__Pyx_BufPtrStrided1d(__pyx_t_7pysteps_6motion_4_vet_float64 *, __pyx_pybuffernd_x_guess.rcbuffer->pybuffer.buf, __pyx_t_31, __pyx_pybuffernd_x_guess.diminfo[0].strides)) - (*__Pyx_BufPtrStrided1d(__pyx_t_7pysteps_6motion_4_vet_float64 *, __pyx_pybuffernd_x_guess.rcbuffer->pybuffer.buf, __pyx_t_32, __pyx_pybuffernd_x_guess.diminfo[0].strides))) * ((*__Pyx_BufPtrStrided1d(__pyx_t_7pysteps_6motion_4_vet_float64 *, __pyx_pybuffernd_y_guess.rcbuffer->pybuffer.buf, __pyx_t_33, __pyx_pybuffernd_y_guess.diminfo[0].strides)) - (*__Pyx_BufPtrStrided1d(__pyx_t_7pysteps_6motion_4_vet_float64 *, __pyx_pybuffernd_y_guess.rcbuffer->pybuffer.buf, __pyx_t_34, __pyx_pybuffernd_y_guess.diminfo[0].strides))));
  
                                /* "pysteps/motion/_vet.pyx":436
   *             sector_area = (x_guess[l1] - x_guess[l0]) * (y_guess[m1] - y_guess[m0])
   * 
   *             interp_coef[0, i, j] = (x_guess[l1] * y_guess[m1]             # <<<<<<<<<<<<<<
   *                                     - x[i] * y_guess[m1]
   *                                     - x_guess[l1] * y[j]
   */
                                __pyx_t_35 = __pyx_v_l1;
                                __pyx_t_36 = __pyx_v_m1;
  
                                /* "pysteps/motion/_vet.pyx":437
   * 
   *             interp_coef[0, i, j] = (x_guess[l1] * y_guess[m1]
   *                                     - x[i] * y_guess[m1]             # <<<<<<<<<<<<<<
   *                                     - x_guess[l1] * y[j]
   *                                     + x[i] * y[j]) / sector_area
   */
                                __pyx_t_37 = __pyx_v_i;
                                __pyx_t_38 = __pyx_v_m1;
  
                                /* "pysteps/motion/_vet.pyx":438
   *             interp_coef[0, i, j] = (x_guess[l1] * y_guess[m1]
   *                                     - x[i] * y_guess[m1]
   *                                     - x_guess[l1] * y[j]             # <<<<<<<<<<<<<<
   *                                     + x[i] * y[j]) / sector_area
   * 
   */
                                __pyx_t_39 = __pyx_v_l1;
                                __pyx_t_40 = __pyx_v_j;
  
                                /* "pysteps/motion/_vet.pyx":439
   *                                     - x[i] * y_guess[m1]
   *                                     - x_guess[l1] * y[j]
   *                                     + x[i] * y[j]) / sector_area             # <<<<<<<<<<<<<<
   * 
   *             interp_coef[1, i, j] = (-x_guess[l1] * y_guess[m0]
   */
                                __pyx_t_41 = __pyx_v_i;
                                __pyx_t_42 = __pyx_v_j;
  
                                /* "pysteps/motion/_vet.pyx":436
   *             sector_area = (x_guess[l1] - x_guess[l0]) * (y_guess[m1] - y_guess[m0])
   * 
   *             interp_coef[0, i, j] = (x_guess[l1] * y_guess[m1]             # <<<<<<<<<<<<<<
   *                                     - x[i] * y_guess[m1]
   *                                     - x_guess[l1] * y[j]
   */
                                __pyx_t_43 = 0;
                                __pyx_t_44 = __pyx_v_i;
                                __pyx_t_45 = __pyx_v_j;
                                *__Pyx_BufPtrStrided3d(__pyx_t_7pysteps_6motion_4_vet_float64 *, __pyx_pybuffernd_interp_coef.rcbuffer->pybuffer.buf, __pyx_t_43, __pyx_pybuffernd_interp_coef.diminfo[0].strides, __pyx_t_44, __pyx_pybuffernd_interp_coef.diminfo[1].strides, __pyx_t_45, __pyx_pybuffernd_interp_coef.diminfo[2].strides) = ((((((*__Pyx_BufPtrStrided1d(__pyx_t_7pysteps_6motion_4_vet_float64 *, __pyx_pybuffernd_x_guess.rcbuffer->pybuffer.buf, __pyx_t_35, __pyx_pybuffernd_x_guess.diminfo[0].strides)) * (*__Pyx_BufPtrStrided1d(__pyx_t_7pysteps_6motion_4_vet_float64 *, __pyx_pybuffernd_y_guess.rcbuffer->pybuffer.buf, __pyx_t_36, __pyx_pybuffernd_y_guess.diminfo[0].strides))) - ((*__Pyx_BufPtrStrided1d(__pyx_t_7pysteps_6motion_4_vet_float64 *, __pyx_pybuffernd_x.rcbuffer->pybuffer.buf, __pyx_t_37, __pyx_pybuffernd_x.diminfo[0].strides)) * (*__Pyx_BufPtrStrided1d(__pyx_t_7pysteps_6motion_4_vet_float64 *, __pyx_pybuffernd_y_guess.rcbuffer->pybuffer.buf, __pyx_t_38, __pyx_pybuffernd_y_guess.diminfo[0].strides)))) - ((*__Pyx_BufPtrStrided1d(__pyx_t_7pysteps_6motion_4_vet_float64 *, __pyx_pybuffernd_x_guess.rcbuffer->pybuffer.buf, __pyx_t_39, __pyx_pybuffernd_x_guess.diminfo[0].strides)) * (*__Pyx_BufPtrStrided1d(__pyx_t_7pysteps_6motion_4_vet_float64 *, __pyx_pybuffernd_y.rcbuffer->pybuffer.buf, __pyx_t_40, __pyx_pybuffernd_y.diminfo[0].strides)))) + ((*__Pyx_BufPtrStrided1d(__pyx_t_7pysteps_6motion_4_vet_float64 *, __pyx_pybuffernd_x.rcbuffer->pybuffer.buf, __pyx_t_41, __pyx_pybuffernd_x.diminfo[0].strides)) * (*__Pyx_BufPtrStrided1d(__pyx_t_7pysteps_6motion_4_vet_float64 *, __pyx_pybuffernd_y.rcbuffer->pybuffer.buf, __pyx_t_42, __pyx_pybuffernd_y.diminfo[0].strides)))) / __pyx_v_sector_area);
  
                                /* "pysteps/motion/_vet.pyx":441
   *                                     + x[i] * y[j]) / sector_area
   * 
   *             interp_coef[1, i, j] = (-x_guess[l1] * y_guess[m0]             # <<<<<<<<<<<<<<
   *                                     + x[i] * y_guess[m0]
   *                                     + x_guess[l1] * y[j]
   */
                                __pyx_t_46 = __pyx_v_l1;
                                __pyx_t_47 = __pyx_v_m0;
  
                                /* "pysteps/motion/_vet.pyx":442
   * 
   *             interp_coef[1, i, j] = (-x_guess[l1] * y_guess[m0]
   *                                     + x[i] * y_guess[m0]             # <<<<<<<<<<<<<<
   *                                     + x_guess[l1] * y[j]
   *                                     - x[i] * y[j]) / sector_area
   */
                                __pyx_t_48 = __pyx_v_i;
                                __pyx_t_49 = __pyx_v_m0;
  
                                /* "pysteps/motion/_vet.pyx":443
   *             interp_coef[1, i, j] = (-x_guess[l1] * y_guess[m0]
   *                                     + x[i] * y_guess[m0]
   *                                     + x_guess[l1] * y[j]             # <<<<<<<<<<<<<<
   *                                     - x[i] * y[j]) / sector_area
   * 
   */
                                __pyx_t_50 = __pyx_v_l1;
                                __pyx_t_51 = __pyx_v_j;
  
                                /* "pysteps/motion/_vet.pyx":444
   *                                     + x[i] * y_guess[m0]
   *                                     + x_guess[l1] * y[j]
   *                                     - x[i] * y[j]) / sector_area             # <<<<<<<<<<<<<<
   * 
   *             interp_coef[2, i, j] = (-x_guess[l0] * y_guess[m1]
   */
                                __pyx_t_52 = __pyx_v_i;
                                __pyx_t_53 = __pyx_v_j;
  
                                /* "pysteps/motion/_vet.pyx":441
   *                                     + x[i] * y[j]) / sector_area
   * 
   *             interp_coef[1, i, j] = (-x_guess[l1] * y_guess[m0]             # <<<<<<<<<<<<<<
   *                                     + x[i] * y_guess[m0]
   *                                     + x_guess[l1] * y[j]
   */
                                __pyx_t_54 = 1;
                                __pyx_t_55 = __pyx_v_i;
                                __pyx_t_56 = __pyx_v_j;
                                *__Pyx_BufPtrStrided3d(__pyx_t_7pysteps_6motion_4_vet_float64 *, __pyx_pybuffernd_interp_coef.rcbuffer->pybuffer.buf, __pyx_t_54, __pyx_pybuffernd_interp_coef.diminfo[0].strides, __pyx_t_55, __pyx_pybuffernd_interp_coef.diminfo[1].strides, __pyx_t_56, __pyx_pybuffernd_interp_coef.diminfo[2].strides) = ((((((-(*__Pyx_BufPtrStrided1d(__pyx_t_7pysteps_6motion_4_vet_float64 *, __pyx_pybuffernd_x_guess.rcbuffer->pybuffer.buf, __pyx_t_46, __pyx_pybuffernd_x_guess.diminfo[0].strides))) * (*__Pyx_BufPtrStrided1d(__pyx_t_7pysteps_6motion_4_vet_float64 *, __pyx_pybuffernd_y_guess.rcbuffer->pybuffer.buf, __pyx_t_47, __pyx_pybuffernd_y_guess.diminfo[0].strides))) + ((*__Pyx_BufPtrStrided1d(__pyx_t_7pysteps_6motion_4_vet_float64 *, __pyx_pybuffernd_x.rcbuffer->pybuffer.buf, __pyx_t_48, __pyx_pybuffernd_x.diminfo[0].strides)) * (*__Pyx_BufPtrStrided1d(__pyx_t_7pysteps_6motion_4_vet_float64 *, __pyx_pybuffernd_y_guess.rcbuffer->pybuffer.buf, __pyx_t_49, __pyx_pybuffernd_y_guess.diminfo[0].strides)))) + ((*__Pyx_BufPtrStrided1d(__pyx_t_7pysteps_6motion_4_vet_float64 *, __pyx_pybuffernd_x_guess.rcbuffer->pybuffer.buf, __pyx_t_50, __pyx_pybuffernd_x_guess.diminfo[0].strides)) * (*__Pyx_BufPtrStrided1d(__pyx_t_7pysteps_6motion_4_vet_float64 *, __pyx_pybuffernd_y.rcbuffer->pybuffer.buf, __pyx_t_51, __pyx_pybuffernd_y.diminfo[0].strides)))) - ((*__Pyx_BufPtrStrided1d(__pyx_t_7pysteps_6motion_4_vet_float64 *, __pyx_pybuffernd_x.rcbuffer->pybuffer.buf, __pyx_t_52, __pyx_pybuffernd_x.diminfo[0].strides)) * (*__Pyx_BufPtrStrided1d(__pyx_t_7pysteps_6motion_4_vet_float64 *, __pyx_pybuffernd_y.rcbuffer->pybuffer.buf, __pyx_t_53, __pyx_pybuffernd_y.diminfo[0].strides)))) / __pyx_v_sector_area);
  
                                /* "pysteps/motion/_vet.pyx":446
   *                                     - x[i] * y[j]) / sector_area
   * 
   *             interp_coef[2, i, j] = (-x_guess[l0] * y_guess[m1]             # <<<<<<<<<<<<<<
   *                                     + x[i] * y_guess[m1]
   *                                     + x_guess[l0] * y[j]
   */
                                __pyx_t_57 = __pyx_v_l0;
                                __pyx_t_58 = __pyx_v_m1;
  
                                /* "pysteps/motion/_vet.pyx":447
   * 
   *             interp_coef[2, i, j] = (-x_guess[l0] * y_guess[m1]
   *                                     + x[i] * y_guess[m1]             # <<<<<<<<<<<<<<
   *                                     + x_guess[l0] * y[j]
   *                                     - x[i] * y[j]) / sector_area
   */
                                __pyx_t_59 = __pyx_v_i;
                                __pyx_t_60 = __pyx_v_m1;
  
                                /* "pysteps/motion/_vet.pyx":448
   *             interp_coef[2, i, j] = (-x_guess[l0] * y_guess[m1]
   *                                     + x[i] * y_guess[m1]
   *                                     + x_guess[l0] * y[j]             # <<<<<<<<<<<<<<
   *                                     - x[i] * y[j]) / sector_area
   * 
   */
                                __pyx_t_61 = __pyx_v_l0;
                                __pyx_t_62 = __pyx_v_j;
  
                                /* "pysteps/motion/_vet.pyx":449
   *                                     + x[i] * y_guess[m1]
   *                                     + x_guess[l0] * y[j]
   *                                     - x[i] * y[j]) / sector_area             # <<<<<<<<<<<<<<
   * 
   *             interp_coef[3, i, j] = (x_guess[l0] * y_guess[m0]
   */
                                __pyx_t_63 = __pyx_v_i;
                                __pyx_t_64 = __pyx_v_j;
  
                                /* "pysteps/motion/_vet.pyx":446
   *                                     - x[i] * y[j]) / sector_area
   * 
   *             interp_coef[2, i, j] = (-x_guess[l0] * y_guess[m1]             # <<<<<<<<<<<<<<
   *                                     + x[i] * y_guess[m1]
   *                                     + x_guess[l0] * y[j]
   */
                                __pyx_t_65 = 2;
                                __pyx_t_66 = __pyx_v_i;
                                __pyx_t_67 = __pyx_v_j;
                                *__Pyx_BufPtrStrided3d(__pyx_t_7pysteps_6motion_4_vet_float64 *, __pyx_pybuffernd_interp_coef.rcbuffer->pybuffer.buf, __pyx_t_65, __pyx_pybuffernd_interp_coef.diminfo[0].strides, __pyx_t_66, __pyx_pybuffernd_interp_coef.diminfo[1].strides, __pyx_t_67, __pyx_pybuffernd_interp_coef.diminfo[2].strides) = ((((((-(*__Pyx_BufPtrStrided1d(__pyx_t_7pysteps_6motion_4_vet_float64 *, __pyx_pybuffernd_x_guess.rcbuffer->pybuffer.buf, __pyx_t_57, __pyx_pybuffernd_x_guess.diminfo[0].strides))) * (*__Pyx_BufPtrStrided1d(__pyx_t_7pysteps_6motion_4_vet_float64 *, __pyx_pybuffernd_y_guess.rcbuffer->pybuffer.buf, __pyx_t_58, __pyx_pybuffernd_y_guess.diminfo[0].strides))) + ((*__Pyx_BufPtrStrided1d(__pyx_t_7pysteps_6motion_4_vet_float64 *, __pyx_pybuffernd_x.rcbuffer->pybuffer.buf, __pyx_t_59, __pyx_pybuffernd_x.diminfo[0].strides)) * (*__Pyx_BufPtrStrided1d(__pyx_t_7pysteps_6motion_4_vet_float64 *, __pyx_pybuffernd_y_guess.rcbuffer->pybuffer.buf, __pyx_t_60, __pyx_pybuffernd_y_guess.diminfo[0].strides)))) + ((*__Pyx_BufPtrStrided1d(__pyx_t_7pysteps_6motion_4_vet_float64 *, __pyx_pybuffernd_x_guess.rcbuffer->pybuffer.buf, __pyx_t_61, __pyx_pybuffernd_x_guess.diminfo[0].strides)) * (*__Pyx_BufPtrStrided1d(__pyx_t_7pysteps_6motion_4_vet_float64 *, __pyx_pybuffernd_y.rcbuffer->pybuffer.buf, __pyx_t_62, __pyx_pybuffernd_y.diminfo[0].strides)))) - ((*__Pyx_BufPtrStrided1d(__pyx_t_7pysteps_6motion_4_vet_float64 *, __pyx_pybuffernd_x.rcbuffer->pybuffer.buf, __pyx_t_63, __pyx_pybuffernd_x.diminfo[0].strides)) * (*__Pyx_BufPtrStrided1d(__pyx_t_7pysteps_6motion_4_vet_float64 *, __pyx_pybuffernd_y.rcbuffer->pybuffer.buf, __pyx_t_64, __pyx_pybuffernd_y.diminfo[0].strides)))) / __pyx_v_sector_area);
  
                                /* "pysteps/motion/_vet.pyx":451
   *                                     - x[i] * y[j]) / sector_area
   * 
   *             interp_coef[3, i, j] = (x_guess[l0] * y_guess[m0]             # <<<<<<<<<<<<<<
   *                                     - x[i] * y_guess[m0]
   *                                     - x_guess[l0] * y[j]
   */
                                __pyx_t_68 = __pyx_v_l0;
                                __pyx_t_69 = __pyx_v_m0;
  
                                /* "pysteps/motion/_vet.pyx":452
   * 
   *             interp_coef[3, i, j] = (x_guess[l0] * y_guess[m0]
   *                                     - x[i] * y_guess[m0]             # <<<<<<<<<<<<<<
   *                                     - x_guess[l0] * y[j]
   *                                     + x[i] * y[j]) / sector_area
   */
                                __pyx_t_70 = __pyx_v_i;
                                __pyx_t_71 = __pyx_v_m0;
  
                                /* "pysteps/motion/_vet.pyx":453
   *             interp_coef[3, i, j] = (x_guess[l0] * y_guess[m0]
   *                                     - x[i] * y_guess[m0]
   *                                     - x_guess[l0] * y[j]             # <<<<<<<<<<<<<<
   *                                     + x[i] * y[j]) / sector_area
   * 
   */
                                __pyx_t_72 = __pyx_v_l0;
                                __pyx_t_73 = __pyx_v_j;
  
                                /* "pysteps/motion/_vet.pyx":454
   *                                     - x[i] * y_guess[m0]
   *                                     - x_guess[l0] * y[j]
   *                                     + x[i] * y[j]) / sector_area             # <<<<<<<<<<<<<<
   * 
   *             for xy in range(2):
   */
                                __pyx_t_74 = __pyx_v_i;
                                __pyx_t_75 = __pyx_v_j;
  
                                /* "pysteps/motion/_vet.pyx":451
   *                                     - x[i] * y[j]) / sector_area
   * 
   *             interp_coef[3, i, j] = (x_guess[l0] * y_guess[m0]             # <<<<<<<<<<<<<<
   *                                     - x[i] * y_guess[m0]
   *                                     - x_guess[l0] * y[j]
   */
                                __pyx_t_76 = 3;
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   *                 for i in range(i_min[l], i_max[l]):
   *                     for j in range(j_min[m - 1], j_max[m - 1]):
   *                         grad_residuals[0, l, m] = grad_residuals[0, l, m] + \             # <<<<<<<<<<<<<<
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   *                     for j in range(j_min[m - 1], j_max[m - 1]):
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   *                                                   (_gradient_data[0, i, j]             # <<<<<<<<<<<<<<
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   *                         grad_residuals[0, l, m] = grad_residuals[0, l, m] + \
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   *                                                    * interp_coef[1, i, j])             # <<<<<<<<<<<<<<
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   *                         grad_residuals[1, l, m] = grad_residuals[1, l, m] + \
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   *                     for j in range(j_min[m - 1], j_max[m - 1]):
   *                         grad_residuals[0, l, m] = grad_residuals[0, l, m] + \             # <<<<<<<<<<<<<<
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              /* "pysteps/motion/_vet.pyx":526
   *                                                    * interp_coef[1, i, j])
   * 
   *                         grad_residuals[1, l, m] = grad_residuals[1, l, m] + \             # <<<<<<<<<<<<<<
   *                                                   (_gradient_data[1, i, j]  # TODO: Check this line!
   *                                                    * interp_coef[1, i, j])
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              /* "pysteps/motion/_vet.pyx":527
   * 
   *                         grad_residuals[1, l, m] = grad_residuals[1, l, m] + \
   *                                                   (_gradient_data[1, i, j]  # TODO: Check this line!             # <<<<<<<<<<<<<<
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   *                         grad_residuals[1, l, m] = grad_residuals[1, l, m] + \
   *                                                   (_gradient_data[1, i, j]  # TODO: Check this line!
   *                                                    * interp_coef[1, i, j])             # <<<<<<<<<<<<<<
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   *         for l in range(1, x_sectors):  #, schedule='dynamic', nogil=True):
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              /* "pysteps/motion/_vet.pyx":526
   *                                                    * interp_coef[1, i, j])
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   *                         grad_residuals[1, l, m] = grad_residuals[1, l, m] + \             # <<<<<<<<<<<<<<
   *                                                   (_gradient_data[1, i, j]  # TODO: Check this line!
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   *                                                    * interp_coef[1, i, j])
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   *         for l in range(1, x_sectors):  #, schedule='dynamic', nogil=True):             # <<<<<<<<<<<<<<
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        /* "pysteps/motion/_vet.pyx":531
   * 
   *         for l in range(1, x_sectors):  #, schedule='dynamic', nogil=True):
   *             for m in range(y_sectors):             # <<<<<<<<<<<<<<
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          /* "pysteps/motion/_vet.pyx":532
   *         for l in range(1, x_sectors):  #, schedule='dynamic', nogil=True):
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   *                 for i in range(i_min[l - 1], i_max[l - 1]):             # <<<<<<<<<<<<<<
   *                     for j in range(j_min[m], j_max[m]):
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   *                         grad_residuals[0, l, m] += (_gradient_data[0, i, j]
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   *                         grad_residuals[0, l, m] += (_gradient_data[0, i, j]             # <<<<<<<<<<<<<<
   *                                                     * interp_coef[2, i, j])
   *                         grad_residuals[1, l, m] += (_gradient_data[1, i, j]
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   *                     for j in range(j_min[m], j_max[m]):
   *                         grad_residuals[0, l, m] += (_gradient_data[0, i, j]
   *                                                     * interp_coef[2, i, j])             # <<<<<<<<<<<<<<
   *                         grad_residuals[1, l, m] += (_gradient_data[1, i, j]
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   *                     for j in range(j_min[m], j_max[m]):
   *                         grad_residuals[0, l, m] += (_gradient_data[0, i, j]             # <<<<<<<<<<<<<<
   *                                                     * interp_coef[2, i, j])
   *                         grad_residuals[1, l, m] += (_gradient_data[1, i, j]
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              /* "pysteps/motion/_vet.pyx":536
   *                         grad_residuals[0, l, m] += (_gradient_data[0, i, j]
   *                                                     * interp_coef[2, i, j])
   *                         grad_residuals[1, l, m] += (_gradient_data[1, i, j]             # <<<<<<<<<<<<<<
   *                                                     * interp_coef[2, i, j])
   * 
   */
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              /* "pysteps/motion/_vet.pyx":537
   *                                                     * interp_coef[2, i, j])
   *                         grad_residuals[1, l, m] += (_gradient_data[1, i, j]
   *                                                     * interp_coef[2, i, j])             # <<<<<<<<<<<<<<
   * 
   *             for m in range(1, y_sectors):
   */
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              /* "pysteps/motion/_vet.pyx":536
   *                         grad_residuals[0, l, m] += (_gradient_data[0, i, j]
   *                                                     * interp_coef[2, i, j])
   *                         grad_residuals[1, l, m] += (_gradient_data[1, i, j]             # <<<<<<<<<<<<<<
   *                                                     * interp_coef[2, i, j])
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   *                                                     * interp_coef[2, i, j])
   * 
   *             for m in range(1, y_sectors):             # <<<<<<<<<<<<<<
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   * 
   *             for m in range(1, y_sectors):
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            /* "pysteps/motion/_vet.pyx":541
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   *                         grad_residuals[0, l, m] += (_gradient_data[0, i, j]             # <<<<<<<<<<<<<<
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   *                         grad_residuals[0, l, m] += (_gradient_data[0, i, j]
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   *                 for m in range(1, y_sectors - 1):
   *                     df_dx2 = (sector_displacement[axis, l + 1, m]             # <<<<<<<<<<<<<<
   *                               - 2 * sector_displacement[axis, l, m]
   *                               + sector_displacement[axis, l - 1, m])
   */
            __pyx_t_232 = __pyx_v_axis;
            __pyx_t_233 = (__pyx_v_l + 1);
            __pyx_t_234 = __pyx_v_m;
  
            /* "pysteps/motion/_vet.pyx":576
   *                 for m in range(1, y_sectors - 1):
   *                     df_dx2 = (sector_displacement[axis, l + 1, m]
   *                               - 2 * sector_displacement[axis, l, m]             # <<<<<<<<<<<<<<
   *                               + sector_displacement[axis, l - 1, m])
   * 
   */
            __pyx_t_235 = __pyx_v_axis;
            __pyx_t_236 = __pyx_v_l;
            __pyx_t_237 = __pyx_v_m;
  
            /* "pysteps/motion/_vet.pyx":577
   *                     df_dx2 = (sector_displacement[axis, l + 1, m]
   *                               - 2 * sector_displacement[axis, l, m]
   *                               + sector_displacement[axis, l - 1, m])             # <<<<<<<<<<<<<<
   * 
   *                     df_dx2 = df_dx2 / (x_sector_size * x_sector_size)
   */
            __pyx_t_238 = __pyx_v_axis;
            __pyx_t_239 = (__pyx_v_l - 1);
            __pyx_t_240 = __pyx_v_m;
            __pyx_v_df_dx2 = (((*__Pyx_BufPtrStrided3d(__pyx_t_7pysteps_6motion_4_vet_float64 *, __pyx_pybuffernd_sector_displacement.rcbuffer->pybuffer.buf, __pyx_t_232, __pyx_pybuffernd_sector_displacement.diminfo[0].strides, __pyx_t_233, __pyx_pybuffernd_sector_displacement.diminfo[1].strides, __pyx_t_234, __pyx_pybuffernd_sector_displacement.diminfo[2].strides)) - (2.0 * (*__Pyx_BufPtrStrided3d(__pyx_t_7pysteps_6motion_4_vet_float64 *, __pyx_pybuffernd_sector_displacement.rcbuffer->pybuffer.buf, __pyx_t_235, __pyx_pybuffernd_sector_displacement.diminfo[0].strides, __pyx_t_236, __pyx_pybuffernd_sector_displacement.diminfo[1].strides, __pyx_t_237, __pyx_pybuffernd_sector_displacement.diminfo[2].strides)))) + (*__Pyx_BufPtrStrided3d(__pyx_t_7pysteps_6motion_4_vet_float64 *, __pyx_pybuffernd_sector_displacement.rcbuffer->pybuffer.buf, __pyx_t_238, __pyx_pybuffernd_sector_displacement.diminfo[0].strides, __pyx_t_239, __pyx_pybuffernd_sector_displacement.diminfo[1].strides, __pyx_t_240, __pyx_pybuffernd_sector_displacement.diminfo[2].strides)));
  
            /* "pysteps/motion/_vet.pyx":579
   *                               + sector_displacement[axis, l - 1, m])
   * 
   *                     df_dx2 = df_dx2 / (x_sector_size * x_sector_size)             # <<<<<<<<<<<<<<
   * 
   *                     df_dy2 = (sector_displacement[axis, l, m + 1]
   */
            __pyx_v_df_dx2 = (__pyx_v_df_dx2 / ((__pyx_t_7pysteps_6motion_4_vet_float64)(__pyx_v_x_sector_size * __pyx_v_x_sector_size)));
  
            /* "pysteps/motion/_vet.pyx":581
   *                     df_dx2 = df_dx2 / (x_sector_size * x_sector_size)
   * 
   *                     df_dy2 = (sector_displacement[axis, l, m + 1]             # <<<<<<<<<<<<<<
   *                               - 2 * sector_displacement[axis, l, m]
   *                               + sector_displacement[axis, l, m - 1])
   */
            __pyx_t_241 = __pyx_v_axis;
            __pyx_t_242 = __pyx_v_l;
            __pyx_t_243 = (__pyx_v_m + 1);
  
            /* "pysteps/motion/_vet.pyx":582
   * 
   *                     df_dy2 = (sector_displacement[axis, l, m + 1]
   *                               - 2 * sector_displacement[axis, l, m]             # <<<<<<<<<<<<<<
   *                               + sector_displacement[axis, l, m - 1])
   * 
   */
            __pyx_t_244 = __pyx_v_axis;
            __pyx_t_245 = __pyx_v_l;
            __pyx_t_246 = __pyx_v_m;
  
            /* "pysteps/motion/_vet.pyx":583
   *                     df_dy2 = (sector_displacement[axis, l, m + 1]
   *                               - 2 * sector_displacement[axis, l, m]
   *                               + sector_displacement[axis, l, m - 1])             # <<<<<<<<<<<<<<
   * 
   *                     df_dy2 = df_dy2 / (y_sector_size * y_sector_size)
   */
            __pyx_t_247 = __pyx_v_axis;
            __pyx_t_248 = __pyx_v_l;
            __pyx_t_249 = (__pyx_v_m - 1);
            __pyx_v_df_dy2 = (((*__Pyx_BufPtrStrided3d(__pyx_t_7pysteps_6motion_4_vet_float64 *, __pyx_pybuffernd_sector_displacement.rcbuffer->pybuffer.buf, __pyx_t_241, __pyx_pybuffernd_sector_displacement.diminfo[0].strides, __pyx_t_242, __pyx_pybuffernd_sector_displacement.diminfo[1].strides, __pyx_t_243, __pyx_pybuffernd_sector_displacement.diminfo[2].strides)) - (2.0 * (*__Pyx_BufPtrStrided3d(__pyx_t_7pysteps_6motion_4_vet_float64 *, __pyx_pybuffernd_sector_displacement.rcbuffer->pybuffer.buf, __pyx_t_244, __pyx_pybuffernd_sector_displacement.diminfo[0].strides, __pyx_t_245, __pyx_pybuffernd_sector_displacement.diminfo[1].strides, __pyx_t_246, __pyx_pybuffernd_sector_displacement.diminfo[2].strides)))) + (*__Pyx_BufPtrStrided3d(__pyx_t_7pysteps_6motion_4_vet_float64 *, __pyx_pybuffernd_sector_displacement.rcbuffer->pybuffer.buf, __pyx_t_247, __pyx_pybuffernd_sector_displacement.diminfo[0].strides, __pyx_t_248, __pyx_pybuffernd_sector_displacement.diminfo[1].strides, __pyx_t_249, __pyx_pybuffernd_sector_displacement.diminfo[2].strides)));
  
            /* "pysteps/motion/_vet.pyx":585
   *                               + sector_displacement[axis, l, m - 1])
   * 
   *                     df_dy2 = df_dy2 / (y_sector_size * y_sector_size)             # <<<<<<<<<<<<<<
   * 
   *                     df_dxdy = (sector_displacement[axis, l + 1, m + 1]
   */
            __pyx_v_df_dy2 = (__pyx_v_df_dy2 / ((__pyx_t_7pysteps_6motion_4_vet_float64)(__pyx_v_y_sector_size * __pyx_v_y_sector_size)));
  
            /* "pysteps/motion/_vet.pyx":587
   *                     df_dy2 = df_dy2 / (y_sector_size * y_sector_size)
   * 
   *                     df_dxdy = (sector_displacement[axis, l + 1, m + 1]             # <<<<<<<<<<<<<<
   *                                - sector_displacement[axis, l + 1, m - 1]
   *                                - sector_displacement[axis, l - 1, m + 1]
   */
            __pyx_t_250 = __pyx_v_axis;
            __pyx_t_251 = (__pyx_v_l + 1);
            __pyx_t_252 = (__pyx_v_m + 1);
  
            /* "pysteps/motion/_vet.pyx":588
   * 
   *                     df_dxdy = (sector_displacement[axis, l + 1, m + 1]
   *                                - sector_displacement[axis, l + 1, m - 1]             # <<<<<<<<<<<<<<
   *                                - sector_displacement[axis, l - 1, m + 1]
   *                                + sector_displacement[axis, l - 1, m - 1])
   */
            __pyx_t_253 = __pyx_v_axis;
            __pyx_t_254 = (__pyx_v_l + 1);
            __pyx_t_255 = (__pyx_v_m - 1);
  
            /* "pysteps/motion/_vet.pyx":589
   *                     df_dxdy = (sector_displacement[axis, l + 1, m + 1]
   *                                - sector_displacement[axis, l + 1, m - 1]
   *                                - sector_displacement[axis, l - 1, m + 1]             # <<<<<<<<<<<<<<
   *                                + sector_displacement[axis, l - 1, m - 1])
   *                     df_dxdy = df_dxdy / (4 * x_sector_size * y_sector_size)
   */
            __pyx_t_256 = __pyx_v_axis;
            __pyx_t_257 = (__pyx_v_l - 1);
            __pyx_t_258 = (__pyx_v_m + 1);
  
            /* "pysteps/motion/_vet.pyx":590
   *                                - sector_displacement[axis, l + 1, m - 1]
   *                                - sector_displacement[axis, l - 1, m + 1]
   *                                + sector_displacement[axis, l - 1, m - 1])             # <<<<<<<<<<<<<<
   *                     df_dxdy = df_dxdy / (4 * x_sector_size * y_sector_size)
   * 
   */
            __pyx_t_259 = __pyx_v_axis;
            __pyx_t_260 = (__pyx_v_l - 1);
            __pyx_t_261 = (__pyx_v_m - 1);
            __pyx_v_df_dxdy = ((((*__Pyx_BufPtrStrided3d(__pyx_t_7pysteps_6motion_4_vet_float64 *, __pyx_pybuffernd_sector_displacement.rcbuffer->pybuffer.buf, __pyx_t_250, __pyx_pybuffernd_sector_displacement.diminfo[0].strides, __pyx_t_251, __pyx_pybuffernd_sector_displacement.diminfo[1].strides, __pyx_t_252, __pyx_pybuffernd_sector_displacement.diminfo[2].strides)) - (*__Pyx_BufPtrStrided3d(__pyx_t_7pysteps_6motion_4_vet_float64 *, __pyx_pybuffernd_sector_displacement.rcbuffer->pybuffer.buf, __pyx_t_253, __pyx_pybuffernd_sector_displacement.diminfo[0].strides, __pyx_t_254, __pyx_pybuffernd_sector_displacement.diminfo[1].strides, __pyx_t_255, __pyx_pybuffernd_sector_displacement.diminfo[2].strides))) - (*__Pyx_BufPtrStrided3d(__pyx_t_7pysteps_6motion_4_vet_float64 *, __pyx_pybuffernd_sector_displacement.rcbuffer->pybuffer.buf, __pyx_t_256, __pyx_pybuffernd_sector_displacement.diminfo[0].strides, __pyx_t_257, __pyx_pybuffernd_sector_displacement.diminfo[1].strides, __pyx_t_258, __pyx_pybuffernd_sector_displacement.diminfo[2].strides))) + (*__Pyx_BufPtrStrided3d(__pyx_t_7pysteps_6motion_4_vet_float64 *, __pyx_pybuffernd_sector_displacement.rcbuffer->pybuffer.buf, __pyx_t_259, __pyx_pybuffernd_sector_displacement.diminfo[0].strides, __pyx_t_260, __pyx_pybuffernd_sector_displacement.diminfo[1].strides, __pyx_t_261, __pyx_pybuffernd_sector_displacement.diminfo[2].strides)));
  
            /* "pysteps/motion/_vet.pyx":591
   *                                - sector_displacement[axis, l - 1, m + 1]
   *                                + sector_displacement[axis, l - 1, m - 1])
   *                     df_dxdy = df_dxdy / (4 * x_sector_size * y_sector_size)             # <<<<<<<<<<<<<<
   * 
   *                     if gradient:
   */
            __pyx_v_df_dxdy = (__pyx_v_df_dxdy / ((__pyx_t_7pysteps_6motion_4_vet_float64)((4 * __pyx_v_x_sector_size) * __pyx_v_y_sector_size)));
  
            /* "pysteps/motion/_vet.pyx":593
   *                     df_dxdy = df_dxdy / (4 * x_sector_size * y_sector_size)
   * 
   *                     if gradient:             # <<<<<<<<<<<<<<
   *                         grad_smooth[axis, l, m] -= 2 * df_dx2
   *                         grad_smooth[axis, l + 1, m] += df_dx2
   */
            __pyx_t_1 = (__pyx_v_gradient != 0);
            if (__pyx_t_1) {
  
              /* "pysteps/motion/_vet.pyx":594
   * 
   *                     if gradient:
   *                         grad_smooth[axis, l, m] -= 2 * df_dx2             # <<<<<<<<<<<<<<
   *                         grad_smooth[axis, l + 1, m] += df_dx2
   *                         grad_smooth[axis, l - 1, m] += df_dx2
   */
              __pyx_t_262 = __pyx_v_axis;
              __pyx_t_263 = __pyx_v_l;
              __pyx_t_264 = __pyx_v_m;
              *__Pyx_BufPtrStrided3d(__pyx_t_7pysteps_6motion_4_vet_float64 *, __pyx_pybuffernd_grad_smooth.rcbuffer->pybuffer.buf, __pyx_t_262, __pyx_pybuffernd_grad_smooth.diminfo[0].strides, __pyx_t_263, __pyx_pybuffernd_grad_smooth.diminfo[1].strides, __pyx_t_264, __pyx_pybuffernd_grad_smooth.diminfo[2].strides) -= (2.0 * __pyx_v_df_dx2);
  
              /* "pysteps/motion/_vet.pyx":595
   *                     if gradient:
   *                         grad_smooth[axis, l, m] -= 2 * df_dx2
   *                         grad_smooth[axis, l + 1, m] += df_dx2             # <<<<<<<<<<<<<<
   *                         grad_smooth[axis, l - 1, m] += df_dx2
   * 
   */
              __pyx_t_265 = __pyx_v_axis;
              __pyx_t_266 = (__pyx_v_l + 1);
              __pyx_t_267 = __pyx_v_m;
              *__Pyx_BufPtrStrided3d(__pyx_t_7pysteps_6motion_4_vet_float64 *, __pyx_pybuffernd_grad_smooth.rcbuffer->pybuffer.buf, __pyx_t_265, __pyx_pybuffernd_grad_smooth.diminfo[0].strides, __pyx_t_266, __pyx_pybuffernd_grad_smooth.diminfo[1].strides, __pyx_t_267, __pyx_pybuffernd_grad_smooth.diminfo[2].strides) += __pyx_v_df_dx2;
  
              /* "pysteps/motion/_vet.pyx":596
   *                         grad_smooth[axis, l, m] -= 2 * df_dx2
   *                         grad_smooth[axis, l + 1, m] += df_dx2
   *                         grad_smooth[axis, l - 1, m] += df_dx2             # <<<<<<<<<<<<<<
   * 
   *                         grad_smooth[axis, l, m] -= 2 * df_dy2
   */
              __pyx_t_268 = __pyx_v_axis;
              __pyx_t_269 = (__pyx_v_l - 1);
              __pyx_t_270 = __pyx_v_m;
              *__Pyx_BufPtrStrided3d(__pyx_t_7pysteps_6motion_4_vet_float64 *, __pyx_pybuffernd_grad_smooth.rcbuffer->pybuffer.buf, __pyx_t_268, __pyx_pybuffernd_grad_smooth.diminfo[0].strides, __pyx_t_269, __pyx_pybuffernd_grad_smooth.diminfo[1].strides, __pyx_t_270, __pyx_pybuffernd_grad_smooth.diminfo[2].strides) += __pyx_v_df_dx2;
  
              /* "pysteps/motion/_vet.pyx":598
   *                         grad_smooth[axis, l - 1, m] += df_dx2
   * 
   *                         grad_smooth[axis, l, m] -= 2 * df_dy2             # <<<<<<<<<<<<<<
   *                         grad_smooth[axis, l, m - 1] += df_dy2
   *                         grad_smooth[axis, l, m + 1] += df_dy2
   */
              __pyx_t_271 = __pyx_v_axis;
              __pyx_t_272 = __pyx_v_l;
              __pyx_t_273 = __pyx_v_m;
              *__Pyx_BufPtrStrided3d(__pyx_t_7pysteps_6motion_4_vet_float64 *, __pyx_pybuffernd_grad_smooth.rcbuffer->pybuffer.buf, __pyx_t_271, __pyx_pybuffernd_grad_smooth.diminfo[0].strides, __pyx_t_272, __pyx_pybuffernd_grad_smooth.diminfo[1].strides, __pyx_t_273, __pyx_pybuffernd_grad_smooth.diminfo[2].strides) -= (2.0 * __pyx_v_df_dy2);
  
              /* "pysteps/motion/_vet.pyx":599
   * 
   *                         grad_smooth[axis, l, m] -= 2 * df_dy2
   *                         grad_smooth[axis, l, m - 1] += df_dy2             # <<<<<<<<<<<<<<
   *                         grad_smooth[axis, l, m + 1] += df_dy2
   * 
   */
              __pyx_t_274 = __pyx_v_axis;
              __pyx_t_275 = __pyx_v_l;
              __pyx_t_276 = (__pyx_v_m - 1);
              *__Pyx_BufPtrStrided3d(__pyx_t_7pysteps_6motion_4_vet_float64 *, __pyx_pybuffernd_grad_smooth.rcbuffer->pybuffer.buf, __pyx_t_274, __pyx_pybuffernd_grad_smooth.diminfo[0].strides, __pyx_t_275, __pyx_pybuffernd_grad_smooth.diminfo[1].strides, __pyx_t_276, __pyx_pybuffernd_grad_smooth.diminfo[2].strides) += __pyx_v_df_dy2;
  
              /* "pysteps/motion/_vet.pyx":600
   *                         grad_smooth[axis, l, m] -= 2 * df_dy2
   *                         grad_smooth[axis, l, m - 1] += df_dy2
   *                         grad_smooth[axis, l, m + 1] += df_dy2             # <<<<<<<<<<<<<<
   * 
   *                         grad_smooth[axis, l - 1, m - 1] += df_dxdy
   */
              __pyx_t_277 = __pyx_v_axis;
              __pyx_t_278 = __pyx_v_l;
              __pyx_t_279 = (__pyx_v_m + 1);
              *__Pyx_BufPtrStrided3d(__pyx_t_7pysteps_6motion_4_vet_float64 *, __pyx_pybuffernd_grad_smooth.rcbuffer->pybuffer.buf, __pyx_t_277, __pyx_pybuffernd_grad_smooth.diminfo[0].strides, __pyx_t_278, __pyx_pybuffernd_grad_smooth.diminfo[1].strides, __pyx_t_279, __pyx_pybuffernd_grad_smooth.diminfo[2].strides) += __pyx_v_df_dy2;
  
              /* "pysteps/motion/_vet.pyx":602
   *                         grad_smooth[axis, l, m + 1] += df_dy2
   * 
   *                         grad_smooth[axis, l - 1, m - 1] += df_dxdy             # <<<<<<<<<<<<<<
   *                         grad_smooth[axis, l - 1, m + 1] -= df_dxdy
   *                         grad_smooth[axis, l + 1, m - 1] -= df_dxdy
   */
              __pyx_t_280 = __pyx_v_axis;
              __pyx_t_281 = (__pyx_v_l - 1);
              __pyx_t_282 = (__pyx_v_m - 1);
              *__Pyx_BufPtrStrided3d(__pyx_t_7pysteps_6motion_4_vet_float64 *, __pyx_pybuffernd_grad_smooth.rcbuffer->pybuffer.buf, __pyx_t_280, __pyx_pybuffernd_grad_smooth.diminfo[0].strides, __pyx_t_281, __pyx_pybuffernd_grad_smooth.diminfo[1].strides, __pyx_t_282, __pyx_pybuffernd_grad_smooth.diminfo[2].strides) += __pyx_v_df_dxdy;
  
              /* "pysteps/motion/_vet.pyx":603
   * 
   *                         grad_smooth[axis, l - 1, m - 1] += df_dxdy
   *                         grad_smooth[axis, l - 1, m + 1] -= df_dxdy             # <<<<<<<<<<<<<<
   *                         grad_smooth[axis, l + 1, m - 1] -= df_dxdy
   *                         grad_smooth[axis, l + 1, m + 1] += df_dxdy
   */
              __pyx_t_283 = __pyx_v_axis;
              __pyx_t_284 = (__pyx_v_l - 1);
              __pyx_t_285 = (__pyx_v_m + 1);
              *__Pyx_BufPtrStrided3d(__pyx_t_7pysteps_6motion_4_vet_float64 *, __pyx_pybuffernd_grad_smooth.rcbuffer->pybuffer.buf, __pyx_t_283, __pyx_pybuffernd_grad_smooth.diminfo[0].strides, __pyx_t_284, __pyx_pybuffernd_grad_smooth.diminfo[1].strides, __pyx_t_285, __pyx_pybuffernd_grad_smooth.diminfo[2].strides) -= __pyx_v_df_dxdy;
  
              /* "pysteps/motion/_vet.pyx":604
   *                         grad_smooth[axis, l - 1, m - 1] += df_dxdy
   *                         grad_smooth[axis, l - 1, m + 1] -= df_dxdy
   *                         grad_smooth[axis, l + 1, m - 1] -= df_dxdy             # <<<<<<<<<<<<<<
   *                         grad_smooth[axis, l + 1, m + 1] += df_dxdy
   * 
   */
              __pyx_t_286 = __pyx_v_axis;
              __pyx_t_287 = (__pyx_v_l + 1);
              __pyx_t_288 = (__pyx_v_m - 1);
              *__Pyx_BufPtrStrided3d(__pyx_t_7pysteps_6motion_4_vet_float64 *, __pyx_pybuffernd_grad_smooth.rcbuffer->pybuffer.buf, __pyx_t_286, __pyx_pybuffernd_grad_smooth.diminfo[0].strides, __pyx_t_287, __pyx_pybuffernd_grad_smooth.diminfo[1].strides, __pyx_t_288, __pyx_pybuffernd_grad_smooth.diminfo[2].strides) -= __pyx_v_df_dxdy;
  
              /* "pysteps/motion/_vet.pyx":605
   *                         grad_smooth[axis, l - 1, m + 1] -= df_dxdy
   *                         grad_smooth[axis, l + 1, m - 1] -= df_dxdy
   *                         grad_smooth[axis, l + 1, m + 1] += df_dxdy             # <<<<<<<<<<<<<<
   * 
   *                     inloop_smoothness_penalty = (df_dx2 * df_dx2
   */
              __pyx_t_289 = __pyx_v_axis;
              __pyx_t_290 = (__pyx_v_l + 1);
              __pyx_t_291 = (__pyx_v_m + 1);
              *__Pyx_BufPtrStrided3d(__pyx_t_7pysteps_6motion_4_vet_float64 *, __pyx_pybuffernd_grad_smooth.rcbuffer->pybuffer.buf, __pyx_t_289, __pyx_pybuffernd_grad_smooth.diminfo[0].strides, __pyx_t_290, __pyx_pybuffernd_grad_smooth.diminfo[1].strides, __pyx_t_291, __pyx_pybuffernd_grad_smooth.diminfo[2].strides) += __pyx_v_df_dxdy;
  
              /* "pysteps/motion/_vet.pyx":593
   *                     df_dxdy = df_dxdy / (4 * x_sector_size * y_sector_size)
   * 
   *                     if gradient:             # <<<<<<<<<<<<<<
   *                         grad_smooth[axis, l, m] -= 2 * df_dx2
   *                         grad_smooth[axis, l + 1, m] += df_dx2
   */
            }
  
            /* "pysteps/motion/_vet.pyx":609
   *                     inloop_smoothness_penalty = (df_dx2 * df_dx2
   *                                                  + 2 * df_dxdy * df_dxdy
   *                                                  + df_dy2 * df_dy2)             # <<<<<<<<<<<<<<
   * 
   *                     smoothness_penalty += inloop_smoothness_penalty
   */
            __pyx_v_inloop_smoothness_penalty = (((__pyx_v_df_dx2 * __pyx_v_df_dx2) + ((2.0 * __pyx_v_df_dxdy) * __pyx_v_df_dxdy)) + (__pyx_v_df_dy2 * __pyx_v_df_dy2));
  
            /* "pysteps/motion/_vet.pyx":611
   *                                                  + df_dy2 * df_dy2)
   * 
   *                     smoothness_penalty += inloop_smoothness_penalty             # <<<<<<<<<<<<<<
   * 
   *         smoothness_penalty *= smooth_gain  #* x_sector_size * y_sector_size
   */
            __pyx_v_smoothness_penalty = (__pyx_v_smoothness_penalty + __pyx_v_inloop_smoothness_penalty);
          }
        }
      }
  
      /* "pysteps/motion/_vet.pyx":613
   *                     smoothness_penalty += inloop_smoothness_penalty
   * 
   *         smoothness_penalty *= smooth_gain  #* x_sector_size * y_sector_size             # <<<<<<<<<<<<<<
   * 
   *     if gradient:
   */
      __pyx_v_smoothness_penalty = (__pyx_v_smoothness_penalty * __pyx_v_smooth_gain);
  
      /* "pysteps/motion/_vet.pyx":566
   *     cdef float64 inloop_smoothness_penalty
   * 
   *     if smooth_gain > 0.:             # <<<<<<<<<<<<<<
   * 
   *         for axis in range(2):  #, schedule='dynamic', nogil=True):
   */
    }
  
    /* "pysteps/motion/_vet.pyx":615
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   *                 if   t == NPY_BYTE:        f = "b"
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   *                 elif t == NPY_SHORT:       f = "h"             # <<<<<<<<<<<<<<
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   *                 elif t == NPY_UBYTE:       f = "B"
   *                 elif t == NPY_SHORT:       f = "h"
   *                 elif t == NPY_USHORT:      f = "H"             # <<<<<<<<<<<<<<
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   *                 elif t == NPY_USHORT:      f = "H"
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   *                 elif t == NPY_ULONG:       f = "L"             # <<<<<<<<<<<<<<
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      case 'f': return sizeof(__Pyx_st_float) - sizeof(float);
      case 'd': return sizeof(__Pyx_st_double) - sizeof(double);
      case 'g': return sizeof(__Pyx_st_longdouble) - sizeof(long double);
      case 'P': case 'O': return sizeof(__Pyx_st_void_p) - sizeof(void*);
      default:
        __Pyx_BufFmt_RaiseUnexpectedChar(ch);
        return 0;
      }
  }
  /* These are for computing the padding at the end of the struct to align
     on the first member of the struct. This will probably the same as above,
     but we don't have any guarantees.
   */
  typedef struct { short x; char c; } __Pyx_pad_short;
  typedef struct { int x; char c; } __Pyx_pad_int;
  typedef struct { long x; char c; } __Pyx_pad_long;
  typedef struct { float x; char c; } __Pyx_pad_float;
  typedef struct { double x; char c; } __Pyx_pad_double;
  typedef struct { long double x; char c; } __Pyx_pad_longdouble;
  typedef struct { void *x; char c; } __Pyx_pad_void_p;
  #ifdef HAVE_LONG_LONG
  typedef struct { PY_LONG_LONG x; char c; } __Pyx_pad_longlong;
  #endif
  static size_t __Pyx_BufFmt_TypeCharToPadding(char ch, CYTHON_UNUSED int is_complex) {
    switch (ch) {
      case '?': case 'c': case 'b': case 'B': case 's': case 'p': return 1;
      case 'h': case 'H': return sizeof(__Pyx_pad_short) - sizeof(short);
      case 'i': case 'I': return sizeof(__Pyx_pad_int) - sizeof(int);
      case 'l': case 'L': return sizeof(__Pyx_pad_long) - sizeof(long);
  #ifdef HAVE_LONG_LONG
      case 'q': case 'Q': return sizeof(__Pyx_pad_longlong) - sizeof(PY_LONG_LONG);
  #endif
      case 'f': return sizeof(__Pyx_pad_float) - sizeof(float);
      case 'd': return sizeof(__Pyx_pad_double) - sizeof(double);
      case 'g': return sizeof(__Pyx_pad_longdouble) - sizeof(long double);
      case 'P': case 'O': return sizeof(__Pyx_pad_void_p) - sizeof(void*);
      default:
        __Pyx_BufFmt_RaiseUnexpectedChar(ch);
        return 0;
      }
  }
  static char __Pyx_BufFmt_TypeCharToGroup(char ch, int is_complex) {
    switch (ch) {
      case 'c':
          return 'H';
      case 'b': case 'h': case 'i':
      case 'l': case 'q': case 's': case 'p':
          return 'I';
      case 'B': case 'H': case 'I': case 'L': case 'Q':
          return 'U';
      case 'f': case 'd': case 'g':
          return (is_complex ? 'C' : 'R');
      case 'O':
          return 'O';
      case 'P':
          return 'P';
      default: {
        __Pyx_BufFmt_RaiseUnexpectedChar(ch);
        return 0;
      }
    }
  }
  static void __Pyx_BufFmt_RaiseExpected(__Pyx_BufFmt_Context* ctx) {
    if (ctx->head == NULL || ctx->head->field == &ctx->root) {
      const char* expected;
      const char* quote;
      if (ctx->head == NULL) {
        expected = "end";
        quote = "";
      } else {
        expected = ctx->head->field->type->name;
        quote = "'";
      }
      PyErr_Format(PyExc_ValueError,
                   "Buffer dtype mismatch, expected %s%s%s but got %s",
                   quote, expected, quote,
                   __Pyx_BufFmt_DescribeTypeChar(ctx->enc_type, ctx->is_complex));
    } else {
      __Pyx_StructField* field = ctx->head->field;
      __Pyx_StructField* parent = (ctx->head - 1)->field;
      PyErr_Format(PyExc_ValueError,
                   "Buffer dtype mismatch, expected '%s' but got %s in '%s.%s'",
                   field->type->name, __Pyx_BufFmt_DescribeTypeChar(ctx->enc_type, ctx->is_complex),
                   parent->type->name, field->name);
    }
  }
  static int __Pyx_BufFmt_ProcessTypeChunk(__Pyx_BufFmt_Context* ctx) {
    char group;
    size_t size, offset, arraysize = 1;
    if (ctx->enc_type == 0) return 0;
    if (ctx->head->field->type->arraysize[0]) {
      int i, ndim = 0;
      if (ctx->enc_type == 's' || ctx->enc_type == 'p') {
          ctx->is_valid_array = ctx->head->field->type->ndim == 1;
          ndim = 1;
          if (ctx->enc_count != ctx->head->field->type->arraysize[0]) {
              PyErr_Format(PyExc_ValueError,
                           "Expected a dimension of size %zu, got %zu",
                           ctx->head->field->type->arraysize[0], ctx->enc_count);
              return -1;
          }
      }
      if (!ctx->is_valid_array) {
        PyErr_Format(PyExc_ValueError, "Expected %d dimensions, got %d",
                     ctx->head->field->type->ndim, ndim);
        return -1;
      }
      for (i = 0; i < ctx->head->field->type->ndim; i++) {
        arraysize *= ctx->head->field->type->arraysize[i];
      }
      ctx->is_valid_array = 0;
      ctx->enc_count = 1;
    }
    group = __Pyx_BufFmt_TypeCharToGroup(ctx->enc_type, ctx->is_complex);
    do {
      __Pyx_StructField* field = ctx->head->field;
      __Pyx_TypeInfo* type = field->type;
      if (ctx->enc_packmode == '@' || ctx->enc_packmode == '^') {
        size = __Pyx_BufFmt_TypeCharToNativeSize(ctx->enc_type, ctx->is_complex);
      } else {
        size = __Pyx_BufFmt_TypeCharToStandardSize(ctx->enc_type, ctx->is_complex);
      }
      if (ctx->enc_packmode == '@') {
        size_t align_at = __Pyx_BufFmt_TypeCharToAlignment(ctx->enc_type, ctx->is_complex);
        size_t align_mod_offset;
        if (align_at == 0) return -1;
        align_mod_offset = ctx->fmt_offset % align_at;
        if (align_mod_offset > 0) ctx->fmt_offset += align_at - align_mod_offset;
        if (ctx->struct_alignment == 0)
            ctx->struct_alignment = __Pyx_BufFmt_TypeCharToPadding(ctx->enc_type,
                                                                   ctx->is_complex);
      }
      if (type->size != size || type->typegroup != group) {
        if (type->typegroup == 'C' && type->fields != NULL) {
          size_t parent_offset = ctx->head->parent_offset + field->offset;
          ++ctx->head;
          ctx->head->field = type->fields;
          ctx->head->parent_offset = parent_offset;
          continue;
        }
        if ((type->typegroup == 'H' || group == 'H') && type->size == size) {
        } else {
            __Pyx_BufFmt_RaiseExpected(ctx);
            return -1;
        }
      }
      offset = ctx->head->parent_offset + field->offset;
      if (ctx->fmt_offset != offset) {
        PyErr_Format(PyExc_ValueError,
                     "Buffer dtype mismatch; next field is at offset %" CYTHON_FORMAT_SSIZE_T "d but %" CYTHON_FORMAT_SSIZE_T "d expected",
                     (Py_ssize_t)ctx->fmt_offset, (Py_ssize_t)offset);
        return -1;
      }
      ctx->fmt_offset += size;
      if (arraysize)
        ctx->fmt_offset += (arraysize - 1) * size;
      --ctx->enc_count;
      while (1) {
        if (field == &ctx->root) {
          ctx->head = NULL;
          if (ctx->enc_count != 0) {
            __Pyx_BufFmt_RaiseExpected(ctx);
            return -1;
          }
          break;
        }
        ctx->head->field = ++field;
        if (field->type == NULL) {
          --ctx->head;
          field = ctx->head->field;
          continue;
        } else if (field->type->typegroup == 'S') {
          size_t parent_offset = ctx->head->parent_offset + field->offset;
          if (field->type->fields->type == NULL) continue;
          field = field->type->fields;
          ++ctx->head;
          ctx->head->field = field;
          ctx->head->parent_offset = parent_offset;
          break;
        } else {
          break;
        }
      }
    } while (ctx->enc_count);
    ctx->enc_type = 0;
    ctx->is_complex = 0;
    return 0;
  }
  static PyObject *
  __pyx_buffmt_parse_array(__Pyx_BufFmt_Context* ctx, const char** tsp)
  {
      const char *ts = *tsp;
      int i = 0, number;
      int ndim = ctx->head->field->type->ndim;
  ;
      ++ts;
      if (ctx->new_count != 1) {
          PyErr_SetString(PyExc_ValueError,
                          "Cannot handle repeated arrays in format string");
          return NULL;
      }
      if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
      while (*ts && *ts != ')') {
          switch (*ts) {
              case ' ': case '\f': case '\r': case '\n': case '\t': case '\v':  continue;
              default:  break;
          }
          number = __Pyx_BufFmt_ExpectNumber(&ts);
          if (number == -1) return NULL;
          if (i < ndim && (size_t) number != ctx->head->field->type->arraysize[i])
              return PyErr_Format(PyExc_ValueError,
                          "Expected a dimension of size %zu, got %d",
                          ctx->head->field->type->arraysize[i], number);
          if (*ts != ',' && *ts != ')')
              return PyErr_Format(PyExc_ValueError,
                                  "Expected a comma in format string, got '%c'", *ts);
          if (*ts == ',') ts++;
          i++;
      }
      if (i != ndim)
          return PyErr_Format(PyExc_ValueError, "Expected %d dimension(s), got %d",
                              ctx->head->field->type->ndim, i);
      if (!*ts) {
          PyErr_SetString(PyExc_ValueError,
                          "Unexpected end of format string, expected ')'");
          return NULL;
      }
      ctx->is_valid_array = 1;
      ctx->new_count = 1;
      *tsp = ++ts;
      return Py_None;
  }
  static const char* __Pyx_BufFmt_CheckString(__Pyx_BufFmt_Context* ctx, const char* ts) {
    int got_Z = 0;
    while (1) {
      switch(*ts) {
        case 0:
          if (ctx->enc_type != 0 && ctx->head == NULL) {
            __Pyx_BufFmt_RaiseExpected(ctx);
            return NULL;
          }
          if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
          if (ctx->head != NULL) {
            __Pyx_BufFmt_RaiseExpected(ctx);
            return NULL;
          }
          return ts;
        case ' ':
        case '\r':
        case '\n':
          ++ts;
          break;
        case '<':
          if (!__Pyx_Is_Little_Endian()) {
            PyErr_SetString(PyExc_ValueError, "Little-endian buffer not supported on big-endian compiler");
            return NULL;
          }
          ctx->new_packmode = '=';
          ++ts;
          break;
        case '>':
        case '!':
          if (__Pyx_Is_Little_Endian()) {
            PyErr_SetString(PyExc_ValueError, "Big-endian buffer not supported on little-endian compiler");
            return NULL;
          }
          ctx->new_packmode = '=';
          ++ts;
          break;
        case '=':
        case '@':
        case '^':
          ctx->new_packmode = *ts++;
          break;
        case 'T':
          {
            const char* ts_after_sub;
            size_t i, struct_count = ctx->new_count;
            size_t struct_alignment = ctx->struct_alignment;
            ctx->new_count = 1;
            ++ts;
            if (*ts != '{') {
              PyErr_SetString(PyExc_ValueError, "Buffer acquisition: Expected '{' after 'T'");
              return NULL;
            }
            if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
            ctx->enc_type = 0;
            ctx->enc_count = 0;
            ctx->struct_alignment = 0;
            ++ts;
            ts_after_sub = ts;
            for (i = 0; i != struct_count; ++i) {
              ts_after_sub = __Pyx_BufFmt_CheckString(ctx, ts);
              if (!ts_after_sub) return NULL;
            }
            ts = ts_after_sub;
            if (struct_alignment) ctx->struct_alignment = struct_alignment;
          }
          break;
        case '}':
          {
            size_t alignment = ctx->struct_alignment;
            ++ts;
            if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
            ctx->enc_type = 0;
            if (alignment && ctx->fmt_offset % alignment) {
              ctx->fmt_offset += alignment - (ctx->fmt_offset % alignment);
            }
          }
          return ts;
        case 'x':
          if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
          ctx->fmt_offset += ctx->new_count;
          ctx->new_count = 1;
          ctx->enc_count = 0;
          ctx->enc_type = 0;
          ctx->enc_packmode = ctx->new_packmode;
          ++ts;
          break;
        case 'Z':
          got_Z = 1;
          ++ts;
          if (*ts != 'f' && *ts != 'd' && *ts != 'g') {
            __Pyx_BufFmt_RaiseUnexpectedChar('Z');
            return NULL;
          }
          CYTHON_FALLTHROUGH;
        case 'c': case 'b': case 'B': case 'h': case 'H': case 'i': case 'I':
        case 'l': case 'L': case 'q': case 'Q':
        case 'f': case 'd': case 'g':
        case 'O': case 'p':
          if (ctx->enc_type == *ts && got_Z == ctx->is_complex &&
              ctx->enc_packmode == ctx->new_packmode) {
            ctx->enc_count += ctx->new_count;
            ctx->new_count = 1;
            got_Z = 0;
            ++ts;
            break;
          }
          CYTHON_FALLTHROUGH;
        case 's':
          if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
          ctx->enc_count = ctx->new_count;
          ctx->enc_packmode = ctx->new_packmode;
          ctx->enc_type = *ts;
          ctx->is_complex = got_Z;
          ++ts;
          ctx->new_count = 1;
          got_Z = 0;
          break;
        case ':':
          ++ts;
          while(*ts != ':') ++ts;
          ++ts;
          break;
        case '(':
          if (!__pyx_buffmt_parse_array(ctx, &ts)) return NULL;
          break;
        default:
          {
            int number = __Pyx_BufFmt_ExpectNumber(&ts);
            if (number == -1) return NULL;
            ctx->new_count = (size_t)number;
          }
      }
    }
  }
  
  /* BufferGetAndValidate */
    static CYTHON_INLINE void __Pyx_SafeReleaseBuffer(Py_buffer* info) {
    if (unlikely(info->buf == NULL)) return;
    if (info->suboffsets == __Pyx_minusones) info->suboffsets = NULL;
    __Pyx_ReleaseBuffer(info);
  }
  static void __Pyx_ZeroBuffer(Py_buffer* buf) {
    buf->buf = NULL;
    buf->obj = NULL;
    buf->strides = __Pyx_zeros;
    buf->shape = __Pyx_zeros;
    buf->suboffsets = __Pyx_minusones;
  }
  static int __Pyx__GetBufferAndValidate(
          Py_buffer* buf, PyObject* obj,  __Pyx_TypeInfo* dtype, int flags,
          int nd, int cast, __Pyx_BufFmt_StackElem* stack)
  {
    buf->buf = NULL;
    if (unlikely(__Pyx_GetBuffer(obj, buf, flags) == -1)) {
      __Pyx_ZeroBuffer(buf);
      return -1;
    }
    if (unlikely(buf->ndim != nd)) {
      PyErr_Format(PyExc_ValueError,
                   "Buffer has wrong number of dimensions (expected %d, got %d)",
                   nd, buf->ndim);
      goto fail;
    }
    if (!cast) {
      __Pyx_BufFmt_Context ctx;
      __Pyx_BufFmt_Init(&ctx, stack, dtype);
      if (!__Pyx_BufFmt_CheckString(&ctx, buf->format)) goto fail;
    }
    if (unlikely((size_t)buf->itemsize != dtype->size)) {
      PyErr_Format(PyExc_ValueError,
        "Item size of buffer (%" CYTHON_FORMAT_SSIZE_T "d byte%s) does not match size of '%s' (%" CYTHON_FORMAT_SSIZE_T "d byte%s)",
        buf->itemsize, (buf->itemsize > 1) ? "s" : "",
        dtype->name, (Py_ssize_t)dtype->size, (dtype->size > 1) ? "s" : "");
      goto fail;
    }
    if (buf->suboffsets == NULL) buf->suboffsets = __Pyx_minusones;
    return 0;
  fail:;
    __Pyx_SafeReleaseBuffer(buf);
    return -1;
  }
  
  /* 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)
  #else
  static CYTHON_INLINE PyObject *__Pyx__GetModuleGlobalName(PyObject *name)
  #endif
  {
      PyObject *result;
  #if !CYTHON_AVOID_BORROWED_REFS
  #if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x030500A1
      result = _PyDict_GetItem_KnownHash(__pyx_d, name, ((PyASCIIObject *) name)->hash);
      __PYX_UPDATE_DICT_CACHE(__pyx_d, result, *dict_cached_value, *dict_version)
      if (likely(result)) {
          return __Pyx_NewRef(result);
      } else if (unlikely(PyErr_Occurred())) {
          return NULL;
      }
  #else
      result = PyDict_GetItem(__pyx_d, name);
      __PYX_UPDATE_DICT_CACHE(__pyx_d, result, *dict_cached_value, *dict_version)
      if (likely(result)) {
          return __Pyx_NewRef(result);
      }
  #endif
  #else
      result = PyObject_GetItem(__pyx_d, name);
      __PYX_UPDATE_DICT_CACHE(__pyx_d, result, *dict_cached_value, *dict_version)
      if (likely(result)) {
          return __Pyx_NewRef(result);
      }
      PyErr_Clear();
  #endif
      return __Pyx_GetBuiltinName(name);
  }
  
  /* PyObjectCall */
    #if CYTHON_COMPILING_IN_CPYTHON
  static CYTHON_INLINE PyObject* __Pyx_PyObject_Call(PyObject *func, PyObject *arg, PyObject *kw) {
      PyObject *result;
      ternaryfunc call = func->ob_type->tp_call;
      if (unlikely(!call))
          return PyObject_Call(func, arg, kw);
      if (unlikely(Py_EnterRecursiveCall((char*)" while calling a Python object")))
          return NULL;
      result = (*call)(func, arg, kw);
      Py_LeaveRecursiveCall();
      if (unlikely(!result) && unlikely(!PyErr_Occurred())) {
          PyErr_SetString(
              PyExc_SystemError,
              "NULL result without error in PyObject_Call");
      }
      return result;
  }
  #endif
  
  /* ExtTypeTest */
    static CYTHON_INLINE int __Pyx_TypeTest(PyObject *obj, PyTypeObject *type) {
      if (unlikely(!type)) {
          PyErr_SetString(PyExc_SystemError, "Missing type object");
          return 0;
      }
      if (likely(__Pyx_TypeCheck(obj, type)))
          return 1;
      PyErr_Format(PyExc_TypeError, "Cannot convert %.200s to %.200s",
                   Py_TYPE(obj)->tp_name, type->tp_name);
      return 0;
  }
  
  /* PyErrFetchRestore */
    #if CYTHON_FAST_THREAD_STATE
  static CYTHON_INLINE void __Pyx_ErrRestoreInState(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb) {
      PyObject *tmp_type, *tmp_value, *tmp_tb;
      tmp_type = tstate->curexc_type;
      tmp_value = tstate->curexc_value;
      tmp_tb = tstate->curexc_traceback;
      tstate->curexc_type = type;
      tstate->curexc_value = value;
      tstate->curexc_traceback = tb;
      Py_XDECREF(tmp_type);
      Py_XDECREF(tmp_value);
      Py_XDECREF(tmp_tb);
  }
  static CYTHON_INLINE void __Pyx_ErrFetchInState(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb) {
      *type = tstate->curexc_type;
      *value = tstate->curexc_value;
      *tb = tstate->curexc_traceback;
      tstate->curexc_type = 0;
      tstate->curexc_value = 0;
      tstate->curexc_traceback = 0;
  }
  #endif
  
  /* RaiseException */
    #if PY_MAJOR_VERSION < 3
  static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb,
                          CYTHON_UNUSED PyObject *cause) {
      __Pyx_PyThreadState_declare
      Py_XINCREF(type);
      if (!value || value == Py_None)
          value = NULL;
      else
          Py_INCREF(value);
      if (!tb || tb == Py_None)
          tb = NULL;
      else {
          Py_INCREF(tb);
          if (!PyTraceBack_Check(tb)) {
              PyErr_SetString(PyExc_TypeError,
                  "raise: arg 3 must be a traceback or None");
              goto raise_error;
          }
      }
      if (PyType_Check(type)) {
  #if CYTHON_COMPILING_IN_PYPY
          if (!value) {
              Py_INCREF(Py_None);
              value = Py_None;
          }
  #endif
          PyErr_NormalizeException(&type, &value, &tb);
      } else {
          if (value) {
              PyErr_SetString(PyExc_TypeError,
                  "instance exception may not have a separate value");
              goto raise_error;
          }
          value = type;
          type = (PyObject*) Py_TYPE(type);
          Py_INCREF(type);
          if (!PyType_IsSubtype((PyTypeObject *)type, (PyTypeObject *)PyExc_BaseException)) {
              PyErr_SetString(PyExc_TypeError,
                  "raise: exception class must be a subclass of BaseException");
              goto raise_error;
          }
      }
      __Pyx_PyThreadState_assign
      __Pyx_ErrRestore(type, value, tb);
      return;
  raise_error:
      Py_XDECREF(value);
      Py_XDECREF(type);
      Py_XDECREF(tb);
      return;
  }
  #else
  static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb, PyObject *cause) {
      PyObject* owned_instance = NULL;
      if (tb == Py_None) {
          tb = 0;
      } else if (tb && !PyTraceBack_Check(tb)) {
          PyErr_SetString(PyExc_TypeError,
              "raise: arg 3 must be a traceback or None");
          goto bad;
      }
      if (value == Py_None)
          value = 0;
      if (PyExceptionInstance_Check(type)) {
          if (value) {
              PyErr_SetString(PyExc_TypeError,
                  "instance exception may not have a separate value");
              goto bad;
          }
          value = type;
          type = (PyObject*) Py_TYPE(value);
      } else if (PyExceptionClass_Check(type)) {
          PyObject *instance_class = NULL;
          if (value && PyExceptionInstance_Check(value)) {
              instance_class = (PyObject*) Py_TYPE(value);
              if (instance_class != type) {
                  int is_subclass = PyObject_IsSubclass(instance_class, type);
                  if (!is_subclass) {
                      instance_class = NULL;
                  } else if (unlikely(is_subclass == -1)) {
                      goto bad;
                  } else {
                      type = instance_class;
                  }
              }
          }
          if (!instance_class) {
              PyObject *args;
              if (!value)
                  args = PyTuple_New(0);
              else if (PyTuple_Check(value)) {
                  Py_INCREF(value);
                  args = value;
              } else
                  args = PyTuple_Pack(1, value);
              if (!args)
                  goto bad;
              owned_instance = PyObject_Call(type, args, NULL);
              Py_DECREF(args);
              if (!owned_instance)
                  goto bad;
              value = owned_instance;
              if (!PyExceptionInstance_Check(value)) {
                  PyErr_Format(PyExc_TypeError,
                               "calling %R should have returned an instance of "
                               "BaseException, not %R",
                               type, Py_TYPE(value));
                  goto bad;
              }
          }
      } else {
          PyErr_SetString(PyExc_TypeError,
              "raise: exception class must be a subclass of BaseException");
          goto bad;
      }
      if (cause) {
          PyObject *fixed_cause;
          if (cause == Py_None) {
              fixed_cause = NULL;
          } else if (PyExceptionClass_Check(cause)) {
              fixed_cause = PyObject_CallObject(cause, NULL);
              if (fixed_cause == NULL)
                  goto bad;
          } else if (PyExceptionInstance_Check(cause)) {
              fixed_cause = cause;
              Py_INCREF(fixed_cause);
          } else {
              PyErr_SetString(PyExc_TypeError,
                              "exception causes must derive from "
                              "BaseException");
              goto bad;
          }
          PyException_SetCause(value, fixed_cause);
      }
      PyErr_SetObject(type, value);
      if (tb) {
  #if CYTHON_COMPILING_IN_PYPY
          PyObject *tmp_type, *tmp_value, *tmp_tb;
          PyErr_Fetch(&tmp_type, &tmp_value, &tmp_tb);
          Py_INCREF(tb);
          PyErr_Restore(tmp_type, tmp_value, tb);
          Py_XDECREF(tmp_tb);
  #else
          PyThreadState *tstate = __Pyx_PyThreadState_Current;
          PyObject* tmp_tb = tstate->curexc_traceback;
          if (tb != tmp_tb) {
              Py_INCREF(tb);
              tstate->curexc_traceback = tb;
              Py_XDECREF(tmp_tb);
          }
  #endif
      }
  bad:
      Py_XDECREF(owned_instance);
      return;
  }
  #endif
  
  /* BufferFallbackError */
    static void __Pyx_RaiseBufferFallbackError(void) {
    PyErr_SetString(PyExc_ValueError,
       "Buffer acquisition failed on assignment; and then reacquiring the old buffer failed too!");
  }
  
  /* PyCFunctionFastCall */
    #if CYTHON_FAST_PYCCALL
  static CYTHON_INLINE PyObject * __Pyx_PyCFunction_FastCall(PyObject *func_obj, PyObject **args, Py_ssize_t nargs) {
      PyCFunctionObject *func = (PyCFunctionObject*)func_obj;
      PyCFunction meth = PyCFunction_GET_FUNCTION(func);
      PyObject *self = PyCFunction_GET_SELF(func);
      int flags = PyCFunction_GET_FLAGS(func);
      assert(PyCFunction_Check(func));
      assert(METH_FASTCALL == (flags & ~(METH_CLASS | METH_STATIC | METH_COEXIST | METH_KEYWORDS | METH_STACKLESS)));
      assert(nargs >= 0);
      assert(nargs == 0 || args != NULL);
      /* _PyCFunction_FastCallDict() must not be called with an exception set,
         because it may clear it (directly or indirectly) and so the
         caller loses its exception */
      assert(!PyErr_Occurred());
      if ((PY_VERSION_HEX < 0x030700A0) || unlikely(flags & METH_KEYWORDS)) {
          return (*((__Pyx_PyCFunctionFastWithKeywords)(void*)meth)) (self, args, nargs, NULL);
      } else {
          return (*((__Pyx_PyCFunctionFast)(void*)meth)) (self, args, nargs);
      }
  }
  #endif
  
  /* PyFunctionFastCall */
    #if CYTHON_FAST_PYCALL
  static PyObject* __Pyx_PyFunction_FastCallNoKw(PyCodeObject *co, PyObject **args, Py_ssize_t na,
                                                 PyObject *globals) {
      PyFrameObject *f;
      PyThreadState *tstate = __Pyx_PyThreadState_Current;
      PyObject **fastlocals;
      Py_ssize_t i;
      PyObject *result;
      assert(globals != NULL);
      /* XXX Perhaps we should create a specialized
         PyFrame_New() that doesn't take locals, but does
         take builtins without sanity checking them.
         */
      assert(tstate != NULL);
      f = PyFrame_New(tstate, co, globals, NULL);
      if (f == NULL) {
          return NULL;
      }
      fastlocals = __Pyx_PyFrame_GetLocalsplus(f);
      for (i = 0; i < na; i++) {
          Py_INCREF(*args);
          fastlocals[i] = *args++;
      }
      result = PyEval_EvalFrameEx(f,0);
      ++tstate->recursion_depth;
      Py_DECREF(f);
      --tstate->recursion_depth;
      return result;
  }
  #if 1 || PY_VERSION_HEX < 0x030600B1
  static PyObject *__Pyx_PyFunction_FastCallDict(PyObject *func, PyObject **args, Py_ssize_t nargs, PyObject *kwargs) {
      PyCodeObject *co = (PyCodeObject *)PyFunction_GET_CODE(func);
      PyObject *globals = PyFunction_GET_GLOBALS(func);
      PyObject *argdefs = PyFunction_GET_DEFAULTS(func);
      PyObject *closure;
  #if PY_MAJOR_VERSION >= 3
      PyObject *kwdefs;
  #endif
      PyObject *kwtuple, **k;
      PyObject **d;
      Py_ssize_t nd;
      Py_ssize_t nk;
      PyObject *result;
      assert(kwargs == NULL || PyDict_Check(kwargs));
      nk = kwargs ? PyDict_Size(kwargs) : 0;
      if (Py_EnterRecursiveCall((char*)" while calling a Python object")) {
          return NULL;
      }
      if (
  #if PY_MAJOR_VERSION >= 3
              co->co_kwonlyargcount == 0 &&
  #endif
              likely(kwargs == NULL || nk == 0) &&
              co->co_flags == (CO_OPTIMIZED | CO_NEWLOCALS | CO_NOFREE)) {
          if (argdefs == NULL && co->co_argcount == nargs) {
              result = __Pyx_PyFunction_FastCallNoKw(co, args, nargs, globals);
              goto done;
          }
          else if (nargs == 0 && argdefs != NULL
                   && co->co_argcount == Py_SIZE(argdefs)) {
              /* function called with no arguments, but all parameters have
                 a default value: use default values as arguments .*/
              args = &PyTuple_GET_ITEM(argdefs, 0);
              result =__Pyx_PyFunction_FastCallNoKw(co, args, Py_SIZE(argdefs), globals);
              goto done;
          }
      }
      if (kwargs != NULL) {
          Py_ssize_t pos, i;
          kwtuple = PyTuple_New(2 * nk);
          if (kwtuple == NULL) {
              result = NULL;
              goto done;
          }
          k = &PyTuple_GET_ITEM(kwtuple, 0);
          pos = i = 0;
          while (PyDict_Next(kwargs, &pos, &k[i], &k[i+1])) {
              Py_INCREF(k[i]);
              Py_INCREF(k[i+1]);
              i += 2;
          }
          nk = i / 2;
      }
      else {
          kwtuple = NULL;
          k = NULL;
      }
      closure = PyFunction_GET_CLOSURE(func);
  #if PY_MAJOR_VERSION >= 3
      kwdefs = PyFunction_GET_KW_DEFAULTS(func);
  #endif
      if (argdefs != NULL) {
          d = &PyTuple_GET_ITEM(argdefs, 0);
          nd = Py_SIZE(argdefs);
      }
      else {
          d = NULL;
          nd = 0;
      }
  #if PY_MAJOR_VERSION >= 3
      result = PyEval_EvalCodeEx((PyObject*)co, globals, (PyObject *)NULL,
                                 args, (int)nargs,
                                 k, (int)nk,
                                 d, (int)nd, kwdefs, closure);
  #else
      result = PyEval_EvalCodeEx(co, globals, (PyObject *)NULL,
                                 args, (int)nargs,
                                 k, (int)nk,
                                 d, (int)nd, closure);
  #endif
      Py_XDECREF(kwtuple);
  done:
      Py_LeaveRecursiveCall();
      return result;
  }
  #endif
  #endif
  
  /* PyObjectCall2Args */
    static CYTHON_UNUSED PyObject* __Pyx_PyObject_Call2Args(PyObject* function, PyObject* arg1, PyObject* arg2) {
      PyObject *args, *result = NULL;
      #if CYTHON_FAST_PYCALL
      if (PyFunction_Check(function)) {
          PyObject *args[2] = {arg1, arg2};
          return __Pyx_PyFunction_FastCall(function, args, 2);
      }
      #endif
      #if CYTHON_FAST_PYCCALL
      if (__Pyx_PyFastCFunction_Check(function)) {
          PyObject *args[2] = {arg1, arg2};
          return __Pyx_PyCFunction_FastCall(function, args, 2);
      }
      #endif
      args = PyTuple_New(2);
      if (unlikely(!args)) goto done;
      Py_INCREF(arg1);
      PyTuple_SET_ITEM(args, 0, arg1);
      Py_INCREF(arg2);
      PyTuple_SET_ITEM(args, 1, arg2);
      Py_INCREF(function);
      result = __Pyx_PyObject_Call(function, args, NULL);
      Py_DECREF(args);
      Py_DECREF(function);
  done:
      return result;
  }
  
  /* PyObjectCallMethO */
    #if CYTHON_COMPILING_IN_CPYTHON
  static CYTHON_INLINE PyObject* __Pyx_PyObject_CallMethO(PyObject *func, PyObject *arg) {
      PyObject *self, *result;
      PyCFunction cfunc;
      cfunc = PyCFunction_GET_FUNCTION(func);
      self = PyCFunction_GET_SELF(func);
      if (unlikely(Py_EnterRecursiveCall((char*)" while calling a Python object")))
          return NULL;
      result = cfunc(self, arg);
      Py_LeaveRecursiveCall();
      if (unlikely(!result) && unlikely(!PyErr_Occurred())) {
          PyErr_SetString(
              PyExc_SystemError,
              "NULL result without error in PyObject_Call");
      }
      return result;
  }
  #endif
  
  /* PyObjectCallOneArg */
    #if CYTHON_COMPILING_IN_CPYTHON
  static PyObject* __Pyx__PyObject_CallOneArg(PyObject *func, PyObject *arg) {
      PyObject *result;
      PyObject *args = PyTuple_New(1);
      if (unlikely(!args)) return NULL;
      Py_INCREF(arg);
      PyTuple_SET_ITEM(args, 0, arg);
      result = __Pyx_PyObject_Call(func, args, NULL);
      Py_DECREF(args);
      return result;
  }
  static CYTHON_INLINE PyObject* __Pyx_PyObject_CallOneArg(PyObject *func, PyObject *arg) {
  #if CYTHON_FAST_PYCALL
      if (PyFunction_Check(func)) {
          return __Pyx_PyFunction_FastCall(func, &arg, 1);
      }
  #endif
      if (likely(PyCFunction_Check(func))) {
          if (likely(PyCFunction_GET_FLAGS(func) & METH_O)) {
              return __Pyx_PyObject_CallMethO(func, arg);
  #if CYTHON_FAST_PYCCALL
          } else if (PyCFunction_GET_FLAGS(func) & METH_FASTCALL) {
              return __Pyx_PyCFunction_FastCall(func, &arg, 1);
  #endif
          }
      }
      return __Pyx__PyObject_CallOneArg(func, arg);
  }
  #else
  static CYTHON_INLINE PyObject* __Pyx_PyObject_CallOneArg(PyObject *func, PyObject *arg) {
      PyObject *result;
      PyObject *args = PyTuple_Pack(1, arg);
      if (unlikely(!args)) return NULL;
      result = __Pyx_PyObject_Call(func, args, NULL);
      Py_DECREF(args);
      return result;
  }
  #endif
  
  /* RaiseTooManyValuesToUnpack */
    static CYTHON_INLINE void __Pyx_RaiseTooManyValuesError(Py_ssize_t expected) {
      PyErr_Format(PyExc_ValueError,
                   "too many values to unpack (expected %" CYTHON_FORMAT_SSIZE_T "d)", expected);
  }
  
  /* RaiseNeedMoreValuesToUnpack */
    static CYTHON_INLINE void __Pyx_RaiseNeedMoreValuesError(Py_ssize_t index) {
      PyErr_Format(PyExc_ValueError,
                   "need more than %" CYTHON_FORMAT_SSIZE_T "d value%.1s to unpack",
                   index, (index == 1) ? "" : "s");
  }
  
  /* IterFinish */
    static CYTHON_INLINE int __Pyx_IterFinish(void) {
  #if CYTHON_FAST_THREAD_STATE
      PyThreadState *tstate = __Pyx_PyThreadState_Current;
      PyObject* exc_type = tstate->curexc_type;
      if (unlikely(exc_type)) {
          if (likely(__Pyx_PyErr_GivenExceptionMatches(exc_type, PyExc_StopIteration))) {
              PyObject *exc_value, *exc_tb;
              exc_value = tstate->curexc_value;
              exc_tb = tstate->curexc_traceback;
              tstate->curexc_type = 0;
              tstate->curexc_value = 0;
              tstate->curexc_traceback = 0;
              Py_DECREF(exc_type);
              Py_XDECREF(exc_value);
              Py_XDECREF(exc_tb);
              return 0;
          } else {
              return -1;
          }
      }
      return 0;
  #else
      if (unlikely(PyErr_Occurred())) {
          if (likely(PyErr_ExceptionMatches(PyExc_StopIteration))) {
              PyErr_Clear();
              return 0;
          } else {
              return -1;
          }
      }
      return 0;
  #endif
  }
  
  /* UnpackItemEndCheck */
    static int __Pyx_IternextUnpackEndCheck(PyObject *retval, Py_ssize_t expected) {
      if (unlikely(retval)) {
          Py_DECREF(retval);
          __Pyx_RaiseTooManyValuesError(expected);
          return -1;
      } else {
          return __Pyx_IterFinish();
      }
      return 0;
  }
  
  /* PyIntBinop */
    #if !CYTHON_COMPILING_IN_PYPY
  static PyObject* __Pyx_PyInt_SubtractObjC(PyObject *op1, PyObject *op2, CYTHON_UNUSED long intval, int inplace, int zerodivision_check) {
      (void)inplace;
      (void)zerodivision_check;
      #if PY_MAJOR_VERSION < 3
      if (likely(PyInt_CheckExact(op1))) {
          const long b = intval;
          long x;
          long a = PyInt_AS_LONG(op1);
              x = (long)((unsigned long)a - b);
              if (likely((x^a) >= 0 || (x^~b) >= 0))
                  return PyInt_FromLong(x);
              return PyLong_Type.tp_as_number->nb_subtract(op1, op2);
      }
      #endif
      #if CYTHON_USE_PYLONG_INTERNALS
      if (likely(PyLong_CheckExact(op1))) {
          const long b = intval;
          long a, x;
  #ifdef HAVE_LONG_LONG
          const PY_LONG_LONG llb = intval;
          PY_LONG_LONG lla, llx;
  #endif
          const digit* digits = ((PyLongObject*)op1)->ob_digit;
          const Py_ssize_t size = Py_SIZE(op1);
          if (likely(__Pyx_sst_abs(size) <= 1)) {
              a = likely(size) ? digits[0] : 0;
              if (size == -1) a = -a;
          } else {
              switch (size) {
                  case -2:
                      if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
                          a = -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                          break;
  #ifdef HAVE_LONG_LONG
                      } else if (8 * sizeof(PY_LONG_LONG) - 1 > 2 * PyLong_SHIFT) {
                          lla = -(PY_LONG_LONG) (((((unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                          goto long_long;
  #endif
                      }
                      CYTHON_FALLTHROUGH;
                  case 2:
                      if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
                          a = (long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                          break;
  #ifdef HAVE_LONG_LONG
                      } else if (8 * sizeof(PY_LONG_LONG) - 1 > 2 * PyLong_SHIFT) {
                          lla = (PY_LONG_LONG) (((((unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                          goto long_long;
  #endif
                      }
                      CYTHON_FALLTHROUGH;
                  case -3:
                      if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
                          a = -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                          break;
  #ifdef HAVE_LONG_LONG
                      } else if (8 * sizeof(PY_LONG_LONG) - 1 > 3 * PyLong_SHIFT) {
                          lla = -(PY_LONG_LONG) (((((((unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                          goto long_long;
  #endif
                      }
                      CYTHON_FALLTHROUGH;
                  case 3:
                      if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
                          a = (long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                          break;
  #ifdef HAVE_LONG_LONG
                      } else if (8 * sizeof(PY_LONG_LONG) - 1 > 3 * PyLong_SHIFT) {
                          lla = (PY_LONG_LONG) (((((((unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                          goto long_long;
  #endif
                      }
                      CYTHON_FALLTHROUGH;
                  case -4:
                      if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {
                          a = -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                          break;
  #ifdef HAVE_LONG_LONG
                      } else if (8 * sizeof(PY_LONG_LONG) - 1 > 4 * PyLong_SHIFT) {
                          lla = -(PY_LONG_LONG) (((((((((unsigned PY_LONG_LONG)digits[3]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                          goto long_long;
  #endif
                      }
                      CYTHON_FALLTHROUGH;
                  case 4:
                      if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {
                          a = (long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                          break;
  #ifdef HAVE_LONG_LONG
                      } else if (8 * sizeof(PY_LONG_LONG) - 1 > 4 * PyLong_SHIFT) {
                          lla = (PY_LONG_LONG) (((((((((unsigned PY_LONG_LONG)digits[3]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                          goto long_long;
  #endif
                      }
                      CYTHON_FALLTHROUGH;
                  default: return PyLong_Type.tp_as_number->nb_subtract(op1, op2);
              }
          }
                  x = a - b;
              return PyLong_FromLong(x);
  #ifdef HAVE_LONG_LONG
          long_long:
                  llx = lla - llb;
              return PyLong_FromLongLong(llx);
  #endif
          
          
      }
      #endif
      if (PyFloat_CheckExact(op1)) {
          const long b = intval;
          double a = PyFloat_AS_DOUBLE(op1);
              double result;
              PyFPE_START_PROTECT("subtract", return NULL)
              result = ((double)a) - (double)b;
              PyFPE_END_PROTECT(result)
              return PyFloat_FromDouble(result);
      }
      return (inplace ? PyNumber_InPlaceSubtract : PyNumber_Subtract)(op1, op2);
  }
  #endif
  
  /* GetItemInt */
    static PyObject *__Pyx_GetItemInt_Generic(PyObject *o, PyObject* j) {
      PyObject *r;
      if (!j) return NULL;
      r = PyObject_GetItem(o, j);
      Py_DECREF(j);
      return r;
  }
  static CYTHON_INLINE PyObject *__Pyx_GetItemInt_List_Fast(PyObject *o, Py_ssize_t i,
                                                                CYTHON_NCP_UNUSED int wraparound,
                                                                CYTHON_NCP_UNUSED int boundscheck) {
  #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
      Py_ssize_t wrapped_i = i;
      if (wraparound & unlikely(i < 0)) {
          wrapped_i += PyList_GET_SIZE(o);
      }
      if ((!boundscheck) || likely(__Pyx_is_valid_index(wrapped_i, PyList_GET_SIZE(o)))) {
          PyObject *r = PyList_GET_ITEM(o, wrapped_i);
          Py_INCREF(r);
          return r;
      }
      return __Pyx_GetItemInt_Generic(o, PyInt_FromSsize_t(i));
  #else
      return PySequence_GetItem(o, i);
  #endif
  }
  static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Tuple_Fast(PyObject *o, Py_ssize_t i,
                                                                CYTHON_NCP_UNUSED int wraparound,
                                                                CYTHON_NCP_UNUSED int boundscheck) {
  #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
      Py_ssize_t wrapped_i = i;
      if (wraparound & unlikely(i < 0)) {
          wrapped_i += PyTuple_GET_SIZE(o);
      }
      if ((!boundscheck) || likely(__Pyx_is_valid_index(wrapped_i, PyTuple_GET_SIZE(o)))) {
          PyObject *r = PyTuple_GET_ITEM(o, wrapped_i);
          Py_INCREF(r);
          return r;
      }
      return __Pyx_GetItemInt_Generic(o, PyInt_FromSsize_t(i));
  #else
      return PySequence_GetItem(o, i);
  #endif
  }
  static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Fast(PyObject *o, Py_ssize_t i, int is_list,
                                                       CYTHON_NCP_UNUSED int wraparound,
                                                       CYTHON_NCP_UNUSED int boundscheck) {
  #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS && CYTHON_USE_TYPE_SLOTS
      if (is_list || PyList_CheckExact(o)) {
          Py_ssize_t n = ((!wraparound) | likely(i >= 0)) ? i : i + PyList_GET_SIZE(o);
          if ((!boundscheck) || (likely(__Pyx_is_valid_index(n, PyList_GET_SIZE(o))))) {
              PyObject *r = PyList_GET_ITEM(o, n);
              Py_INCREF(r);
              return r;
          }
      }
      else if (PyTuple_CheckExact(o)) {
          Py_ssize_t n = ((!wraparound) | likely(i >= 0)) ? i : i + PyTuple_GET_SIZE(o);
          if ((!boundscheck) || likely(__Pyx_is_valid_index(n, PyTuple_GET_SIZE(o)))) {
              PyObject *r = PyTuple_GET_ITEM(o, n);
              Py_INCREF(r);
              return r;
          }
      } else {
          PySequenceMethods *m = Py_TYPE(o)->tp_as_sequence;
          if (likely(m && m->sq_item)) {
              if (wraparound && unlikely(i < 0) && likely(m->sq_length)) {
                  Py_ssize_t l = m->sq_length(o);
                  if (likely(l >= 0)) {
                      i += l;
                  } else {
                      if (!PyErr_ExceptionMatches(PyExc_OverflowError))
                          return NULL;
                      PyErr_Clear();
                  }
              }
              return m->sq_item(o, i);
          }
      }
  #else
      if (is_list || PySequence_Check(o)) {
          return PySequence_GetItem(o, i);
      }
  #endif
      return __Pyx_GetItemInt_Generic(o, PyInt_FromSsize_t(i));
  }
  
  /* ObjectGetItem */
    #if CYTHON_USE_TYPE_SLOTS
  static PyObject *__Pyx_PyObject_GetIndex(PyObject *obj, PyObject* index) {
      PyObject *runerr;
      Py_ssize_t key_value;
      PySequenceMethods *m = Py_TYPE(obj)->tp_as_sequence;
      if (unlikely(!(m && m->sq_item))) {
          PyErr_Format(PyExc_TypeError, "'%.200s' object is not subscriptable", Py_TYPE(obj)->tp_name);
          return NULL;
      }
      key_value = __Pyx_PyIndex_AsSsize_t(index);
      if (likely(key_value != -1 || !(runerr = PyErr_Occurred()))) {
          return __Pyx_GetItemInt_Fast(obj, key_value, 0, 1, 1);
      }
      if (PyErr_GivenExceptionMatches(runerr, PyExc_OverflowError)) {
          PyErr_Clear();
          PyErr_Format(PyExc_IndexError, "cannot fit '%.200s' into an index-sized integer", Py_TYPE(index)->tp_name);
      }
      return NULL;
  }
  static PyObject *__Pyx_PyObject_GetItem(PyObject *obj, PyObject* key) {
      PyMappingMethods *m = Py_TYPE(obj)->tp_as_mapping;
      if (likely(m && m->mp_subscript)) {
          return m->mp_subscript(obj, key);
      }
      return __Pyx_PyObject_GetIndex(obj, key);
  }
  #endif
  
  /* DictGetItem */
    #if PY_MAJOR_VERSION >= 3 && !CYTHON_COMPILING_IN_PYPY
  static PyObject *__Pyx_PyDict_GetItem(PyObject *d, PyObject* key) {
      PyObject *value;
      value = PyDict_GetItemWithError(d, key);
      if (unlikely(!value)) {
          if (!PyErr_Occurred()) {
              if (unlikely(PyTuple_Check(key))) {
                  PyObject* args = PyTuple_Pack(1, key);
                  if (likely(args)) {
                      PyErr_SetObject(PyExc_KeyError, args);
                      Py_DECREF(args);
                  }
              } else {
                  PyErr_SetObject(PyExc_KeyError, key);
              }
          }
          return NULL;
      }
      Py_INCREF(value);
      return value;
  }
  #endif
  
  /* RaiseNoneIterError */
    static CYTHON_INLINE void __Pyx_RaiseNoneNotIterableError(void) {
      PyErr_SetString(PyExc_TypeError, "'NoneType' object is not iterable");
  }
  
  /* GetTopmostException */
    #if CYTHON_USE_EXC_INFO_STACK
  static _PyErr_StackItem *
  __Pyx_PyErr_GetTopmostException(PyThreadState *tstate)
  {
      _PyErr_StackItem *exc_info = tstate->exc_info;
      while ((exc_info->exc_type == NULL || exc_info->exc_type == Py_None) &&
             exc_info->previous_item != NULL)
      {
          exc_info = exc_info->previous_item;
      }
      return exc_info;
  }
  #endif
  
  /* SaveResetException */
    #if CYTHON_FAST_THREAD_STATE
  static CYTHON_INLINE void __Pyx__ExceptionSave(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb) {
      #if CYTHON_USE_EXC_INFO_STACK
      _PyErr_StackItem *exc_info = __Pyx_PyErr_GetTopmostException(tstate);
      *type = exc_info->exc_type;
      *value = exc_info->exc_value;
      *tb = exc_info->exc_traceback;
      #else
      *type = tstate->exc_type;
      *value = tstate->exc_value;
      *tb = tstate->exc_traceback;
      #endif
      Py_XINCREF(*type);
      Py_XINCREF(*value);
      Py_XINCREF(*tb);
  }
  static CYTHON_INLINE void __Pyx__ExceptionReset(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb) {
      PyObject *tmp_type, *tmp_value, *tmp_tb;
      #if CYTHON_USE_EXC_INFO_STACK
      _PyErr_StackItem *exc_info = tstate->exc_info;
      tmp_type = exc_info->exc_type;
      tmp_value = exc_info->exc_value;
      tmp_tb = exc_info->exc_traceback;
      exc_info->exc_type = type;
      exc_info->exc_value = value;
      exc_info->exc_traceback = tb;
      #else
      tmp_type = tstate->exc_type;
      tmp_value = tstate->exc_value;
      tmp_tb = tstate->exc_traceback;
      tstate->exc_type = type;
      tstate->exc_value = value;
      tstate->exc_traceback = tb;
      #endif
      Py_XDECREF(tmp_type);
      Py_XDECREF(tmp_value);
      Py_XDECREF(tmp_tb);
  }
  #endif
  
  /* PyErrExceptionMatches */
    #if CYTHON_FAST_THREAD_STATE
  static int __Pyx_PyErr_ExceptionMatchesTuple(PyObject *exc_type, PyObject *tuple) {
      Py_ssize_t i, n;
      n = PyTuple_GET_SIZE(tuple);
  #if PY_MAJOR_VERSION >= 3
      for (i=0; i<n; i++) {
          if (exc_type == PyTuple_GET_ITEM(tuple, i)) return 1;
      }
  #endif
      for (i=0; i<n; i++) {
          if (__Pyx_PyErr_GivenExceptionMatches(exc_type, PyTuple_GET_ITEM(tuple, i))) return 1;
      }
      return 0;
  }
  static CYTHON_INLINE int __Pyx_PyErr_ExceptionMatchesInState(PyThreadState* tstate, PyObject* err) {
      PyObject *exc_type = tstate->curexc_type;
      if (exc_type == err) return 1;
      if (unlikely(!exc_type)) return 0;
      if (unlikely(PyTuple_Check(err)))
          return __Pyx_PyErr_ExceptionMatchesTuple(exc_type, err);
      return __Pyx_PyErr_GivenExceptionMatches(exc_type, err);
  }
  #endif
  
  /* GetException */
    #if CYTHON_FAST_THREAD_STATE
  static int __Pyx__GetException(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb)
  #else
  static int __Pyx_GetException(PyObject **type, PyObject **value, PyObject **tb)
  #endif
  {
      PyObject *local_type, *local_value, *local_tb;
  #if CYTHON_FAST_THREAD_STATE
      PyObject *tmp_type, *tmp_value, *tmp_tb;
      local_type = tstate->curexc_type;
      local_value = tstate->curexc_value;
      local_tb = tstate->curexc_traceback;
      tstate->curexc_type = 0;
      tstate->curexc_value = 0;
      tstate->curexc_traceback = 0;
  #else
      PyErr_Fetch(&local_type, &local_value, &local_tb);
  #endif
      PyErr_NormalizeException(&local_type, &local_value, &local_tb);
  #if CYTHON_FAST_THREAD_STATE
      if (unlikely(tstate->curexc_type))
  #else
      if (unlikely(PyErr_Occurred()))
  #endif
          goto bad;
      #if PY_MAJOR_VERSION >= 3
      if (local_tb) {
          if (unlikely(PyException_SetTraceback(local_value, local_tb) < 0))
              goto bad;
      }
      #endif
      Py_XINCREF(local_tb);
      Py_XINCREF(local_type);
      Py_XINCREF(local_value);
      *type = local_type;
      *value = local_value;
      *tb = local_tb;
  #if CYTHON_FAST_THREAD_STATE
      #if CYTHON_USE_EXC_INFO_STACK
      {
          _PyErr_StackItem *exc_info = tstate->exc_info;
          tmp_type = exc_info->exc_type;
          tmp_value = exc_info->exc_value;
          tmp_tb = exc_info->exc_traceback;
          exc_info->exc_type = local_type;
          exc_info->exc_value = local_value;
          exc_info->exc_traceback = local_tb;
      }
      #else
      tmp_type = tstate->exc_type;
      tmp_value = tstate->exc_value;
      tmp_tb = tstate->exc_traceback;
      tstate->exc_type = local_type;
      tstate->exc_value = local_value;
      tstate->exc_traceback = local_tb;
      #endif
      Py_XDECREF(tmp_type);
      Py_XDECREF(tmp_value);
      Py_XDECREF(tmp_tb);
  #else
      PyErr_SetExcInfo(local_type, local_value, local_tb);
  #endif
      return 0;
  bad:
      *type = 0;
      *value = 0;
      *tb = 0;
      Py_XDECREF(local_type);
      Py_XDECREF(local_value);
      Py_XDECREF(local_tb);
      return -1;
  }
  
  /* TypeImport */
    #ifndef __PYX_HAVE_RT_ImportType
  #define __PYX_HAVE_RT_ImportType
  static PyTypeObject *__Pyx_ImportType(PyObject *module, const char *module_name, const char *class_name,
      size_t size, enum __Pyx_ImportType_CheckSize check_size)
  {
      PyObject *result = 0;
      char warning[200];
      Py_ssize_t basicsize;
  #ifdef Py_LIMITED_API
      PyObject *py_basicsize;
  #endif
      result = PyObject_GetAttrString(module, class_name);
      if (!result)
          goto bad;
      if (!PyType_Check(result)) {
          PyErr_Format(PyExc_TypeError,
              "%.200s.%.200s is not a type object",
              module_name, class_name);
          goto bad;
      }
  #ifndef Py_LIMITED_API
      basicsize = ((PyTypeObject *)result)->tp_basicsize;
  #else
      py_basicsize = PyObject_GetAttrString(result, "__basicsize__");
      if (!py_basicsize)
          goto bad;
      basicsize = PyLong_AsSsize_t(py_basicsize);
      Py_DECREF(py_basicsize);
      py_basicsize = 0;
      if (basicsize == (Py_ssize_t)-1 && PyErr_Occurred())
          goto bad;
  #endif
      if ((size_t)basicsize < size) {
          PyErr_Format(PyExc_ValueError,
              "%.200s.%.200s size changed, may indicate binary incompatibility. "
              "Expected %zd from C header, got %zd from PyObject",
              module_name, class_name, size, basicsize);
          goto bad;
      }
      if (check_size == __Pyx_ImportType_CheckSize_Error && (size_t)basicsize != size) {
          PyErr_Format(PyExc_ValueError,
              "%.200s.%.200s size changed, may indicate binary incompatibility. "
              "Expected %zd from C header, got %zd from PyObject",
              module_name, class_name, size, basicsize);
          goto bad;
      }
      else if (check_size == __Pyx_ImportType_CheckSize_Warn && (size_t)basicsize > size) {
          PyOS_snprintf(warning, sizeof(warning),
              "%s.%s size changed, may indicate binary incompatibility. "
              "Expected %zd from C header, got %zd from PyObject",
              module_name, class_name, size, basicsize);
          if (PyErr_WarnEx(NULL, warning, 0) < 0) goto bad;
      }
      return (PyTypeObject *)result;
  bad:
      Py_XDECREF(result);
      return NULL;
  }
  #endif
  
  /* Import */
    static PyObject *__Pyx_Import(PyObject *name, PyObject *from_list, int level) {
      PyObject *empty_list = 0;
      PyObject *module = 0;
      PyObject *global_dict = 0;
      PyObject *empty_dict = 0;
      PyObject *list;
      #if PY_MAJOR_VERSION < 3
      PyObject *py_import;
      py_import = __Pyx_PyObject_GetAttrStr(__pyx_b, __pyx_n_s_import);
      if (!py_import)
          goto bad;
      #endif
      if (from_list)
          list = from_list;
      else {
          empty_list = PyList_New(0);
          if (!empty_list)
              goto bad;
          list = empty_list;
      }
      global_dict = PyModule_GetDict(__pyx_m);
      if (!global_dict)
          goto bad;
      empty_dict = PyDict_New();
      if (!empty_dict)
          goto bad;
      {
          #if PY_MAJOR_VERSION >= 3
          if (level == -1) {
              if (strchr(__Pyx_MODULE_NAME, '.')) {
                  module = PyImport_ImportModuleLevelObject(
                      name, global_dict, empty_dict, list, 1);
                  if (!module) {
                      if (!PyErr_ExceptionMatches(PyExc_ImportError))
                          goto bad;
                      PyErr_Clear();
                  }
              }
              level = 0;
          }
          #endif
          if (!module) {
              #if PY_MAJOR_VERSION < 3
              PyObject *py_level = PyInt_FromLong(level);
              if (!py_level)
                  goto bad;
              module = PyObject_CallFunctionObjArgs(py_import,
                  name, global_dict, empty_dict, list, py_level, (PyObject *)NULL);
              Py_DECREF(py_level);
              #else
              module = PyImport_ImportModuleLevelObject(
                  name, global_dict, empty_dict, list, level);
              #endif
          }
      }
  bad:
      #if PY_MAJOR_VERSION < 3
      Py_XDECREF(py_import);
      #endif
      Py_XDECREF(empty_list);
      Py_XDECREF(empty_dict);
      return module;
  }
  
  /* CLineInTraceback */
    #ifndef CYTHON_CLINE_IN_TRACEBACK
  static int __Pyx_CLineForTraceback(PyThreadState *tstate, int c_line) {
      PyObject *use_cline;
      PyObject *ptype, *pvalue, *ptraceback;
  #if CYTHON_COMPILING_IN_CPYTHON
      PyObject **cython_runtime_dict;
  #endif
      if (unlikely(!__pyx_cython_runtime)) {
          return c_line;
      }
      __Pyx_ErrFetchInState(tstate, &ptype, &pvalue, &ptraceback);
  #if CYTHON_COMPILING_IN_CPYTHON
      cython_runtime_dict = _PyObject_GetDictPtr(__pyx_cython_runtime);
      if (likely(cython_runtime_dict)) {
          __PYX_PY_DICT_LOOKUP_IF_MODIFIED(
              use_cline, *cython_runtime_dict,
              __Pyx_PyDict_GetItemStr(*cython_runtime_dict, __pyx_n_s_cline_in_traceback))
      } else
  #endif
      {
        PyObject *use_cline_obj = __Pyx_PyObject_GetAttrStr(__pyx_cython_runtime, __pyx_n_s_cline_in_traceback);
        if (use_cline_obj) {
          use_cline = PyObject_Not(use_cline_obj) ? Py_False : Py_True;
          Py_DECREF(use_cline_obj);
        } else {
          PyErr_Clear();
          use_cline = NULL;
        }
      }
      if (!use_cline) {
          c_line = 0;
          PyObject_SetAttr(__pyx_cython_runtime, __pyx_n_s_cline_in_traceback, Py_False);
      }
      else if (use_cline == Py_False || (use_cline != Py_True && PyObject_Not(use_cline) != 0)) {
          c_line = 0;
      }
      __Pyx_ErrRestoreInState(tstate, ptype, pvalue, ptraceback);
      return c_line;
  }
  #endif
  
  /* CodeObjectCache */
    static int __pyx_bisect_code_objects(__Pyx_CodeObjectCacheEntry* entries, int count, int code_line) {
      int start = 0, mid = 0, end = count - 1;
      if (end >= 0 && code_line > entries[end].code_line) {
          return count;
      }
      while (start < end) {
          mid = start + (end - start) / 2;
          if (code_line < entries[mid].code_line) {
              end = mid;
          } else if (code_line > entries[mid].code_line) {
               start = mid + 1;
          } else {
              return mid;
          }
      }
      if (code_line <= entries[mid].code_line) {
          return mid;
      } else {
          return mid + 1;
      }
  }
  static PyCodeObject *__pyx_find_code_object(int code_line) {
      PyCodeObject* code_object;
      int pos;
      if (unlikely(!code_line) || unlikely(!__pyx_code_cache.entries)) {
          return NULL;
      }
      pos = __pyx_bisect_code_objects(__pyx_code_cache.entries, __pyx_code_cache.count, code_line);
      if (unlikely(pos >= __pyx_code_cache.count) || unlikely(__pyx_code_cache.entries[pos].code_line != code_line)) {
          return NULL;
      }
      code_object = __pyx_code_cache.entries[pos].code_object;
      Py_INCREF(code_object);
      return code_object;
  }
  static void __pyx_insert_code_object(int code_line, PyCodeObject* code_object) {
      int pos, i;
      __Pyx_CodeObjectCacheEntry* entries = __pyx_code_cache.entries;
      if (unlikely(!code_line)) {
          return;
      }
      if (unlikely(!entries)) {
          entries = (__Pyx_CodeObjectCacheEntry*)PyMem_Malloc(64*sizeof(__Pyx_CodeObjectCacheEntry));
          if (likely(entries)) {
              __pyx_code_cache.entries = entries;
              __pyx_code_cache.max_count = 64;
              __pyx_code_cache.count = 1;
              entries[0].code_line = code_line;
              entries[0].code_object = code_object;
              Py_INCREF(code_object);
          }
          return;
      }
      pos = __pyx_bisect_code_objects(__pyx_code_cache.entries, __pyx_code_cache.count, code_line);
      if ((pos < __pyx_code_cache.count) && unlikely(__pyx_code_cache.entries[pos].code_line == code_line)) {
          PyCodeObject* tmp = entries[pos].code_object;
          entries[pos].code_object = code_object;
          Py_DECREF(tmp);
          return;
      }
      if (__pyx_code_cache.count == __pyx_code_cache.max_count) {
          int new_max = __pyx_code_cache.max_count + 64;
          entries = (__Pyx_CodeObjectCacheEntry*)PyMem_Realloc(
              __pyx_code_cache.entries, (size_t)new_max*sizeof(__Pyx_CodeObjectCacheEntry));
          if (unlikely(!entries)) {
              return;
          }
          __pyx_code_cache.entries = entries;
          __pyx_code_cache.max_count = new_max;
      }
      for (i=__pyx_code_cache.count; i>pos; i--) {
          entries[i] = entries[i-1];
      }
      entries[pos].code_line = code_line;
      entries[pos].code_object = code_object;
      __pyx_code_cache.count++;
      Py_INCREF(code_object);
  }
  
  /* AddTraceback */
    #include "compile.h"
  #include "frameobject.h"
  #include "traceback.h"
  static PyCodeObject* __Pyx_CreateCodeObjectForTraceback(
              const char *funcname, int c_line,
              int py_line, const char *filename) {
      PyCodeObject *py_code = 0;
      PyObject *py_srcfile = 0;
      PyObject *py_funcname = 0;
      #if PY_MAJOR_VERSION < 3
      py_srcfile = PyString_FromString(filename);
      #else
      py_srcfile = PyUnicode_FromString(filename);
      #endif
      if (!py_srcfile) goto bad;
      if (c_line) {
          #if PY_MAJOR_VERSION < 3
          py_funcname = PyString_FromFormat( "%s (%s:%d)", funcname, __pyx_cfilenm, c_line);
          #else
          py_funcname = PyUnicode_FromFormat( "%s (%s:%d)", funcname, __pyx_cfilenm, c_line);
          #endif
      }
      else {
          #if PY_MAJOR_VERSION < 3
          py_funcname = PyString_FromString(funcname);
          #else
          py_funcname = PyUnicode_FromString(funcname);
          #endif
      }
      if (!py_funcname) goto bad;
      py_code = __Pyx_PyCode_New(
          0,
          0,
          0,
          0,
          0,
          __pyx_empty_bytes, /*PyObject *code,*/
          __pyx_empty_tuple, /*PyObject *consts,*/
          __pyx_empty_tuple, /*PyObject *names,*/
          __pyx_empty_tuple, /*PyObject *varnames,*/
          __pyx_empty_tuple, /*PyObject *freevars,*/
          __pyx_empty_tuple, /*PyObject *cellvars,*/
          py_srcfile,   /*PyObject *filename,*/
          py_funcname,  /*PyObject *name,*/
          py_line,
          __pyx_empty_bytes  /*PyObject *lnotab*/
      );
      Py_DECREF(py_srcfile);
      Py_DECREF(py_funcname);
      return py_code;
  bad:
      Py_XDECREF(py_srcfile);
      Py_XDECREF(py_funcname);
      return NULL;
  }
  static void __Pyx_AddTraceback(const char *funcname, int c_line,
                                 int py_line, const char *filename) {
      PyCodeObject *py_code = 0;
      PyFrameObject *py_frame = 0;
      PyThreadState *tstate = __Pyx_PyThreadState_Current;
      if (c_line) {
          c_line = __Pyx_CLineForTraceback(tstate, c_line);
      }
      py_code = __pyx_find_code_object(c_line ? -c_line : py_line);
      if (!py_code) {
          py_code = __Pyx_CreateCodeObjectForTraceback(
              funcname, c_line, py_line, filename);
          if (!py_code) goto bad;
          __pyx_insert_code_object(c_line ? -c_line : py_line, py_code);
      }
      py_frame = PyFrame_New(
          tstate,            /*PyThreadState *tstate,*/
          py_code,           /*PyCodeObject *code,*/
          __pyx_d,    /*PyObject *globals,*/
          0                  /*PyObject *locals*/
      );
      if (!py_frame) goto bad;
      __Pyx_PyFrame_SetLineNumber(py_frame, py_line);
      PyTraceBack_Here(py_frame);
  bad:
      Py_XDECREF(py_code);
      Py_XDECREF(py_frame);
  }
  
  #if PY_MAJOR_VERSION < 3
  static int __Pyx_GetBuffer(PyObject *obj, Py_buffer *view, int flags) {
      if (PyObject_CheckBuffer(obj)) return PyObject_GetBuffer(obj, view, flags);
          if (__Pyx_TypeCheck(obj, __pyx_ptype_5numpy_ndarray)) return __pyx_pw_5numpy_7ndarray_1__getbuffer__(obj, view, flags);
      PyErr_Format(PyExc_TypeError, "'%.200s' does not have the buffer interface", Py_TYPE(obj)->tp_name);
      return -1;
  }
  static void __Pyx_ReleaseBuffer(Py_buffer *view) {
      PyObject *obj = view->obj;
      if (!obj) return;
      if (PyObject_CheckBuffer(obj)) {
          PyBuffer_Release(view);
          return;
      }
      if ((0)) {}
          else if (__Pyx_TypeCheck(obj, __pyx_ptype_5numpy_ndarray)) __pyx_pw_5numpy_7ndarray_3__releasebuffer__(obj, view);
      view->obj = NULL;
      Py_DECREF(obj);
  }
  #endif
  
  
    /* CIntToPy */
    static CYTHON_INLINE PyObject* __Pyx_PyInt_From_Py_intptr_t(Py_intptr_t value) {
      const Py_intptr_t neg_one = (Py_intptr_t) ((Py_intptr_t) 0 - (Py_intptr_t) 1), const_zero = (Py_intptr_t) 0;
      const int is_unsigned = neg_one > const_zero;
      if (is_unsigned) {
          if (sizeof(Py_intptr_t) < sizeof(long)) {
              return PyInt_FromLong((long) value);
          } else if (sizeof(Py_intptr_t) <= sizeof(unsigned long)) {
              return PyLong_FromUnsignedLong((unsigned long) value);
  #ifdef HAVE_LONG_LONG
          } else if (sizeof(Py_intptr_t) <= sizeof(unsigned PY_LONG_LONG)) {
              return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value);
  #endif
          }
      } else {
          if (sizeof(Py_intptr_t) <= sizeof(long)) {
              return PyInt_FromLong((long) value);
  #ifdef HAVE_LONG_LONG
          } else if (sizeof(Py_intptr_t) <= sizeof(PY_LONG_LONG)) {
              return PyLong_FromLongLong((PY_LONG_LONG) value);
  #endif
          }
      }
      {
          int one = 1; int little = (int)*(unsigned char *)&one;
          unsigned char *bytes = (unsigned char *)&value;
          return _PyLong_FromByteArray(bytes, sizeof(Py_intptr_t),
                                       little, !is_unsigned);
      }
  }
  
  /* 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_long(long value) {
      const long neg_one = (long) ((long) 0 - (long) 1), const_zero = (long) 0;
      const int is_unsigned = neg_one > const_zero;
      if (is_unsigned) {
          if (sizeof(long) < sizeof(long)) {
              return PyInt_FromLong((long) value);
          } else if (sizeof(long) <= sizeof(unsigned long)) {
              return PyLong_FromUnsignedLong((unsigned long) value);
  #ifdef HAVE_LONG_LONG
          } else if (sizeof(long) <= sizeof(unsigned PY_LONG_LONG)) {
              return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value);
  #endif
          }
      } else {
          if (sizeof(long) <= sizeof(long)) {
              return PyInt_FromLong((long) value);
  #ifdef HAVE_LONG_LONG
          } else if (sizeof(long) <= sizeof(PY_LONG_LONG)) {
              return PyLong_FromLongLong((PY_LONG_LONG) value);
  #endif
          }
      }
      {
          int one = 1; int little = (int)*(unsigned char *)&one;
          unsigned char *bytes = (unsigned char *)&value;
          return _PyLong_FromByteArray(bytes, sizeof(long),
                                       little, !is_unsigned);
      }
  }
  
  /* Declarations */
    #if CYTHON_CCOMPLEX
    #ifdef __cplusplus
      static CYTHON_INLINE __pyx_t_float_complex __pyx_t_float_complex_from_parts(float x, float y) {
        return ::std::complex< float >(x, y);
      }
    #else
      static CYTHON_INLINE __pyx_t_float_complex __pyx_t_float_complex_from_parts(float x, float y) {
        return x + y*(__pyx_t_float_complex)_Complex_I;
      }
    #endif
  #else
      static CYTHON_INLINE __pyx_t_float_complex __pyx_t_float_complex_from_parts(float x, float y) {
        __pyx_t_float_complex z;
        z.real = x;
        z.imag = y;
        return z;
      }
  #endif
  
  /* Arithmetic */
    #if CYTHON_CCOMPLEX
  #else
      static CYTHON_INLINE int __Pyx_c_eq_float(__pyx_t_float_complex a, __pyx_t_float_complex b) {
         return (a.real == b.real) && (a.imag == b.imag);
      }
      static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_sum_float(__pyx_t_float_complex a, __pyx_t_float_complex b) {
          __pyx_t_float_complex z;
          z.real = a.real + b.real;
          z.imag = a.imag + b.imag;
          return z;
      }
      static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_diff_float(__pyx_t_float_complex a, __pyx_t_float_complex b) {
          __pyx_t_float_complex z;
          z.real = a.real - b.real;
          z.imag = a.imag - b.imag;
          return z;
      }
      static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_prod_float(__pyx_t_float_complex a, __pyx_t_float_complex b) {
          __pyx_t_float_complex z;
          z.real = a.real * b.real - a.imag * b.imag;
          z.imag = a.real * b.imag + a.imag * b.real;
          return z;
      }
      #if 1
      static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_quot_float(__pyx_t_float_complex a, __pyx_t_float_complex b) {
          if (b.imag == 0) {
              return __pyx_t_float_complex_from_parts(a.real / b.real, a.imag / b.real);
          } else if (fabsf(b.real) >= fabsf(b.imag)) {
              if (b.real == 0 && b.imag == 0) {
                  return __pyx_t_float_complex_from_parts(a.real / b.real, a.imag / b.imag);
              } else {
                  float r = b.imag / b.real;
                  float s = (float)(1.0) / (b.real + b.imag * r);
                  return __pyx_t_float_complex_from_parts(
                      (a.real + a.imag * r) * s, (a.imag - a.real * r) * s);
              }
          } else {
              float r = b.real / b.imag;
              float s = (float)(1.0) / (b.imag + b.real * r);
              return __pyx_t_float_complex_from_parts(
                  (a.real * r + a.imag) * s, (a.imag * r - a.real) * s);
          }
      }
      #else
      static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_quot_float(__pyx_t_float_complex a, __pyx_t_float_complex b) {
          if (b.imag == 0) {
              return __pyx_t_float_complex_from_parts(a.real / b.real, a.imag / b.real);
          } else {
              float denom = b.real * b.real + b.imag * b.imag;
              return __pyx_t_float_complex_from_parts(
                  (a.real * b.real + a.imag * b.imag) / denom,
                  (a.imag * b.real - a.real * b.imag) / denom);
          }
      }
      #endif
      static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_neg_float(__pyx_t_float_complex a) {
          __pyx_t_float_complex z;
          z.real = -a.real;
          z.imag = -a.imag;
          return z;
      }
      static CYTHON_INLINE int __Pyx_c_is_zero_float(__pyx_t_float_complex a) {
         return (a.real == 0) && (a.imag == 0);
      }
      static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_conj_float(__pyx_t_float_complex a) {
          __pyx_t_float_complex z;
          z.real =  a.real;
          z.imag = -a.imag;
          return z;
      }
      #if 1
          static CYTHON_INLINE float __Pyx_c_abs_float(__pyx_t_float_complex z) {
            #if !defined(HAVE_HYPOT) || defined(_MSC_VER)
              return sqrtf(z.real*z.real + z.imag*z.imag);
            #else
              return hypotf(z.real, z.imag);
            #endif
          }
          static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_pow_float(__pyx_t_float_complex a, __pyx_t_float_complex b) {
              __pyx_t_float_complex z;
              float r, lnr, theta, z_r, z_theta;
              if (b.imag == 0 && b.real == (int)b.real) {
                  if (b.real < 0) {
                      float denom = a.real * a.real + a.imag * a.imag;
                      a.real = a.real / denom;
                      a.imag = -a.imag / denom;
                      b.real = -b.real;
                  }
                  switch ((int)b.real) {
                      case 0:
                          z.real = 1;
                          z.imag = 0;
                          return z;
                      case 1:
                          return a;
                      case 2:
                          z = __Pyx_c_prod_float(a, a);
                          return __Pyx_c_prod_float(a, a);
                      case 3:
                          z = __Pyx_c_prod_float(a, a);
                          return __Pyx_c_prod_float(z, a);
                      case 4:
                          z = __Pyx_c_prod_float(a, a);
                          return __Pyx_c_prod_float(z, z);
                  }
              }
              if (a.imag == 0) {
                  if (a.real == 0) {
                      return a;
                  } else if (b.imag == 0) {
                      z.real = powf(a.real, b.real);
                      z.imag = 0;
                      return z;
                  } else if (a.real > 0) {
                      r = a.real;
                      theta = 0;
                  } else {
                      r = -a.real;
                      theta = atan2f(0.0, -1.0);
                  }
              } else {
                  r = __Pyx_c_abs_float(a);
                  theta = atan2f(a.imag, a.real);
              }
              lnr = logf(r);
              z_r = expf(lnr * b.real - theta * b.imag);
              z_theta = theta * b.real + lnr * b.imag;
              z.real = z_r * cosf(z_theta);
              z.imag = z_r * sinf(z_theta);
              return z;
          }
      #endif
  #endif
  
  /* Declarations */
    #if CYTHON_CCOMPLEX
    #ifdef __cplusplus
      static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double x, double y) {
        return ::std::complex< double >(x, y);
      }
    #else
      static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double x, double y) {
        return x + y*(__pyx_t_double_complex)_Complex_I;
      }
    #endif
  #else
      static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double x, double y) {
        __pyx_t_double_complex z;
        z.real = x;
        z.imag = y;
        return z;
      }
  #endif
  
  /* Arithmetic */
    #if CYTHON_CCOMPLEX
  #else
      static CYTHON_INLINE int __Pyx_c_eq_double(__pyx_t_double_complex a, __pyx_t_double_complex b) {
         return (a.real == b.real) && (a.imag == b.imag);
      }
      static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_sum_double(__pyx_t_double_complex a, __pyx_t_double_complex b) {
          __pyx_t_double_complex z;
          z.real = a.real + b.real;
          z.imag = a.imag + b.imag;
          return z;
      }
      static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_diff_double(__pyx_t_double_complex a, __pyx_t_double_complex b) {
          __pyx_t_double_complex z;
          z.real = a.real - b.real;
          z.imag = a.imag - b.imag;
          return z;
      }
      static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_prod_double(__pyx_t_double_complex a, __pyx_t_double_complex b) {
          __pyx_t_double_complex z;
          z.real = a.real * b.real - a.imag * b.imag;
          z.imag = a.real * b.imag + a.imag * b.real;
          return z;
      }
      #if 1
      static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_quot_double(__pyx_t_double_complex a, __pyx_t_double_complex b) {
          if (b.imag == 0) {
              return __pyx_t_double_complex_from_parts(a.real / b.real, a.imag / b.real);
          } else if (fabs(b.real) >= fabs(b.imag)) {
              if (b.real == 0 && b.imag == 0) {
                  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);
                  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);
              return __pyx_t_double_complex_from_parts(
                  (a.real * r + a.imag) * s, (a.imag * r - a.real) * s);
          }
      }
      #else
      static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_quot_double(__pyx_t_double_complex a, __pyx_t_double_complex b) {
          if (b.imag == 0) {
              return __pyx_t_double_complex_from_parts(a.real / b.real, a.imag / b.real);
          } else {
              double denom = b.real * b.real + b.imag * b.imag;
              return __pyx_t_double_complex_from_parts(
                  (a.real * b.real + a.imag * b.imag) / denom,
                  (a.imag * b.real - a.real * b.imag) / denom);
          }
      }
      #endif
      static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_neg_double(__pyx_t_double_complex a) {
          __pyx_t_double_complex z;
          z.real = -a.real;
          z.imag = -a.imag;
          return z;
      }
      static CYTHON_INLINE int __Pyx_c_is_zero_double(__pyx_t_double_complex a) {
         return (a.real == 0) && (a.imag == 0);
      }
      static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_conj_double(__pyx_t_double_complex a) {
          __pyx_t_double_complex z;
          z.real =  a.real;
          z.imag = -a.imag;
          return z;
      }
      #if 1
          static CYTHON_INLINE double __Pyx_c_abs_double(__pyx_t_double_complex z) {
            #if !defined(HAVE_HYPOT) || defined(_MSC_VER)
              return sqrt(z.real*z.real + z.imag*z.imag);
            #else
              return hypot(z.real, z.imag);
            #endif
          }
          static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_pow_double(__pyx_t_double_complex a, __pyx_t_double_complex b) {
              __pyx_t_double_complex z;
              double r, lnr, theta, z_r, z_theta;
              if (b.imag == 0 && b.real == (int)b.real) {
                  if (b.real < 0) {
                      double denom = a.real * a.real + a.imag * a.imag;
                      a.real = a.real / denom;
                      a.imag = -a.imag / denom;
                      b.real = -b.real;
                  }
                  switch ((int)b.real) {
                      case 0:
                          z.real = 1;
                          z.imag = 0;
                          return z;
                      case 1:
                          return a;
                      case 2:
                          z = __Pyx_c_prod_double(a, a);
                          return __Pyx_c_prod_double(a, a);
                      case 3:
                          z = __Pyx_c_prod_double(a, a);
                          return __Pyx_c_prod_double(z, a);
                      case 4:
                          z = __Pyx_c_prod_double(a, a);
                          return __Pyx_c_prod_double(z, z);
                  }
              }
              if (a.imag == 0) {
                  if (a.real == 0) {
                      return a;
                  } else if (b.imag == 0) {
                      z.real = pow(a.real, b.real);
                      z.imag = 0;
                      return z;
                  } else if (a.real > 0) {
                      r = a.real;
                      theta = 0;
                  } else {
                      r = -a.real;
                      theta = atan2(0.0, -1.0);
                  }
              } else {
                  r = __Pyx_c_abs_double(a);
                  theta = atan2(a.imag, a.real);
              }
              lnr = log(r);
              z_r = exp(lnr * b.real - theta * b.imag);
              z_theta = theta * b.real + lnr * b.imag;
              z.real = z_r * cos(z_theta);
              z.imag = z_r * sin(z_theta);
              return z;
          }
      #endif
  #endif
  
  /* CIntToPy */
    static CYTHON_INLINE PyObject* __Pyx_PyInt_From_int(int value) {
      const int neg_one = (int) ((int) 0 - (int) 1), const_zero = (int) 0;
      const int is_unsigned = neg_one > const_zero;
      if (is_unsigned) {
          if (sizeof(int) < sizeof(long)) {
              return PyInt_FromLong((long) value);
          } else if (sizeof(int) <= sizeof(unsigned long)) {
              return PyLong_FromUnsignedLong((unsigned long) value);
  #ifdef HAVE_LONG_LONG
          } else if (sizeof(int) <= sizeof(unsigned PY_LONG_LONG)) {
              return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value);
  #endif
          }
      } else {
          if (sizeof(int) <= sizeof(long)) {
              return PyInt_FromLong((long) value);
  #ifdef HAVE_LONG_LONG
          } else if (sizeof(int) <= sizeof(PY_LONG_LONG)) {
              return PyLong_FromLongLong((PY_LONG_LONG) value);
  #endif
          }
      }
      {
          int one = 1; int little = (int)*(unsigned char *)&one;
          unsigned char *bytes = (unsigned char *)&value;
          return _PyLong_FromByteArray(bytes, sizeof(int),
                                       little, !is_unsigned);
      }
  }
  
  /* CIntToPy */
    static CYTHON_INLINE PyObject* __Pyx_PyInt_From_enum__NPY_TYPES(enum NPY_TYPES value) {
      const enum NPY_TYPES neg_one = (enum NPY_TYPES) ((enum NPY_TYPES) 0 - (enum NPY_TYPES) 1), const_zero = (enum NPY_TYPES) 0;
      const int is_unsigned = neg_one > const_zero;
      if (is_unsigned) {
          if (sizeof(enum NPY_TYPES) < sizeof(long)) {
              return PyInt_FromLong((long) value);
          } else if (sizeof(enum NPY_TYPES) <= sizeof(unsigned long)) {
              return PyLong_FromUnsignedLong((unsigned long) value);
  #ifdef HAVE_LONG_LONG
          } else if (sizeof(enum NPY_TYPES) <= sizeof(unsigned PY_LONG_LONG)) {
              return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value);
  #endif
          }
      } else {
          if (sizeof(enum NPY_TYPES) <= sizeof(long)) {
              return PyInt_FromLong((long) value);
  #ifdef HAVE_LONG_LONG
          } else if (sizeof(enum NPY_TYPES) <= sizeof(PY_LONG_LONG)) {
              return PyLong_FromLongLong((PY_LONG_LONG) value);
  #endif
          }
      }
      {
          int one = 1; int little = (int)*(unsigned char *)&one;
          unsigned char *bytes = (unsigned char *)&value;
          return _PyLong_FromByteArray(bytes, sizeof(enum NPY_TYPES),
                                       little, !is_unsigned);
      }
  }
  
  /* CIntFromPy */
    static CYTHON_INLINE Py_intptr_t __Pyx_PyInt_As_Py_intptr_t(PyObject *x) {
      const Py_intptr_t neg_one = (Py_intptr_t) ((Py_intptr_t) 0 - (Py_intptr_t) 1), const_zero = (Py_intptr_t) 0;
      const int is_unsigned = neg_one > const_zero;
  #if PY_MAJOR_VERSION < 3
      if (likely(PyInt_Check(x))) {
          if (sizeof(Py_intptr_t) < sizeof(long)) {
              __PYX_VERIFY_RETURN_INT(Py_intptr_t, long, PyInt_AS_LONG(x))
          } else {
              long val = PyInt_AS_LONG(x);
              if (is_unsigned && unlikely(val < 0)) {
                  goto raise_neg_overflow;
              }
              return (Py_intptr_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 (Py_intptr_t) 0;
                  case  1: __PYX_VERIFY_RETURN_INT(Py_intptr_t, digit, digits[0])
                  case 2:
                      if (8 * sizeof(Py_intptr_t) > 1 * PyLong_SHIFT) {
                          if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
                              __PYX_VERIFY_RETURN_INT(Py_intptr_t, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                          } else if (8 * sizeof(Py_intptr_t) >= 2 * PyLong_SHIFT) {
                              return (Py_intptr_t) (((((Py_intptr_t)digits[1]) << PyLong_SHIFT) | (Py_intptr_t)digits[0]));
                          }
                      }
                      break;
                  case 3:
                      if (8 * sizeof(Py_intptr_t) > 2 * PyLong_SHIFT) {
                          if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
                              __PYX_VERIFY_RETURN_INT(Py_intptr_t, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                          } else if (8 * sizeof(Py_intptr_t) >= 3 * PyLong_SHIFT) {
                              return (Py_intptr_t) (((((((Py_intptr_t)digits[2]) << PyLong_SHIFT) | (Py_intptr_t)digits[1]) << PyLong_SHIFT) | (Py_intptr_t)digits[0]));
                          }
                      }
                      break;
                  case 4:
                      if (8 * sizeof(Py_intptr_t) > 3 * PyLong_SHIFT) {
                          if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
                              __PYX_VERIFY_RETURN_INT(Py_intptr_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(Py_intptr_t) >= 4 * PyLong_SHIFT) {
                              return (Py_intptr_t) (((((((((Py_intptr_t)digits[3]) << PyLong_SHIFT) | (Py_intptr_t)digits[2]) << PyLong_SHIFT) | (Py_intptr_t)digits[1]) << PyLong_SHIFT) | (Py_intptr_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 (Py_intptr_t) -1;
                  if (unlikely(result == 1))
                      goto raise_neg_overflow;
              }
  #endif
              if (sizeof(Py_intptr_t) <= sizeof(unsigned long)) {
                  __PYX_VERIFY_RETURN_INT_EXC(Py_intptr_t, unsigned long, PyLong_AsUnsignedLong(x))
  #ifdef HAVE_LONG_LONG
              } else if (sizeof(Py_intptr_t) <= sizeof(unsigned PY_LONG_LONG)) {
                  __PYX_VERIFY_RETURN_INT_EXC(Py_intptr_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 (Py_intptr_t) 0;
                  case -1: __PYX_VERIFY_RETURN_INT(Py_intptr_t, sdigit, (sdigit) (-(sdigit)digits[0]))
                  case  1: __PYX_VERIFY_RETURN_INT(Py_intptr_t,  digit, +digits[0])
                  case -2:
                      if (8 * sizeof(Py_intptr_t) - 1 > 1 * PyLong_SHIFT) {
                          if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
                              __PYX_VERIFY_RETURN_INT(Py_intptr_t, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                          } else if (8 * sizeof(Py_intptr_t) - 1 > 2 * PyLong_SHIFT) {
                              return (Py_intptr_t) (((Py_intptr_t)-1)*(((((Py_intptr_t)digits[1]) << PyLong_SHIFT) | (Py_intptr_t)digits[0])));
                          }
                      }
                      break;
                  case 2:
                      if (8 * sizeof(Py_intptr_t) > 1 * PyLong_SHIFT) {
                          if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
                              __PYX_VERIFY_RETURN_INT(Py_intptr_t, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                          } else if (8 * sizeof(Py_intptr_t) - 1 > 2 * PyLong_SHIFT) {
                              return (Py_intptr_t) ((((((Py_intptr_t)digits[1]) << PyLong_SHIFT) | (Py_intptr_t)digits[0])));
                          }
                      }
                      break;
                  case -3:
                      if (8 * sizeof(Py_intptr_t) - 1 > 2 * PyLong_SHIFT) {
                          if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
                              __PYX_VERIFY_RETURN_INT(Py_intptr_t, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                          } else if (8 * sizeof(Py_intptr_t) - 1 > 3 * PyLong_SHIFT) {
                              return (Py_intptr_t) (((Py_intptr_t)-1)*(((((((Py_intptr_t)digits[2]) << PyLong_SHIFT) | (Py_intptr_t)digits[1]) << PyLong_SHIFT) | (Py_intptr_t)digits[0])));
                          }
                      }
                      break;
                  case 3:
                      if (8 * sizeof(Py_intptr_t) > 2 * PyLong_SHIFT) {
                          if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
                              __PYX_VERIFY_RETURN_INT(Py_intptr_t, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                          } else if (8 * sizeof(Py_intptr_t) - 1 > 3 * PyLong_SHIFT) {
                              return (Py_intptr_t) ((((((((Py_intptr_t)digits[2]) << PyLong_SHIFT) | (Py_intptr_t)digits[1]) << PyLong_SHIFT) | (Py_intptr_t)digits[0])));
                          }
                      }
                      break;
                  case -4:
                      if (8 * sizeof(Py_intptr_t) - 1 > 3 * PyLong_SHIFT) {
                          if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
                              __PYX_VERIFY_RETURN_INT(Py_intptr_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(Py_intptr_t) - 1 > 4 * PyLong_SHIFT) {
                              return (Py_intptr_t) (((Py_intptr_t)-1)*(((((((((Py_intptr_t)digits[3]) << PyLong_SHIFT) | (Py_intptr_t)digits[2]) << PyLong_SHIFT) | (Py_intptr_t)digits[1]) << PyLong_SHIFT) | (Py_intptr_t)digits[0])));
                          }
                      }
                      break;
                  case 4:
                      if (8 * sizeof(Py_intptr_t) > 3 * PyLong_SHIFT) {
                          if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
                              __PYX_VERIFY_RETURN_INT(Py_intptr_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(Py_intptr_t) - 1 > 4 * PyLong_SHIFT) {
                              return (Py_intptr_t) ((((((((((Py_intptr_t)digits[3]) << PyLong_SHIFT) | (Py_intptr_t)digits[2]) << PyLong_SHIFT) | (Py_intptr_t)digits[1]) << PyLong_SHIFT) | (Py_intptr_t)digits[0])));
                          }
                      }
                      break;
              }
  #endif
              if (sizeof(Py_intptr_t) <= sizeof(long)) {
                  __PYX_VERIFY_RETURN_INT_EXC(Py_intptr_t, long, PyLong_AsLong(x))
  #ifdef HAVE_LONG_LONG
              } else if (sizeof(Py_intptr_t) <= sizeof(PY_LONG_LONG)) {
                  __PYX_VERIFY_RETURN_INT_EXC(Py_intptr_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
              Py_intptr_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 (Py_intptr_t) -1;
          }
      } else {
          Py_intptr_t val;
          PyObject *tmp = __Pyx_PyNumber_IntOrLong(x);
          if (!tmp) return (Py_intptr_t) -1;
          val = __Pyx_PyInt_As_Py_intptr_t(tmp);
          Py_DECREF(tmp);
          return val;
      }
  raise_overflow:
      PyErr_SetString(PyExc_OverflowError,
          "value too large to convert to Py_intptr_t");
      return (Py_intptr_t) -1;
  raise_neg_overflow:
      PyErr_SetString(PyExc_OverflowError,
          "can't convert negative value to Py_intptr_t");
      return (Py_intptr_t) -1;
  }
  
  /* CIntFromPy */
    static CYTHON_INLINE int __Pyx_PyInt_As_int(PyObject *x) {
      const int neg_one = (int) ((int) 0 - (int) 1), const_zero = (int) 0;
      const int is_unsigned = neg_one > const_zero;
  #if PY_MAJOR_VERSION < 3
      if (likely(PyInt_Check(x))) {
          if (sizeof(int) < sizeof(long)) {
              __PYX_VERIFY_RETURN_INT(int, long, PyInt_AS_LONG(x))
          } else {
              long val = PyInt_AS_LONG(x);
              if (is_unsigned && unlikely(val < 0)) {
                  goto raise_neg_overflow;
              }
              return (int) 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 (int) 0;
                  case  1: __PYX_VERIFY_RETURN_INT(int, digit, digits[0])
                  case 2:
                      if (8 * sizeof(int) > 1 * PyLong_SHIFT) {
                          if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
                              __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                          } else if (8 * sizeof(int) >= 2 * PyLong_SHIFT) {
                              return (int) (((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0]));
                          }
                      }
                      break;
                  case 3:
                      if (8 * sizeof(int) > 2 * PyLong_SHIFT) {
                          if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
                              __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                          } else if (8 * sizeof(int) >= 3 * PyLong_SHIFT) {
                              return (int) (((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0]));
                          }
                      }
                      break;
                  case 4:
                      if (8 * sizeof(int) > 3 * PyLong_SHIFT) {
                          if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
                              __PYX_VERIFY_RETURN_INT(int, 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(int) >= 4 * PyLong_SHIFT) {
                              return (int) (((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)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 (int) -1;
                  if (unlikely(result == 1))
                      goto raise_neg_overflow;
              }
  #endif
              if (sizeof(int) <= sizeof(unsigned long)) {
                  __PYX_VERIFY_RETURN_INT_EXC(int, unsigned long, PyLong_AsUnsignedLong(x))
  #ifdef HAVE_LONG_LONG
              } else if (sizeof(int) <= sizeof(unsigned PY_LONG_LONG)) {
                  __PYX_VERIFY_RETURN_INT_EXC(int, 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 (int) 0;
                  case -1: __PYX_VERIFY_RETURN_INT(int, sdigit, (sdigit) (-(sdigit)digits[0]))
                  case  1: __PYX_VERIFY_RETURN_INT(int,  digit, +digits[0])
                  case -2:
                      if (8 * sizeof(int) - 1 > 1 * PyLong_SHIFT) {
                          if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
                              __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                          } else if (8 * sizeof(int) - 1 > 2 * PyLong_SHIFT) {
                              return (int) (((int)-1)*(((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
                          }
                      }
                      break;
                  case 2:
                      if (8 * sizeof(int) > 1 * PyLong_SHIFT) {
                          if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
                              __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                          } else if (8 * sizeof(int) - 1 > 2 * PyLong_SHIFT) {
                              return (int) ((((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
                          }
                      }
                      break;
                  case -3:
                      if (8 * sizeof(int) - 1 > 2 * PyLong_SHIFT) {
                          if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
                              __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                          } else if (8 * sizeof(int) - 1 > 3 * PyLong_SHIFT) {
                              return (int) (((int)-1)*(((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
                          }
                      }
                      break;
                  case 3:
                      if (8 * sizeof(int) > 2 * PyLong_SHIFT) {
                          if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
                              __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                          } else if (8 * sizeof(int) - 1 > 3 * PyLong_SHIFT) {
                              return (int) ((((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
                          }
                      }
                      break;
                  case -4:
                      if (8 * sizeof(int) - 1 > 3 * PyLong_SHIFT) {
                          if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
                              __PYX_VERIFY_RETURN_INT(int, 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(int) - 1 > 4 * PyLong_SHIFT) {
                              return (int) (((int)-1)*(((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
                          }
                      }
                      break;
                  case 4:
                      if (8 * sizeof(int) > 3 * PyLong_SHIFT) {
                          if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
                              __PYX_VERIFY_RETURN_INT(int, 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(int) - 1 > 4 * PyLong_SHIFT) {
                              return (int) ((((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
                          }
                      }
                      break;
              }
  #endif
              if (sizeof(int) <= sizeof(long)) {
                  __PYX_VERIFY_RETURN_INT_EXC(int, long, PyLong_AsLong(x))
  #ifdef HAVE_LONG_LONG
              } else if (sizeof(int) <= sizeof(PY_LONG_LONG)) {
                  __PYX_VERIFY_RETURN_INT_EXC(int, 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
              int 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 (int) -1;
          }
      } else {
          int val;
          PyObject *tmp = __Pyx_PyNumber_IntOrLong(x);
          if (!tmp) return (int) -1;
          val = __Pyx_PyInt_As_int(tmp);
          Py_DECREF(tmp);
          return val;
      }
  raise_overflow:
      PyErr_SetString(PyExc_OverflowError,
          "value too large to convert to int");
      return (int) -1;
  raise_neg_overflow:
      PyErr_SetString(PyExc_OverflowError,
          "can't convert negative value to int");
      return (int) -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;
      const int is_unsigned = neg_one > const_zero;
  #if PY_MAJOR_VERSION < 3
      if (likely(PyInt_Check(x))) {
          if (sizeof(long) < sizeof(long)) {
              __PYX_VERIFY_RETURN_INT(long, long, PyInt_AS_LONG(x))
          } else {
              long val = PyInt_AS_LONG(x);
              if (is_unsigned && unlikely(val < 0)) {
                  goto raise_neg_overflow;
              }
              return (long) 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 (long) 0;
                  case  1: __PYX_VERIFY_RETURN_INT(long, digit, digits[0])
                  case 2:
                      if (8 * sizeof(long) > 1 * PyLong_SHIFT) {
                          if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
                              __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                          } else if (8 * sizeof(long) >= 2 * PyLong_SHIFT) {
                              return (long) (((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0]));
                          }
                      }
                      break;
                  case 3:
                      if (8 * sizeof(long) > 2 * PyLong_SHIFT) {
                          if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
                              __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                          } else if (8 * sizeof(long) >= 3 * PyLong_SHIFT) {
                              return (long) (((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0]));
                          }
                      }
                      break;
                  case 4:
                      if (8 * sizeof(long) > 3 * PyLong_SHIFT) {
                          if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
                              __PYX_VERIFY_RETURN_INT(long, 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(long) >= 4 * PyLong_SHIFT) {
                              return (long) (((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)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 (long) -1;
                  if (unlikely(result == 1))
                      goto raise_neg_overflow;
              }
  #endif
              if (sizeof(long) <= sizeof(unsigned long)) {
                  __PYX_VERIFY_RETURN_INT_EXC(long, unsigned long, PyLong_AsUnsignedLong(x))
  #ifdef HAVE_LONG_LONG
              } else if (sizeof(long) <= sizeof(unsigned PY_LONG_LONG)) {
                  __PYX_VERIFY_RETURN_INT_EXC(long, 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 (long) 0;
                  case -1: __PYX_VERIFY_RETURN_INT(long, sdigit, (sdigit) (-(sdigit)digits[0]))
                  case  1: __PYX_VERIFY_RETURN_INT(long,  digit, +digits[0])
                  case -2:
                      if (8 * sizeof(long) - 1 > 1 * PyLong_SHIFT) {
                          if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
                              __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                          } else if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
                              return (long) (((long)-1)*(((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
                          }
                      }
                      break;
                  case 2:
                      if (8 * sizeof(long) > 1 * PyLong_SHIFT) {
                          if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
                              __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                          } else if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
                              return (long) ((((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
                          }
                      }
                      break;
                  case -3:
                      if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
                          if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
                              __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                          } else if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
                              return (long) (((long)-1)*(((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
                          }
                      }
                      break;
                  case 3:
                      if (8 * sizeof(long) > 2 * PyLong_SHIFT) {
                          if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
                              __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                          } else if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
                              return (long) ((((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
                          }
                      }
                      break;
                  case -4:
                      if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
                          if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
                              __PYX_VERIFY_RETURN_INT(long, 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(long) - 1 > 4 * PyLong_SHIFT) {
                              return (long) (((long)-1)*(((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
                          }
                      }
                      break;
                  case 4:
                      if (8 * sizeof(long) > 3 * PyLong_SHIFT) {
                          if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
                              __PYX_VERIFY_RETURN_INT(long, 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(long) - 1 > 4 * PyLong_SHIFT) {
                              return (long) ((((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
                          }
                      }
                      break;
              }
  #endif
              if (sizeof(long) <= sizeof(long)) {
                  __PYX_VERIFY_RETURN_INT_EXC(long, long, PyLong_AsLong(x))
  #ifdef HAVE_LONG_LONG
              } else if (sizeof(long) <= sizeof(PY_LONG_LONG)) {
                  __PYX_VERIFY_RETURN_INT_EXC(long, 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
              long 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 (long) -1;
          }
      } else {
          long val;
          PyObject *tmp = __Pyx_PyNumber_IntOrLong(x);
          if (!tmp) return (long) -1;
          val = __Pyx_PyInt_As_long(tmp);
          Py_DECREF(tmp);
          return val;
      }
  raise_overflow:
      PyErr_SetString(PyExc_OverflowError,
          "value too large to convert to long");
      return (long) -1;
  raise_neg_overflow:
      PyErr_SetString(PyExc_OverflowError,
          "can't convert negative value to long");
      return (long) -1;
  }
  
  /* FastTypeChecks */
    #if CYTHON_COMPILING_IN_CPYTHON
  static int __Pyx_InBases(PyTypeObject *a, PyTypeObject *b) {
      while (a) {
          a = a->tp_base;
          if (a == b)
              return 1;
      }
      return b == &PyBaseObject_Type;
  }
  static CYTHON_INLINE int __Pyx_IsSubtype(PyTypeObject *a, PyTypeObject *b) {
      PyObject *mro;
      if (a == b) return 1;
      mro = a->tp_mro;
      if (likely(mro)) {
          Py_ssize_t i, n;
          n = PyTuple_GET_SIZE(mro);
          for (i = 0; i < n; i++) {
              if (PyTuple_GET_ITEM(mro, i) == (PyObject *)b)
                  return 1;
          }
          return 0;
      }
      return __Pyx_InBases(a, b);
  }
  #if PY_MAJOR_VERSION == 2
  static int __Pyx_inner_PyErr_GivenExceptionMatches2(PyObject *err, PyObject* exc_type1, PyObject* exc_type2) {
      PyObject *exception, *value, *tb;
      int res;
      __Pyx_PyThreadState_declare
      __Pyx_PyThreadState_assign
      __Pyx_ErrFetch(&exception, &value, &tb);
      res = exc_type1 ? PyObject_IsSubclass(err, exc_type1) : 0;
      if (unlikely(res == -1)) {
          PyErr_WriteUnraisable(err);
          res = 0;
      }
      if (!res) {
          res = PyObject_IsSubclass(err, exc_type2);
          if (unlikely(res == -1)) {
              PyErr_WriteUnraisable(err);
              res = 0;
          }
      }
      __Pyx_ErrRestore(exception, value, tb);
      return res;
  }
  #else
  static CYTHON_INLINE int __Pyx_inner_PyErr_GivenExceptionMatches2(PyObject *err, PyObject* exc_type1, PyObject *exc_type2) {
      int res = exc_type1 ? __Pyx_IsSubtype((PyTypeObject*)err, (PyTypeObject*)exc_type1) : 0;
      if (!res) {
          res = __Pyx_IsSubtype((PyTypeObject*)err, (PyTypeObject*)exc_type2);
      }
      return res;
  }
  #endif
  static int __Pyx_PyErr_GivenExceptionMatchesTuple(PyObject *exc_type, PyObject *tuple) {
      Py_ssize_t i, n;
      assert(PyExceptionClass_Check(exc_type));
      n = PyTuple_GET_SIZE(tuple);
  #if PY_MAJOR_VERSION >= 3
      for (i=0; i<n; i++) {
          if (exc_type == PyTuple_GET_ITEM(tuple, i)) return 1;
      }
  #endif
      for (i=0; i<n; i++) {
          PyObject *t = PyTuple_GET_ITEM(tuple, i);
          #if PY_MAJOR_VERSION < 3
          if (likely(exc_type == t)) return 1;
          #endif
          if (likely(PyExceptionClass_Check(t))) {
              if (__Pyx_inner_PyErr_GivenExceptionMatches2(exc_type, NULL, t)) return 1;
          } else {
          }
      }
      return 0;
  }
  static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches(PyObject *err, PyObject* exc_type) {
      if (likely(err == exc_type)) return 1;
      if (likely(PyExceptionClass_Check(err))) {
          if (likely(PyExceptionClass_Check(exc_type))) {
              return __Pyx_inner_PyErr_GivenExceptionMatches2(err, NULL, exc_type);
          } else if (likely(PyTuple_Check(exc_type))) {
              return __Pyx_PyErr_GivenExceptionMatchesTuple(err, exc_type);
          } else {
          }
      }
      return PyErr_GivenExceptionMatches(err, exc_type);
  }
  static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches2(PyObject *err, PyObject *exc_type1, PyObject *exc_type2) {
      assert(PyExceptionClass_Check(exc_type1));
      assert(PyExceptionClass_Check(exc_type2));
      if (likely(err == exc_type1 || err == exc_type2)) return 1;
      if (likely(PyExceptionClass_Check(err))) {
          return __Pyx_inner_PyErr_GivenExceptionMatches2(err, exc_type1, exc_type2);
      }
      return (PyErr_GivenExceptionMatches(err, exc_type1) || PyErr_GivenExceptionMatches(err, exc_type2));
  }
  #endif
  
  /* CheckBinaryVersion */
    static int __Pyx_check_binary_version(void) {
      char ctversion[4], rtversion[4];
      PyOS_snprintf(ctversion, 4, "%d.%d", PY_MAJOR_VERSION, PY_MINOR_VERSION);
      PyOS_snprintf(rtversion, 4, "%s", Py_GetVersion());
      if (ctversion[0] != rtversion[0] || ctversion[2] != rtversion[2]) {
          char message[200];
          PyOS_snprintf(message, sizeof(message),
                        "compiletime version %s of module '%.100s' "
                        "does not match runtime version %s",
                        ctversion, __Pyx_MODULE_NAME, rtversion);
          return PyErr_WarnEx(NULL, message, 1);
      }
      return 0;
  }
  
  /* InitStrings */
    static int __Pyx_InitStrings(__Pyx_StringTabEntry *t) {
      while (t->p) {
          #if PY_MAJOR_VERSION < 3
          if (t->is_unicode) {
              *t->p = PyUnicode_DecodeUTF8(t->s, t->n - 1, NULL);
          } else if (t->intern) {
              *t->p = PyString_InternFromString(t->s);
          } else {
              *t->p = PyString_FromStringAndSize(t->s, t->n - 1);
          }
          #else
          if (t->is_unicode | t->is_str) {
              if (t->intern) {
                  *t->p = PyUnicode_InternFromString(t->s);
              } else if (t->encoding) {
                  *t->p = PyUnicode_Decode(t->s, t->n - 1, t->encoding, NULL);
              } else {
                  *t->p = PyUnicode_FromStringAndSize(t->s, t->n - 1);
              }
          } else {
              *t->p = PyBytes_FromStringAndSize(t->s, t->n - 1);
          }
          #endif
          if (!*t->p)
              return -1;
          if (PyObject_Hash(*t->p) == -1)
              return -1;
          ++t;
      }
      return 0;
  }
  
  static CYTHON_INLINE PyObject* __Pyx_PyUnicode_FromString(const char* c_str) {
      return __Pyx_PyUnicode_FromStringAndSize(c_str, (Py_ssize_t)strlen(c_str));
  }
  static CYTHON_INLINE const char* __Pyx_PyObject_AsString(PyObject* o) {
      Py_ssize_t ignore;
      return __Pyx_PyObject_AsStringAndSize(o, &ignore);
  }
  #if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII || __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT
  #if !CYTHON_PEP393_ENABLED
  static const char* __Pyx_PyUnicode_AsStringAndSize(PyObject* o, Py_ssize_t *length) {
      char* defenc_c;
      PyObject* defenc = _PyUnicode_AsDefaultEncodedString(o, NULL);
      if (!defenc) return NULL;
      defenc_c = PyBytes_AS_STRING(defenc);
  #if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
      {
          char* end = defenc_c + PyBytes_GET_SIZE(defenc);
          char* c;
          for (c = defenc_c; c < end; c++) {
              if ((unsigned char) (*c) >= 128) {
                  PyUnicode_AsASCIIString(o);
                  return NULL;
              }
          }
      }
  #endif
      *length = PyBytes_GET_SIZE(defenc);
      return defenc_c;
  }
  #else
  static CYTHON_INLINE const char* __Pyx_PyUnicode_AsStringAndSize(PyObject* o, Py_ssize_t *length) {
      if (unlikely(__Pyx_PyUnicode_READY(o) == -1)) return NULL;
  #if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
      if (likely(PyUnicode_IS_ASCII(o))) {
          *length = PyUnicode_GET_LENGTH(o);
          return PyUnicode_AsUTF8(o);
      } else {
          PyUnicode_AsASCIIString(o);
          return NULL;
      }
  #else
      return PyUnicode_AsUTF8AndSize(o, length);
  #endif
  }
  #endif
  #endif
  static CYTHON_INLINE const char* __Pyx_PyObject_AsStringAndSize(PyObject* o, Py_ssize_t *length) {
  #if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII || __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT
      if (
  #if PY_MAJOR_VERSION < 3 && __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
              __Pyx_sys_getdefaultencoding_not_ascii &&
  #endif
              PyUnicode_Check(o)) {
          return __Pyx_PyUnicode_AsStringAndSize(o, length);
      } else
  #endif
  #if (!CYTHON_COMPILING_IN_PYPY) || (defined(PyByteArray_AS_STRING) && defined(PyByteArray_GET_SIZE))
      if (PyByteArray_Check(o)) {
          *length = PyByteArray_GET_SIZE(o);
          return PyByteArray_AS_STRING(o);
      } else
  #endif
      {
          char* result;
          int r = PyBytes_AsStringAndSize(o, &result, length);
          if (unlikely(r < 0)) {
              return NULL;
          } else {
              return result;
          }
      }
  }
  static CYTHON_INLINE int __Pyx_PyObject_IsTrue(PyObject* x) {
     int is_true = x == Py_True;
     if (is_true | (x == Py_False) | (x == Py_None)) return is_true;
     else return PyObject_IsTrue(x);
  }
  static CYTHON_INLINE int __Pyx_PyObject_IsTrueAndDecref(PyObject* x) {
      int retval;
      if (unlikely(!x)) return -1;
      retval = __Pyx_PyObject_IsTrue(x);
      Py_DECREF(x);
      return retval;
  }
  static PyObject* __Pyx_PyNumber_IntOrLongWrongResultType(PyObject* result, const char* type_name) {
  #if PY_MAJOR_VERSION >= 3
      if (PyLong_Check(result)) {
          if (PyErr_WarnFormat(PyExc_DeprecationWarning, 1,
                  "__int__ returned non-int (type %.200s).  "
                  "The ability to return an instance of a strict subclass of int "
                  "is deprecated, and may be removed in a future version of Python.",
                  Py_TYPE(result)->tp_name)) {
              Py_DECREF(result);
              return NULL;
          }
          return result;
      }
  #endif
      PyErr_Format(PyExc_TypeError,
                   "__%.4s__ returned non-%.4s (type %.200s)",
                   type_name, type_name, Py_TYPE(result)->tp_name);
      Py_DECREF(result);
      return NULL;
  }
  static CYTHON_INLINE PyObject* __Pyx_PyNumber_IntOrLong(PyObject* x) {
  #if CYTHON_USE_TYPE_SLOTS
    PyNumberMethods *m;
  #endif
    const char *name = NULL;
    PyObject *res = NULL;
  #if PY_MAJOR_VERSION < 3
    if (likely(PyInt_Check(x) || PyLong_Check(x)))
  #else
    if (likely(PyLong_Check(x)))
  #endif
      return __Pyx_NewRef(x);
  #if CYTHON_USE_TYPE_SLOTS
    m = Py_TYPE(x)->tp_as_number;
    #if PY_MAJOR_VERSION < 3
    if (m && m->nb_int) {
      name = "int";
      res = m->nb_int(x);
    }
    else if (m && m->nb_long) {
      name = "long";
      res = m->nb_long(x);
    }
    #else
    if (likely(m && m->nb_int)) {
      name = "int";
      res = m->nb_int(x);
    }
    #endif
  #else
    if (!PyBytes_CheckExact(x) && !PyUnicode_CheckExact(x)) {
      res = PyNumber_Int(x);
    }
  #endif
    if (likely(res)) {
  #if PY_MAJOR_VERSION < 3
      if (unlikely(!PyInt_Check(res) && !PyLong_Check(res))) {
  #else
      if (unlikely(!PyLong_CheckExact(res))) {
  #endif
          return __Pyx_PyNumber_IntOrLongWrongResultType(res, name);
      }
    }
    else if (!PyErr_Occurred()) {
      PyErr_SetString(PyExc_TypeError,
                      "an integer is required");
    }
    return res;
  }
  static CYTHON_INLINE Py_ssize_t __Pyx_PyIndex_AsSsize_t(PyObject* b) {
    Py_ssize_t ival;
    PyObject *x;
  #if PY_MAJOR_VERSION < 3
    if (likely(PyInt_CheckExact(b))) {
      if (sizeof(Py_ssize_t) >= sizeof(long))
          return PyInt_AS_LONG(b);
      else
          return PyInt_AsSsize_t(b);
    }
  #endif
    if (likely(PyLong_CheckExact(b))) {
      #if CYTHON_USE_PYLONG_INTERNALS
      const digit* digits = ((PyLongObject*)b)->ob_digit;
      const Py_ssize_t size = Py_SIZE(b);
      if (likely(__Pyx_sst_abs(size) <= 1)) {
          ival = likely(size) ? digits[0] : 0;
          if (size == -1) ival = -ival;
          return ival;
      } else {
        switch (size) {
           case 2:
             if (8 * sizeof(Py_ssize_t) > 2 * PyLong_SHIFT) {
               return (Py_ssize_t) (((((size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
             }
             break;
           case -2:
             if (8 * sizeof(Py_ssize_t) > 2 * PyLong_SHIFT) {
               return -(Py_ssize_t) (((((size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
             }
             break;
           case 3:
             if (8 * sizeof(Py_ssize_t) > 3 * PyLong_SHIFT) {
               return (Py_ssize_t) (((((((size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
             }
             break;
           case -3:
             if (8 * sizeof(Py_ssize_t) > 3 * PyLong_SHIFT) {
               return -(Py_ssize_t) (((((((size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
             }
             break;
           case 4:
             if (8 * sizeof(Py_ssize_t) > 4 * PyLong_SHIFT) {
               return (Py_ssize_t) (((((((((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(Py_ssize_t) > 4 * PyLong_SHIFT) {
               return -(Py_ssize_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
      return PyLong_AsSsize_t(b);
    }
    x = PyNumber_Index(b);
    if (!x) return -1;
    ival = PyInt_AsSsize_t(x);
    Py_DECREF(x);
    return ival;
  }
  static CYTHON_INLINE PyObject * __Pyx_PyBool_FromLong(long b) {
    return b ? __Pyx_NewRef(Py_True) : __Pyx_NewRef(Py_False);
  }
  static CYTHON_INLINE PyObject * __Pyx_PyInt_FromSize_t(size_t ival) {
      return PyInt_FromSize_t(ival);
  }
  
  
  #endif /* Py_PYTHON_H */
  