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#define __Pyx_PyString_FormatSafe(a, b)   ((unlikely((a) == Py_None)) ? PyNumber_Remainder(a, b) : __Pyx_PyString_Format(a, b))
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  #define __Pyx_PyBaseString_Check(obj) (PyString_Check(obj) || PyUnicode_Check(obj))
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#define __Pyx_TypeCheck(obj, type) PyObject_TypeCheck(obj, (PyTypeObject *)type)
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  #define PyInt_FromUnicode            PyLong_FromUnicode
  #define PyInt_FromLong               PyLong_FromLong
  #define PyInt_FromSize_t             PyLong_FromSize_t
  #define PyInt_FromSsize_t            PyLong_FromSsize_t
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  #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
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    #define CYTHON_INLINE __inline
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    #define CYTHON_INLINE inline
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    #define CYTHON_INLINE
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#endif
#ifndef CYTHON_RESTRICT
  #if defined(__GNUC__)
    #define CYTHON_RESTRICT __restrict__
  #elif defined(_MSC_VER) && _MSC_VER >= 1400
    #define CYTHON_RESTRICT __restrict
  #elif defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L
    #define CYTHON_RESTRICT restrict
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    #define CYTHON_RESTRICT
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#ifdef NAN
#define __PYX_NAN() ((float) NAN)
#else
static CYTHON_INLINE float __PYX_NAN() {
  /* Initialize NaN. The sign is irrelevant, an exponent with all bits 1 and
   a nonzero mantissa means NaN. If the first bit in the mantissa is 1, it is
   a quiet NaN. */
  float value;
  memset(&value, 0xFF, sizeof(value));
  return value;
}
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#ifdef __cplusplus
template<typename T>
void __Pyx_call_destructor(T* x) {
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}
#endif


#if PY_MAJOR_VERSION >= 3
  #define __Pyx_PyNumber_Divide(x,y)         PyNumber_TrueDivide(x,y)
  #define __Pyx_PyNumber_InPlaceDivide(x,y)  PyNumber_InPlaceTrueDivide(x,y)
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  #define __Pyx_PyNumber_Divide(x,y)         PyNumber_Divide(x,y)
  #define __Pyx_PyNumber_InPlaceDivide(x,y)  PyNumber_InPlaceDivide(x,y)
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#ifndef __PYX_EXTERN_C
  #ifdef __cplusplus
    #define __PYX_EXTERN_C extern "C"
  #else
    #define __PYX_EXTERN_C extern
  #endif
#endif

#if defined(WIN32) || defined(MS_WINDOWS)
#define _USE_MATH_DEFINES
#endif
#include <math.h>
#define __PYX_HAVE__dipy__tracking__distances
#define __PYX_HAVE_API__dipy__tracking__distances
#include "string.h"
#include "stdio.h"
#include "stdlib.h"
#include "numpy/arrayobject.h"
#include "numpy/ufuncobject.h"
#include "dpy_math.h"
#ifdef _OPENMP
#include <omp.h>
#endif /* _OPENMP */

#ifdef PYREX_WITHOUT_ASSERTIONS
#define CYTHON_WITHOUT_ASSERTIONS
#endif

#ifndef CYTHON_UNUSED
# if defined(__GNUC__)
#   if !(defined(__cplusplus)) || (__GNUC__ > 3 || (__GNUC__ == 3 && __GNUC_MINOR__ >= 4))
#     define CYTHON_UNUSED __attribute__ ((__unused__))
#   else
#     define CYTHON_UNUSED
#   endif
# elif defined(__ICC) || (defined(__INTEL_COMPILER) && !defined(_MSC_VER))
#   define CYTHON_UNUSED __attribute__ ((__unused__))
# else
#   define CYTHON_UNUSED
# endif
#endif
typedef struct {PyObject **p; 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_DEFAULT 0
#define __PYX_DEFAULT_STRING_ENCODING ""
#define __Pyx_PyObject_FromString __Pyx_PyBytes_FromString
#define __Pyx_PyObject_FromStringAndSize __Pyx_PyBytes_FromStringAndSize
#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 char* __Pyx_PyObject_AsString(PyObject*);
static CYTHON_INLINE 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_PyObject_AsSString(s)    ((signed char*) __Pyx_PyObject_AsString(s))
#define __Pyx_PyObject_AsUString(s)    ((unsigned char*) __Pyx_PyObject_AsString(s))
#define __Pyx_PyObject_FromUString(s)  __Pyx_PyObject_FromString((const char*)s)
#define __Pyx_PyBytes_FromUString(s)   __Pyx_PyBytes_FromString((const char*)s)
#define __Pyx_PyByteArray_FromUString(s)   __Pyx_PyByteArray_FromString((const char*)s)
#define __Pyx_PyStr_FromUString(s)     __Pyx_PyStr_FromString((const char*)s)
#define __Pyx_PyUnicode_FromUString(s) __Pyx_PyUnicode_FromString((const char*)s)
#if PY_MAJOR_VERSION < 3
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);
}
#else
#define __Pyx_Py_UNICODE_strlen Py_UNICODE_strlen
#endif
#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_Owned_Py_None(b) (Py_INCREF(Py_None), Py_None)
#define __Pyx_PyBool_FromLong(b) ((b) ? (Py_INCREF(Py_True), Py_True) : (Py_INCREF(Py_False), Py_False))
static CYTHON_INLINE int __Pyx_PyObject_IsTrue(PyObject*);
static CYTHON_INLINE PyObject* __Pyx_PyNumber_Int(PyObject* x);
static CYTHON_INLINE Py_ssize_t __Pyx_PyIndex_AsSsize_t(PyObject*);
static CYTHON_INLINE PyObject * __Pyx_PyInt_FromSize_t(size_t);
#if CYTHON_COMPILING_IN_CPYTHON
#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 && __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*) (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;
    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));
    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 PyObject *__pyx_m;
static PyObject *__pyx_d;
static PyObject *__pyx_b;
static PyObject *__pyx_empty_tuple;
static PyObject *__pyx_empty_bytes;
static int __pyx_lineno;
static int __pyx_clineno = 0;
static const char * __pyx_cfilenm= __FILE__;
static const char *__pyx_filename;

#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[] = {
  "dipy/tracking/distances.pyx",
  "__init__.pxd",
  "type.pxd",
};
#define IS_UNSIGNED(type) (((type) -1) > 0)
struct __Pyx_StructField_;
#define __PYX_BUF_FLAGS_PACKED_STRUCT (1 << 0)
typedef struct {
  const char* name;
  struct __Pyx_StructField_* fields;
  size_t size;
  size_t arraysize[8];
  int ndim;
  char typegroup;
  char is_unsigned;
  int flags;
} __Pyx_TypeInfo;
typedef struct __Pyx_StructField_ {
  __Pyx_TypeInfo* type;
  const char* name;
  size_t offset;
} __Pyx_StructField;
typedef struct {
  __Pyx_StructField* field;
  size_t parent_offset;
} __Pyx_BufFmt_StackElem;
typedef struct {
  __Pyx_StructField root;
  __Pyx_BufFmt_StackElem* head;
  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;
} __Pyx_BufFmt_Context;


/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":723
 * # 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;

/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":724
 * 
 * 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;

/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":725
 * 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;

/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":726
 * 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;

/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":730
 * #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;

/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":731
 * 
 * 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;

/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":732
 * ctypedef npy_uint8      uint8_t
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 * ctypedef npy_uint32     uint32_t             # <<<<<<<<<<<<<<
 * ctypedef npy_uint64     uint64_t
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typedef npy_uint32 __pyx_t_5numpy_uint32_t;

/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":733
 * ctypedef npy_uint16     uint16_t
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 * ctypedef npy_uint64     uint64_t             # <<<<<<<<<<<<<<
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typedef npy_uint64 __pyx_t_5numpy_uint64_t;

/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":737
 * #ctypedef npy_uint128    uint128_t
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 * ctypedef npy_float32    float32_t             # <<<<<<<<<<<<<<
 * ctypedef npy_float64    float64_t
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typedef npy_float32 __pyx_t_5numpy_float32_t;

/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":738
 * 
 * ctypedef npy_float32    float32_t
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/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":747
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/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":748
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/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":749
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/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":751
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/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":752
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/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":753
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/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":755
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typedef npy_intp __pyx_t_5numpy_intp_t;

/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":756
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/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":758
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/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":759
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/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":760
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/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":763
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/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":764
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typedef npy_clongdouble __pyx_t_5numpy_clongdouble_t;

/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":766
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typedef npy_cdouble __pyx_t_5numpy_complex_t;
struct __pyx_t_4dipy_8tracking_9distances_LSC_Cluster;
typedef struct __pyx_t_4dipy_8tracking_9distances_LSC_Cluster __pyx_t_4dipy_8tracking_9distances_LSC_Cluster;

/* "dipy/tracking/distances.pyx":1460
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struct __pyx_t_4dipy_8tracking_9distances_LSC_Cluster {
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#define __Pyx_GetItemInt(o, i, type, is_signed, to_py_func, is_list, wraparound, boundscheck) \
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/* Module declarations from 'dipy.tracking.distances' */
static PyArray_Descr *__pyx_v_4dipy_8tracking_9distances_f32_dt = 0;
static __pyx_t_5numpy_float32_t __pyx_v_4dipy_8tracking_9distances_inf;
static CYTHON_INLINE PyArrayObject *__pyx_f_4dipy_8tracking_9distances_as_float_3vec(PyObject *); /*proto*/
static CYTHON_INLINE float *__pyx_f_4dipy_8tracking_9distances_asfp(PyArrayObject *); /*proto*/
static CYTHON_INLINE float __pyx_f_4dipy_8tracking_9distances_cnorm_3vec(float *); /*proto*/
static CYTHON_INLINE void __pyx_f_4dipy_8tracking_9distances_cnormalized_3vec(float *, float *); /*proto*/
static CYTHON_INLINE float __pyx_f_4dipy_8tracking_9distances_cinner_3vecs(float *, float *); /*proto*/
static CYTHON_INLINE void __pyx_f_4dipy_8tracking_9distances_csub_3vecs(float *, float *, float *); /*proto*/
static CYTHON_INLINE void __pyx_f_4dipy_8tracking_9distances_cadd_3vecs(float *, float *, float *); /*proto*/
static CYTHON_INLINE void __pyx_f_4dipy_8tracking_9distances_cmul_3vecs(float *, float *, float *); /*proto*/
static CYTHON_INLINE void __pyx_f_4dipy_8tracking_9distances_cmul_3vec(float, float *, float *); /*proto*/
static CYTHON_INLINE __pyx_t_5numpy_float32_t __pyx_f_4dipy_8tracking_9distances_czhang(size_t, __pyx_t_5numpy_float32_t *, size_t, __pyx_t_5numpy_float32_t *, __pyx_t_5numpy_float32_t *, int); /*proto*/
static CYTHON_INLINE void __pyx_f_4dipy_8tracking_9distances_min_distances(size_t, __pyx_t_5numpy_float32_t *, size_t, __pyx_t_5numpy_float32_t *, __pyx_t_5numpy_float32_t *, __pyx_t_5numpy_float32_t *); /*proto*/
static float __pyx_f_4dipy_8tracking_9distances_clee_perpendicular_distance(float *, float *, float *, float *); /*proto*/
static float __pyx_f_4dipy_8tracking_9distances_clee_angle_distance(float *, float *, float *, float *); /*proto*/
static float __pyx_f_4dipy_8tracking_9distances_cintersect_segment_cylinder(float *, float *, float *, float *, float, float *); /*proto*/
static CYTHON_INLINE float __pyx_f_4dipy_8tracking_9distances_cpoint_segment_sq_dist(float *, float *, float *); /*proto*/
static void __pyx_f_4dipy_8tracking_9distances_track_direct_flip_dist(float *, float *, long, float *); /*proto*/
static CYTHON_INLINE void __pyx_f_4dipy_8tracking_9distances_track_direct_flip_3dist(float *, float *, float *, float *, float *, float *, float *); /*proto*/
static __Pyx_TypeInfo __Pyx_TypeInfo_nn___pyx_t_5numpy_float32_t = { "float32_t", NULL, sizeof(__pyx_t_5numpy_float32_t), { 0 }, 0, 'R', 0, 0 };
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#define __Pyx_MODULE_NAME "dipy.tracking.distances"
int __pyx_module_is_main_dipy__tracking__distances = 0;

/* Implementation of 'dipy.tracking.distances' */
static PyObject *__pyx_builtin_range;
static PyObject *__pyx_builtin_ValueError;
static PyObject *__pyx_builtin_object;
static PyObject *__pyx_builtin_RuntimeError;
static PyObject *__pyx_pf_4dipy_8tracking_9distances_normalized_3vec(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_vec); /* proto */
static PyObject *__pyx_pf_4dipy_8tracking_9distances_2norm_3vec(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_vec); /* proto */
static PyObject *__pyx_pf_4dipy_8tracking_9distances_4inner_3vecs(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_vec1, PyObject *__pyx_v_vec2); /* proto */
static PyObject *__pyx_pf_4dipy_8tracking_9distances_6sub_3vecs(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_vec1, PyObject *__pyx_v_vec2); /* proto */
static PyObject *__pyx_pf_4dipy_8tracking_9distances_8add_3vecs(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_vec1, PyObject *__pyx_v_vec2); /* proto */
static PyObject *__pyx_pf_4dipy_8tracking_9distances_10mul_3vecs(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_vec1, PyObject *__pyx_v_vec2); /* proto */
static PyObject *__pyx_pf_4dipy_8tracking_9distances_12mul_3vec(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_a, PyObject *__pyx_v_vec); /* proto */
static PyObject *__pyx_pf_4dipy_8tracking_9distances_14cut_plane(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_tracks, PyObject *__pyx_v_ref); /* proto */
static PyObject *__pyx_pf_4dipy_8tracking_9distances_16most_similar_track_mam(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_tracks, PyObject *__pyx_v_metric); /* proto */
static PyObject *__pyx_pf_4dipy_8tracking_9distances_18bundles_distances_mam(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_tracksA, PyObject *__pyx_v_tracksB, PyObject *__pyx_v_metric); /* proto */
static PyObject *__pyx_pf_4dipy_8tracking_9distances_20bundles_distances_mdf(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_tracksA, PyObject *__pyx_v_tracksB); /* proto */
static PyObject *__pyx_pf_4dipy_8tracking_9distances_22mam_distances(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_xyz1, PyObject *__pyx_v_xyz2, PyObject *__pyx_v_metric); /* proto */
static PyObject *__pyx_pf_4dipy_8tracking_9distances_24minimum_closest_distance(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_xyz1, PyObject *__pyx_v_xyz2); /* proto */
static PyObject *__pyx_pf_4dipy_8tracking_9distances_26lee_perpendicular_distance(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_start0, PyObject *__pyx_v_end0, PyObject *__pyx_v_start1, PyObject *__pyx_v_end1); /* proto */
static PyObject *__pyx_pf_4dipy_8tracking_9distances_28lee_angle_distance(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_start0, PyObject *__pyx_v_end0, PyObject *__pyx_v_start1, PyObject *__pyx_v_end1); /* proto */
static PyObject *__pyx_pf_4dipy_8tracking_9distances_30approx_polygon_track(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_xyz, PyObject *__pyx_v_alpha); /* proto */
static PyObject *__pyx_pf_4dipy_8tracking_9distances_32approximate_mdl_trajectory(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_xyz, PyObject *__pyx_v_alpha); /* proto */
static PyObject *__pyx_pf_4dipy_8tracking_9distances_34intersect_segment_cylinder(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_sa, PyObject *__pyx_v_sb, PyObject *__pyx_v_p, PyObject *__pyx_v_q, PyObject *__pyx_v_r); /* proto */
static PyObject *__pyx_pf_4dipy_8tracking_9distances_36point_segment_sq_distance(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_a, PyObject *__pyx_v_b, PyObject *__pyx_v_c); /* proto */
static PyObject *__pyx_pf_4dipy_8tracking_9distances_38track_dist_3pts(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_tracka, PyObject *__pyx_v_trackb); /* proto */
static PyObject *__pyx_pf_4dipy_8tracking_9distances_40local_skeleton_clustering(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_tracks, PyObject *__pyx_v_d_thr); /* proto */
static PyObject *__pyx_pf_4dipy_8tracking_9distances_42local_skeleton_clustering_3pts(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_tracks, PyObject *__pyx_v_d_thr); /* proto */
static PyObject *__pyx_pf_4dipy_8tracking_9distances_44larch_3split(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_tracks, PyObject *__pyx_v_indices, PyObject *__pyx_v_thr); /* proto */
static PyObject *__pyx_pf_4dipy_8tracking_9distances_46larch_3merge(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_C, PyObject *__pyx_v_thr); /* proto */
static PyObject *__pyx_pf_4dipy_8tracking_9distances_48point_track_sq_distance_check(CYTHON_UNUSED PyObject *__pyx_self, PyArrayObject *__pyx_v_track, PyArrayObject *__pyx_v_point, double __pyx_v_sq_dist_thr); /* proto */
static PyObject *__pyx_pf_4dipy_8tracking_9distances_50track_roi_intersection_check(CYTHON_UNUSED PyObject *__pyx_self, PyArrayObject *__pyx_v_track, PyArrayObject *__pyx_v_roi, double __pyx_v_sq_dist_thr); /* proto */
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static void __pyx_pf_5numpy_7ndarray_2__releasebuffer__(PyArrayObject *__pyx_v_self, Py_buffer *__pyx_v_info); /* proto */
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static char __pyx_k_fvec1[] = "fvec1";
static char __pyx_k_fvec2[] = "fvec2";
static char __pyx_k_fvec3[] = "fvec3";
static char __pyx_k_fvec4[] = "fvec4";
static char __pyx_k_hitMp[] = "hitMp";
static char __pyx_k_int64[] = "int64";
static char __pyx_k_lentA[] = "lentA";
static char __pyx_k_lentB[] = "lentB";
static char __pyx_k_numpy[] = "numpy";
static char __pyx_k_point[] = "point";
static char __pyx_k_range[] = "range";
static char __pyx_k_ref32[] = "ref32";
static char __pyx_k_shape[] = "shape";
static char __pyx_k_t1_pi[] = "t1_pi";
static char __pyx_k_t2_pi[] = "t2_pi";
static char __pyx_k_t_len[] = "t_len";
static char __pyx_k_track[] = "track";
static char __pyx_k_zeros[] = "zeros";
static char __pyx_k_alphac[] = "alphac";
static char __pyx_k_append[] = "append";
static char __pyx_k_argmin[] = "argmin";
static char __pyx_k_cd_thr[] = "cd_thr";
static char __pyx_k_double[] = "double";
static char __pyx_k_hidden[] = "hidden";
static char __pyx_k_hit_no[] = "hit_no";
static char __pyx_k_import[] = "__import__";
static char __pyx_k_krange[] = "krange";
static char __pyx_k_length[] = "length";
static char __pyx_k_metric[] = "metric";
static char __pyx_k_n_hits[] = "n_hits";
static char __pyx_k_normal[] = "normal";
static char __pyx_k_object[] = "object";
static char __pyx_k_points[] = "points";
static char __pyx_k_start0[] = "start0";
static char __pyx_k_start1[] = "start1";
static char __pyx_k_t1_len[] = "t1_len";
static char __pyx_k_t1_ptr[] = "t1_ptr";
static char __pyx_k_t2_len[] = "t2_len";
static char __pyx_k_t2_ptr[] = "t2_ptr";
static char __pyx_k_track1[] = "track1";
static char __pyx_k_track2[] = "track2";
static char __pyx_k_tracka[] = "tracka";
static char __pyx_k_trackb[] = "trackb";
static char __pyx_k_tracks[] = "tracks";
static char __pyx_k_uint64[] = "uint64";
static char __pyx_k_vec_in[] = "vec_in";
static char __pyx_k_N_track[] = "N_track";
static char __pyx_k_asarray[] = "asarray";
static char __pyx_k_cluster[] = "cluster";
static char __pyx_k_float32[] = "float32";
static char __pyx_k_hit_arr[] = "hit_arr";
static char __pyx_k_hit_ptr[] = "hit_ptr";
static char __pyx_k_indices[] = "indices";
static char __pyx_k_itrange[] = "itrange";
static char __pyx_k_one_hit[] = "one_hit";
static char __pyx_k_squeeze[] = "squeeze";
static char __pyx_k_tracksA[] = "tracksA";
static char __pyx_k_tracksB[] = "tracksB";
static char __pyx_k_vec_out[] = "vec_out";
static char __pyx_k_N_tracks[] = "N_tracks";
static char __pyx_k_cost_par[] = "cost_par";
static char __pyx_k_distance[] = "distance";
static char __pyx_k_min_t1t2[] = "min_t1t2";
static char __pyx_k_min_t2t1[] = "min_t2t1";
static char __pyx_k_mul_3vec[] = "mul_3vec";
static char __pyx_k_tracks32[] = "tracks32";
static char __pyx_k_add_3vecs[] = "add_3vecs";
static char __pyx_k_cut_plane[] = "cut_plane";
static char __pyx_k_mean_t1t2[] = "mean_t1t2";
static char __pyx_k_mean_t2t1[] = "mean_t2t1";
static char __pyx_k_mid_index[] = "mid_index";
static char __pyx_k_mul_3vecs[] = "mul_3vecs";
static char __pyx_k_norm_3vec[] = "norm_3vec";
static char __pyx_k_sub_3vecs[] = "sub_3vecs";
static char __pyx_k_track_len[] = "track_len";
static char __pyx_k_tracksA32[] = "tracksA32";
static char __pyx_k_tracksB32[] = "tracksB32";
static char __pyx_k_ValueError[] = "ValueError";
static char __pyx_k_cost_nopar[] = "cost_nopar";
static char __pyx_k_intersects[] = "intersects";
static char __pyx_k_min_buffer[] = "min_buffer";
static char __pyx_k_next_ref_p[] = "next_ref_p";
static char __pyx_k_next_trk_p[] = "next_trk_p";
static char __pyx_k_this_ref_p[] = "this_ref_p";
static char __pyx_k_this_trk_p[] = "this_trk_p";
static char __pyx_k_inner_3vecs[] = "inner_3vecs";
static char __pyx_k_max_hit_len[] = "max_hit_len";
static char __pyx_k_metric_type[] = "metric_type";
static char __pyx_k_sq_dist_thr[] = "sq_dist_thr";
static char __pyx_k_start_index[] = "start_index";
static char __pyx_k_RuntimeError[] = "RuntimeError";
static char __pyx_k_larch_3merge[] = "larch_3merge";
static char __pyx_k_larch_3split[] = "larch_3split";
static char __pyx_k_min_min_t1t2[] = "min_min_t1t2";
static char __pyx_k_min_min_t2t1[] = "min_min_t2t1";
static char __pyx_k_track2others[] = "track2others";
static char __pyx_k_current_index[] = "current_index";
static char __pyx_k_mam_distances[] = "mam_distances";
static char __pyx_k_track_lengths[] = "track_lengths";
static char __pyx_k_normalized_3vec[] = "normalized_3vec";
static char __pyx_k_track_dist_3pts[] = "track_dist_3pts";
static char __pyx_k_distances_buffer[] = "distances_buffer";
static char __pyx_k_sum_track2others[] = "sum_track2others";
static char __pyx_k_ascontiguousarray[] = "ascontiguousarray";
static char __pyx_k_longest_track_len[] = "longest_track_len";
static char __pyx_k_cut_plane_line_191[] = "cut_plane (line 191)";
static char __pyx_k_lee_angle_distance[] = "lee_angle_distance";
static char __pyx_k_longest_track_lenA[] = "longest_track_lenA";
static char __pyx_k_longest_track_lenB[] = "longest_track_lenB";
static char __pyx_k_approx_polygon_track[] = "approx_polygon_track";
static char __pyx_k_bundles_distances_mam[] = "bundles_distances_mam";
static char __pyx_k_bundles_distances_mdf[] = "bundles_distances_mdf";
static char __pyx_k_characteristic_points[] = "characteristic_points";
static char __pyx_k_larch_3split_line_1786[] = "larch_3split (line 1786)";
static char __pyx_k_most_similar_track_mam[] = "most_similar_track_mam";
static char __pyx_k_dipy_tracking_distances[] = "dipy.tracking.distances";
static char __pyx_k_minimum_closest_distance[] = "minimum_closest_distance";
static char __pyx_k_Wrong_argument_for_metric[] = "Wrong argument for metric";
static char __pyx_k_local_skeleton_clustering[] = "local_skeleton_clustering";
static char __pyx_k_point_segment_sq_distance[] = "point_segment_sq_distance";
static char __pyx_k_track_dist_3pts_line_1324[] = "track_dist_3pts (line 1324)";
static char __pyx_k_approximate_mdl_trajectory[] = "approximate_mdl_trajectory";
static char __pyx_k_intersect_segment_cylinder[] = "intersect_segment_cylinder";
static char __pyx_k_lee_perpendicular_distance[] = "lee_perpendicular_distance";
static char __pyx_k_lee_angle_distance_line_941[] = "lee_angle_distance (line 941)";
static char __pyx_k_ndarray_is_not_C_contiguous[] = "ndarray is not C contiguous";
static char __pyx_k_track_roi_intersection_check[] = "track_roi_intersection_check";
static char __pyx_k_point_track_sq_distance_check[] = "point_track_sq_distance_check";
static char __pyx_k_Calculate_the_squared_distance[] = " Calculate the squared distance from a point c to a finite line segment ab.\n\n    Examples\n    --------\n    >>> a=np.array([0,0,0], dtype=np.float32)\n    >>> b=np.array([1,0,0], dtype=np.float32)\n    >>> c=np.array([0,1,0], dtype=np.float32)\n    >>> point_segment_sq_distance(a, b, c)\n    1.0\n    >>> c = np.array([0,3,0], dtype=np.float32)\n    >>> point_segment_sq_distance(a,b,c)\n    9.0\n    >>> c = np.array([-1,1,0], dtype=np.float32)\n    >>> point_segment_sq_distance(a, b, c)\n    2.0\n    ";
static char __pyx_k_Extract_divergence_vectors_and[] = " Extract divergence vectors and points of intersection\n    between planes normal to the reference fiber and other tracks\n\n    Parameters\n    ----------\n    tracks : sequence\n        of tracks as arrays, shape (N1,3) .. (Nm,3)\n    ref : array, shape (N,3)\n        reference track\n\n    Returns\n    -------\n    hits : sequence\n       list of points and rcds (radial coefficient of divergence)``\n\n    Notes\n    -----\n    The orthogonality relationship\n    np.inner(hits[p][q][0:3]-ref[p+1],ref[p+2]-ref[r][p+1]) will hold throughout\n    for every point q in the hits plane at point (p+1) on the reference track.\n\n    Examples\n    --------\n    >>> refx = np.array([[0,0,0],[1,0,0],[2,0,0],[3,0,0]],dtype='float32')\n    >>> bundlex = [np.array([[0.5,1,0],[1.5,2,0],[2.5,3,0]],dtype='float32')]\n    >>> res = cut_plane(bundlex,refx)\n    >>> len(res)\n    2\n    >>> print(res[0])\n    [[ 1.          1.5         0.          0.70710683  0.        ]]\n    >>> print(res[1])\n    [[ 2.          2.5         0.          0.70710677  0.        ]]\n    ";
static char __pyx_k_approx_polygon_track_line_1007[] = "approx_polygon_track (line 1007)";
static char __pyx_k_local_skeleton_clustering_3pts[] = "local_skeleton_clustering_3pts";
static char __pyx_k_Calculate_the_euclidean_distanc[] = " Calculate the euclidean distance between two 3pt tracks\n\n    Both direct and flip distances are calculated but only the smallest is returned\n\n    Parameters\n    ----------\n    a : array, shape (3,3)\n    a three point track\n    b : array, shape (3,3)\n    a three point track\n\n    Returns\n    -------\n    dist :float\n\n    Examples\n    --------\n    >>> a = np.array([[0,0,0],[1,0,0,],[2,0,0]])\n    >>> b = np.array([[3,0,0],[3.5,1,0],[4,2,0]])\n    >>> c = track_dist_3pts(a, b)\n    >>> print('%.6f' % c)\n    2.721573\n    ";
static char __pyx_k_Calculates_angle_distance_metri[] = " Calculates angle distance metric for the distance between two line segments\n\n    Based on Lee , Han & Whang SIGMOD07.\n\n    This function assumes that norm(end0-start0)>norm(end1-start1) i.e. that the\n    first segment will be bigger than the second one.\n\n    Parameters\n    ----------\n    start0 : float array(3,)\n    end0 : float array(3,)\n    start1 : float array(3,)\n    end1 : float array(3,)\n\n    Returns\n    -------\n    angle_distance : float\n\n    Notes\n    -----\n    l_0 = np.inner(end0-start0,end0-start0)\n    l_1 = np.inner(end1-start1,end1-start1)\n\n    cos_theta_squared = np.inner(end0-start0,end1-start1)**2/ (l_0*l_1)\n    return np.sqrt((1-cos_theta_squared)*l_1)\n\n    Examples\n    --------\n    >>> lee_angle_distance([0,0,0],[1,0,0],[3,4,5],[5,4,3])\n    2.0\n    ";
static char __pyx_k_Calculates_perpendicular_distan[] = " Calculates perpendicular distance metric for the distance between two line segments\n\n    Based on Lee , Han & Whang SIGMOD07.\n\n    This function assumes that norm(end0-start0)>norm(end1-start1) i.e. that the\n    first segment will be bigger than the second one.\n\n    Parameters\n    ----------\n    start0 : float array(3,)\n    end0 : float array(3,)\n    start1 : float array(3,)\n    end1 : float array(3,)\n\n    Returns\n    -------\n    perpendicular_distance: float\n\n    Notes\n    -----\n    l0 = np.inner(end0-start0,end0-start0)\n    l1 = np.inner(end1-start1,end1-start1)\n\n    k0=end0-start0\n\n    u1 = np.inner(start1-start0,k0)/l0\n    u2 = np.inner(end1-start0,k0)/l0\n\n    ps = start0+u1*k0\n    pe = start0+u2*k0\n\n    lperp1 = np.sqrt(np.inner(ps-start1,ps-start1))\n    lperp2 = np.sqrt(np.inner(pe-end1,pe-end1))\n\n    if lperp1+lperp2 > 0.:\n        return (lperp1**2+lperp2**2)/(lperp1+lperp2)\n    else:\n        return 0.\n\n    Examples\n    --------\n    >>> d = lee_perpendicular_distance([0,0,0],[1,0,0],[3,4,5],[5,4,3])\n    >>> print('%.6f' % d)\n    5.787888\n    ";
static char __pyx_k_Check_if_a_track_is_intersectin[] = " Check if a track is intersecting a region of interest\n\n    Parameters\n    ----------\n    track: array,float32, shape (N,3)\n    roi: array,float32, shape (M,3)\n    sq_dist_thr: double, threshold, check squared euclidean distance from every roi point\n\n    Returns\n    -------\n    bool: True, if sq_distance <= sq_dist_thr, otherwise False.\n\n    Examples\n    --------\n    >>> roi=np.array([[0,0,0],[1,0,0],[2,0,0]],dtype='f4')\n    >>> t=np.array([[0,0,0],[1,1,1],[2,2,2]],dtype='f4')\n    >>> track_roi_intersection_check(t,roi,1)\n    True\n    >>> track_roi_intersection_check(t,np.array([[10,0,0]],dtype='f4'),1)\n    False\n    ";
static char __pyx_k_Check_if_square_distance_of_tra[] = " Check if square distance of track from point is smaller than threshold\n\n    Parameters\n    ----------\n    track: array,float32, shape (N,3)\n    point: array,float32, shape (3,)\n    sq_dist_thr: double, threshold\n\n    Returns\n    -------\n    bool: True, if sq_distance <= sq_dist_thr, otherwise False.\n\n    Examples\n    --------\n    >>> t=np.random.rand(10,3).astype(np.float32)\n    >>> p=np.array([0.5,0.5,0.5],dtype=np.float32)\n    >>> point_track_sq_distance_check(t,p,2**2)\n    True\n    >>> t=np.array([[0,0,0],[1,1,1],[2,2,2]],dtype='f4')\n    >>> p=np.array([-1,-1.,-1],dtype='f4')\n    >>> point_track_sq_distance_check(t,p,.2**2)\n    False\n    >>> point_track_sq_distance_check(t,p,2**2)\n    True\n    ";
static char __pyx_k_Does_a_first_pass_clustering_Ev[] = " Does a first pass clustering\n\n    Every track can only have 3 pts neither less or more.\n    Use `dipy.tracking.metrics.downsample` to restrict the number of points\n\n    Parameters\n    ----------\n    tracks : sequence\n        of tracks as arrays, shape (N,3) .. (N,3) where N=3\n    d_thr : float\n        Average euclidean distance threshold\n\n    Returns\n    -------\n    C : dict\n       Clusters.\n\n    Examples\n    --------\n    >>> tracks=[np.array([[0,0,0],[1,0,0,],[2,0,0]]),\n    ...         np.array([[3,0,0],[3.5,1,0],[4,2,0]]),\n    ...         np.array([[3.2,0,0],[3.7,1,0],[4.4,2,0]]),\n    ...         np.array([[3.4,0,0],[3.9,1,0],[4.6,2,0]]),\n    ...         np.array([[0,0.2,0],[1,0.2,0],[2,0.2,0]]),\n    ...         np.array([[2,0.2,0],[1,0.2,0],[0,0.2,0]]),\n    ...         np.array([[0,0,0],[0,1,0],[0,2,0]])]\n    >>> C=local_skeleton_clustering_3pts(tracks,d_thr=0.5)\n\n    Notes\n    -----\n    It is possible to visualize the clustering C from the example\n    above using the fvtk module::\n\n        r=fvtk.ren()\n        for c in C:\n            color=np.random.rand(3)\n            for i in C[c]['indices']:\n                fvtk.add(r,fos.line(tracks[i],color))\n        fvtk.show(r)\n\n    ";
static char __pyx_k_Fast_and_simple_trajectory_appr[] = " Fast and simple trajectory approximation algorithm by Eleftherios and Ian\n\n    It will reduce the number of points of the track by keeping\n    intact the start and endpoints of the track and trying to remove\n    as many points as possible without distorting much the shape of\n    the track\n\n    Parameters\n    ----------\n    xyz : array(N,3)\n        initial trajectory\n    alpha : float\n        smoothing parameter (<0.392 smoother, >0.392 rougher) if the\n        trajectory was a smooth circle then with alpha =0.393\n        ~=pi/8. the circle would be approximated with an decahexagon if\n        alpha = 0.7853 ~=pi/4. with an octagon.\n\n    Returns\n    -------\n    characteristic_points: list of M array(3,) points\n\n    Examples\n    --------\n\n    Approximating a helix:\n\n    >>> t=np.linspace(0,1.75*2*np.pi,100)\n    >>> x = np.sin(t)\n    >>> y = np.cos(t)\n    >>> z = t\n    >>> xyz=np.vstack((x,y,z)).T\n    >>> xyza = approx_polygon_track(xyz)\n    >>> len(xyza) < len(xyz)\n    True\n\n    Notes\n    -----\n    Assuming that a good approximation for a circle is an octagon then\n    that means that the points of the octagon will have angle alpha =\n    2*pi/8 = pi/4 . We calculate the angle between every two neighbour\n    segments of a trajectory and if the angle is higher than pi/4 we\n    choose that point as a characteristic point otherwise we move at the\n    next point.\n    ";
static char __pyx_k_Intersect_Segment_S_t_sa_t_sb_s[] = " Intersect Segment S(t) = sa +t(sb-sa), 0 <=t<= 1 against cylinder specified by p,q and r\n\n    See p.197 from Real Time Collision Detection by C. Ericson\n\n    Examples\n    --------\n    Define cylinder using a segment defined by\n\n    >>> p=np.array([0,0,0],dtype=np.float32)\n    >>> q=np.array([1,0,0],dtype=np.float32)\n    >>> r=0.5\n\n    Define segment\n\n    >>> sa=np.array([0.5,1 ,0],dtype=np.float32)\n    >>> sb=np.array([0.5,-1,0],dtype=np.float32)\n\n    Intersection\n\n    >>> intersect_segment_cylinder(sa, sb, p, q, r)\n    (1.0, 0.25, 0.75)\n    ";
static char __pyx_k_Metric_should_be_one_of_avg_min[] = "Metric should be one of avg, min, max";
static char __pyx_k_Optimized_track_distances_simil[] = " Optimized track distances, similarities and clustering algorithms using\ntrack distances\n";
static char __pyx_k_home_eleftherios_Devel_dipy_dip[] = "/home/eleftherios/Devel/dipy/dipy/tracking/distances.pyx";
static char __pyx_k_intersect_segment_cylinder_line[] = "intersect_segment_cylinder (line 1158)";
static char __pyx_k_lee_perpendicular_distance_line[] = "lee_perpendicular_distance (line 838)";
static char __pyx_k_unknown_dtype_code_in_numpy_pxd[] = "unknown dtype code in numpy.pxd (%d)";
static char __pyx_k_Efficient_tractography_clusterin[] = "Efficient tractography clustering\n\n    Every track can needs to have the same number of points.\n    Use `dipy.tracking.metrics.downsample` to restrict the number of points\n\n    Parameters\n    ----------\n    tracks : sequence\n        of tracks as arrays, shape (N,3) .. (N,3) where N=points\n    d_thr : float\n        average euclidean distance threshold\n\n    Returns\n    -------\n    C : dict\n        Clusters.\n\n    Examples\n    --------\n    >>> tracks=[np.array([[0,0,0],[1,0,0,],[2,0,0]]),\n    ...         np.array([[3,0,0],[3.5,1,0],[4,2,0]]),\n    ...         np.array([[3.2,0,0],[3.7,1,0],[4.4,2,0]]),\n    ...         np.array([[3.4,0,0],[3.9,1,0],[4.6,2,0]]),\n    ...         np.array([[0,0.2,0],[1,0.2,0],[2,0.2,0]]),\n    ...         np.array([[2,0.2,0],[1,0.2,0],[0,0.2,0]]),\n    ...         np.array([[0,0,0],[0,1,0],[0,2,0]])]\n    >>> C = local_skeleton_clustering(tracks, d_thr=0.5)\n\n    Notes\n    -----\n    The distance calculated between two tracks::\n\n        t_1       t_2\n\n        0*   a    *0\n          \\       |\n           \\      |\n           1*     |\n            |  b  *1\n            |      \\\n            2*      \\\n                c    *2\n\n    is equal to $(a+b+c)/3$ where $a$ the euclidean distance between ``t_1[0]``\n    and ``t_2[0]``, $b$ between ``t_1[1]`` and ``t_2[1]`` and $c$ between\n    ``t_1[2]`` and ``t_2[2]``. Also the same with t2 flipped (so ``t_1[0]``\n    compared to ``t_2[2]`` etc).\n\n    Visualization:\n\n    It is possible to visualize the clustering C from the example\n    above using the fvtk module::\n\n        from dipy.viz import fvtk\n        r=fvtk.ren()\n        for c in C:\n            color=np.random.rand(3)\n            for i in C[c]['indices']:\n                fvtk.add(r,fvtk.line(tracks[i],color))\n        fvtk.show(r)\n\n    See Also\n    --------\n    dipy.tracking.metrics.downsample\n    ";
static char __pyx_k_Format_string_allocated_too_shor[] = "Format string allocated too short, see comment in numpy.pxd";
static char __pyx_k_Generate_a_first_pass_clustering[] = "Generate a first pass clustering using 3 points on the tracks only.\n\n    Parameters\n    ----------\n    tracks : sequence\n        of tracks as arrays, shape ``(N1,3) .. (Nm,3)``, where 3 points are\n        (first, mid and last)\n    indices : None or sequence, optional\n        Sequence of integer indices of tracks\n    trh : float, optional\n        squared euclidean distance threshold\n\n    Returns\n    -------\n    C : dict\n        A tree graph containing the clusters.\n\n    Notes\n    -----\n    If a 3 point track (3track) is far away from all clusters then add a new\n    cluster and assign this 3track as the rep(representative) track for the new\n    cluster. Otherwise the rep 3track of each cluster is the average track of\n    the cluster.\n\n    Examples\n    --------\n    >>> tracks=[np.array([[0,0,0],[1,0,0,],[2,0,0]],dtype=np.float32),\n    ...         np.array([[3,0,0],[3.5,1,0],[4,2,0]],dtype=np.float32),\n    ...         np.array([[3.2,0,0],[3.7,1,0],[4.4,2,0]],dtype=np.float32),\n    ...         np.array([[3.4,0,0],[3.9,1,0],[4.6,2,0]],dtype=np.float32),\n    ...         np.array([[0,0.2,0],[1,0.2,0],[2,0.2,0]],dtype=np.float32),\n    ...         np.array([[2,0.2,0],[1,0.2,0],[0,0.2,0]],dtype=np.float32),\n    ...         np.array([[0,0,0],[0,1,0],[0,2,0]],dtype=np.float32),\n    ...         np.array([[0.2,0,0],[0.2,1,0],[0.2,2,0]],dtype=np.float32),\n    ...         np.array([[-0.2,0,0],[-0.2,1,0],[-0.2,2,0]],dtype=np.float32)]\n    >>> C = larch_3split(tracks, None, 0.5)\n\n    Here is an example of how to visualize the clustering above::\n\n        from dipy.viz import fvtk\n        r=fvtk.ren()\n        fvtk.add(r,fvtk.line(tracks,fvtk.red))\n        fvtk.show(r)\n        for c in C:\n            color=np.random.rand(3)\n            for i in C[c]['indices']:\n                fos.add(r,fvtk.line(tracks[i],color))\n        fvtk.show(r)\n        for c in C:\n            fvtk.add(r,fos.line(C[c]['rep3']/C[c]['N'],fos.white))\n        fvtk.show(""r)\n    ";
static char __pyx_k_Non_native_byte_order_not_suppor[] = "Non-native byte order not supported";
static char __pyx_k_local_skeleton_clustering_3pts_l[] = "local_skeleton_clustering_3pts (line 1656)";
static char __pyx_k_local_skeleton_clustering_line_1[] = "local_skeleton_clustering (line 1471)";
static char __pyx_k_ndarray_is_not_Fortran_contiguou[] = "ndarray is not Fortran contiguous";
static char __pyx_k_point_segment_sq_distance_line_1[] = "point_segment_sq_distance (line 1271)";
static char __pyx_k_point_track_sq_distance_check_li[] = "point_track_sq_distance_check (line 1953)";
static char __pyx_k_track_roi_intersection_check_lin[] = "track_roi_intersection_check (line 2011)";
static char __pyx_k_Format_string_allocated_too_shor_2[] = "Format string allocated too short.";
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static PyObject *__pyx_n_s_C2;
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static PyObject *__pyx_kp_u_Calculate_the_squared_distance;
static PyObject *__pyx_kp_u_Calculates_angle_distance_metri;
static PyObject *__pyx_kp_u_Calculates_perpendicular_distan;
static PyObject *__pyx_kp_u_Check_if_a_track_is_intersectin;
static PyObject *__pyx_kp_u_Check_if_square_distance_of_tra;
static PyObject *__pyx_n_s_DM;
static PyObject *__pyx_kp_u_Does_a_first_pass_clustering_Ev;
static PyObject *__pyx_kp_u_Efficient_tractography_clusterin;
static PyObject *__pyx_kp_u_Extract_divergence_vectors_and;
static PyObject *__pyx_kp_u_Fast_and_simple_trajectory_appr;
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static PyObject *__pyx_kp_u_track_dist_3pts_line_1324;
static PyObject *__pyx_n_s_track_len;
static PyObject *__pyx_n_s_track_lengths;
static PyObject *__pyx_n_s_track_roi_intersection_check;
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/* "dipy/tracking/distances.pyx":41
 * DEF biggest_float = 3.4028235e+38 #np.finfo('f4').max
 * 
 * cdef inline cnp.ndarray[cnp.float32_t, ndim=1] as_float_3vec(object vec):             # <<<<<<<<<<<<<<
 *     ''' Utility function to convert object to 3D float vector '''
 *     return np.squeeze(np.asarray(vec, dtype=np.float32))
 */

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 */
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 */
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 *                 next_trk_p = asfp(track[q_no+1]) # r             # <<<<<<<<<<<<<<
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 *                 #if np.inner(normal,q-p)*np.inner(normal,r-p) <= 0:
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 */
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 *                 #if np.inner(normal,q-p)*np.inner(normal,r-p) <= 0:
 *                 csub_3vecs(this_trk_p, this_ref_p, qMp) # q-p
 *                 csub_3vecs(next_trk_p, this_ref_p, rMp) # r-p             # <<<<<<<<<<<<<<
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 *                     #if np.inner((r-q),normal) != 0:
 */
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 *                 csub_3vecs(this_trk_p, this_ref_p, qMp) # q-p
 *                 csub_3vecs(next_trk_p, this_ref_p, rMp) # r-p
 *                 if (cinner_3vecs(normal, qMp) * cinner_3vecs(normal, rMp)) <=0:             # <<<<<<<<<<<<<<
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 *                     #if np.inner((r-q),normal) != 0:
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 */
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 *                     #if np.inner((r-q),normal) != 0:
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 *                     beta = cinner_3vecs(rMq, normal)             # <<<<<<<<<<<<<<
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 */
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 *                     csub_3vecs(next_trk_p, this_trk_p, rMq)
 *                     beta = cinner_3vecs(rMq, normal)
 *                     if beta !=0:             # <<<<<<<<<<<<<<
 *                         #alpha = np.inner((p-q),normal)/np.inner((r-q),normal)
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 */
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 *                     if beta !=0:
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 *                         csub_3vecs(this_ref_p, this_trk_p, pMq)             # <<<<<<<<<<<<<<
 *                         alpha = (cinner_3vecs(pMq, normal) /
 *                                   cinner_3vecs(rMq, normal))
 */
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 *                         #alpha = np.inner((p-q),normal)/np.inner((r-q),normal)
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 *                                   cinner_3vecs(rMq, normal))
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 *                         csub_3vecs(this_ref_p, this_trk_p, pMq)
 *                         alpha = (cinner_3vecs(pMq, normal) /
 *                                   cinner_3vecs(rMq, normal))             # <<<<<<<<<<<<<<
 *                         if alpha < 1:
 *                             # hit = q+alpha*(r-q)
 */
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 *                         #alpha = np.inner((p-q),normal)/np.inner((r-q),normal)
 *                         csub_3vecs(this_ref_p, this_trk_p, pMq)
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 *                                   cinner_3vecs(rMq, normal))
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 *                         alpha = (cinner_3vecs(pMq, normal) /
 *                                   cinner_3vecs(rMq, normal))
 *                         if alpha < 1:             # <<<<<<<<<<<<<<
 *                             # hit = q+alpha*(r-q)
 *                             hit[0] = this_trk_p[0]+alpha*rMq[0]
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 *                         if alpha < 1:
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 *                             hit[0] = this_trk_p[0]+alpha*rMq[0]             # <<<<<<<<<<<<<<
 *                             hit[1] = this_trk_p[1]+alpha*rMq[1]
 *                             hit[2] = this_trk_p[2]+alpha*rMq[2]
 */
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 *                             # hit = q+alpha*(r-q)
 *                             hit[0] = this_trk_p[0]+alpha*rMq[0]
 *                             hit[1] = this_trk_p[1]+alpha*rMq[1]             # <<<<<<<<<<<<<<
 *                             hit[2] = this_trk_p[2]+alpha*rMq[2]
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 */
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 *                             hit[0] = this_trk_p[0]+alpha*rMq[0]
 *                             hit[1] = this_trk_p[1]+alpha*rMq[1]
 *                             hit[2] = this_trk_p[2]+alpha*rMq[2]             # <<<<<<<<<<<<<<
 *                             # h-p
 *                             csub_3vecs(hit, this_ref_p, hitMp)
 */
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 *                             hit[2] = this_trk_p[2]+alpha*rMq[2]
 *                             # h-p
 *                             csub_3vecs(hit, this_ref_p, hitMp)             # <<<<<<<<<<<<<<
 *                             # |h-p|
 *                             lhp = cnorm_3vec(hitMp)
 */
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 *                             csub_3vecs(hit, this_ref_p, hitMp)
 *                             # |h-p|
 *                             lhp = cnorm_3vec(hitMp)             # <<<<<<<<<<<<<<
 *                             delta = rMq # just renaming
 *                             # |r-q| == |delta|
 */
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              /* "dipy/tracking/distances.pyx":307
 *                             # |h-p|
 *                             lhp = cnorm_3vec(hitMp)
 *                             delta = rMq # just renaming             # <<<<<<<<<<<<<<
 *                             # |r-q| == |delta|
 *                             ld = cnorm_3vec(delta)
 */
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              /* "dipy/tracking/distances.pyx":309
 *                             delta = rMq # just renaming
 *                             # |r-q| == |delta|
 *                             ld = cnorm_3vec(delta)             # <<<<<<<<<<<<<<
 *                             ''' # Summary of stuff in comments
 *                             # divergence =((r-q)-inner(r-q,normal)*normal)/|r-q|
 */
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              /* "dipy/tracking/distances.pyx":319
 *                             # radial divergence
 *                             # np.inner(delta, (hit-p)) / (ld * lhp)
 *                             if lhp > 0:             # <<<<<<<<<<<<<<
 *                                 rcd = fabs(cinner_3vecs(delta, hitMp)
 *                                            / (ld*lhp))
 */
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 *                             # np.inner(delta, (hit-p)) / (ld * lhp)
 *                             if lhp > 0:
 *                                 rcd = fabs(cinner_3vecs(delta, hitMp)             # <<<<<<<<<<<<<<
 *                                            / (ld*lhp))
 *                             else:
 */
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 *                             if lhp > 0:
 *                                 rcd = fabs(cinner_3vecs(delta, hitMp)
 *                                            / (ld*lhp))             # <<<<<<<<<<<<<<
 *                             else:
 *                                 rcd=0
 */
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                  {__pyx_filename = __pyx_f[0]; __pyx_lineno = 321; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
                }

                /* "dipy/tracking/distances.pyx":320
 *                             # np.inner(delta, (hit-p)) / (ld * lhp)
 *                             if lhp > 0:
 *                                 rcd = fabs(cinner_3vecs(delta, hitMp)             # <<<<<<<<<<<<<<
 *                                            / (ld*lhp))
 *                             else:
 */
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                /* "dipy/tracking/distances.pyx":323
 *                                            / (ld*lhp))
 *                             else:
 *                                 rcd=0             # <<<<<<<<<<<<<<
 *                             # hit data into array
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 * 
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 *                 DM[i,j]=d[1]
 *     return DM             # <<<<<<<<<<<<<<
 * 
 * 
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  /* "dipy/tracking/distances.pyx":541
 * @cython.boundscheck(False)
 * @cython.wraparound(False)
 * def bundles_distances_mdf(tracksA, tracksB):             # <<<<<<<<<<<<<<
 *     ''' Calculate distances between list of tracks A and list of tracks B
 * 
 */

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/* "dipy/tracking/distances.pyx":614
 * 
 * @cython.cdivision(True)
 * cdef inline cnp.float32_t czhang(size_t t1_len,             # <<<<<<<<<<<<<<
 *                                  cnp.float32_t *track1_ptr,
 *                                  size_t t2_len,
 */

static CYTHON_INLINE __pyx_t_5numpy_float32_t __pyx_f_4dipy_8tracking_9distances_czhang(size_t __pyx_v_t1_len, __pyx_t_5numpy_float32_t *__pyx_v_track1_ptr, size_t __pyx_v_t2_len, __pyx_t_5numpy_float32_t *__pyx_v_track2_ptr, __pyx_t_5numpy_float32_t *__pyx_v_min_buffer, int __pyx_v_metric_type) {
  __pyx_t_5numpy_float32_t *__pyx_v_min_t2t1;
  __pyx_t_5numpy_float32_t *__pyx_v_min_t1t2;
  size_t __pyx_v_t1_pi;
  size_t __pyx_v_t2_pi;
  __pyx_t_5numpy_float32_t __pyx_v_mean_t2t1;
  __pyx_t_5numpy_float32_t __pyx_v_mean_t1t2;
  __pyx_t_5numpy_float32_t __pyx_v_dist_val;
  __pyx_t_5numpy_float32_t __pyx_r;
  size_t __pyx_t_1;
  int __pyx_t_2;

  /* "dipy/tracking/distances.pyx":623
 *     cdef:
 *         cnp.float32_t *min_t2t1, *min_t1t2
 *     min_t2t1 = min_buffer             # <<<<<<<<<<<<<<
 *     min_t1t2 = min_buffer + t2_len
 *     min_distances(t1_len, track1_ptr,
 */
  __pyx_v_min_t2t1 = __pyx_v_min_buffer;

  /* "dipy/tracking/distances.pyx":624
 *         cnp.float32_t *min_t2t1, *min_t1t2
 *     min_t2t1 = min_buffer
 *     min_t1t2 = min_buffer + t2_len             # <<<<<<<<<<<<<<
 *     min_distances(t1_len, track1_ptr,
 *                   t2_len, track2_ptr,
 */
  __pyx_v_min_t1t2 = (__pyx_v_min_buffer + __pyx_v_t2_len);

  /* "dipy/tracking/distances.pyx":625
 *     min_t2t1 = min_buffer
 *     min_t1t2 = min_buffer + t2_len
 *     min_distances(t1_len, track1_ptr,             # <<<<<<<<<<<<<<
 *                   t2_len, track2_ptr,
 *                   min_t2t1,
 */
  __pyx_f_4dipy_8tracking_9distances_min_distances(__pyx_v_t1_len, __pyx_v_track1_ptr, __pyx_v_t2_len, __pyx_v_track2_ptr, __pyx_v_min_t2t1, __pyx_v_min_t1t2);

  /* "dipy/tracking/distances.pyx":631
 *     cdef:
 *         size_t t1_pi, t2_pi
 *         cnp.float32_t mean_t2t1 = 0, mean_t1t2 = 0, dist_val             # <<<<<<<<<<<<<<
 *     for t1_pi from 0<= t1_pi < t1_len:
 *         mean_t1t2+=min_t1t2[t1_pi]
 */
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  __pyx_v_mean_t1t2 = 0.0;

  /* "dipy/tracking/distances.pyx":632
 *         size_t t1_pi, t2_pi
 *         cnp.float32_t mean_t2t1 = 0, mean_t1t2 = 0, dist_val
 *     for t1_pi from 0<= t1_pi < t1_len:             # <<<<<<<<<<<<<<
 *         mean_t1t2+=min_t1t2[t1_pi]
 *     mean_t1t2=mean_t1t2/t1_len
 */
  __pyx_t_1 = __pyx_v_t1_len;
  for (__pyx_v_t1_pi = 0; __pyx_v_t1_pi < __pyx_t_1; __pyx_v_t1_pi++) {

    /* "dipy/tracking/distances.pyx":633
 *         cnp.float32_t mean_t2t1 = 0, mean_t1t2 = 0, dist_val
 *     for t1_pi from 0<= t1_pi < t1_len:
 *         mean_t1t2+=min_t1t2[t1_pi]             # <<<<<<<<<<<<<<
 *     mean_t1t2=mean_t1t2/t1_len
 *     for t2_pi from 0<= t2_pi < t2_len:
 */
    __pyx_v_mean_t1t2 = (__pyx_v_mean_t1t2 + (__pyx_v_min_t1t2[__pyx_v_t1_pi]));
  }

  /* "dipy/tracking/distances.pyx":634
 *     for t1_pi from 0<= t1_pi < t1_len:
 *         mean_t1t2+=min_t1t2[t1_pi]
 *     mean_t1t2=mean_t1t2/t1_len             # <<<<<<<<<<<<<<
 *     for t2_pi from 0<= t2_pi < t2_len:
 *         mean_t2t1+=min_t2t1[t2_pi]
 */
  __pyx_v_mean_t1t2 = (__pyx_v_mean_t1t2 / __pyx_v_t1_len);

  /* "dipy/tracking/distances.pyx":635
 *         mean_t1t2+=min_t1t2[t1_pi]
 *     mean_t1t2=mean_t1t2/t1_len
 *     for t2_pi from 0<= t2_pi < t2_len:             # <<<<<<<<<<<<<<
 *         mean_t2t1+=min_t2t1[t2_pi]
 *     mean_t2t1=mean_t2t1/t2_len
 */
  __pyx_t_1 = __pyx_v_t2_len;
  for (__pyx_v_t2_pi = 0; __pyx_v_t2_pi < __pyx_t_1; __pyx_v_t2_pi++) {

    /* "dipy/tracking/distances.pyx":636
 *     mean_t1t2=mean_t1t2/t1_len
 *     for t2_pi from 0<= t2_pi < t2_len:
 *         mean_t2t1+=min_t2t1[t2_pi]             # <<<<<<<<<<<<<<
 *     mean_t2t1=mean_t2t1/t2_len
 *     if metric_type == 0:
 */
    __pyx_v_mean_t2t1 = (__pyx_v_mean_t2t1 + (__pyx_v_min_t2t1[__pyx_v_t2_pi]));
  }

  /* "dipy/tracking/distances.pyx":637
 *     for t2_pi from 0<= t2_pi < t2_len:
 *         mean_t2t1+=min_t2t1[t2_pi]
 *     mean_t2t1=mean_t2t1/t2_len             # <<<<<<<<<<<<<<
 *     if metric_type == 0:
 *         dist_val=(mean_t2t1+mean_t1t2)/2.0
 */
  __pyx_v_mean_t2t1 = (__pyx_v_mean_t2t1 / __pyx_v_t2_len);

  /* "dipy/tracking/distances.pyx":645
 *         else:
 *             dist_val=mean_t1t2
 *     elif metric_type == 2:             # <<<<<<<<<<<<<<
 *         if mean_t2t1 > mean_t1t2:
 *             dist_val=mean_t2t1
 */
  switch (__pyx_v_metric_type) {

    /* "dipy/tracking/distances.pyx":638
 *         mean_t2t1+=min_t2t1[t2_pi]
 *     mean_t2t1=mean_t2t1/t2_len
 *     if metric_type == 0:             # <<<<<<<<<<<<<<
 *         dist_val=(mean_t2t1+mean_t1t2)/2.0
 *     elif metric_type == 1:
 */
    case 0:

    /* "dipy/tracking/distances.pyx":639
 *     mean_t2t1=mean_t2t1/t2_len
 *     if metric_type == 0:
 *         dist_val=(mean_t2t1+mean_t1t2)/2.0             # <<<<<<<<<<<<<<
 *     elif metric_type == 1:
 *         if mean_t2t1 < mean_t1t2:
 */
    __pyx_v_dist_val = ((__pyx_v_mean_t2t1 + __pyx_v_mean_t1t2) / 2.0);
    break;

    /* "dipy/tracking/distances.pyx":640
 *     if metric_type == 0:
 *         dist_val=(mean_t2t1+mean_t1t2)/2.0
 *     elif metric_type == 1:             # <<<<<<<<<<<<<<
 *         if mean_t2t1 < mean_t1t2:
 *             dist_val=mean_t2t1
 */
    case 1:

    /* "dipy/tracking/distances.pyx":641
 *         dist_val=(mean_t2t1+mean_t1t2)/2.0
 *     elif metric_type == 1:
 *         if mean_t2t1 < mean_t1t2:             # <<<<<<<<<<<<<<
 *             dist_val=mean_t2t1
 *         else:
 */
    __pyx_t_2 = ((__pyx_v_mean_t2t1 < __pyx_v_mean_t1t2) != 0);
    if (__pyx_t_2) {

      /* "dipy/tracking/distances.pyx":642
 *     elif metric_type == 1:
 *         if mean_t2t1 < mean_t1t2:
 *             dist_val=mean_t2t1             # <<<<<<<<<<<<<<
 *         else:
 *             dist_val=mean_t1t2
 */
      __pyx_v_dist_val = __pyx_v_mean_t2t1;
      goto __pyx_L7;
    }
    /*else*/ {

      /* "dipy/tracking/distances.pyx":644
 *             dist_val=mean_t2t1
 *         else:
 *             dist_val=mean_t1t2             # <<<<<<<<<<<<<<
 *     elif metric_type == 2:
 *         if mean_t2t1 > mean_t1t2:
 */
      __pyx_v_dist_val = __pyx_v_mean_t1t2;
    }
    __pyx_L7:;
    break;

    /* "dipy/tracking/distances.pyx":645
 *         else:
 *             dist_val=mean_t1t2
 *     elif metric_type == 2:             # <<<<<<<<<<<<<<
 *         if mean_t2t1 > mean_t1t2:
 *             dist_val=mean_t2t1
 */
    case 2:

    /* "dipy/tracking/distances.pyx":646
 *             dist_val=mean_t1t2
 *     elif metric_type == 2:
 *         if mean_t2t1 > mean_t1t2:             # <<<<<<<<<<<<<<
 *             dist_val=mean_t2t1
 *         else:
 */
    __pyx_t_2 = ((__pyx_v_mean_t2t1 > __pyx_v_mean_t1t2) != 0);
    if (__pyx_t_2) {

      /* "dipy/tracking/distances.pyx":647
 *     elif metric_type == 2:
 *         if mean_t2t1 > mean_t1t2:
 *             dist_val=mean_t2t1             # <<<<<<<<<<<<<<
 *         else:
 *             dist_val=mean_t1t2
 */
      __pyx_v_dist_val = __pyx_v_mean_t2t1;
      goto __pyx_L8;
    }
    /*else*/ {

      /* "dipy/tracking/distances.pyx":649
 *             dist_val=mean_t2t1
 *         else:
 *             dist_val=mean_t1t2             # <<<<<<<<<<<<<<
 *     return dist_val
 * 
 */
      __pyx_v_dist_val = __pyx_v_mean_t1t2;
    }
    __pyx_L8:;
    break;
    default: break;
  }

  /* "dipy/tracking/distances.pyx":650
 *         else:
 *             dist_val=mean_t1t2
 *     return dist_val             # <<<<<<<<<<<<<<
 * 
 * @cython.cdivision(True)
 */
  __pyx_r = __pyx_v_dist_val;
  goto __pyx_L0;

  /* "dipy/tracking/distances.pyx":614
 * 
 * @cython.cdivision(True)
 * cdef inline cnp.float32_t czhang(size_t t1_len,             # <<<<<<<<<<<<<<
 *                                  cnp.float32_t *track1_ptr,
 *                                  size_t t2_len,
 */

  /* function exit code */
  __pyx_L0:;
  return __pyx_r;
}

/* "dipy/tracking/distances.pyx":653
 * 
 * @cython.cdivision(True)
 * cdef inline void min_distances(size_t t1_len,             # <<<<<<<<<<<<<<
 *                                cnp.float32_t *track1_ptr,
 *                                size_t t2_len,
 */

static CYTHON_INLINE void __pyx_f_4dipy_8tracking_9distances_min_distances(size_t __pyx_v_t1_len, __pyx_t_5numpy_float32_t *__pyx_v_track1_ptr, size_t __pyx_v_t2_len, __pyx_t_5numpy_float32_t *__pyx_v_track2_ptr, __pyx_t_5numpy_float32_t *__pyx_v_min_t2t1, __pyx_t_5numpy_float32_t *__pyx_v_min_t1t2) {
  __pyx_t_5numpy_float32_t *__pyx_v_t1_pt;
  __pyx_t_5numpy_float32_t *__pyx_v_t2_pt;
  __pyx_t_5numpy_float32_t __pyx_v_d0;
  __pyx_t_5numpy_float32_t __pyx_v_d1;
  __pyx_t_5numpy_float32_t __pyx_v_d2;
  __pyx_t_5numpy_float32_t __pyx_v_delta2;
  int __pyx_v_t1_pi;
  int __pyx_v_t2_pi;
  size_t __pyx_t_1;
  size_t __pyx_t_2;
  int __pyx_t_3;

  /* "dipy/tracking/distances.pyx":663
 *         cnp.float32_t delta2
 *         int t1_pi, t2_pi
 *     for t2_pi from 0<= t2_pi < t2_len:             # <<<<<<<<<<<<<<
 *         min_t2t1[t2_pi] = inf
 *     for t1_pi from 0<= t1_pi < t1_len:
 */
  __pyx_t_1 = __pyx_v_t2_len;
  for (__pyx_v_t2_pi = 0; __pyx_v_t2_pi < __pyx_t_1; __pyx_v_t2_pi++) {

    /* "dipy/tracking/distances.pyx":664
 *         int t1_pi, t2_pi
 *     for t2_pi from 0<= t2_pi < t2_len:
 *         min_t2t1[t2_pi] = inf             # <<<<<<<<<<<<<<
 *     for t1_pi from 0<= t1_pi < t1_len:
 *         min_t1t2[t1_pi] = inf
 */
    (__pyx_v_min_t2t1[__pyx_v_t2_pi]) = __pyx_v_4dipy_8tracking_9distances_inf;
  }

  /* "dipy/tracking/distances.pyx":665
 *     for t2_pi from 0<= t2_pi < t2_len:
 *         min_t2t1[t2_pi] = inf
 *     for t1_pi from 0<= t1_pi < t1_len:             # <<<<<<<<<<<<<<
 *         min_t1t2[t1_pi] = inf
 *     # pointer to current point in track 1
 */
  __pyx_t_1 = __pyx_v_t1_len;
  for (__pyx_v_t1_pi = 0; __pyx_v_t1_pi < __pyx_t_1; __pyx_v_t1_pi++) {

    /* "dipy/tracking/distances.pyx":666
 *         min_t2t1[t2_pi] = inf
 *     for t1_pi from 0<= t1_pi < t1_len:
 *         min_t1t2[t1_pi] = inf             # <<<<<<<<<<<<<<
 *     # pointer to current point in track 1
 *     t1_pt = track1_ptr
 */
    (__pyx_v_min_t1t2[__pyx_v_t1_pi]) = __pyx_v_4dipy_8tracking_9distances_inf;
  }

  /* "dipy/tracking/distances.pyx":668
 *         min_t1t2[t1_pi] = inf
 *     # pointer to current point in track 1
 *     t1_pt = track1_ptr             # <<<<<<<<<<<<<<
 *     # calculate min squared distance between each point in the two
 *     # lines.  Squared distance to delay doing the sqrt until after this
 */
  __pyx_v_t1_pt = __pyx_v_track1_ptr;

  /* "dipy/tracking/distances.pyx":672
 *     # lines.  Squared distance to delay doing the sqrt until after this
 *     # speed-critical loop
 *     for t1_pi from 0<= t1_pi < t1_len:             # <<<<<<<<<<<<<<
 *         # pointer to current point in track 2
 *         t2_pt = track2_ptr
 */
  __pyx_t_1 = __pyx_v_t1_len;
  for (__pyx_v_t1_pi = 0; __pyx_v_t1_pi < __pyx_t_1; __pyx_v_t1_pi++) {

    /* "dipy/tracking/distances.pyx":674
 *     for t1_pi from 0<= t1_pi < t1_len:
 *         # pointer to current point in track 2
 *         t2_pt = track2_ptr             # <<<<<<<<<<<<<<
 *         for t2_pi from 0<= t2_pi < t2_len:
 *             d0 = t1_pt[0] - t2_pt[0]
 */
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    /* "dipy/tracking/distances.pyx":675
 *         # pointer to current point in track 2
 *         t2_pt = track2_ptr
 *         for t2_pi from 0<= t2_pi < t2_len:             # <<<<<<<<<<<<<<
 *             d0 = t1_pt[0] - t2_pt[0]
 *             d1 = t1_pt[1] - t2_pt[1]
 */
    __pyx_t_2 = __pyx_v_t2_len;
    for (__pyx_v_t2_pi = 0; __pyx_v_t2_pi < __pyx_t_2; __pyx_v_t2_pi++) {

      /* "dipy/tracking/distances.pyx":676
 *         t2_pt = track2_ptr
 *         for t2_pi from 0<= t2_pi < t2_len:
 *             d0 = t1_pt[0] - t2_pt[0]             # <<<<<<<<<<<<<<
 *             d1 = t1_pt[1] - t2_pt[1]
 *             d2 = t1_pt[2] - t2_pt[2]
 */
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 *         for t2_pi from 0<= t2_pi < t2_len:
 *             d0 = t1_pt[0] - t2_pt[0]
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static char __pyx_doc_4dipy_8tracking_9distances_26lee_perpendicular_distance[] = " Calculates perpendicular distance metric for the distance between two line segments\n\n    Based on Lee , Han & Whang SIGMOD07.\n\n    This function assumes that norm(end0-start0)>norm(end1-start1) i.e. that the\n    first segment will be bigger than the second one.\n\n    Parameters\n    ----------\n    start0 : float array(3,)\n    end0 : float array(3,)\n    start1 : float array(3,)\n    end1 : float array(3,)\n\n    Returns\n    -------\n    perpendicular_distance: float\n\n    Notes\n    -----\n    l0 = np.inner(end0-start0,end0-start0)\n    l1 = np.inner(end1-start1,end1-start1)\n\n    k0=end0-start0\n\n    u1 = np.inner(start1-start0,k0)/l0\n    u2 = np.inner(end1-start0,k0)/l0\n\n    ps = start0+u1*k0\n    pe = start0+u2*k0\n\n    lperp1 = np.sqrt(np.inner(ps-start1,ps-start1))\n    lperp2 = np.sqrt(np.inner(pe-end1,pe-end1))\n\n    if lperp1+lperp2 > 0.:\n        return (lperp1**2+lperp2**2)/(lperp1+lperp2)\n    else:\n        return 0.\n\n    Examples\n    --------\n    >>> d = lee_perpendicular_distance([0,0,0],[1,0,0],[3,4,5],[5,4,3])\n    >>> print('%.6f' % d)\n    5.787888\n    ";
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static char __pyx_doc_4dipy_8tracking_9distances_28lee_angle_distance[] = " Calculates angle distance metric for the distance between two line segments\n\n    Based on Lee , Han & Whang SIGMOD07.\n\n    This function assumes that norm(end0-start0)>norm(end1-start1) i.e. that the\n    first segment will be bigger than the second one.\n\n    Parameters\n    ----------\n    start0 : float array(3,)\n    end0 : float array(3,)\n    start1 : float array(3,)\n    end1 : float array(3,)\n\n    Returns\n    -------\n    angle_distance : float\n\n    Notes\n    -----\n    l_0 = np.inner(end0-start0,end0-start0)\n    l_1 = np.inner(end1-start1,end1-start1)\n\n    cos_theta_squared = np.inner(end0-start0,end1-start1)**2/ (l_0*l_1)\n    return np.sqrt((1-cos_theta_squared)*l_1)\n\n    Examples\n    --------\n    >>> lee_angle_distance([0,0,0],[1,0,0],[3,4,5],[5,4,3])\n    2.0\n    ";
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static char __pyx_doc_4dipy_8tracking_9distances_30approx_polygon_track[] = " Fast and simple trajectory approximation algorithm by Eleftherios and Ian\n\n    It will reduce the number of points of the track by keeping\n    intact the start and endpoints of the track and trying to remove\n    as many points as possible without distorting much the shape of\n    the track\n\n    Parameters\n    ----------\n    xyz : array(N,3)\n        initial trajectory\n    alpha : float\n        smoothing parameter (<0.392 smoother, >0.392 rougher) if the\n        trajectory was a smooth circle then with alpha =0.393\n        ~=pi/8. the circle would be approximated with an decahexagon if\n        alpha = 0.7853 ~=pi/4. with an octagon.\n\n    Returns\n    -------\n    characteristic_points: list of M array(3,) points\n\n    Examples\n    --------\n\n    Approximating a helix:\n\n    >>> t=np.linspace(0,1.75*2*np.pi,100)\n    >>> x = np.sin(t)\n    >>> y = np.cos(t)\n    >>> z = t\n    >>> xyz=np.vstack((x,y,z)).T\n    >>> xyza = approx_polygon_track(xyz)\n    >>> len(xyza) < len(xyz)\n    True\n\n    Notes\n    -----\n    Assuming that a good approximation for a circle is an octagon then\n    that means that the points of the octagon will have angle alpha =\n    2*pi/8 = pi/4 . We calculate the angle between every two neighbour\n    segments of a trajectory and if the angle is higher than pi/4 we\n    choose that point as a characteristic point otherwise we move at the\n    next point.\n    ";
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 *         #print start_index,current_index
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 *         #print start_index,current_index
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 *             fvec4 = as_float_3vec(track[i+1])
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 *             fvec4 = as_float_3vec(track[i+1])
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 *             cost_par += dpy_log2(clee_angle_distance(<float *>fvec3.data,<float *>fvec4.data,<float *>fvec1.data,<float *>fvec2.data))
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 *             fvec4 = as_float_3vec(track[i+1])
 *             cost_par += dpy_log2(clee_perpendicular_distance(<float *>fvec3.data,<float *>fvec4.data,<float *>fvec1.data,<float *>fvec2.data))
 *             cost_par += dpy_log2(clee_angle_distance(<float *>fvec3.data,<float *>fvec4.data,<float *>fvec1.data,<float *>fvec2.data))             # <<<<<<<<<<<<<<
 *             csub_3vecs(<float *>fvec4.data,<float *>fvec3.data,tmp)
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 *             cost_par += dpy_log2(clee_perpendicular_distance(<float *>fvec3.data,<float *>fvec4.data,<float *>fvec1.data,<float *>fvec2.data))
 *             cost_par += dpy_log2(clee_angle_distance(<float *>fvec3.data,<float *>fvec4.data,<float *>fvec1.data,<float *>fvec2.data))
 *             csub_3vecs(<float *>fvec4.data,<float *>fvec3.data,tmp)             # <<<<<<<<<<<<<<
 *             cost_nopar += dpy_log2(cinner_3vecs(tmp,tmp))
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 *             cost_par += dpy_log2(clee_angle_distance(<float *>fvec3.data,<float *>fvec4.data,<float *>fvec1.data,<float *>fvec2.data))
 *             csub_3vecs(<float *>fvec4.data,<float *>fvec3.data,tmp)
 *             cost_nopar += dpy_log2(cinner_3vecs(tmp,tmp))             # <<<<<<<<<<<<<<
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 *             csub_3vecs(<float *>fvec4.data,<float *>fvec3.data,tmp)
 *             cost_nopar += dpy_log2(cinner_3vecs(tmp,tmp))
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 *             characteristic_points.append(track[current_index-1])
 *             start_index = current_index-1
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 *             start_index = current_index-1
 *             length = 2
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 *     characteristic_points.append(track[-1])             # <<<<<<<<<<<<<<
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  /* "dipy/tracking/distances.pyx":1215
 *         float epsilon_float=5.96e-08
 * 
 *     csub_3vecs(q,p,d)             # <<<<<<<<<<<<<<
 *     csub_3vecs(sa,p,m)
 *     csub_3vecs(sb,sa,n)
 */
  __pyx_f_4dipy_8tracking_9distances_csub_3vecs(__pyx_v_q, __pyx_v_p, __pyx_v_d);

  /* "dipy/tracking/distances.pyx":1216
 * 
 *     csub_3vecs(q,p,d)
 *     csub_3vecs(sa,p,m)             # <<<<<<<<<<<<<<
 *     csub_3vecs(sb,sa,n)
 * 
 */
  __pyx_f_4dipy_8tracking_9distances_csub_3vecs(__pyx_v_sa, __pyx_v_p, __pyx_v_m);

  /* "dipy/tracking/distances.pyx":1217
 *     csub_3vecs(q,p,d)
 *     csub_3vecs(sa,p,m)
 *     csub_3vecs(sb,sa,n)             # <<<<<<<<<<<<<<
 * 
 *     md=cinner_3vecs(m,d)
 */
  __pyx_f_4dipy_8tracking_9distances_csub_3vecs(__pyx_v_sb, __pyx_v_sa, __pyx_v_n);

  /* "dipy/tracking/distances.pyx":1219
 *     csub_3vecs(sb,sa,n)
 * 
 *     md=cinner_3vecs(m,d)             # <<<<<<<<<<<<<<
 *     nd=cinner_3vecs(n,d)
 *     dd=cinner_3vecs(d,d)
 */
  __pyx_v_md = __pyx_f_4dipy_8tracking_9distances_cinner_3vecs(__pyx_v_m, __pyx_v_d);

  /* "dipy/tracking/distances.pyx":1220
 * 
 *     md=cinner_3vecs(m,d)
 *     nd=cinner_3vecs(n,d)             # <<<<<<<<<<<<<<
 *     dd=cinner_3vecs(d,d)
 * 
 */
  __pyx_v_nd = __pyx_f_4dipy_8tracking_9distances_cinner_3vecs(__pyx_v_n, __pyx_v_d);

  /* "dipy/tracking/distances.pyx":1221
 *     md=cinner_3vecs(m,d)
 *     nd=cinner_3vecs(n,d)
 *     dd=cinner_3vecs(d,d)             # <<<<<<<<<<<<<<
 * 
 *     #test if segment fully outside either endcap of cylinder
 */
  __pyx_v_dd = __pyx_f_4dipy_8tracking_9distances_cinner_3vecs(__pyx_v_d, __pyx_v_d);

  /* "dipy/tracking/distances.pyx":1224
 * 
 *     #test if segment fully outside either endcap of cylinder
 *     if md < 0. and md + nd < 0.:  return 0 #segment outside p side             # <<<<<<<<<<<<<<
 *     if md > dd and md + nd > dd:  return 0 #segment outside q side
 * 
 */
  __pyx_t_2 = ((__pyx_v_md < 0.) != 0);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L4_bool_binop_done;
  }
  __pyx_t_2 = (((__pyx_v_md + __pyx_v_nd) < 0.) != 0);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L4_bool_binop_done:;
  if (__pyx_t_1) {
    __pyx_r = 0.0;
    goto __pyx_L0;
  }

  /* "dipy/tracking/distances.pyx":1225
 *     #test if segment fully outside either endcap of cylinder
 *     if md < 0. and md + nd < 0.:  return 0 #segment outside p side
 *     if md > dd and md + nd > dd:  return 0 #segment outside q side             # <<<<<<<<<<<<<<
 * 
 *     nn=cinner_3vecs(n,n)
 */
  __pyx_t_2 = ((__pyx_v_md > __pyx_v_dd) != 0);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L7_bool_binop_done;
  }
  __pyx_t_2 = (((__pyx_v_md + __pyx_v_nd) > __pyx_v_dd) != 0);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L7_bool_binop_done:;
  if (__pyx_t_1) {
    __pyx_r = 0.0;
    goto __pyx_L0;
  }

  /* "dipy/tracking/distances.pyx":1227
 *     if md > dd and md + nd > dd:  return 0 #segment outside q side
 * 
 *     nn=cinner_3vecs(n,n)             # <<<<<<<<<<<<<<
 *     mn=cinner_3vecs(m,n)
 *     a=dd*nn-nd*nd
 */
  __pyx_v_nn = __pyx_f_4dipy_8tracking_9distances_cinner_3vecs(__pyx_v_n, __pyx_v_n);

  /* "dipy/tracking/distances.pyx":1228
 * 
 *     nn=cinner_3vecs(n,n)
 *     mn=cinner_3vecs(m,n)             # <<<<<<<<<<<<<<
 *     a=dd*nn-nd*nd
 *     k=cinner_3vecs(m,m) -r*r
 */
  __pyx_v_mn = __pyx_f_4dipy_8tracking_9distances_cinner_3vecs(__pyx_v_m, __pyx_v_n);

  /* "dipy/tracking/distances.pyx":1229
 *     nn=cinner_3vecs(n,n)
 *     mn=cinner_3vecs(m,n)
 *     a=dd*nn-nd*nd             # <<<<<<<<<<<<<<
 *     k=cinner_3vecs(m,m) -r*r
 *     c=dd*k-md*md
 */
  __pyx_v_a = ((__pyx_v_dd * __pyx_v_nn) - (__pyx_v_nd * __pyx_v_nd));

  /* "dipy/tracking/distances.pyx":1230
 *     mn=cinner_3vecs(m,n)
 *     a=dd*nn-nd*nd
 *     k=cinner_3vecs(m,m) -r*r             # <<<<<<<<<<<<<<
 *     c=dd*k-md*md
 * 
 */
  __pyx_v_k = (__pyx_f_4dipy_8tracking_9distances_cinner_3vecs(__pyx_v_m, __pyx_v_m) - (__pyx_v_r * __pyx_v_r));

  /* "dipy/tracking/distances.pyx":1231
 *     a=dd*nn-nd*nd
 *     k=cinner_3vecs(m,m) -r*r
 *     c=dd*k-md*md             # <<<<<<<<<<<<<<
 * 
 *     if fabs(a) < epsilon_float:
 */
  __pyx_v_c = ((__pyx_v_dd * __pyx_v_k) - (__pyx_v_md * __pyx_v_md));

  /* "dipy/tracking/distances.pyx":1233
 *     c=dd*k-md*md
 * 
 *     if fabs(a) < epsilon_float:             # <<<<<<<<<<<<<<
 *         #segment runs parallel to cylinder axis
 *         if c>0.:  return 0. # segment lies outside cylinder
 */
  __pyx_t_1 = ((fabs(__pyx_v_a) < __pyx_v_epsilon_float) != 0);
  if (__pyx_t_1) {

    /* "dipy/tracking/distances.pyx":1235
 *     if fabs(a) < epsilon_float:
 *         #segment runs parallel to cylinder axis
 *         if c>0.:  return 0. # segment lies outside cylinder             # <<<<<<<<<<<<<<
 *         if md < 0.:
 *             t[0]=-mn/nn # intersect against p endcap
 */
    __pyx_t_1 = ((__pyx_v_c > 0.) != 0);
    if (__pyx_t_1) {
      __pyx_r = 0.;
      goto __pyx_L0;
    }

    /* "dipy/tracking/distances.pyx":1236
 *         #segment runs parallel to cylinder axis
 *         if c>0.:  return 0. # segment lies outside cylinder
 *         if md < 0.:             # <<<<<<<<<<<<<<
 *             t[0]=-mn/nn # intersect against p endcap
 *         elif md > dd :
 */
    __pyx_t_1 = ((__pyx_v_md < 0.) != 0);
    if (__pyx_t_1) {

      /* "dipy/tracking/distances.pyx":1237
 *         if c>0.:  return 0. # segment lies outside cylinder
 *         if md < 0.:
 *             t[0]=-mn/nn # intersect against p endcap             # <<<<<<<<<<<<<<
 *         elif md > dd :
 *             t[0]=(nd-mn)/nn # intersect against q endcap
 */
      __pyx_t_3 = (-__pyx_v_mn);
      if (unlikely(__pyx_v_nn == 0)) {
        #ifdef WITH_THREAD
        PyGILState_STATE __pyx_gilstate_save = PyGILState_Ensure();
        #endif
        PyErr_SetString(PyExc_ZeroDivisionError, "float division");
        #ifdef WITH_THREAD
        PyGILState_Release(__pyx_gilstate_save);
        #endif
        {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1237; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
      }
      (__pyx_v_t[0]) = (__pyx_t_3 / __pyx_v_nn);
      goto __pyx_L11;
    }

    /* "dipy/tracking/distances.pyx":1238
 *         if md < 0.:
 *             t[0]=-mn/nn # intersect against p endcap
 *         elif md > dd :             # <<<<<<<<<<<<<<
 *             t[0]=(nd-mn)/nn # intersect against q endcap
 *         else:
 */
    __pyx_t_1 = ((__pyx_v_md > __pyx_v_dd) != 0);
    if (__pyx_t_1) {

      /* "dipy/tracking/distances.pyx":1239
 *             t[0]=-mn/nn # intersect against p endcap
 *         elif md > dd :
 *             t[0]=(nd-mn)/nn # intersect against q endcap             # <<<<<<<<<<<<<<
 *         else:
 *             t[0]=0. # lies inside cylinder
 */
      __pyx_t_3 = (__pyx_v_nd - __pyx_v_mn);
      if (unlikely(__pyx_v_nn == 0)) {
        #ifdef WITH_THREAD
        PyGILState_STATE __pyx_gilstate_save = PyGILState_Ensure();
        #endif
        PyErr_SetString(PyExc_ZeroDivisionError, "float division");
        #ifdef WITH_THREAD
        PyGILState_Release(__pyx_gilstate_save);
        #endif
        {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1239; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
      }
      (__pyx_v_t[0]) = (__pyx_t_3 / __pyx_v_nn);
      goto __pyx_L11;
    }
    /*else*/ {

      /* "dipy/tracking/distances.pyx":1241
 *             t[0]=(nd-mn)/nn # intersect against q endcap
 *         else:
 *             t[0]=0. # lies inside cylinder             # <<<<<<<<<<<<<<
 *         return 1
 * 
 */
      (__pyx_v_t[0]) = 0.;
    }
    __pyx_L11:;

    /* "dipy/tracking/distances.pyx":1242
 *         else:
 *             t[0]=0. # lies inside cylinder
 *         return 1             # <<<<<<<<<<<<<<
 * 
 *     b=dd*mn -nd*md
 */
    __pyx_r = 1.0;
    goto __pyx_L0;
  }

  /* "dipy/tracking/distances.pyx":1244
 *         return 1
 * 
 *     b=dd*mn -nd*md             # <<<<<<<<<<<<<<
 *     discr=b*b-a*c
 *     if discr < 0.: return 0. # no real roots ; no intersection
 */
  __pyx_v_b = ((__pyx_v_dd * __pyx_v_mn) - (__pyx_v_nd * __pyx_v_md));

  /* "dipy/tracking/distances.pyx":1245
 * 
 *     b=dd*mn -nd*md
 *     discr=b*b-a*c             # <<<<<<<<<<<<<<
 *     if discr < 0.: return 0. # no real roots ; no intersection
 * 
 */
  __pyx_v_discr = ((__pyx_v_b * __pyx_v_b) - (__pyx_v_a * __pyx_v_c));

  /* "dipy/tracking/distances.pyx":1246
 *     b=dd*mn -nd*md
 *     discr=b*b-a*c
 *     if discr < 0.: return 0. # no real roots ; no intersection             # <<<<<<<<<<<<<<
 * 
 *     t[0]=(-b-sqrt(discr))/a
 */
  __pyx_t_1 = ((__pyx_v_discr < 0.) != 0);
  if (__pyx_t_1) {
    __pyx_r = 0.;
    goto __pyx_L0;
  }

  /* "dipy/tracking/distances.pyx":1248
 *     if discr < 0.: return 0. # no real roots ; no intersection
 * 
 *     t[0]=(-b-sqrt(discr))/a             # <<<<<<<<<<<<<<
 *     t[1]=(-b+sqrt(discr))/a
 *     if t[0]<0. or t[0] > 1. : return 0. # intersection lies outside segment
 */
  __pyx_t_3 = ((-__pyx_v_b) - sqrt(__pyx_v_discr));
  if (unlikely(__pyx_v_a == 0)) {
    #ifdef WITH_THREAD
    PyGILState_STATE __pyx_gilstate_save = PyGILState_Ensure();
    #endif
    PyErr_SetString(PyExc_ZeroDivisionError, "float division");
    #ifdef WITH_THREAD
    PyGILState_Release(__pyx_gilstate_save);
    #endif
    {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1248; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  }
  (__pyx_v_t[0]) = (__pyx_t_3 / __pyx_v_a);

  /* "dipy/tracking/distances.pyx":1249
 * 
 *     t[0]=(-b-sqrt(discr))/a
 *     t[1]=(-b+sqrt(discr))/a             # <<<<<<<<<<<<<<
 *     if t[0]<0. or t[0] > 1. : return 0. # intersection lies outside segment
 * 
 */
  __pyx_t_3 = ((-__pyx_v_b) + sqrt(__pyx_v_discr));
  if (unlikely(__pyx_v_a == 0)) {
    #ifdef WITH_THREAD
    PyGILState_STATE __pyx_gilstate_save = PyGILState_Ensure();
    #endif
    PyErr_SetString(PyExc_ZeroDivisionError, "float division");
    #ifdef WITH_THREAD
    PyGILState_Release(__pyx_gilstate_save);
    #endif
    {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1249; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  }
  (__pyx_v_t[1]) = (__pyx_t_3 / __pyx_v_a);

  /* "dipy/tracking/distances.pyx":1250
 *     t[0]=(-b-sqrt(discr))/a
 *     t[1]=(-b+sqrt(discr))/a
 *     if t[0]<0. or t[0] > 1. : return 0. # intersection lies outside segment             # <<<<<<<<<<<<<<
 * 
 *     if md + t[0]* nd < 0.:
 */
  __pyx_t_2 = (((__pyx_v_t[0]) < 0.) != 0);
  if (!__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L14_bool_binop_done;
  }
  __pyx_t_2 = (((__pyx_v_t[0]) > 1.) != 0);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L14_bool_binop_done:;
  if (__pyx_t_1) {
    __pyx_r = 0.;
    goto __pyx_L0;
  }

  /* "dipy/tracking/distances.pyx":1252
 *     if t[0]<0. or t[0] > 1. : return 0. # intersection lies outside segment
 * 
 *     if md + t[0]* nd < 0.:             # <<<<<<<<<<<<<<
 *         #intersection outside cylinder on 'p' side
 *         if nd <= 0. : return 0. # segment pointing away from endcap
 */
  __pyx_t_1 = (((__pyx_v_md + ((__pyx_v_t[0]) * __pyx_v_nd)) < 0.) != 0);
  if (__pyx_t_1) {

    /* "dipy/tracking/distances.pyx":1254
 *     if md + t[0]* nd < 0.:
 *         #intersection outside cylinder on 'p' side
 *         if nd <= 0. : return 0. # segment pointing away from endcap             # <<<<<<<<<<<<<<
 *         t[0]=-md/nd
 *         #keep intersection if Dot(S(t)-p,S(t)-p) <= r^2
 */
    __pyx_t_1 = ((__pyx_v_nd <= 0.) != 0);
    if (__pyx_t_1) {
      __pyx_r = 0.;
      goto __pyx_L0;
    }

    /* "dipy/tracking/distances.pyx":1255
 *         #intersection outside cylinder on 'p' side
 *         if nd <= 0. : return 0. # segment pointing away from endcap
 *         t[0]=-md/nd             # <<<<<<<<<<<<<<
 *         #keep intersection if Dot(S(t)-p,S(t)-p) <= r^2
 *         if k+2*t[0]*(mn+t[0]*nn) <=0.:
 */
    __pyx_t_3 = (-__pyx_v_md);
    if (unlikely(__pyx_v_nd == 0)) {
      #ifdef WITH_THREAD
      PyGILState_STATE __pyx_gilstate_save = PyGILState_Ensure();
      #endif
      PyErr_SetString(PyExc_ZeroDivisionError, "float division");
      #ifdef WITH_THREAD
      PyGILState_Release(__pyx_gilstate_save);
      #endif
      {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1255; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
    }
    (__pyx_v_t[0]) = (__pyx_t_3 / __pyx_v_nd);

    /* "dipy/tracking/distances.pyx":1257
 *         t[0]=-md/nd
 *         #keep intersection if Dot(S(t)-p,S(t)-p) <= r^2
 *         if k+2*t[0]*(mn+t[0]*nn) <=0.:             # <<<<<<<<<<<<<<
 *             return 1.
 * 
 */
    __pyx_t_1 = (((__pyx_v_k + ((2.0 * (__pyx_v_t[0])) * (__pyx_v_mn + ((__pyx_v_t[0]) * __pyx_v_nn)))) <= 0.) != 0);
    if (__pyx_t_1) {

      /* "dipy/tracking/distances.pyx":1258
 *         #keep intersection if Dot(S(t)-p,S(t)-p) <= r^2
 *         if k+2*t[0]*(mn+t[0]*nn) <=0.:
 *             return 1.             # <<<<<<<<<<<<<<
 * 
 *     elif md+t[0]*nd > dd :
 */
      __pyx_r = 1.;
      goto __pyx_L0;
    }
    goto __pyx_L16;
  }

  /* "dipy/tracking/distances.pyx":1260
 *             return 1.
 * 
 *     elif md+t[0]*nd > dd :             # <<<<<<<<<<<<<<
 *         #intersection outside cylinder on 'q' side
 *         if nd >= 0.: return 0. # segment pointing away from endcap
 */
  __pyx_t_1 = (((__pyx_v_md + ((__pyx_v_t[0]) * __pyx_v_nd)) > __pyx_v_dd) != 0);
  if (__pyx_t_1) {

    /* "dipy/tracking/distances.pyx":1262
 *     elif md+t[0]*nd > dd :
 *         #intersection outside cylinder on 'q' side
 *         if nd >= 0.: return 0. # segment pointing away from endcap             # <<<<<<<<<<<<<<
 *         t[0]= (dd-md)/nd
 *         #keep intersection if Dot(S(t)-q,S(t)-q) <= r^2
 */
    __pyx_t_1 = ((__pyx_v_nd >= 0.) != 0);
    if (__pyx_t_1) {
      __pyx_r = 0.;
      goto __pyx_L0;
    }

    /* "dipy/tracking/distances.pyx":1263
 *         #intersection outside cylinder on 'q' side
 *         if nd >= 0.: return 0. # segment pointing away from endcap
 *         t[0]= (dd-md)/nd             # <<<<<<<<<<<<<<
 *         #keep intersection if Dot(S(t)-q,S(t)-q) <= r^2
 *         if k+dd-2*md+t[0]*(2*(mn-nd)+t[0]*nn) <= 0.:
 */
    __pyx_t_3 = (__pyx_v_dd - __pyx_v_md);
    if (unlikely(__pyx_v_nd == 0)) {
      #ifdef WITH_THREAD
      PyGILState_STATE __pyx_gilstate_save = PyGILState_Ensure();
      #endif
      PyErr_SetString(PyExc_ZeroDivisionError, "float division");
      #ifdef WITH_THREAD
      PyGILState_Release(__pyx_gilstate_save);
      #endif
      {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1263; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
    }
    (__pyx_v_t[0]) = (__pyx_t_3 / __pyx_v_nd);

    /* "dipy/tracking/distances.pyx":1265
 *         t[0]= (dd-md)/nd
 *         #keep intersection if Dot(S(t)-q,S(t)-q) <= r^2
 *         if k+dd-2*md+t[0]*(2*(mn-nd)+t[0]*nn) <= 0.:             # <<<<<<<<<<<<<<
 *             return 1.
 *     # segment intersects cylinder between the endcaps; t is correct
 */
    __pyx_t_1 = (((((__pyx_v_k + __pyx_v_dd) - (2.0 * __pyx_v_md)) + ((__pyx_v_t[0]) * ((2.0 * (__pyx_v_mn - __pyx_v_nd)) + ((__pyx_v_t[0]) * __pyx_v_nn)))) <= 0.) != 0);
    if (__pyx_t_1) {

      /* "dipy/tracking/distances.pyx":1266
 *         #keep intersection if Dot(S(t)-q,S(t)-q) <= r^2
 *         if k+dd-2*md+t[0]*(2*(mn-nd)+t[0]*nn) <= 0.:
 *             return 1.             # <<<<<<<<<<<<<<
 *     # segment intersects cylinder between the endcaps; t is correct
 *     return 1.
 */
      __pyx_r = 1.;
      goto __pyx_L0;
    }
    goto __pyx_L16;
  }
  __pyx_L16:;

  /* "dipy/tracking/distances.pyx":1268
 *             return 1.
 *     # segment intersects cylinder between the endcaps; t is correct
 *     return 1.             # <<<<<<<<<<<<<<
 * 
 * 
 */
  __pyx_r = 1.;
  goto __pyx_L0;

  /* "dipy/tracking/distances.pyx":1198
 *     return tmp, ct[0], ct[1]
 * 
 * cdef float cintersect_segment_cylinder(float *sa,float *sb,float *p, float *q, float r, float *t):             # <<<<<<<<<<<<<<
 *     ''' Intersect Segment S(t) = sa +t(sb-sa), 0 <=t<= 1 against cylinder specified by p,q and r
 * 
 */

  /* function exit code */
  __pyx_L1_error:;
  __Pyx_WriteUnraisable("dipy.tracking.distances.cintersect_segment_cylinder", __pyx_clineno, __pyx_lineno, __pyx_filename, 0);
  __pyx_r = 0;
  __pyx_L0:;
  __Pyx_RefNannyFinishContext();
  return __pyx_r;
}

/* "dipy/tracking/distances.pyx":1271
 * 
 * 
 * def point_segment_sq_distance(a, b, c):             # <<<<<<<<<<<<<<
 *     ''' Calculate the squared distance from a point c to a finite line segment ab.
 * 
 */

/* Python wrapper */
static PyObject *__pyx_pw_4dipy_8tracking_9distances_37point_segment_sq_distance(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds); /*proto*/
static char __pyx_doc_4dipy_8tracking_9distances_36point_segment_sq_distance[] = " Calculate the squared distance from a point c to a finite line segment ab.\n\n    Examples\n    --------\n    >>> a=np.array([0,0,0], dtype=np.float32)\n    >>> b=np.array([1,0,0], dtype=np.float32)\n    >>> c=np.array([0,1,0], dtype=np.float32)\n    >>> point_segment_sq_distance(a, b, c)\n    1.0\n    >>> c = np.array([0,3,0], dtype=np.float32)\n    >>> point_segment_sq_distance(a,b,c)\n    9.0\n    >>> c = np.array([-1,1,0], dtype=np.float32)\n    >>> point_segment_sq_distance(a, b, c)\n    2.0\n    ";
static PyMethodDef __pyx_mdef_4dipy_8tracking_9distances_37point_segment_sq_distance = {"point_segment_sq_distance", (PyCFunction)__pyx_pw_4dipy_8tracking_9distances_37point_segment_sq_distance, METH_VARARGS|METH_KEYWORDS, __pyx_doc_4dipy_8tracking_9distances_36point_segment_sq_distance};
static PyObject *__pyx_pw_4dipy_8tracking_9distances_37point_segment_sq_distance(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds) {
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  int __pyx_v_i;
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  float __pyx_v_tmp2;
  float __pyx_v_tmp3;
  float __pyx_v_tmp1f;
  float __pyx_v_tmp3f;

  /* "dipy/tracking/distances.pyx":1441
 *     cdef:
 *         int i
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 * 
 *     #for i in range(3):
 */
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  __pyx_v_tmp2 = 0.0;
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  __pyx_v_tmp1f = 0.0;
  __pyx_v_tmp3f = 0.0;

  /* "dipy/tracking/distances.pyx":1444
 * 
 *     #for i in range(3):
 *     for i from 0<=i<3:             # <<<<<<<<<<<<<<
 *         tmp1=tmp1+(a1[i]-a2[i])*(a1[i]-a2[i])
 *         tmp2=tmp2+(b1[i]-b2[i])*(b1[i]-b2[i])
 */
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    /* "dipy/tracking/distances.pyx":1445
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 *         tmp2=tmp2+(b1[i]-b2[i])*(b1[i]-b2[i])
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 *     for i from 0<=i<3:
 *         tmp1=tmp1+(a1[i]-a2[i])*(a1[i]-a2[i])
 *         tmp2=tmp2+(b1[i]-b2[i])*(b1[i]-b2[i])             # <<<<<<<<<<<<<<
 *         tmp3=tmp3+(c1[i]-c2[i])*(c1[i]-c2[i])
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 *         tmp2=tmp2+(b1[i]-b2[i])*(b1[i]-b2[i])
 *         tmp3=tmp3+(c1[i]-c2[i])*(c1[i]-c2[i])             # <<<<<<<<<<<<<<
 *         tmp1f=tmp1f+(a1[i]-c2[i])*(a1[i]-c2[i])
 *         tmp3f=tmp3f+(c1[i]-a2[i])*(c1[i]-a2[i])
 */
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 *         tmp2=tmp2+(b1[i]-b2[i])*(b1[i]-b2[i])
 *         tmp3=tmp3+(c1[i]-c2[i])*(c1[i]-c2[i])
 *         tmp1f=tmp1f+(a1[i]-c2[i])*(a1[i]-c2[i])             # <<<<<<<<<<<<<<
 *         tmp3f=tmp3f+(c1[i]-a2[i])*(c1[i]-a2[i])
 * 
 */
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    /* "dipy/tracking/distances.pyx":1449
 *         tmp3=tmp3+(c1[i]-c2[i])*(c1[i]-c2[i])
 *         tmp1f=tmp1f+(a1[i]-c2[i])*(a1[i]-c2[i])
 *         tmp3f=tmp3f+(c1[i]-a2[i])*(c1[i]-a2[i])             # <<<<<<<<<<<<<<
 * 
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 */
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  /* "dipy/tracking/distances.pyx":1451
 *         tmp3f=tmp3f+(c1[i]-a2[i])*(c1[i]-a2[i])
 * 
 *     out[0]=(sqrt(tmp1)+sqrt(tmp2)+sqrt(tmp3))/3.0             # <<<<<<<<<<<<<<
 *     out[1]=(sqrt(tmp1f)+sqrt(tmp2)+sqrt(tmp3f))/3.0
 * 
 */
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  /* "dipy/tracking/distances.pyx":1452
 * 
 *     out[0]=(sqrt(tmp1)+sqrt(tmp2)+sqrt(tmp3))/3.0
 *     out[1]=(sqrt(tmp1f)+sqrt(tmp2)+sqrt(tmp3f))/3.0             # <<<<<<<<<<<<<<
 * 
 *     #out[0]=(tmp1+tmp2+tmp3)/3.0
 */
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  /* "dipy/tracking/distances.pyx":1424
 * 
 * @cython.cdivision(True)
 * cdef inline void track_direct_flip_3dist(float *a1, float *b1,float  *c1,float *a2, float *b2, float *c2, float *out) nogil:             # <<<<<<<<<<<<<<
 *     ''' Calculate the euclidean distance between two 3pt tracks
 *     both direct and flip are given as output
 */

  /* function exit code */
}

/* "dipy/tracking/distances.pyx":1471
 * @cython.wraparound(False)
 * @cython.cdivision(True)
 * def local_skeleton_clustering(tracks, d_thr=10):             # <<<<<<<<<<<<<<
 *     r"""Efficient tractography clustering
 * 
 */

/* Python wrapper */
static PyObject *__pyx_pw_4dipy_8tracking_9distances_41local_skeleton_clustering(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds); /*proto*/
static char __pyx_doc_4dipy_8tracking_9distances_40local_skeleton_clustering[] = "Efficient tractography clustering\n\n    Every track can needs to have the same number of points.\n    Use `dipy.tracking.metrics.downsample` to restrict the number of points\n\n    Parameters\n    ----------\n    tracks : sequence\n        of tracks as arrays, shape (N,3) .. (N,3) where N=points\n    d_thr : float\n        average euclidean distance threshold\n\n    Returns\n    -------\n    C : dict\n        Clusters.\n\n    Examples\n    --------\n    >>> tracks=[np.array([[0,0,0],[1,0,0,],[2,0,0]]),\n    ...         np.array([[3,0,0],[3.5,1,0],[4,2,0]]),\n    ...         np.array([[3.2,0,0],[3.7,1,0],[4.4,2,0]]),\n    ...         np.array([[3.4,0,0],[3.9,1,0],[4.6,2,0]]),\n    ...         np.array([[0,0.2,0],[1,0.2,0],[2,0.2,0]]),\n    ...         np.array([[2,0.2,0],[1,0.2,0],[0,0.2,0]]),\n    ...         np.array([[0,0,0],[0,1,0],[0,2,0]])]\n    >>> C = local_skeleton_clustering(tracks, d_thr=0.5)\n\n    Notes\n    -----\n    The distance calculated between two tracks::\n\n        t_1       t_2\n\n        0*   a    *0\n          \\       |\n           \\      |\n           1*     |\n            |  b  *1\n            |      \\\n            2*      \\\n                c    *2\n\n    is equal to $(a+b+c)/3$ where $a$ the euclidean distance between ``t_1[0]``\n    and ``t_2[0]``, $b$ between ``t_1[1]`` and ``t_2[1]`` and $c$ between\n    ``t_1[2]`` and ``t_2[2]``. Also the same with t2 flipped (so ``t_1[0]``\n    compared to ``t_2[2]`` etc).\n\n    Visualization:\n\n    It is possible to visualize the clustering C from the example\n    above using the fvtk module::\n\n        from dipy.viz import fvtk\n        r=fvtk.ren()\n        for c in C:\n            color=np.random.rand(3)\n            for i in C[c]['indices']:\n                fvtk.add(r,fvtk.line(tracks[i],color))\n        fvtk.show(r)\n\n    See Also\n    --------\n    dipy.tracking.metrics.downsample\n    ";
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 *         cit=it
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 * 
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 * 
 *             alld=<float *>calloc(lenC,sizeof(float))             # <<<<<<<<<<<<<<
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 * 
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 *             for k from 0<=k<lenC:
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 *             alld=<float *>calloc(lenC,sizeof(float))
 *             flip=<long *>calloc(lenC,sizeof(long))
 *             for k from 0<=k<lenC:             # <<<<<<<<<<<<<<
 *                 for i from 0<=i<dim:
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 *             flip=<long *>calloc(lenC,sizeof(long))
 *             for k from 0<=k<lenC:
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 *                     hid[i]=cluster[k].hidden[i]/<float>cluster[k].N
 * 
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 *             for k from 0<=k<lenC:
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 * 
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 * 
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 * 
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 *                     d[0]=d[1]
 *                     flip[k]=1
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 * 
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 *                     flip[k]=1
 *                 alld[k]=d[0]
 */
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 *                 if d[1]<d[0]:
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 *                 alld[k]=d[0]
 * 
 */
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 *                     flip[k]=1
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 * 
 *             m_d = biggest_float
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 *                 alld[k]=d[0]
 * 
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 *             for k from 0<=k<lenC:
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 *                 if alld[k] < m_d:
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 *             #find minimum distance and index
 *             for k from 0<=k<lenC:
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 *                     m_d=alld[k]
 *                     i_k=k
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 *                     i_k=k
 * 
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 * 
 *             if m_d < cd_thr:
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 *                     i_k=k
 * 
 *             if m_d < cd_thr:             # <<<<<<<<<<<<<<
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 *                     for i from 0<=i<rows:
 *                         for j from 0<=j<3:
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 *                     for i from 0<=i<rows:             # <<<<<<<<<<<<<<
 *                         for j from 0<=j<3:
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 *                     for i from 0<=i<rows:
 *                         for j from 0<=j<3:             # <<<<<<<<<<<<<<
 *                             cluster[i_k].hidden[i*3+j]+=ptr[(rows-1-i)*3+j]
 *                 else:
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 *                     for i from 0<=i<rows:
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 *                 else:
 *                      for i from 0<=i<rows:
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 *                         for j from 0<=j<3:
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 *                             cluster[i_k].hidden[i*3+j]+=ptr[i*3+j]
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 *                 cluster[i_k].N+=1
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 *                 cluster[i_k].N+=1             # <<<<<<<<<<<<<<
 *                 cluster[i_k].indices=<long *>realloc(cluster[i_k].indices,cluster[i_k].N*sizeof(long))
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 *     cdef cnp.ndarray[cnp.float32_t, ndim=1] fvec1 = as_float_3vec(vec1)
 *     cdef cnp.ndarray[cnp.float32_t, ndim=1] fvec2 = as_float_3vec(vec2)
 *     cdef cnp.ndarray[cnp.float32_t, ndim=1] vec_out = np.zeros((3,), np.float32)             # <<<<<<<<<<<<<<
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  __Pyx_GIVEREF(__pyx_tuple__2);

  /* "dipy/tracking/distances.pyx":153
 *     cdef cnp.ndarray[cnp.float32_t, ndim=1] fvec1 = as_float_3vec(vec1)
 *     cdef cnp.ndarray[cnp.float32_t, ndim=1] fvec2 = as_float_3vec(vec2)
 *     cdef cnp.ndarray[cnp.float32_t, ndim=1] vec_out = np.zeros((3,), np.float32)             # <<<<<<<<<<<<<<
 *     cadd_3vecs(<float *>fvec1.data, <float*>fvec2.data, <float *>vec_out.data)
 *     return vec_out
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  __pyx_tuple__3 = PyTuple_Pack(1, __pyx_int_3); if (unlikely(!__pyx_tuple__3)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 153; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
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  /* "dipy/tracking/distances.pyx":166
 *     cdef cnp.ndarray[cnp.float32_t, ndim=1] fvec1 = as_float_3vec(vec1)
 *     cdef cnp.ndarray[cnp.float32_t, ndim=1] fvec2 = as_float_3vec(vec2)
 *     cdef cnp.ndarray[cnp.float32_t, ndim=1] vec_out = np.zeros((3,), np.float32)             # <<<<<<<<<<<<<<
 *     cmul_3vecs(<float *>fvec1.data, <float*>fvec2.data, <float *>vec_out.data)
 *     return vec_out
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  __pyx_tuple__4 = PyTuple_Pack(1, __pyx_int_3); if (unlikely(!__pyx_tuple__4)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 166; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
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  /* "dipy/tracking/distances.pyx":177
 * def mul_3vec(a, vec):
 *     cdef cnp.ndarray[cnp.float32_t, ndim=1] fvec = as_float_3vec(vec)
 *     cdef cnp.ndarray[cnp.float32_t, ndim=1] vec_out = np.zeros((3,), np.float32)             # <<<<<<<<<<<<<<
 *     cmul_3vec(a,<float *>fvec.data, <float *>vec_out.data)
 *     return vec_out
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  __pyx_tuple__5 = PyTuple_Pack(1, __pyx_int_3); if (unlikely(!__pyx_tuple__5)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 177; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
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  /* "dipy/tracking/distances.pyx":326
 *                             # hit data into array
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  __Pyx_GOTREF(__pyx_tuple__6);
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  __pyx_tuple__7 = PyTuple_Pack(1, __pyx_tuple__6); if (unlikely(!__pyx_tuple__7)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 326; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
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  __Pyx_GIVEREF(__pyx_tuple__7);

  /* "dipy/tracking/distances.pyx":346
 *         Hit.append(hit_arr)
 *         #Div.append(divs[1:])
 *     return Hit[1:]             # <<<<<<<<<<<<<<
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 * 
 */
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  /* "dipy/tracking/distances.pyx":400
 *         metric_type = 2
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 *         raise ValueError('Metric should be one of avg, min, max')             # <<<<<<<<<<<<<<
 *     # preprocess tracks
 *     cdef:
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  __Pyx_GIVEREF(__pyx_tuple__9);

  /* "dipy/tracking/distances.pyx":490
 *         metric_type = 2
 *     else:
 *         raise ValueError('Metric should be one of avg, min, max')             # <<<<<<<<<<<<<<
 *     # preprocess tracks
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  __pyx_tuple__10 = PyTuple_Pack(1, __pyx_kp_s_Metric_should_be_one_of_avg_min); if (unlikely(!__pyx_tuple__10)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 490; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
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  __Pyx_GIVEREF(__pyx_tuple__10);

  /* "dipy/tracking/distances.pyx":777
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 * 
 * 
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  __pyx_tuple__11 = PyTuple_Pack(1, __pyx_kp_s_Wrong_argument_for_metric); if (unlikely(!__pyx_tuple__11)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 777; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __Pyx_GOTREF(__pyx_tuple__11);
  __Pyx_GIVEREF(__pyx_tuple__11);

  /* "dipy/tracking/distances.pyx":1709
 *     #Network C
 *     C={0:{'indices':[0],'hidden':tracks[0].copy(),'N':1}}
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 * 
 *     #for (it,t) in enumerate(tracks[1:]):
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  __Pyx_GOTREF(__pyx_tuple__12);
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  __pyx_tuple__13 = PyTuple_Pack(1, __pyx_tuple__12); if (unlikely(!__pyx_tuple__13)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1709; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
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  __Pyx_GIVEREF(__pyx_tuple__13);

  /* "dipy/tracking/distances.pyx":1852
 *     else:
 *         C={0:{'indices':[indices[0]],'rep3':tracks[indices[0]].copy(),'N':1}}
 *         itrange=indices[1:]             # <<<<<<<<<<<<<<
 * 
 *     ts=np.zeros((3,3),dtype=np.float32)
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  __pyx_slice__14 = PySlice_New(__pyx_int_1, Py_None, Py_None); if (unlikely(!__pyx_slice__14)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1852; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
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  __Pyx_GIVEREF(__pyx_slice__14);

  /* "dipy/tracking/distances.pyx":1854
 *         itrange=indices[1:]
 * 
 *     ts=np.zeros((3,3),dtype=np.float32)             # <<<<<<<<<<<<<<
 *     for it in itrange:
 *         track=np.ascontiguousarray(tracks[it],dtype=f32_dt)
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  __pyx_tuple__15 = PyTuple_Pack(2, __pyx_int_3, __pyx_int_3); if (unlikely(!__pyx_tuple__15)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1854; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __Pyx_GOTREF(__pyx_tuple__15);
  __Pyx_GIVEREF(__pyx_tuple__15);
  __pyx_tuple__16 = PyTuple_Pack(1, __pyx_tuple__15); if (unlikely(!__pyx_tuple__16)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1854; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
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  __Pyx_GIVEREF(__pyx_tuple__16);

  /* "dipy/tracking/distances.pyx":1910
 *     '''
 * 
 *     cdef cnp.ndarray[cnp.float32_t, ndim=2] h=np.zeros((3,3),dtype=np.float32)             # <<<<<<<<<<<<<<
 *     cdef cnp.ndarray[cnp.float32_t, ndim=2] ch=np.zeros((3,3),dtype=np.float32)
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  __pyx_tuple__17 = PyTuple_Pack(2, __pyx_int_3, __pyx_int_3); if (unlikely(!__pyx_tuple__17)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1910; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __Pyx_GOTREF(__pyx_tuple__17);
  __Pyx_GIVEREF(__pyx_tuple__17);
  __pyx_tuple__18 = PyTuple_Pack(1, __pyx_tuple__17); if (unlikely(!__pyx_tuple__18)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1910; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
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  __Pyx_GIVEREF(__pyx_tuple__18);

  /* "dipy/tracking/distances.pyx":1911
 * 
 *     cdef cnp.ndarray[cnp.float32_t, ndim=2] h=np.zeros((3,3),dtype=np.float32)
 *     cdef cnp.ndarray[cnp.float32_t, ndim=2] ch=np.zeros((3,3),dtype=np.float32)             # <<<<<<<<<<<<<<
 *     cdef int lenC,k,c
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  __pyx_tuple__19 = PyTuple_Pack(2, __pyx_int_3, __pyx_int_3); if (unlikely(!__pyx_tuple__19)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1911; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __Pyx_GOTREF(__pyx_tuple__19);
  __Pyx_GIVEREF(__pyx_tuple__19);
  __pyx_tuple__20 = PyTuple_Pack(1, __pyx_tuple__19); if (unlikely(!__pyx_tuple__20)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1911; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
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  __Pyx_GIVEREF(__pyx_tuple__20);

  /* "dipy/tracking/distances.pyx":1915
 *     cdef float d[2]
 * 
 *     ts=np.zeros((3,3),dtype=np.float32)             # <<<<<<<<<<<<<<
 * 
 *     lenC=len(C)
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  __pyx_tuple__21 = PyTuple_Pack(2, __pyx_int_3, __pyx_int_3); if (unlikely(!__pyx_tuple__21)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1915; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __Pyx_GOTREF(__pyx_tuple__21);
  __Pyx_GIVEREF(__pyx_tuple__21);
  __pyx_tuple__22 = PyTuple_Pack(1, __pyx_tuple__21); if (unlikely(!__pyx_tuple__22)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1915; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
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  /* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":215
 *             if ((flags & pybuf.PyBUF_C_CONTIGUOUS == pybuf.PyBUF_C_CONTIGUOUS)
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 *                 raise ValueError(u"ndarray is not C contiguous")             # <<<<<<<<<<<<<<
 * 
 *             if ((flags & pybuf.PyBUF_F_CONTIGUOUS == pybuf.PyBUF_F_CONTIGUOUS)
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  __pyx_tuple__23 = PyTuple_Pack(1, __pyx_kp_u_ndarray_is_not_C_contiguous); if (unlikely(!__pyx_tuple__23)) {__pyx_filename = __pyx_f[1]; __pyx_lineno = 215; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __Pyx_GOTREF(__pyx_tuple__23);
  __Pyx_GIVEREF(__pyx_tuple__23);

  /* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":219
 *             if ((flags & pybuf.PyBUF_F_CONTIGUOUS == pybuf.PyBUF_F_CONTIGUOUS)
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 *                 raise ValueError(u"ndarray is not Fortran contiguous")             # <<<<<<<<<<<<<<
 * 
 *             info.buf = PyArray_DATA(self)
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  __pyx_tuple__24 = PyTuple_Pack(1, __pyx_kp_u_ndarray_is_not_Fortran_contiguou); if (unlikely(!__pyx_tuple__24)) {__pyx_filename = __pyx_f[1]; __pyx_lineno = 219; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __Pyx_GOTREF(__pyx_tuple__24);
  __Pyx_GIVEREF(__pyx_tuple__24);

  /* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":257
 *                 if ((descr.byteorder == c'>' and little_endian) or
 *                     (descr.byteorder == c'<' and not little_endian)):
 *                     raise ValueError(u"Non-native byte order not supported")             # <<<<<<<<<<<<<<
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 *                 elif t == NPY_UBYTE:       f = "B"
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  __pyx_tuple__25 = PyTuple_Pack(1, __pyx_kp_u_Non_native_byte_order_not_suppor); if (unlikely(!__pyx_tuple__25)) {__pyx_filename = __pyx_f[1]; __pyx_lineno = 257; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __Pyx_GOTREF(__pyx_tuple__25);
  __Pyx_GIVEREF(__pyx_tuple__25);

  /* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":799
 * 
 *         if (end - f) - <int>(new_offset - offset[0]) < 15:
 *             raise RuntimeError(u"Format string allocated too short, see comment in numpy.pxd")             # <<<<<<<<<<<<<<
 * 
 *         if ((child.byteorder == c'>' and little_endian) or
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  __pyx_tuple__26 = PyTuple_Pack(1, __pyx_kp_u_Format_string_allocated_too_shor); if (unlikely(!__pyx_tuple__26)) {__pyx_filename = __pyx_f[1]; __pyx_lineno = 799; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __Pyx_GOTREF(__pyx_tuple__26);
  __Pyx_GIVEREF(__pyx_tuple__26);

  /* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":803
 *         if ((child.byteorder == c'>' and little_endian) or
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 *             raise ValueError(u"Non-native byte order not supported")             # <<<<<<<<<<<<<<
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  __pyx_tuple__27 = PyTuple_Pack(1, __pyx_kp_u_Non_native_byte_order_not_suppor); if (unlikely(!__pyx_tuple__27)) {__pyx_filename = __pyx_f[1]; __pyx_lineno = 803; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
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  __Pyx_GIVEREF(__pyx_tuple__27);

  /* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":823
 *             t = child.type_num
 *             if end - f < 5:
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 * 
 *             # Until ticket #99 is fixed, use integers to avoid warnings
 */
  __pyx_tuple__28 = PyTuple_Pack(1, __pyx_kp_u_Format_string_allocated_too_shor_2); if (unlikely(!__pyx_tuple__28)) {__pyx_filename = __pyx_f[1]; __pyx_lineno = 823; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __Pyx_GOTREF(__pyx_tuple__28);
  __Pyx_GIVEREF(__pyx_tuple__28);

  /* "dipy/tracking/distances.pyx":50
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 * 
 * def normalized_3vec(vec):             # <<<<<<<<<<<<<<
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 * 
 */
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  __Pyx_GOTREF(__pyx_tuple__29);
  __Pyx_GIVEREF(__pyx_tuple__29);
  __pyx_codeobj__30 = (PyObject*)__Pyx_PyCode_New(1, 0, 3, 0, 0, __pyx_empty_bytes, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_tuple__29, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_kp_s_home_eleftherios_Devel_dipy_dip, __pyx_n_s_normalized_3vec, 50, __pyx_empty_bytes); if (unlikely(!__pyx_codeobj__30)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 50; __pyx_clineno = __LINE__; goto __pyx_L1_error;}

  /* "dipy/tracking/distances.pyx":69
 * 
 * 
 * def norm_3vec(vec):             # <<<<<<<<<<<<<<
 *     ''' Euclidean (L2) norm of length 3 vector
 * 
 */
  __pyx_tuple__31 = PyTuple_Pack(2, __pyx_n_s_vec, __pyx_n_s_vec_in); if (unlikely(!__pyx_tuple__31)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 69; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __Pyx_GOTREF(__pyx_tuple__31);
  __Pyx_GIVEREF(__pyx_tuple__31);
  __pyx_codeobj__32 = (PyObject*)__Pyx_PyCode_New(1, 0, 2, 0, 0, __pyx_empty_bytes, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_tuple__31, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_kp_s_home_eleftherios_Devel_dipy_dip, __pyx_n_s_norm_3vec, 69, __pyx_empty_bytes); if (unlikely(!__pyx_codeobj__32)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 69; __pyx_clineno = __LINE__; goto __pyx_L1_error;}

  /* "dipy/tracking/distances.pyx":122
 * 
 * 
 * def inner_3vecs(vec1, vec2):             # <<<<<<<<<<<<<<
 *     cdef cnp.ndarray[cnp.float32_t, ndim=1] fvec1 = as_float_3vec(vec1)
 *     cdef cnp.ndarray[cnp.float32_t, ndim=1] fvec2 = as_float_3vec(vec2)
 */
  __pyx_tuple__33 = PyTuple_Pack(4, __pyx_n_s_vec1, __pyx_n_s_vec2, __pyx_n_s_fvec1, __pyx_n_s_fvec2); if (unlikely(!__pyx_tuple__33)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 122; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __Pyx_GOTREF(__pyx_tuple__33);
  __Pyx_GIVEREF(__pyx_tuple__33);
  __pyx_codeobj__34 = (PyObject*)__Pyx_PyCode_New(2, 0, 4, 0, 0, __pyx_empty_bytes, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_tuple__33, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_kp_s_home_eleftherios_Devel_dipy_dip, __pyx_n_s_inner_3vecs, 122, __pyx_empty_bytes); if (unlikely(!__pyx_codeobj__34)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 122; __pyx_clineno = __LINE__; goto __pyx_L1_error;}

  /* "dipy/tracking/distances.pyx":136
 * 
 * 
 * def sub_3vecs(vec1, vec2):             # <<<<<<<<<<<<<<
 *     cdef cnp.ndarray[cnp.float32_t, ndim=1] fvec1 = as_float_3vec(vec1)
 *     cdef cnp.ndarray[cnp.float32_t, ndim=1] fvec2 = as_float_3vec(vec2)
 */
  __pyx_tuple__35 = PyTuple_Pack(5, __pyx_n_s_vec1, __pyx_n_s_vec2, __pyx_n_s_fvec1, __pyx_n_s_fvec2, __pyx_n_s_vec_out); if (unlikely(!__pyx_tuple__35)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 136; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __Pyx_GOTREF(__pyx_tuple__35);
  __Pyx_GIVEREF(__pyx_tuple__35);
  __pyx_codeobj__36 = (PyObject*)__Pyx_PyCode_New(2, 0, 5, 0, 0, __pyx_empty_bytes, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_tuple__35, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_kp_s_home_eleftherios_Devel_dipy_dip, __pyx_n_s_sub_3vecs, 136, __pyx_empty_bytes); if (unlikely(!__pyx_codeobj__36)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 136; __pyx_clineno = __LINE__; goto __pyx_L1_error;}

  /* "dipy/tracking/distances.pyx":150
 * 
 * 
 * def add_3vecs(vec1, vec2):             # <<<<<<<<<<<<<<
 *     cdef cnp.ndarray[cnp.float32_t, ndim=1] fvec1 = as_float_3vec(vec1)
 *     cdef cnp.ndarray[cnp.float32_t, ndim=1] fvec2 = as_float_3vec(vec2)
 */
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  /* "dipy/tracking/distances.pyx":163
 *         vec_out[i] = vec1[i]+vec2[i]
 * 
 * def mul_3vecs(vec1, vec2):             # <<<<<<<<<<<<<<
 *     cdef cnp.ndarray[cnp.float32_t, ndim=1] fvec1 = as_float_3vec(vec1)
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  /* "dipy/tracking/distances.pyx":175
 *         vec_out[i] = vec1[i]*vec2[i]
 * 
 * def mul_3vec(a, vec):             # <<<<<<<<<<<<<<
 *     cdef cnp.ndarray[cnp.float32_t, ndim=1] fvec = as_float_3vec(vec)
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  /* "dipy/tracking/distances.pyx":191
 * 
 * 
 * def cut_plane(tracks,ref):             # <<<<<<<<<<<<<<
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  /* "dipy/tracking/distances.pyx":352
 * 
 * 
 * def most_similar_track_mam(tracks,metric='avg'):             # <<<<<<<<<<<<<<
 *     ''' Find the most similar track in a bundle
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 */
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  /* "dipy/tracking/distances.pyx":462
 * @cython.boundscheck(False)
 * @cython.wraparound(False)
 * def bundles_distances_mam(tracksA, tracksB, metric='avg'):             # <<<<<<<<<<<<<<
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 */
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  /* "dipy/tracking/distances.pyx":541
 * @cython.boundscheck(False)
 * @cython.wraparound(False)
 * def bundles_distances_mdf(tracksA, tracksB):             # <<<<<<<<<<<<<<
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 */
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  /* "dipy/tracking/distances.pyx":694
 * 
 * 
 * def mam_distances(xyz1,xyz2,metric='all'):             # <<<<<<<<<<<<<<
 *     ''' Min/Max/Mean Average Minimum Distance between tracks xyz1 and xyz2
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 */
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  /* "dipy/tracking/distances.pyx":780
 * 
 * 
 * def minimum_closest_distance(xyz1,xyz2):             # <<<<<<<<<<<<<<
 *     ''' Find the minimum distance between two curves xyz1, xyz2
 * 
 */
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  /* "dipy/tracking/distances.pyx":838
 * 
 * 
 * def lee_perpendicular_distance(start0, end0, start1, end1):             # <<<<<<<<<<<<<<
 *     ''' Calculates perpendicular distance metric for the distance between two line segments
 * 
 */
  __pyx_tuple__55 = PyTuple_Pack(8, __pyx_n_s_start0, __pyx_n_s_end0, __pyx_n_s_start1, __pyx_n_s_end1, __pyx_n_s_fvec1, __pyx_n_s_fvec2, __pyx_n_s_fvec3, __pyx_n_s_fvec4); if (unlikely(!__pyx_tuple__55)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 838; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
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  /* "dipy/tracking/distances.pyx":941
 * 
 * 
 * def lee_angle_distance(start0, end0, start1, end1):             # <<<<<<<<<<<<<<
 *     ''' Calculates angle distance metric for the distance between two line segments
 * 
 */
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  /* "dipy/tracking/distances.pyx":1007
 * 
 * 
 * def approx_polygon_track(xyz,alpha=0.392):             # <<<<<<<<<<<<<<
 *     ''' Fast and simple trajectory approximation algorithm by Eleftherios and Ian
 * 
 */
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  /* "dipy/tracking/distances.pyx":1091
 * 
 * 
 * def approximate_mdl_trajectory(xyz, alpha=1.):             # <<<<<<<<<<<<<<
 *     ''' Implementation of Lee et al Approximate Trajectory
 *     Partitioning Algorithm
 */
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  /* "dipy/tracking/distances.pyx":1158
 * 
 * 
 * def intersect_segment_cylinder(sa,sb,p,q,r):             # <<<<<<<<<<<<<<
 *     ''' Intersect Segment S(t) = sa +t(sb-sa), 0 <=t<= 1 against cylinder specified by p,q and r
 * 
 */
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  /* "dipy/tracking/distances.pyx":1271
 * 
 * 
 * def point_segment_sq_distance(a, b, c):             # <<<<<<<<<<<<<<
 *     ''' Calculate the squared distance from a point c to a finite line segment ab.
 * 
 */
  __pyx_tuple__65 = PyTuple_Pack(8, __pyx_n_s_a, __pyx_n_s_b, __pyx_n_s_c, __pyx_n_s_ca, __pyx_n_s_cb, __pyx_n_s_cc, __pyx_n_s_cr, __pyx_n_s_ct); if (unlikely(!__pyx_tuple__65)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1271; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
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typedef struct { char c; long x; } __Pyx_st_long;
typedef struct { char c; float x; } __Pyx_st_float;
typedef struct { char c; double x; } __Pyx_st_double;
typedef struct { char c; long double x; } __Pyx_st_longdouble;
typedef struct { char c; void *x; } __Pyx_st_void_p;
#ifdef HAVE_LONG_LONG
typedef struct { char c; PY_LONG_LONG x; } __Pyx_st_longlong;
#endif
static size_t __Pyx_BufFmt_TypeCharToAlignment(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_st_short) - sizeof(short);
    case 'i': case 'I': return sizeof(__Pyx_st_int) - sizeof(int);
    case 'l': case 'L': return sizeof(__Pyx_st_long) - sizeof(long);
#ifdef HAVE_LONG_LONG
    case 'q': case 'Q': return sizeof(__Pyx_st_longlong) - sizeof(PY_LONG_LONG);
#endif
    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 CYTHON_INLINE 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_IsLittleEndian()) {
          PyErr_SetString(PyExc_ValueError, "Little-endian buffer not supported on big-endian compiler");
          return NULL;
        }
        ctx->new_packmode = '=';
        ++ts;
        break;
      case '>':
      case '!':
        if (__Pyx_IsLittleEndian()) {
          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;
        }
      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;
        }
      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;
        }
    }
  }
}
static CYTHON_INLINE 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 CYTHON_INLINE int __Pyx_GetBufferAndValidate(
        Py_buffer* buf, PyObject* obj,  __Pyx_TypeInfo* dtype, int flags,
        int nd, int cast, __Pyx_BufFmt_StackElem* stack)
{
  if (obj == Py_None || obj == NULL) {
    __Pyx_ZeroBuffer(buf);
    return 0;
  }
  buf->buf = NULL;
  if (__Pyx_GetBuffer(obj, buf, flags) == -1) goto fail;
  if (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 ((unsigned)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_ZeroBuffer(buf);
  return -1;
}
static CYTHON_INLINE void __Pyx_SafeReleaseBuffer(Py_buffer* info) {
  if (info->buf == NULL) return;
  if (info->suboffsets == __Pyx_minusones) info->suboffsets = NULL;
  __Pyx_ReleaseBuffer(info);
}

static CYTHON_INLINE void __Pyx_ErrRestore(PyObject *type, PyObject *value, PyObject *tb) {
#if CYTHON_COMPILING_IN_CPYTHON
    PyObject *tmp_type, *tmp_value, *tmp_tb;
    PyThreadState *tstate = PyThreadState_GET();
    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);
#else
    PyErr_Restore(type, value, tb);
#endif
}
static CYTHON_INLINE void __Pyx_ErrFetch(PyObject **type, PyObject **value, PyObject **tb) {
#if CYTHON_COMPILING_IN_CPYTHON
    PyThreadState *tstate = PyThreadState_GET();
    *type = tstate->curexc_type;
    *value = tstate->curexc_value;
    *tb = tstate->curexc_traceback;
    tstate->curexc_type = 0;
    tstate->curexc_value = 0;
    tstate->curexc_traceback = 0;
#else
    PyErr_Fetch(type, value, tb);
#endif
}

static void __Pyx_WriteUnraisable(const char *name, CYTHON_UNUSED int clineno,
                                  CYTHON_UNUSED int lineno, CYTHON_UNUSED const char *filename,
                                  int full_traceback) {
    PyObject *old_exc, *old_val, *old_tb;
    PyObject *ctx;
    __Pyx_ErrFetch(&old_exc, &old_val, &old_tb);
    if (full_traceback) {
        Py_XINCREF(old_exc);
        Py_XINCREF(old_val);
        Py_XINCREF(old_tb);
        __Pyx_ErrRestore(old_exc, old_val, old_tb);
        PyErr_PrintEx(1);
    }
    #if PY_MAJOR_VERSION < 3
    ctx = PyString_FromString(name);
    #else
    ctx = PyUnicode_FromString(name);
    #endif
    __Pyx_ErrRestore(old_exc, old_val, old_tb);
    if (!ctx) {
        PyErr_WriteUnraisable(Py_None);
    } else {
        PyErr_WriteUnraisable(ctx);
        Py_DECREF(ctx);
    }
}

static void __Pyx_RaiseArgtupleInvalid(
    const char* func_name,
    int exact,
    Py_ssize_t num_min,
    Py_ssize_t num_max,
    Py_ssize_t num_found)
{
    Py_ssize_t num_expected;
    const char *more_or_less;
    if (num_found < num_min) {
        num_expected = num_min;
        more_or_less = "at least";
    } else {
        num_expected = num_max;
        more_or_less = "at most";
    }
    if (exact) {
        more_or_less = "exactly";
    }
    PyErr_Format(PyExc_TypeError,
                 "%.200s() takes %.8s %" CYTHON_FORMAT_SSIZE_T "d positional argument%.1s (%" CYTHON_FORMAT_SSIZE_T "d given)",
                 func_name, more_or_less, num_expected,
                 (num_expected == 1) ? "" : "s", num_found);
}

static void __Pyx_RaiseDoubleKeywordsError(
    const char* func_name,
    PyObject* kw_name)
{
    PyErr_Format(PyExc_TypeError,
        #if PY_MAJOR_VERSION >= 3
        "%s() got multiple values for keyword argument '%U'", func_name, kw_name);
        #else
        "%s() got multiple values for keyword argument '%s'", func_name,
        PyString_AsString(kw_name));
        #endif
}

static int __Pyx_ParseOptionalKeywords(
    PyObject *kwds,
    PyObject **argnames[],
    PyObject *kwds2,
    PyObject *values[],
    Py_ssize_t num_pos_args,
    const char* function_name)
{
    PyObject *key = 0, *value = 0;
    Py_ssize_t pos = 0;
    PyObject*** name;
    PyObject*** first_kw_arg = argnames + num_pos_args;
    while (PyDict_Next(kwds, &pos, &key, &value)) {
        name = first_kw_arg;
        while (*name && (**name != key)) name++;
        if (*name) {
            values[name-argnames] = value;
            continue;
        }
        name = first_kw_arg;
        #if PY_MAJOR_VERSION < 3
        if (likely(PyString_CheckExact(key)) || likely(PyString_Check(key))) {
            while (*name) {
                if ((CYTHON_COMPILING_IN_PYPY || PyString_GET_SIZE(**name) == PyString_GET_SIZE(key))
                        && _PyString_Eq(**name, key)) {
                    values[name-argnames] = value;
                    break;
                }
                name++;
            }
            if (*name) continue;
            else {
                PyObject*** argname = argnames;
                while (argname != first_kw_arg) {
                    if ((**argname == key) || (
                            (CYTHON_COMPILING_IN_PYPY || PyString_GET_SIZE(**argname) == PyString_GET_SIZE(key))
                             && _PyString_Eq(**argname, key))) {
                        goto arg_passed_twice;
                    }
                    argname++;
                }
            }
        } else
        #endif
        if (likely(PyUnicode_Check(key))) {
            while (*name) {
                int cmp = (**name == key) ? 0 :
                #if !CYTHON_COMPILING_IN_PYPY && PY_MAJOR_VERSION >= 3
                    (PyUnicode_GET_SIZE(**name) != PyUnicode_GET_SIZE(key)) ? 1 :
                #endif
                    PyUnicode_Compare(**name, key);
                if (cmp < 0 && unlikely(PyErr_Occurred())) goto bad;
                if (cmp == 0) {
                    values[name-argnames] = value;
                    break;
                }
                name++;
            }
            if (*name) continue;
            else {
                PyObject*** argname = argnames;
                while (argname != first_kw_arg) {
                    int cmp = (**argname == key) ? 0 :
                    #if !CYTHON_COMPILING_IN_PYPY && PY_MAJOR_VERSION >= 3
                        (PyUnicode_GET_SIZE(**argname) != PyUnicode_GET_SIZE(key)) ? 1 :
                    #endif
                        PyUnicode_Compare(**argname, key);
                    if (cmp < 0 && unlikely(PyErr_Occurred())) goto bad;
                    if (cmp == 0) goto arg_passed_twice;
                    argname++;
                }
            }
        } else
            goto invalid_keyword_type;
        if (kwds2) {
            if (unlikely(PyDict_SetItem(kwds2, key, value))) goto bad;
        } else {
            goto invalid_keyword;
        }
    }
    return 0;
arg_passed_twice:
    __Pyx_RaiseDoubleKeywordsError(function_name, key);
    goto bad;
invalid_keyword_type:
    PyErr_Format(PyExc_TypeError,
        "%.200s() keywords must be strings", function_name);
    goto bad;
invalid_keyword:
    PyErr_Format(PyExc_TypeError,
    #if PY_MAJOR_VERSION < 3
        "%.200s() got an unexpected keyword argument '%.200s'",
        function_name, PyString_AsString(key));
    #else
        "%s() got an unexpected keyword argument '%U'",
        function_name, key);
    #endif
bad:
    return -1;
}

static void __Pyx_RaiseBufferFallbackError(void) {
  PyErr_SetString(PyExc_ValueError,
     "Buffer acquisition failed on assignment; and then reacquiring the old buffer failed too!");
}

static CYTHON_INLINE 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,
                                                              int wraparound, int boundscheck) {
#if CYTHON_COMPILING_IN_CPYTHON
    if (wraparound & unlikely(i < 0)) i += PyList_GET_SIZE(o);
    if ((!boundscheck) || likely((0 <= i) & (i < PyList_GET_SIZE(o)))) {
        PyObject *r = PyList_GET_ITEM(o, 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,
                                                              int wraparound, int boundscheck) {
#if CYTHON_COMPILING_IN_CPYTHON
    if (wraparound & unlikely(i < 0)) i += PyTuple_GET_SIZE(o);
    if ((!boundscheck) || likely((0 <= i) & (i < PyTuple_GET_SIZE(o)))) {
        PyObject *r = PyTuple_GET_ITEM(o, 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, int wraparound, int boundscheck) {
#if CYTHON_COMPILING_IN_CPYTHON
    if (is_list || PyList_CheckExact(o)) {
        Py_ssize_t n = ((!wraparound) | likely(i >= 0)) ? i : i + PyList_GET_SIZE(o);
        if ((!boundscheck) || (likely((n >= 0) & (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((n >= 0) & (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))
                        PyErr_Clear();
                    else
                        return NULL;
                }
            }
            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));
}

static void __Pyx_RaiseBufferIndexError(int axis) {
  PyErr_Format(PyExc_IndexError,
     "Out of bounds on buffer access (axis %d)", axis);
}

static PyObject* __Pyx_PyObject_CallMethod1(PyObject* obj, PyObject* method_name, PyObject* arg) {
    PyObject *method, *result = NULL;
    method = __Pyx_PyObject_GetAttrStr(obj, method_name);
    if (unlikely(!method)) goto bad;
#if CYTHON_COMPILING_IN_CPYTHON
    if (likely(PyMethod_Check(method))) {
        PyObject *self = PyMethod_GET_SELF(method);
        if (likely(self)) {
            PyObject *args;
            PyObject *function = PyMethod_GET_FUNCTION(method);
            args = PyTuple_New(2);
            if (unlikely(!args)) goto bad;
            Py_INCREF(self);
            PyTuple_SET_ITEM(args, 0, self);
            Py_INCREF(arg);
            PyTuple_SET_ITEM(args, 1, arg);
            Py_INCREF(function);
            Py_DECREF(method); method = NULL;
            result = __Pyx_PyObject_Call(function, args, NULL);
            Py_DECREF(args);
            Py_DECREF(function);
            return result;
        }
    }
#endif
    result = __Pyx_PyObject_CallOneArg(method, arg);
bad:
    Py_XDECREF(method);
    return result;
}

static CYTHON_INLINE int __Pyx_PyObject_Append(PyObject* L, PyObject* x) {
    if (likely(PyList_CheckExact(L))) {
        if (unlikely(__Pyx_PyList_Append(L, x) < 0)) return -1;
    } else {
        PyObject* retval = __Pyx_PyObject_CallMethod1(L, __pyx_n_s_append, x);
        if (unlikely(!retval))
            return -1;
        Py_DECREF(retval);
    }
    return 0;
}

static CYTHON_INLINE int __Pyx_SetItemInt_Generic(PyObject *o, PyObject *j, PyObject *v) {
    int r;
    if (!j) return -1;
    r = PyObject_SetItem(o, j, v);
    Py_DECREF(j);
    return r;
}
static CYTHON_INLINE int __Pyx_SetItemInt_Fast(PyObject *o, Py_ssize_t i, PyObject *v,
                                               int is_list, int wraparound, int boundscheck) {
#if CYTHON_COMPILING_IN_CPYTHON
    if (is_list || PyList_CheckExact(o)) {
        Py_ssize_t n = (!wraparound) ? i : ((likely(i >= 0)) ? i : i + PyList_GET_SIZE(o));
        if ((!boundscheck) || likely((n >= 0) & (n < PyList_GET_SIZE(o)))) {
            PyObject* old = PyList_GET_ITEM(o, n);
            Py_INCREF(v);
            PyList_SET_ITEM(o, n, v);
            Py_DECREF(old);
            return 1;
        }
    } else {
        PySequenceMethods *m = Py_TYPE(o)->tp_as_sequence;
        if (likely(m && m->sq_ass_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))
                        PyErr_Clear();
                    else
                        return -1;
                }
            }
            return m->sq_ass_item(o, i, v);
        }
    }
#else
#if CYTHON_COMPILING_IN_PYPY
    if (is_list || (PySequence_Check(o) && !PyDict_Check(o))) {
#else
    if (is_list || PySequence_Check(o)) {
#endif
        return PySequence_SetItem(o, i, v);
    }
#endif
    return __Pyx_SetItemInt_Generic(o, PyInt_FromSsize_t(i), v);
}

static CYTHON_INLINE PyObject* __Pyx_PyObject_GetSlice(
        PyObject* obj, Py_ssize_t cstart, Py_ssize_t cstop,
        PyObject** _py_start, PyObject** _py_stop, PyObject** _py_slice,
        int has_cstart, int has_cstop, CYTHON_UNUSED int wraparound) {
#if CYTHON_COMPILING_IN_CPYTHON
    PyMappingMethods* mp;
#if PY_MAJOR_VERSION < 3
    PySequenceMethods* ms = Py_TYPE(obj)->tp_as_sequence;
    if (likely(ms && ms->sq_slice)) {
        if (!has_cstart) {
            if (_py_start && (*_py_start != Py_None)) {
                cstart = __Pyx_PyIndex_AsSsize_t(*_py_start);
                if ((cstart == (Py_ssize_t)-1) && PyErr_Occurred()) goto bad;
            } else
                cstart = 0;
        }
        if (!has_cstop) {
            if (_py_stop && (*_py_stop != Py_None)) {
                cstop = __Pyx_PyIndex_AsSsize_t(*_py_stop);
                if ((cstop == (Py_ssize_t)-1) && PyErr_Occurred()) goto bad;
            } else
                cstop = PY_SSIZE_T_MAX;
        }
        if (wraparound && unlikely((cstart < 0) | (cstop < 0)) && likely(ms->sq_length)) {
            Py_ssize_t l = ms->sq_length(obj);
            if (likely(l >= 0)) {
                if (cstop < 0) {
                    cstop += l;
                    if (cstop < 0) cstop = 0;
                }
                if (cstart < 0) {
                    cstart += l;
                    if (cstart < 0) cstart = 0;
                }
            } else {
                if (PyErr_ExceptionMatches(PyExc_OverflowError))
                    PyErr_Clear();
                else
                    goto bad;
            }
        }
        return ms->sq_slice(obj, cstart, cstop);
    }
#endif
    mp = Py_TYPE(obj)->tp_as_mapping;
    if (likely(mp && mp->mp_subscript))
#endif
    {
        PyObject* result;
        PyObject *py_slice, *py_start, *py_stop;
        if (_py_slice) {
            py_slice = *_py_slice;
        } else {
            PyObject* owned_start = NULL;
            PyObject* owned_stop = NULL;
            if (_py_start) {
                py_start = *_py_start;
            } else {
                if (has_cstart) {
                    owned_start = py_start = PyInt_FromSsize_t(cstart);
                    if (unlikely(!py_start)) goto bad;
                } else
                    py_start = Py_None;
            }
            if (_py_stop) {
                py_stop = *_py_stop;
            } else {
                if (has_cstop) {
                    owned_stop = py_stop = PyInt_FromSsize_t(cstop);
                    if (unlikely(!py_stop)) {
                        Py_XDECREF(owned_start);
                        goto bad;
                    }
                } else
                    py_stop = Py_None;
            }
            py_slice = PySlice_New(py_start, py_stop, Py_None);
            Py_XDECREF(owned_start);
            Py_XDECREF(owned_stop);
            if (unlikely(!py_slice)) goto bad;
        }
#if CYTHON_COMPILING_IN_CPYTHON
        result = mp->mp_subscript(obj, py_slice);
#else
        result = PyObject_GetItem(obj, py_slice);
#endif
        if (!_py_slice) {
            Py_DECREF(py_slice);
        }
        return result;
    }
    PyErr_Format(PyExc_TypeError,
        "'%.200s' object is unsliceable", Py_TYPE(obj)->tp_name);
bad:
    return NULL;
}

static CYTHON_INLINE int __Pyx_PyBytes_Equals(PyObject* s1, PyObject* s2, int equals) {
#if CYTHON_COMPILING_IN_PYPY
    return PyObject_RichCompareBool(s1, s2, equals);
#else
    if (s1 == s2) {
        return (equals == Py_EQ);
    } else if (PyBytes_CheckExact(s1) & PyBytes_CheckExact(s2)) {
        const char *ps1, *ps2;
        Py_ssize_t length = PyBytes_GET_SIZE(s1);
        if (length != PyBytes_GET_SIZE(s2))
            return (equals == Py_NE);
        ps1 = PyBytes_AS_STRING(s1);
        ps2 = PyBytes_AS_STRING(s2);
        if (ps1[0] != ps2[0]) {
            return (equals == Py_NE);
        } else if (length == 1) {
            return (equals == Py_EQ);
        } else {
            int result = memcmp(ps1, ps2, (size_t)length);
            return (equals == Py_EQ) ? (result == 0) : (result != 0);
        }
    } else if ((s1 == Py_None) & PyBytes_CheckExact(s2)) {
        return (equals == Py_NE);
    } else if ((s2 == Py_None) & PyBytes_CheckExact(s1)) {
        return (equals == Py_NE);
    } else {
        int result;
        PyObject* py_result = PyObject_RichCompare(s1, s2, equals);
        if (!py_result)
            return -1;
        result = __Pyx_PyObject_IsTrue(py_result);
        Py_DECREF(py_result);
        return result;
    }
#endif
}

static CYTHON_INLINE int __Pyx_PyUnicode_Equals(PyObject* s1, PyObject* s2, int equals) {
#if CYTHON_COMPILING_IN_PYPY
    return PyObject_RichCompareBool(s1, s2, equals);
#else
#if PY_MAJOR_VERSION < 3
    PyObject* owned_ref = NULL;
#endif
    int s1_is_unicode, s2_is_unicode;
    if (s1 == s2) {
        goto return_eq;
    }
    s1_is_unicode = PyUnicode_CheckExact(s1);
    s2_is_unicode = PyUnicode_CheckExact(s2);
#if PY_MAJOR_VERSION < 3
    if ((s1_is_unicode & (!s2_is_unicode)) && PyString_CheckExact(s2)) {
        owned_ref = PyUnicode_FromObject(s2);
        if (unlikely(!owned_ref))
            return -1;
        s2 = owned_ref;
        s2_is_unicode = 1;
    } else if ((s2_is_unicode & (!s1_is_unicode)) && PyString_CheckExact(s1)) {
        owned_ref = PyUnicode_FromObject(s1);
        if (unlikely(!owned_ref))
            return -1;
        s1 = owned_ref;
        s1_is_unicode = 1;
    } else if (((!s2_is_unicode) & (!s1_is_unicode))) {
        return __Pyx_PyBytes_Equals(s1, s2, equals);
    }
#endif
    if (s1_is_unicode & s2_is_unicode) {
        Py_ssize_t length;
        int kind;
        void *data1, *data2;
        if (unlikely(__Pyx_PyUnicode_READY(s1) < 0) || unlikely(__Pyx_PyUnicode_READY(s2) < 0))
            return -1;
        length = __Pyx_PyUnicode_GET_LENGTH(s1);
        if (length != __Pyx_PyUnicode_GET_LENGTH(s2)) {
            goto return_ne;
        }
        kind = __Pyx_PyUnicode_KIND(s1);
        if (kind != __Pyx_PyUnicode_KIND(s2)) {
            goto return_ne;
        }
        data1 = __Pyx_PyUnicode_DATA(s1);
        data2 = __Pyx_PyUnicode_DATA(s2);
        if (__Pyx_PyUnicode_READ(kind, data1, 0) != __Pyx_PyUnicode_READ(kind, data2, 0)) {
            goto return_ne;
        } else if (length == 1) {
            goto return_eq;
        } else {
            int result = memcmp(data1, data2, (size_t)(length * kind));
            #if PY_MAJOR_VERSION < 3
            Py_XDECREF(owned_ref);
            #endif
            return (equals == Py_EQ) ? (result == 0) : (result != 0);
        }
    } else if ((s1 == Py_None) & s2_is_unicode) {
        goto return_ne;
    } else if ((s2 == Py_None) & s1_is_unicode) {
        goto return_ne;
    } else {
        int result;
        PyObject* py_result = PyObject_RichCompare(s1, s2, equals);
        if (!py_result)
            return -1;
        result = __Pyx_PyObject_IsTrue(py_result);
        Py_DECREF(py_result);
        return result;
    }
return_eq:
    #if PY_MAJOR_VERSION < 3
    Py_XDECREF(owned_ref);
    #endif
    return (equals == Py_EQ);
return_ne:
    #if PY_MAJOR_VERSION < 3
    Py_XDECREF(owned_ref);
    #endif
    return (equals == Py_NE);
#endif
}

#if PY_MAJOR_VERSION < 3
static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb,
                        CYTHON_UNUSED PyObject *cause) {
    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_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) {
                if (PyObject_IsSubclass(instance_class, type)) {
                    type = instance_class;
                } else {
                    instance_class = NULL;
                }
            }
        }
        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 PY_VERSION_HEX >= 0x03030000
    if (cause) {
#else
    if (cause && cause != Py_None) {
#endif
        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 = PyThreadState_GET();
        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

#if CYTHON_COMPILING_IN_CPYTHON
static CYTHON_INLINE PyObject* __Pyx_PyObject_CallNoArg(PyObject *func) {
#ifdef __Pyx_CyFunction_USED
    if (likely(PyCFunction_Check(func) || PyObject_TypeCheck(func, __pyx_CyFunctionType))) {
#else
    if (likely(PyCFunction_Check(func))) {
#endif
        if (likely(PyCFunction_GET_FLAGS(func) & METH_NOARGS)) {
            return __Pyx_PyObject_CallMethO(func, NULL);
        }
    }
    return __Pyx_PyObject_Call(func, __pyx_empty_tuple, NULL);
}
#endif

static CYTHON_INLINE PyObject* __Pyx_PyDict_Keys(PyObject* d) {
    if (PY_MAJOR_VERSION >= 3)
        return __Pyx_PyObject_CallMethod1((PyObject*)&PyDict_Type, __pyx_n_s_keys, d);
    else
        return PyDict_Keys(d);
}

static CYTHON_INLINE int __Pyx_DelItem_Generic(PyObject *o, PyObject *j) {
    int r;
    if (!j) return -1;
    r = PyObject_DelItem(o, j);
    Py_DECREF(j);
    return r;
}
static CYTHON_INLINE int __Pyx_DelItemInt_Fast(PyObject *o, Py_ssize_t i,
                                               CYTHON_UNUSED int is_list, int wraparound) {
#if CYTHON_COMPILING_IN_PYPY
    if (is_list || PySequence_Check(o)) {
        return PySequence_DelItem(o, i);
    }
#else
    PySequenceMethods *m = Py_TYPE(o)->tp_as_sequence;
    if (likely(m && m->sq_ass_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))
                    PyErr_Clear();
                else
                    return -1;
            }
        }
        return m->sq_ass_item(o, i, (PyObject *)NULL);
    }
#endif
    return __Pyx_DelItem_Generic(o, PyInt_FromSsize_t(i));
}

static void __Pyx_RaiseArgumentTypeInvalid(const char* name, PyObject *obj, PyTypeObject *type) {
    PyErr_Format(PyExc_TypeError,
        "Argument '%.200s' has incorrect type (expected %.200s, got %.200s)",
        name, type->tp_name, Py_TYPE(obj)->tp_name);
}
static CYTHON_INLINE int __Pyx_ArgTypeTest(PyObject *obj, PyTypeObject *type, int none_allowed,
    const char *name, int exact)
{
    if (unlikely(!type)) {
        PyErr_SetString(PyExc_SystemError, "Missing type object");
        return 0;
    }
    if (none_allowed && obj == Py_None) return 1;
    else if (exact) {
        if (likely(Py_TYPE(obj) == type)) return 1;
        #if PY_MAJOR_VERSION == 2
        else if ((type == &PyBaseString_Type) && likely(__Pyx_PyBaseString_CheckExact(obj))) return 1;
        #endif
    }
    else {
        if (likely(PyObject_TypeCheck(obj, type))) return 1;
    }
    __Pyx_RaiseArgumentTypeInvalid(name, obj, type);
    return 0;
}

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);
}

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");
}

static CYTHON_INLINE void __Pyx_RaiseNoneNotIterableError(void) {
    PyErr_SetString(PyExc_TypeError, "'NoneType' object is not iterable");
}

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) / 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);
}

#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;
    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(
        PyThreadState_GET(), /*PyThreadState *tstate,*/
        py_code,             /*PyCodeObject *code,*/
        __pyx_d,      /*PyObject *globals,*/
        0                    /*PyObject *locals*/
    );
    if (!py_frame) goto bad;
    py_frame->f_lineno = 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 (PyObject_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 (PyObject_TypeCheck(obj, __pyx_ptype_5numpy_ndarray)) { __pyx_pw_5numpy_7ndarray_3__releasebuffer__(obj, view); return; }
    Py_DECREF(obj);
    view->obj = NULL;
}
#endif


            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_VERSION_HEX < 0x03030000
    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, '.')) {
                #if PY_VERSION_HEX < 0x03030000
                PyObject *py_level = PyInt_FromLong(1);
                if (!py_level)
                    goto bad;
                module = PyObject_CallFunctionObjArgs(py_import,
                    name, global_dict, empty_dict, list, py_level, NULL);
                Py_DECREF(py_level);
                #else
                module = PyImport_ImportModuleLevelObject(
                    name, global_dict, empty_dict, list, 1);
                #endif
                if (!module) {
                    if (!PyErr_ExceptionMatches(PyExc_ImportError))
                        goto bad;
                    PyErr_Clear();
                }
            }
            level = 0;
        }
        #endif
        if (!module) {
            #if PY_VERSION_HEX < 0x03030000
            PyObject *py_level = PyInt_FromLong(level);
            if (!py_level)
                goto bad;
            module = PyObject_CallFunctionObjArgs(py_import,
                name, global_dict, empty_dict, list, py_level, NULL);
            Py_DECREF(py_level);
            #else
            module = PyImport_ImportModuleLevelObject(
                name, global_dict, empty_dict, list, level);
            #endif
        }
    }
bad:
    #if PY_VERSION_HEX < 0x03030000
    Py_XDECREF(py_import);
    #endif
    Py_XDECREF(empty_list);
    Py_XDECREF(empty_dict);
    return module;
}

#define __PYX_VERIFY_RETURN_INT(target_type, func_type, func_value)       \
    {                                                                     \
        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 (is_unsigned && unlikely(value < zero))                \
                    goto raise_neg_overflow;                              \
                else                                                      \
                    goto raise_overflow;                                  \
            }                                                             \
        }                                                                 \
        return (target_type) value;                                       \
    }

#if CYTHON_COMPILING_IN_CPYTHON && PY_MAJOR_VERSION >= 3
 #if CYTHON_USE_PYLONG_INTERNALS
  #include "longintrepr.h"
 #endif
#endif

static CYTHON_INLINE int __Pyx_PyInt_As_int(PyObject *x) {
    const int neg_one = (int) -1, const_zero = 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_COMPILING_IN_CPYTHON && PY_MAJOR_VERSION >= 3
 #if CYTHON_USE_PYLONG_INTERNALS
            switch (Py_SIZE(x)) {
                case  0: return 0;
                case  1: __PYX_VERIFY_RETURN_INT(int, digit, ((PyLongObject*)x)->ob_digit[0]);
            }
 #endif
#endif
            if (unlikely(Py_SIZE(x) < 0)) {
                goto raise_neg_overflow;
            }
            if (sizeof(int) <= sizeof(unsigned long)) {
                __PYX_VERIFY_RETURN_INT(int, unsigned long, PyLong_AsUnsignedLong(x))
            } else if (sizeof(int) <= sizeof(unsigned long long)) {
                __PYX_VERIFY_RETURN_INT(int, unsigned long long, PyLong_AsUnsignedLongLong(x))
            }
        } else {
#if CYTHON_COMPILING_IN_CPYTHON && PY_MAJOR_VERSION >= 3
 #if CYTHON_USE_PYLONG_INTERNALS
            switch (Py_SIZE(x)) {
                case  0: return 0;
                case  1: __PYX_VERIFY_RETURN_INT(int,  digit, +(((PyLongObject*)x)->ob_digit[0]));
                case -1: __PYX_VERIFY_RETURN_INT(int, sdigit, -(sdigit) ((PyLongObject*)x)->ob_digit[0]);
            }
 #endif
#endif
            if (sizeof(int) <= sizeof(long)) {
                __PYX_VERIFY_RETURN_INT(int, long, PyLong_AsLong(x))
            } else if (sizeof(int) <= sizeof(long long)) {
                __PYX_VERIFY_RETURN_INT(int, long long, PyLong_AsLongLong(x))
            }
        }
        {
#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_Int(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_Int(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;
}

static CYTHON_INLINE size_t __Pyx_PyInt_As_size_t(PyObject *x) {
    const size_t neg_one = (size_t) -1, const_zero = 0;
    const int is_unsigned = neg_one > const_zero;
#if PY_MAJOR_VERSION < 3
    if (likely(PyInt_Check(x))) {
        if (sizeof(size_t) < sizeof(long)) {
            __PYX_VERIFY_RETURN_INT(size_t, long, PyInt_AS_LONG(x))
        } else {
            long val = PyInt_AS_LONG(x);
            if (is_unsigned && unlikely(val < 0)) {
                goto raise_neg_overflow;
            }
            return (size_t) val;
        }
    } else
#endif
    if (likely(PyLong_Check(x))) {
        if (is_unsigned) {
#if CYTHON_COMPILING_IN_CPYTHON && PY_MAJOR_VERSION >= 3
 #if CYTHON_USE_PYLONG_INTERNALS
            switch (Py_SIZE(x)) {
                case  0: return 0;
                case  1: __PYX_VERIFY_RETURN_INT(size_t, digit, ((PyLongObject*)x)->ob_digit[0]);
            }
 #endif
#endif
            if (unlikely(Py_SIZE(x) < 0)) {
                goto raise_neg_overflow;
            }
            if (sizeof(size_t) <= sizeof(unsigned long)) {
                __PYX_VERIFY_RETURN_INT(size_t, unsigned long, PyLong_AsUnsignedLong(x))
            } else if (sizeof(size_t) <= sizeof(unsigned long long)) {
                __PYX_VERIFY_RETURN_INT(size_t, unsigned long long, PyLong_AsUnsignedLongLong(x))
            }
        } else {
#if CYTHON_COMPILING_IN_CPYTHON && PY_MAJOR_VERSION >= 3
 #if CYTHON_USE_PYLONG_INTERNALS
            switch (Py_SIZE(x)) {
                case  0: return 0;
                case  1: __PYX_VERIFY_RETURN_INT(size_t,  digit, +(((PyLongObject*)x)->ob_digit[0]));
                case -1: __PYX_VERIFY_RETURN_INT(size_t, sdigit, -(sdigit) ((PyLongObject*)x)->ob_digit[0]);
            }
 #endif
#endif
            if (sizeof(size_t) <= sizeof(long)) {
                __PYX_VERIFY_RETURN_INT(size_t, long, PyLong_AsLong(x))
            } else if (sizeof(size_t) <= sizeof(long long)) {
                __PYX_VERIFY_RETURN_INT(size_t, long long, PyLong_AsLongLong(x))
            }
        }
        {
#if CYTHON_COMPILING_IN_PYPY && !defined(_PyLong_AsByteArray)
            PyErr_SetString(PyExc_RuntimeError,
                            "_PyLong_AsByteArray() not available in PyPy, cannot convert large numbers");
#else
            size_t val;
            PyObject *v = __Pyx_PyNumber_Int(x);
 #if PY_MAJOR_VERSION < 3
            if (likely(v) && !PyLong_Check(v)) {
                PyObject *tmp = v;
                v = PyNumber_Long(tmp);
                Py_DECREF(tmp);
            }
 #endif
            if (likely(v)) {
                int one = 1; int is_little = (int)*(unsigned char *)&one;
                unsigned char *bytes = (unsigned char *)&val;
                int ret = _PyLong_AsByteArray((PyLongObject *)v,
                                              bytes, sizeof(val),
                                              is_little, !is_unsigned);
                Py_DECREF(v);
                if (likely(!ret))
                    return val;
            }
#endif
            return (size_t) -1;
        }
    } else {
        size_t val;
        PyObject *tmp = __Pyx_PyNumber_Int(x);
        if (!tmp) return (size_t) -1;
        val = __Pyx_PyInt_As_size_t(tmp);
        Py_DECREF(tmp);
        return val;
    }
raise_overflow:
    PyErr_SetString(PyExc_OverflowError,
        "value too large to convert to size_t");
    return (size_t) -1;
raise_neg_overflow:
    PyErr_SetString(PyExc_OverflowError,
        "can't convert negative value to size_t");
    return (size_t) -1;
}

static CYTHON_INLINE PyObject* __Pyx_PyInt_From_long(long value) {
    const long neg_one = (long) -1, const_zero = 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);
        } else if (sizeof(long) <= sizeof(unsigned long long)) {
            return PyLong_FromUnsignedLongLong((unsigned long long) value);
        }
    } else {
        if (sizeof(long) <= sizeof(long)) {
            return PyInt_FromLong((long) value);
        } else if (sizeof(long) <= sizeof(long long)) {
            return PyLong_FromLongLong((long long) value);
        }
    }
    {
        int one = 1; int little = (int)*(unsigned char *)&one;
        unsigned char *bytes = (unsigned char *)&value;
        return _PyLong_FromByteArray(bytes, sizeof(long),
                                     little, !is_unsigned);
    }
}

static CYTHON_INLINE long __Pyx_PyInt_As_long(PyObject *x) {
    const long neg_one = (long) -1, const_zero = 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_COMPILING_IN_CPYTHON && PY_MAJOR_VERSION >= 3
 #if CYTHON_USE_PYLONG_INTERNALS
            switch (Py_SIZE(x)) {
                case  0: return 0;
                case  1: __PYX_VERIFY_RETURN_INT(long, digit, ((PyLongObject*)x)->ob_digit[0]);
            }
 #endif
#endif
            if (unlikely(Py_SIZE(x) < 0)) {
                goto raise_neg_overflow;
            }
            if (sizeof(long) <= sizeof(unsigned long)) {
                __PYX_VERIFY_RETURN_INT(long, unsigned long, PyLong_AsUnsignedLong(x))
            } else if (sizeof(long) <= sizeof(unsigned long long)) {
                __PYX_VERIFY_RETURN_INT(long, unsigned long long, PyLong_AsUnsignedLongLong(x))
            }
        } else {
#if CYTHON_COMPILING_IN_CPYTHON && PY_MAJOR_VERSION >= 3
 #if CYTHON_USE_PYLONG_INTERNALS
            switch (Py_SIZE(x)) {
                case  0: return 0;
                case  1: __PYX_VERIFY_RETURN_INT(long,  digit, +(((PyLongObject*)x)->ob_digit[0]));
                case -1: __PYX_VERIFY_RETURN_INT(long, sdigit, -(sdigit) ((PyLongObject*)x)->ob_digit[0]);
            }
 #endif
#endif
            if (sizeof(long) <= sizeof(long)) {
                __PYX_VERIFY_RETURN_INT(long, long, PyLong_AsLong(x))
            } else if (sizeof(long) <= sizeof(long long)) {
                __PYX_VERIFY_RETURN_INT(long, long long, PyLong_AsLongLong(x))
            }
        }
        {
#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_Int(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_Int(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;
}

static CYTHON_INLINE PyObject* __Pyx_PyInt_From_int(int value) {
    const int neg_one = (int) -1, const_zero = 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);
        } else if (sizeof(int) <= sizeof(unsigned long long)) {
            return PyLong_FromUnsignedLongLong((unsigned long long) value);
        }
    } else {
        if (sizeof(int) <= sizeof(long)) {
            return PyInt_FromLong((long) value);
        } else if (sizeof(int) <= sizeof(long long)) {
            return PyLong_FromLongLong((long long) value);
        }
    }
    {
        int one = 1; int little = (int)*(unsigned char *)&one;
        unsigned char *bytes = (unsigned char *)&value;
        return _PyLong_FromByteArray(bytes, sizeof(int),
                                     little, !is_unsigned);
    }
}

#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

#if CYTHON_CCOMPLEX
#else
    static CYTHON_INLINE int __Pyx_c_eqf(__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_sumf(__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_difff(__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_prodf(__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;
    }
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_quotf(__pyx_t_float_complex a, __pyx_t_float_complex b) {
        __pyx_t_float_complex z;
        float denom = b.real * b.real + b.imag * b.imag;
        z.real = (a.real * b.real + a.imag * b.imag) / denom;
        z.imag = (a.imag * b.real - a.real * b.imag) / denom;
        return z;
    }
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_negf(__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_zerof(__pyx_t_float_complex a) {
       return (a.real == 0) && (a.imag == 0);
    }
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_conjf(__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_absf(__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_powf(__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_prodf(a, a);
                        return __Pyx_c_prodf(a, a);
                    case 3:
                        z = __Pyx_c_prodf(a, a);
                        return __Pyx_c_prodf(z, a);
                    case 4:
                        z = __Pyx_c_prodf(a, a);
                        return __Pyx_c_prodf(z, z);
                }
            }
            if (a.imag == 0) {
                if (a.real == 0) {
                    return a;
                }
                r = a.real;
                theta = 0;
            } else {
                r = __Pyx_c_absf(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

#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

#if CYTHON_CCOMPLEX
#else
    static CYTHON_INLINE int __Pyx_c_eq(__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(__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(__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(__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;
    }
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_quot(__pyx_t_double_complex a, __pyx_t_double_complex b) {
        __pyx_t_double_complex z;
        double denom = b.real * b.real + b.imag * b.imag;
        z.real = (a.real * b.real + a.imag * b.imag) / denom;
        z.imag = (a.imag * b.real - a.real * b.imag) / denom;
        return z;
    }
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_neg(__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(__pyx_t_double_complex a) {
       return (a.real == 0) && (a.imag == 0);
    }
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_conj(__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(__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(__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(a, a);
                        return __Pyx_c_prod(a, a);
                    case 3:
                        z = __Pyx_c_prod(a, a);
                        return __Pyx_c_prod(z, a);
                    case 4:
                        z = __Pyx_c_prod(a, a);
                        return __Pyx_c_prod(z, z);
                }
            }
            if (a.imag == 0) {
                if (a.real == 0) {
                    return a;
                }
                r = a.real;
                theta = 0;
            } else {
                r = __Pyx_c_abs(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

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;
}

#ifndef __PYX_HAVE_RT_ImportModule
#define __PYX_HAVE_RT_ImportModule
static PyObject *__Pyx_ImportModule(const char *name) {
    PyObject *py_name = 0;
    PyObject *py_module = 0;
    py_name = __Pyx_PyIdentifier_FromString(name);
    if (!py_name)
        goto bad;
    py_module = PyImport_Import(py_name);
    Py_DECREF(py_name);
    return py_module;
bad:
    Py_XDECREF(py_name);
    return 0;
}
#endif

#ifndef __PYX_HAVE_RT_ImportType
#define __PYX_HAVE_RT_ImportType
static PyTypeObject *__Pyx_ImportType(const char *module_name, const char *class_name,
    size_t size, int strict)
{
    PyObject *py_module = 0;
    PyObject *result = 0;
    PyObject *py_name = 0;
    char warning[200];
    Py_ssize_t basicsize;
#ifdef Py_LIMITED_API
    PyObject *py_basicsize;
#endif
    py_module = __Pyx_ImportModule(module_name);
    if (!py_module)
        goto bad;
    py_name = __Pyx_PyIdentifier_FromString(class_name);
    if (!py_name)
        goto bad;
    result = PyObject_GetAttr(py_module, py_name);
    Py_DECREF(py_name);
    py_name = 0;
    Py_DECREF(py_module);
    py_module = 0;
    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 (!strict && (size_t)basicsize > size) {
        PyOS_snprintf(warning, sizeof(warning),
            "%s.%s size changed, may indicate binary incompatibility",
            module_name, class_name);
        if (PyErr_WarnEx(NULL, warning, 0) < 0) goto bad;
    }
    else if ((size_t)basicsize != size) {
        PyErr_Format(PyExc_ValueError,
            "%.200s.%.200s has the wrong size, try recompiling",
            module_name, class_name);
        goto bad;
    }
    return (PyTypeObject *)result;
bad:
    Py_XDECREF(py_module);
    Py_XDECREF(result);
    return NULL;
}
#endif

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;
        ++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 char* __Pyx_PyObject_AsString(PyObject* o) {
    Py_ssize_t ignore;
    return __Pyx_PyObject_AsStringAndSize(o, &ignore);
}
static CYTHON_INLINE 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)) {
#if PY_VERSION_HEX < 0x03030000
        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
        if (__Pyx_PyUnicode_READY(o) == -1) return NULL;
#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
        if (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
    } else
#endif
#if !CYTHON_COMPILING_IN_PYPY
    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 PyObject* __Pyx_PyNumber_Int(PyObject* x) {
  PyNumberMethods *m;
  const char *name = NULL;
  PyObject *res = NULL;
#if PY_MAJOR_VERSION < 3
  if (PyInt_Check(x) || PyLong_Check(x))
#else
  if (PyLong_Check(x))
#endif
    return Py_INCREF(x), x;
  m = Py_TYPE(x)->tp_as_number;
#if PY_MAJOR_VERSION < 3
  if (m && m->nb_int) {
    name = "int";
    res = PyNumber_Int(x);
  }
  else if (m && m->nb_long) {
    name = "long";
    res = PyNumber_Long(x);
  }
#else
  if (m && m->nb_int) {
    name = "int";
    res = PyNumber_Long(x);
  }
#endif
  if (res) {
#if PY_MAJOR_VERSION < 3
    if (!PyInt_Check(res) && !PyLong_Check(res)) {
#else
    if (!PyLong_Check(res)) {
#endif
      PyErr_Format(PyExc_TypeError,
                   "__%.4s__ returned non-%.4s (type %.200s)",
                   name, name, Py_TYPE(res)->tp_name);
      Py_DECREF(res);
      return NULL;
    }
  }
  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)))
      return PyInt_AS_LONG(b);
#endif
  if (likely(PyLong_CheckExact(b))) {
    #if CYTHON_COMPILING_IN_CPYTHON && PY_MAJOR_VERSION >= 3
     #if CYTHON_USE_PYLONG_INTERNALS
       switch (Py_SIZE(b)) {
       case -1: return -(sdigit)((PyLongObject*)b)->ob_digit[0];
       case  0: return 0;
       case  1: return ((PyLongObject*)b)->ob_digit[0];
       }
     #endif
    #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_PyInt_FromSize_t(size_t ival) {
    return PyInt_FromSize_t(ival);
}


#endif /* Py_PYTHON_H */
