From e083f90ad09a3bd42beffea1e996f3b4a9b3ff76 Mon Sep 17 00:00:00 2001 From: Rémi Flamary Date: Thu, 27 Oct 2016 12:34:42 +0200 Subject: rename emd module to lp --- ot/__init__.py | 6 +- ot/emd/EMD.h | 29 - ot/emd/EMD_wrap.cpp | 120 - ot/emd/__init__.py | 3 - ot/emd/core.h | 103 - ot/emd/emd.cpp | 6507 --------------------------------------- ot/emd/emd.pyx | 71 - ot/emd/full_bipartitegraph.h | 215 -- ot/emd/network_simplex_simple.h | 1543 ---------- ot/lp/EMD.h | 29 + ot/lp/EMD_wrap.cpp | 120 + ot/lp/__init__.py | 3 + ot/lp/core.h | 103 + ot/lp/emd.cpp | 6507 +++++++++++++++++++++++++++++++++++++++ ot/lp/emd.pyx | 71 + ot/lp/full_bipartitegraph.h | 215 ++ ot/lp/network_simplex_simple.h | 1543 ++++++++++ ot/optim.py | 2 +- 18 files changed, 8596 insertions(+), 8594 deletions(-) delete mode 100644 ot/emd/EMD.h delete mode 100644 ot/emd/EMD_wrap.cpp delete mode 100644 ot/emd/__init__.py delete mode 100644 ot/emd/core.h delete mode 100644 ot/emd/emd.cpp delete mode 100644 ot/emd/emd.pyx delete mode 100644 ot/emd/full_bipartitegraph.h delete mode 100644 ot/emd/network_simplex_simple.h create mode 100644 ot/lp/EMD.h create mode 100644 ot/lp/EMD_wrap.cpp create mode 100644 ot/lp/__init__.py create mode 100644 ot/lp/core.h create mode 100644 ot/lp/emd.cpp create mode 100644 ot/lp/emd.pyx create mode 100644 ot/lp/full_bipartitegraph.h create mode 100644 ot/lp/network_simplex_simple.h (limited to 'ot') diff --git a/ot/__init__.py b/ot/__init__.py index 4c3c40e..87119e5 100644 --- a/ot/__init__.py +++ b/ot/__init__.py @@ -5,15 +5,17 @@ from . import utils from . import datasets from . import plot from . import bregman +from . import lp from . import da from . import optim + # OT functions -from ot.emd import emd +from ot.lp import emd from ot.bregman import sinkhorn,barycenter from ot.da import sinkhorn_lpl1_mm # utils functions from utils import dist,unif -__all__ = ["emd","sinkhorn","utils",'datasets','bregman','plot','dist','unif','barycenter','sinkhorn_lpl1_mm','da','optim'] +__all__ = ["emd","sinkhorn","utils",'datasets','bregman','lp','plot','dist','unif','barycenter','sinkhorn_lpl1_mm','da','optim'] diff --git a/ot/emd/EMD.h b/ot/emd/EMD.h deleted file mode 100644 index 40d7192..0000000 --- a/ot/emd/EMD.h +++ /dev/null @@ -1,29 +0,0 @@ -/* This file is a c++ wrapper function for computing the transportation cost - * between two vectors given a cost matrix. - * - * It was written by Antoine Rolet (2014) and mainly consists of a wrapper - * of the code written by Nicolas Bonneel available on this page - * http://people.seas.harvard.edu/~nbonneel/FastTransport/ - * - * It was then modified to make it more amenable to python inline calling - * - * Please give relevant credit to the original author (Nicolas Bonneel) if - * you use this code for a publication. - * - */ - - -#ifndef EMD_H -#define EMD_H - -#include -#include -#include "network_simplex_simple.h" - -using namespace lemon; -typedef unsigned int node_id_type; - - -void EMD_wrap(int n1,int n2, double *X, double *Y,double *D, double *G, double *cost); - -#endif diff --git a/ot/emd/EMD_wrap.cpp b/ot/emd/EMD_wrap.cpp deleted file mode 100644 index 52cd262..0000000 --- a/ot/emd/EMD_wrap.cpp +++ /dev/null @@ -1,120 +0,0 @@ -/* This file is a c++ wrapper function for computing the transportation cost - * between two vectors given a cost matrix. - * - * It was written by Antoine Rolet (2014) and mainly consists of a wrapper - * of the code written by Nicolas Bonneel available on this page - * http://people.seas.harvard.edu/~nbonneel/FastTransport/ - * - * It was then modified to make it more amenable to python inline calling - * - * Please give relevant credit to the original author (Nicolas Bonneel) if - * you use this code for a publication. - * - */ - -#include "EMD.h" - - -void EMD_wrap(int n1,int n2, double *X, double *Y,double *D, double *G, double *cost) { -// beware M and C anre strored in row major C style!!! - int n, m, i,cur; - double max,max_iter; - - - typedef FullBipartiteDigraph Digraph; - DIGRAPH_TYPEDEFS(FullBipartiteDigraph); - - // Get the number of non zero coordinates for r and c - n=0; - for (node_id_type i=0; i0) { - n++; - } - } - m=0; - for (node_id_type i=0; i0) { - m++; - } - } - - - // Define the graph - - std::vector indI(n), indJ(m); - std::vector weights1(n), weights2(m); - Digraph di(n, m); - NetworkSimplexSimple net(di, true, n+m, n*m,max_iter); - - // Set supply and demand, don't account for 0 values (faster) - - max=0; - cur=0; - for (node_id_type i=0; i0) { - weights1[ di.nodeFromId(cur) ] = val; - max+=val; - indI[cur++]=i; - } - } - - // Demand is actually negative supply... - - max=0; - cur=0; - for (node_id_type i=0; i0) { - weights2[ di.nodeFromId(cur) ] = -val; - indJ[cur++]=i; - - max-=val; - } - } - - - net.supplyMap(&weights1[0], n, &weights2[0], m); - - // Set the cost of each edge - max=0; - for (node_id_type i=0; imax) { - max=val; - } - } - } - - - // Solve the problem with the network simplex algorithm - - int ret=net.run(); - if (ret!=(int)net.OPTIMAL) { - if (ret==(int)net.INFEASIBLE) { - std::cout << "Infeasible problem"; - } - if (ret==(int)net.UNBOUNDED) - { - std::cout << "Unbounded problem"; - } - } else - { - for (node_id_type i=0; i -#include - - -// Disable the following warnings when compiling with MSVC: -// C4250: 'class1' : inherits 'class2::member' via dominance -// C4355: 'this' : used in base member initializer list -// C4503: 'function' : decorated name length exceeded, name was truncated -// C4800: 'type' : forcing value to bool 'true' or 'false' (performance warning) -// C4996: 'function': was declared deprecated -#ifdef _MSC_VER -#pragma warning( disable : 4250 4355 4503 4800 4996 ) -#endif - -///\file -///\brief LEMON core utilities. -/// -///This header file contains core utilities for LEMON. -///It is automatically included by all graph types, therefore it usually -///do not have to be included directly. - -namespace lemon { - - /// \brief Dummy type to make it easier to create invalid iterators. - /// - /// Dummy type to make it easier to create invalid iterators. - /// See \ref INVALID for the usage. - struct Invalid { - public: - bool operator==(Invalid) { return true; } - bool operator!=(Invalid) { return false; } - bool operator< (Invalid) { return false; } - }; - - /// \brief Invalid iterators. - /// - /// \ref Invalid is a global type that converts to each iterator - /// in such a way that the value of the target iterator will be invalid. -#ifdef LEMON_ONLY_TEMPLATES - const Invalid INVALID = Invalid(); -#else - extern const Invalid INVALID; -#endif - - /// \addtogroup gutils - /// @{ - - ///Create convenience typedefs for the digraph types and iterators - - ///This \c \#define creates convenient type definitions for the following - ///types of \c Digraph: \c Node, \c NodeIt, \c Arc, \c ArcIt, \c InArcIt, - ///\c OutArcIt, \c BoolNodeMap, \c IntNodeMap, \c DoubleNodeMap, - ///\c BoolArcMap, \c IntArcMap, \c DoubleArcMap. - /// - ///\note If the graph type is a dependent type, ie. the graph type depend - ///on a template parameter, then use \c TEMPLATE_DIGRAPH_TYPEDEFS() - ///macro. -#define DIGRAPH_TYPEDEFS(Digraph) \ - typedef Digraph::Node Node; 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if (unlikely(!__pyx_t_1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 21; __pyx_clineno = __LINE__; goto __pyx_L1_error;} - __Pyx_GOTREF(__pyx_t_1); - if (PyDict_SetItem(__pyx_d, __pyx_n_s_emd, __pyx_t_1) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 21; __pyx_clineno = __LINE__; goto __pyx_L1_error;} - __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0; - - /* "ot/emd/emd.pyx":1 - * # -*- coding: utf-8 -*- # <<<<<<<<<<<<<< - * """ - * Created on Thu Sep 11 08:42:08 2014 - */ - __pyx_t_1 = PyDict_New(); if (unlikely(!__pyx_t_1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;} - __Pyx_GOTREF(__pyx_t_1); - if (PyDict_SetItem(__pyx_d, __pyx_n_s_test, __pyx_t_1) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;} - __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0; - - /* "../../../../usr/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":976 - * arr.base = baseptr - * - * cdef inline object get_array_base(ndarray arr): # <<<<<<<<<<<<<< - * if arr.base is NULL: - * return None - */ - - /*--- Wrapped vars code ---*/ - - goto __pyx_L0; - __pyx_L1_error:; - __Pyx_XDECREF(__pyx_t_1); - if (__pyx_m) { - if (__pyx_d) { - __Pyx_AddTraceback("init ot.emd.emd", __pyx_clineno, __pyx_lineno, __pyx_filename); - } - Py_DECREF(__pyx_m); __pyx_m = 0; - } else if (!PyErr_Occurred()) { - PyErr_SetString(PyExc_ImportError, "init ot.emd.emd"); - } - __pyx_L0:; - __Pyx_RefNannyFinishContext(); - #if PY_MAJOR_VERSION < 3 - return; - #else - return __pyx_m; - #endif -} - -/* --- Runtime support code --- */ -#if CYTHON_REFNANNY -static __Pyx_RefNannyAPIStruct *__Pyx_RefNannyImportAPI(const char *modname) { - PyObject *m = NULL, *p = NULL; - void *r = NULL; - m = PyImport_ImportModule((char *)modname); - if (!m) goto end; - p = PyObject_GetAttrString(m, (char *)"RefNannyAPI"); - if (!p) goto end; - r = PyLong_AsVoidPtr(p); -end: - Py_XDECREF(p); - Py_XDECREF(m); - return (__Pyx_RefNannyAPIStruct *)r; -} -#endif - -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; 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"" : "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) ? 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- 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 PyObject *__Pyx_GetBuiltinName(PyObject *name) { - PyObject* result = __Pyx_PyObject_GetAttrStr(__pyx_b, name); - if (unlikely(!result)) { - PyErr_Format(PyExc_NameError, -#if PY_MAJOR_VERSION >= 3 - "name '%U' is not defined", name); -#else - "name '%.200s' is not defined", PyString_AS_STRING(name)); -#endif - } - return result; -} - -static CYTHON_INLINE PyObject *__Pyx_GetModuleGlobalName(PyObject *name) { - PyObject *result; -#if CYTHON_COMPILING_IN_CPYTHON - result = PyDict_GetItem(__pyx_d, name); - if (likely(result)) { - Py_INCREF(result); - } else { -#else - result = PyObject_GetItem(__pyx_d, name); - if (!result) { - PyErr_Clear(); -#endif - result = __Pyx_GetBuiltinName(name); - } - return result; -} - -#if CYTHON_COMPILING_IN_CPYTHON -static CYTHON_INLINE PyObject* __Pyx_PyObject_Call(PyObject *func, PyObject *arg, PyObject *kw) { - PyObject *result; - ternaryfunc call = func->ob_type->tp_call; - if (unlikely(!call)) - return PyObject_Call(func, arg, kw); - if (unlikely(Py_EnterRecursiveCall((char*)" while calling a Python object"))) - return NULL; - result = (*call)(func, arg, kw); - Py_LeaveRecursiveCall(); - if (unlikely(!result) && unlikely(!PyErr_Occurred())) { - PyErr_SetString( - PyExc_SystemError, - "NULL result without error in PyObject_Call"); - } - return result; -} -#endif - -#if CYTHON_COMPILING_IN_CPYTHON -static CYTHON_INLINE PyObject* __Pyx_PyObject_CallMethO(PyObject *func, PyObject *arg) { - PyObject *self, *result; - PyCFunction cfunc; - cfunc = PyCFunction_GET_FUNCTION(func); - self = PyCFunction_GET_SELF(func); - if (unlikely(Py_EnterRecursiveCall((char*)" while calling a Python object"))) - return NULL; - result = cfunc(self, arg); - Py_LeaveRecursiveCall(); - if (unlikely(!result) && unlikely(!PyErr_Occurred())) { - PyErr_SetString( - PyExc_SystemError, - "NULL result without error in PyObject_Call"); - } - return result; -} -#endif - -#if CYTHON_COMPILING_IN_CPYTHON -static PyObject* __Pyx__PyObject_CallOneArg(PyObject *func, PyObject *arg) { - PyObject *result; - PyObject *args = PyTuple_New(1); - if (unlikely(!args)) return NULL; - Py_INCREF(arg); - PyTuple_SET_ITEM(args, 0, arg); - result = __Pyx_PyObject_Call(func, args, NULL); - Py_DECREF(args); - return result; -} -static CYTHON_INLINE PyObject* __Pyx_PyObject_CallOneArg(PyObject *func, PyObject *arg) { -#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_O)) { - return __Pyx_PyObject_CallMethO(func, arg); - } - } - return __Pyx__PyObject_CallOneArg(func, arg); -} -#else -static CYTHON_INLINE PyObject* __Pyx_PyObject_CallOneArg(PyObject *func, PyObject *arg) { - PyObject *result; - PyObject *args = PyTuple_Pack(1, arg); - if (unlikely(!args)) return NULL; - result = __Pyx_PyObject_Call(func, args, NULL); - Py_DECREF(args); - return result; -} -#endif - -static CYTHON_INLINE int __Pyx_TypeTest(PyObject *obj, PyTypeObject *type) { - if (unlikely(!type)) { - PyErr_SetString(PyExc_SystemError, "Missing type object"); - return 0; - } - if (likely(PyObject_TypeCheck(obj, type))) - return 1; - PyErr_Format(PyExc_TypeError, "Cannot convert %.200s to %.200s", - Py_TYPE(obj)->tp_name, type->tp_name); - return 0; -} - -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 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 -} - -#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) { - int is_subclass = PyObject_IsSubclass(instance_class, type); - if (!is_subclass) { - instance_class = NULL; - } else if (unlikely(is_subclass == -1)) { - goto bad; - } else { - type = instance_class; - } - } - } - if (!instance_class) { - PyObject *args; - if (!value) - args = PyTuple_New(0); - else if (PyTuple_Check(value)) { - Py_INCREF(value); - args = value; - } else - args = PyTuple_Pack(1, value); - if (!args) - goto bad; - owned_instance = PyObject_Call(type, args, NULL); - Py_DECREF(args); - if (!owned_instance) - goto bad; - value = owned_instance; - if (!PyExceptionInstance_Check(value)) { - PyErr_Format(PyExc_TypeError, - "calling %R should have returned an instance of " - "BaseException, not %R", - type, Py_TYPE(value)); - goto bad; - } - } - } else { - PyErr_SetString(PyExc_TypeError, - "raise: exception class must be a subclass of BaseException"); - goto bad; - } -#if 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 - -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 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; -} - -static int __pyx_bisect_code_objects(__Pyx_CodeObjectCacheEntry* entries, int count, int code_line) { - int start = 0, mid = 0, end = count - 1; - if (end >= 0 && code_line > entries[end].code_line) { - return count; - } - while (start < end) { - mid = start + (end - start) / 2; - if (code_line < entries[mid].code_line) { - end = mid; - } else if (code_line > entries[mid].code_line) { - start = mid + 1; - } else { - return mid; - } - } - if (code_line <= entries[mid].code_line) { - return mid; - } else { - return mid + 1; - } -} -static PyCodeObject *__pyx_find_code_object(int code_line) { - PyCodeObject* code_object; - int pos; - if (unlikely(!code_line) || unlikely(!__pyx_code_cache.entries)) { - return NULL; - } - pos = __pyx_bisect_code_objects(__pyx_code_cache.entries, __pyx_code_cache.count, code_line); - if (unlikely(pos >= __pyx_code_cache.count) || unlikely(__pyx_code_cache.entries[pos].code_line != code_line)) { - return NULL; - } - code_object = __pyx_code_cache.entries[pos].code_object; - Py_INCREF(code_object); - return code_object; -} -static void __pyx_insert_code_object(int code_line, PyCodeObject* code_object) { - int pos, i; - __Pyx_CodeObjectCacheEntry* entries = __pyx_code_cache.entries; - if (unlikely(!code_line)) { - return; - } - if (unlikely(!entries)) { - entries = (__Pyx_CodeObjectCacheEntry*)PyMem_Malloc(64*sizeof(__Pyx_CodeObjectCacheEntry)); - if (likely(entries)) { - __pyx_code_cache.entries = entries; - __pyx_code_cache.max_count = 64; - __pyx_code_cache.count = 1; - entries[0].code_line = code_line; - entries[0].code_object = code_object; - Py_INCREF(code_object); - } - return; - } - pos = __pyx_bisect_code_objects(__pyx_code_cache.entries, __pyx_code_cache.count, code_line); - if ((pos < __pyx_code_cache.count) && unlikely(__pyx_code_cache.entries[pos].code_line == code_line)) { - PyCodeObject* tmp = entries[pos].code_object; - entries[pos].code_object = code_object; - Py_DECREF(tmp); - return; - } - if (__pyx_code_cache.count == __pyx_code_cache.max_count) { - int new_max = __pyx_code_cache.max_count + 64; - entries = (__Pyx_CodeObjectCacheEntry*)PyMem_Realloc( - __pyx_code_cache.entries, (size_t)new_max*sizeof(__Pyx_CodeObjectCacheEntry)); - if (unlikely(!entries)) { - return; - } - __pyx_code_cache.entries = entries; - __pyx_code_cache.max_count = new_max; - } - for (i=__pyx_code_cache.count; i>pos; i--) { - entries[i] = entries[i-1]; - } - entries[pos].code_line = code_line; - entries[pos].code_object = code_object; - __pyx_code_cache.count++; - Py_INCREF(code_object); -} - -#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 CYTHON_INLINE PyObject* __Pyx_PyInt_From_int(int value) { - const int neg_one = (int) -1, const_zero = (int) 0; - const int is_unsigned = neg_one > const_zero; - if (is_unsigned) { - if (sizeof(int) < sizeof(long)) { - return PyInt_FromLong((long) value); - } else if (sizeof(int) <= sizeof(unsigned long)) { - return PyLong_FromUnsignedLong((unsigned long) value); - } else if (sizeof(int) <= sizeof(unsigned PY_LONG_LONG)) { - return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value); - } - } else { - if (sizeof(int) <= sizeof(long)) { - return PyInt_FromLong((long) value); - } else if (sizeof(int) <= sizeof(PY_LONG_LONG)) { - return PyLong_FromLongLong((PY_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 - -#define __PYX_VERIFY_RETURN_INT(target_type, func_type, func_value)\ - __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, 0) -#define __PYX_VERIFY_RETURN_INT_EXC(target_type, func_type, func_value)\ - __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, 1) -#define __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, exc)\ - {\ - func_type value = func_value;\ - if (sizeof(target_type) < sizeof(func_type)) {\ - if (unlikely(value != (func_type) (target_type) value)) {\ - func_type zero = 0;\ - if (exc && unlikely(value == (func_type)-1 && PyErr_Occurred()))\ - return (target_type) -1;\ - if (is_unsigned && unlikely(value < zero))\ - goto raise_neg_overflow;\ - else\ - goto raise_overflow;\ - }\ - }\ - return (target_type) value;\ - } - -#if CYTHON_USE_PYLONG_INTERNALS - #include "longintrepr.h" -#endif - -static CYTHON_INLINE int __Pyx_PyInt_As_int(PyObject *x) { - const int neg_one = (int) -1, const_zero = (int) 0; - const int is_unsigned = neg_one > const_zero; -#if PY_MAJOR_VERSION < 3 - if (likely(PyInt_Check(x))) { - if (sizeof(int) < sizeof(long)) { - __PYX_VERIFY_RETURN_INT(int, long, PyInt_AS_LONG(x)) - } else { - long val = PyInt_AS_LONG(x); - if (is_unsigned && unlikely(val < 0)) { - goto raise_neg_overflow; - } - return (int) val; - } - } else -#endif - if (likely(PyLong_Check(x))) { - if (is_unsigned) { -#if CYTHON_USE_PYLONG_INTERNALS - const digit* digits = ((PyLongObject*)x)->ob_digit; - switch (Py_SIZE(x)) { - case 0: return (int) 0; - case 1: __PYX_VERIFY_RETURN_INT(int, digit, digits[0]) - case 2: - if (8 * sizeof(int) > 1 * PyLong_SHIFT) { - if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) { - __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) - } else if (8 * sizeof(int) >= 2 * PyLong_SHIFT) { - return (int) (((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0])); - } - } - break; - case 3: - if (8 * sizeof(int) > 2 * PyLong_SHIFT) { - if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) { - __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) - } else if (8 * sizeof(int) >= 3 * PyLong_SHIFT) { - return (int) (((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])); - } - } - break; - case 4: - if (8 * sizeof(int) > 3 * PyLong_SHIFT) { - if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) { - __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) - } else if (8 * sizeof(int) >= 4 * PyLong_SHIFT) { - return (int) (((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])); - } - } - break; - } -#endif -#if CYTHON_COMPILING_IN_CPYTHON - if (unlikely(Py_SIZE(x) < 0)) { - goto raise_neg_overflow; - } -#else - { - int result = PyObject_RichCompareBool(x, Py_False, Py_LT); - if (unlikely(result < 0)) - return (int) -1; - if (unlikely(result == 1)) - goto raise_neg_overflow; - } -#endif - if (sizeof(int) <= sizeof(unsigned long)) { - __PYX_VERIFY_RETURN_INT_EXC(int, unsigned long, PyLong_AsUnsignedLong(x)) - } else if (sizeof(int) <= sizeof(unsigned PY_LONG_LONG)) { - __PYX_VERIFY_RETURN_INT_EXC(int, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x)) - } - } else { -#if CYTHON_USE_PYLONG_INTERNALS - const digit* digits = ((PyLongObject*)x)->ob_digit; - switch (Py_SIZE(x)) { - case 0: return (int) 0; - case -1: __PYX_VERIFY_RETURN_INT(int, sdigit, -(sdigit) digits[0]) - case 1: __PYX_VERIFY_RETURN_INT(int, digit, +digits[0]) - case -2: - if (8 * sizeof(int) - 1 > 1 * PyLong_SHIFT) { - if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) { - __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) - } else if (8 * sizeof(int) - 1 > 2 * PyLong_SHIFT) { - return (int) (((int)-1)*(((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0]))); - } - } - break; - case 2: - if (8 * sizeof(int) > 1 * PyLong_SHIFT) { - if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) { - __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) - } else if (8 * sizeof(int) - 1 > 2 * PyLong_SHIFT) { - return (int) ((((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0]))); - } - } - break; - case -3: - if (8 * sizeof(int) - 1 > 2 * PyLong_SHIFT) { - if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) { - __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) - } else if (8 * sizeof(int) - 1 > 3 * PyLong_SHIFT) { - return (int) (((int)-1)*(((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0]))); - } - } - break; - case 3: - if (8 * sizeof(int) > 2 * PyLong_SHIFT) { - if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) { - __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) - } else if (8 * sizeof(int) - 1 > 3 * PyLong_SHIFT) { - return (int) ((((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0]))); - } - } - break; - case -4: - if (8 * sizeof(int) - 1 > 3 * PyLong_SHIFT) { - if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) { - __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) - } else if (8 * sizeof(int) - 1 > 4 * PyLong_SHIFT) { - return (int) (((int)-1)*(((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0]))); - } - } - break; - case 4: - if (8 * sizeof(int) > 3 * PyLong_SHIFT) { - if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) { - __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) - } else if (8 * sizeof(int) - 1 > 4 * PyLong_SHIFT) { - return (int) ((((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0]))); - } - } - break; - } -#endif - if (sizeof(int) <= sizeof(long)) { - __PYX_VERIFY_RETURN_INT_EXC(int, long, PyLong_AsLong(x)) - } else if (sizeof(int) <= sizeof(PY_LONG_LONG)) { - __PYX_VERIFY_RETURN_INT_EXC(int, PY_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 PyObject* __Pyx_PyInt_From_enum__NPY_TYPES(enum NPY_TYPES value) { - const enum NPY_TYPES neg_one = (enum NPY_TYPES) -1, const_zero = (enum NPY_TYPES) 0; - const int is_unsigned = neg_one > const_zero; - if (is_unsigned) { - if (sizeof(enum NPY_TYPES) < sizeof(long)) { - return PyInt_FromLong((long) value); - } else if (sizeof(enum NPY_TYPES) <= sizeof(unsigned long)) { - return PyLong_FromUnsignedLong((unsigned long) value); - } else if (sizeof(enum NPY_TYPES) <= sizeof(unsigned PY_LONG_LONG)) { - return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value); - } - } else { - if (sizeof(enum NPY_TYPES) <= sizeof(long)) { - return PyInt_FromLong((long) value); - } else if (sizeof(enum NPY_TYPES) <= sizeof(PY_LONG_LONG)) { - return PyLong_FromLongLong((PY_LONG_LONG) value); - } - } - { - int one = 1; int little = (int)*(unsigned char *)&one; - unsigned char *bytes = (unsigned char *)&value; - return _PyLong_FromByteArray(bytes, sizeof(enum NPY_TYPES), - little, !is_unsigned); - } -} - -static CYTHON_INLINE PyObject* __Pyx_PyInt_From_long(long value) { - const long neg_one = (long) -1, const_zero = (long) 0; - const int is_unsigned = neg_one > const_zero; - if (is_unsigned) { - if (sizeof(long) < sizeof(long)) { - return PyInt_FromLong((long) value); - } else if (sizeof(long) <= sizeof(unsigned long)) { - return PyLong_FromUnsignedLong((unsigned long) value); - } else if (sizeof(long) <= sizeof(unsigned PY_LONG_LONG)) { - return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value); - } - } else { - if (sizeof(long) <= sizeof(long)) { - return PyInt_FromLong((long) value); - } else if (sizeof(long) <= sizeof(PY_LONG_LONG)) { - return PyLong_FromLongLong((PY_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 = (long) 0; - const int is_unsigned = neg_one > const_zero; -#if PY_MAJOR_VERSION < 3 - if (likely(PyInt_Check(x))) { - if (sizeof(long) < sizeof(long)) { - __PYX_VERIFY_RETURN_INT(long, long, PyInt_AS_LONG(x)) - } else { - long val = PyInt_AS_LONG(x); - if (is_unsigned && unlikely(val < 0)) { - goto raise_neg_overflow; - } - return (long) val; - } - } else -#endif - if (likely(PyLong_Check(x))) { - if (is_unsigned) { -#if CYTHON_USE_PYLONG_INTERNALS - const digit* digits = ((PyLongObject*)x)->ob_digit; - switch (Py_SIZE(x)) { - case 0: return (long) 0; - case 1: __PYX_VERIFY_RETURN_INT(long, digit, digits[0]) - case 2: - if (8 * sizeof(long) > 1 * PyLong_SHIFT) { - if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) { - __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) - } else if (8 * sizeof(long) >= 2 * PyLong_SHIFT) { - return (long) (((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0])); - } - } - break; - case 3: - if (8 * sizeof(long) > 2 * PyLong_SHIFT) { - if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) { - __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) - } else if (8 * sizeof(long) >= 3 * PyLong_SHIFT) { - return (long) (((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])); - } - } - break; - case 4: - if (8 * sizeof(long) > 3 * PyLong_SHIFT) { - if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) { - __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) - } else if (8 * sizeof(long) >= 4 * PyLong_SHIFT) { - return (long) (((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])); - } - } - break; - } -#endif -#if CYTHON_COMPILING_IN_CPYTHON - if (unlikely(Py_SIZE(x) < 0)) { - goto raise_neg_overflow; - } -#else - { - int result = PyObject_RichCompareBool(x, Py_False, Py_LT); - if (unlikely(result < 0)) - return (long) -1; - if (unlikely(result == 1)) - goto raise_neg_overflow; - } -#endif - if (sizeof(long) <= sizeof(unsigned long)) { - __PYX_VERIFY_RETURN_INT_EXC(long, unsigned long, PyLong_AsUnsignedLong(x)) - } else if (sizeof(long) <= sizeof(unsigned PY_LONG_LONG)) { - __PYX_VERIFY_RETURN_INT_EXC(long, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x)) - } - } else { -#if CYTHON_USE_PYLONG_INTERNALS - const digit* digits = ((PyLongObject*)x)->ob_digit; - switch (Py_SIZE(x)) { - case 0: return (long) 0; - case -1: __PYX_VERIFY_RETURN_INT(long, sdigit, -(sdigit) digits[0]) - case 1: __PYX_VERIFY_RETURN_INT(long, digit, +digits[0]) - case -2: - if (8 * sizeof(long) - 1 > 1 * PyLong_SHIFT) { - if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) { - __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) - } else if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) { - return (long) (((long)-1)*(((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0]))); - } - } - break; - case 2: - if (8 * sizeof(long) > 1 * PyLong_SHIFT) { - if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) { - __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) - } else if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) { - return (long) ((((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0]))); - } - } - break; - case -3: - if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) { - if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) { - __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) - } else if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) { - return (long) (((long)-1)*(((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0]))); - } - } - break; - case 3: - if (8 * sizeof(long) > 2 * PyLong_SHIFT) { - if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) { - __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) - } else if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) { - return (long) ((((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0]))); - } - } - break; - case -4: - if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) { - if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) { - __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) - } else if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) { - return (long) (((long)-1)*(((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0]))); - } - } - break; - case 4: - if (8 * sizeof(long) > 3 * PyLong_SHIFT) { - if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) { - __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) - } else if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) { - return (long) ((((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0]))); - } - } - break; - } -#endif - if (sizeof(long) <= sizeof(long)) { - __PYX_VERIFY_RETURN_INT_EXC(long, long, PyLong_AsLong(x)) - } else if (sizeof(long) <= sizeof(PY_LONG_LONG)) { - __PYX_VERIFY_RETURN_INT_EXC(long, PY_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 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 CYTHON_COMPILING_IN_CPYTHON && (__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) || (defined(PyByteArray_AS_STRING) && defined(PyByteArray_GET_SIZE)) - if (PyByteArray_Check(o)) { - *length = PyByteArray_GET_SIZE(o); - return PyByteArray_AS_STRING(o); - } else -#endif - { - char* result; - int r = PyBytes_AsStringAndSize(o, &result, length); - if (unlikely(r < 0)) { - return NULL; - } else { - return result; - } - } -} -static CYTHON_INLINE int __Pyx_PyObject_IsTrue(PyObject* x) { - int is_true = x == Py_True; - if (is_true | (x == Py_False) | (x == Py_None)) return is_true; - else return PyObject_IsTrue(x); -} -static CYTHON_INLINE 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 __Pyx_NewRef(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))) { - if (sizeof(Py_ssize_t) >= sizeof(long)) - return PyInt_AS_LONG(b); - else - return PyInt_AsSsize_t(x); - } -#endif - if (likely(PyLong_CheckExact(b))) { - #if CYTHON_USE_PYLONG_INTERNALS - const digit* digits = ((PyLongObject*)b)->ob_digit; - const Py_ssize_t size = Py_SIZE(b); - if (likely(__Pyx_sst_abs(size) <= 1)) { - ival = likely(size) ? digits[0] : 0; - if (size == -1) ival = -ival; - return ival; - } else { - switch (size) { - case 2: - if (8 * sizeof(Py_ssize_t) > 2 * PyLong_SHIFT) { - return (Py_ssize_t) (((((size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0])); - } - break; - case -2: - if (8 * sizeof(Py_ssize_t) > 2 * PyLong_SHIFT) { - return -(Py_ssize_t) (((((size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0])); - } - break; - case 3: - if (8 * sizeof(Py_ssize_t) > 3 * PyLong_SHIFT) { - return (Py_ssize_t) (((((((size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0])); - } - break; - case -3: - if (8 * sizeof(Py_ssize_t) > 3 * PyLong_SHIFT) { - return -(Py_ssize_t) (((((((size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0])); - } - break; - case 4: - if (8 * sizeof(Py_ssize_t) > 4 * PyLong_SHIFT) { - return (Py_ssize_t) (((((((((size_t)digits[3]) << PyLong_SHIFT) | (size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0])); - } - break; - case -4: - if (8 * sizeof(Py_ssize_t) > 4 * PyLong_SHIFT) { - return -(Py_ssize_t) (((((((((size_t)digits[3]) << PyLong_SHIFT) | (size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0])); - } - break; - } - } - #endif - return PyLong_AsSsize_t(b); - } - x = PyNumber_Index(b); - if (!x) return -1; - ival = PyInt_AsSsize_t(x); - Py_DECREF(x); - return ival; -} -static CYTHON_INLINE PyObject * __Pyx_PyInt_FromSize_t(size_t ival) { - return PyInt_FromSize_t(ival); -} - - -#endif /* Py_PYTHON_H */ diff --git a/ot/emd/emd.pyx b/ot/emd/emd.pyx deleted file mode 100644 index 753b195..0000000 --- a/ot/emd/emd.pyx +++ /dev/null @@ -1,71 +0,0 @@ -# -*- coding: utf-8 -*- -""" -Created on Thu Sep 11 08:42:08 2014 - -@author: rflamary -""" -import numpy as np -cimport numpy as np - -cimport cython - - - -cdef extern from "EMD.h": - void EMD_wrap(int n1,int n2, double *X, double *Y,double *D, double *G, double *cost) - - - -@cython.boundscheck(False) -@cython.wraparound(False) -def emd( np.ndarray[double, ndim=1, mode="c"] a,np.ndarray[double, ndim=1, mode="c"] b,np.ndarray[double, ndim=2, mode="c"] M): - """ - Solves the Earth Movers distance problem and returns the optimal transport matrix - - gamm=emd(a,b,M) - - .. math:: - \gamma = arg\min_\gamma <\gamma,M>_F - - s.t. \gamma 1 = a - - \gamma^T 1= b - - \gamma\geq 0 - where : - - - M is the metric cost matrix - - a and b are the sample weights - - Parameters - ---------- - a : (ns,) ndarray - samples in the source domain (uniform waigth if empty) - b : (nt,) ndarray - samples in the target domain (uniform waigth if empty) - M : (ns,nt) ndarray - loss matrix - - - Returns - ------- - gamma: (ns x nt) ndarray - Optimal transportation matrix for the given parameters - - """ - cdef int n1= M.shape[0] - cdef int n2= M.shape[1] - - cdef float cost=0 - cdef np.ndarray[double, ndim=2, mode="c"] G=np.zeros([n1, n2]) - - if not len(a): - a=np.ones((n1,))/n1 - - if not len(b): - b=np.ones((n2,))/n2 - - # calling the function - EMD_wrap(n1,n2, a.data, b.data, M.data, G.data, &cost) - - return G diff --git a/ot/emd/full_bipartitegraph.h b/ot/emd/full_bipartitegraph.h deleted file mode 100644 index 87a1bec..0000000 --- a/ot/emd/full_bipartitegraph.h +++ /dev/null @@ -1,215 +0,0 @@ -/* -*- mode: C++; indent-tabs-mode: nil; -*- - * - * This file has been adapted by Nicolas Bonneel (2013), - * from full_graph.h from LEMON, a generic C++ optimization library, - * to implement a lightweight fully connected bipartite graph. A previous - * version of this file is used as part of the Displacement Interpolation - * project, - * Web: http://www.cs.ubc.ca/labs/imager/tr/2011/DisplacementInterpolation/ - * - * - **** Original file Copyright Notice : - * Copyright (C) 2003-2010 - * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport - * (Egervary Research Group on Combinatorial Optimization, EGRES). - * - * Permission to use, modify and distribute this software is granted - * provided that this copyright notice appears in all copies. For - * precise terms see the accompanying LICENSE file. - * - * This software is provided "AS IS" with no warranty of any kind, - * express or implied, and with no claim as to its suitability for any - * purpose. - * - */ - -#ifndef LEMON_FULL_BIPARTITE_GRAPH_H -#define LEMON_FULL_BIPARTITE_GRAPH_H - -#include "core.h" - -///\ingroup graphs -///\file -///\brief FullBipartiteDigraph and FullBipartiteGraph classes. - - -namespace lemon { - - - class FullBipartiteDigraphBase { - public: - - typedef FullBipartiteDigraphBase Digraph; - - //class Node; - typedef int Node; - //class Arc; - typedef long long Arc; - - protected: - - int _node_num; - long long _arc_num; - - FullBipartiteDigraphBase() {} - - void construct(int n1, int n2) { _node_num = n1+n2; _arc_num = n1 * n2; _n1=n1; _n2=n2;} - - public: - - int _n1, _n2; - - - Node operator()(int ix) const { return Node(ix); } - static int index(const Node& node) { return node; } - - Arc arc(const Node& s, const Node& t) const { - if (s<_n1 && t>=_n1) - return Arc(s * _n2 + (t-_n1) ); - else - return Arc(-1); - } - - int nodeNum() const { return _node_num; } - long long arcNum() const { return _arc_num; } - - int maxNodeId() const { return _node_num - 1; } - long long maxArcId() const { return _arc_num - 1; } - - Node source(Arc arc) const { return arc / _n2; } - Node target(Arc arc) const { return (arc % _n2) + _n1; } - - static int id(Node node) { return node; } - static long long id(Arc arc) { return arc; } - - static Node nodeFromId(int id) { return Node(id);} - static Arc arcFromId(int id) { return Arc(id);} - - - Arc findArc(Node s, Node t, Arc prev = -1) const { - return prev == -1 ? arc(s, t) : -1; - } - - void first(Node& node) const { - node = _node_num - 1; - } - - static void next(Node& node) { - --node; - } - - void first(Arc& arc) const { - arc = _arc_num - 1; - } - - static void next(Arc& arc) { - --arc; - } - - void firstOut(Arc& arc, const Node& node) const { - if (node>=_n1) - arc = -1; - else - arc = (node + 1) * _n2 - 1; - } - - void nextOut(Arc& arc) const { - if (arc % _n2 == 0) arc = 0; - --arc; - } - - void firstIn(Arc& arc, const Node& node) const { - if (node<_n1) - arc = -1; - else - arc = _arc_num + node - _node_num; - } - - void nextIn(Arc& arc) const { - arc -= _n2; - if (arc < 0) arc = -1; - } - - }; - - /// \ingroup graphs - /// - /// \brief A directed full graph class. - /// - /// FullBipartiteDigraph is a simple and fast implmenetation of directed full - /// (complete) graphs. It contains an arc from each node to each node - /// (including a loop for each node), therefore the number of arcs - /// is the square of the number of nodes. - /// This class is completely static and it needs constant memory space. - /// Thus you can neither add nor delete nodes or arcs, however - /// the structure can be resized using resize(). - /// - /// This type fully conforms to the \ref concepts::Digraph "Digraph concept". - /// Most of its member functions and nested classes are documented - /// only in the concept class. - /// - /// This class provides constant time counting for nodes and arcs. - /// - /// \note FullBipartiteDigraph and FullBipartiteGraph classes are very similar, - /// but there are two differences. While this class conforms only - /// to the \ref concepts::Digraph "Digraph" concept, FullBipartiteGraph - /// conforms to the \ref concepts::Graph "Graph" concept, - /// moreover FullBipartiteGraph does not contain a loop for each - /// node as this class does. - /// - /// \sa FullBipartiteGraph - class FullBipartiteDigraph : public FullBipartiteDigraphBase { - typedef FullBipartiteDigraphBase Parent; - - public: - - /// \brief Default constructor. - /// - /// Default constructor. The number of nodes and arcs will be zero. - FullBipartiteDigraph() { construct(0,0); } - - /// \brief Constructor - /// - /// Constructor. - /// \param n The number of the nodes. - FullBipartiteDigraph(int n1, int n2) { construct(n1, n2); } - - - /// \brief Returns the node with the given index. - /// - /// Returns the node with the given index. Since this structure is - /// completely static, the nodes can be indexed with integers from - /// the range [0..nodeNum()-1]. - /// The index of a node is the same as its ID. - /// \sa index() - Node operator()(int ix) const { return Parent::operator()(ix); } - - /// \brief Returns the index of the given node. - /// - /// Returns the index of the given node. Since this structure is - /// completely static, the nodes can be indexed with integers from - /// the range [0..nodeNum()-1]. - /// The index of a node is the same as its ID. - /// \sa operator()() - static int index(const Node& node) { return Parent::index(node); } - - /// \brief Returns the arc connecting the given nodes. - /// - /// Returns the arc connecting the given nodes. - /*Arc arc(Node u, Node v) const { - return Parent::arc(u, v); - }*/ - - /// \brief Number of nodes. - int nodeNum() const { return Parent::nodeNum(); } - /// \brief Number of arcs. - long long arcNum() const { return Parent::arcNum(); } - }; - - - - -} //namespace lemon - - -#endif //LEMON_FULL_GRAPH_H diff --git a/ot/emd/network_simplex_simple.h b/ot/emd/network_simplex_simple.h deleted file mode 100644 index 64856a0..0000000 --- a/ot/emd/network_simplex_simple.h +++ /dev/null @@ -1,1543 +0,0 @@ -/* -*- mode: C++; indent-tabs-mode: nil; -*- - * - * - * This file has been adapted by Nicolas Bonneel (2013), - * from network_simplex.h from LEMON, a generic C++ optimization library, - * to implement a lightweight network simplex for mass transport, more - * memory efficient that the original file. A previous version of this file - * is used as part of the Displacement Interpolation project, - * Web: http://www.cs.ubc.ca/labs/imager/tr/2011/DisplacementInterpolation/ - * - * - **** Original file Copyright Notice : - * - * Copyright (C) 2003-2010 - * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport - * (Egervary Research Group on Combinatorial Optimization, EGRES). - * - * Permission to use, modify and distribute this software is granted - * provided that this copyright notice appears in all copies. For - * precise terms see the accompanying LICENSE file. - * - * This software is provided "AS IS" with no warranty of any kind, - * express or implied, and with no claim as to its suitability for any - * purpose. - * - */ - -#ifndef LEMON_NETWORK_SIMPLEX_SIMPLE_H -#define LEMON_NETWORK_SIMPLEX_SIMPLE_H -#define DEBUG_LVL 0 -#define EPSILON 10*2.2204460492503131e-016 -#define MAX_DEBUG_ITER 100000 - - -/// \ingroup min_cost_flow_algs -/// -/// \file -/// \brief Network Simplex algorithm for finding a minimum cost flow. - -// if your compiler has troubles with stdext or hashmaps, just comment the following line to use a slower std::map instead -//#define HASHMAP - -#include -#include -#include -#ifdef HASHMAP -#include -#else -#include -#endif -#include -//#include "core.h" -//#include "lmath.h" - -//#include "sparse_array_n.h" -#include "full_bipartitegraph.h" - -#define INVALIDNODE -1 -#define INVALID (-1) - -namespace lemon { - - - template - class ProxyObject; - - template - class SparseValueVector - { - public: - SparseValueVector(int n=0) - { - } - void resize(int n=0){}; - T operator[](const int id) const - { -#ifdef HASHMAP - typename stdext::hash_map::const_iterator it = data.find(id); -#else - typename std::map::const_iterator it = data.find(id); -#endif - if (it==data.end()) - return 0; - else - return it->second; - } - - ProxyObject operator[](const int id) - { - return ProxyObject( this, id ); - } - - //private: -#ifdef HASHMAP - stdext::hash_map data; -#else - std::map data; -#endif - - }; - - template - class ProxyObject { - public: - ProxyObject( SparseValueVector *v, int idx ){_v=v; _idx=idx;}; - ProxyObject & operator=( const T &v ) { - // If we get here, we know that operator[] was called to perform a write access, - // so we can insert an item in the vector if needed - if (v!=0) - _v->data[_idx]=v; - return *this; - } - - operator T() { - // If we get here, we know that operator[] was called to perform a read access, - // so we can simply return the existing object -#ifdef HASHMAP - typename stdext::hash_map::iterator it = _v->data.find(_idx); -#else - typename std::map::iterator it = _v->data.find(_idx); -#endif - if (it==_v->data.end()) - return 0; - else - return it->second; - } - - void operator+=(T val) - { - if (val==0) return; -#ifdef HASHMAP - typename stdext::hash_map::iterator it = _v->data.find(_idx); -#else - typename std::map::iterator it = _v->data.find(_idx); -#endif - if (it==_v->data.end()) - _v->data[_idx] = val; - else - { - T sum = it->second + val; - if (sum==0) - _v->data.erase(it); - else - it->second = sum; - } - } - void operator-=(T val) - { - if (val==0) return; -#ifdef HASHMAP - typename stdext::hash_map::iterator it = _v->data.find(_idx); -#else - typename std::map::iterator it = _v->data.find(_idx); -#endif - if (it==_v->data.end()) - _v->data[_idx] = -val; - else - { - T sum = it->second - val; - if (sum==0) - _v->data.erase(it); - else - it->second = sum; - } - } - - SparseValueVector *_v; - int _idx; - }; - - - - /// \addtogroup min_cost_flow_algs - /// @{ - - /// \brief Implementation of the primal Network Simplex algorithm - /// for finding a \ref min_cost_flow "minimum cost flow". - /// - /// \ref NetworkSimplexSimple implements the primal Network Simplex algorithm - /// for finding a \ref min_cost_flow "minimum cost flow" - /// \ref amo93networkflows, \ref dantzig63linearprog, - /// \ref kellyoneill91netsimplex. - /// This algorithm is a highly efficient specialized version of the - /// linear programming simplex method directly for the minimum cost - /// flow problem. - /// - /// In general, %NetworkSimplexSimple is the fastest implementation available - /// in LEMON for this problem. - /// Moreover, it supports both directions of the supply/demand inequality - /// constraints. For more information, see \ref SupplyType. - /// - /// Most of the parameters of the problem (except for the digraph) - /// can be given using separate functions, and the algorithm can be - /// executed using the \ref run() function. If some parameters are not - /// specified, then default values will be used. - /// - /// \tparam GR The digraph type the algorithm runs on. - /// \tparam V The number type used for flow amounts, capacity bounds - /// and supply values in the algorithm. By default, it is \c int. - /// \tparam C The number type used for costs and potentials in the - /// algorithm. By default, it is the same as \c V. - /// - /// \warning Both number types must be signed and all input data must - /// be integer. - /// - /// \note %NetworkSimplexSimple provides five different pivot rule - /// implementations, from which the most efficient one is used - /// by default. For more information, see \ref PivotRule. - template - class NetworkSimplexSimple - { - public: - - /// \brief Constructor. - /// - /// The constructor of the class. - /// - /// \param graph The digraph the algorithm runs on. - /// \param arc_mixing Indicate if the arcs have to be stored in a - /// mixed order in the internal data structure. - /// In special cases, it could lead to better overall performance, - /// but it is usually slower. Therefore it is disabled by default. - NetworkSimplexSimple(const GR& graph, bool arc_mixing, int nbnodes, long long nb_arcs,double maxiters) : - _graph(graph), //_arc_id(graph), - _arc_mixing(arc_mixing), _init_nb_nodes(nbnodes), _init_nb_arcs(nb_arcs), - MAX(std::numeric_limits::max()), - INF(std::numeric_limits::has_infinity ? - std::numeric_limits::infinity() : MAX) - { - // Reset data structures - reset(); - max_iter=maxiters; - } - - /// The type of the flow amounts, capacity bounds and supply values - typedef V Value; - /// The type of the arc costs - typedef C Cost; - - public: - - /// \brief Problem type constants for the \c run() function. - /// - /// Enum type containing the problem type constants that can be - /// returned by the \ref run() function of the algorithm. - enum ProblemType { - /// The problem has no feasible solution (flow). - INFEASIBLE, - /// The problem has optimal solution (i.e. it is feasible and - /// bounded), and the algorithm has found optimal flow and node - /// potentials (primal and dual solutions). - OPTIMAL, - /// The objective function of the problem is unbounded, i.e. - /// there is a directed cycle having negative total cost and - /// infinite upper bound. - UNBOUNDED - }; - - /// \brief Constants for selecting the type of the supply constraints. - /// - /// Enum type containing constants for selecting the supply type, - /// i.e. the direction of the inequalities in the supply/demand - /// constraints of the \ref min_cost_flow "minimum cost flow problem". - /// - /// The default supply type is \c GEQ, the \c LEQ type can be - /// selected using \ref supplyType(). - /// The equality form is a special case of both supply types. - enum SupplyType { - /// This option means that there are "greater or equal" - /// supply/demand constraints in the definition of the problem. - GEQ, - /// This option means that there are "less or equal" - /// supply/demand constraints in the definition of the problem. - LEQ - }; - - - - private: - - double max_iter; - TEMPLATE_DIGRAPH_TYPEDEFS(GR); - - typedef std::vector IntVector; - typedef std::vector UHalfIntVector; - typedef std::vector ValueVector; - typedef std::vector CostVector; - // typedef SparseValueVector CostVector; - typedef std::vector BoolVector; - // Note: vector is used instead of vector for efficiency reasons - - // State constants for arcs - enum ArcState { - STATE_UPPER = -1, - STATE_TREE = 0, - STATE_LOWER = 1 - }; - - typedef std::vector StateVector; - // Note: vector is used instead of vector for - // efficiency reasons - - private: - - // Data related to the underlying digraph - const GR &_graph; - int _node_num; - int _arc_num; - int _all_arc_num; - int _search_arc_num; - - // Parameters of the problem - SupplyType _stype; - Value _sum_supply; - - inline int _node_id(int n) const {return _node_num-n-1;} ; - - //IntArcMap _arc_id; - UHalfIntVector _source; - UHalfIntVector _target; - bool _arc_mixing; - public: - // Node and arc data - CostVector _cost; - ValueVector _supply; - ValueVector _flow; - //SparseValueVector _flow; - CostVector _pi; - - - private: - // Data for storing the spanning tree structure - IntVector _parent; - IntVector _pred; - IntVector _thread; - IntVector _rev_thread; - IntVector _succ_num; - IntVector _last_succ; - IntVector _dirty_revs; - BoolVector _forward; - StateVector _state; - int _root; - - // Temporary data used in the current pivot iteration - int in_arc, join, u_in, v_in, u_out, v_out; - int first, second, right, last; - int stem, par_stem, new_stem; - Value delta; - - const Value MAX; - - int mixingCoeff; - - public: - - /// \brief Constant for infinite upper bounds (capacities). - /// - /// Constant for infinite upper bounds (capacities). - /// It is \c std::numeric_limits::infinity() if available, - /// \c std::numeric_limits::max() otherwise. - const Value INF; - - private: - - // thank you to DVK and MizardX from StackOverflow for this function! - inline int sequence(int k) const { - int smallv = (k > num_total_big_subsequence_numbers) & 1; - - k -= num_total_big_subsequence_numbers * smallv; - int subsequence_length2 = subsequence_length- smallv; - int subsequence_num = (k / subsequence_length2) + num_big_subseqiences * smallv; - int subsequence_offset = (k % subsequence_length2) * mixingCoeff; - - return subsequence_offset + subsequence_num; - } - int subsequence_length; - int num_big_subseqiences; - int num_total_big_subsequence_numbers; - - inline int getArcID(const Arc &arc) const - { - //int n = _arc_num-arc._id-1; - int n = _arc_num-GR::id(arc)-1; - - //int a = mixingCoeff*(n%mixingCoeff) + n/mixingCoeff; - //int b = _arc_id[arc]; - if (_arc_mixing) - return sequence(n); - else - return n; - } - - // finally unused because too slow - inline int getSource(const int arc) const - { - //int a = _source[arc]; - //return a; - - int n = _arc_num-arc-1; - if (_arc_mixing) - n = mixingCoeff*(n%mixingCoeff) + n/mixingCoeff; - - int b; - if (n>=0) - b = _node_id(_graph.source(GR::arcFromId( n ) )); - else - { - n = arc+1-_arc_num; - if ( n<=_node_num) - b = _node_num; - else - if ( n>=_graph._n1) - b = _graph._n1; - else - b = _graph._n1-n; - } - - return b; - } - - - - // Implementation of the Block Search pivot rule - class BlockSearchPivotRule - { - private: - - // References to the NetworkSimplexSimple class - const UHalfIntVector &_source; - const UHalfIntVector &_target; - const CostVector &_cost; - const StateVector &_state; - const CostVector &_pi; - int &_in_arc; - int _search_arc_num; - - // Pivot rule data - int _block_size; - int _next_arc; - NetworkSimplexSimple &_ns; - - public: - - // Constructor - BlockSearchPivotRule(NetworkSimplexSimple &ns) : - _source(ns._source), _target(ns._target), - _cost(ns._cost), _state(ns._state), _pi(ns._pi), - _in_arc(ns.in_arc), _search_arc_num(ns._search_arc_num), - _next_arc(0),_ns(ns) - { - // The main parameters of the pivot rule - const double BLOCK_SIZE_FACTOR = 1.0; - const int MIN_BLOCK_SIZE = 10; - - _block_size = std::max( int(BLOCK_SIZE_FACTOR * - std::sqrt(double(_search_arc_num))), - MIN_BLOCK_SIZE ); - } - // Find next entering arc - bool findEnteringArc() { - Cost c, min = 0; - int e; - int cnt = _block_size; - double a; - for (e = _next_arc; e != _search_arc_num; ++e) { - c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); - if (c < min) { - min = c; - _in_arc = e; - } - if (--cnt == 0) { - a=fabs(_pi[_source[_in_arc]])>fabs(_pi[_target[_in_arc]]) ? fabs(_pi[_source[_in_arc]]):fabs(_pi[_target[_in_arc]]); - a=a>fabs(_cost[_in_arc])?a:fabs(_cost[_in_arc]); - if (min < -EPSILON*a) goto search_end; - cnt = _block_size; - } - } - for (e = 0; e != _next_arc; ++e) { - c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); - if (c < min) { - min = c; - _in_arc = e; - } - if (--cnt == 0) { - a=fabs(_pi[_source[_in_arc]])>fabs(_pi[_target[_in_arc]]) ? fabs(_pi[_source[_in_arc]]):fabs(_pi[_target[_in_arc]]); - a=a>fabs(_cost[_in_arc])?a:fabs(_cost[_in_arc]); - if (min < -EPSILON*a) goto search_end; - cnt = _block_size; - } - } - a=fabs(_pi[_source[_in_arc]])>fabs(_pi[_target[_in_arc]]) ? fabs(_pi[_source[_in_arc]]):fabs(_pi[_target[_in_arc]]); - a=a>fabs(_cost[_in_arc])?a:fabs(_cost[_in_arc]); - if (min >= -EPSILON*a) return false; - - search_end: - _next_arc = e; - return true; - } - - }; //class BlockSearchPivotRule - - - - public: - - - - int _init_nb_nodes; - long long _init_nb_arcs; - - /// \name Parameters - /// The parameters of the algorithm can be specified using these - /// functions. - - /// @{ - - - /// \brief Set the costs of the arcs. - /// - /// This function sets the costs of the arcs. - /// If it is not used before calling \ref run(), the costs - /// will be set to \c 1 on all arcs. - /// - /// \param map An arc map storing the costs. - /// Its \c Value type must be convertible to the \c Cost type - /// of the algorithm. - /// - /// \return (*this) - template - NetworkSimplexSimple& costMap(const CostMap& map) { - Arc a; _graph.first(a); - for (; a != INVALID; _graph.next(a)) { - _cost[getArcID(a)] = map[a]; - } - return *this; - } - - - /// \brief Set the costs of one arc. - /// - /// This function sets the costs of one arcs. - /// Done for memory reasons - /// - /// \param arc An arc. - /// \param arc A cost - /// - /// \return (*this) - template - NetworkSimplexSimple& setCost(const Arc& arc, const Value cost) { - _cost[getArcID(arc)] = cost; - return *this; - } - - - /// \brief Set the supply values of the nodes. - /// - /// This function sets the supply values of the nodes. - /// If neither this function nor \ref stSupply() is used before - /// calling \ref run(), the supply of each node will be set to zero. - /// - /// \param map A node map storing the supply values. - /// Its \c Value type must be convertible to the \c Value type - /// of the algorithm. - /// - /// \return (*this) - template - NetworkSimplexSimple& supplyMap(const SupplyMap& map) { - Node n; _graph.first(n); - for (; n != INVALIDNODE; _graph.next(n)) { - _supply[_node_id(n)] = map[n]; - } - return *this; - } - template - NetworkSimplexSimple& supplyMap(const SupplyMap* map1, int n1, const SupplyMap* map2, int n2) { - Node n; _graph.first(n); - for (; n != INVALIDNODE; _graph.next(n)) { - if (n - NetworkSimplexSimple& supplyMapAll(SupplyMap val1, int n1, SupplyMap val2, int n2) { - Node n; _graph.first(n); - for (; n != INVALIDNODE; _graph.next(n)) { - if (n(*this) - NetworkSimplexSimple& stSupply(const Node& s, const Node& t, Value k) { - for (int i = 0; i != _node_num; ++i) { - _supply[i] = 0; - } - _supply[_node_id(s)] = k; - _supply[_node_id(t)] = -k; - return *this; - } - - /// \brief Set the type of the supply constraints. - /// - /// This function sets the type of the supply/demand constraints. - /// If it is not used before calling \ref run(), the \ref GEQ supply - /// type will be used. - /// - /// For more information, see \ref SupplyType. - /// - /// \return (*this) - NetworkSimplexSimple& supplyType(SupplyType supply_type) { - _stype = supply_type; - return *this; - } - - /// @} - - /// \name Execution Control - /// The algorithm can be executed using \ref run(). - - /// @{ - - /// \brief Run the algorithm. - /// - /// This function runs the algorithm. - /// The paramters can be specified using functions \ref lowerMap(), - /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply(), - /// \ref supplyType(). - /// For example, - /// \code - /// NetworkSimplexSimple ns(graph); - /// ns.lowerMap(lower).upperMap(upper).costMap(cost) - /// .supplyMap(sup).run(); - /// \endcode - /// - /// This function can be called more than once. All the given parameters - /// are kept for the next call, unless \ref resetParams() or \ref reset() - /// is used, thus only the modified parameters have to be set again. - /// If the underlying digraph was also modified after the construction - /// of the class (or the last \ref reset() call), then the \ref reset() - /// function must be called. - /// - /// \param pivot_rule The pivot rule that will be used during the - /// algorithm. For more information, see \ref PivotRule. - /// - /// \return \c INFEASIBLE if no feasible flow exists, - /// \n \c OPTIMAL if the problem has optimal solution - /// (i.e. it is feasible and bounded), and the algorithm has found - /// optimal flow and node potentials (primal and dual solutions), - /// \n \c UNBOUNDED if the objective function of the problem is - /// unbounded, i.e. there is a directed cycle having negative total - /// cost and infinite upper bound. - /// - /// \see ProblemType, PivotRule - /// \see resetParams(), reset() - ProblemType run() { -#if DEBUG_LVL>0 - mexPrintf("OPTIMAL = %d\nINFEASIBLE = %d\nUNBOUNDED = %d\n",OPTIMAL,INFEASIBLE,UNBOUNDED); - mexEvalString("drawnow;"); -#endif - - if (!init()) return INFEASIBLE; -#if DEBUG_LVL>0 - mexPrintf("Init done, starting iterations\n"); - mexEvalString("drawnow;"); -#endif - return start(); - } - - /// \brief Reset all the parameters that have been given before. - /// - /// This function resets all the paramaters that have been given - /// before using functions \ref lowerMap(), \ref upperMap(), - /// \ref costMap(), \ref supplyMap(), \ref stSupply(), \ref supplyType(). - /// - /// It is useful for multiple \ref run() calls. Basically, all the given - /// parameters are kept for the next \ref run() call, unless - /// \ref resetParams() or \ref reset() is used. - /// If the underlying digraph was also modified after the construction - /// of the class or the last \ref reset() call, then the \ref reset() - /// function must be used, otherwise \ref resetParams() is sufficient. - /// - /// For example, - /// \code - /// NetworkSimplexSimple ns(graph); - /// - /// // First run - /// ns.lowerMap(lower).upperMap(upper).costMap(cost) - /// .supplyMap(sup).run(); - /// - /// // Run again with modified cost map (resetParams() is not called, - /// // so only the cost map have to be set again) - /// cost[e] += 100; - /// ns.costMap(cost).run(); - /// - /// // Run again from scratch using resetParams() - /// // (the lower bounds will be set to zero on all arcs) - /// ns.resetParams(); - /// ns.upperMap(capacity).costMap(cost) - /// .supplyMap(sup).run(); - /// \endcode - /// - /// \return (*this) - /// - /// \see reset(), run() - NetworkSimplexSimple& resetParams() { - for (int i = 0; i != _node_num; ++i) { - _supply[i] = 0; - } - for (int i = 0; i != _arc_num; ++i) { - _cost[i] = 1; - } - _stype = GEQ; - return *this; - } - - - - int divid (int x, int y) - { - return (x-x%y)/y; - } - - /// \brief Reset the internal data structures and all the parameters - /// that have been given before. - /// - /// This function resets the internal data structures and all the - /// paramaters that have been given before using functions \ref lowerMap(), - /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply(), - /// \ref supplyType(). - /// - /// It is useful for multiple \ref run() calls. Basically, all the given - /// parameters are kept for the next \ref run() call, unless - /// \ref resetParams() or \ref reset() is used. - /// If the underlying digraph was also modified after the construction - /// of the class or the last \ref reset() call, then the \ref reset() - /// function must be used, otherwise \ref resetParams() is sufficient. - /// - /// See \ref resetParams() for examples. - /// - /// \return (*this) - /// - /// \see resetParams(), run() - NetworkSimplexSimple& reset() { - // Resize vectors - _node_num = _init_nb_nodes; - _arc_num = _init_nb_arcs; - int all_node_num = _node_num + 1; - int max_arc_num = _arc_num + 2 * _node_num; - - _source.resize(max_arc_num); - _target.resize(max_arc_num); - - _cost.resize(max_arc_num); - _supply.resize(all_node_num); - _flow.resize(max_arc_num); - _pi.resize(all_node_num); - - _parent.resize(all_node_num); - _pred.resize(all_node_num); - _forward.resize(all_node_num); - _thread.resize(all_node_num); - _rev_thread.resize(all_node_num); - _succ_num.resize(all_node_num); - _last_succ.resize(all_node_num); - _state.resize(max_arc_num); - - - //_arc_mixing=false; - if (_arc_mixing) { - // Store the arcs in a mixed order - int k = std::max(int(std::sqrt(double(_arc_num))), 10); - mixingCoeff = k; - subsequence_length = _arc_num / mixingCoeff + 1; - num_big_subseqiences = _arc_num % mixingCoeff; - num_total_big_subsequence_numbers = subsequence_length * num_big_subseqiences; - - int i = 0, j = 0; - Arc a; _graph.first(a); - for (; a != INVALID; _graph.next(a)) { - _source[i] = _node_id(_graph.source(a)); - _target[i] = _node_id(_graph.target(a)); - //_arc_id[a] = i; - if ((i += k) >= _arc_num) i = ++j; - } - } else { - // Store the arcs in the original order - int i = 0; - Arc a; _graph.first(a); - for (; a != INVALID; _graph.next(a), ++i) { - _source[i] = _node_id(_graph.source(a)); - _target[i] = _node_id(_graph.target(a)); - //_arc_id[a] = i; - } - } - - // Reset parameters - resetParams(); - return *this; - } - - /// @} - - /// \name Query Functions - /// The results of the algorithm can be obtained using these - /// functions.\n - /// The \ref run() function must be called before using them. - - /// @{ - - /// \brief Return the total cost of the found flow. - /// - /// This function returns the total cost of the found flow. - /// Its complexity is O(e). - /// - /// \note The return type of the function can be specified as a - /// template parameter. For example, - /// \code - /// ns.totalCost(); - /// \endcode - /// It is useful if the total cost cannot be stored in the \c Cost - /// type of the algorithm, which is the default return type of the - /// function. - /// - /// \pre \ref run() must be called before using this function. - /*template - Number totalCost() const { - Number c = 0; - for (ArcIt a(_graph); a != INVALID; ++a) { - int i = getArcID(a); - c += Number(_flow[i]) * Number(_cost[i]); - } - return c; - }*/ - - template - Number totalCost() const { - Number c = 0; - - /*#ifdef HASHMAP - typename stdext::hash_map::const_iterator it; - #else - typename std::map::const_iterator it; - #endif - for (it = _flow.data.begin(); it!=_flow.data.end(); ++it) - c += Number(it->second) * Number(_cost[it->first]); - return c;*/ - - for (int i=0; i<_flow.size(); i++) - c += _flow[i] * Number(_cost[i]); - return c; - - } - -#ifndef DOXYGEN - Cost totalCost() const { - return totalCost(); - } -#endif - - /// \brief Return the flow on the given arc. - /// - /// This function returns the flow on the given arc. - /// - /// \pre \ref run() must be called before using this function. - Value flow(const Arc& a) const { - return _flow[getArcID(a)]; - } - - /// \brief Return the flow map (the primal solution). - /// - /// This function copies the flow value on each arc into the given - /// map. The \c Value type of the algorithm must be convertible to - /// the \c Value type of the map. - /// - /// \pre \ref run() must be called before using this function. - template - void flowMap(FlowMap &map) const { - Arc a; _graph.first(a); - for (; a != INVALID; _graph.next(a)) { - map.set(a, _flow[getArcID(a)]); - } - } - - /// \brief Return the potential (dual value) of the given node. - /// - /// This function returns the potential (dual value) of the - /// given node. - /// - /// \pre \ref run() must be called before using this function. - Cost potential(const Node& n) const { - return _pi[_node_id(n)]; - } - - /// \brief Return the potential map (the dual solution). - /// - /// This function copies the potential (dual value) of each node - /// into the given map. - /// The \c Cost type of the algorithm must be convertible to the - /// \c Value type of the map. - /// - /// \pre \ref run() must be called before using this function. - template - void potentialMap(PotentialMap &map) const { - Node n; _graph.first(n); - for (; n != INVALID; _graph.next(n)) { - map.set(n, _pi[_node_id(n)]); - } - } - - /// @} - - private: - - // Initialize internal data structures - bool init() { - if (_node_num == 0) return false; - /* - // Check the sum of supply values - _sum_supply = 0; - for (int i = 0; i != _node_num; ++i) { - _sum_supply += _supply[i]; - } - if ( !((_stype == GEQ && _sum_supply <= _epsilon ) || - (_stype == LEQ && _sum_supply >= -_epsilon )) ) return false; - */ - - // Initialize artifical cost - Cost ART_COST; - if (std::numeric_limits::is_exact) { - ART_COST = std::numeric_limits::max() / 2 + 1; - } else { - ART_COST = 0; - for (int i = 0; i != _arc_num; ++i) { - if (_cost[i] > ART_COST) ART_COST = _cost[i]; - } - ART_COST = (ART_COST + 1) * _node_num; - } - - // Initialize arc maps - for (int i = 0; i != _arc_num; ++i) { - //_flow[i] = 0; //by default, the sparse matrix is empty - _state[i] = STATE_LOWER; - } - - // Set data for the artificial root node - _root = _node_num; - _parent[_root] = -1; - _pred[_root] = -1; - _thread[_root] = 0; - _rev_thread[0] = _root; - _succ_num[_root] = _node_num + 1; - _last_succ[_root] = _root - 1; - _supply[_root] = -_sum_supply; - _pi[_root] = 0; - - // Add artificial arcs and initialize the spanning tree data structure - if (_sum_supply == 0) { - // EQ supply constraints - _search_arc_num = _arc_num; - _all_arc_num = _arc_num + _node_num; - for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) { - _parent[u] = _root; - _pred[u] = e; - _thread[u] = u + 1; - _rev_thread[u + 1] = u; - _succ_num[u] = 1; - _last_succ[u] = u; - _state[e] = STATE_TREE; - if (_supply[u] >= 0) { - _forward[u] = true; - _pi[u] = 0; - _source[e] = u; - _target[e] = _root; - _flow[e] = _supply[u]; - _cost[e] = 0; - } else { - _forward[u] = false; - _pi[u] = ART_COST; - _source[e] = _root; - _target[e] = u; - _flow[e] = -_supply[u]; - _cost[e] = ART_COST; - } - } - } - else if (_sum_supply > 0) { - // LEQ supply constraints - _search_arc_num = _arc_num + _node_num; - int f = _arc_num + _node_num; - for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) { - _parent[u] = _root; - _thread[u] = u + 1; - _rev_thread[u + 1] = u; - _succ_num[u] = 1; - _last_succ[u] = u; - if (_supply[u] >= 0) { - _forward[u] = true; - _pi[u] = 0; - _pred[u] = e; - _source[e] = u; - _target[e] = _root; - _flow[e] = _supply[u]; - _cost[e] = 0; - _state[e] = STATE_TREE; - } else { - _forward[u] = false; - _pi[u] = ART_COST; - _pred[u] = f; - _source[f] = _root; - _target[f] = u; - _flow[f] = -_supply[u]; - _cost[f] = ART_COST; - _state[f] = STATE_TREE; - _source[e] = u; - _target[e] = _root; - //_flow[e] = 0; //by default, the sparse matrix is empty - _cost[e] = 0; - _state[e] = STATE_LOWER; - ++f; - } - } - _all_arc_num = f; - } - else { - // GEQ supply constraints - _search_arc_num = _arc_num + _node_num; - int f = _arc_num + _node_num; - for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) { - _parent[u] = _root; - _thread[u] = u + 1; - _rev_thread[u + 1] = u; - _succ_num[u] = 1; - _last_succ[u] = u; - if (_supply[u] <= 0) { - _forward[u] = false; - _pi[u] = 0; - _pred[u] = e; - _source[e] = _root; - _target[e] = u; - _flow[e] = -_supply[u]; - _cost[e] = 0; - _state[e] = STATE_TREE; - } else { - _forward[u] = true; - _pi[u] = -ART_COST; - _pred[u] = f; - _source[f] = u; - _target[f] = _root; - _flow[f] = _supply[u]; - _state[f] = STATE_TREE; - _cost[f] = ART_COST; - _source[e] = _root; - _target[e] = u; - //_flow[e] = 0; //by default, the sparse matrix is empty - _cost[e] = 0; - _state[e] = STATE_LOWER; - ++f; - } - } - _all_arc_num = f; - } - - return true; - } - - // Find the join node - void findJoinNode() { - int u = _source[in_arc]; - int v = _target[in_arc]; - while (u != v) { - if (_succ_num[u] < _succ_num[v]) { - u = _parent[u]; - } else { - v = _parent[v]; - } - } - join = u; - } - - // Find the leaving arc of the cycle and returns true if the - // leaving arc is not the same as the entering arc - bool findLeavingArc() { - // Initialize first and second nodes according to the direction - // of the cycle - if (_state[in_arc] == STATE_LOWER) { - first = _source[in_arc]; - second = _target[in_arc]; - } else { - first = _target[in_arc]; - second = _source[in_arc]; - } - delta = INF; - int result = 0; - Value d; - int e; - - // Search the cycle along the path form the first node to the root - for (int u = first; u != join; u = _parent[u]) { - e = _pred[u]; - d = _forward[u] ? _flow[e] : INF ; - if (d < delta) { - delta = d; - u_out = u; - result = 1; - } - } - // Search the cycle along the path form the second node to the root - for (int u = second; u != join; u = _parent[u]) { - e = _pred[u]; - d = _forward[u] ? INF : _flow[e]; - if (d <= delta) { - delta = d; - u_out = u; - result = 2; - } - } - - if (result == 1) { - u_in = first; - v_in = second; - } else { - u_in = second; - v_in = first; - } - return result != 0; - } - - // Change _flow and _state vectors - void changeFlow(bool change) { - // Augment along the cycle - if (delta > 0) { - Value val = _state[in_arc] * delta; - _flow[in_arc] += val; - for (int u = _source[in_arc]; u != join; u = _parent[u]) { - _flow[_pred[u]] += _forward[u] ? -val : val; - } - for (int u = _target[in_arc]; u != join; u = _parent[u]) { - _flow[_pred[u]] += _forward[u] ? val : -val; - } - } - // Update the state of the entering and leaving arcs - if (change) { - _state[in_arc] = STATE_TREE; - _state[_pred[u_out]] = - (_flow[_pred[u_out]] == 0) ? STATE_LOWER : STATE_UPPER; - } else { - _state[in_arc] = -_state[in_arc]; - } - } - - // Update the tree structure - void updateTreeStructure() { - int u, w; - int old_rev_thread = _rev_thread[u_out]; - int old_succ_num = _succ_num[u_out]; - int old_last_succ = _last_succ[u_out]; - v_out = _parent[u_out]; - - u = _last_succ[u_in]; // the last successor of u_in - right = _thread[u]; // the node after it - - // Handle the case when old_rev_thread equals to v_in - // (it also means that join and v_out coincide) - if (old_rev_thread == v_in) { - last = _thread[_last_succ[u_out]]; - } else { - last = _thread[v_in]; - } - - // Update _thread and _parent along the stem nodes (i.e. the nodes - // between u_in and u_out, whose parent have to be changed) - _thread[v_in] = stem = u_in; - _dirty_revs.clear(); - _dirty_revs.push_back(v_in); - par_stem = v_in; - while (stem != u_out) { - // Insert the next stem node into the thread list - new_stem = _parent[stem]; - _thread[u] = new_stem; - _dirty_revs.push_back(u); - - // Remove the subtree of stem from the thread list - w = _rev_thread[stem]; - _thread[w] = right; - _rev_thread[right] = w; - - // Change the parent node and shift stem nodes - _parent[stem] = par_stem; - par_stem = stem; - stem = new_stem; - - // Update u and right - u = _last_succ[stem] == _last_succ[par_stem] ? - _rev_thread[par_stem] : _last_succ[stem]; - right = _thread[u]; - } - _parent[u_out] = par_stem; - _thread[u] = last; - _rev_thread[last] = u; - _last_succ[u_out] = u; - - // Remove the subtree of u_out from the thread list except for - // the case when old_rev_thread equals to v_in - // (it also means that join and v_out coincide) - if (old_rev_thread != v_in) { - _thread[old_rev_thread] = right; - _rev_thread[right] = old_rev_thread; - } - - // Update _rev_thread using the new _thread values - for (int i = 0; i != int(_dirty_revs.size()); ++i) { - u = _dirty_revs[i]; - _rev_thread[_thread[u]] = u; - } - - // Update _pred, _forward, _last_succ and _succ_num for the - // stem nodes from u_out to u_in - int tmp_sc = 0, tmp_ls = _last_succ[u_out]; - u = u_out; - while (u != u_in) { - w = _parent[u]; - _pred[u] = _pred[w]; - _forward[u] = !_forward[w]; - tmp_sc += _succ_num[u] - _succ_num[w]; - _succ_num[u] = tmp_sc; - _last_succ[w] = tmp_ls; - u = w; - } - _pred[u_in] = in_arc; - _forward[u_in] = (u_in == _source[in_arc]); - _succ_num[u_in] = old_succ_num; - - // Set limits for updating _last_succ form v_in and v_out - // towards the root - int up_limit_in = -1; - int up_limit_out = -1; - if (_last_succ[join] == v_in) { - up_limit_out = join; - } else { - up_limit_in = join; - } - - // Update _last_succ from v_in towards the root - for (u = v_in; u != up_limit_in && _last_succ[u] == v_in; - u = _parent[u]) { - _last_succ[u] = _last_succ[u_out]; - } - // Update _last_succ from v_out towards the root - if (join != old_rev_thread && v_in != old_rev_thread) { - for (u = v_out; u != up_limit_out && _last_succ[u] == old_last_succ; - u = _parent[u]) { - _last_succ[u] = old_rev_thread; - } - } else { - for (u = v_out; u != up_limit_out && _last_succ[u] == old_last_succ; - u = _parent[u]) { - _last_succ[u] = _last_succ[u_out]; - } - } - - // Update _succ_num from v_in to join - for (u = v_in; u != join; u = _parent[u]) { - _succ_num[u] += old_succ_num; - } - // Update _succ_num from v_out to join - for (u = v_out; u != join; u = _parent[u]) { - _succ_num[u] -= old_succ_num; - } - } - - // Update potentials - void updatePotential() { - Cost sigma = _forward[u_in] ? - _pi[v_in] - _pi[u_in] - _cost[_pred[u_in]] : - _pi[v_in] - _pi[u_in] + _cost[_pred[u_in]]; - // Update potentials in the subtree, which has been moved - int end = _thread[_last_succ[u_in]]; - for (int u = u_in; u != end; u = _thread[u]) { - _pi[u] += sigma; - } - } - - // Heuristic initial pivots - bool initialPivots() { - Value curr, total = 0; - std::vector supply_nodes, demand_nodes; - Node u; _graph.first(u); - for (; u != INVALIDNODE; _graph.next(u)) { - curr = _supply[_node_id(u)]; - if (curr > 0) { - total += curr; - supply_nodes.push_back(u); - } - else if (curr < 0) { - demand_nodes.push_back(u); - } - } - if (_sum_supply > 0) total -= _sum_supply; - if (total <= 0) return true; - - IntVector arc_vector; - if (_sum_supply >= 0) { - if (supply_nodes.size() == 1 && demand_nodes.size() == 1) { - // Perform a reverse graph search from the sink to the source - //typename GR::template NodeMap reached(_graph, false); - BoolVector reached(_node_num, false); - Node s = supply_nodes[0], t = demand_nodes[0]; - std::vector stack; - reached[t] = true; - stack.push_back(t); - while (!stack.empty()) { - Node u, v = stack.back(); - stack.pop_back(); - if (v == s) break; - Arc a; _graph.firstIn(a, v); - for (; a != INVALID; _graph.nextIn(a)) { - if (reached[u = _graph.source(a)]) continue; - int j = getArcID(a); - if (INF >= total) { - arc_vector.push_back(j); - reached[u] = true; - stack.push_back(u); - } - } - } - } else { - // Find the min. cost incomming arc for each demand node - for (int i = 0; i != int(demand_nodes.size()); ++i) { - Node v = demand_nodes[i]; - Cost c, min_cost = std::numeric_limits::max(); - Arc min_arc = INVALID; - Arc a; _graph.firstIn(a, v); - for (; a != INVALID; _graph.nextIn(a)) { - c = _cost[getArcID(a)]; - if (c < min_cost) { - min_cost = c; - min_arc = a; - } - } - if (min_arc != INVALID) { - arc_vector.push_back(getArcID(min_arc)); - } - } - } - } else { - // Find the min. cost outgoing arc for each supply node - for (int i = 0; i != int(supply_nodes.size()); ++i) { - Node u = supply_nodes[i]; - Cost c, min_cost = std::numeric_limits::max(); - Arc min_arc = INVALID; - Arc a; _graph.firstOut(a, u); - for (; a != INVALID; _graph.nextOut(a)) { - c = _cost[getArcID(a)]; - if (c < min_cost) { - min_cost = c; - min_arc = a; - } - } - if (min_arc != INVALID) { - arc_vector.push_back(getArcID(min_arc)); - } - } - } - - // Perform heuristic initial pivots - for (int i = 0; i != int(arc_vector.size()); ++i) { - in_arc = arc_vector[i]; - // l'erreur est probablement ici... - if (_state[in_arc] * (_cost[in_arc] + _pi[_source[in_arc]] - - _pi[_target[in_arc]]) >= 0) continue; - findJoinNode(); - bool change = findLeavingArc(); - if (delta >= MAX) return false; - changeFlow(change); - if (change) { - updateTreeStructure(); - updatePotential(); - } - } - return true; - } - - // Execute the algorithm - ProblemType start() { - return start(); - } - - template - ProblemType start() { - PivotRuleImpl pivot(*this); - double prevCost=-1; - - // Perform heuristic initial pivots - if (!initialPivots()) return UNBOUNDED; - -#if DEBUG_LVL>0 - int niter=0; -#endif - int iter_number=0; - //pivot.setDantzig(true); - // Execute the Network Simplex algorithm - while (pivot.findEnteringArc()) { - if(++iter_number>=max_iter&&max_iter>0){ - char errMess[1000]; - // sprintf( errMess, "RESULT MIGHT BE INACURATE\nMax number of iteration reached, currently \%d. Sometimes iterations go on in cycle even though the solution has been reached, to check if it's the case here have a look at the minimal reduced cost. If it is very close to machine precision, you might actually have the correct solution, if not try setting the maximum number of iterations a bit higher",iter_number ); - // mexWarnMsgTxt(errMess); - break; - } -#if DEBUG_LVL>0 - if(niter>MAX_DEBUG_ITER) - break; - if(++niter%1000==0||niter%1000==1){ - double curCost=totalCost(); - double sumFlow=0; - double a; - a= (fabs(_pi[_source[in_arc]])>=fabs(_pi[_target[in_arc]])) ? fabs(_pi[_source[in_arc]]) : fabs(_pi[_target[in_arc]]); - a=a>=fabs(_cost[in_arc])?a:fabs(_cost[in_arc]); - for (int i=0; i<_flow.size(); i++) { - sumFlow+=_state[i]*_flow[i]; - } - mexPrintf("Sum of the flow %.100f\n%d iterations, current cost=%.20f\nReduced cost=%.30f\nPrecision =%.30f\n",sumFlow,niter, curCost,_state[in_arc] * (_cost[in_arc] + _pi[_source[in_arc]] -_pi[_target[in_arc]]), -EPSILON*(a)); - mexPrintf("Arc in = (%d,%d)\n",_node_id(_source[in_arc]),_node_id(_target[in_arc])); - mexPrintf("Supplies = (%f,%f)\n",_supply[_source[in_arc]],_supply[_target[in_arc]]); - - mexPrintf("%.30f\n%.30f\n%.30f\n%.30f\n%",_cost[in_arc],_pi[_source[in_arc]],_pi[_target[in_arc]],a); - mexEvalString("drawnow;"); - } -#endif - - findJoinNode(); - bool change = findLeavingArc(); - if (delta >= MAX) return UNBOUNDED; - changeFlow(change); - if (change) { - updateTreeStructure(); - updatePotential(); - } -#if DEBUG_LVL>0 - else{ - mexPrintf("No change\n"); - } -#endif -#if DEBUG_LVL>1 - mexPrintf("Arc in = (%d,%d)\n",_source[in_arc],_target[in_arc]); -#endif - - } - - -#if DEBUG_LVL>0 - double curCost=totalCost(); - double sumFlow=0; - double a; - a= (fabs(_pi[_source[in_arc]])>=fabs(_pi[_target[in_arc]])) ? fabs(_pi[_source[in_arc]]) : fabs(_pi[_target[in_arc]]); - a=a>=fabs(_cost[in_arc])?a:fabs(_cost[in_arc]); - for (int i=0; i<_flow.size(); i++) { - sumFlow+=_state[i]*_flow[i]; - } - mexPrintf("Sum of the flow %.100f\n%d iterations, current cost=%.20f\nReduced cost=%.30f\nPrecision =%.30f",sumFlow,niter, curCost,_state[in_arc] * (_cost[in_arc] + _pi[_source[in_arc]] -_pi[_target[in_arc]]), -EPSILON*(a)); - mexPrintf("Arc in = (%d,%d)\n",_node_id(_source[in_arc]),_node_id(_target[in_arc])); - mexPrintf("Supplies = (%f,%f)\n",_supply[_source[in_arc]],_supply[_target[in_arc]]); - - mexEvalString("drawnow;"); -#endif - -#if DEBUG_LVL>1 - double sumFlow=0; - for (int i=0; i<_flow.size(); i++) { - sumFlow+=_state[i]*_flow[i]; - if (_state[i]==STATE_TREE) { - mexPrintf("Non zero value at (%d,%d)\n",_node_num+1-_source[i],_node_num+1-_target[i]); - } - } - mexPrintf("Sum of the flow %.100f\n%d iterations, current cost=%.20f\n",sumFlow,niter, totalCost()); - mexEvalString("drawnow;"); -#endif - // Check feasibility - for (int e = _search_arc_num; e != _all_arc_num; ++e) { - if (_flow[e] != 0){ - if (abs(_flow[e]) > EPSILON) - return INFEASIBLE; - else - _flow[e]=0; - - } - } - - // Shift potentials to meet the requirements of the GEQ/LEQ type - // optimality conditions - if (_sum_supply == 0) { - if (_stype == GEQ) { - Cost max_pot = -std::numeric_limits::max(); - for (int i = 0; i != _node_num; ++i) { - if (_pi[i] > max_pot) max_pot = _pi[i]; - } - if (max_pot > 0) { - for (int i = 0; i != _node_num; ++i) - _pi[i] -= max_pot; - } - } else { - Cost min_pot = std::numeric_limits::max(); - for (int i = 0; i != _node_num; ++i) { - if (_pi[i] < min_pot) min_pot = _pi[i]; - } - if (min_pot < 0) { - for (int i = 0; i != _node_num; ++i) - _pi[i] -= min_pot; - } - } - } - - return OPTIMAL; - } - - }; //class NetworkSimplexSimple - - ///@} - -} //namespace lemon - -#endif //LEMON_NETWORK_SIMPLEX_H diff --git a/ot/lp/EMD.h b/ot/lp/EMD.h new file mode 100644 index 0000000..40d7192 --- /dev/null +++ b/ot/lp/EMD.h @@ -0,0 +1,29 @@ +/* This file is a c++ wrapper function for computing the transportation cost + * between two vectors given a cost matrix. + * + * It was written by Antoine Rolet (2014) and mainly consists of a wrapper + * of the code written by Nicolas Bonneel available on this page + * http://people.seas.harvard.edu/~nbonneel/FastTransport/ + * + * It was then modified to make it more amenable to python inline calling + * + * Please give relevant credit to the original author (Nicolas Bonneel) if + * you use this code for a publication. + * + */ + + +#ifndef EMD_H +#define EMD_H + +#include +#include +#include "network_simplex_simple.h" + +using namespace lemon; +typedef unsigned int node_id_type; + + +void EMD_wrap(int n1,int n2, double *X, double *Y,double *D, double *G, double *cost); + +#endif diff --git a/ot/lp/EMD_wrap.cpp b/ot/lp/EMD_wrap.cpp new file mode 100644 index 0000000..52cd262 --- /dev/null +++ b/ot/lp/EMD_wrap.cpp @@ -0,0 +1,120 @@ +/* This file is a c++ wrapper function for computing the transportation cost + * between two vectors given a cost matrix. + * + * It was written by Antoine Rolet (2014) and mainly consists of a wrapper + * of the code written by Nicolas Bonneel available on this page + * http://people.seas.harvard.edu/~nbonneel/FastTransport/ + * + * It was then modified to make it more amenable to python inline calling + * + * Please give relevant credit to the original author (Nicolas Bonneel) if + * you use this code for a publication. + * + */ + +#include "EMD.h" + + +void EMD_wrap(int n1,int n2, double *X, double *Y,double *D, double *G, double *cost) { +// beware M and C anre strored in row major C style!!! + int n, m, i,cur; + double max,max_iter; + + + typedef FullBipartiteDigraph Digraph; + DIGRAPH_TYPEDEFS(FullBipartiteDigraph); + + // Get the number of non zero coordinates for r and c + n=0; + for (node_id_type i=0; i0) { + n++; + } + } + m=0; + for (node_id_type i=0; i0) { + m++; + } + } + + + // Define the graph + + std::vector indI(n), indJ(m); + std::vector weights1(n), weights2(m); + Digraph di(n, m); + NetworkSimplexSimple net(di, true, n+m, n*m,max_iter); + + // Set supply and demand, don't account for 0 values (faster) + + max=0; + cur=0; + for (node_id_type i=0; i0) { + weights1[ di.nodeFromId(cur) ] = val; + max+=val; + indI[cur++]=i; + } + } + + // Demand is actually negative supply... + + max=0; + cur=0; + for (node_id_type i=0; i0) { + weights2[ di.nodeFromId(cur) ] = -val; + indJ[cur++]=i; + + max-=val; + } + } + + + net.supplyMap(&weights1[0], n, &weights2[0], m); + + // Set the cost of each edge + max=0; + for (node_id_type i=0; imax) { + max=val; + } + } + } + + + // Solve the problem with the network simplex algorithm + + int ret=net.run(); + if (ret!=(int)net.OPTIMAL) { + if (ret==(int)net.INFEASIBLE) { + std::cout << "Infeasible problem"; + } + if (ret==(int)net.UNBOUNDED) + { + std::cout << "Unbounded problem"; + } + } else + { + for (node_id_type i=0; i +#include + + +// Disable the following warnings when compiling with MSVC: +// C4250: 'class1' : inherits 'class2::member' via dominance +// C4355: 'this' : used in base member initializer list +// C4503: 'function' : decorated name length exceeded, name was truncated +// C4800: 'type' : forcing value to bool 'true' or 'false' (performance warning) +// C4996: 'function': was declared deprecated +#ifdef _MSC_VER +#pragma warning( disable : 4250 4355 4503 4800 4996 ) +#endif + +///\file +///\brief LEMON core utilities. +/// +///This header file contains core utilities for LEMON. +///It is automatically included by all graph types, therefore it usually +///do not have to be included directly. + +namespace lemon { + + /// \brief Dummy type to make it easier to create invalid iterators. + /// + /// Dummy type to make it easier to create invalid iterators. + /// See \ref INVALID for the usage. + struct Invalid { + public: + bool operator==(Invalid) { return true; } + bool operator!=(Invalid) { return false; } + bool operator< (Invalid) { return false; } + }; + + /// \brief Invalid iterators. + /// + /// \ref Invalid is a global type that converts to each iterator + /// in such a way that the value of the target iterator will be invalid. +#ifdef LEMON_ONLY_TEMPLATES + const Invalid INVALID = Invalid(); +#else + extern const Invalid INVALID; +#endif + + /// \addtogroup gutils + /// @{ + + ///Create convenience typedefs for the digraph types and iterators + + ///This \c \#define creates convenient type definitions for the following + ///types of \c Digraph: \c Node, \c NodeIt, \c Arc, \c ArcIt, \c InArcIt, + ///\c OutArcIt, \c BoolNodeMap, \c IntNodeMap, \c DoubleNodeMap, + ///\c BoolArcMap, \c IntArcMap, \c DoubleArcMap. + /// + ///\note If the graph type is a dependent type, ie. the graph type depend + ///on a template parameter, then use \c TEMPLATE_DIGRAPH_TYPEDEFS() + ///macro. +#define DIGRAPH_TYPEDEFS(Digraph) \ + typedef Digraph::Node Node; \ + typedef Digraph::Arc Arc; \ + + + ///Create convenience typedefs for the digraph types and iterators + + ///\see DIGRAPH_TYPEDEFS + /// + ///\note Use this macro, if the graph type is a dependent type, + ///ie. the graph type depend on a template parameter. +#define TEMPLATE_DIGRAPH_TYPEDEFS(Digraph) \ + typedef typename Digraph::Node Node; \ + typedef typename Digraph::Arc Arc; \ + + + +} //namespace lemon + +#endif diff --git a/ot/lp/emd.cpp b/ot/lp/emd.cpp new file mode 100644 index 0000000..2343af6 --- /dev/null +++ b/ot/lp/emd.cpp @@ -0,0 +1,6507 @@ +/* Generated by Cython 0.23.4 */ + +/* BEGIN: Cython Metadata +{ + "distutils": { + "depends": [ + "/usr/lib/python2.7/dist-packages/numpy/core/include/numpy/arrayobject.h", + "/usr/lib/python2.7/dist-packages/numpy/core/include/numpy/ufuncobject.h", + "ot/emd/EMD.h" + ], + "include_dirs": [ + "/usr/lib/python2.7/dist-packages/numpy/core/include", + "/home/rflamary/PYTHON/POT/ot/emd" + ], + "language": "c++" + } +} +END: Cython Metadata */ + +#define PY_SSIZE_T_CLEAN +#include "Python.h" +#ifndef Py_PYTHON_H + #error Python headers needed to compile C extensions, please install development version of Python. +#elif PY_VERSION_HEX < 0x02060000 || (0x03000000 <= PY_VERSION_HEX && PY_VERSION_HEX < 0x03020000) + #error Cython requires Python 2.6+ or Python 3.2+. +#else +#define CYTHON_ABI "0_23_4" +#include +#ifndef offsetof +#define offsetof(type, member) ( (size_t) & ((type*)0) -> member ) +#endif +#if !defined(WIN32) && !defined(MS_WINDOWS) + #ifndef __stdcall + #define __stdcall + #endif + #ifndef __cdecl + #define __cdecl + #endif + #ifndef __fastcall + #define __fastcall + #endif +#endif +#ifndef DL_IMPORT + #define DL_IMPORT(t) t +#endif +#ifndef DL_EXPORT + #define DL_EXPORT(t) t +#endif +#ifndef PY_LONG_LONG + #define PY_LONG_LONG LONG_LONG +#endif +#ifndef Py_HUGE_VAL + #define Py_HUGE_VAL HUGE_VAL +#endif +#ifdef PYPY_VERSION +#define CYTHON_COMPILING_IN_PYPY 1 +#define CYTHON_COMPILING_IN_CPYTHON 0 +#else +#define CYTHON_COMPILING_IN_PYPY 0 +#define CYTHON_COMPILING_IN_CPYTHON 1 +#endif +#if !defined(CYTHON_USE_PYLONG_INTERNALS) && CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x02070000 +#define CYTHON_USE_PYLONG_INTERNALS 1 +#endif +#if CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x02070600 && !defined(Py_OptimizeFlag) +#define Py_OptimizeFlag 0 +#endif +#define __PYX_BUILD_PY_SSIZE_T "n" +#define CYTHON_FORMAT_SSIZE_T "z" +#if PY_MAJOR_VERSION < 3 + #define __Pyx_BUILTIN_MODULE_NAME "__builtin__" + #define __Pyx_PyCode_New(a, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)\ + PyCode_New(a+k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos) + #define __Pyx_DefaultClassType PyClass_Type +#else + #define __Pyx_BUILTIN_MODULE_NAME "builtins" + #define __Pyx_PyCode_New(a, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)\ + PyCode_New(a, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos) + #define __Pyx_DefaultClassType PyType_Type +#endif +#ifndef Py_TPFLAGS_CHECKTYPES + #define Py_TPFLAGS_CHECKTYPES 0 +#endif +#ifndef Py_TPFLAGS_HAVE_INDEX + #define Py_TPFLAGS_HAVE_INDEX 0 +#endif +#ifndef Py_TPFLAGS_HAVE_NEWBUFFER + #define Py_TPFLAGS_HAVE_NEWBUFFER 0 +#endif +#ifndef Py_TPFLAGS_HAVE_FINALIZE + #define Py_TPFLAGS_HAVE_FINALIZE 0 +#endif +#if PY_VERSION_HEX > 0x03030000 && defined(PyUnicode_KIND) + #define CYTHON_PEP393_ENABLED 1 + #define __Pyx_PyUnicode_READY(op) (likely(PyUnicode_IS_READY(op)) ?\ + 0 : _PyUnicode_Ready((PyObject *)(op))) + #define __Pyx_PyUnicode_GET_LENGTH(u) PyUnicode_GET_LENGTH(u) + #define __Pyx_PyUnicode_READ_CHAR(u, i) PyUnicode_READ_CHAR(u, i) + #define __Pyx_PyUnicode_KIND(u) PyUnicode_KIND(u) + #define __Pyx_PyUnicode_DATA(u) PyUnicode_DATA(u) + #define __Pyx_PyUnicode_READ(k, d, i) PyUnicode_READ(k, d, i) +#else + #define CYTHON_PEP393_ENABLED 0 + #define __Pyx_PyUnicode_READY(op) (0) + #define __Pyx_PyUnicode_GET_LENGTH(u) PyUnicode_GET_SIZE(u) + #define __Pyx_PyUnicode_READ_CHAR(u, i) ((Py_UCS4)(PyUnicode_AS_UNICODE(u)[i])) + #define __Pyx_PyUnicode_KIND(u) (sizeof(Py_UNICODE)) + #define __Pyx_PyUnicode_DATA(u) ((void*)PyUnicode_AS_UNICODE(u)) + #define __Pyx_PyUnicode_READ(k, d, i) ((void)(k), (Py_UCS4)(((Py_UNICODE*)d)[i])) +#endif +#if CYTHON_COMPILING_IN_PYPY + #define __Pyx_PyUnicode_Concat(a, b) PyNumber_Add(a, b) + #define __Pyx_PyUnicode_ConcatSafe(a, b) PyNumber_Add(a, b) +#else + #define __Pyx_PyUnicode_Concat(a, b) PyUnicode_Concat(a, b) + #define __Pyx_PyUnicode_ConcatSafe(a, b) ((unlikely((a) == Py_None) || unlikely((b) == Py_None)) ?\ + PyNumber_Add(a, b) : __Pyx_PyUnicode_Concat(a, b)) +#endif +#if CYTHON_COMPILING_IN_PYPY && !defined(PyUnicode_Contains) + #define PyUnicode_Contains(u, s) PySequence_Contains(u, s) +#endif +#define __Pyx_PyString_FormatSafe(a, b) ((unlikely((a) == Py_None)) ? 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PyNumber_Remainder(a, b) : PyUnicode_Format(a, b)) +#if PY_MAJOR_VERSION >= 3 + #define __Pyx_PyString_Format(a, b) PyUnicode_Format(a, b) +#else + #define __Pyx_PyString_Format(a, b) PyString_Format(a, b) +#endif +#if PY_MAJOR_VERSION >= 3 + #define PyBaseString_Type PyUnicode_Type + #define PyStringObject PyUnicodeObject + #define PyString_Type PyUnicode_Type + #define PyString_Check PyUnicode_Check + #define PyString_CheckExact PyUnicode_CheckExact +#endif +#if PY_MAJOR_VERSION >= 3 + #define __Pyx_PyBaseString_Check(obj) PyUnicode_Check(obj) + #define __Pyx_PyBaseString_CheckExact(obj) PyUnicode_CheckExact(obj) +#else + #define __Pyx_PyBaseString_Check(obj) (PyString_Check(obj) || PyUnicode_Check(obj)) + #define __Pyx_PyBaseString_CheckExact(obj) (PyString_CheckExact(obj) || PyUnicode_CheckExact(obj)) +#endif +#ifndef PySet_CheckExact + #define PySet_CheckExact(obj) (Py_TYPE(obj) == &PySet_Type) +#endif +#define __Pyx_TypeCheck(obj, type) PyObject_TypeCheck(obj, (PyTypeObject *)type) +#if PY_MAJOR_VERSION >= 3 + #define PyIntObject PyLongObject + #define PyInt_Type PyLong_Type + #define PyInt_Check(op) PyLong_Check(op) + #define PyInt_CheckExact(op) PyLong_CheckExact(op) + #define PyInt_FromString PyLong_FromString + #define PyInt_FromUnicode PyLong_FromUnicode + #define PyInt_FromLong PyLong_FromLong + #define PyInt_FromSize_t PyLong_FromSize_t + #define PyInt_FromSsize_t PyLong_FromSsize_t + #define PyInt_AsLong PyLong_AsLong + #define PyInt_AS_LONG PyLong_AS_LONG + #define PyInt_AsSsize_t PyLong_AsSsize_t + #define PyInt_AsUnsignedLongMask PyLong_AsUnsignedLongMask + #define PyInt_AsUnsignedLongLongMask PyLong_AsUnsignedLongLongMask + #define PyNumber_Int PyNumber_Long +#endif +#if PY_MAJOR_VERSION >= 3 + #define PyBoolObject PyLongObject +#endif +#if PY_MAJOR_VERSION >= 3 && CYTHON_COMPILING_IN_PYPY + #ifndef PyUnicode_InternFromString + #define PyUnicode_InternFromString(s) PyUnicode_FromString(s) + #endif +#endif +#if PY_VERSION_HEX < 0x030200A4 + typedef long Py_hash_t; + #define __Pyx_PyInt_FromHash_t PyInt_FromLong + #define __Pyx_PyInt_AsHash_t PyInt_AsLong +#else + #define __Pyx_PyInt_FromHash_t PyInt_FromSsize_t + #define __Pyx_PyInt_AsHash_t PyInt_AsSsize_t +#endif +#if PY_MAJOR_VERSION >= 3 + #define __Pyx_PyMethod_New(func, self, klass) ((self) ? PyMethod_New(func, self) : PyInstanceMethod_New(func)) +#else + #define __Pyx_PyMethod_New(func, self, klass) PyMethod_New(func, self, klass) +#endif +#if PY_VERSION_HEX >= 0x030500B1 +#define __Pyx_PyAsyncMethodsStruct PyAsyncMethods +#define __Pyx_PyType_AsAsync(obj) (Py_TYPE(obj)->tp_as_async) +#elif CYTHON_COMPILING_IN_CPYTHON && PY_MAJOR_VERSION >= 3 +typedef struct { + unaryfunc am_await; + unaryfunc am_aiter; + unaryfunc am_anext; +} __Pyx_PyAsyncMethodsStruct; +#define __Pyx_PyType_AsAsync(obj) ((__Pyx_PyAsyncMethodsStruct*) (Py_TYPE(obj)->tp_reserved)) +#else +#define __Pyx_PyType_AsAsync(obj) NULL +#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 + #else + #define CYTHON_RESTRICT + #endif +#endif +#define __Pyx_void_to_None(void_result) ((void)(void_result), Py_INCREF(Py_None), Py_None) + +#ifndef __cplusplus + #error "Cython files generated with the C++ option must be compiled with a C++ compiler." +#endif +#ifndef CYTHON_INLINE + #define CYTHON_INLINE inline +#endif +template +void __Pyx_call_destructor(T& x) { + x.~T(); +} +template +class __Pyx_FakeReference { + public: + __Pyx_FakeReference() : ptr(NULL) { } + __Pyx_FakeReference(const T& ref) : ptr(const_cast(&ref)) { } + T *operator->() { return ptr; } + operator T&() { return *ptr; } + private: + T *ptr; +}; + +#if defined(WIN32) || defined(MS_WINDOWS) + #define _USE_MATH_DEFINES +#endif +#include +#ifdef NAN +#define __PYX_NAN() ((float) NAN) +#else +static CYTHON_INLINE float __PYX_NAN() { + float value; + memset(&value, 0xFF, sizeof(value)); + return value; +} +#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) +#else + #define __Pyx_PyNumber_Divide(x,y) PyNumber_Divide(x,y) + #define __Pyx_PyNumber_InPlaceDivide(x,y) PyNumber_InPlaceDivide(x,y) +#endif + +#ifndef __PYX_EXTERN_C + #ifdef __cplusplus + #define __PYX_EXTERN_C extern "C" + #else + #define __PYX_EXTERN_C extern + #endif +#endif + +#define __PYX_HAVE__ot__emd__emd +#define __PYX_HAVE_API__ot__emd__emd +#include "string.h" +#include "stdio.h" +#include "stdlib.h" +#include "numpy/arrayobject.h" +#include "numpy/ufuncobject.h" +#include "EMD.h" +#ifdef _OPENMP +#include +#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 +#ifndef CYTHON_NCP_UNUSED +# if CYTHON_COMPILING_IN_CPYTHON +# define CYTHON_NCP_UNUSED +# else +# define CYTHON_NCP_UNUSED 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_uchar_cast(c) ((unsigned char)c) +#define __Pyx_long_cast(x) ((long)x) +#define __Pyx_fits_Py_ssize_t(v, type, is_signed) (\ + (sizeof(type) < sizeof(Py_ssize_t)) ||\ + (sizeof(type) > sizeof(Py_ssize_t) &&\ + likely(v < (type)PY_SSIZE_T_MAX ||\ + v == (type)PY_SSIZE_T_MAX) &&\ + (!is_signed || likely(v > (type)PY_SSIZE_T_MIN ||\ + v == (type)PY_SSIZE_T_MIN))) ||\ + (sizeof(type) == sizeof(Py_ssize_t) &&\ + (is_signed || likely(v < (type)PY_SSIZE_T_MAX ||\ + v == (type)PY_SSIZE_T_MAX))) ) +#if defined (__cplusplus) && __cplusplus >= 201103L + #include + #define __Pyx_sst_abs(value) std::abs(value) +#elif SIZEOF_INT >= SIZEOF_SIZE_T + #define __Pyx_sst_abs(value) abs(value) +#elif SIZEOF_LONG >= SIZEOF_SIZE_T + #define __Pyx_sst_abs(value) labs(value) +#elif defined (_MSC_VER) && defined (_M_X64) + #define __Pyx_sst_abs(value) _abs64(value) +#elif defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L + #define __Pyx_sst_abs(value) llabs(value) +#elif defined (__GNUC__) + #define __Pyx_sst_abs(value) __builtin_llabs(value) +#else + #define __Pyx_sst_abs(value) ((value<0) ? -value : value) +#endif +static CYTHON_INLINE 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_FromCString(s) __Pyx_PyObject_FromString((const char*)s) +#define __Pyx_PyBytes_FromCString(s) __Pyx_PyBytes_FromString((const char*)s) +#define __Pyx_PyByteArray_FromCString(s) __Pyx_PyByteArray_FromString((const char*)s) +#define __Pyx_PyStr_FromCString(s) __Pyx_PyStr_FromString((const char*)s) +#define __Pyx_PyUnicode_FromCString(s) __Pyx_PyUnicode_FromString((const char*)s) +#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_NewRef(obj) (Py_INCREF(obj), obj) +#define __Pyx_Owned_Py_None(b) __Pyx_NewRef(Py_None) +#define __Pyx_PyBool_FromLong(b) ((b) ? __Pyx_NewRef(Py_True) : __Pyx_NewRef(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*) "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 + #else + #include + #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[] = { + "ot/emd/emd.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/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":725 + * # 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/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":726 + * + * 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/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":727 + * 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/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":728 + * 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/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":732 + * #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/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":733 + * + * 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/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":734 + * ctypedef npy_uint8 uint8_t + * ctypedef npy_uint16 uint16_t + * ctypedef npy_uint32 uint32_t # <<<<<<<<<<<<<< + * ctypedef npy_uint64 uint64_t + * #ctypedef npy_uint96 uint96_t + */ +typedef npy_uint32 __pyx_t_5numpy_uint32_t; + +/* "../../../../usr/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":735 + * ctypedef npy_uint16 uint16_t + * ctypedef npy_uint32 uint32_t + * ctypedef npy_uint64 uint64_t # <<<<<<<<<<<<<< + * #ctypedef npy_uint96 uint96_t + * #ctypedef npy_uint128 uint128_t + */ +typedef npy_uint64 __pyx_t_5numpy_uint64_t; + +/* "../../../../usr/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":739 + * #ctypedef npy_uint128 uint128_t + * + * ctypedef npy_float32 float32_t # <<<<<<<<<<<<<< + * ctypedef npy_float64 float64_t + * #ctypedef npy_float80 float80_t + */ +typedef npy_float32 __pyx_t_5numpy_float32_t; + +/* "../../../../usr/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":740 + * + * ctypedef npy_float32 float32_t + * ctypedef npy_float64 float64_t # <<<<<<<<<<<<<< + * #ctypedef npy_float80 float80_t + * #ctypedef npy_float128 float128_t + */ +typedef npy_float64 __pyx_t_5numpy_float64_t; + +/* "../../../../usr/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":749 + * # The int types are mapped a bit surprising -- + * # numpy.int corresponds to 'l' and numpy.long to 'q' + * ctypedef npy_long int_t # <<<<<<<<<<<<<< + * ctypedef npy_longlong long_t + * ctypedef npy_longlong longlong_t + */ +typedef npy_long __pyx_t_5numpy_int_t; + +/* "../../../../usr/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":750 + * # numpy.int corresponds to 'l' and numpy.long to 'q' + * ctypedef npy_long int_t + * ctypedef npy_longlong long_t # <<<<<<<<<<<<<< + * ctypedef npy_longlong longlong_t + * + */ +typedef npy_longlong __pyx_t_5numpy_long_t; + +/* "../../../../usr/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":751 + * ctypedef npy_long int_t + * ctypedef npy_longlong long_t + * ctypedef npy_longlong longlong_t # <<<<<<<<<<<<<< + * + * ctypedef npy_ulong uint_t + */ +typedef npy_longlong __pyx_t_5numpy_longlong_t; + +/* "../../../../usr/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":753 + * ctypedef npy_longlong longlong_t + * + * ctypedef npy_ulong uint_t # <<<<<<<<<<<<<< + * ctypedef npy_ulonglong ulong_t + * ctypedef npy_ulonglong ulonglong_t + */ +typedef npy_ulong __pyx_t_5numpy_uint_t; + +/* "../../../../usr/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":754 + * + * ctypedef npy_ulong uint_t + * ctypedef npy_ulonglong ulong_t # <<<<<<<<<<<<<< + * ctypedef npy_ulonglong ulonglong_t + * + */ +typedef npy_ulonglong __pyx_t_5numpy_ulong_t; + +/* "../../../../usr/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":755 + * ctypedef npy_ulong uint_t + * ctypedef npy_ulonglong ulong_t + * ctypedef npy_ulonglong ulonglong_t # <<<<<<<<<<<<<< + * + * ctypedef npy_intp intp_t + */ +typedef npy_ulonglong __pyx_t_5numpy_ulonglong_t; + +/* "../../../../usr/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":757 + * ctypedef npy_ulonglong ulonglong_t + * + * ctypedef npy_intp intp_t # <<<<<<<<<<<<<< + * ctypedef npy_uintp uintp_t + * + */ +typedef npy_intp __pyx_t_5numpy_intp_t; + +/* "../../../../usr/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":758 + * + * ctypedef npy_intp intp_t + * ctypedef npy_uintp uintp_t # <<<<<<<<<<<<<< + * + * ctypedef npy_double float_t + */ +typedef npy_uintp __pyx_t_5numpy_uintp_t; + +/* "../../../../usr/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":760 + * ctypedef npy_uintp uintp_t + * + * ctypedef npy_double float_t # <<<<<<<<<<<<<< + * ctypedef npy_double double_t + * ctypedef npy_longdouble longdouble_t + */ +typedef npy_double __pyx_t_5numpy_float_t; + +/* "../../../../usr/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":761 + * + * ctypedef npy_double float_t + * ctypedef npy_double double_t # <<<<<<<<<<<<<< + * ctypedef npy_longdouble longdouble_t + * + */ +typedef npy_double __pyx_t_5numpy_double_t; + +/* "../../../../usr/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":762 + * ctypedef npy_double float_t + * ctypedef npy_double double_t + * ctypedef npy_longdouble longdouble_t # <<<<<<<<<<<<<< + * + * ctypedef npy_cfloat cfloat_t + */ +typedef npy_longdouble __pyx_t_5numpy_longdouble_t; +#if CYTHON_CCOMPLEX + #ifdef __cplusplus + typedef ::std::complex< float > __pyx_t_float_complex; + #else + typedef float _Complex __pyx_t_float_complex; + #endif +#else + typedef struct { float real, imag; } __pyx_t_float_complex; +#endif + +#if CYTHON_CCOMPLEX + #ifdef __cplusplus + typedef ::std::complex< double > __pyx_t_double_complex; + #else + typedef double _Complex __pyx_t_double_complex; + #endif +#else + typedef struct { double real, imag; } __pyx_t_double_complex; +#endif + + +/*--- Type declarations ---*/ + +/* "../../../../usr/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":764 + * ctypedef npy_longdouble longdouble_t + * + * ctypedef npy_cfloat cfloat_t # <<<<<<<<<<<<<< + * ctypedef npy_cdouble cdouble_t + * ctypedef npy_clongdouble clongdouble_t + */ +typedef npy_cfloat __pyx_t_5numpy_cfloat_t; + +/* "../../../../usr/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":765 + * + * ctypedef npy_cfloat cfloat_t + * ctypedef npy_cdouble cdouble_t # <<<<<<<<<<<<<< + * ctypedef npy_clongdouble clongdouble_t + * + */ +typedef npy_cdouble __pyx_t_5numpy_cdouble_t; + +/* "../../../../usr/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":766 + * ctypedef npy_cfloat cfloat_t + * ctypedef npy_cdouble cdouble_t + * ctypedef npy_clongdouble clongdouble_t # <<<<<<<<<<<<<< + * + * ctypedef npy_cdouble complex_t + */ +typedef npy_clongdouble __pyx_t_5numpy_clongdouble_t; + +/* "../../../../usr/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":768 + * ctypedef npy_clongdouble clongdouble_t + * + * ctypedef npy_cdouble complex_t # <<<<<<<<<<<<<< + * + * cdef inline object PyArray_MultiIterNew1(a): + */ +typedef npy_cdouble __pyx_t_5numpy_complex_t; + +/* --- Runtime support code (head) --- */ +#ifndef CYTHON_REFNANNY + #define CYTHON_REFNANNY 0 +#endif +#if CYTHON_REFNANNY + typedef struct { + void (*INCREF)(void*, PyObject*, int); + void (*DECREF)(void*, PyObject*, int); + void (*GOTREF)(void*, PyObject*, int); + void (*GIVEREF)(void*, PyObject*, int); + void* (*SetupContext)(const char*, int, const char*); + void (*FinishContext)(void**); + } __Pyx_RefNannyAPIStruct; + static __Pyx_RefNannyAPIStruct *__Pyx_RefNanny = NULL; + static __Pyx_RefNannyAPIStruct *__Pyx_RefNannyImportAPI(const char *modname); + #define __Pyx_RefNannyDeclarations void *__pyx_refnanny = NULL; +#ifdef WITH_THREAD + #define __Pyx_RefNannySetupContext(name, acquire_gil)\ + if (acquire_gil) {\ + PyGILState_STATE __pyx_gilstate_save = PyGILState_Ensure();\ + __pyx_refnanny = __Pyx_RefNanny->SetupContext((name), __LINE__, __FILE__);\ + PyGILState_Release(__pyx_gilstate_save);\ + } else {\ + __pyx_refnanny = __Pyx_RefNanny->SetupContext((name), __LINE__, __FILE__);\ + } +#else + #define __Pyx_RefNannySetupContext(name, acquire_gil)\ + __pyx_refnanny = __Pyx_RefNanny->SetupContext((name), __LINE__, __FILE__) +#endif + #define __Pyx_RefNannyFinishContext()\ + __Pyx_RefNanny->FinishContext(&__pyx_refnanny) + #define __Pyx_INCREF(r) __Pyx_RefNanny->INCREF(__pyx_refnanny, (PyObject *)(r), __LINE__) + #define __Pyx_DECREF(r) __Pyx_RefNanny->DECREF(__pyx_refnanny, (PyObject *)(r), __LINE__) + #define __Pyx_GOTREF(r) __Pyx_RefNanny->GOTREF(__pyx_refnanny, (PyObject *)(r), __LINE__) + #define __Pyx_GIVEREF(r) __Pyx_RefNanny->GIVEREF(__pyx_refnanny, (PyObject *)(r), __LINE__) + #define __Pyx_XINCREF(r) do { if((r) != NULL) {__Pyx_INCREF(r); }} while(0) + #define __Pyx_XDECREF(r) do { if((r) != NULL) {__Pyx_DECREF(r); }} while(0) + #define __Pyx_XGOTREF(r) do { if((r) != NULL) {__Pyx_GOTREF(r); }} while(0) + #define __Pyx_XGIVEREF(r) do { if((r) != NULL) {__Pyx_GIVEREF(r);}} while(0) +#else + #define __Pyx_RefNannyDeclarations + #define __Pyx_RefNannySetupContext(name, acquire_gil) + #define __Pyx_RefNannyFinishContext() + #define __Pyx_INCREF(r) Py_INCREF(r) + #define __Pyx_DECREF(r) Py_DECREF(r) + #define __Pyx_GOTREF(r) + #define __Pyx_GIVEREF(r) + #define __Pyx_XINCREF(r) Py_XINCREF(r) + #define __Pyx_XDECREF(r) Py_XDECREF(r) + #define __Pyx_XGOTREF(r) + #define __Pyx_XGIVEREF(r) +#endif +#define __Pyx_XDECREF_SET(r, v) do {\ + PyObject *tmp = (PyObject *) r;\ + r = v; __Pyx_XDECREF(tmp);\ + } while (0) +#define __Pyx_DECREF_SET(r, v) do {\ + PyObject *tmp = (PyObject *) r;\ + r = v; __Pyx_DECREF(tmp);\ + } while (0) +#define __Pyx_CLEAR(r) do { PyObject* tmp = ((PyObject*)(r)); r = NULL; __Pyx_DECREF(tmp);} while(0) +#define __Pyx_XCLEAR(r) do { if((r) != NULL) {PyObject* tmp = ((PyObject*)(r)); r = NULL; __Pyx_DECREF(tmp);}} while(0) + +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); + +static void __Pyx_RaiseDoubleKeywordsError(const char* func_name, PyObject* kw_name); + +static int __Pyx_ParseOptionalKeywords(PyObject *kwds, PyObject **argnames[],\ + PyObject *kwds2, PyObject *values[], Py_ssize_t num_pos_args,\ + const char* function_name); + +static CYTHON_INLINE int __Pyx_ArgTypeTest(PyObject *obj, PyTypeObject *type, int none_allowed, + const char *name, int exact); + +static CYTHON_INLINE int __Pyx_GetBufferAndValidate(Py_buffer* buf, PyObject* obj, + __Pyx_TypeInfo* dtype, int flags, int nd, int cast, __Pyx_BufFmt_StackElem* stack); +static CYTHON_INLINE void __Pyx_SafeReleaseBuffer(Py_buffer* info); + +#if CYTHON_COMPILING_IN_CPYTHON +static CYTHON_INLINE PyObject* __Pyx_PyObject_GetAttrStr(PyObject* obj, PyObject* attr_name) { + PyTypeObject* tp = Py_TYPE(obj); + if (likely(tp->tp_getattro)) + return tp->tp_getattro(obj, attr_name); +#if PY_MAJOR_VERSION < 3 + if (likely(tp->tp_getattr)) + return tp->tp_getattr(obj, PyString_AS_STRING(attr_name)); +#endif + return PyObject_GetAttr(obj, attr_name); +} +#else +#define __Pyx_PyObject_GetAttrStr(o,n) PyObject_GetAttr(o,n) +#endif + +static PyObject *__Pyx_GetBuiltinName(PyObject *name); + +static CYTHON_INLINE PyObject *__Pyx_GetModuleGlobalName(PyObject *name); + +#if CYTHON_COMPILING_IN_CPYTHON +static CYTHON_INLINE PyObject* __Pyx_PyObject_Call(PyObject *func, PyObject *arg, PyObject *kw); +#else +#define __Pyx_PyObject_Call(func, arg, kw) PyObject_Call(func, arg, kw) +#endif + +#if CYTHON_COMPILING_IN_CPYTHON +static CYTHON_INLINE PyObject* __Pyx_PyObject_CallMethO(PyObject *func, PyObject *arg); +#endif + +static CYTHON_INLINE PyObject* __Pyx_PyObject_CallOneArg(PyObject *func, PyObject *arg); + +static CYTHON_INLINE int __Pyx_TypeTest(PyObject *obj, PyTypeObject *type); + +static void __Pyx_RaiseBufferFallbackError(void); + +static CYTHON_INLINE void __Pyx_ErrRestore(PyObject *type, PyObject *value, PyObject *tb); +static CYTHON_INLINE void __Pyx_ErrFetch(PyObject **type, PyObject **value, PyObject **tb); + +static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb, PyObject *cause); + +#if PY_MAJOR_VERSION >= 3 && !CYTHON_COMPILING_IN_PYPY +static PyObject *__Pyx_PyDict_GetItem(PyObject *d, PyObject* key) { + PyObject *value; + value = PyDict_GetItemWithError(d, key); + if (unlikely(!value)) { + if (!PyErr_Occurred()) { + PyObject* args = PyTuple_Pack(1, key); + if (likely(args)) + PyErr_SetObject(PyExc_KeyError, args); + Py_XDECREF(args); + } + return NULL; + } + Py_INCREF(value); + return value; +} +#else + #define __Pyx_PyDict_GetItem(d, key) PyObject_GetItem(d, key) +#endif + +static CYTHON_INLINE void __Pyx_RaiseTooManyValuesError(Py_ssize_t expected); + +static CYTHON_INLINE void __Pyx_RaiseNeedMoreValuesError(Py_ssize_t index); + +static CYTHON_INLINE void __Pyx_RaiseNoneNotIterableError(void); + +static PyObject *__Pyx_Import(PyObject *name, PyObject *from_list, int level); + +typedef struct { + int code_line; + PyCodeObject* code_object; +} __Pyx_CodeObjectCacheEntry; +struct __Pyx_CodeObjectCache { + int count; + int max_count; + __Pyx_CodeObjectCacheEntry* entries; +}; +static struct __Pyx_CodeObjectCache __pyx_code_cache = {0,0,NULL}; +static int __pyx_bisect_code_objects(__Pyx_CodeObjectCacheEntry* entries, int count, int code_line); +static PyCodeObject *__pyx_find_code_object(int code_line); +static void __pyx_insert_code_object(int code_line, PyCodeObject* code_object); + +static void __Pyx_AddTraceback(const char *funcname, int c_line, + int py_line, const char *filename); + +typedef struct { + Py_ssize_t shape, strides, suboffsets; +} __Pyx_Buf_DimInfo; +typedef struct { + size_t refcount; + Py_buffer pybuffer; +} __Pyx_Buffer; +typedef struct { + __Pyx_Buffer *rcbuffer; + char *data; + __Pyx_Buf_DimInfo diminfo[8]; +} __Pyx_LocalBuf_ND; + +#if PY_MAJOR_VERSION < 3 + static int __Pyx_GetBuffer(PyObject *obj, Py_buffer *view, int flags); + static void __Pyx_ReleaseBuffer(Py_buffer *view); +#else + #define __Pyx_GetBuffer PyObject_GetBuffer + #define __Pyx_ReleaseBuffer PyBuffer_Release +#endif + + +static Py_ssize_t __Pyx_zeros[] = {0, 0, 0, 0, 0, 0, 0, 0}; +static Py_ssize_t __Pyx_minusones[] = {-1, -1, -1, -1, -1, -1, -1, -1}; + +static CYTHON_INLINE PyObject* __Pyx_PyInt_From_int(int value); + +#if CYTHON_CCOMPLEX + #ifdef __cplusplus + #define __Pyx_CREAL(z) ((z).real()) + #define __Pyx_CIMAG(z) ((z).imag()) + #else + #define __Pyx_CREAL(z) (__real__(z)) + #define __Pyx_CIMAG(z) (__imag__(z)) + #endif +#else + #define __Pyx_CREAL(z) ((z).real) + #define __Pyx_CIMAG(z) ((z).imag) +#endif +#if (defined(_WIN32) || defined(__clang__)) && defined(__cplusplus) && CYTHON_CCOMPLEX + #define __Pyx_SET_CREAL(z,x) ((z).real(x)) + #define __Pyx_SET_CIMAG(z,y) ((z).imag(y)) +#else + #define __Pyx_SET_CREAL(z,x) __Pyx_CREAL(z) = (x) + #define __Pyx_SET_CIMAG(z,y) __Pyx_CIMAG(z) = (y) +#endif + +static CYTHON_INLINE __pyx_t_float_complex __pyx_t_float_complex_from_parts(float, float); + +#if CYTHON_CCOMPLEX + #define __Pyx_c_eqf(a, b) ((a)==(b)) + #define __Pyx_c_sumf(a, b) ((a)+(b)) + #define __Pyx_c_difff(a, b) ((a)-(b)) + #define __Pyx_c_prodf(a, b) ((a)*(b)) + #define __Pyx_c_quotf(a, b) ((a)/(b)) + #define __Pyx_c_negf(a) (-(a)) + #ifdef __cplusplus + #define __Pyx_c_is_zerof(z) ((z)==(float)0) + #define __Pyx_c_conjf(z) (::std::conj(z)) + #if 1 + #define __Pyx_c_absf(z) (::std::abs(z)) + #define __Pyx_c_powf(a, b) (::std::pow(a, b)) + #endif + #else + #define __Pyx_c_is_zerof(z) ((z)==0) + #define __Pyx_c_conjf(z) (conjf(z)) + #if 1 + #define __Pyx_c_absf(z) (cabsf(z)) + #define __Pyx_c_powf(a, b) (cpowf(a, b)) + #endif + #endif +#else + static CYTHON_INLINE int __Pyx_c_eqf(__pyx_t_float_complex, __pyx_t_float_complex); + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_sumf(__pyx_t_float_complex, __pyx_t_float_complex); + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_difff(__pyx_t_float_complex, __pyx_t_float_complex); + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_prodf(__pyx_t_float_complex, __pyx_t_float_complex); + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_quotf(__pyx_t_float_complex, __pyx_t_float_complex); + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_negf(__pyx_t_float_complex); + static CYTHON_INLINE int __Pyx_c_is_zerof(__pyx_t_float_complex); + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_conjf(__pyx_t_float_complex); + #if 1 + static CYTHON_INLINE float __Pyx_c_absf(__pyx_t_float_complex); + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_powf(__pyx_t_float_complex, __pyx_t_float_complex); + #endif +#endif + +static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double, double); + +#if CYTHON_CCOMPLEX + #define __Pyx_c_eq(a, b) ((a)==(b)) + #define __Pyx_c_sum(a, b) ((a)+(b)) + #define __Pyx_c_diff(a, b) ((a)-(b)) + #define __Pyx_c_prod(a, b) ((a)*(b)) + #define __Pyx_c_quot(a, b) ((a)/(b)) + #define __Pyx_c_neg(a) (-(a)) + #ifdef __cplusplus + #define __Pyx_c_is_zero(z) ((z)==(double)0) + #define __Pyx_c_conj(z) (::std::conj(z)) + #if 1 + #define __Pyx_c_abs(z) (::std::abs(z)) + #define __Pyx_c_pow(a, b) (::std::pow(a, b)) + #endif + #else + #define __Pyx_c_is_zero(z) ((z)==0) + #define __Pyx_c_conj(z) (conj(z)) + #if 1 + #define __Pyx_c_abs(z) (cabs(z)) + #define __Pyx_c_pow(a, b) (cpow(a, b)) + #endif + #endif +#else + static CYTHON_INLINE int __Pyx_c_eq(__pyx_t_double_complex, __pyx_t_double_complex); + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_sum(__pyx_t_double_complex, __pyx_t_double_complex); + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_diff(__pyx_t_double_complex, __pyx_t_double_complex); + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_prod(__pyx_t_double_complex, __pyx_t_double_complex); + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_quot(__pyx_t_double_complex, __pyx_t_double_complex); + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_neg(__pyx_t_double_complex); + static CYTHON_INLINE int __Pyx_c_is_zero(__pyx_t_double_complex); + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_conj(__pyx_t_double_complex); + #if 1 + static CYTHON_INLINE double __Pyx_c_abs(__pyx_t_double_complex); + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_pow(__pyx_t_double_complex, __pyx_t_double_complex); + #endif +#endif + +static CYTHON_INLINE int __Pyx_PyInt_As_int(PyObject *); + +static CYTHON_INLINE PyObject* __Pyx_PyInt_From_enum__NPY_TYPES(enum NPY_TYPES value); + +static CYTHON_INLINE PyObject* __Pyx_PyInt_From_long(long value); + +static CYTHON_INLINE long __Pyx_PyInt_As_long(PyObject *); + +static int __Pyx_check_binary_version(void); + +#if !defined(__Pyx_PyIdentifier_FromString) +#if PY_MAJOR_VERSION < 3 + #define __Pyx_PyIdentifier_FromString(s) PyString_FromString(s) +#else + #define __Pyx_PyIdentifier_FromString(s) PyUnicode_FromString(s) +#endif +#endif + +static PyObject *__Pyx_ImportModule(const char *name); + +static PyTypeObject *__Pyx_ImportType(const char *module_name, const char *class_name, size_t size, int strict); + +static int __Pyx_InitStrings(__Pyx_StringTabEntry *t); + + +/* Module declarations from 'cpython.buffer' */ + +/* Module declarations from 'libc.string' */ + +/* Module declarations from 'libc.stdio' */ + +/* Module declarations from '__builtin__' */ + +/* Module declarations from 'cpython.type' */ +static PyTypeObject *__pyx_ptype_7cpython_4type_type = 0; + +/* Module declarations from 'cpython' */ + +/* Module declarations from 'cpython.object' */ + +/* Module declarations from 'cpython.ref' */ + +/* Module declarations from 'libc.stdlib' */ + +/* Module declarations from 'numpy' */ + +/* Module declarations from 'numpy' */ +static PyTypeObject *__pyx_ptype_5numpy_dtype = 0; +static PyTypeObject *__pyx_ptype_5numpy_flatiter = 0; +static PyTypeObject *__pyx_ptype_5numpy_broadcast = 0; +static PyTypeObject *__pyx_ptype_5numpy_ndarray = 0; +static PyTypeObject *__pyx_ptype_5numpy_ufunc = 0; +static CYTHON_INLINE char *__pyx_f_5numpy__util_dtypestring(PyArray_Descr *, char *, char *, int *); /*proto*/ + +/* Module declarations from 'cython' */ + +/* Module declarations from 'ot.emd.emd' */ +static __Pyx_TypeInfo __Pyx_TypeInfo_double = { "double", NULL, sizeof(double), { 0 }, 0, 'R', 0, 0 }; +#define __Pyx_MODULE_NAME "ot.emd.emd" +int __pyx_module_is_main_ot__emd__emd = 0; + +/* Implementation of 'ot.emd.emd' */ +static PyObject *__pyx_builtin_ValueError; +static PyObject *__pyx_builtin_range; +static PyObject *__pyx_builtin_RuntimeError; +static char __pyx_k_B[] = "B"; +static char __pyx_k_G[] = "G"; +static char __pyx_k_H[] = "H"; +static char __pyx_k_I[] = "I"; +static char __pyx_k_L[] = "L"; +static char __pyx_k_M[] = "M"; +static char __pyx_k_O[] = "O"; 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if (unlikely(!__pyx_t_1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 21; __pyx_clineno = __LINE__; goto __pyx_L1_error;} + __Pyx_GOTREF(__pyx_t_1); + if (PyDict_SetItem(__pyx_d, __pyx_n_s_emd, __pyx_t_1) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 21; __pyx_clineno = __LINE__; goto __pyx_L1_error;} + __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0; + + /* "ot/emd/emd.pyx":1 + * # -*- coding: utf-8 -*- # <<<<<<<<<<<<<< + * """ + * Created on Thu Sep 11 08:42:08 2014 + */ + __pyx_t_1 = PyDict_New(); if (unlikely(!__pyx_t_1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;} + __Pyx_GOTREF(__pyx_t_1); + if (PyDict_SetItem(__pyx_d, __pyx_n_s_test, __pyx_t_1) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;} + __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0; + + /* "../../../../usr/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":976 + * arr.base = baseptr + * + * cdef inline object get_array_base(ndarray arr): # <<<<<<<<<<<<<< + * if arr.base is NULL: + * return None + */ + + /*--- Wrapped vars code ---*/ + + goto __pyx_L0; + __pyx_L1_error:; + __Pyx_XDECREF(__pyx_t_1); + if (__pyx_m) { + if (__pyx_d) { + __Pyx_AddTraceback("init ot.emd.emd", __pyx_clineno, __pyx_lineno, __pyx_filename); + } + Py_DECREF(__pyx_m); __pyx_m = 0; + } else if (!PyErr_Occurred()) { + PyErr_SetString(PyExc_ImportError, "init ot.emd.emd"); + } + __pyx_L0:; + __Pyx_RefNannyFinishContext(); + #if PY_MAJOR_VERSION < 3 + return; + #else + return __pyx_m; + #endif +} + +/* --- Runtime support code --- */ +#if CYTHON_REFNANNY +static __Pyx_RefNannyAPIStruct *__Pyx_RefNannyImportAPI(const char *modname) { + PyObject *m = NULL, *p = NULL; + void *r = NULL; + m = PyImport_ImportModule((char *)modname); + if (!m) goto end; + p = PyObject_GetAttrString(m, (char *)"RefNannyAPI"); + if (!p) goto end; + r = PyLong_AsVoidPtr(p); +end: + Py_XDECREF(p); + Py_XDECREF(m); + return (__Pyx_RefNannyAPIStruct *)r; +} +#endif + +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_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 int __Pyx_IsLittleEndian(void) { + unsigned int n = 1; + return *(unsigned char*)(&n) != 0; +} +static void __Pyx_BufFmt_Init(__Pyx_BufFmt_Context* ctx, + __Pyx_BufFmt_StackElem* stack, + __Pyx_TypeInfo* type) { + stack[0].field = &ctx->root; + stack[0].parent_offset = 0; + ctx->root.type = type; + ctx->root.name = "buffer dtype"; + ctx->root.offset = 0; + ctx->head = stack; + ctx->head->field = &ctx->root; + ctx->fmt_offset = 0; + ctx->head->parent_offset = 0; + ctx->new_packmode = '@'; + ctx->enc_packmode = '@'; + ctx->new_count = 1; + ctx->enc_count = 0; + ctx->enc_type = 0; + ctx->is_complex = 0; + ctx->is_valid_array = 0; + ctx->struct_alignment = 0; + while (type->typegroup == 'S') { + ++ctx->head; + ctx->head->field = type->fields; + ctx->head->parent_offset = 0; + type = type->fields->type; + } +} +static int __Pyx_BufFmt_ParseNumber(const char** ts) { + int count; + const char* t = *ts; + if (*t < '0' || *t > '9') { + return -1; + } else { + count = *t++ - '0'; + while (*t >= '0' && *t < '9') { + count *= 10; + count += *t++ - '0'; + } + } + *ts = t; + return count; +} +static int __Pyx_BufFmt_ExpectNumber(const char **ts) { + int number = __Pyx_BufFmt_ParseNumber(ts); + if (number == -1) + PyErr_Format(PyExc_ValueError,\ + "Does not understand character buffer dtype format string ('%c')", **ts); + return number; +} +static void __Pyx_BufFmt_RaiseUnexpectedChar(char ch) { + PyErr_Format(PyExc_ValueError, + "Unexpected format string character: '%c'", ch); +} +static const char* __Pyx_BufFmt_DescribeTypeChar(char ch, int is_complex) { + switch (ch) { + case 'c': return "'char'"; + case 'b': return "'signed char'"; + case 'B': return "'unsigned char'"; + case 'h': return "'short'"; + case 'H': return "'unsigned short'"; + case 'i': return "'int'"; + case 'I': return "'unsigned int'"; + case 'l': return "'long'"; + case 'L': return "'unsigned long'"; + case 'q': return "'long long'"; + case 'Q': return "'unsigned long long'"; + case 'f': return (is_complex ? "'complex float'" : "'float'"); + case 'd': return (is_complex ? "'complex double'" : "'double'"); + case 'g': return (is_complex ? "'complex long double'" : "'long double'"); + case 'T': return "a struct"; + case 'O': return "Python object"; + case 'P': return "a pointer"; + case 's': case 'p': return "a string"; + case 0: return "end"; + default: return "unparseable format string"; + } +} +static size_t __Pyx_BufFmt_TypeCharToStandardSize(char ch, int is_complex) { + switch (ch) { + case '?': case 'c': case 'b': case 'B': case 's': case 'p': return 1; + case 'h': case 'H': return 2; + case 'i': case 'I': case 'l': case 'L': return 4; + case 'q': case 'Q': return 8; + case 'f': return (is_complex ? 8 : 4); + case 'd': return (is_complex ? 16 : 8); + case 'g': { + PyErr_SetString(PyExc_ValueError, "Python does not define a standard format string size for long double ('g').."); + return 0; + } + case 'O': case 'P': return sizeof(void*); + default: + __Pyx_BufFmt_RaiseUnexpectedChar(ch); + return 0; + } +} +static size_t __Pyx_BufFmt_TypeCharToNativeSize(char ch, int is_complex) { + switch (ch) { + case 'c': case 'b': case 'B': case 's': case 'p': return 1; + case 'h': case 'H': return sizeof(short); + case 'i': case 'I': return sizeof(int); + case 'l': case 'L': return sizeof(long); + #ifdef HAVE_LONG_LONG + case 'q': case 'Q': return sizeof(PY_LONG_LONG); + #endif + case 'f': return sizeof(float) * (is_complex ? 2 : 1); + case 'd': return sizeof(double) * (is_complex ? 2 : 1); + case 'g': return sizeof(long double) * (is_complex ? 2 : 1); + case 'O': case 'P': return sizeof(void*); + default: { + __Pyx_BufFmt_RaiseUnexpectedChar(ch); + return 0; + } + } +} +typedef struct { char c; short x; } __Pyx_st_short; +typedef struct { char c; int x; } __Pyx_st_int; +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 PyObject *__Pyx_GetBuiltinName(PyObject *name) { + PyObject* result = __Pyx_PyObject_GetAttrStr(__pyx_b, name); + if (unlikely(!result)) { + PyErr_Format(PyExc_NameError, +#if PY_MAJOR_VERSION >= 3 + "name '%U' is not defined", name); +#else + "name '%.200s' is not defined", PyString_AS_STRING(name)); +#endif + } + return result; +} + +static CYTHON_INLINE PyObject *__Pyx_GetModuleGlobalName(PyObject *name) { + PyObject *result; +#if CYTHON_COMPILING_IN_CPYTHON + result = PyDict_GetItem(__pyx_d, name); + if (likely(result)) { + Py_INCREF(result); + } else { +#else + result = PyObject_GetItem(__pyx_d, name); + if (!result) { + PyErr_Clear(); +#endif + result = __Pyx_GetBuiltinName(name); + } + return result; +} + +#if CYTHON_COMPILING_IN_CPYTHON +static CYTHON_INLINE PyObject* __Pyx_PyObject_Call(PyObject *func, PyObject *arg, PyObject *kw) { + PyObject *result; + ternaryfunc call = func->ob_type->tp_call; + if (unlikely(!call)) + return PyObject_Call(func, arg, kw); + if (unlikely(Py_EnterRecursiveCall((char*)" while calling a Python object"))) + return NULL; + result = (*call)(func, arg, kw); + Py_LeaveRecursiveCall(); + if (unlikely(!result) && unlikely(!PyErr_Occurred())) { + PyErr_SetString( + PyExc_SystemError, + "NULL result without error in PyObject_Call"); + } + return result; +} +#endif + +#if CYTHON_COMPILING_IN_CPYTHON +static CYTHON_INLINE PyObject* __Pyx_PyObject_CallMethO(PyObject *func, PyObject *arg) { + PyObject *self, *result; + PyCFunction cfunc; + cfunc = PyCFunction_GET_FUNCTION(func); + self = PyCFunction_GET_SELF(func); + if (unlikely(Py_EnterRecursiveCall((char*)" while calling a Python object"))) + return NULL; + result = cfunc(self, arg); + Py_LeaveRecursiveCall(); + if (unlikely(!result) && unlikely(!PyErr_Occurred())) { + PyErr_SetString( + PyExc_SystemError, + "NULL result without error in PyObject_Call"); + } + return result; +} +#endif + +#if CYTHON_COMPILING_IN_CPYTHON +static PyObject* __Pyx__PyObject_CallOneArg(PyObject *func, PyObject *arg) { + PyObject *result; + PyObject *args = PyTuple_New(1); + if (unlikely(!args)) return NULL; + Py_INCREF(arg); + PyTuple_SET_ITEM(args, 0, arg); + result = __Pyx_PyObject_Call(func, args, NULL); + Py_DECREF(args); + return result; +} +static CYTHON_INLINE PyObject* __Pyx_PyObject_CallOneArg(PyObject *func, PyObject *arg) { +#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_O)) { + return __Pyx_PyObject_CallMethO(func, arg); + } + } + return __Pyx__PyObject_CallOneArg(func, arg); +} +#else +static CYTHON_INLINE PyObject* __Pyx_PyObject_CallOneArg(PyObject *func, PyObject *arg) { + PyObject *result; + PyObject *args = PyTuple_Pack(1, arg); + if (unlikely(!args)) return NULL; + result = __Pyx_PyObject_Call(func, args, NULL); + Py_DECREF(args); + return result; +} +#endif + +static CYTHON_INLINE int __Pyx_TypeTest(PyObject *obj, PyTypeObject *type) { + if (unlikely(!type)) { + PyErr_SetString(PyExc_SystemError, "Missing type object"); + return 0; + } + if (likely(PyObject_TypeCheck(obj, type))) + return 1; + PyErr_Format(PyExc_TypeError, "Cannot convert %.200s to %.200s", + Py_TYPE(obj)->tp_name, type->tp_name); + return 0; +} + +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 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 +} + +#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) { + int is_subclass = PyObject_IsSubclass(instance_class, type); + if (!is_subclass) { + instance_class = NULL; + } else if (unlikely(is_subclass == -1)) { + goto bad; + } else { + type = instance_class; + } + } + } + if (!instance_class) { + PyObject *args; + if (!value) + args = PyTuple_New(0); + else if (PyTuple_Check(value)) { + Py_INCREF(value); + args = value; + } else + args = PyTuple_Pack(1, value); + if (!args) + goto bad; + owned_instance = PyObject_Call(type, args, NULL); + Py_DECREF(args); + if (!owned_instance) + goto bad; + value = owned_instance; + if (!PyExceptionInstance_Check(value)) { + PyErr_Format(PyExc_TypeError, + "calling %R should have returned an instance of " + "BaseException, not %R", + type, Py_TYPE(value)); + goto bad; + } + } + } else { + PyErr_SetString(PyExc_TypeError, + "raise: exception class must be a subclass of BaseException"); + goto bad; + } +#if 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 + +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 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; +} + +static int __pyx_bisect_code_objects(__Pyx_CodeObjectCacheEntry* entries, int count, int code_line) { + int start = 0, mid = 0, end = count - 1; + if (end >= 0 && code_line > entries[end].code_line) { + return count; + } + while (start < end) { + mid = start + (end - start) / 2; + if (code_line < entries[mid].code_line) { + end = mid; + } else if (code_line > entries[mid].code_line) { + start = mid + 1; + } else { + return mid; + } + } + if (code_line <= entries[mid].code_line) { + return mid; + } else { + return mid + 1; + } +} +static PyCodeObject *__pyx_find_code_object(int code_line) { + PyCodeObject* code_object; + int pos; + if (unlikely(!code_line) || unlikely(!__pyx_code_cache.entries)) { + return NULL; + } + pos = __pyx_bisect_code_objects(__pyx_code_cache.entries, __pyx_code_cache.count, code_line); + if (unlikely(pos >= __pyx_code_cache.count) || unlikely(__pyx_code_cache.entries[pos].code_line != code_line)) { + return NULL; + } + code_object = __pyx_code_cache.entries[pos].code_object; + Py_INCREF(code_object); + return code_object; +} +static void __pyx_insert_code_object(int code_line, PyCodeObject* code_object) { + int pos, i; + __Pyx_CodeObjectCacheEntry* entries = __pyx_code_cache.entries; + if (unlikely(!code_line)) { + return; + } + if (unlikely(!entries)) { + entries = (__Pyx_CodeObjectCacheEntry*)PyMem_Malloc(64*sizeof(__Pyx_CodeObjectCacheEntry)); + if (likely(entries)) { + __pyx_code_cache.entries = entries; + __pyx_code_cache.max_count = 64; + __pyx_code_cache.count = 1; + entries[0].code_line = code_line; + entries[0].code_object = code_object; + Py_INCREF(code_object); + } + return; + } + pos = __pyx_bisect_code_objects(__pyx_code_cache.entries, __pyx_code_cache.count, code_line); + if ((pos < __pyx_code_cache.count) && unlikely(__pyx_code_cache.entries[pos].code_line == code_line)) { + PyCodeObject* tmp = entries[pos].code_object; + entries[pos].code_object = code_object; + Py_DECREF(tmp); + return; + } + if (__pyx_code_cache.count == __pyx_code_cache.max_count) { + int new_max = __pyx_code_cache.max_count + 64; + entries = (__Pyx_CodeObjectCacheEntry*)PyMem_Realloc( + __pyx_code_cache.entries, (size_t)new_max*sizeof(__Pyx_CodeObjectCacheEntry)); + if (unlikely(!entries)) { + return; + } + __pyx_code_cache.entries = entries; + __pyx_code_cache.max_count = new_max; + } + for (i=__pyx_code_cache.count; i>pos; i--) { + entries[i] = entries[i-1]; + } + entries[pos].code_line = code_line; + entries[pos].code_object = code_object; + __pyx_code_cache.count++; + Py_INCREF(code_object); +} + +#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 CYTHON_INLINE PyObject* __Pyx_PyInt_From_int(int value) { + const int neg_one = (int) -1, const_zero = (int) 0; + const int is_unsigned = neg_one > const_zero; + if (is_unsigned) { + if (sizeof(int) < sizeof(long)) { + return PyInt_FromLong((long) value); + } else if (sizeof(int) <= sizeof(unsigned long)) { + return PyLong_FromUnsignedLong((unsigned long) value); + } else if (sizeof(int) <= sizeof(unsigned PY_LONG_LONG)) { + return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value); + } + } else { + if (sizeof(int) <= sizeof(long)) { + return PyInt_FromLong((long) value); + } else if (sizeof(int) <= sizeof(PY_LONG_LONG)) { + return PyLong_FromLongLong((PY_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 + +#define __PYX_VERIFY_RETURN_INT(target_type, func_type, func_value)\ + __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, 0) +#define __PYX_VERIFY_RETURN_INT_EXC(target_type, func_type, func_value)\ + __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, 1) +#define __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, exc)\ + {\ + func_type value = func_value;\ + if (sizeof(target_type) < sizeof(func_type)) {\ + if (unlikely(value != (func_type) (target_type) value)) {\ + func_type zero = 0;\ + if (exc && unlikely(value == (func_type)-1 && PyErr_Occurred()))\ + return (target_type) -1;\ + if (is_unsigned && unlikely(value < zero))\ + goto raise_neg_overflow;\ + else\ + goto raise_overflow;\ + }\ + }\ + return (target_type) value;\ + } + +#if CYTHON_USE_PYLONG_INTERNALS + #include "longintrepr.h" +#endif + +static CYTHON_INLINE int __Pyx_PyInt_As_int(PyObject *x) { + const int neg_one = (int) -1, const_zero = (int) 0; + const int is_unsigned = neg_one > const_zero; +#if PY_MAJOR_VERSION < 3 + if (likely(PyInt_Check(x))) { + if (sizeof(int) < sizeof(long)) { + __PYX_VERIFY_RETURN_INT(int, long, PyInt_AS_LONG(x)) + } else { + long val = PyInt_AS_LONG(x); + if (is_unsigned && unlikely(val < 0)) { + goto raise_neg_overflow; + } + return (int) val; + } + } else +#endif + if (likely(PyLong_Check(x))) { + if (is_unsigned) { +#if CYTHON_USE_PYLONG_INTERNALS + const digit* digits = ((PyLongObject*)x)->ob_digit; + switch (Py_SIZE(x)) { + case 0: return (int) 0; + case 1: __PYX_VERIFY_RETURN_INT(int, digit, digits[0]) + case 2: + if (8 * sizeof(int) > 1 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(int) >= 2 * PyLong_SHIFT) { + return (int) (((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0])); + } + } + break; + case 3: + if (8 * sizeof(int) > 2 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(int) >= 3 * PyLong_SHIFT) { + return (int) (((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])); + } + } + break; + case 4: + if (8 * sizeof(int) > 3 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(int) >= 4 * PyLong_SHIFT) { + return (int) (((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])); + } + } + break; + } +#endif +#if CYTHON_COMPILING_IN_CPYTHON + if (unlikely(Py_SIZE(x) < 0)) { + goto raise_neg_overflow; + } +#else + { + int result = PyObject_RichCompareBool(x, Py_False, Py_LT); + if (unlikely(result < 0)) + return (int) -1; + if (unlikely(result == 1)) + goto raise_neg_overflow; + } +#endif + if (sizeof(int) <= sizeof(unsigned long)) { + __PYX_VERIFY_RETURN_INT_EXC(int, unsigned long, PyLong_AsUnsignedLong(x)) + } else if (sizeof(int) <= sizeof(unsigned PY_LONG_LONG)) { + __PYX_VERIFY_RETURN_INT_EXC(int, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x)) + } + } else { +#if CYTHON_USE_PYLONG_INTERNALS + const digit* digits = ((PyLongObject*)x)->ob_digit; + switch (Py_SIZE(x)) { + case 0: return (int) 0; + case -1: __PYX_VERIFY_RETURN_INT(int, sdigit, -(sdigit) digits[0]) + case 1: __PYX_VERIFY_RETURN_INT(int, digit, +digits[0]) + case -2: + if (8 * sizeof(int) - 1 > 1 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(int) - 1 > 2 * PyLong_SHIFT) { + return (int) (((int)-1)*(((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0]))); + } + } + break; + case 2: + if (8 * sizeof(int) > 1 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(int) - 1 > 2 * PyLong_SHIFT) { + return (int) ((((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0]))); + } + } + break; + case -3: + if (8 * sizeof(int) - 1 > 2 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(int) - 1 > 3 * PyLong_SHIFT) { + return (int) (((int)-1)*(((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0]))); + } + } + break; + case 3: + if (8 * sizeof(int) > 2 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(int) - 1 > 3 * PyLong_SHIFT) { + return (int) ((((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0]))); + } + } + break; + case -4: + if (8 * sizeof(int) - 1 > 3 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(int) - 1 > 4 * PyLong_SHIFT) { + return (int) (((int)-1)*(((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0]))); + } + } + break; + case 4: + if (8 * sizeof(int) > 3 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(int) - 1 > 4 * PyLong_SHIFT) { + return (int) ((((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0]))); + } + } + break; + } +#endif + if (sizeof(int) <= sizeof(long)) { + __PYX_VERIFY_RETURN_INT_EXC(int, long, PyLong_AsLong(x)) + } else if (sizeof(int) <= sizeof(PY_LONG_LONG)) { + __PYX_VERIFY_RETURN_INT_EXC(int, PY_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 PyObject* __Pyx_PyInt_From_enum__NPY_TYPES(enum NPY_TYPES value) { + const enum NPY_TYPES neg_one = (enum NPY_TYPES) -1, const_zero = (enum NPY_TYPES) 0; + const int is_unsigned = neg_one > const_zero; + if (is_unsigned) { + if (sizeof(enum NPY_TYPES) < sizeof(long)) { + return PyInt_FromLong((long) value); + } else if (sizeof(enum NPY_TYPES) <= sizeof(unsigned long)) { + return PyLong_FromUnsignedLong((unsigned long) value); + } else if (sizeof(enum NPY_TYPES) <= sizeof(unsigned PY_LONG_LONG)) { + return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value); + } + } else { + if (sizeof(enum NPY_TYPES) <= sizeof(long)) { + return PyInt_FromLong((long) value); + } else if (sizeof(enum NPY_TYPES) <= sizeof(PY_LONG_LONG)) { + return PyLong_FromLongLong((PY_LONG_LONG) value); + } + } + { + int one = 1; int little = (int)*(unsigned char *)&one; + unsigned char *bytes = (unsigned char *)&value; + return _PyLong_FromByteArray(bytes, sizeof(enum NPY_TYPES), + little, !is_unsigned); + } +} + +static CYTHON_INLINE PyObject* __Pyx_PyInt_From_long(long value) { + const long neg_one = (long) -1, const_zero = (long) 0; + const int is_unsigned = neg_one > const_zero; + if (is_unsigned) { + if (sizeof(long) < sizeof(long)) { + return PyInt_FromLong((long) value); + } else if (sizeof(long) <= sizeof(unsigned long)) { + return PyLong_FromUnsignedLong((unsigned long) value); + } else if (sizeof(long) <= sizeof(unsigned PY_LONG_LONG)) { + return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value); + } + } else { + if (sizeof(long) <= sizeof(long)) { + return PyInt_FromLong((long) value); + } else if (sizeof(long) <= sizeof(PY_LONG_LONG)) { + return PyLong_FromLongLong((PY_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 = (long) 0; + const int is_unsigned = neg_one > const_zero; +#if PY_MAJOR_VERSION < 3 + if (likely(PyInt_Check(x))) { + if (sizeof(long) < sizeof(long)) { + __PYX_VERIFY_RETURN_INT(long, long, PyInt_AS_LONG(x)) + } else { + long val = PyInt_AS_LONG(x); + if (is_unsigned && unlikely(val < 0)) { + goto raise_neg_overflow; + } + return (long) val; + } + } else +#endif + if (likely(PyLong_Check(x))) { + if (is_unsigned) { +#if CYTHON_USE_PYLONG_INTERNALS + const digit* digits = ((PyLongObject*)x)->ob_digit; + switch (Py_SIZE(x)) { + case 0: return (long) 0; + case 1: __PYX_VERIFY_RETURN_INT(long, digit, digits[0]) + case 2: + if (8 * sizeof(long) > 1 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(long) >= 2 * PyLong_SHIFT) { + return (long) (((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0])); + } + } + break; + case 3: + if (8 * sizeof(long) > 2 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(long) >= 3 * PyLong_SHIFT) { + return (long) (((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])); + } + } + break; + case 4: + if (8 * sizeof(long) > 3 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(long) >= 4 * PyLong_SHIFT) { + return (long) (((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])); + } + } + break; + } +#endif +#if CYTHON_COMPILING_IN_CPYTHON + if (unlikely(Py_SIZE(x) < 0)) { + goto raise_neg_overflow; + } +#else + { + int result = PyObject_RichCompareBool(x, Py_False, Py_LT); + if (unlikely(result < 0)) + return (long) -1; + if (unlikely(result == 1)) + goto raise_neg_overflow; + } +#endif + if (sizeof(long) <= sizeof(unsigned long)) { + __PYX_VERIFY_RETURN_INT_EXC(long, unsigned long, PyLong_AsUnsignedLong(x)) + } else if (sizeof(long) <= sizeof(unsigned PY_LONG_LONG)) { + __PYX_VERIFY_RETURN_INT_EXC(long, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x)) + } + } else { +#if CYTHON_USE_PYLONG_INTERNALS + const digit* digits = ((PyLongObject*)x)->ob_digit; + switch (Py_SIZE(x)) { + case 0: return (long) 0; + case -1: __PYX_VERIFY_RETURN_INT(long, sdigit, -(sdigit) digits[0]) + case 1: __PYX_VERIFY_RETURN_INT(long, digit, +digits[0]) + case -2: + if (8 * sizeof(long) - 1 > 1 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) { + return (long) (((long)-1)*(((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0]))); + } + } + break; + case 2: + if (8 * sizeof(long) > 1 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) { + return (long) ((((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0]))); + } + } + break; + case -3: + if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) { + return (long) (((long)-1)*(((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0]))); + } + } + break; + case 3: + if (8 * sizeof(long) > 2 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) { + return (long) ((((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0]))); + } + } + break; + case -4: + if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) { + return (long) (((long)-1)*(((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0]))); + } + } + break; + case 4: + if (8 * sizeof(long) > 3 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) { + return (long) ((((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0]))); + } + } + break; + } +#endif + if (sizeof(long) <= sizeof(long)) { + __PYX_VERIFY_RETURN_INT_EXC(long, long, PyLong_AsLong(x)) + } else if (sizeof(long) <= sizeof(PY_LONG_LONG)) { + __PYX_VERIFY_RETURN_INT_EXC(long, PY_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 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 CYTHON_COMPILING_IN_CPYTHON && (__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) || (defined(PyByteArray_AS_STRING) && defined(PyByteArray_GET_SIZE)) + if (PyByteArray_Check(o)) { + *length = PyByteArray_GET_SIZE(o); + return PyByteArray_AS_STRING(o); + } else +#endif + { + char* result; + int r = PyBytes_AsStringAndSize(o, &result, length); + if (unlikely(r < 0)) { + return NULL; + } else { + return result; + } + } +} +static CYTHON_INLINE int __Pyx_PyObject_IsTrue(PyObject* x) { + int is_true = x == Py_True; + if (is_true | (x == Py_False) | (x == Py_None)) return is_true; + else return PyObject_IsTrue(x); +} +static CYTHON_INLINE 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 __Pyx_NewRef(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))) { + if (sizeof(Py_ssize_t) >= sizeof(long)) + return PyInt_AS_LONG(b); + else + return PyInt_AsSsize_t(x); + } +#endif + if (likely(PyLong_CheckExact(b))) { + #if CYTHON_USE_PYLONG_INTERNALS + const digit* digits = ((PyLongObject*)b)->ob_digit; + const Py_ssize_t size = Py_SIZE(b); + if (likely(__Pyx_sst_abs(size) <= 1)) { + ival = likely(size) ? digits[0] : 0; + if (size == -1) ival = -ival; + return ival; + } else { + switch (size) { + case 2: + if (8 * sizeof(Py_ssize_t) > 2 * PyLong_SHIFT) { + return (Py_ssize_t) (((((size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0])); + } + break; + case -2: + if (8 * sizeof(Py_ssize_t) > 2 * PyLong_SHIFT) { + return -(Py_ssize_t) (((((size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0])); + } + break; + case 3: + if (8 * sizeof(Py_ssize_t) > 3 * PyLong_SHIFT) { + return (Py_ssize_t) (((((((size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0])); + } + break; + case -3: + if (8 * sizeof(Py_ssize_t) > 3 * PyLong_SHIFT) { + return -(Py_ssize_t) (((((((size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0])); + } + break; + case 4: + if (8 * sizeof(Py_ssize_t) > 4 * PyLong_SHIFT) { + return (Py_ssize_t) (((((((((size_t)digits[3]) << PyLong_SHIFT) | (size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0])); + } + break; + case -4: + if (8 * sizeof(Py_ssize_t) > 4 * PyLong_SHIFT) { + return -(Py_ssize_t) (((((((((size_t)digits[3]) << PyLong_SHIFT) | (size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0])); + } + break; + } + } + #endif + return PyLong_AsSsize_t(b); + } + x = PyNumber_Index(b); + if (!x) return -1; + ival = PyInt_AsSsize_t(x); + Py_DECREF(x); + return ival; +} +static CYTHON_INLINE PyObject * __Pyx_PyInt_FromSize_t(size_t ival) { + return PyInt_FromSize_t(ival); +} + + +#endif /* Py_PYTHON_H */ diff --git a/ot/lp/emd.pyx b/ot/lp/emd.pyx new file mode 100644 index 0000000..753b195 --- /dev/null +++ b/ot/lp/emd.pyx @@ -0,0 +1,71 @@ +# -*- coding: utf-8 -*- +""" +Created on Thu Sep 11 08:42:08 2014 + +@author: rflamary +""" +import numpy as np +cimport numpy as np + +cimport cython + + + +cdef extern from "EMD.h": + void EMD_wrap(int n1,int n2, double *X, double *Y,double *D, double *G, double *cost) + + + +@cython.boundscheck(False) +@cython.wraparound(False) +def emd( np.ndarray[double, ndim=1, mode="c"] a,np.ndarray[double, ndim=1, mode="c"] b,np.ndarray[double, ndim=2, mode="c"] M): + """ + Solves the Earth Movers distance problem and returns the optimal transport matrix + + gamm=emd(a,b,M) + + .. math:: + \gamma = arg\min_\gamma <\gamma,M>_F + + s.t. \gamma 1 = a + + \gamma^T 1= b + + \gamma\geq 0 + where : + + - M is the metric cost matrix + - a and b are the sample weights + + Parameters + ---------- + a : (ns,) ndarray + samples in the source domain (uniform waigth if empty) + b : (nt,) ndarray + samples in the target domain (uniform waigth if empty) + M : (ns,nt) ndarray + loss matrix + + + Returns + ------- + gamma: (ns x nt) ndarray + Optimal transportation matrix for the given parameters + + """ + cdef int n1= M.shape[0] + cdef int n2= M.shape[1] + + cdef float cost=0 + cdef np.ndarray[double, ndim=2, mode="c"] G=np.zeros([n1, n2]) + + if not len(a): + a=np.ones((n1,))/n1 + + if not len(b): + b=np.ones((n2,))/n2 + + # calling the function + EMD_wrap(n1,n2, a.data, b.data, M.data, G.data, &cost) + + return G diff --git a/ot/lp/full_bipartitegraph.h b/ot/lp/full_bipartitegraph.h new file mode 100644 index 0000000..87a1bec --- /dev/null +++ b/ot/lp/full_bipartitegraph.h @@ -0,0 +1,215 @@ +/* -*- mode: C++; indent-tabs-mode: nil; -*- + * + * This file has been adapted by Nicolas Bonneel (2013), + * from full_graph.h from LEMON, a generic C++ optimization library, + * to implement a lightweight fully connected bipartite graph. A previous + * version of this file is used as part of the Displacement Interpolation + * project, + * Web: http://www.cs.ubc.ca/labs/imager/tr/2011/DisplacementInterpolation/ + * + * + **** Original file Copyright Notice : + * Copyright (C) 2003-2010 + * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport + * (Egervary Research Group on Combinatorial Optimization, EGRES). + * + * Permission to use, modify and distribute this software is granted + * provided that this copyright notice appears in all copies. For + * precise terms see the accompanying LICENSE file. + * + * This software is provided "AS IS" with no warranty of any kind, + * express or implied, and with no claim as to its suitability for any + * purpose. + * + */ + +#ifndef LEMON_FULL_BIPARTITE_GRAPH_H +#define LEMON_FULL_BIPARTITE_GRAPH_H + +#include "core.h" + +///\ingroup graphs +///\file +///\brief FullBipartiteDigraph and FullBipartiteGraph classes. + + +namespace lemon { + + + class FullBipartiteDigraphBase { + public: + + typedef FullBipartiteDigraphBase Digraph; + + //class Node; + typedef int Node; + //class Arc; + typedef long long Arc; + + protected: + + int _node_num; + long long _arc_num; + + FullBipartiteDigraphBase() {} + + void construct(int n1, int n2) { _node_num = n1+n2; _arc_num = n1 * n2; _n1=n1; _n2=n2;} + + public: + + int _n1, _n2; + + + Node operator()(int ix) const { return Node(ix); } + static int index(const Node& node) { return node; } + + Arc arc(const Node& s, const Node& t) const { + if (s<_n1 && t>=_n1) + return Arc(s * _n2 + (t-_n1) ); + else + return Arc(-1); + } + + int nodeNum() const { return _node_num; } + long long arcNum() const { return _arc_num; } + + int maxNodeId() const { return _node_num - 1; } + long long maxArcId() const { return _arc_num - 1; } + + Node source(Arc arc) const { return arc / _n2; } + Node target(Arc arc) const { return (arc % _n2) + _n1; } + + static int id(Node node) { return node; } + static long long id(Arc arc) { return arc; } + + static Node nodeFromId(int id) { return Node(id);} + static Arc arcFromId(int id) { return Arc(id);} + + + Arc findArc(Node s, Node t, Arc prev = -1) const { + return prev == -1 ? arc(s, t) : -1; + } + + void first(Node& node) const { + node = _node_num - 1; + } + + static void next(Node& node) { + --node; + } + + void first(Arc& arc) const { + arc = _arc_num - 1; + } + + static void next(Arc& arc) { + --arc; + } + + void firstOut(Arc& arc, const Node& node) const { + if (node>=_n1) + arc = -1; + else + arc = (node + 1) * _n2 - 1; + } + + void nextOut(Arc& arc) const { + if (arc % _n2 == 0) arc = 0; + --arc; + } + + void firstIn(Arc& arc, const Node& node) const { + if (node<_n1) + arc = -1; + else + arc = _arc_num + node - _node_num; + } + + void nextIn(Arc& arc) const { + arc -= _n2; + if (arc < 0) arc = -1; + } + + }; + + /// \ingroup graphs + /// + /// \brief A directed full graph class. + /// + /// FullBipartiteDigraph is a simple and fast implmenetation of directed full + /// (complete) graphs. It contains an arc from each node to each node + /// (including a loop for each node), therefore the number of arcs + /// is the square of the number of nodes. + /// This class is completely static and it needs constant memory space. + /// Thus you can neither add nor delete nodes or arcs, however + /// the structure can be resized using resize(). + /// + /// This type fully conforms to the \ref concepts::Digraph "Digraph concept". + /// Most of its member functions and nested classes are documented + /// only in the concept class. + /// + /// This class provides constant time counting for nodes and arcs. + /// + /// \note FullBipartiteDigraph and FullBipartiteGraph classes are very similar, + /// but there are two differences. While this class conforms only + /// to the \ref concepts::Digraph "Digraph" concept, FullBipartiteGraph + /// conforms to the \ref concepts::Graph "Graph" concept, + /// moreover FullBipartiteGraph does not contain a loop for each + /// node as this class does. + /// + /// \sa FullBipartiteGraph + class FullBipartiteDigraph : public FullBipartiteDigraphBase { + typedef FullBipartiteDigraphBase Parent; + + public: + + /// \brief Default constructor. + /// + /// Default constructor. The number of nodes and arcs will be zero. + FullBipartiteDigraph() { construct(0,0); } + + /// \brief Constructor + /// + /// Constructor. + /// \param n The number of the nodes. + FullBipartiteDigraph(int n1, int n2) { construct(n1, n2); } + + + /// \brief Returns the node with the given index. + /// + /// Returns the node with the given index. Since this structure is + /// completely static, the nodes can be indexed with integers from + /// the range [0..nodeNum()-1]. + /// The index of a node is the same as its ID. + /// \sa index() + Node operator()(int ix) const { return Parent::operator()(ix); } + + /// \brief Returns the index of the given node. + /// + /// Returns the index of the given node. Since this structure is + /// completely static, the nodes can be indexed with integers from + /// the range [0..nodeNum()-1]. + /// The index of a node is the same as its ID. + /// \sa operator()() + static int index(const Node& node) { return Parent::index(node); } + + /// \brief Returns the arc connecting the given nodes. + /// + /// Returns the arc connecting the given nodes. + /*Arc arc(Node u, Node v) const { + return Parent::arc(u, v); + }*/ + + /// \brief Number of nodes. + int nodeNum() const { return Parent::nodeNum(); } + /// \brief Number of arcs. + long long arcNum() const { return Parent::arcNum(); } + }; + + + + +} //namespace lemon + + +#endif //LEMON_FULL_GRAPH_H diff --git a/ot/lp/network_simplex_simple.h b/ot/lp/network_simplex_simple.h new file mode 100644 index 0000000..64856a0 --- /dev/null +++ b/ot/lp/network_simplex_simple.h @@ -0,0 +1,1543 @@ +/* -*- mode: C++; indent-tabs-mode: nil; -*- + * + * + * This file has been adapted by Nicolas Bonneel (2013), + * from network_simplex.h from LEMON, a generic C++ optimization library, + * to implement a lightweight network simplex for mass transport, more + * memory efficient that the original file. A previous version of this file + * is used as part of the Displacement Interpolation project, + * Web: http://www.cs.ubc.ca/labs/imager/tr/2011/DisplacementInterpolation/ + * + * + **** Original file Copyright Notice : + * + * Copyright (C) 2003-2010 + * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport + * (Egervary Research Group on Combinatorial Optimization, EGRES). + * + * Permission to use, modify and distribute this software is granted + * provided that this copyright notice appears in all copies. For + * precise terms see the accompanying LICENSE file. + * + * This software is provided "AS IS" with no warranty of any kind, + * express or implied, and with no claim as to its suitability for any + * purpose. + * + */ + +#ifndef LEMON_NETWORK_SIMPLEX_SIMPLE_H +#define LEMON_NETWORK_SIMPLEX_SIMPLE_H +#define DEBUG_LVL 0 +#define EPSILON 10*2.2204460492503131e-016 +#define MAX_DEBUG_ITER 100000 + + +/// \ingroup min_cost_flow_algs +/// +/// \file +/// \brief Network Simplex algorithm for finding a minimum cost flow. + +// if your compiler has troubles with stdext or hashmaps, just comment the following line to use a slower std::map instead +//#define HASHMAP + +#include +#include +#include +#ifdef HASHMAP +#include +#else +#include +#endif +#include +//#include "core.h" +//#include "lmath.h" + +//#include "sparse_array_n.h" +#include "full_bipartitegraph.h" + +#define INVALIDNODE -1 +#define INVALID (-1) + +namespace lemon { + + + template + class ProxyObject; + + template + class SparseValueVector + { + public: + SparseValueVector(int n=0) + { + } + void resize(int n=0){}; + T operator[](const int id) const + { +#ifdef HASHMAP + typename stdext::hash_map::const_iterator it = data.find(id); +#else + typename std::map::const_iterator it = data.find(id); +#endif + if (it==data.end()) + return 0; + else + return it->second; + } + + ProxyObject operator[](const int id) + { + return ProxyObject( this, id ); + } + + //private: +#ifdef HASHMAP + stdext::hash_map data; +#else + std::map data; +#endif + + }; + + template + class ProxyObject { + public: + ProxyObject( SparseValueVector *v, int idx ){_v=v; _idx=idx;}; + ProxyObject & operator=( const T &v ) { + // If we get here, we know that operator[] was called to perform a write access, + // so we can insert an item in the vector if needed + if (v!=0) + _v->data[_idx]=v; + return *this; + } + + operator T() { + // If we get here, we know that operator[] was called to perform a read access, + // so we can simply return the existing object +#ifdef HASHMAP + typename stdext::hash_map::iterator it = _v->data.find(_idx); +#else + typename std::map::iterator it = _v->data.find(_idx); +#endif + if (it==_v->data.end()) + return 0; + else + return it->second; + } + + void operator+=(T val) + { + if (val==0) return; +#ifdef HASHMAP + typename stdext::hash_map::iterator it = _v->data.find(_idx); +#else + typename std::map::iterator it = _v->data.find(_idx); +#endif + if (it==_v->data.end()) + _v->data[_idx] = val; + else + { + T sum = it->second + val; + if (sum==0) + _v->data.erase(it); + else + it->second = sum; + } + } + void operator-=(T val) + { + if (val==0) return; +#ifdef HASHMAP + typename stdext::hash_map::iterator it = _v->data.find(_idx); +#else + typename std::map::iterator it = _v->data.find(_idx); +#endif + if (it==_v->data.end()) + _v->data[_idx] = -val; + else + { + T sum = it->second - val; + if (sum==0) + _v->data.erase(it); + else + it->second = sum; + } + } + + SparseValueVector *_v; + int _idx; + }; + + + + /// \addtogroup min_cost_flow_algs + /// @{ + + /// \brief Implementation of the primal Network Simplex algorithm + /// for finding a \ref min_cost_flow "minimum cost flow". + /// + /// \ref NetworkSimplexSimple implements the primal Network Simplex algorithm + /// for finding a \ref min_cost_flow "minimum cost flow" + /// \ref amo93networkflows, \ref dantzig63linearprog, + /// \ref kellyoneill91netsimplex. + /// This algorithm is a highly efficient specialized version of the + /// linear programming simplex method directly for the minimum cost + /// flow problem. + /// + /// In general, %NetworkSimplexSimple is the fastest implementation available + /// in LEMON for this problem. + /// Moreover, it supports both directions of the supply/demand inequality + /// constraints. For more information, see \ref SupplyType. + /// + /// Most of the parameters of the problem (except for the digraph) + /// can be given using separate functions, and the algorithm can be + /// executed using the \ref run() function. If some parameters are not + /// specified, then default values will be used. + /// + /// \tparam GR The digraph type the algorithm runs on. + /// \tparam V The number type used for flow amounts, capacity bounds + /// and supply values in the algorithm. By default, it is \c int. + /// \tparam C The number type used for costs and potentials in the + /// algorithm. By default, it is the same as \c V. + /// + /// \warning Both number types must be signed and all input data must + /// be integer. + /// + /// \note %NetworkSimplexSimple provides five different pivot rule + /// implementations, from which the most efficient one is used + /// by default. For more information, see \ref PivotRule. + template + class NetworkSimplexSimple + { + public: + + /// \brief Constructor. + /// + /// The constructor of the class. + /// + /// \param graph The digraph the algorithm runs on. + /// \param arc_mixing Indicate if the arcs have to be stored in a + /// mixed order in the internal data structure. + /// In special cases, it could lead to better overall performance, + /// but it is usually slower. Therefore it is disabled by default. + NetworkSimplexSimple(const GR& graph, bool arc_mixing, int nbnodes, long long nb_arcs,double maxiters) : + _graph(graph), //_arc_id(graph), + _arc_mixing(arc_mixing), _init_nb_nodes(nbnodes), _init_nb_arcs(nb_arcs), + MAX(std::numeric_limits::max()), + INF(std::numeric_limits::has_infinity ? + std::numeric_limits::infinity() : MAX) + { + // Reset data structures + reset(); + max_iter=maxiters; + } + + /// The type of the flow amounts, capacity bounds and supply values + typedef V Value; + /// The type of the arc costs + typedef C Cost; + + public: + + /// \brief Problem type constants for the \c run() function. + /// + /// Enum type containing the problem type constants that can be + /// returned by the \ref run() function of the algorithm. + enum ProblemType { + /// The problem has no feasible solution (flow). + INFEASIBLE, + /// The problem has optimal solution (i.e. it is feasible and + /// bounded), and the algorithm has found optimal flow and node + /// potentials (primal and dual solutions). + OPTIMAL, + /// The objective function of the problem is unbounded, i.e. + /// there is a directed cycle having negative total cost and + /// infinite upper bound. + UNBOUNDED + }; + + /// \brief Constants for selecting the type of the supply constraints. + /// + /// Enum type containing constants for selecting the supply type, + /// i.e. the direction of the inequalities in the supply/demand + /// constraints of the \ref min_cost_flow "minimum cost flow problem". + /// + /// The default supply type is \c GEQ, the \c LEQ type can be + /// selected using \ref supplyType(). + /// The equality form is a special case of both supply types. + enum SupplyType { + /// This option means that there are "greater or equal" + /// supply/demand constraints in the definition of the problem. + GEQ, + /// This option means that there are "less or equal" + /// supply/demand constraints in the definition of the problem. + LEQ + }; + + + + private: + + double max_iter; + TEMPLATE_DIGRAPH_TYPEDEFS(GR); + + typedef std::vector IntVector; + typedef std::vector UHalfIntVector; + typedef std::vector ValueVector; + typedef std::vector CostVector; + // typedef SparseValueVector CostVector; + typedef std::vector BoolVector; + // Note: vector is used instead of vector for efficiency reasons + + // State constants for arcs + enum ArcState { + STATE_UPPER = -1, + STATE_TREE = 0, + STATE_LOWER = 1 + }; + + typedef std::vector StateVector; + // Note: vector is used instead of vector for + // efficiency reasons + + private: + + // Data related to the underlying digraph + const GR &_graph; + int _node_num; + int _arc_num; + int _all_arc_num; + int _search_arc_num; + + // Parameters of the problem + SupplyType _stype; + Value _sum_supply; + + inline int _node_id(int n) const {return _node_num-n-1;} ; + + //IntArcMap _arc_id; + UHalfIntVector _source; + UHalfIntVector _target; + bool _arc_mixing; + public: + // Node and arc data + CostVector _cost; + ValueVector _supply; + ValueVector _flow; + //SparseValueVector _flow; + CostVector _pi; + + + private: + // Data for storing the spanning tree structure + IntVector _parent; + IntVector _pred; + IntVector _thread; + IntVector _rev_thread; + IntVector _succ_num; + IntVector _last_succ; + IntVector _dirty_revs; + BoolVector _forward; + StateVector _state; + int _root; + + // Temporary data used in the current pivot iteration + int in_arc, join, u_in, v_in, u_out, v_out; + int first, second, right, last; + int stem, par_stem, new_stem; + Value delta; + + const Value MAX; + + int mixingCoeff; + + public: + + /// \brief Constant for infinite upper bounds (capacities). + /// + /// Constant for infinite upper bounds (capacities). + /// It is \c std::numeric_limits::infinity() if available, + /// \c std::numeric_limits::max() otherwise. + const Value INF; + + private: + + // thank you to DVK and MizardX from StackOverflow for this function! + inline int sequence(int k) const { + int smallv = (k > num_total_big_subsequence_numbers) & 1; + + k -= num_total_big_subsequence_numbers * smallv; + int subsequence_length2 = subsequence_length- smallv; + int subsequence_num = (k / subsequence_length2) + num_big_subseqiences * smallv; + int subsequence_offset = (k % subsequence_length2) * mixingCoeff; + + return subsequence_offset + subsequence_num; + } + int subsequence_length; + int num_big_subseqiences; + int num_total_big_subsequence_numbers; + + inline int getArcID(const Arc &arc) const + { + //int n = _arc_num-arc._id-1; + int n = _arc_num-GR::id(arc)-1; + + //int a = mixingCoeff*(n%mixingCoeff) + n/mixingCoeff; + //int b = _arc_id[arc]; + if (_arc_mixing) + return sequence(n); + else + return n; + } + + // finally unused because too slow + inline int getSource(const int arc) const + { + //int a = _source[arc]; + //return a; + + int n = _arc_num-arc-1; + if (_arc_mixing) + n = mixingCoeff*(n%mixingCoeff) + n/mixingCoeff; + + int b; + if (n>=0) + b = _node_id(_graph.source(GR::arcFromId( n ) )); + else + { + n = arc+1-_arc_num; + if ( n<=_node_num) + b = _node_num; + else + if ( n>=_graph._n1) + b = _graph._n1; + else + b = _graph._n1-n; + } + + return b; + } + + + + // Implementation of the Block Search pivot rule + class BlockSearchPivotRule + { + private: + + // References to the NetworkSimplexSimple class + const UHalfIntVector &_source; + const UHalfIntVector &_target; + const CostVector &_cost; + const StateVector &_state; + const CostVector &_pi; + int &_in_arc; + int _search_arc_num; + + // Pivot rule data + int _block_size; + int _next_arc; + NetworkSimplexSimple &_ns; + + public: + + // Constructor + BlockSearchPivotRule(NetworkSimplexSimple &ns) : + _source(ns._source), _target(ns._target), + _cost(ns._cost), _state(ns._state), _pi(ns._pi), + _in_arc(ns.in_arc), _search_arc_num(ns._search_arc_num), + _next_arc(0),_ns(ns) + { + // The main parameters of the pivot rule + const double BLOCK_SIZE_FACTOR = 1.0; + const int MIN_BLOCK_SIZE = 10; + + _block_size = std::max( int(BLOCK_SIZE_FACTOR * + std::sqrt(double(_search_arc_num))), + MIN_BLOCK_SIZE ); + } + // Find next entering arc + bool findEnteringArc() { + Cost c, min = 0; + int e; + int cnt = _block_size; + double a; + for (e = _next_arc; e != _search_arc_num; ++e) { + c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); + if (c < min) { + min = c; + _in_arc = e; + } + if (--cnt == 0) { + a=fabs(_pi[_source[_in_arc]])>fabs(_pi[_target[_in_arc]]) ? fabs(_pi[_source[_in_arc]]):fabs(_pi[_target[_in_arc]]); + a=a>fabs(_cost[_in_arc])?a:fabs(_cost[_in_arc]); + if (min < -EPSILON*a) goto search_end; + cnt = _block_size; + } + } + for (e = 0; e != _next_arc; ++e) { + c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); + if (c < min) { + min = c; + _in_arc = e; + } + if (--cnt == 0) { + a=fabs(_pi[_source[_in_arc]])>fabs(_pi[_target[_in_arc]]) ? fabs(_pi[_source[_in_arc]]):fabs(_pi[_target[_in_arc]]); + a=a>fabs(_cost[_in_arc])?a:fabs(_cost[_in_arc]); + if (min < -EPSILON*a) goto search_end; + cnt = _block_size; + } + } + a=fabs(_pi[_source[_in_arc]])>fabs(_pi[_target[_in_arc]]) ? fabs(_pi[_source[_in_arc]]):fabs(_pi[_target[_in_arc]]); + a=a>fabs(_cost[_in_arc])?a:fabs(_cost[_in_arc]); + if (min >= -EPSILON*a) return false; + + search_end: + _next_arc = e; + return true; + } + + }; //class BlockSearchPivotRule + + + + public: + + + + int _init_nb_nodes; + long long _init_nb_arcs; + + /// \name Parameters + /// The parameters of the algorithm can be specified using these + /// functions. + + /// @{ + + + /// \brief Set the costs of the arcs. + /// + /// This function sets the costs of the arcs. + /// If it is not used before calling \ref run(), the costs + /// will be set to \c 1 on all arcs. + /// + /// \param map An arc map storing the costs. + /// Its \c Value type must be convertible to the \c Cost type + /// of the algorithm. + /// + /// \return (*this) + template + NetworkSimplexSimple& costMap(const CostMap& map) { + Arc a; _graph.first(a); + for (; a != INVALID; _graph.next(a)) { + _cost[getArcID(a)] = map[a]; + } + return *this; + } + + + /// \brief Set the costs of one arc. + /// + /// This function sets the costs of one arcs. + /// Done for memory reasons + /// + /// \param arc An arc. + /// \param arc A cost + /// + /// \return (*this) + template + NetworkSimplexSimple& setCost(const Arc& arc, const Value cost) { + _cost[getArcID(arc)] = cost; + return *this; + } + + + /// \brief Set the supply values of the nodes. + /// + /// This function sets the supply values of the nodes. + /// If neither this function nor \ref stSupply() is used before + /// calling \ref run(), the supply of each node will be set to zero. + /// + /// \param map A node map storing the supply values. + /// Its \c Value type must be convertible to the \c Value type + /// of the algorithm. + /// + /// \return (*this) + template + NetworkSimplexSimple& supplyMap(const SupplyMap& map) { + Node n; _graph.first(n); + for (; n != INVALIDNODE; _graph.next(n)) { + _supply[_node_id(n)] = map[n]; + } + return *this; + } + template + NetworkSimplexSimple& supplyMap(const SupplyMap* map1, int n1, const SupplyMap* map2, int n2) { + Node n; _graph.first(n); + for (; n != INVALIDNODE; _graph.next(n)) { + if (n + NetworkSimplexSimple& supplyMapAll(SupplyMap val1, int n1, SupplyMap val2, int n2) { + Node n; _graph.first(n); + for (; n != INVALIDNODE; _graph.next(n)) { + if (n(*this) + NetworkSimplexSimple& stSupply(const Node& s, const Node& t, Value k) { + for (int i = 0; i != _node_num; ++i) { + _supply[i] = 0; + } + _supply[_node_id(s)] = k; + _supply[_node_id(t)] = -k; + return *this; + } + + /// \brief Set the type of the supply constraints. + /// + /// This function sets the type of the supply/demand constraints. + /// If it is not used before calling \ref run(), the \ref GEQ supply + /// type will be used. + /// + /// For more information, see \ref SupplyType. + /// + /// \return (*this) + NetworkSimplexSimple& supplyType(SupplyType supply_type) { + _stype = supply_type; + return *this; + } + + /// @} + + /// \name Execution Control + /// The algorithm can be executed using \ref run(). + + /// @{ + + /// \brief Run the algorithm. + /// + /// This function runs the algorithm. + /// The paramters can be specified using functions \ref lowerMap(), + /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply(), + /// \ref supplyType(). + /// For example, + /// \code + /// NetworkSimplexSimple ns(graph); + /// ns.lowerMap(lower).upperMap(upper).costMap(cost) + /// .supplyMap(sup).run(); + /// \endcode + /// + /// This function can be called more than once. All the given parameters + /// are kept for the next call, unless \ref resetParams() or \ref reset() + /// is used, thus only the modified parameters have to be set again. + /// If the underlying digraph was also modified after the construction + /// of the class (or the last \ref reset() call), then the \ref reset() + /// function must be called. + /// + /// \param pivot_rule The pivot rule that will be used during the + /// algorithm. For more information, see \ref PivotRule. + /// + /// \return \c INFEASIBLE if no feasible flow exists, + /// \n \c OPTIMAL if the problem has optimal solution + /// (i.e. it is feasible and bounded), and the algorithm has found + /// optimal flow and node potentials (primal and dual solutions), + /// \n \c UNBOUNDED if the objective function of the problem is + /// unbounded, i.e. there is a directed cycle having negative total + /// cost and infinite upper bound. + /// + /// \see ProblemType, PivotRule + /// \see resetParams(), reset() + ProblemType run() { +#if DEBUG_LVL>0 + mexPrintf("OPTIMAL = %d\nINFEASIBLE = %d\nUNBOUNDED = %d\n",OPTIMAL,INFEASIBLE,UNBOUNDED); + mexEvalString("drawnow;"); +#endif + + if (!init()) return INFEASIBLE; +#if DEBUG_LVL>0 + mexPrintf("Init done, starting iterations\n"); + mexEvalString("drawnow;"); +#endif + return start(); + } + + /// \brief Reset all the parameters that have been given before. + /// + /// This function resets all the paramaters that have been given + /// before using functions \ref lowerMap(), \ref upperMap(), + /// \ref costMap(), \ref supplyMap(), \ref stSupply(), \ref supplyType(). + /// + /// It is useful for multiple \ref run() calls. Basically, all the given + /// parameters are kept for the next \ref run() call, unless + /// \ref resetParams() or \ref reset() is used. + /// If the underlying digraph was also modified after the construction + /// of the class or the last \ref reset() call, then the \ref reset() + /// function must be used, otherwise \ref resetParams() is sufficient. + /// + /// For example, + /// \code + /// NetworkSimplexSimple ns(graph); + /// + /// // First run + /// ns.lowerMap(lower).upperMap(upper).costMap(cost) + /// .supplyMap(sup).run(); + /// + /// // Run again with modified cost map (resetParams() is not called, + /// // so only the cost map have to be set again) + /// cost[e] += 100; + /// ns.costMap(cost).run(); + /// + /// // Run again from scratch using resetParams() + /// // (the lower bounds will be set to zero on all arcs) + /// ns.resetParams(); + /// ns.upperMap(capacity).costMap(cost) + /// .supplyMap(sup).run(); + /// \endcode + /// + /// \return (*this) + /// + /// \see reset(), run() + NetworkSimplexSimple& resetParams() { + for (int i = 0; i != _node_num; ++i) { + _supply[i] = 0; + } + for (int i = 0; i != _arc_num; ++i) { + _cost[i] = 1; + } + _stype = GEQ; + return *this; + } + + + + int divid (int x, int y) + { + return (x-x%y)/y; + } + + /// \brief Reset the internal data structures and all the parameters + /// that have been given before. + /// + /// This function resets the internal data structures and all the + /// paramaters that have been given before using functions \ref lowerMap(), + /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply(), + /// \ref supplyType(). + /// + /// It is useful for multiple \ref run() calls. Basically, all the given + /// parameters are kept for the next \ref run() call, unless + /// \ref resetParams() or \ref reset() is used. + /// If the underlying digraph was also modified after the construction + /// of the class or the last \ref reset() call, then the \ref reset() + /// function must be used, otherwise \ref resetParams() is sufficient. + /// + /// See \ref resetParams() for examples. + /// + /// \return (*this) + /// + /// \see resetParams(), run() + NetworkSimplexSimple& reset() { + // Resize vectors + _node_num = _init_nb_nodes; + _arc_num = _init_nb_arcs; + int all_node_num = _node_num + 1; + int max_arc_num = _arc_num + 2 * _node_num; + + _source.resize(max_arc_num); + _target.resize(max_arc_num); + + _cost.resize(max_arc_num); + _supply.resize(all_node_num); + _flow.resize(max_arc_num); + _pi.resize(all_node_num); + + _parent.resize(all_node_num); + _pred.resize(all_node_num); + _forward.resize(all_node_num); + _thread.resize(all_node_num); + _rev_thread.resize(all_node_num); + _succ_num.resize(all_node_num); + _last_succ.resize(all_node_num); + _state.resize(max_arc_num); + + + //_arc_mixing=false; + if (_arc_mixing) { + // Store the arcs in a mixed order + int k = std::max(int(std::sqrt(double(_arc_num))), 10); + mixingCoeff = k; + subsequence_length = _arc_num / mixingCoeff + 1; + num_big_subseqiences = _arc_num % mixingCoeff; + num_total_big_subsequence_numbers = subsequence_length * num_big_subseqiences; + + int i = 0, j = 0; + Arc a; _graph.first(a); + for (; a != INVALID; _graph.next(a)) { + _source[i] = _node_id(_graph.source(a)); + _target[i] = _node_id(_graph.target(a)); + //_arc_id[a] = i; + if ((i += k) >= _arc_num) i = ++j; + } + } else { + // Store the arcs in the original order + int i = 0; + Arc a; _graph.first(a); + for (; a != INVALID; _graph.next(a), ++i) { + _source[i] = _node_id(_graph.source(a)); + _target[i] = _node_id(_graph.target(a)); + //_arc_id[a] = i; + } + } + + // Reset parameters + resetParams(); + return *this; + } + + /// @} + + /// \name Query Functions + /// The results of the algorithm can be obtained using these + /// functions.\n + /// The \ref run() function must be called before using them. + + /// @{ + + /// \brief Return the total cost of the found flow. + /// + /// This function returns the total cost of the found flow. + /// Its complexity is O(e). + /// + /// \note The return type of the function can be specified as a + /// template parameter. For example, + /// \code + /// ns.totalCost(); + /// \endcode + /// It is useful if the total cost cannot be stored in the \c Cost + /// type of the algorithm, which is the default return type of the + /// function. + /// + /// \pre \ref run() must be called before using this function. + /*template + Number totalCost() const { + Number c = 0; + for (ArcIt a(_graph); a != INVALID; ++a) { + int i = getArcID(a); + c += Number(_flow[i]) * Number(_cost[i]); + } + return c; + }*/ + + template + Number totalCost() const { + Number c = 0; + + /*#ifdef HASHMAP + typename stdext::hash_map::const_iterator it; + #else + typename std::map::const_iterator it; + #endif + for (it = _flow.data.begin(); it!=_flow.data.end(); ++it) + c += Number(it->second) * Number(_cost[it->first]); + return c;*/ + + for (int i=0; i<_flow.size(); i++) + c += _flow[i] * Number(_cost[i]); + return c; + + } + +#ifndef DOXYGEN + Cost totalCost() const { + return totalCost(); + } +#endif + + /// \brief Return the flow on the given arc. + /// + /// This function returns the flow on the given arc. + /// + /// \pre \ref run() must be called before using this function. + Value flow(const Arc& a) const { + return _flow[getArcID(a)]; + } + + /// \brief Return the flow map (the primal solution). + /// + /// This function copies the flow value on each arc into the given + /// map. The \c Value type of the algorithm must be convertible to + /// the \c Value type of the map. + /// + /// \pre \ref run() must be called before using this function. + template + void flowMap(FlowMap &map) const { + Arc a; _graph.first(a); + for (; a != INVALID; _graph.next(a)) { + map.set(a, _flow[getArcID(a)]); + } + } + + /// \brief Return the potential (dual value) of the given node. + /// + /// This function returns the potential (dual value) of the + /// given node. + /// + /// \pre \ref run() must be called before using this function. + Cost potential(const Node& n) const { + return _pi[_node_id(n)]; + } + + /// \brief Return the potential map (the dual solution). + /// + /// This function copies the potential (dual value) of each node + /// into the given map. + /// The \c Cost type of the algorithm must be convertible to the + /// \c Value type of the map. + /// + /// \pre \ref run() must be called before using this function. + template + void potentialMap(PotentialMap &map) const { + Node n; _graph.first(n); + for (; n != INVALID; _graph.next(n)) { + map.set(n, _pi[_node_id(n)]); + } + } + + /// @} + + private: + + // Initialize internal data structures + bool init() { + if (_node_num == 0) return false; + /* + // Check the sum of supply values + _sum_supply = 0; + for (int i = 0; i != _node_num; ++i) { + _sum_supply += _supply[i]; + } + if ( !((_stype == GEQ && _sum_supply <= _epsilon ) || + (_stype == LEQ && _sum_supply >= -_epsilon )) ) return false; + */ + + // Initialize artifical cost + Cost ART_COST; + if (std::numeric_limits::is_exact) { + ART_COST = std::numeric_limits::max() / 2 + 1; + } else { + ART_COST = 0; + for (int i = 0; i != _arc_num; ++i) { + if (_cost[i] > ART_COST) ART_COST = _cost[i]; + } + ART_COST = (ART_COST + 1) * _node_num; + } + + // Initialize arc maps + for (int i = 0; i != _arc_num; ++i) { + //_flow[i] = 0; //by default, the sparse matrix is empty + _state[i] = STATE_LOWER; + } + + // Set data for the artificial root node + _root = _node_num; + _parent[_root] = -1; + _pred[_root] = -1; + _thread[_root] = 0; + _rev_thread[0] = _root; + _succ_num[_root] = _node_num + 1; + _last_succ[_root] = _root - 1; + _supply[_root] = -_sum_supply; + _pi[_root] = 0; + + // Add artificial arcs and initialize the spanning tree data structure + if (_sum_supply == 0) { + // EQ supply constraints + _search_arc_num = _arc_num; + _all_arc_num = _arc_num + _node_num; + for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) { + _parent[u] = _root; + _pred[u] = e; + _thread[u] = u + 1; + _rev_thread[u + 1] = u; + _succ_num[u] = 1; + _last_succ[u] = u; + _state[e] = STATE_TREE; + if (_supply[u] >= 0) { + _forward[u] = true; + _pi[u] = 0; + _source[e] = u; + _target[e] = _root; + _flow[e] = _supply[u]; + _cost[e] = 0; + } else { + _forward[u] = false; + _pi[u] = ART_COST; + _source[e] = _root; + _target[e] = u; + _flow[e] = -_supply[u]; + _cost[e] = ART_COST; + } + } + } + else if (_sum_supply > 0) { + // LEQ supply constraints + _search_arc_num = _arc_num + _node_num; + int f = _arc_num + _node_num; + for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) { + _parent[u] = _root; + _thread[u] = u + 1; + _rev_thread[u + 1] = u; + _succ_num[u] = 1; + _last_succ[u] = u; + if (_supply[u] >= 0) { + _forward[u] = true; + _pi[u] = 0; + _pred[u] = e; + _source[e] = u; + _target[e] = _root; + _flow[e] = _supply[u]; + _cost[e] = 0; + _state[e] = STATE_TREE; + } else { + _forward[u] = false; + _pi[u] = ART_COST; + _pred[u] = f; + _source[f] = _root; + _target[f] = u; + _flow[f] = -_supply[u]; + _cost[f] = ART_COST; + _state[f] = STATE_TREE; + _source[e] = u; + _target[e] = _root; + //_flow[e] = 0; //by default, the sparse matrix is empty + _cost[e] = 0; + _state[e] = STATE_LOWER; + ++f; + } + } + _all_arc_num = f; + } + else { + // GEQ supply constraints + _search_arc_num = _arc_num + _node_num; + int f = _arc_num + _node_num; + for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) { + _parent[u] = _root; + _thread[u] = u + 1; + _rev_thread[u + 1] = u; + _succ_num[u] = 1; + _last_succ[u] = u; + if (_supply[u] <= 0) { + _forward[u] = false; + _pi[u] = 0; + _pred[u] = e; + _source[e] = _root; + _target[e] = u; + _flow[e] = -_supply[u]; + _cost[e] = 0; + _state[e] = STATE_TREE; + } else { + _forward[u] = true; + _pi[u] = -ART_COST; + _pred[u] = f; + _source[f] = u; + _target[f] = _root; + _flow[f] = _supply[u]; + _state[f] = STATE_TREE; + _cost[f] = ART_COST; + _source[e] = _root; + _target[e] = u; + //_flow[e] = 0; //by default, the sparse matrix is empty + _cost[e] = 0; + _state[e] = STATE_LOWER; + ++f; + } + } + _all_arc_num = f; + } + + return true; + } + + // Find the join node + void findJoinNode() { + int u = _source[in_arc]; + int v = _target[in_arc]; + while (u != v) { + if (_succ_num[u] < _succ_num[v]) { + u = _parent[u]; + } else { + v = _parent[v]; + } + } + join = u; + } + + // Find the leaving arc of the cycle and returns true if the + // leaving arc is not the same as the entering arc + bool findLeavingArc() { + // Initialize first and second nodes according to the direction + // of the cycle + if (_state[in_arc] == STATE_LOWER) { + first = _source[in_arc]; + second = _target[in_arc]; + } else { + first = _target[in_arc]; + second = _source[in_arc]; + } + delta = INF; + int result = 0; + Value d; + int e; + + // Search the cycle along the path form the first node to the root + for (int u = first; u != join; u = _parent[u]) { + e = _pred[u]; + d = _forward[u] ? _flow[e] : INF ; + if (d < delta) { + delta = d; + u_out = u; + result = 1; + } + } + // Search the cycle along the path form the second node to the root + for (int u = second; u != join; u = _parent[u]) { + e = _pred[u]; + d = _forward[u] ? INF : _flow[e]; + if (d <= delta) { + delta = d; + u_out = u; + result = 2; + } + } + + if (result == 1) { + u_in = first; + v_in = second; + } else { + u_in = second; + v_in = first; + } + return result != 0; + } + + // Change _flow and _state vectors + void changeFlow(bool change) { + // Augment along the cycle + if (delta > 0) { + Value val = _state[in_arc] * delta; + _flow[in_arc] += val; + for (int u = _source[in_arc]; u != join; u = _parent[u]) { + _flow[_pred[u]] += _forward[u] ? -val : val; + } + for (int u = _target[in_arc]; u != join; u = _parent[u]) { + _flow[_pred[u]] += _forward[u] ? val : -val; + } + } + // Update the state of the entering and leaving arcs + if (change) { + _state[in_arc] = STATE_TREE; + _state[_pred[u_out]] = + (_flow[_pred[u_out]] == 0) ? STATE_LOWER : STATE_UPPER; + } else { + _state[in_arc] = -_state[in_arc]; + } + } + + // Update the tree structure + void updateTreeStructure() { + int u, w; + int old_rev_thread = _rev_thread[u_out]; + int old_succ_num = _succ_num[u_out]; + int old_last_succ = _last_succ[u_out]; + v_out = _parent[u_out]; + + u = _last_succ[u_in]; // the last successor of u_in + right = _thread[u]; // the node after it + + // Handle the case when old_rev_thread equals to v_in + // (it also means that join and v_out coincide) + if (old_rev_thread == v_in) { + last = _thread[_last_succ[u_out]]; + } else { + last = _thread[v_in]; + } + + // Update _thread and _parent along the stem nodes (i.e. the nodes + // between u_in and u_out, whose parent have to be changed) + _thread[v_in] = stem = u_in; + _dirty_revs.clear(); + _dirty_revs.push_back(v_in); + par_stem = v_in; + while (stem != u_out) { + // Insert the next stem node into the thread list + new_stem = _parent[stem]; + _thread[u] = new_stem; + _dirty_revs.push_back(u); + + // Remove the subtree of stem from the thread list + w = _rev_thread[stem]; + _thread[w] = right; + _rev_thread[right] = w; + + // Change the parent node and shift stem nodes + _parent[stem] = par_stem; + par_stem = stem; + stem = new_stem; + + // Update u and right + u = _last_succ[stem] == _last_succ[par_stem] ? + _rev_thread[par_stem] : _last_succ[stem]; + right = _thread[u]; + } + _parent[u_out] = par_stem; + _thread[u] = last; + _rev_thread[last] = u; + _last_succ[u_out] = u; + + // Remove the subtree of u_out from the thread list except for + // the case when old_rev_thread equals to v_in + // (it also means that join and v_out coincide) + if (old_rev_thread != v_in) { + _thread[old_rev_thread] = right; + _rev_thread[right] = old_rev_thread; + } + + // Update _rev_thread using the new _thread values + for (int i = 0; i != int(_dirty_revs.size()); ++i) { + u = _dirty_revs[i]; + _rev_thread[_thread[u]] = u; + } + + // Update _pred, _forward, _last_succ and _succ_num for the + // stem nodes from u_out to u_in + int tmp_sc = 0, tmp_ls = _last_succ[u_out]; + u = u_out; + while (u != u_in) { + w = _parent[u]; + _pred[u] = _pred[w]; + _forward[u] = !_forward[w]; + tmp_sc += _succ_num[u] - _succ_num[w]; + _succ_num[u] = tmp_sc; + _last_succ[w] = tmp_ls; + u = w; + } + _pred[u_in] = in_arc; + _forward[u_in] = (u_in == _source[in_arc]); + _succ_num[u_in] = old_succ_num; + + // Set limits for updating _last_succ form v_in and v_out + // towards the root + int up_limit_in = -1; + int up_limit_out = -1; + if (_last_succ[join] == v_in) { + up_limit_out = join; + } else { + up_limit_in = join; + } + + // Update _last_succ from v_in towards the root + for (u = v_in; u != up_limit_in && _last_succ[u] == v_in; + u = _parent[u]) { + _last_succ[u] = _last_succ[u_out]; + } + // Update _last_succ from v_out towards the root + if (join != old_rev_thread && v_in != old_rev_thread) { + for (u = v_out; u != up_limit_out && _last_succ[u] == old_last_succ; + u = _parent[u]) { + _last_succ[u] = old_rev_thread; + } + } else { + for (u = v_out; u != up_limit_out && _last_succ[u] == old_last_succ; + u = _parent[u]) { + _last_succ[u] = _last_succ[u_out]; + } + } + + // Update _succ_num from v_in to join + for (u = v_in; u != join; u = _parent[u]) { + _succ_num[u] += old_succ_num; + } + // Update _succ_num from v_out to join + for (u = v_out; u != join; u = _parent[u]) { + _succ_num[u] -= old_succ_num; + } + } + + // Update potentials + void updatePotential() { + Cost sigma = _forward[u_in] ? + _pi[v_in] - _pi[u_in] - _cost[_pred[u_in]] : + _pi[v_in] - _pi[u_in] + _cost[_pred[u_in]]; + // Update potentials in the subtree, which has been moved + int end = _thread[_last_succ[u_in]]; + for (int u = u_in; u != end; u = _thread[u]) { + _pi[u] += sigma; + } + } + + // Heuristic initial pivots + bool initialPivots() { + Value curr, total = 0; + std::vector supply_nodes, demand_nodes; + Node u; _graph.first(u); + for (; u != INVALIDNODE; _graph.next(u)) { + curr = _supply[_node_id(u)]; + if (curr > 0) { + total += curr; + supply_nodes.push_back(u); + } + else if (curr < 0) { + demand_nodes.push_back(u); + } + } + if (_sum_supply > 0) total -= _sum_supply; + if (total <= 0) return true; + + IntVector arc_vector; + if (_sum_supply >= 0) { + if (supply_nodes.size() == 1 && demand_nodes.size() == 1) { + // Perform a reverse graph search from the sink to the source + //typename GR::template NodeMap reached(_graph, false); + BoolVector reached(_node_num, false); + Node s = supply_nodes[0], t = demand_nodes[0]; + std::vector stack; + reached[t] = true; + stack.push_back(t); + while (!stack.empty()) { + Node u, v = stack.back(); + stack.pop_back(); + if (v == s) break; + Arc a; _graph.firstIn(a, v); + for (; a != INVALID; _graph.nextIn(a)) { + if (reached[u = _graph.source(a)]) continue; + int j = getArcID(a); + if (INF >= total) { + arc_vector.push_back(j); + reached[u] = true; + stack.push_back(u); + } + } + } + } else { + // Find the min. cost incomming arc for each demand node + for (int i = 0; i != int(demand_nodes.size()); ++i) { + Node v = demand_nodes[i]; + Cost c, min_cost = std::numeric_limits::max(); + Arc min_arc = INVALID; + Arc a; _graph.firstIn(a, v); + for (; a != INVALID; _graph.nextIn(a)) { + c = _cost[getArcID(a)]; + if (c < min_cost) { + min_cost = c; + min_arc = a; + } + } + if (min_arc != INVALID) { + arc_vector.push_back(getArcID(min_arc)); + } + } + } + } else { + // Find the min. cost outgoing arc for each supply node + for (int i = 0; i != int(supply_nodes.size()); ++i) { + Node u = supply_nodes[i]; + Cost c, min_cost = std::numeric_limits::max(); + Arc min_arc = INVALID; + Arc a; _graph.firstOut(a, u); + for (; a != INVALID; _graph.nextOut(a)) { + c = _cost[getArcID(a)]; + if (c < min_cost) { + min_cost = c; + min_arc = a; + } + } + if (min_arc != INVALID) { + arc_vector.push_back(getArcID(min_arc)); + } + } + } + + // Perform heuristic initial pivots + for (int i = 0; i != int(arc_vector.size()); ++i) { + in_arc = arc_vector[i]; + // l'erreur est probablement ici... + if (_state[in_arc] * (_cost[in_arc] + _pi[_source[in_arc]] - + _pi[_target[in_arc]]) >= 0) continue; + findJoinNode(); + bool change = findLeavingArc(); + if (delta >= MAX) return false; + changeFlow(change); + if (change) { + updateTreeStructure(); + updatePotential(); + } + } + return true; + } + + // Execute the algorithm + ProblemType start() { + return start(); + } + + template + ProblemType start() { + PivotRuleImpl pivot(*this); + double prevCost=-1; + + // Perform heuristic initial pivots + if (!initialPivots()) return UNBOUNDED; + +#if DEBUG_LVL>0 + int niter=0; +#endif + int iter_number=0; + //pivot.setDantzig(true); + // Execute the Network Simplex algorithm + while (pivot.findEnteringArc()) { + if(++iter_number>=max_iter&&max_iter>0){ + char errMess[1000]; + // sprintf( errMess, "RESULT MIGHT BE INACURATE\nMax number of iteration reached, currently \%d. Sometimes iterations go on in cycle even though the solution has been reached, to check if it's the case here have a look at the minimal reduced cost. If it is very close to machine precision, you might actually have the correct solution, if not try setting the maximum number of iterations a bit higher",iter_number ); + // mexWarnMsgTxt(errMess); + break; + } +#if DEBUG_LVL>0 + if(niter>MAX_DEBUG_ITER) + break; + if(++niter%1000==0||niter%1000==1){ + double curCost=totalCost(); + double sumFlow=0; + double a; + a= (fabs(_pi[_source[in_arc]])>=fabs(_pi[_target[in_arc]])) ? fabs(_pi[_source[in_arc]]) : fabs(_pi[_target[in_arc]]); + a=a>=fabs(_cost[in_arc])?a:fabs(_cost[in_arc]); + for (int i=0; i<_flow.size(); i++) { + sumFlow+=_state[i]*_flow[i]; + } + mexPrintf("Sum of the flow %.100f\n%d iterations, current cost=%.20f\nReduced cost=%.30f\nPrecision =%.30f\n",sumFlow,niter, curCost,_state[in_arc] * (_cost[in_arc] + _pi[_source[in_arc]] -_pi[_target[in_arc]]), -EPSILON*(a)); + mexPrintf("Arc in = (%d,%d)\n",_node_id(_source[in_arc]),_node_id(_target[in_arc])); + mexPrintf("Supplies = (%f,%f)\n",_supply[_source[in_arc]],_supply[_target[in_arc]]); + + mexPrintf("%.30f\n%.30f\n%.30f\n%.30f\n%",_cost[in_arc],_pi[_source[in_arc]],_pi[_target[in_arc]],a); + mexEvalString("drawnow;"); + } +#endif + + findJoinNode(); + bool change = findLeavingArc(); + if (delta >= MAX) return UNBOUNDED; + changeFlow(change); + if (change) { + updateTreeStructure(); + updatePotential(); + } +#if DEBUG_LVL>0 + else{ + mexPrintf("No change\n"); + } +#endif +#if DEBUG_LVL>1 + mexPrintf("Arc in = (%d,%d)\n",_source[in_arc],_target[in_arc]); +#endif + + } + + +#if DEBUG_LVL>0 + double curCost=totalCost(); + double sumFlow=0; + double a; + a= (fabs(_pi[_source[in_arc]])>=fabs(_pi[_target[in_arc]])) ? fabs(_pi[_source[in_arc]]) : fabs(_pi[_target[in_arc]]); + a=a>=fabs(_cost[in_arc])?a:fabs(_cost[in_arc]); + for (int i=0; i<_flow.size(); i++) { + sumFlow+=_state[i]*_flow[i]; + } + mexPrintf("Sum of the flow %.100f\n%d iterations, current cost=%.20f\nReduced cost=%.30f\nPrecision =%.30f",sumFlow,niter, curCost,_state[in_arc] * (_cost[in_arc] + _pi[_source[in_arc]] -_pi[_target[in_arc]]), -EPSILON*(a)); + mexPrintf("Arc in = (%d,%d)\n",_node_id(_source[in_arc]),_node_id(_target[in_arc])); + mexPrintf("Supplies = (%f,%f)\n",_supply[_source[in_arc]],_supply[_target[in_arc]]); + + mexEvalString("drawnow;"); +#endif + +#if DEBUG_LVL>1 + double sumFlow=0; + for (int i=0; i<_flow.size(); i++) { + sumFlow+=_state[i]*_flow[i]; + if (_state[i]==STATE_TREE) { + mexPrintf("Non zero value at (%d,%d)\n",_node_num+1-_source[i],_node_num+1-_target[i]); + } + } + mexPrintf("Sum of the flow %.100f\n%d iterations, current cost=%.20f\n",sumFlow,niter, totalCost()); + mexEvalString("drawnow;"); +#endif + // Check feasibility + for (int e = _search_arc_num; e != _all_arc_num; ++e) { + if (_flow[e] != 0){ + if (abs(_flow[e]) > EPSILON) + return INFEASIBLE; + else + _flow[e]=0; + + } + } + + // Shift potentials to meet the requirements of the GEQ/LEQ type + // optimality conditions + if (_sum_supply == 0) { + if (_stype == GEQ) { + Cost max_pot = -std::numeric_limits::max(); + for (int i = 0; i != _node_num; ++i) { + if (_pi[i] > max_pot) max_pot = _pi[i]; + } + if (max_pot > 0) { + for (int i = 0; i != _node_num; ++i) + _pi[i] -= max_pot; + } + } else { + Cost min_pot = std::numeric_limits::max(); + for (int i = 0; i != _node_num; ++i) { + if (_pi[i] < min_pot) min_pot = _pi[i]; + } + if (min_pot < 0) { + for (int i = 0; i != _node_num; ++i) + _pi[i] -= min_pot; + } + } + } + + return OPTIMAL; + } + + }; //class NetworkSimplexSimple + + ///@} + +} //namespace lemon + +#endif //LEMON_NETWORK_SIMPLEX_H diff --git a/ot/optim.py b/ot/optim.py index 66bbfb5..e6373ce 100644 --- a/ot/optim.py +++ b/ot/optim.py @@ -8,7 +8,7 @@ Created on Wed Oct 26 15:08:19 2016 import numpy as np import scipy as sp from scipy.optimize.linesearch import scalar_search_armijo -from emd import emd +from lp import emd # The corresponding scipy function does not work for matrices def line_search_armijo(f,xk,pk,gfk,old_fval,args=(),c1=1e-4,alpha0=0.99): -- cgit v1.2.3