在阅读本文之前，通过阅读/略读第1节中的教程，可以帮助您熟悉Python C扩展的基础知识。 Extending and Embedding the Python Interpreter 而在 How to extend NumPy
umath模块是一个计算机生成的C模块，可以创建许多ufunc。它提供了许多关于如何创建通用函数的例子。创建自己的ufunc来使用ufunc机器也不难。假设您有一个函数，您希望在它的输入上逐元素地操作它。通过创建新的ufunc，您将获得一个处理
广播
N维循环
使用最少内存的自动类型转换
可选输出阵列
创建自己的ufunc并不困难。所需的只是为您想要支持的每种数据类型提供一个一维循环。每个一维循环必须有一个特定的签名，并且只能使用固定大小数据类型的UFUNC。下面给出了用于创建新UFUNC以处理内置数据类型的函数调用。另一种机制用于为用户定义的数据类型注册UFunc。
在接下来的几节中，我们将给出一些示例代码，这些代码可以很容易地修改以创建您自己的UFUNC。这些例子依次是更完整或更复杂的logit函数版本，这是统计建模中的一个常见函数。Logit也很有趣，因为由于IEEE标准（特别是IEEE754）的魔力，下面创建的所有Logit函数都自动具有以下行为。
>>> logit(0) -inf >>> logit(1) inf >>> logit(2) nan >>> logit(-2) nan
这很好，因为函数编写器不必手动传播inf或nan。
为了比较和启发读者，我们提供了一个不使用numpy的logit的C扩展的简单实现。
要做到这一点，我们需要两个文件。第一个是包含实际代码的C文件，第二个是用于创建模块的setup.py文件。
#include <Python.h> #include <math.h> /* * spammodule.c * This is the C code for a non-numpy Python extension to * define the logit function, where logit(p) = log(p/(1-p)). * This function will not work on numpy arrays automatically. * numpy.vectorize must be called in python to generate * a numpy-friendly function. * * Details explaining the Python-C API can be found under * 'Extending and Embedding' and 'Python/C API' at * docs.python.org . */ /* This declares the logit function */ static PyObject* spam_logit(PyObject *self, PyObject *args); /* * This tells Python what methods this module has. * See the Python-C API for more information. */ static PyMethodDef SpamMethods[] = { {"logit", spam_logit, METH_VARARGS, "compute logit"}, {NULL, NULL, 0, NULL} }; /* * This actually defines the logit function for * input args from Python. */ static PyObject* spam_logit(PyObject *self, PyObject *args) { double p; /* This parses the Python argument into a double */ if(!PyArg_ParseTuple(args, "d", &p)) { return NULL; } /* THE ACTUAL LOGIT FUNCTION */ p = p/(1-p); p = log(p); /*This builds the answer back into a python object */ return Py_BuildValue("d", p); } /* This initiates the module using the above definitions. */ static struct PyModuleDef moduledef = { PyModuleDef_HEAD_INIT, "spam", NULL, -1, SpamMethods, NULL, NULL, NULL, NULL }; PyMODINIT_FUNC PyInit_spam(void) { PyObject *m; m = PyModule_Create(&moduledef); if (!m) { return NULL; } return m; }
要使用setup.py文件，请将setup.py和spammodule.c放在同一文件夹中。然后python setup.py build将构建要导入的模块，或者setup.py install将模块安装到站点包目录中。
''' setup.py file for spammodule.c Calling $python setup.py build_ext --inplace will build the extension library in the current file. Calling $python setup.py build will build a file that looks like ./build/lib*, where lib* is a file that begins with lib. The library will be in this file and end with a C library extension, such as .so Calling $python setup.py install will install the module in your site-packages file. See the distutils section of 'Extending and Embedding the Python Interpreter' at docs.python.org for more information. ''' from distutils.core import setup, Extension module1 = Extension('spam', sources=['spammodule.c'], include_dirs=['/usr/local/lib']) setup(name = 'spam', version='1.0', description='This is my spam package', ext_modules = [module1])
一旦垃圾邮件模块导入到python中，就可以通过spam.logit调用logit。请注意，上面使用的函数不能像对numpy数组那样应用。要做到这一点，我们必须称之为numpy.vectorize。例如，如果在包含垃圾邮件库或已安装垃圾邮件的文件中打开了python解释器，则可以执行以下命令：
>>> import numpy as np >>> import spam >>> spam.logit(0) -inf >>> spam.logit(1) inf >>> spam.logit(0.5) 0.0 >>> x = np.linspace(0,1,10) >>> spam.logit(x) TypeError: only length-1 arrays can be converted to Python scalars >>> f = np.vectorize(spam.logit) >>> f(x) array([ -inf, -2.07944154, -1.25276297, -0.69314718, -0.22314355, 0.22314355, 0.69314718, 1.25276297, 2.07944154, inf])
产生的logit函数不快！numpy.vectorize只是在spam.logit上循环。循环是在C级别完成的，但是numpy数组一直在被解析和构建备份。这个很贵。当作者将numpy.vectorize（spam.logit）与下面构造的logit ufuncs进行比较时，logit ufuncs几乎快了4倍。当然，根据功能的性质，可以进行较大或较小的加速。
为了简单起见，我们为单个数据类型提供了一个ufunc，即“f8”双精度。与前一节一样，我们首先给出.c文件，然后给出用于创建包含ufunc的模块的setup.py文件。
代码中与ufunc的实际计算相对应的位置用标记/ * 开始主ufunc计算 * /和/ * 结束主UFUNC计算 * 。这些行之间的代码是必须更改才能创建自己的ufunc的主要内容。
#include "Python.h" #include "math.h" #include "numpy/ndarraytypes.h" #include "numpy/ufuncobject.h" #include "numpy/npy_3kcompat.h" /* * single_type_logit.c * This is the C code for creating your own * NumPy ufunc for a logit function. * * In this code we only define the ufunc for * a single dtype. The computations that must * be replaced to create a ufunc for * a different function are marked with BEGIN * and END. * * Details explaining the Python-C API can be found under * 'Extending and Embedding' and 'Python/C API' at * docs.python.org . */ static PyMethodDef LogitMethods[] = { {NULL, NULL, 0, NULL} }; /* The loop definition must precede the PyMODINIT_FUNC. */ static void double_logit(char **args, npy_intp *dimensions, npy_intp* steps, void* data) { npy_intp i; npy_intp n = dimensions[0]; char *in = args[0], *out = args[1]; npy_intp in_step = steps[0], out_step = steps[1]; double tmp; for (i = 0; i < n; i++) { /*BEGIN main ufunc computation*/ tmp = *(double *)in; tmp /= 1-tmp; *((double *)out) = log(tmp); /*END main ufunc computation*/ in += in_step; out += out_step; } } /*This a pointer to the above function*/ PyUFuncGenericFunction funcs[1] = {&double_logit}; /* These are the input and return dtypes of logit.*/ static char types[2] = {NPY_DOUBLE, NPY_DOUBLE}; static void *data[1] = {NULL}; static struct PyModuleDef moduledef = { PyModuleDef_HEAD_INIT, "npufunc", NULL, -1, LogitMethods, NULL, NULL, NULL, NULL }; PyMODINIT_FUNC PyInit_npufunc(void) { PyObject *m, *logit, *d; m = PyModule_Create(&moduledef); if (!m) { return NULL; } import_array(); import_umath(); logit = PyUFunc_FromFuncAndData(funcs, data, types, 1, 1, 1, PyUFunc_None, "logit", "logit_docstring", 0); d = PyModule_GetDict(m); PyDict_SetItemString(d, "logit", logit); Py_DECREF(logit); return m; }
这是上述代码的setup.py文件。与以前一样，可以通过在命令提示下调用python setup.py build来构建模块，也可以通过python setup.py install安装到站点包中。
''' setup.py file for logit.c Note that since this is a numpy extension we use numpy.distutils instead of distutils from the python standard library. Calling $python setup.py build_ext --inplace will build the extension library in the current file. Calling $python setup.py build will build a file that looks like ./build/lib*, where lib* is a file that begins with lib. The library will be in this file and end with a C library extension, such as .so Calling $python setup.py install will install the module in your site-packages file. See the distutils section of 'Extending and Embedding the Python Interpreter' at docs.python.org and the documentation on numpy.distutils for more information. ''' def configuration(parent_package='', top_path=None): import numpy from numpy.distutils.misc_util import Configuration config = Configuration('npufunc_directory', parent_package, top_path) config.add_extension('npufunc', ['single_type_logit.c']) return config if __name__ == "__main__": from numpy.distutils.core import setup setup(configuration=configuration)
安装完成后，可以按如下方式导入和使用。
>>> import numpy as np >>> import npufunc >>> npufunc.logit(0.5) 0.0 >>> a = np.linspace(0,1,5) >>> npufunc.logit(a) array([ -inf, -1.09861229, 0. , 1.09861229, inf])
最后，我们给出一个完整的ufunc示例，其中包含半浮点数、浮点数、双精度数和长双精度数的内部循环。和前面的部分一样，我们首先给出.c文件，然后给出相应的setup.py文件。
代码中与ufunc的实际计算相对应的位置标记为/ * 开始主ufunc计算 * /和/ * 结束主UFUNC计算 * 。这些行之间的代码是必须更改才能创建自己的ufunc的主要内容。
#include "Python.h" #include "math.h" #include "numpy/ndarraytypes.h" #include "numpy/ufuncobject.h" #include "numpy/halffloat.h" /* * multi_type_logit.c * This is the C code for creating your own * NumPy ufunc for a logit function. * * Each function of the form type_logit defines the * logit function for a different numpy dtype. Each * of these functions must be modified when you * create your own ufunc. The computations that must * be replaced to create a ufunc for * a different function are marked with BEGIN * and END. * * Details explaining the Python-C API can be found under * 'Extending and Embedding' and 'Python/C API' at * docs.python.org . * */ static PyMethodDef LogitMethods[] = { {NULL, NULL, 0, NULL} }; /* The loop definitions must precede the PyMODINIT_FUNC. */ static void long_double_logit(char **args, npy_intp *dimensions, npy_intp* steps, void* data) { npy_intp i; npy_intp n = dimensions[0]; char *in = args[0], *out=args[1]; npy_intp in_step = steps[0], out_step = steps[1]; long double tmp; for (i = 0; i < n; i++) { /*BEGIN main ufunc computation*/ tmp = *(long double *)in; tmp /= 1-tmp; *((long double *)out) = logl(tmp); /*END main ufunc computation*/ in += in_step; out += out_step; } } static void double_logit(char **args, npy_intp *dimensions, npy_intp* steps, void* data) { npy_intp i; npy_intp n = dimensions[0]; char *in = args[0], *out = args[1]; npy_intp in_step = steps[0], out_step = steps[1]; double tmp; for (i = 0; i < n; i++) { /*BEGIN main ufunc computation*/ tmp = *(double *)in; tmp /= 1-tmp; *((double *)out) = log(tmp); /*END main ufunc computation*/ in += in_step; out += out_step; } } static void float_logit(char **args, npy_intp *dimensions, npy_intp* steps, void* data) { npy_intp i; npy_intp n = dimensions[0]; char *in=args[0], *out = args[1]; npy_intp in_step = steps[0], out_step = steps[1]; float tmp; for (i = 0; i < n; i++) { /*BEGIN main ufunc computation*/ tmp = *(float *)in; tmp /= 1-tmp; *((float *)out) = logf(tmp); /*END main ufunc computation*/ in += in_step; out += out_step; } } static void half_float_logit(char **args, npy_intp *dimensions, npy_intp* steps, void* data) { npy_intp i; npy_intp n = dimensions[0]; char *in = args[0], *out = args[1]; npy_intp in_step = steps[0], out_step = steps[1]; float tmp; for (i = 0; i < n; i++) { /*BEGIN main ufunc computation*/ tmp = *(npy_half *)in; tmp = npy_half_to_float(tmp); tmp /= 1-tmp; tmp = logf(tmp); *((npy_half *)out) = npy_float_to_half(tmp); /*END main ufunc computation*/ in += in_step; out += out_step; } } /*This gives pointers to the above functions*/ PyUFuncGenericFunction funcs[4] = {&half_float_logit, &float_logit, &double_logit, &long_double_logit}; static char types[8] = {NPY_HALF, NPY_HALF, NPY_FLOAT, NPY_FLOAT, NPY_DOUBLE,NPY_DOUBLE, NPY_LONGDOUBLE, NPY_LONGDOUBLE}; static void *data[4] = {NULL, NULL, NULL, NULL}; static struct PyModuleDef moduledef = { PyModuleDef_HEAD_INIT, "npufunc", NULL, -1, LogitMethods, NULL, NULL, NULL, NULL }; PyMODINIT_FUNC PyInit_npufunc(void) { PyObject *m, *logit, *d; m = PyModule_Create(&moduledef); if (!m) { return NULL; } import_array(); import_umath(); logit = PyUFunc_FromFuncAndData(funcs, data, types, 4, 1, 1, PyUFunc_None, "logit", "logit_docstring", 0); d = PyModule_GetDict(m); PyDict_SetItemString(d, "logit", logit); Py_DECREF(logit); return m; }
''' setup.py file for logit.c Note that since this is a numpy extension we use numpy.distutils instead of distutils from the python standard library. Calling $python setup.py build_ext --inplace will build the extension library in the current file. Calling $python setup.py build will build a file that looks like ./build/lib*, where lib* is a file that begins with lib. The library will be in this file and end with a C library extension, such as .so Calling $python setup.py install will install the module in your site-packages file. See the distutils section of 'Extending and Embedding the Python Interpreter' at docs.python.org and the documentation on numpy.distutils for more information. ''' def configuration(parent_package='', top_path=None): import numpy from numpy.distutils.misc_util import Configuration from numpy.distutils.misc_util import get_info #Necessary for the half-float d-type. info = get_info('npymath') config = Configuration('npufunc_directory', parent_package, top_path) config.add_extension('npufunc', ['multi_type_logit.c'], extra_info=info) return config if __name__ == "__main__": from numpy.distutils.core import setup setup(configuration=configuration)
最后一个例子是一个带有多个参数的ufunc。它是对具有单个数据类型的数据的logit ufunc代码的修改。我们计算（A） logit（a） B）
我们只给出C代码，因为setup.py文件与中的setup.py文件完全相同。 Example NumPy ufunc for one dtype 除了那条线
config.add_extension('npufunc', ['single_type_logit.c'])
替换为
config.add_extension('npufunc', ['multi_arg_logit.c'])
C文件如下。生成的ufunc接受两个参数a和b。它返回一个元组，其第一个元素是 b，第二个元素是logit（a B）请注意，它自动支持广播，以及ufunc的所有其他属性。
#include "Python.h" #include "math.h" #include "numpy/ndarraytypes.h" #include "numpy/ufuncobject.h" #include "numpy/halffloat.h" /* * multi_arg_logit.c * This is the C code for creating your own * NumPy ufunc for a multiple argument, multiple * return value ufunc. The places where the * ufunc computation is carried out are marked * with comments. * * Details explaining the Python-C API can be found under * 'Extending and Embedding' and 'Python/C API' at * docs.python.org . * */ static PyMethodDef LogitMethods[] = { {NULL, NULL, 0, NULL} }; /* The loop definition must precede the PyMODINIT_FUNC. */ static void double_logitprod(char **args, npy_intp *dimensions, npy_intp* steps, void* data) { npy_intp i; npy_intp n = dimensions[0]; char *in1 = args[0], *in2 = args[1]; char *out1 = args[2], *out2 = args[3]; npy_intp in1_step = steps[0], in2_step = steps[1]; npy_intp out1_step = steps[2], out2_step = steps[3]; double tmp; for (i = 0; i < n; i++) { /*BEGIN main ufunc computation*/ tmp = *(double *)in1; tmp *= *(double *)in2; *((double *)out1) = tmp; *((double *)out2) = log(tmp/(1-tmp)); /*END main ufunc computation*/ in1 += in1_step; in2 += in2_step; out1 += out1_step; out2 += out2_step; } } /*This a pointer to the above function*/ PyUFuncGenericFunction funcs[1] = {&double_logitprod}; /* These are the input and return dtypes of logit.*/ static char types[4] = {NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE}; static void *data[1] = {NULL}; static struct PyModuleDef moduledef = { PyModuleDef_HEAD_INIT, "npufunc", NULL, -1, LogitMethods, NULL, NULL, NULL, NULL }; PyMODINIT_FUNC PyInit_npufunc(void) { PyObject *m, *logit, *d; m = PyModule_Create(&moduledef); if (!m) { return NULL; } import_array(); import_umath(); logit = PyUFunc_FromFuncAndData(funcs, data, types, 1, 2, 2, PyUFunc_None, "logit", "logit_docstring", 0); d = PyModule_GetDict(m); PyDict_SetItemString(d, "logit", logit); Py_DECREF(logit); return m; }
此示例演示如何为结构化数组数据类型创建UFUNC。对于这个例子，我们展示了一个普通的ufunc，用于添加两个数据类型为“u8，u8，u8”的数组。由于调用 PyUFunc_FromFuncAndData 没有为自定义数据类型和结构化数组数据类型完全注册UFUNC。我们还需要打电话 PyUFunc_RegisterLoopForDescr 完成UFUNC的设置。
PyUFunc_FromFuncAndData
PyUFunc_RegisterLoopForDescr
config.add_extension('npufunc', ['add_triplet.c'])
C文件如下。
#include "Python.h" #include "math.h" #include "numpy/ndarraytypes.h" #include "numpy/ufuncobject.h" #include "numpy/npy_3kcompat.h" /* * add_triplet.c * This is the C code for creating your own * NumPy ufunc for a structured array dtype. * * Details explaining the Python-C API can be found under * 'Extending and Embedding' and 'Python/C API' at * docs.python.org . */ static PyMethodDef StructUfuncTestMethods[] = { {NULL, NULL, 0, NULL} }; /* The loop definition must precede the PyMODINIT_FUNC. */ static void add_uint64_triplet(char **args, npy_intp *dimensions, npy_intp* steps, void* data) { npy_intp i; npy_intp is1=steps[0]; npy_intp is2=steps[1]; npy_intp os=steps[2]; npy_intp n=dimensions[0]; uint64_t *x, *y, *z; char *i1=args[0]; char *i2=args[1]; char *op=args[2]; for (i = 0; i < n; i++) { x = (uint64_t*)i1; y = (uint64_t*)i2; z = (uint64_t*)op; z[0] = x[0] + y[0]; z[1] = x[1] + y[1]; z[2] = x[2] + y[2]; i1 += is1; i2 += is2; op += os; } } /* This a pointer to the above function */ PyUFuncGenericFunction funcs[1] = {&add_uint64_triplet}; /* These are the input and return dtypes of add_uint64_triplet. */ static char types[3] = {NPY_UINT64, NPY_UINT64, NPY_UINT64}; static void *data[1] = {NULL}; static struct PyModuleDef moduledef = { PyModuleDef_HEAD_INIT, "struct_ufunc_test", NULL, -1, StructUfuncTestMethods, NULL, NULL, NULL, NULL }; PyMODINIT_FUNC PyInit_struct_ufunc_test(void) { PyObject *m, *add_triplet, *d; PyObject *dtype_dict; PyArray_Descr *dtype; PyArray_Descr *dtypes[3]; m = PyModule_Create(&moduledef); if (m == NULL) { return NULL; } import_array(); import_umath(); /* Create a new ufunc object */ add_triplet = PyUFunc_FromFuncAndData(NULL, NULL, NULL, 0, 2, 1, PyUFunc_None, "add_triplet", "add_triplet_docstring", 0); dtype_dict = Py_BuildValue("[(s, s), (s, s), (s, s)]", "f0", "u8", "f1", "u8", "f2", "u8"); PyArray_DescrConverter(dtype_dict, &dtype); Py_DECREF(dtype_dict); dtypes[0] = dtype; dtypes[1] = dtype; dtypes[2] = dtype; /* Register ufunc for structured dtype */ PyUFunc_RegisterLoopForDescr(add_triplet, dtype, &add_uint64_triplet, dtypes, NULL); d = PyModule_GetDict(m); PyDict_SetItemString(d, "add_triplet", add_triplet); Py_DECREF(add_triplet); return m; }
返回的ufunc对象是可调用的python对象。它应该放在（模块）字典中，名称与ufunc创建例程的name参数中使用的名称相同。以下示例改编自umath模块
static PyUFuncGenericFunction atan2_functions[] = { PyUFunc_ff_f, PyUFunc_dd_d, PyUFunc_gg_g, PyUFunc_OO_O_method}; static void* atan2_data[] = { (void *)atan2f,(void *) atan2, (void *)atan2l,(void *)"arctan2"}; static char atan2_signatures[] = { NPY_FLOAT, NPY_FLOAT, NPY_FLOAT, NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, NPY_LONGDOUBLE, NPY_LONGDOUBLE, NPY_LONGDOUBLE NPY_OBJECT, NPY_OBJECT, NPY_OBJECT}; ... /* in the module initialization code */ PyObject *f, *dict, *module; ... dict = PyModule_GetDict(module); ... f = PyUFunc_FromFuncAndData(atan2_functions, atan2_data, atan2_signatures, 4, 2, 1, PyUFunc_None, "arctan2", "a safe and correct arctan(x1/x2)", 0); PyDict_SetItemString(dict, "arctan2", f); Py_DECREF(f); ...