Using Python as glue Many people like to say that Python is a fantastic glue language. Hopefully, this Chapter will convince you that this is true. The first adopters of Python for science were typically people who used it to glue together large application codes running on super-computers. Not only was it much nicer to code in Python than in a shell script or Perl, in addition, the ability to easily extend Python made it relatively easy to create new classes and types specifically adapted to the problems being solved. From the interactions of these early contributors, Numeric emerged as an array-like object that could be used to pass data between these applications. As Numeric has matured and developed into NumPy, people have been able to write more code directly in NumPy. Often this code is fast-enough for production use, but there are still times that there is a need to access compiled code. Either to get that last bit of efficiency out of the algorithm or to make it easier to access widely-available codes written in C/C++ or Fortran. This chapter will review many of the tools that are available for the purpose of accessing code written in other compiled languages. There are many resources available for learning to call other compiled libraries from Python and the purpose of this Chapter is not to make you an expert. The main goal is to make you aware of some of the possibilities so that you will know what to “Google” in order to learn more.  Calling other compiled libraries from Python While Python is a great language and a pleasure to code in, its dynamic nature results in overhead that can cause some code ( i.e. raw computations inside of for loops) to be up 10-100 times slower than equivalent code written in a static compiled language. In addition, it can cause memory usage to be larger than necessary as temporary arrays are created and destroyed during computation. For many types of computing needs, the extra slow-down and memory consumption can often not be spared (at least for time- or memory- critical portions of your code). Therefore one of the most common needs is to call out from Python code to a fast, machine-code routine (e.g. compiled using C/C++ or Fortran). The fact that this is relatively easy to do is a big reason why Python is such an excellent high-level language for scientific and engineering programming. Their are two basic approaches to calling compiled code: writing an extension module that is then imported to Python using the import command, or calling a shared-library subroutine directly from Python using the ctypes module. Writing an extension module is the most common method.  Warning Calling C-code from Python can result in Python crashes if you are not careful. None of the approaches in this chapter are immune. You have to know something about the way data is handled by both NumPy and by the third-party library being used.    Hand-generated wrappers Extension modules were discussed in Writing an extension module. The most basic way to interface with compiled code is to write an extension module and construct a module method that calls the compiled code. For improved readability, your method should take advantage of the PyArg_ParseTuple call to convert between Python objects and C data-types. For standard C data-types there is probably already a built-in converter. For others you may need to write your own converter and use the "O&" format string which allows you to specify a function that will be used to perform the conversion from the Python object to whatever C-structures are needed. Once the conversions to the appropriate C-structures and C data-types have been performed, the next step in the wrapper is to call the underlying function. This is straightforward if the underlying function is in C or C++. However, in order to call Fortran code you must be familiar with how Fortran subroutines are called from C/C++ using your compiler and platform. This can vary somewhat platforms and compilers (which is another reason f2py makes life much simpler for interfacing Fortran code) but generally involves underscore mangling of the name and the fact that all variables are passed by reference (i.e. all arguments are pointers). The advantage of the hand-generated wrapper is that you have complete control over how the C-library gets used and called which can lead to a lean and tight interface with minimal over-head. The disadvantage is that you have to write, debug, and maintain C-code, although most of it can be adapted using the time-honored technique of “cutting-pasting-and-modifying” from other extension modules. Because, the procedure of calling out to additional C-code is fairly regimented, code-generation procedures have been developed to make this process easier. One of these code-generation techniques is distributed with NumPy and allows easy integration with Fortran and (simple) C code. This package, f2py, will be covered briefly in the next section.   f2py F2py allows you to automatically construct an extension module that interfaces to routines in Fortran 77/90/95 code. It has the ability to parse Fortran 77/90/95 code and automatically generate Python signatures for the subroutines it encounters, or you can guide how the subroutine interfaces with Python by constructing an interface-definition-file (or modifying the f2py-produced one).  Creating source for a basic extension module Probably the easiest way to introduce f2py is to offer a simple example. Here is one of the subroutines contained in a file named add.f C
      SUBROUTINE ZADD(A,B,C,N)
C
      DOUBLE COMPLEX A(*)
      DOUBLE COMPLEX B(*)
      DOUBLE COMPLEX C(*)
      INTEGER N
      DO 20 J = 1, N
         C(J) = A(J)+B(J)
 20   CONTINUE
      END
 This routine simply adds the elements in two contiguous arrays and places the result in a third. The memory for all three arrays must be provided by the calling routine. A very basic interface to this routine can be automatically generated by f2py: f2py -m add add.f
 You should be able to run this command assuming your search-path is set-up properly. This command will produce an extension module named addmodule.c in the current directory. This extension module can now be compiled and used from Python just like any other extension module.   Creating a compiled extension module You can also get f2py to both compile add.f along with the produced extension module leaving only a shared-library extension file that can be imported from Python: f2py -c -m add add.f
 This command leaves a file named add.{ext} in the current directory (where {ext} is the appropriate extension for a Python extension module on your platform — so, pyd, etc. ). This module may then be imported from Python. It will contain a method for each subroutine in add (zadd, cadd, dadd, sadd). The docstring of each method contains information about how the module method may be called: >>> import add
>>> print(add.zadd.__doc__)
zadd(a,b,c,n)

Wrapper for ``zadd``.

Parameters
----------
a : input rank-1 array('D') with bounds (*)
b : input rank-1 array('D') with bounds (*)
c : input rank-1 array('D') with bounds (*)
n : input int
   Improving the basic interface The default interface is a very literal translation of the Fortran code into Python. The Fortran array arguments must now be NumPy arrays and the integer argument should be an integer. The interface will attempt to convert all arguments to their required types (and shapes) and issue an error if unsuccessful. However, because it knows nothing about the semantics of the arguments (such that C is an output and n should really match the array sizes), it is possible to abuse this function in ways that can cause Python to crash. For example: >>> add.zadd([1, 2, 3], [1, 2], [3, 4], 1000)
 will cause a program crash on most systems. Under the covers, the lists are being converted to proper arrays but then the underlying add loop is told to cycle way beyond the borders of the allocated memory. In order to improve the interface, directives should be provided. This is accomplished by constructing an interface definition file. It is usually best to start from the interface file that f2py can produce (where it gets its default behavior from). To get f2py to generate the interface file use the -h option: f2py -h add.pyf -m add add.f
 This command leaves the file add.pyf in the current directory. The section of this file corresponding to zadd is: subroutine zadd(a,b,c,n) ! in :add:add.f
   double complex dimension(*) :: a
   double complex dimension(*) :: b
   double complex dimension(*) :: c
   integer :: n
end subroutine zadd
 By placing intent directives and checking code, the interface can be cleaned up quite a bit until the Python module method is both easier to use and more robust. subroutine zadd(a,b,c,n) ! in :add:add.f
   double complex dimension(n) :: a
   double complex dimension(n) :: b
   double complex intent(out),dimension(n) :: c
   integer intent(hide),depend(a) :: n=len(a)
end subroutine zadd
 The intent directive, intent(out) is used to tell f2py that c is an output variable and should be created by the interface before being passed to the underlying code. The intent(hide) directive tells f2py to not allow the user to specify the variable, n, but instead to get it from the size of a. The depend( a ) directive is necessary to tell f2py that the value of n depends on the input a (so that it won’t try to create the variable n until the variable a is created). After modifying add.pyf, the new Python module file can be generated by compiling both add.f and add.pyf: f2py -c add.pyf add.f
 The new interface has docstring: >>> import add
>>> print(add.zadd.__doc__)
c = zadd(a,b)

Wrapper for ``zadd``.

Parameters
----------
a : input rank-1 array('D') with bounds (n)
b : input rank-1 array('D') with bounds (n)

Returns
-------
c : rank-1 array('D') with bounds (n)
 Now, the function can be called in a much more robust way: >>> add.zadd([1, 2, 3], [4, 5, 6])
array([5.+0.j, 7.+0.j, 9.+0.j])
 Notice the automatic conversion to the correct format that occurred.   Inserting directives in Fortran source The nice interface can also be generated automatically by placing the variable directives as special comments in the original Fortran code. Thus, if the source code is modified to contain: C
      SUBROUTINE ZADD(A,B,C,N)
C
CF2PY INTENT(OUT) :: C
CF2PY INTENT(HIDE) :: N
CF2PY DOUBLE COMPLEX :: A(N)
CF2PY DOUBLE COMPLEX :: B(N)
CF2PY DOUBLE COMPLEX :: C(N)
      DOUBLE COMPLEX A(*)
      DOUBLE COMPLEX B(*)
      DOUBLE COMPLEX C(*)
      INTEGER N
      DO 20 J = 1, N
         C(J) = A(J) + B(J)
 20   CONTINUE
      END
 Then, one can compile the extension module using: f2py -c -m add add.f
 The resulting signature for the function add.zadd is exactly the same one that was created previously. If the original source code had contained A(N) instead of A(*) and so forth with B and C, then nearly the same interface can be obtained by placing the INTENT(OUT) :: C comment line in the source code. The only difference is that N would be an optional input that would default to the length of A.   A filtering example For comparison with the other methods to be discussed. Here is another example of a function that filters a two-dimensional array of double precision floating-point numbers using a fixed averaging filter. The advantage of using Fortran to index into multi-dimensional arrays should be clear from this example.       SUBROUTINE DFILTER2D(A,B,M,N)
C
      DOUBLE PRECISION A(M,N)
      DOUBLE PRECISION B(M,N)
      INTEGER N, M
CF2PY INTENT(OUT) :: B
CF2PY INTENT(HIDE) :: N
CF2PY INTENT(HIDE) :: M
      DO 20 I = 2,M-1
         DO 40 J=2,N-1
            B(I,J) = A(I,J) +
     $           (A(I-1,J)+A(I+1,J) +
     $            A(I,J-1)+A(I,J+1) )*0.5D0 +
     $           (A(I-1,J-1) + A(I-1,J+1) +
     $            A(I+1,J-1) + A(I+1,J+1))*0.25D0
 40      CONTINUE
 20   CONTINUE
      END
 This code can be compiled and linked into an extension module named filter using: f2py -c -m filter filter.f
 This will produce an extension module named filter.so in the current directory with a method named dfilter2d that returns a filtered version of the input.   Calling f2py from Python The f2py program is written in Python and can be run from inside your code to compile Fortran code at runtime, as follows: from numpy import f2py
with open("add.f") as sourcefile:
    sourcecode = sourcefile.read()
f2py.compile(sourcecode, modulename='add')
import add
 The source string can be any valid Fortran code. If you want to save the extension-module source code then a suitable file-name can be provided by the source_fn keyword to the compile function.   Automatic extension module generation If you want to distribute your f2py extension module, then you only need to include the .pyf file and the Fortran code. The distutils extensions in NumPy allow you to define an extension module entirely in terms of this interface file. A valid setup.py file allowing distribution of the add.f module (as part of the package f2py_examples so that it would be loaded as f2py_examples.add) is: def configuration(parent_package='', top_path=None)
    from numpy.distutils.misc_util import Configuration
    config = Configuration('f2py_examples',parent_package, top_path)
    config.add_extension('add', sources=['add.pyf','add.f'])
    return config

if __name__ == '__main__':
    from numpy.distutils.core import setup
    setup(**configuration(top_path='').todict())
 Installation of the new package is easy using: pip install .
 assuming you have the proper permissions to write to the main site- packages directory for the version of Python you are using. For the resulting package to work, you need to create a file named __init__.py (in the same directory as add.pyf). Notice the extension module is defined entirely in terms of the add.pyf and add.f files. The conversion of the .pyf file to a .c file is handled by numpy.disutils.   Conclusion The interface definition file (.pyf) is how you can fine-tune the interface between Python and Fortran. There is decent documentation for f2py at F2PY user guide and reference manual. There is also more information on using f2py (including how to use it to wrap C codes) at the “Interfacing With Other Languages” heading of the SciPy Cookbook. The f2py method of linking compiled code is currently the most sophisticated and integrated approach. It allows clean separation of Python with compiled code while still allowing for separate distribution of the extension module. The only draw-back is that it requires the existence of a Fortran compiler in order for a user to install the code. However, with the existence of the free-compilers g77, gfortran, and g95, as well as high-quality commercial compilers, this restriction is not particularly onerous. In our opinion, Fortran is still the easiest way to write fast and clear code for scientific computing. It handles complex numbers, and multi-dimensional indexing in the most straightforward way. Be aware, however, that some Fortran compilers will not be able to optimize code as well as good hand- written C-code.    Cython Cython is a compiler for a Python dialect that adds (optional) static typing for speed, and allows mixing C or C++ code into your modules. It produces C or C++ extensions that can be compiled and imported in Python code. If you are writing an extension module that will include quite a bit of your own algorithmic code as well, then Cython is a good match. Among its features is the ability to easily and quickly work with multidimensional arrays. Notice that Cython is an extension-module generator only. Unlike f2py, it includes no automatic facility for compiling and linking the extension module (which must be done in the usual fashion). It does provide a modified distutils class called build_ext which lets you build an extension module from a .pyx source. Thus, you could write in a setup.py file: from Cython.Distutils import build_ext
from distutils.extension import Extension
from distutils.core import setup
import numpy

setup(name='mine', description='Nothing',
      ext_modules=[Extension('filter', ['filter.pyx'],
                             include_dirs=[numpy.get_include()])],
      cmdclass = {'build_ext':build_ext})
 Adding the NumPy include directory is, of course, only necessary if you are using NumPy arrays in the extension module (which is what we assume you are using Cython for). The distutils extensions in NumPy also include support for automatically producing the extension-module and linking it from a .pyx file. It works so that if the user does not have Cython installed, then it looks for a file with the same file-name but a .c extension which it then uses instead of trying to produce the .c file again. If you just use Cython to compile a standard Python module, then you will get a C extension module that typically runs a bit faster than the equivalent Python module. Further speed increases can be gained by using the cdef keyword to statically define C variables. Let’s look at two examples we’ve seen before to see how they might be implemented using Cython. These examples were compiled into extension modules using Cython 0.21.1.  Complex addition in Cython Here is part of a Cython module named add.pyx which implements the complex addition functions we previously implemented using f2py: cimport cython
cimport numpy as np
import numpy as np

# We need to initialize NumPy.
np.import_array()

#@cython.boundscheck(False)
def zadd(in1, in2):
    cdef double complex[:] a = in1.ravel()
    cdef double complex[:] b = in2.ravel()

    out = np.empty(a.shape[0], np.complex64)
    cdef double complex[:] c = out.ravel()

    for i in range(c.shape[0]):
        c[i].real = a[i].real + b[i].real
        c[i].imag = a[i].imag + b[i].imag

    return out
 This module shows use of the cimport statement to load the definitions from the numpy.pxd header that ships with Cython. It looks like NumPy is imported twice; cimport only makes the NumPy C-API available, while the regular import causes a Python-style import at runtime and makes it possible to call into the familiar NumPy Python API. The example also demonstrates Cython’s “typed memoryviews”, which are like NumPy arrays at the C level, in the sense that they are shaped and strided arrays that know their own extent (unlike a C array addressed through a bare pointer). The syntax double complex[:] denotes a one-dimensional array (vector) of doubles, with arbitrary strides. A contiguous array of ints would be int[::1], while a matrix of floats would be float[:, :]. Shown commented is the cython.boundscheck decorator, which turns bounds-checking for memory view accesses on or off on a per-function basis. We can use this to further speed up our code, at the expense of safety (or a manual check prior to entering the loop). Other than the view syntax, the function is immediately readable to a Python programmer. Static typing of the variable i is implicit. Instead of the view syntax, we could also have used Cython’s special NumPy array syntax, but the view syntax is preferred.   Image filter in Cython The two-dimensional example we created using Fortran is just as easy to write in Cython: cimport numpy as np
import numpy as np

np.import_array()

def filter(img):
    cdef double[:, :] a = np.asarray(img, dtype=np.double)
    out = np.zeros(img.shape, dtype=np.double)
    cdef double[:, ::1] b = out

    cdef np.npy_intp i, j

    for i in range(1, a.shape[0] - 1):
        for j in range(1, a.shape[1] - 1):
            b[i, j] = (a[i, j]
                       + .5 * (  a[i-1, j] + a[i+1, j]
                               + a[i, j-1] + a[i, j+1])
                       + .25 * (  a[i-1, j-1] + a[i-1, j+1]
                                + a[i+1, j-1] + a[i+1, j+1]))

    return out
 This 2-d averaging filter runs quickly because the loop is in C and the pointer computations are done only as needed. If the code above is compiled as a module image, then a 2-d image, img, can be filtered using this code very quickly using: import image
out = image.filter(img)
 Regarding the code, two things are of note: firstly, it is impossible to return a memory view to Python. Instead, a NumPy array out is first created, and then a view b onto this array is used for the computation. Secondly, the view b is typed double[:, ::1]. This means 2-d array with contiguous rows, i.e., C matrix order. Specifying the order explicitly can speed up some algorithms since they can skip stride computations.   Conclusion Cython is the extension mechanism of choice for several scientific Python libraries, including Scipy, Pandas, SAGE, scikit-image and scikit-learn, as well as the XML processing library LXML. The language and compiler are well-maintained. There are several disadvantages of using Cython:  When coding custom algorithms, and sometimes when wrapping existing C libraries, some familiarity with C is required. In particular, when using C memory management (malloc and friends), it’s easy to introduce memory leaks. However, just compiling a Python module renamed to .pyx can already speed it up, and adding a few type declarations can give dramatic speedups in some code. It is easy to lose a clean separation between Python and C which makes re-using your C-code for other non-Python-related projects more difficult. The C-code generated by Cython is hard to read and modify (and typically compiles with annoying but harmless warnings).  One big advantage of Cython-generated extension modules is that they are easy to distribute. In summary, Cython is a very capable tool for either gluing C code or generating an extension module quickly and should not be over-looked. It is especially useful for people that can’t or won’t write C or Fortran code.    ctypes Ctypes is a Python extension module, included in the stdlib, that allows you to call an arbitrary function in a shared library directly from Python. This approach allows you to interface with C-code directly from Python. This opens up an enormous number of libraries for use from Python. The drawback, however, is that coding mistakes can lead to ugly program crashes very easily (just as can happen in C) because there is little type or bounds checking done on the parameters. This is especially true when array data is passed in as a pointer to a raw memory location. The responsibility is then on you that the subroutine will not access memory outside the actual array area. But, if you don’t mind living a little dangerously ctypes can be an effective tool for quickly taking advantage of a large shared library (or writing extended functionality in your own shared library). Because the ctypes approach exposes a raw interface to the compiled code it is not always tolerant of user mistakes. Robust use of the ctypes module typically involves an additional layer of Python code in order to check the data types and array bounds of objects passed to the underlying subroutine. This additional layer of checking (not to mention the conversion from ctypes objects to C-data-types that ctypes itself performs), will make the interface slower than a hand-written extension-module interface. However, this overhead should be negligible if the C-routine being called is doing any significant amount of work. If you are a great Python programmer with weak C skills, ctypes is an easy way to write a useful interface to a (shared) library of compiled code. To use ctypes you must  Have a shared library. Load the shared library. Convert the Python objects to ctypes-understood arguments. Call the function from the library with the ctypes arguments.   Having a shared library There are several requirements for a shared library that can be used with ctypes that are platform specific. This guide assumes you have some familiarity with making a shared library on your system (or simply have a shared library available to you). Items to remember are:  A shared library must be compiled in a special way ( e.g. using the -shared flag with gcc).
On some platforms (e.g. Windows), a shared library requires a .def file that specifies the functions to be exported. For example a mylib.def file might contain: LIBRARY mylib.dll
EXPORTS
cool_function1
cool_function2
 Alternatively, you may be able to use the storage-class specifier __declspec(dllexport) in the C-definition of the function to avoid the need for this .def file.   There is no standard way in Python distutils to create a standard shared library (an extension module is a “special” shared library Python understands) in a cross-platform manner. Thus, a big disadvantage of ctypes at the time of writing this book is that it is difficult to distribute in a cross-platform manner a Python extension that uses ctypes and includes your own code which should be compiled as a shared library on the users system.   Loading the shared library A simple, but robust way to load the shared library is to get the absolute path name and load it using the cdll object of ctypes: lib = ctypes.cdll[<full_path_name>]
 However, on Windows accessing an attribute of the cdll method will load the first DLL by that name found in the current directory or on the PATH. Loading the absolute path name requires a little finesse for cross-platform work since the extension of shared libraries varies. There is a ctypes.util.find_library utility available that can simplify the process of finding the library to load but it is not foolproof. Complicating matters, different platforms have different default extensions used by shared libraries (e.g. .dll – Windows, .so – Linux, .dylib – Mac OS X). This must also be taken into account if you are using ctypes to wrap code that needs to work on several platforms. NumPy provides a convenience function called ctypeslib.load_library (name, path). This function takes the name of the shared library (including any prefix like ‘lib’ but excluding the extension) and a path where the shared library can be located. It returns a ctypes library object or raises an OSError if the library cannot be found or raises an ImportError if the ctypes module is not available. (Windows users: the ctypes library object loaded using load_library is always loaded assuming cdecl calling convention. See the ctypes documentation under ctypes.windll and/or ctypes.oledll for ways to load libraries under other calling conventions). The functions in the shared library are available as attributes of the ctypes library object (returned from ctypeslib.load_library) or as items using lib['func_name'] syntax. The latter method for retrieving a function name is particularly useful if the function name contains characters that are not allowable in Python variable names.   Converting arguments Python ints/longs, strings, and unicode objects are automatically converted as needed to equivalent ctypes arguments The None object is also converted automatically to a NULL pointer. All other Python objects must be converted to ctypes-specific types. There are two ways around this restriction that allow ctypes to integrate with other objects.  Don’t set the argtypes attribute of the function object and define an _as_parameter_ method for the object you want to pass in. The _as_parameter_ method must return a Python int which will be passed directly to the function. Set the argtypes attribute to a list whose entries contain objects with a classmethod named from_param that knows how to convert your object to an object that ctypes can understand (an int/long, string, unicode, or object with the _as_parameter_ attribute).  NumPy uses both methods with a preference for the second method because it can be safer. The ctypes attribute of the ndarray returns an object that has an _as_parameter_ attribute which returns an integer representing the address of the ndarray to which it is associated. As a result, one can pass this ctypes attribute object directly to a function expecting a pointer to the data in your ndarray. The caller must be sure that the ndarray object is of the correct type, shape, and has the correct flags set or risk nasty crashes if the data-pointer to inappropriate arrays are passed in. To implement the second method, NumPy provides the class-factory function ndpointer in the numpy.ctypeslib module. This class-factory function produces an appropriate class that can be placed in an argtypes attribute entry of a ctypes function. The class will contain a from_param method which ctypes will use to convert any ndarray passed in to the function to a ctypes-recognized object. In the process, the conversion will perform checking on any properties of the ndarray that were specified by the user in the call to ndpointer. Aspects of the ndarray that can be checked include the data-type, the number-of-dimensions, the shape, and/or the state of the flags on any array passed. The return value of the from_param method is the ctypes attribute of the array which (because it contains the _as_parameter_ attribute pointing to the array data area) can be used by ctypes directly. The ctypes attribute of an ndarray is also endowed with additional attributes that may be convenient when passing additional information about the array into a ctypes function. The attributes data, shape, and strides can provide ctypes compatible types corresponding to the data-area, the shape, and the strides of the array. The data attribute returns a c_void_p representing a pointer to the data area. The shape and strides attributes each return an array of ctypes integers (or None representing a NULL pointer, if a 0-d array). The base ctype of the array is a ctype integer of the same size as a pointer on the platform. There are also methods data_as({ctype}), shape_as(<base ctype>), and strides_as(<base
ctype>). These return the data as a ctype object of your choice and the shape/strides arrays using an underlying base type of your choice. For convenience, the ctypeslib module also contains c_intp as a ctypes integer data-type whose size is the same as the size of c_void_p on the platform (its value is None if ctypes is not installed).   Calling the function The function is accessed as an attribute of or an item from the loaded shared-library. Thus, if ./mylib.so has a function named cool_function1, it may be accessed either as: lib = numpy.ctypeslib.load_library('mylib','.')
func1 = lib.cool_function1  # or equivalently
func1 = lib['cool_function1']
 In ctypes, the return-value of a function is set to be ‘int’ by default. This behavior can be changed by setting the restype attribute of the function. Use None for the restype if the function has no return value (‘void’): func1.restype = None
 As previously discussed, you can also set the argtypes attribute of the function in order to have ctypes check the types of the input arguments when the function is called. Use the ndpointer factory function to generate a ready-made class for data-type, shape, and flags checking on your new function. The ndpointer function has the signature   ndpointer(dtype=None, ndim=None, shape=None, flags=None)

Keyword arguments with the value None are not checked. Specifying a keyword enforces checking of that aspect of the ndarray on conversion to a ctypes-compatible object. The dtype keyword can be any object understood as a data-type object. The ndim keyword should be an integer, and the shape keyword should be an integer or a sequence of integers. The flags keyword specifies the minimal flags that are required on any array passed in. This can be specified as a string of comma separated requirements, an integer indicating the requirement bits OR’d together, or a flags object returned from the flags attribute of an array with the necessary requirements.
 Using an ndpointer class in the argtypes method can make it significantly safer to call a C function using ctypes and the data- area of an ndarray. You may still want to wrap the function in an additional Python wrapper to make it user-friendly (hiding some obvious arguments and making some arguments output arguments). In this process, the requires function in NumPy may be useful to return the right kind of array from a given input.   Complete example In this example, we will demonstrate how the addition function and the filter function implemented previously using the other approaches can be implemented using ctypes. First, the C code which implements the algorithms contains the functions zadd, dadd, sadd, cadd, and dfilter2d. The zadd function is: /* Add arrays of contiguous data */
typedef struct {double real; double imag;} cdouble;
typedef struct {float real; float imag;} cfloat;
void zadd(cdouble *a, cdouble *b, cdouble *c, long n)
{
    while (n--) {
        c->real = a->real + b->real;
        c->imag = a->imag + b->imag;
        a++; b++; c++;
    }
}
 with similar code for cadd, dadd, and sadd that handles complex float, double, and float data-types, respectively: void cadd(cfloat *a, cfloat *b, cfloat *c, long n)
{
        while (n--) {
                c->real = a->real + b->real;
                c->imag = a->imag + b->imag;
                a++; b++; c++;
        }
}
void dadd(double *a, double *b, double *c, long n)
{
        while (n--) {
                *c++ = *a++ + *b++;
        }
}
void sadd(float *a, float *b, float *c, long n)
{
        while (n--) {
                *c++ = *a++ + *b++;
        }
}
 The code.c file also contains the function dfilter2d: /*
 * Assumes b is contiguous and has strides that are multiples of
 * sizeof(double)
 */
void
dfilter2d(double *a, double *b, ssize_t *astrides, ssize_t *dims)
{
    ssize_t i, j, M, N, S0, S1;
    ssize_t r, c, rm1, rp1, cp1, cm1;

    M = dims[0]; N = dims[1];
    S0 = astrides[0]/sizeof(double);
    S1 = astrides[1]/sizeof(double);
    for (i = 1; i < M - 1; i++) {
        r = i*S0;
        rp1 = r + S0;
        rm1 = r - S0;
        for (j = 1; j < N - 1; j++) {
            c = j*S1;
            cp1 = j + S1;
            cm1 = j - S1;
            b[i*N + j] = a[r + c] +
                (a[rp1 + c] + a[rm1 + c] +
                 a[r + cp1] + a[r + cm1])*0.5 +
                (a[rp1 + cp1] + a[rp1 + cm1] +
                 a[rm1 + cp1] + a[rm1 + cp1])*0.25;
        }
    }
}
 A possible advantage this code has over the Fortran-equivalent code is that it takes arbitrarily strided (i.e. non-contiguous arrays) and may also run faster depending on the optimization capability of your compiler. But, it is an obviously more complicated than the simple code in filter.f. This code must be compiled into a shared library. On my Linux system this is accomplished using: gcc -o code.so -shared code.c
 Which creates a shared_library named code.so in the current directory. On Windows don’t forget to either add __declspec(dllexport) in front of void on the line preceding each function definition, or write a code.def file that lists the names of the functions to be exported. A suitable Python interface to this shared library should be constructed. To do this create a file named interface.py with the following lines at the top: __all__ = ['add', 'filter2d']

import numpy as np
import os

_path = os.path.dirname('__file__')
lib = np.ctypeslib.load_library('code', _path)
_typedict = {'zadd' : complex, 'sadd' : np.single,
             'cadd' : np.csingle, 'dadd' : float}
for name in _typedict.keys():
    val = getattr(lib, name)
    val.restype = None
    _type = _typedict[name]
    val.argtypes = [np.ctypeslib.ndpointer(_type,
                      flags='aligned, contiguous'),
                    np.ctypeslib.ndpointer(_type,
                      flags='aligned, contiguous'),
                    np.ctypeslib.ndpointer(_type,
                      flags='aligned, contiguous,'\
                            'writeable'),
                    np.ctypeslib.c_intp]
 This code loads the shared library named code.{ext} located in the same path as this file. It then adds a return type of void to the functions contained in the library. It also adds argument checking to the functions in the library so that ndarrays can be passed as the first three arguments along with an integer (large enough to hold a pointer on the platform) as the fourth argument. Setting up the filtering function is similar and allows the filtering function to be called with ndarray arguments as the first two arguments and with pointers to integers (large enough to handle the strides and shape of an ndarray) as the last two arguments.: lib.dfilter2d.restype=None
lib.dfilter2d.argtypes = [np.ctypeslib.ndpointer(float, ndim=2,
                                       flags='aligned'),
                          np.ctypeslib.ndpointer(float, ndim=2,
                                 flags='aligned, contiguous,'\
                                       'writeable'),
                          ctypes.POINTER(np.ctypeslib.c_intp),
                          ctypes.POINTER(np.ctypeslib.c_intp)]
 Next, define a simple selection function that chooses which addition function to call in the shared library based on the data-type: def select(dtype):
    if dtype.char in ['?bBhHf']:
        return lib.sadd, single
    elif dtype.char in ['F']:
        return lib.cadd, csingle
    elif dtype.char in ['DG']:
        return lib.zadd, complex
    else:
        return lib.dadd, float
    return func, ntype
 Finally, the two functions to be exported by the interface can be written simply as: def add(a, b):
    requires = ['CONTIGUOUS', 'ALIGNED']
    a = np.asanyarray(a)
    func, dtype = select(a.dtype)
    a = np.require(a, dtype, requires)
    b = np.require(b, dtype, requires)
    c = np.empty_like(a)
    func(a,b,c,a.size)
    return c
 and: def filter2d(a):
    a = np.require(a, float, ['ALIGNED'])
    b = np.zeros_like(a)
    lib.dfilter2d(a, b, a.ctypes.strides, a.ctypes.shape)
    return b
   Conclusion Using ctypes is a powerful way to connect Python with arbitrary C-code. Its advantages for extending Python include
clean separation of C code from Python code  no need to learn a new syntax except Python and C allows re-use of C code functionality in shared libraries written for other purposes can be obtained with a simple Python wrapper and search for the library.   easy integration with NumPy through the ctypes attribute full argument checking with the ndpointer class factory  Its disadvantages include  It is difficult to distribute an extension module made using ctypes because of a lack of support for building shared libraries in distutils. You must have shared-libraries of your code (no static libraries). Very little support for C++ code and its different library-calling conventions. You will probably need a C wrapper around C++ code to use with ctypes (or just use Boost.Python instead).  Because of the difficulty in distributing an extension module made using ctypes, f2py and Cython are still the easiest ways to extend Python for package creation. However, ctypes is in some cases a useful alternative. This should bring more features to ctypes that should eliminate the difficulty in extending Python and distributing the extension using ctypes.    Additional tools you may find useful These tools have been found useful by others using Python and so are included here. They are discussed separately because they are either older ways to do things now handled by f2py, Cython, or ctypes (SWIG, PyFort) or because of a lack of reasonable documentation (SIP, Boost). Links to these methods are not included since the most relevant can be found using Google or some other search engine, and any links provided here would be quickly dated. Do not assume that inclusion in this list means that the package deserves attention. Information about these packages are collected here because many people have found them useful and we’d like to give you as many options as possible for tackling the problem of easily integrating your code.  SWIG Simplified Wrapper and Interface Generator (SWIG) is an old and fairly stable method for wrapping C/C++-libraries to a large variety of other languages. It does not specifically understand NumPy arrays but can be made usable with NumPy through the use of typemaps. There are some sample typemaps in the numpy/tools/swig directory under numpy.i together with an example module that makes use of them. SWIG excels at wrapping large C/C++ libraries because it can (almost) parse their headers and auto-produce an interface. Technically, you need to generate a .i file that defines the interface. Often, however, this .i file can be parts of the header itself. The interface usually needs a bit of tweaking to be very useful. This ability to parse C/C++ headers and auto-generate the interface still makes SWIG a useful approach to adding functionalilty from C/C++ into Python, despite the other methods that have emerged that are more targeted to Python. SWIG can actually target extensions for several languages, but the typemaps usually have to be language-specific. Nonetheless, with modifications to the Python-specific typemaps, SWIG can be used to interface a library with other languages such as Perl, Tcl, and Ruby. My experience with SWIG has been generally positive in that it is relatively easy to use and quite powerful. It has been used often before becoming more proficient at writing C-extensions. However, writing custom interfaces with SWIG is often troublesome because it must be done using the concept of typemaps which are not Python specific and are written in a C-like syntax. Therefore, other gluing strategies are preferred and SWIG would be probably considered only to wrap a very-large C/C++ library. Nonetheless, there are others who use SWIG quite happily.   SIP SIP is another tool for wrapping C/C++ libraries that is Python specific and appears to have very good support for C++. Riverbank Computing developed SIP in order to create Python bindings to the QT library. An interface file must be written to generate the binding, but the interface file looks a lot like a C/C++ header file. While SIP is not a full C++ parser, it understands quite a bit of C++ syntax as well as its own special directives that allow modification of how the Python binding is accomplished. It also allows the user to define mappings between Python types and C/C++ structures and classes.   Boost Python Boost is a repository of C++ libraries and Boost.Python is one of those libraries which provides a concise interface for binding C++ classes and functions to Python. The amazing part of the Boost.Python approach is that it works entirely in pure C++ without introducing a new syntax. Many users of C++ report that Boost.Python makes it possible to combine the best of both worlds in a seamless fashion. Using Boost to wrap simple C-subroutines is usually over-kill. Its primary purpose is to make C++ classes available in Python. So, if you have a set of C++ classes that need to be integrated cleanly into Python, consider learning about and using Boost.Python.   PyFort PyFort is a nice tool for wrapping Fortran and Fortran-like C-code into Python with support for Numeric arrays. It was written by Paul Dubois, a distinguished computer scientist and the very first maintainer of Numeric (now retired). It is worth mentioning in the hopes that somebody will update PyFort to work with NumPy arrays as well which now support either Fortran or C-style contiguous arrays.


numpy.number.__class_getitem__ method   number.__class_getitem__(item, /)

Return a parametrized wrapper around the number type.  New in version 1.22.   Returns

aliastypes.GenericAlias

A parametrized number type.      See also  PEP 585

Type hinting generics in standard collections.    Notes This method is only available for python 3.9 and later. Examples >>> from typing import Any
>>> import numpy as np
 >>> np.signedinteger[Any]
numpy.signedinteger[typing.Any]


numpy.absolute   numpy.absolute(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) = <ufunc 'absolute'>

Calculate the absolute value element-wise. np.abs is a shorthand for this function.  Parameters

xarray_like

Input array.
outndarray, None, or tuple of ndarray and None, optional

A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.
wherearray_like, optional

This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized.  **kwargs

For other keyword-only arguments, see the ufunc docs.    Returns

absolutendarray

An ndarray containing the absolute value of each element in x. For complex input, a + ib, the absolute value is \(\sqrt{ a^2 + b^2 }\). This is a scalar if x is a scalar.     Examples >>> x = np.array([-1.2, 1.2])
>>> np.absolute(x)
array([ 1.2,  1.2])
>>> np.absolute(1.2 + 1j)
1.5620499351813308
 Plot the function over [-10, 10]: >>> import matplotlib.pyplot as plt
 >>> x = np.linspace(start=-10, stop=10, num=101)
>>> plt.plot(x, np.absolute(x))
>>> plt.show()
    Plot the function over the complex plane: >>> xx = x + 1j * x[:, np.newaxis]
>>> plt.imshow(np.abs(xx), extent=[-10, 10, -10, 10], cmap='gray')
>>> plt.show()
    The abs function can be used as a shorthand for np.absolute on ndarrays. >>> x = np.array([-1.2, 1.2])
>>> abs(x)
array([1.2, 1.2])


numpy.add   numpy.add(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) = <ufunc 'add'>

Add arguments element-wise.  Parameters

x1, x2array_like

The arrays to be added. If x1.shape != x2.shape, they must be broadcastable to a common shape (which becomes the shape of the output).
outndarray, None, or tuple of ndarray and None, optional

A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.
wherearray_like, optional

This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized.  **kwargs

For other keyword-only arguments, see the ufunc docs.    Returns

addndarray or scalar

The sum of x1 and x2, element-wise. This is a scalar if both x1 and x2 are scalars.     Notes Equivalent to x1 + x2 in terms of array broadcasting. Examples >>> np.add(1.0, 4.0)
5.0
>>> x1 = np.arange(9.0).reshape((3, 3))
>>> x2 = np.arange(3.0)
>>> np.add(x1, x2)
array([[  0.,   2.,   4.],
       [  3.,   5.,   7.],
       [  6.,   8.,  10.]])
 The + operator can be used as a shorthand for np.add on ndarrays. >>> x1 = np.arange(9.0).reshape((3, 3))
>>> x2 = np.arange(3.0)
>>> x1 + x2
array([[ 0.,  2.,  4.],
       [ 3.,  5.,  7.],
       [ 6.,  8., 10.]])


numpy.all   numpy.all(a, axis=None, out=None, keepdims=<no value>, *, where=<no value>)[source]

Test whether all array elements along a given axis evaluate to True.  Parameters

aarray_like

Input array or object that can be converted to an array.
axisNone or int or tuple of ints, optional

Axis or axes along which a logical AND reduction is performed. The default (axis=None) is to perform a logical AND over all the dimensions of the input array. axis may be negative, in which case it counts from the last to the first axis.  New in version 1.7.0.  If this is a tuple of ints, a reduction is performed on multiple axes, instead of a single axis or all the axes as before.
outndarray, optional

Alternate output array in which to place the result. It must have the same shape as the expected output and its type is preserved (e.g., if dtype(out) is float, the result will consist of 0.0’s and 1.0’s). See Output type determination for more details.
keepdimsbool, optional

If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the input array. If the default value is passed, then keepdims will not be passed through to the all method of sub-classes of ndarray, however any non-default value will be. If the sub-class’ method does not implement keepdims any exceptions will be raised.
wherearray_like of bool, optional

Elements to include in checking for all True values. See reduce for details.  New in version 1.20.0.     Returns

allndarray, bool

A new boolean or array is returned unless out is specified, in which case a reference to out is returned.      See also  ndarray.all

equivalent method  any

Test whether any element along a given axis evaluates to True.    Notes Not a Number (NaN), positive infinity and negative infinity evaluate to True because these are not equal to zero. Examples >>> np.all([[True,False],[True,True]])
False
 >>> np.all([[True,False],[True,True]], axis=0)
array([ True, False])
 >>> np.all([-1, 4, 5])
True
 >>> np.all([1.0, np.nan])
True
 >>> np.all([[True, True], [False, True]], where=[[True], [False]])
True
 >>> o=np.array(False)
>>> z=np.all([-1, 4, 5], out=o)
>>> id(z), id(o), z
(28293632, 28293632, array(True)) # may vary


numpy.allclose   numpy.allclose(a, b, rtol=1e-05, atol=1e-08, equal_nan=False)[source]

Returns True if two arrays are element-wise equal within a tolerance. The tolerance values are positive, typically very small numbers. The relative difference (rtol * abs(b)) and the absolute difference atol are added together to compare against the absolute difference between a and b. NaNs are treated as equal if they are in the same place and if equal_nan=True. Infs are treated as equal if they are in the same place and of the same sign in both arrays.  Parameters

a, barray_like

Input arrays to compare.
rtolfloat

The relative tolerance parameter (see Notes).
atolfloat

The absolute tolerance parameter (see Notes).
equal_nanbool

Whether to compare NaN’s as equal. If True, NaN’s in a will be considered equal to NaN’s in b in the output array.  New in version 1.10.0.     Returns

allclosebool

Returns True if the two arrays are equal within the given tolerance; False otherwise.      See also
isclose, all, any, equal

  Notes If the following equation is element-wise True, then allclose returns True. absolute(a - b) <= (atol + rtol * absolute(b)) The above equation is not symmetric in a and b, so that allclose(a, b) might be different from allclose(b, a) in some rare cases. The comparison of a and b uses standard broadcasting, which means that a and b need not have the same shape in order for allclose(a, b) to evaluate to True. The same is true for equal but not array_equal. allclose is not defined for non-numeric data types. bool is considered a numeric data-type for this purpose. Examples >>> np.allclose([1e10,1e-7], [1.00001e10,1e-8])
False
>>> np.allclose([1e10,1e-8], [1.00001e10,1e-9])
True
>>> np.allclose([1e10,1e-8], [1.0001e10,1e-9])
False
>>> np.allclose([1.0, np.nan], [1.0, np.nan])
False
>>> np.allclose([1.0, np.nan], [1.0, np.nan], equal_nan=True)
True


numpy.amax   numpy.amax(a, axis=None, out=None, keepdims=<no value>, initial=<no value>, where=<no value>)[source]

Return the maximum of an array or maximum along an axis.  Parameters

aarray_like

Input data.
axisNone or int or tuple of ints, optional

Axis or axes along which to operate. By default, flattened input is used.  New in version 1.7.0.  If this is a tuple of ints, the maximum is selected over multiple axes, instead of a single axis or all the axes as before.
outndarray, optional

Alternative output array in which to place the result. Must be of the same shape and buffer length as the expected output. See Output type determination for more details.
keepdimsbool, optional

If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the input array. If the default value is passed, then keepdims will not be passed through to the amax method of sub-classes of ndarray, however any non-default value will be. If the sub-class’ method does not implement keepdims any exceptions will be raised.
initialscalar, optional

The minimum value of an output element. Must be present to allow computation on empty slice. See reduce for details.  New in version 1.15.0.
wherearray_like of bool, optional

Elements to compare for the maximum. See reduce for details.  New in version 1.17.0.     Returns

amaxndarray or scalar

Maximum of a. If axis is None, the result is a scalar value. If axis is given, the result is an array of dimension a.ndim - 1.      See also  amin

The minimum value of an array along a given axis, propagating any NaNs.  nanmax

The maximum value of an array along a given axis, ignoring any NaNs.  maximum

Element-wise maximum of two arrays, propagating any NaNs.  fmax

Element-wise maximum of two arrays, ignoring any NaNs.  argmax

Return the indices of the maximum values.
nanmin, minimum, fmin

  Notes NaN values are propagated, that is if at least one item is NaN, the corresponding max value will be NaN as well. To ignore NaN values (MATLAB behavior), please use nanmax. Don’t use amax for element-wise comparison of 2 arrays; when a.shape[0] is 2, maximum(a[0], a[1]) is faster than amax(a, axis=0). Examples >>> a = np.arange(4).reshape((2,2))
>>> a
array([[0, 1],
       [2, 3]])
>>> np.amax(a)           # Maximum of the flattened array
3
>>> np.amax(a, axis=0)   # Maxima along the first axis
array([2, 3])
>>> np.amax(a, axis=1)   # Maxima along the second axis
array([1, 3])
>>> np.amax(a, where=[False, True], initial=-1, axis=0)
array([-1,  3])
>>> b = np.arange(5, dtype=float)
>>> b[2] = np.NaN
>>> np.amax(b)
nan
>>> np.amax(b, where=~np.isnan(b), initial=-1)
4.0
>>> np.nanmax(b)
4.0
 You can use an initial value to compute the maximum of an empty slice, or to initialize it to a different value: >>> np.amax([[-50], [10]], axis=-1, initial=0)
array([ 0, 10])
 Notice that the initial value is used as one of the elements for which the maximum is determined, unlike for the default argument Python’s max function, which is only used for empty iterables. >>> np.amax([5], initial=6)
6
>>> max([5], default=6)
5


numpy.amin   numpy.amin(a, axis=None, out=None, keepdims=<no value>, initial=<no value>, where=<no value>)[source]

Return the minimum of an array or minimum along an axis.  Parameters

aarray_like

Input data.
axisNone or int or tuple of ints, optional

Axis or axes along which to operate. By default, flattened input is used.  New in version 1.7.0.  If this is a tuple of ints, the minimum is selected over multiple axes, instead of a single axis or all the axes as before.
outndarray, optional

Alternative output array in which to place the result. Must be of the same shape and buffer length as the expected output. See Output type determination for more details.
keepdimsbool, optional

If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the input array. If the default value is passed, then keepdims will not be passed through to the amin method of sub-classes of ndarray, however any non-default value will be. If the sub-class’ method does not implement keepdims any exceptions will be raised.
initialscalar, optional

The maximum value of an output element. Must be present to allow computation on empty slice. See reduce for details.  New in version 1.15.0.
wherearray_like of bool, optional

Elements to compare for the minimum. See reduce for details.  New in version 1.17.0.     Returns

aminndarray or scalar

Minimum of a. If axis is None, the result is a scalar value. If axis is given, the result is an array of dimension a.ndim - 1.      See also  amax

The maximum value of an array along a given axis, propagating any NaNs.  nanmin

The minimum value of an array along a given axis, ignoring any NaNs.  minimum

Element-wise minimum of two arrays, propagating any NaNs.  fmin

Element-wise minimum of two arrays, ignoring any NaNs.  argmin

Return the indices of the minimum values.
nanmax, maximum, fmax

  Notes NaN values are propagated, that is if at least one item is NaN, the corresponding min value will be NaN as well. To ignore NaN values (MATLAB behavior), please use nanmin. Don’t use amin for element-wise comparison of 2 arrays; when a.shape[0] is 2, minimum(a[0], a[1]) is faster than amin(a, axis=0). Examples >>> a = np.arange(4).reshape((2,2))
>>> a
array([[0, 1],
       [2, 3]])
>>> np.amin(a)           # Minimum of the flattened array
0
>>> np.amin(a, axis=0)   # Minima along the first axis
array([0, 1])
>>> np.amin(a, axis=1)   # Minima along the second axis
array([0, 2])
>>> np.amin(a, where=[False, True], initial=10, axis=0)
array([10,  1])
 >>> b = np.arange(5, dtype=float)
>>> b[2] = np.NaN
>>> np.amin(b)
nan
>>> np.amin(b, where=~np.isnan(b), initial=10)
0.0
>>> np.nanmin(b)
0.0
 >>> np.amin([[-50], [10]], axis=-1, initial=0)
array([-50,   0])
 Notice that the initial value is used as one of the elements for which the minimum is determined, unlike for the default argument Python’s max function, which is only used for empty iterables. Notice that this isn’t the same as Python’s default argument. >>> np.amin([6], initial=5)
5
>>> min([6], default=5)
6


numpy.angle   numpy.angle(z, deg=False)[source]

Return the angle of the complex argument.  Parameters

zarray_like

A complex number or sequence of complex numbers.
degbool, optional

Return angle in degrees if True, radians if False (default).    Returns

anglendarray or scalar

The counterclockwise angle from the positive real axis on the complex plane in the range (-pi, pi], with dtype as numpy.float64.  Changed in version 1.16.0: This function works on subclasses of ndarray like ma.array.       See also  arctan2
absolute
  Notes Although the angle of the complex number 0 is undefined, numpy.angle(0) returns the value 0. Examples >>> np.angle([1.0, 1.0j, 1+1j])               # in radians
array([ 0.        ,  1.57079633,  0.78539816]) # may vary
>>> np.angle(1+1j, deg=True)                  # in degrees
45.0


numpy.any   numpy.any(a, axis=None, out=None, keepdims=<no value>, *, where=<no value>)[source]

Test whether any array element along a given axis evaluates to True. Returns single boolean unless axis is not None  Parameters

aarray_like

Input array or object that can be converted to an array.
axisNone or int or tuple of ints, optional

Axis or axes along which a logical OR reduction is performed. The default (axis=None) is to perform a logical OR over all the dimensions of the input array. axis may be negative, in which case it counts from the last to the first axis.  New in version 1.7.0.  If this is a tuple of ints, a reduction is performed on multiple axes, instead of a single axis or all the axes as before.
outndarray, optional

Alternate output array in which to place the result. It must have the same shape as the expected output and its type is preserved (e.g., if it is of type float, then it will remain so, returning 1.0 for True and 0.0 for False, regardless of the type of a). See Output type determination for more details.
keepdimsbool, optional

If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the input array. If the default value is passed, then keepdims will not be passed through to the any method of sub-classes of ndarray, however any non-default value will be. If the sub-class’ method does not implement keepdims any exceptions will be raised.
wherearray_like of bool, optional

Elements to include in checking for any True values. See reduce for details.  New in version 1.20.0.     Returns

anybool or ndarray

A new boolean or ndarray is returned unless out is specified, in which case a reference to out is returned.      See also  ndarray.any

equivalent method  all

Test whether all elements along a given axis evaluate to True.    Notes Not a Number (NaN), positive infinity and negative infinity evaluate to True because these are not equal to zero. Examples >>> np.any([[True, False], [True, True]])
True
 >>> np.any([[True, False], [False, False]], axis=0)
array([ True, False])
 >>> np.any([-1, 0, 5])
True
 >>> np.any(np.nan)
True
 >>> np.any([[True, False], [False, False]], where=[[False], [True]])
False
 >>> o=np.array(False)
>>> z=np.any([-1, 4, 5], out=o)
>>> z, o
(array(True), array(True))
>>> # Check now that z is a reference to o
>>> z is o
True
>>> id(z), id(o) # identity of z and o
(191614240, 191614240)


numpy.append   numpy.append(arr, values, axis=None)[source]

Append values to the end of an array.  Parameters

arrarray_like

Values are appended to a copy of this array.
valuesarray_like

These values are appended to a copy of arr. It must be of the correct shape (the same shape as arr, excluding axis). If axis is not specified, values can be any shape and will be flattened before use.
axisint, optional

The axis along which values are appended. If axis is not given, both arr and values are flattened before use.    Returns

appendndarray

A copy of arr with values appended to axis. Note that append does not occur in-place: a new array is allocated and filled. If axis is None, out is a flattened array.      See also  insert

Insert elements into an array.  delete

Delete elements from an array.    Examples >>> np.append([1, 2, 3], [[4, 5, 6], [7, 8, 9]])
array([1, 2, 3, ..., 7, 8, 9])
 When axis is specified, values must have the correct shape. >>> np.append([[1, 2, 3], [4, 5, 6]], [[7, 8, 9]], axis=0)
array([[1, 2, 3],
       [4, 5, 6],
       [7, 8, 9]])
>>> np.append([[1, 2, 3], [4, 5, 6]], [7, 8, 9], axis=0)
Traceback (most recent call last):
    ...
ValueError: all the input arrays must have same number of dimensions, but
the array at index 0 has 2 dimension(s) and the array at index 1 has 1
dimension(s)


numpy.apply_along_axis   numpy.apply_along_axis(func1d, axis, arr, *args, **kwargs)[source]

Apply a function to 1-D slices along the given axis. Execute func1d(a, *args, **kwargs) where func1d operates on 1-D arrays and a is a 1-D slice of arr along axis. This is equivalent to (but faster than) the following use of ndindex and s_, which sets each of ii, jj, and kk to a tuple of indices: Ni, Nk = a.shape[:axis], a.shape[axis+1:]
for ii in ndindex(Ni):
    for kk in ndindex(Nk):
        f = func1d(arr[ii + s_[:,] + kk])
        Nj = f.shape
        for jj in ndindex(Nj):
            out[ii + jj + kk] = f[jj]
 Equivalently, eliminating the inner loop, this can be expressed as: Ni, Nk = a.shape[:axis], a.shape[axis+1:]
for ii in ndindex(Ni):
    for kk in ndindex(Nk):
        out[ii + s_[...,] + kk] = func1d(arr[ii + s_[:,] + kk])
  Parameters

func1dfunction (M,) -> (Nj…)

This function should accept 1-D arrays. It is applied to 1-D slices of arr along the specified axis.
axisinteger

Axis along which arr is sliced.
arrndarray (Ni…, M, Nk…)

Input array.
argsany

Additional arguments to func1d.
kwargsany

Additional named arguments to func1d.  New in version 1.9.0.     Returns

outndarray (Ni…, Nj…, Nk…)

The output array. The shape of out is identical to the shape of arr, except along the axis dimension. This axis is removed, and replaced with new dimensions equal to the shape of the return value of func1d. So if func1d returns a scalar out will have one fewer dimensions than arr.      See also  apply_over_axes

Apply a function repeatedly over multiple axes.    Examples >>> def my_func(a):
...     """Average first and last element of a 1-D array"""
...     return (a[0] + a[-1]) * 0.5
>>> b = np.array([[1,2,3], [4,5,6], [7,8,9]])
>>> np.apply_along_axis(my_func, 0, b)
array([4., 5., 6.])
>>> np.apply_along_axis(my_func, 1, b)
array([2.,  5.,  8.])
 For a function that returns a 1D array, the number of dimensions in outarr is the same as arr. >>> b = np.array([[8,1,7], [4,3,9], [5,2,6]])
>>> np.apply_along_axis(sorted, 1, b)
array([[1, 7, 8],
       [3, 4, 9],
       [2, 5, 6]])
 For a function that returns a higher dimensional array, those dimensions are inserted in place of the axis dimension. >>> b = np.array([[1,2,3], [4,5,6], [7,8,9]])
>>> np.apply_along_axis(np.diag, -1, b)
array([[[1, 0, 0],
        [0, 2, 0],
        [0, 0, 3]],
       [[4, 0, 0],
        [0, 5, 0],
        [0, 0, 6]],
       [[7, 0, 0],
        [0, 8, 0],
        [0, 0, 9]]])


numpy.apply_over_axes   numpy.apply_over_axes(func, a, axes)[source]

Apply a function repeatedly over multiple axes. func is called as res = func(a, axis), where axis is the first element of axes. The result res of the function call must have either the same dimensions as a or one less dimension. If res has one less dimension than a, a dimension is inserted before axis. The call to func is then repeated for each axis in axes, with res as the first argument.  Parameters

funcfunction

This function must take two arguments, func(a, axis).
aarray_like

Input array.
axesarray_like

Axes over which func is applied; the elements must be integers.    Returns

apply_over_axisndarray

The output array. The number of dimensions is the same as a, but the shape can be different. This depends on whether func changes the shape of its output with respect to its input.      See also  apply_along_axis

Apply a function to 1-D slices of an array along the given axis.    Notes This function is equivalent to tuple axis arguments to reorderable ufuncs with keepdims=True. Tuple axis arguments to ufuncs have been available since version 1.7.0. Examples >>> a = np.arange(24).reshape(2,3,4)
>>> a
array([[[ 0,  1,  2,  3],
        [ 4,  5,  6,  7],
        [ 8,  9, 10, 11]],
       [[12, 13, 14, 15],
        [16, 17, 18, 19],
        [20, 21, 22, 23]]])
 Sum over axes 0 and 2. The result has same number of dimensions as the original array: >>> np.apply_over_axes(np.sum, a, [0,2])
array([[[ 60],
        [ 92],
        [124]]])
 Tuple axis arguments to ufuncs are equivalent: >>> np.sum(a, axis=(0,2), keepdims=True)
array([[[ 60],
        [ 92],
        [124]]])


numpy.arange   numpy.arange([start, ]stop, [step, ]dtype=None, *, like=None)

Return evenly spaced values within a given interval. Values are generated within the half-open interval [start, stop) (in other words, the interval including start but excluding stop). For integer arguments the function is equivalent to the Python built-in range function, but returns an ndarray rather than a list. When using a non-integer step, such as 0.1, it is often better to use numpy.linspace. See the warnings section below for more information.  Parameters

startinteger or real, optional

Start of interval. The interval includes this value. The default start value is 0.
stopinteger or real

End of interval. The interval does not include this value, except in some cases where step is not an integer and floating point round-off affects the length of out.
stepinteger or real, optional

Spacing between values. For any output out, this is the distance between two adjacent values, out[i+1] - out[i]. The default step size is 1. If step is specified as a position argument, start must also be given.
dtypedtype

The type of the output array. If dtype is not given, infer the data type from the other input arguments.
likearray_like

Reference object to allow the creation of arrays which are not NumPy arrays. If an array-like passed in as like supports the __array_function__ protocol, the result will be defined by it. In this case, it ensures the creation of an array object compatible with that passed in via this argument.  New in version 1.20.0.     Returns

arangendarray

Array of evenly spaced values. For floating point arguments, the length of the result is ceil((stop - start)/step). Because of floating point overflow, this rule may result in the last element of out being greater than stop.      Warning The length of the output might not be numerically stable. Another stability issue is due to the internal implementation of numpy.arange. The actual step value used to populate the array is dtype(start + step) - dtype(start) and not step. Precision loss can occur here, due to casting or due to using floating points when start is much larger than step. This can lead to unexpected behaviour. For example: >>> np.arange(0, 5, 0.5, dtype=int)
array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0])
>>> np.arange(-3, 3, 0.5, dtype=int)
array([-3, -2, -1,  0,  1,  2,  3,  4,  5,  6,  7,  8])
 In such cases, the use of numpy.linspace should be preferred.   See also  numpy.linspace

Evenly spaced numbers with careful handling of endpoints.  numpy.ogrid

Arrays of evenly spaced numbers in N-dimensions.  numpy.mgrid

Grid-shaped arrays of evenly spaced numbers in N-dimensions.    Examples >>> np.arange(3)
array([0, 1, 2])
>>> np.arange(3.0)
array([ 0.,  1.,  2.])
>>> np.arange(3,7)
array([3, 4, 5, 6])
>>> np.arange(3,7,2)
array([3, 5])


numpy.arccos   numpy.arccos(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) = <ufunc 'arccos'>

Trigonometric inverse cosine, element-wise. The inverse of cos so that, if y = cos(x), then x = arccos(y).  Parameters

xarray_like

x-coordinate on the unit circle. For real arguments, the domain is [-1, 1].
outndarray, None, or tuple of ndarray and None, optional

A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.
wherearray_like, optional

This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized.  **kwargs

For other keyword-only arguments, see the ufunc docs.    Returns

anglendarray

The angle of the ray intersecting the unit circle at the given x-coordinate in radians [0, pi]. This is a scalar if x is a scalar.      See also
cos, arctan, arcsin, emath.arccos

  Notes arccos is a multivalued function: for each x there are infinitely many numbers z such that cos(z) = x. The convention is to return the angle z whose real part lies in [0, pi]. For real-valued input data types, arccos always returns real output. For each value that cannot be expressed as a real number or infinity, it yields nan and sets the invalid floating point error flag. For complex-valued input, arccos is a complex analytic function that has branch cuts [-inf, -1] and [1, inf] and is continuous from above on the former and from below on the latter. The inverse cos is also known as acos or cos^-1. References M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, 10th printing, 1964, pp. 79. https://personal.math.ubc.ca/~cbm/aands/page_79.htm Examples We expect the arccos of 1 to be 0, and of -1 to be pi: >>> np.arccos([1, -1])
array([ 0.        ,  3.14159265])
 Plot arccos: >>> import matplotlib.pyplot as plt
>>> x = np.linspace(-1, 1, num=100)
>>> plt.plot(x, np.arccos(x))
>>> plt.axis('tight')
>>> plt.show()


numpy.arccosh   numpy.arccosh(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) = <ufunc 'arccosh'>

Inverse hyperbolic cosine, element-wise.  Parameters

xarray_like

Input array.
outndarray, None, or tuple of ndarray and None, optional

A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.
wherearray_like, optional

This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized.  **kwargs

For other keyword-only arguments, see the ufunc docs.    Returns

arccoshndarray

Array of the same shape as x. This is a scalar if x is a scalar.      See also
cosh, arcsinh, sinh, arctanh, tanh

  Notes arccosh is a multivalued function: for each x there are infinitely many numbers z such that cosh(z) = x. The convention is to return the z whose imaginary part lies in [-pi, pi] and the real part in [0, inf]. For real-valued input data types, arccosh always returns real output. For each value that cannot be expressed as a real number or infinity, it yields nan and sets the invalid floating point error flag. For complex-valued input, arccosh is a complex analytical function that has a branch cut [-inf, 1] and is continuous from above on it. References  1
M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, 10th printing, 1964, pp. 86. https://personal.math.ubc.ca/~cbm/aands/page_86.htm  2
Wikipedia, “Inverse hyperbolic function”, https://en.wikipedia.org/wiki/Arccosh   Examples >>> np.arccosh([np.e, 10.0])
array([ 1.65745445,  2.99322285])
>>> np.arccosh(1)
0.0


numpy.arcsin   numpy.arcsin(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) = <ufunc 'arcsin'>

Inverse sine, element-wise.  Parameters

xarray_like

y-coordinate on the unit circle.
outndarray, None, or tuple of ndarray and None, optional

A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.
wherearray_like, optional

This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized.  **kwargs

For other keyword-only arguments, see the ufunc docs.    Returns

anglendarray

The inverse sine of each element in x, in radians and in the closed interval [-pi/2, pi/2]. This is a scalar if x is a scalar.      See also
sin, cos, arccos, tan, arctan, arctan2, emath.arcsin

  Notes arcsin is a multivalued function: for each x there are infinitely many numbers z such that \(sin(z) = x\). The convention is to return the angle z whose real part lies in [-pi/2, pi/2]. For real-valued input data types, arcsin always returns real output. For each value that cannot be expressed as a real number or infinity, it yields nan and sets the invalid floating point error flag. For complex-valued input, arcsin is a complex analytic function that has, by convention, the branch cuts [-inf, -1] and [1, inf] and is continuous from above on the former and from below on the latter. The inverse sine is also known as asin or sin^{-1}. References Abramowitz, M. and Stegun, I. A., Handbook of Mathematical Functions, 10th printing, New York: Dover, 1964, pp. 79ff. https://personal.math.ubc.ca/~cbm/aands/page_79.htm Examples >>> np.arcsin(1)     # pi/2
1.5707963267948966
>>> np.arcsin(-1)    # -pi/2
-1.5707963267948966
>>> np.arcsin(0)
0.0


numpy.arcsinh   numpy.arcsinh(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) = <ufunc 'arcsinh'>

Inverse hyperbolic sine element-wise.  Parameters

xarray_like

Input array.
outndarray, None, or tuple of ndarray and None, optional

A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.
wherearray_like, optional

This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized.  **kwargs

For other keyword-only arguments, see the ufunc docs.    Returns

outndarray or scalar

Array of the same shape as x. This is a scalar if x is a scalar.     Notes arcsinh is a multivalued function: for each x there are infinitely many numbers z such that sinh(z) = x. The convention is to return the z whose imaginary part lies in [-pi/2, pi/2]. For real-valued input data types, arcsinh always returns real output. For each value that cannot be expressed as a real number or infinity, it returns nan and sets the invalid floating point error flag. For complex-valued input, arccos is a complex analytical function that has branch cuts [1j, infj] and [-1j, -infj] and is continuous from the right on the former and from the left on the latter. The inverse hyperbolic sine is also known as asinh or sinh^-1. References  1
M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, 10th printing, 1964, pp. 86. https://personal.math.ubc.ca/~cbm/aands/page_86.htm  2
Wikipedia, “Inverse hyperbolic function”, https://en.wikipedia.org/wiki/Arcsinh   Examples >>> np.arcsinh(np.array([np.e, 10.0]))
array([ 1.72538256,  2.99822295])


numpy.arctan   numpy.arctan(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) = <ufunc 'arctan'>

Trigonometric inverse tangent, element-wise. The inverse of tan, so that if y = tan(x) then x = arctan(y).  Parameters

xarray_like

outndarray, None, or tuple of ndarray and None, optional

A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.
wherearray_like, optional

This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized.  **kwargs

For other keyword-only arguments, see the ufunc docs.    Returns

outndarray or scalar

Out has the same shape as x. Its real part is in [-pi/2, pi/2] (arctan(+/-inf) returns +/-pi/2). This is a scalar if x is a scalar.      See also  arctan2

The “four quadrant” arctan of the angle formed by (x, y) and the positive x-axis.  angle

Argument of complex values.    Notes arctan is a multi-valued function: for each x there are infinitely many numbers z such that tan(z) = x. The convention is to return the angle z whose real part lies in [-pi/2, pi/2]. For real-valued input data types, arctan always returns real output. For each value that cannot be expressed as a real number or infinity, it yields nan and sets the invalid floating point error flag. For complex-valued input, arctan is a complex analytic function that has [1j, infj] and [-1j, -infj] as branch cuts, and is continuous from the left on the former and from the right on the latter. The inverse tangent is also known as atan or tan^{-1}. References Abramowitz, M. and Stegun, I. A., Handbook of Mathematical Functions, 10th printing, New York: Dover, 1964, pp. 79. https://personal.math.ubc.ca/~cbm/aands/page_79.htm Examples We expect the arctan of 0 to be 0, and of 1 to be pi/4: >>> np.arctan([0, 1])
array([ 0.        ,  0.78539816])
 >>> np.pi/4
0.78539816339744828
 Plot arctan: >>> import matplotlib.pyplot as plt
>>> x = np.linspace(-10, 10)
>>> plt.plot(x, np.arctan(x))
>>> plt.axis('tight')
>>> plt.show()


numpy.arctan2   numpy.arctan2(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) = <ufunc 'arctan2'>

Element-wise arc tangent of x1/x2 choosing the quadrant correctly. The quadrant (i.e., branch) is chosen so that arctan2(x1, x2) is the signed angle in radians between the ray ending at the origin and passing through the point (1,0), and the ray ending at the origin and passing through the point (x2, x1). (Note the role reversal: the “y-coordinate” is the first function parameter, the “x-coordinate” is the second.) By IEEE convention, this function is defined for x2 = +/-0 and for either or both of x1 and x2 = +/-inf (see Notes for specific values). This function is not defined for complex-valued arguments; for the so-called argument of complex values, use angle.  Parameters

x1array_like, real-valued

y-coordinates.
x2array_like, real-valued

x-coordinates. If x1.shape != x2.shape, they must be broadcastable to a common shape (which becomes the shape of the output).
outndarray, None, or tuple of ndarray and None, optional

A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.
wherearray_like, optional

This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized.  **kwargs

For other keyword-only arguments, see the ufunc docs.    Returns

anglendarray

Array of angles in radians, in the range [-pi, pi]. This is a scalar if both x1 and x2 are scalars.      See also
arctan, tan, angle

  Notes arctan2 is identical to the atan2 function of the underlying C library. The following special values are defined in the C standard: [1]
x1 x2 arctan2(x1,x2)
+/- 0 +0 +/- 0
+/- 0 -0 +/- pi
> 0 +/-inf +0 / +pi
< 0 +/-inf -0 / -pi
+/-inf +inf +/- (pi/4)
+/-inf -inf +/- (3*pi/4)   Note that +0 and -0 are distinct floating point numbers, as are +inf and -inf. References  1
ISO/IEC standard 9899:1999, “Programming language C.”   Examples Consider four points in different quadrants: >>> x = np.array([-1, +1, +1, -1])
>>> y = np.array([-1, -1, +1, +1])
>>> np.arctan2(y, x) * 180 / np.pi
array([-135.,  -45.,   45.,  135.])
 Note the order of the parameters. arctan2 is defined also when x2 = 0 and at several other special points, obtaining values in the range [-pi, pi]: >>> np.arctan2([1., -1.], [0., 0.])
array([ 1.57079633, -1.57079633])
>>> np.arctan2([0., 0., np.inf], [+0., -0., np.inf])
array([ 0.        ,  3.14159265,  0.78539816])


numpy.arctanh   numpy.arctanh(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) = <ufunc 'arctanh'>

Inverse hyperbolic tangent element-wise.  Parameters

xarray_like

Input array.
outndarray, None, or tuple of ndarray and None, optional

A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.
wherearray_like, optional

This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized.  **kwargs

For other keyword-only arguments, see the ufunc docs.    Returns

outndarray or scalar

Array of the same shape as x. This is a scalar if x is a scalar.      See also  emath.arctanh
  Notes arctanh is a multivalued function: for each x there are infinitely many numbers z such that tanh(z) = x. The convention is to return the z whose imaginary part lies in [-pi/2, pi/2]. For real-valued input data types, arctanh always returns real output. For each value that cannot be expressed as a real number or infinity, it yields nan and sets the invalid floating point error flag. For complex-valued input, arctanh is a complex analytical function that has branch cuts [-1, -inf] and [1, inf] and is continuous from above on the former and from below on the latter. The inverse hyperbolic tangent is also known as atanh or tanh^-1. References  1
M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, 10th printing, 1964, pp. 86. https://personal.math.ubc.ca/~cbm/aands/page_86.htm  2
Wikipedia, “Inverse hyperbolic function”, https://en.wikipedia.org/wiki/Arctanh   Examples >>> np.arctanh([0, -0.5])
array([ 0.        , -0.54930614])


numpy.argmax   numpy.argmax(a, axis=None, out=None, *, keepdims=<no value>)[source]

Returns the indices of the maximum values along an axis.  Parameters

aarray_like

Input array.
axisint, optional

By default, the index is into the flattened array, otherwise along the specified axis.
outarray, optional

If provided, the result will be inserted into this array. It should be of the appropriate shape and dtype.
keepdimsbool, optional

If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the array.  New in version 1.22.0.     Returns

index_arrayndarray of ints

Array of indices into the array. It has the same shape as a.shape with the dimension along axis removed. If keepdims is set to True, then the size of axis will be 1 with the resulting array having same shape as a.shape.      See also
ndarray.argmax, argmin

amax

The maximum value along a given axis.  unravel_index

Convert a flat index into an index tuple.  take_along_axis

Apply np.expand_dims(index_array, axis) from argmax to an array as if by calling max.    Notes In case of multiple occurrences of the maximum values, the indices corresponding to the first occurrence are returned. Examples >>> a = np.arange(6).reshape(2,3) + 10
>>> a
array([[10, 11, 12],
       [13, 14, 15]])
>>> np.argmax(a)
5
>>> np.argmax(a, axis=0)
array([1, 1, 1])
>>> np.argmax(a, axis=1)
array([2, 2])
 Indexes of the maximal elements of a N-dimensional array: >>> ind = np.unravel_index(np.argmax(a, axis=None), a.shape)
>>> ind
(1, 2)
>>> a[ind]
15
 >>> b = np.arange(6)
>>> b[1] = 5
>>> b
array([0, 5, 2, 3, 4, 5])
>>> np.argmax(b)  # Only the first occurrence is returned.
1
 >>> x = np.array([[4,2,3], [1,0,3]])
>>> index_array = np.argmax(x, axis=-1)
>>> # Same as np.amax(x, axis=-1, keepdims=True)
>>> np.take_along_axis(x, np.expand_dims(index_array, axis=-1), axis=-1)
array([[4],
       [3]])
>>> # Same as np.amax(x, axis=-1)
>>> np.take_along_axis(x, np.expand_dims(index_array, axis=-1), axis=-1).squeeze(axis=-1)
array([4, 3])
 Setting keepdims to True, >>> x = np.arange(24).reshape((2, 3, 4))
>>> res = np.argmax(x, axis=1, keepdims=True)
>>> res.shape
(2, 1, 4)


numpy.argmin   numpy.argmin(a, axis=None, out=None, *, keepdims=<no value>)[source]

Returns the indices of the minimum values along an axis.  Parameters

aarray_like

Input array.
axisint, optional

By default, the index is into the flattened array, otherwise along the specified axis.
outarray, optional

If provided, the result will be inserted into this array. It should be of the appropriate shape and dtype.
keepdimsbool, optional

If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the array.  New in version 1.22.0.     Returns

index_arrayndarray of ints

Array of indices into the array. It has the same shape as a.shape with the dimension along axis removed. If keepdims is set to True, then the size of axis will be 1 with the resulting array having same shape as a.shape.      See also
ndarray.argmin, argmax

amin

The minimum value along a given axis.  unravel_index

Convert a flat index into an index tuple.  take_along_axis

Apply np.expand_dims(index_array, axis) from argmin to an array as if by calling min.    Notes In case of multiple occurrences of the minimum values, the indices corresponding to the first occurrence are returned. Examples >>> a = np.arange(6).reshape(2,3) + 10
>>> a
array([[10, 11, 12],
       [13, 14, 15]])
>>> np.argmin(a)
0
>>> np.argmin(a, axis=0)
array([0, 0, 0])
>>> np.argmin(a, axis=1)
array([0, 0])
 Indices of the minimum elements of a N-dimensional array: >>> ind = np.unravel_index(np.argmin(a, axis=None), a.shape)
>>> ind
(0, 0)
>>> a[ind]
10
 >>> b = np.arange(6) + 10
>>> b[4] = 10
>>> b
array([10, 11, 12, 13, 10, 15])
>>> np.argmin(b)  # Only the first occurrence is returned.
0
 >>> x = np.array([[4,2,3], [1,0,3]])
>>> index_array = np.argmin(x, axis=-1)
>>> # Same as np.amin(x, axis=-1, keepdims=True)
>>> np.take_along_axis(x, np.expand_dims(index_array, axis=-1), axis=-1)
array([[2],
       [0]])
>>> # Same as np.amax(x, axis=-1)
>>> np.take_along_axis(x, np.expand_dims(index_array, axis=-1), axis=-1).squeeze(axis=-1)
array([2, 0])
 Setting keepdims to True, >>> x = np.arange(24).reshape((2, 3, 4))
>>> res = np.argmin(x, axis=1, keepdims=True)
>>> res.shape
(2, 1, 4)


numpy.argpartition   numpy.argpartition(a, kth, axis=- 1, kind='introselect', order=None)[source]

Perform an indirect partition along the given axis using the algorithm specified by the kind keyword. It returns an array of indices of the same shape as a that index data along the given axis in partitioned order.  New in version 1.8.0.   Parameters

aarray_like

Array to sort.
kthint or sequence of ints

Element index to partition by. The k-th element will be in its final sorted position and all smaller elements will be moved before it and all larger elements behind it. The order all elements in the partitions is undefined. If provided with a sequence of k-th it will partition all of them into their sorted position at once.  Deprecated since version 1.22.0: Passing booleans as index is deprecated.
axisint or None, optional

Axis along which to sort. The default is -1 (the last axis). If None, the flattened array is used.
kind{‘introselect’}, optional

Selection algorithm. Default is ‘introselect’
orderstr or list of str, optional

When a is an array with fields defined, this argument specifies which fields to compare first, second, etc. A single field can be specified as a string, and not all fields need be specified, but unspecified fields will still be used, in the order in which they come up in the dtype, to break ties.    Returns

index_arrayndarray, int

Array of indices that partition a along the specified axis. If a is one-dimensional, a[index_array] yields a partitioned a. More generally, np.take_along_axis(a, index_array, axis=a) always yields the partitioned a, irrespective of dimensionality.      See also  partition

Describes partition algorithms used.  ndarray.partition

Inplace partition.  argsort

Full indirect sort.  take_along_axis

Apply index_array from argpartition to an array as if by calling partition.    Notes See partition for notes on the different selection algorithms. Examples One dimensional array: >>> x = np.array([3, 4, 2, 1])
>>> x[np.argpartition(x, 3)]
array([2, 1, 3, 4])
>>> x[np.argpartition(x, (1, 3))]
array([1, 2, 3, 4])
 >>> x = [3, 4, 2, 1]
>>> np.array(x)[np.argpartition(x, 3)]
array([2, 1, 3, 4])
 Multi-dimensional array: >>> x = np.array([[3, 4, 2], [1, 3, 1]])
>>> index_array = np.argpartition(x, kth=1, axis=-1)
>>> np.take_along_axis(x, index_array, axis=-1)  # same as np.partition(x, kth=1)
array([[2, 3, 4],
       [1, 1, 3]])


numpy.argsort   numpy.argsort(a, axis=- 1, kind=None, order=None)[source]

Returns the indices that would sort an array. Perform an indirect sort along the given axis using the algorithm specified by the kind keyword. It returns an array of indices of the same shape as a that index data along the given axis in sorted order.  Parameters

aarray_like

Array to sort.
axisint or None, optional

Axis along which to sort. The default is -1 (the last axis). If None, the flattened array is used.
kind{‘quicksort’, ‘mergesort’, ‘heapsort’, ‘stable’}, optional

Sorting algorithm. The default is ‘quicksort’. Note that both ‘stable’ and ‘mergesort’ use timsort under the covers and, in general, the actual implementation will vary with data type. The ‘mergesort’ option is retained for backwards compatibility.  Changed in version 1.15.0.: The ‘stable’ option was added.
orderstr or list of str, optional

When a is an array with fields defined, this argument specifies which fields to compare first, second, etc. A single field can be specified as a string, and not all fields need be specified, but unspecified fields will still be used, in the order in which they come up in the dtype, to break ties.    Returns

index_arrayndarray, int

Array of indices that sort a along the specified axis. If a is one-dimensional, a[index_array] yields a sorted a. More generally, np.take_along_axis(a, index_array, axis=axis) always yields the sorted a, irrespective of dimensionality.      See also  sort

Describes sorting algorithms used.  lexsort

Indirect stable sort with multiple keys.  ndarray.sort

Inplace sort.  argpartition

Indirect partial sort.  take_along_axis

Apply index_array from argsort to an array as if by calling sort.    Notes See sort for notes on the different sorting algorithms. As of NumPy 1.4.0 argsort works with real/complex arrays containing nan values. The enhanced sort order is documented in sort. Examples One dimensional array: >>> x = np.array([3, 1, 2])
>>> np.argsort(x)
array([1, 2, 0])
 Two-dimensional array: >>> x = np.array([[0, 3], [2, 2]])
>>> x
array([[0, 3],
       [2, 2]])
 >>> ind = np.argsort(x, axis=0)  # sorts along first axis (down)
>>> ind
array([[0, 1],
       [1, 0]])
>>> np.take_along_axis(x, ind, axis=0)  # same as np.sort(x, axis=0)
array([[0, 2],
       [2, 3]])
 >>> ind = np.argsort(x, axis=1)  # sorts along last axis (across)
>>> ind
array([[0, 1],
       [0, 1]])
>>> np.take_along_axis(x, ind, axis=1)  # same as np.sort(x, axis=1)
array([[0, 3],
       [2, 2]])
 Indices of the sorted elements of a N-dimensional array: >>> ind = np.unravel_index(np.argsort(x, axis=None), x.shape)
>>> ind
(array([0, 1, 1, 0]), array([0, 0, 1, 1]))
>>> x[ind]  # same as np.sort(x, axis=None)
array([0, 2, 2, 3])
 Sorting with keys: >>> x = np.array([(1, 0), (0, 1)], dtype=[('x', '<i4'), ('y', '<i4')])
>>> x
array([(1, 0), (0, 1)],
      dtype=[('x', '<i4'), ('y', '<i4')])
 >>> np.argsort(x, order=('x','y'))
array([1, 0])
 >>> np.argsort(x, order=('y','x'))
array([0, 1])


numpy.argwhere   numpy.argwhere(a)[source]

Find the indices of array elements that are non-zero, grouped by element.  Parameters

aarray_like

Input data.    Returns

index_array(N, a.ndim) ndarray

Indices of elements that are non-zero. Indices are grouped by element. This array will have shape (N, a.ndim) where N is the number of non-zero items.      See also
where, nonzero

  Notes np.argwhere(a) is almost the same as np.transpose(np.nonzero(a)), but produces a result of the correct shape for a 0D array. The output of argwhere is not suitable for indexing arrays. For this purpose use nonzero(a) instead. Examples >>> x = np.arange(6).reshape(2,3)
>>> x
array([[0, 1, 2],
       [3, 4, 5]])
>>> np.argwhere(x>1)
array([[0, 2],
       [1, 0],
       [1, 1],
       [1, 2]])


numpy.around   numpy.around(a, decimals=0, out=None)[source]

Evenly round to the given number of decimals.  Parameters

aarray_like

Input data.
decimalsint, optional

Number of decimal places to round to (default: 0). If decimals is negative, it specifies the number of positions to the left of the decimal point.
outndarray, optional

Alternative output array in which to place the result. It must have the same shape as the expected output, but the type of the output values will be cast if necessary. See Output type determination for more details.    Returns

rounded_arrayndarray

An array of the same type as a, containing the rounded values. Unless out was specified, a new array is created. A reference to the result is returned. The real and imaginary parts of complex numbers are rounded separately. The result of rounding a float is a float.      See also  ndarray.round

equivalent method
ceil, fix, floor, rint, trunc

  Notes For values exactly halfway between rounded decimal values, NumPy rounds to the nearest even value. Thus 1.5 and 2.5 round to 2.0, -0.5 and 0.5 round to 0.0, etc. np.around uses a fast but sometimes inexact algorithm to round floating-point datatypes. For positive decimals it is equivalent to np.true_divide(np.rint(a * 10**decimals), 10**decimals), which has error due to the inexact representation of decimal fractions in the IEEE floating point standard [1] and errors introduced when scaling by powers of ten. For instance, note the extra “1” in the following: >>> np.round(56294995342131.5, 3)
56294995342131.51
 If your goal is to print such values with a fixed number of decimals, it is preferable to use numpy’s float printing routines to limit the number of printed decimals: >>> np.format_float_positional(56294995342131.5, precision=3)
'56294995342131.5'
 The float printing routines use an accurate but much more computationally demanding algorithm to compute the number of digits after the decimal point. Alternatively, Python’s builtin round function uses a more accurate but slower algorithm for 64-bit floating point values: >>> round(56294995342131.5, 3)
56294995342131.5
>>> np.round(16.055, 2), round(16.055, 2)  # equals 16.0549999999999997
(16.06, 16.05)
 References  1
“Lecture Notes on the Status of IEEE 754”, William Kahan, https://people.eecs.berkeley.edu/~wkahan/ieee754status/IEEE754.PDF   Examples >>> np.around([0.37, 1.64])
array([0., 2.])
>>> np.around([0.37, 1.64], decimals=1)
array([0.4, 1.6])
>>> np.around([.5, 1.5, 2.5, 3.5, 4.5]) # rounds to nearest even value
array([0., 2., 2., 4., 4.])
>>> np.around([1,2,3,11], decimals=1) # ndarray of ints is returned
array([ 1,  2,  3, 11])
>>> np.around([1,2,3,11], decimals=-1)
array([ 0,  0,  0, 10])