SciPy

Python Types and C-Structures

Several new types are defined in the C-code. Most of these are accessible from Python, but a few are not exposed due to their limited use. Every new Python type has an associated PyObject * with an internal structure that includes a pointer to a “method table” that defines how the new object behaves in Python. When you receive a Python object into C code, you always get a pointer to a PyObject structure. Because a PyObject structure is very generic and defines only PyObject_HEAD, by itself it is not very interesting. However, different objects contain more details after the PyObject_HEAD (but you have to cast to the correct type to access them — or use accessor functions or macros).

New Python Types Defined

Python types are the functional equivalent in C of classes in Python. By constructing a new Python type you make available a new object for Python. The ndarray object is an example of a new type defined in C. New types are defined in C by two basic steps:

  1. creating a C-structure (usually named Py{Name}Object) that is binary- compatible with the PyObject structure itself but holds the additional information needed for that particular object;
  2. populating the PyTypeObject table (pointed to by the ob_type member of the PyObject structure) with pointers to functions that implement the desired behavior for the type.

Instead of special method names which define behavior for Python classes, there are “function tables” which point to functions that implement the desired results. Since Python 2.2, the PyTypeObject itself has become dynamic which allows C types that can be “sub-typed “from other C-types in C, and sub-classed in Python. The children types inherit the attributes and methods from their parent(s).

There are two major new types: the ndarray ( PyArray_Type ) and the ufunc ( PyUFunc_Type ). Additional types play a supportive role: the PyArrayIter_Type, the PyArrayMultiIter_Type, and the PyArrayDescr_Type . The PyArrayIter_Type is the type for a flat iterator for an ndarray (the object that is returned when getting the flat attribute). The PyArrayMultiIter_Type is the type of the object returned when calling broadcast (). It handles iteration and broadcasting over a collection of nested sequences. Also, the PyArrayDescr_Type is the data-type-descriptor type whose instances describe the data. Finally, there are 21 new scalar-array types which are new Python scalars corresponding to each of the fundamental data types available for arrays. An additional 10 other types are place holders that allow the array scalars to fit into a hierarchy of actual Python types.

PyArray_Type

PyArray_Type

The Python type of the ndarray is PyArray_Type. In C, every ndarray is a pointer to a PyArrayObject structure. The ob_type member of this structure contains a pointer to the PyArray_Type typeobject.

PyArrayObject

The PyArrayObject C-structure contains all of the required information for an array. All instances of an ndarray (and its subclasses) will have this structure. For future compatibility, these structure members should normally be accessed using the provided macros. If you need a shorter name, then you can make use of NPY_AO which is defined to be equivalent to PyArrayObject.

typedef struct PyArrayObject {
    PyObject_HEAD
    char *data;
    int nd;
    npy_intp *dimensions;
    npy_intp *strides;
    PyObject *base;
    PyArray_Descr *descr;
    int flags;
    PyObject *weakreflist;
} PyArrayObject;
PyArrayObject.PyObject_HEAD

This is needed by all Python objects. It consists of (at least) a reference count member ( ob_refcnt ) and a pointer to the typeobject ( ob_type ). (Other elements may also be present if Python was compiled with special options see Include/object.h in the Python source tree for more information). The ob_type member points to a Python type object.

char *PyArrayObject.data

A pointer to the first element of the array. This pointer can (and normally should) be recast to the data type of the array.

int PyArrayObject.nd

An integer providing the number of dimensions for this array. When nd is 0, the array is sometimes called a rank-0 array. Such arrays have undefined dimensions and strides and cannot be accessed. NPY_MAXDIMS is the largest number of dimensions for any array.

npy_intp PyArrayObject.dimensions

An array of integers providing the shape in each dimension as long as nd \geq 1. The integer is always large enough to hold a pointer on the platform, so the dimension size is only limited by memory.

npy_intp *PyArrayObject.strides

An array of integers providing for each dimension the number of bytes that must be skipped to get to the next element in that dimension.

PyObject *PyArrayObject.base

This member is used to hold a pointer to another Python object that is related to this array. There are two use cases: 1) If this array does not own its own memory, then base points to the Python object that owns it (perhaps another array object), 2) If this array has the NPY_ARRAY_UPDATEIFCOPY flag set, then this array is a working copy of a “misbehaved” array. As soon as this array is deleted, the array pointed to by base will be updated with the contents of this array.

PyArray_Descr *PyArrayObject.descr

A pointer to a data-type descriptor object (see below). The data-type descriptor object is an instance of a new built-in type which allows a generic description of memory. There is a descriptor structure for each data type supported. This descriptor structure contains useful information about the type as well as a pointer to a table of function pointers to implement specific functionality.

int PyArrayObject.flags

Flags indicating how the memory pointed to by data is to be interpreted. Possible flags are NPY_ARRAY_C_CONTIGUOUS, NPY_ARRAY_F_CONTIGUOUS, NPY_ARRAY_OWNDATA, NPY_ARRAY_ALIGNED, NPY_ARRAY_WRITEABLE, and NPY_ARRAY_UPDATEIFCOPY.

PyObject *PyArrayObject.weakreflist

This member allows array objects to have weak references (using the weakref module).

PyArrayDescr_Type

PyArrayDescr_Type

The PyArrayDescr_Type is the built-in type of the data-type-descriptor objects used to describe how the bytes comprising the array are to be interpreted. There are 21 statically-defined PyArray_Descr objects for the built-in data-types. While these participate in reference counting, their reference count should never reach zero. There is also a dynamic table of user-defined PyArray_Descr objects that is also maintained. Once a data-type-descriptor object is “registered” it should never be deallocated either. The function PyArray_DescrFromType (...) can be used to retrieve a PyArray_Descr object from an enumerated type-number (either built-in or user- defined).

PyArray_Descr

The format of the PyArray_Descr structure that lies at the heart of the PyArrayDescr_Type is

typedef struct {
    PyObject_HEAD
    PyTypeObject *typeobj;
    char kind;
    char type;
    char byteorder;
    char unused;
    int flags;
    int type_num;
    int elsize;
    int alignment;
    PyArray_ArrayDescr *subarray;
    PyObject *fields;
    PyArray_ArrFuncs *f;
} PyArray_Descr;
PyTypeObject *PyArray_Descr.typeobj

Pointer to a typeobject that is the corresponding Python type for the elements of this array. For the builtin types, this points to the corresponding array scalar. For user-defined types, this should point to a user-defined typeobject. This typeobject can either inherit from array scalars or not. If it does not inherit from array scalars, then the NPY_USE_GETITEM and NPY_USE_SETITEM flags should be set in the flags member.

char PyArray_Descr.kind

A character code indicating the kind of array (using the array interface typestring notation). A ‘b’ represents Boolean, a ‘i’ represents signed integer, a ‘u’ represents unsigned integer, ‘f’ represents floating point, ‘c’ represents complex floating point, ‘S’ represents 8-bit character string, ‘U’ represents 32-bit/character unicode string, and ‘V’ repesents arbitrary.

char PyArray_Descr.type

A traditional character code indicating the data type.

char PyArray_Descr.byteorder

A character indicating the byte-order: ‘>’ (big-endian), ‘<’ (little- endian), ‘=’ (native), ‘|’ (irrelevant, ignore). All builtin data- types have byteorder ‘=’.

int PyArray_Descr.flags

A data-type bit-flag that determines if the data-type exhibits object- array like behavior. Each bit in this member is a flag which are named as:

NPY_ITEM_REFCOUNT
NPY_ITEM_HASOBJECT

Indicates that items of this data-type must be reference counted (using Py_INCREF and Py_DECREF ).

NPY_LIST_PICKLE

Indicates arrays of this data-type must be converted to a list before pickling.

NPY_ITEM_IS_POINTER

Indicates the item is a pointer to some other data-type

NPY_NEEDS_INIT

Indicates memory for this data-type must be initialized (set to 0) on creation.

NPY_NEEDS_PYAPI

Indicates this data-type requires the Python C-API during access (so don’t give up the GIL if array access is going to be needed).

NPY_USE_GETITEM

On array access use the f->getitem function pointer instead of the standard conversion to an array scalar. Must use if you don’t define an array scalar to go along with the data-type.

NPY_USE_SETITEM

When creating a 0-d array from an array scalar use f->setitem instead of the standard copy from an array scalar. Must use if you don’t define an array scalar to go along with the data-type.

NPY_FROM_FIELDS

The bits that are inherited for the parent data-type if these bits are set in any field of the data-type. Currently ( NPY_NEEDS_INIT | NPY_LIST_PICKLE | NPY_ITEM_REFCOUNT | NPY_NEEDS_PYAPI ).

NPY_OBJECT_DTYPE_FLAGS

Bits set for the object data-type: ( NPY_LIST_PICKLE | NPY_USE_GETITEM | NPY_ITEM_IS_POINTER | NPY_REFCOUNT | NPY_NEEDS_INIT | NPY_NEEDS_PYAPI).

PyDataType_FLAGCHK(PyArray_Descr *dtype, int flags)

Return true if all the given flags are set for the data-type object.

PyDataType_REFCHK(PyArray_Descr *dtype)

Equivalent to PyDataType_FLAGCHK (dtype, NPY_ITEM_REFCOUNT).

int PyArray_Descr.type_num

A number that uniquely identifies the data type. For new data-types, this number is assigned when the data-type is registered.

int PyArray_Descr.elsize

For data types that are always the same size (such as long), this holds the size of the data type. For flexible data types where different arrays can have a different elementsize, this should be 0.

int PyArray_Descr.alignment

A number providing alignment information for this data type. Specifically, it shows how far from the start of a 2-element structure (whose first element is a char ), the compiler places an item of this type: offsetof(struct {char c; type v;}, v)

PyArray_ArrayDescr *PyArray_Descr.subarray

If this is non- NULL, then this data-type descriptor is a C-style contiguous array of another data-type descriptor. In other-words, each element that this descriptor describes is actually an array of some other base descriptor. This is most useful as the data-type descriptor for a field in another data-type descriptor. The fields member should be NULL if this is non- NULL (the fields member of the base descriptor can be non- NULL however). The PyArray_ArrayDescr structure is defined using

typedef struct {
    PyArray_Descr *base;
    PyObject *shape;
} PyArray_ArrayDescr;

The elements of this structure are:

PyArray_Descr *PyArray_ArrayDescr.base

The data-type-descriptor object of the base-type.

PyObject *PyArray_ArrayDescr.shape

The shape (always C-style contiguous) of the sub-array as a Python tuple.

PyObject *PyArray_Descr.fields

If this is non-NULL, then this data-type-descriptor has fields described by a Python dictionary whose keys are names (and also titles if given) and whose values are tuples that describe the fields. Recall that a data-type-descriptor always describes a fixed-length set of bytes. A field is a named sub-region of that total, fixed-length collection. A field is described by a tuple composed of another data- type-descriptor and a byte offset. Optionally, the tuple may contain a title which is normally a Python string. These tuples are placed in this dictionary keyed by name (and also title if given).

PyArray_ArrFuncs *PyArray_Descr.f

A pointer to a structure containing functions that the type needs to implement internal features. These functions are not the same thing as the universal functions (ufuncs) described later. Their signatures can vary arbitrarily.

PyArray_ArrFuncs

Functions implementing internal features. Not all of these function pointers must be defined for a given type. The required members are nonzero, copyswap, copyswapn, setitem, getitem, and cast. These are assumed to be non- NULL and NULL entries will cause a program crash. The other functions may be NULL which will just mean reduced functionality for that data-type. (Also, the nonzero function will be filled in with a default function if it is NULL when you register a user-defined data-type).

typedef struct {
    PyArray_VectorUnaryFunc *cast[NPY_NTYPES];
    PyArray_GetItemFunc *getitem;
    PyArray_SetItemFunc *setitem;
    PyArray_CopySwapNFunc *copyswapn;
    PyArray_CopySwapFunc *copyswap;
    PyArray_CompareFunc *compare;
    PyArray_ArgFunc *argmax;
    PyArray_DotFunc *dotfunc;
    PyArray_ScanFunc *scanfunc;
    PyArray_FromStrFunc *fromstr;
    PyArray_NonzeroFunc *nonzero;
    PyArray_FillFunc *fill;
    PyArray_FillWithScalarFunc *fillwithscalar;
    PyArray_SortFunc *sort[NPY_NSORTS];
    PyArray_ArgSortFunc *argsort[NPY_NSORTS];
    PyObject *castdict;
    PyArray_ScalarKindFunc *scalarkind;
    int **cancastscalarkindto;
    int *cancastto;
    int listpickle
} PyArray_ArrFuncs;

The concept of a behaved segment is used in the description of the function pointers. A behaved segment is one that is aligned and in native machine byte-order for the data-type. The nonzero, copyswap, copyswapn, getitem, and setitem functions can (and must) deal with mis-behaved arrays. The other functions require behaved memory segments.

void cast(void *from, void *to, npy_intp n, void *fromarr,
void *toarr)

An array of function pointers to cast from the current type to all of the other builtin types. Each function casts a contiguous, aligned, and notswapped buffer pointed at by from to a contiguous, aligned, and notswapped buffer pointed at by to The number of items to cast is given by n, and the arguments fromarr and toarr are interpreted as PyArrayObjects for flexible arrays to get itemsize information.

PyObject *getitem(void *data, void *arr)

A pointer to a function that returns a standard Python object from a single element of the array object arr pointed to by data. This function must be able to deal with “misbehaved “(misaligned and/or swapped) arrays correctly.

int setitem(PyObject *item, void *data, void *arr)

A pointer to a function that sets the Python object item into the array, arr, at the position pointed to by data . This function deals with “misbehaved” arrays. If successful, a zero is returned, otherwise, a negative one is returned (and a Python error set).

void copyswapn(void *dest, npy_intp dstride, void *src,
npy_intp sstride, npy_intp n, int swap, void *arr)
void copyswap(void *dest, void *src, int swap, void *arr)

These members are both pointers to functions to copy data from src to dest and swap if indicated. The value of arr is only used for flexible ( NPY_STRING, NPY_UNICODE, and NPY_VOID ) arrays (and is obtained from arr->descr->elsize ). The second function copies a single value, while the first loops over n values with the provided strides. These functions can deal with misbehaved src data. If src is NULL then no copy is performed. If swap is 0, then no byteswapping occurs. It is assumed that dest and src do not overlap. If they overlap, then use memmove (...) first followed by copyswap(n) with NULL valued src.

int compare(const void* d1, const void* d2, void* arr)

A pointer to a function that compares two elements of the array, arr, pointed to by d1 and d2. This function requires behaved (aligned and not swapped) arrays. The return value is 1 if * d1 > * d2, 0 if * d1 == * d2, and -1 if * d1 < * d2. The array object arr is used to retrieve itemsize and field information for flexible arrays.

int argmax(void* data, npy_intp n, npy_intp* max_ind,
void* arr)

A pointer to a function that retrieves the index of the largest of n elements in arr beginning at the element pointed to by data. This function requires that the memory segment be contiguous and behaved. The return value is always 0. The index of the largest element is returned in max_ind.

void dotfunc(void* ip1, npy_intp is1, void* ip2, npy_intp is2,
void* op, npy_intp n, void* arr)

A pointer to a function that multiplies two n -length sequences together, adds them, and places the result in element pointed to by op of arr. The start of the two sequences are pointed to by ip1 and ip2. To get to the next element in each sequence requires a jump of is1 and is2 bytes, respectively. This function requires behaved (though not necessarily contiguous) memory.

int scanfunc(FILE* fd, void* ip, void* sep, void* arr)

A pointer to a function that scans (scanf style) one element of the corresponding type from the file descriptor fd into the array memory pointed to by ip. The array is assumed to be behaved. If sep is not NULL, then a separator string is also scanned from the file before returning. The last argument arr is the array to be scanned into. A 0 is returned if the scan is successful. A negative number indicates something went wrong: -1 means the end of file was reached before the separator string could be scanned, -4 means that the end of file was reached before the element could be scanned, and -3 means that the element could not be interpreted from the format string. Requires a behaved array.

int fromstr(char* str, void* ip, char** endptr, void* arr)

A pointer to a function that converts the string pointed to by str to one element of the corresponding type and places it in the memory location pointed to by ip. After the conversion is completed, *endptr points to the rest of the string. The last argument arr is the array into which ip points (needed for variable-size data- types). Returns 0 on success or -1 on failure. Requires a behaved array.

Bool nonzero(void* data, void* arr)

A pointer to a function that returns TRUE if the item of arr pointed to by data is nonzero. This function can deal with misbehaved arrays.

void fill(void* data, npy_intp length, void* arr)

A pointer to a function that fills a contiguous array of given length with data. The first two elements of the array must already be filled- in. From these two values, a delta will be computed and the values from item 3 to the end will be computed by repeatedly adding this computed delta. The data buffer must be well-behaved.

void fillwithscalar(void* buffer, npy_intp length,
void* value, void* arr)

A pointer to a function that fills a contiguous buffer of the given length with a single scalar value whose address is given. The final argument is the array which is needed to get the itemsize for variable-length arrays.

int sort(void* start, npy_intp length, void* arr)

An array of function pointers to a particular sorting algorithms. A particular sorting algorithm is obtained using a key (so far NPY_QUICKSORT, :data`NPY_HEAPSORT`, and NPY_MERGESORT are defined). These sorts are done in-place assuming contiguous and aligned data.

int argsort(void* start, npy_intp* result, npy_intp length,
void *arr)

An array of function pointers to sorting algorithms for this data type. The same sorting algorithms as for sort are available. The indices producing the sort are returned in result (which must be initialized with indices 0 to length-1 inclusive).

PyObject *castdict

Either NULL or a dictionary containing low-level casting functions for user- defined data-types. Each function is wrapped in a PyCObject * and keyed by the data-type number.

NPY_SCALARKIND scalarkind(PyArrayObject* arr)

A function to determine how scalars of this type should be interpreted. The argument is NULL or a 0-dimensional array containing the data (if that is needed to determine the kind of scalar). The return value must be of type NPY_SCALARKIND.

int **cancastscalarkindto

Either NULL or an array of NPY_NSCALARKINDS pointers. These pointers should each be either NULL or a pointer to an array of integers (terminated by NPY_NOTYPE) indicating data-types that a scalar of this data-type of the specified kind can be cast to safely (this usually means without losing precision).

int *cancastto

Either NULL or an array of integers (terminated by NPY_NOTYPE ) indicated data-types that this data-type can be cast to safely (this usually means without losing precision).

int listpickle

Unused.

The PyArray_Type typeobject implements many of the features of Python objects including the tp_as_number, tp_as_sequence, tp_as_mapping, and tp_as_buffer interfaces. The rich comparison (tp_richcompare) is also used along with new-style attribute lookup for methods (tp_methods) and properties (tp_getset). The PyArray_Type can also be sub-typed.

Tip

The tp_as_number methods use a generic approach to call whatever function has been registered for handling the operation. The function PyNumeric_SetOps(..) can be used to register functions to handle particular mathematical operations (for all arrays). When the umath module is imported, it sets the numeric operations for all arrays to the corresponding ufuncs. The tp_str and tp_repr methods can also be altered using PyString_SetStringFunction(...).

PyUFunc_Type

PyUFunc_Type

The ufunc object is implemented by creation of the PyUFunc_Type. It is a very simple type that implements only basic getattribute behavior, printing behavior, and has call behavior which allows these objects to act like functions. The basic idea behind the ufunc is to hold a reference to fast 1-dimensional (vector) loops for each data type that supports the operation. These one-dimensional loops all have the same signature and are the key to creating a new ufunc. They are called by the generic looping code as appropriate to implement the N-dimensional function. There are also some generic 1-d loops defined for floating and complexfloating arrays that allow you to define a ufunc using a single scalar function (e.g. atanh).

PyUFuncObject

The core of the ufunc is the PyUFuncObject which contains all the information needed to call the underlying C-code loops that perform the actual work. It has the following structure:

typedef struct {
    PyObject_HEAD
    int nin;
    int nout;
    int nargs;
    int identity;
    PyUFuncGenericFunction *functions;
    void **data;
    int ntypes;
    int check_return;
    const char *name;
    char *types;
    const char *doc;
    void *ptr;
    PyObject *obj;
    PyObject *userloops;
    npy_uint32 *op_flags;
    npy_uint32 *iter_flags;
} PyUFuncObject;
PyUFuncObject.PyObject_HEAD

required for all Python objects.

int PyUFuncObject.nin

The number of input arguments.

int PyUFuncObject.nout

The number of output arguments.

int PyUFuncObject.nargs

The total number of arguments (nin + nout). This must be less than NPY_MAXARGS.

int PyUFuncObject.identity

Either PyUFunc_One, PyUFunc_Zero, or PyUFunc_None to indicate the identity for this operation. It is only used for a reduce-like call on an empty array.

void PyUFuncObject.functions(char** args, npy_intp* dims,
npy_intp* steps, void* extradata)

An array of function pointers — one for each data type supported by the ufunc. This is the vector loop that is called to implement the underlying function dims [0] times. The first argument, args, is an array of nargs pointers to behaved memory. Pointers to the data for the input arguments are first, followed by the pointers to the data for the output arguments. How many bytes must be skipped to get to the next element in the sequence is specified by the corresponding entry in the steps array. The last argument allows the loop to receive extra information. This is commonly used so that a single, generic vector loop can be used for multiple functions. In this case, the actual scalar function to call is passed in as extradata. The size of this function pointer array is ntypes.

void **PyUFuncObject.data

Extra data to be passed to the 1-d vector loops or NULL if no extra-data is needed. This C-array must be the same size ( i.e. ntypes) as the functions array. NULL is used if extra_data is not needed. Several C-API calls for UFuncs are just 1-d vector loops that make use of this extra data to receive a pointer to the actual function to call.

int PyUFuncObject.ntypes

The number of supported data types for the ufunc. This number specifies how many different 1-d loops (of the builtin data types) are available.

int PyUFuncObject.check_return

Obsolete and unused. However, it is set by the corresponding entry in the main ufunc creation routine: PyUFunc_FromFuncAndData (...).

char *PyUFuncObject.name

A string name for the ufunc. This is used dynamically to build the __doc__ attribute of ufuncs.

char *PyUFuncObject.types

An array of nargs \times ntypes 8-bit type_numbers which contains the type signature for the function for each of the supported (builtin) data types. For each of the ntypes functions, the corresponding set of type numbers in this array shows how the args argument should be interpreted in the 1-d vector loop. These type numbers do not have to be the same type and mixed-type ufuncs are supported.

char *PyUFuncObject.doc

Documentation for the ufunc. Should not contain the function signature as this is generated dynamically when __doc__ is retrieved.

void *PyUFuncObject.ptr

Any dynamically allocated memory. Currently, this is used for dynamic ufuncs created from a python function to store room for the types, data, and name members.

PyObject *PyUFuncObject.obj

For ufuncs dynamically created from python functions, this member holds a reference to the underlying Python function.

PyObject *PyUFuncObject.userloops

A dictionary of user-defined 1-d vector loops (stored as CObject ptrs) for user-defined types. A loop may be registered by the user for any user-defined type. It is retrieved by type number. User defined type numbers are always larger than NPY_USERDEF.

npy_uint32 PyUFuncObject.op_flags

Override the default operand flags for each ufunc operand.

npy_uint32 PyUFuncObject.iter_flags

Override the default nditer flags for the ufunc.

PyArrayIter_Type

PyArrayIter_Type

This is an iterator object that makes it easy to loop over an N-dimensional array. It is the object returned from the flat attribute of an ndarray. It is also used extensively throughout the implementation internals to loop over an N-dimensional array. The tp_as_mapping interface is implemented so that the iterator object can be indexed (using 1-d indexing), and a few methods are implemented through the tp_methods table. This object implements the next method and can be used anywhere an iterator can be used in Python.

PyArrayIterObject

The C-structure corresponding to an object of PyArrayIter_Type is the PyArrayIterObject. The PyArrayIterObject is used to keep track of a pointer into an N-dimensional array. It contains associated information used to quickly march through the array. The pointer can be adjusted in three basic ways: 1) advance to the “next” position in the array in a C-style contiguous fashion, 2) advance to an arbitrary N-dimensional coordinate in the array, and 3) advance to an arbitrary one-dimensional index into the array. The members of the PyArrayIterObject structure are used in these calculations. Iterator objects keep their own dimension and strides information about an array. This can be adjusted as needed for “broadcasting,” or to loop over only specific dimensions.

typedef struct {
    PyObject_HEAD
    int   nd_m1;
    npy_intp  index;
    npy_intp  size;
    npy_intp  coordinates[NPY_MAXDIMS];
    npy_intp  dims_m1[NPY_MAXDIMS];
    npy_intp  strides[NPY_MAXDIMS];
    npy_intp  backstrides[NPY_MAXDIMS];
    npy_intp  factors[NPY_MAXDIMS];
    PyArrayObject *ao;
    char  *dataptr;
    Bool  contiguous;
} PyArrayIterObject;
int PyArrayIterObject.nd_m1

N-1 where N is the number of dimensions in the underlying array.

npy_intp PyArrayIterObject.index

The current 1-d index into the array.

npy_intp PyArrayIterObject.size

The total size of the underlying array.

npy_intp *PyArrayIterObject.coordinates

An N -dimensional index into the array.

npy_intp *PyArrayIterObject.dims_m1

The size of the array minus 1 in each dimension.

npy_intp *PyArrayIterObject.strides

The strides of the array. How many bytes needed to jump to the next element in each dimension.

npy_intp *PyArrayIterObject.backstrides

How many bytes needed to jump from the end of a dimension back to its beginning. Note that backstrides [k]= strides [k]*d ims_m1 [k], but it is stored here as an optimization.

npy_intp *PyArrayIterObject.factors

This array is used in computing an N-d index from a 1-d index. It contains needed products of the dimensions.

PyArrayObject *PyArrayIterObject.ao

A pointer to the underlying ndarray this iterator was created to represent.

char *PyArrayIterObject.dataptr

This member points to an element in the ndarray indicated by the index.

Bool PyArrayIterObject.contiguous

This flag is true if the underlying array is NPY_ARRAY_C_CONTIGUOUS. It is used to simplify calculations when possible.

How to use an array iterator on a C-level is explained more fully in later sections. Typically, you do not need to concern yourself with the internal structure of the iterator object, and merely interact with it through the use of the macros PyArray_ITER_NEXT (it), PyArray_ITER_GOTO (it, dest), or PyArray_ITER_GOTO1D (it, index). All of these macros require the argument it to be a PyArrayIterObject *.

PyArrayMultiIter_Type

PyArrayMultiIter_Type

This type provides an iterator that encapsulates the concept of broadcasting. It allows N arrays to be broadcast together so that the loop progresses in C-style contiguous fashion over the broadcasted array. The corresponding C-structure is the PyArrayMultiIterObject whose memory layout must begin any object, obj, passed in to the PyArray_Broadcast (obj) function. Broadcasting is performed by adjusting array iterators so that each iterator represents the broadcasted shape and size, but has its strides adjusted so that the correct element from the array is used at each iteration.

PyArrayMultiIterObject
typedef struct {
    PyObject_HEAD
    int numiter;
    npy_intp size;
    npy_intp index;
    int nd;
    npy_intp dimensions[NPY_MAXDIMS];
    PyArrayIterObject *iters[NPY_MAXDIMS];
} PyArrayMultiIterObject;
PyArrayMultiIterObject.PyObject_HEAD

Needed at the start of every Python object (holds reference count and type identification).

int PyArrayMultiIterObject.numiter

The number of arrays that need to be broadcast to the same shape.

npy_intp PyArrayMultiIterObject.size

The total broadcasted size.

npy_intp PyArrayMultiIterObject.index

The current (1-d) index into the broadcasted result.

int PyArrayMultiIterObject.nd

The number of dimensions in the broadcasted result.

npy_intp *PyArrayMultiIterObject.dimensions

The shape of the broadcasted result (only nd slots are used).

PyArrayIterObject **PyArrayMultiIterObject.iters

An array of iterator objects that holds the iterators for the arrays to be broadcast together. On return, the iterators are adjusted for broadcasting.

PyArrayNeighborhoodIter_Type

PyArrayNeighborhoodIter_Type

This is an iterator object that makes it easy to loop over an N-dimensional neighborhood.

PyArrayNeighborhoodIterObject

The C-structure corresponding to an object of PyArrayNeighborhoodIter_Type is the PyArrayNeighborhoodIterObject.

PyArrayFlags_Type

PyArrayFlags_Type

When the flags attribute is retrieved from Python, a special builtin object of this type is constructed. This special type makes it easier to work with the different flags by accessing them as attributes or by accessing them as if the object were a dictionary with the flag names as entries.

ScalarArrayTypes

There is a Python type for each of the different built-in data types that can be present in the array Most of these are simple wrappers around the corresponding data type in C. The C-names for these types are Py{TYPE}ArrType_Type where {TYPE} can be

Bool, Byte, Short, Int, Long, LongLong, UByte, UShort, UInt, ULong, ULongLong, Half, Float, Double, LongDouble, CFloat, CDouble, CLongDouble, String, Unicode, Void, and Object.

These type names are part of the C-API and can therefore be created in extension C-code. There is also a PyIntpArrType_Type and a PyUIntpArrType_Type that are simple substitutes for one of the integer types that can hold a pointer on the platform. The structure of these scalar objects is not exposed to C-code. The function PyArray_ScalarAsCtype (..) can be used to extract the C-type value from the array scalar and the function PyArray_Scalar (...) can be used to construct an array scalar from a C-value.

Other C-Structures

A few new C-structures were found to be useful in the development of NumPy. These C-structures are used in at least one C-API call and are therefore documented here. The main reason these structures were defined is to make it easy to use the Python ParseTuple C-API to convert from Python objects to a useful C-Object.

PyArray_Dims

PyArray_Dims

This structure is very useful when shape and/or strides information is supposed to be interpreted. The structure is:

typedef struct {
    npy_intp *ptr;
    int len;
} PyArray_Dims;

The members of this structure are

npy_intp *PyArray_Dims.ptr

A pointer to a list of (npy_intp) integers which usually represent array shape or array strides.

int PyArray_Dims.len

The length of the list of integers. It is assumed safe to access ptr [0] to ptr [len-1].

PyArray_Chunk

PyArray_Chunk

This is equivalent to the buffer object structure in Python up to the ptr member. On 32-bit platforms (i.e. if NPY_SIZEOF_INT == NPY_SIZEOF_INTP), the len member also matches an equivalent member of the buffer object. It is useful to represent a generic single-segment chunk of memory.

typedef struct {
    PyObject_HEAD
    PyObject *base;
    void *ptr;
    npy_intp len;
    int flags;
} PyArray_Chunk;

The members are

PyArray_Chunk.PyObject_HEAD

Necessary for all Python objects. Included here so that the PyArray_Chunk structure matches that of the buffer object (at least to the len member).

PyObject *PyArray_Chunk.base

The Python object this chunk of memory comes from. Needed so that memory can be accounted for properly.

void *PyArray_Chunk.ptr

A pointer to the start of the single-segment chunk of memory.

npy_intp PyArray_Chunk.len

The length of the segment in bytes.

int PyArray_Chunk.flags

Any data flags (e.g. NPY_ARRAY_WRITEABLE ) that should be used to interpret the memory.

PyArrayInterface

PyArrayInterface

The PyArrayInterface structure is defined so that NumPy and other extension modules can use the rapid array interface protocol. The __array_struct__ method of an object that supports the rapid array interface protocol should return a PyCObject that contains a pointer to a PyArrayInterface structure with the relevant details of the array. After the new array is created, the attribute should be DECREF‘d which will free the PyArrayInterface structure. Remember to INCREF the object (whose __array_struct__ attribute was retrieved) and point the base member of the new PyArrayObject to this same object. In this way the memory for the array will be managed correctly.

typedef struct {
    int two;
    int nd;
    char typekind;
    int itemsize;
    int flags;
    npy_intp *shape;
    npy_intp *strides;
    void *data;
    PyObject *descr;
} PyArrayInterface;
int PyArrayInterface.two

the integer 2 as a sanity check.

int PyArrayInterface.nd

the number of dimensions in the array.

char PyArrayInterface.typekind

A character indicating what kind of array is present according to the typestring convention with ‘t’ -> bitfield, ‘b’ -> Boolean, ‘i’ -> signed integer, ‘u’ -> unsigned integer, ‘f’ -> floating point, ‘c’ -> complex floating point, ‘O’ -> object, ‘S’ -> (byte-)string, ‘U’ -> unicode, ‘V’ -> void.

int PyArrayInterface.itemsize

The number of bytes each item in the array requires.

int PyArrayInterface.flags

Any of the bits NPY_ARRAY_C_CONTIGUOUS (1), NPY_ARRAY_F_CONTIGUOUS (2), NPY_ARRAY_ALIGNED (0x100), NPY_ARRAY_NOTSWAPPED (0x200), or NPY_ARRAY_WRITEABLE (0x400) to indicate something about the data. The NPY_ARRAY_ALIGNED, NPY_ARRAY_C_CONTIGUOUS, and NPY_ARRAY_F_CONTIGUOUS flags can actually be determined from the other parameters. The flag NPY_ARR_HAS_DESCR (0x800) can also be set to indicate to objects consuming the version 3 array interface that the descr member of the structure is present (it will be ignored by objects consuming version 2 of the array interface).

npy_intp *PyArrayInterface.shape

An array containing the size of the array in each dimension.

npy_intp *PyArrayInterface.strides

An array containing the number of bytes to jump to get to the next element in each dimension.

void *PyArrayInterface.data

A pointer to the first element of the array.

PyObject *PyArrayInterface.descr

A Python object describing the data-type in more detail (same as the descr key in __array_interface__). This can be NULL if typekind and itemsize provide enough information. This field is also ignored unless ARR_HAS_DESCR flag is on in flags.

Internally used structures

Internally, the code uses some additional Python objects primarily for memory management. These types are not accessible directly from Python, and are not exposed to the C-API. They are included here only for completeness and assistance in understanding the code.

PyUFuncLoopObject

A loose wrapper for a C-structure that contains the information needed for looping. This is useful if you are trying to understand the ufunc looping code. The PyUFuncLoopObject is the associated C-structure. It is defined in the ufuncobject.h header.

PyUFuncReduceObject

A loose wrapper for the C-structure that contains the information needed for reduce-like methods of ufuncs. This is useful if you are trying to understand the reduce, accumulate, and reduce-at code. The PyUFuncReduceObject is the associated C-structure. It is defined in the ufuncobject.h header.

PyUFunc_Loop1d

A simple linked-list of C-structures containing the information needed to define a 1-d loop for a ufunc for every defined signature of a user-defined data-type.

PyArrayMapIter_Type

Advanced indexing is handled with this Python type. It is simply a loose wrapper around the C-structure containing the variables needed for advanced array indexing. The associated C-structure, PyArrayMapIterObject, is useful if you are trying to understand the advanced-index mapping code. It is defined in the arrayobject.h header. This type is not exposed to Python and could be replaced with a C-structure. As a Python type it takes advantage of reference- counted memory management.