galois.GFBase

class galois.GFBase(array, dtype=<class 'numpy.int64'>)

Bases: numpy.ndarray

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Note

This is an abstract base class for all Galois fields. It cannot be instantiated directly.

__init__()

Initialize self. See help(type(self)) for accurate signature.

Methods

Elements([dtype])
Ones(shape[, dtype])
Random([shape, low, high, dtype])
Zeros(shape[, dtype])
__init__()	Initialize self.
all([axis, out, keepdims])	Returns True if all elements evaluate to True.
any([axis, out, keepdims])	Returns True if any of the elements of a evaluate to True.
argmax([axis, out])	Return indices of the maximum values along the given axis.
argmin([axis, out])	Return indices of the minimum values along the given axis of a.
argpartition(kth[, axis, kind, order])	Returns the indices that would partition this array.
argsort([axis, kind, order])	Returns the indices that would sort this array.
astype(dtype[, order, casting, subok, copy])	Copy of the array, cast to a specified type.
byteswap([inplace])	Swap the bytes of the array elements
choose(choices[, out, mode])	Use an index array to construct a new array from a set of choices.
clip([min, max, out])	Return an array whose values are limited to [min, max].
compress(condition[, axis, out])	Return selected slices of this array along given axis.
conj()	Complex-conjugate all elements.
conjugate()	Return the complex conjugate, element-wise.
copy([order])	Return a copy of the array.
cumprod([axis, dtype, out])	Return the cumulative product of the elements along the given axis.
cumsum([axis, dtype, out])	Return the cumulative sum of the elements along the given axis.
diagonal([offset, axis1, axis2])	Return specified diagonals.
dot(b[, out])	Dot product of two arrays.
dump(file)	Dump a pickle of the array to the specified file.
dumps()	Returns the pickle of the array as a string.
fill(value)	Fill the array with a scalar value.
flatten([order])	Return a copy of the array collapsed into one dimension.
getfield(dtype[, offset])	Returns a field of the given array as a certain type.
item(*args)	Copy an element of an array to a standard Python scalar and return it.
itemset(*args)	Insert scalar into an array (scalar is cast to array’s dtype, if possible)
max([axis, out, keepdims, initial, where])	Return the maximum along a given axis.
mean([axis, dtype, out, keepdims])	Returns the average of the array elements along given axis.
min([axis, out, keepdims, initial, where])	Return the minimum along a given axis.
newbyteorder([new_order])	Return the array with the same data viewed with a different byte order.
nonzero()	Return the indices of the elements that are non-zero.
partition(kth[, axis, kind, order])	Rearranges the elements in the array in such a way that the value of the element in kth position is in the position it would be in a sorted array.
prod([axis, dtype, out, keepdims, initial, …])	Return the product of the array elements over the given axis
ptp([axis, out, keepdims])	Peak to peak (maximum - minimum) value along a given axis.
put(indices, values[, mode])	Set a.flat[n] = values[n] for all n in indices.
ravel([order])	Return a flattened array.
repeat(repeats[, axis])	Repeat elements of an array.
reshape(shape[, order])	Returns an array containing the same data with a new shape.
resize(new_shape[, refcheck])	Change shape and size of array in-place.
round([decimals, out])	Return a with each element rounded to the given number of decimals.
searchsorted(v[, side, sorter])	Find indices where elements of v should be inserted in a to maintain order.
setfield(val, dtype[, offset])	Put a value into a specified place in a field defined by a data-type.
setflags([write, align, uic])	Set array flags WRITEABLE, ALIGNED, (WRITEBACKIFCOPY and UPDATEIFCOPY), respectively.
sort([axis, kind, order])	Sort an array in-place.
squeeze([axis])	Remove single-dimensional entries from the shape of a.
std([axis, dtype, out, ddof, keepdims])	Returns the standard deviation of the array elements along given axis.
sum([axis, dtype, out, keepdims, initial, where])	Return the sum of the array elements over the given axis.
swapaxes(axis1, axis2)	Return a view of the array with axis1 and axis2 interchanged.
take(indices[, axis, out, mode])	Return an array formed from the elements of a at the given indices.
target(target)	Retarget the just-in-time compiled numba ufuncs.
tobytes([order])	Construct Python bytes containing the raw data bytes in the array.
tofile(fid[, sep, format])	Write array to a file as text or binary (default).
tolist()	Return the array as an a.ndim-levels deep nested list of Python scalars.
tostring([order])	A compatibility alias for tobytes, with exactly the same behavior.
trace([offset, axis1, axis2, dtype, out])	Return the sum along diagonals of the array.
transpose(*axes)	Returns a view of the array with axes transposed.
var([axis, dtype, out, ddof, keepdims])	Returns the variance of the array elements, along given axis.
view([dtype][, type])	New view of array with the same data.

Attributes

T	The transposed array.
alpha	The primitive element of the Galois field GF(p^m).
base	Base object if memory is from some other object.
characteristic	The characteristic p, which must be prime, of the Galois field GF(p^m).
ctypes	An object to simplify the interaction of the array with the ctypes module.
data	Python buffer object pointing to the start of the array’s data.
dtype	Data-type of the array’s elements.
dtypes	List of valid integer numpy dtypes that are compatible with this Galois field array class.
flags	Information about the memory layout of the array.
flat	A 1-D iterator over the array.
imag	The imaginary part of the array.
itemsize	Length of one array element in bytes.
nbytes	Total bytes consumed by the elements of the array.
ndim	Number of array dimensions.
order	The order p^m of the Galois field GF(p^m).
power	The power m, which must be non-negative, of the Galois field GF(p^m).
prim_poly	The primitive polynomial of the Galois field GF(p^m).
real	The real part of the array.
shape	Tuple of array dimensions.
size	Number of elements in the array.
strides	Tuple of bytes to step in each dimension when traversing an array.

classmethod Elements(dtype=<class 'numpy.int64'>)

classmethod Ones(shape, dtype=<class 'numpy.int64'>)

classmethod Random(shape=(), low=0, high=None, dtype=<class 'numpy.int64'>)

classmethod Zeros(shape, dtype=<class 'numpy.int64'>)

astype(dtype, order='K', casting='unsafe', subok=True, copy=True)

Copy of the array, cast to a specified type.

Parameters

• dtype (str or dtype) – Typecode or data-type to which the array is cast.

• order ({'C', 'F', 'A', 'K'}, optional) – Controls the memory layout order of the result. ‘C’ means C order, ‘F’ means Fortran order, ‘A’ means ‘F’ order if all the arrays are Fortran contiguous, ‘C’ order otherwise, and ‘K’ means as close to the order the array elements appear in memory as possible. Default is ‘K’.

• casting ({'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional) –

  Controls what kind of data casting may occur. Defaults to ‘unsafe’ for backwards compatibility.

  • ’no’ means the data types should not be cast at all.

  • ’equiv’ means only byte-order changes are allowed.

  • ’safe’ means only casts which can preserve values are allowed.

  • ’same_kind’ means only safe casts or casts within a kind, like float64 to float32, are allowed.

  • ’unsafe’ means any data conversions may be done.

• subok (bool, optional) – If True, then sub-classes will be passed-through (default), otherwise the returned array will be forced to be a base-class array.

• copy (bool, optional) – By default, astype always returns a newly allocated array. If this is set to false, and the dtype, order, and subok requirements are satisfied, the input array is returned instead of a copy.

Returns

arr_t – Unless copy is False and the other conditions for returning the input array are satisfied (see description for copy input parameter), arr_t is a new array of the same shape as the input array, with dtype, order given by dtype, order.

Return type

ndarray

Notes

Changed in version 1.17.0: Casting between a simple data type and a structured one is possible only for “unsafe” casting. Casting to multiple fields is allowed, but casting from multiple fields is not.

Changed in version 1.9.0: Casting from numeric to string types in ‘safe’ casting mode requires that the string dtype length is long enough to store the max integer/float value converted.

Raises

ComplexWarning – When casting from complex to float or int. To avoid this, one should use a.real.astype(t).

Examples

>>> x = np.array([1, 2, 2.5])
>>> x
array([1. ,  2. ,  2.5])

>>> x.astype(int)
array([1, 2, 2])

classmethod target(target)

Retarget the just-in-time compiled numba ufuncs.

Parameters

target (str) – Either “cpu”, “parallel”, or “cuda”.

alpha = None

The primitive element of the Galois field GF(p^m). The primitive element is a root of the primitive polynomial, such that prim_poly(alpha) = 0. The primitive element also generates the field GF(p^m) = {0, 1, alpha^1, alpha*2, …, alpha^(p^m - 2)}.

Type

int

characteristic = None

The characteristic p, which must be prime, of the Galois field GF(p^m). Adding p copies of any element will always result in 0.

Type

int

dtypes = []

List of valid integer numpy dtypes that are compatible with this Galois field array class.

Type

list

order = None

The order p^m of the Galois field GF(p^m). The order of the field is also equal to the field’s size.

Type

int

power = None

The power m, which must be non-negative, of the Galois field GF(p^m).

Type

int

prim_poly = None

The primitive polynomial of the Galois field GF(p^m). The primitve polynomial must have coefficients in GF(p).

Type

galois.Poly