viqa.utils.ImageArray¶

class viqa.utils.ImageArray(input_array)[source]¶

Class for image arrays.

This class is a subclass of numpy.ndarray and adds attributes for image statistics.

mean_value¶

Mean of the image array

Type:: float

median¶

Median of the image array

Type:: float

variance¶

Variance of the image array

Type:: float

standarddev¶

Standard deviation of the image array

Type:: float

skewness¶

Skewness of the image array

Type:: float

kurtosis¶

Kurtosis of the image array

Type:: float

histogram¶

Histogram of the image array

Type:: tuple

minimum¶

Minimum value of the image array

Type:: float

maximum¶

Maximum value of the image array

Type:: float

Parameters:: input_array (np.ndarray) – Numpy array containing the data
Returns:: obj – New instance of the ImageArray class
Return type:: ImageArray

calculate_statistics()[source]¶

Calculate statistics of the image array.

The following statistics are calculated:

mean
median
variance
standard deviation
skewness
kurtosis
histogram
minimum
maximum

describe(path: str | PathLike | None = None, filename: str | None = None) → dict[source]¶

Export image statistics to a csv file.

Parameters:

path (str or os.PathLike, optional) – Path to the directory where the csv file should be saved
filename (str, optional) – Name of the csv file

Returns:

stats – Dictionary containing the image statistics

Return type:

dict

Warns:

RuntimeWarning – If no path or filename is provided. Statistics are not exported.

Examples

>>> import numpy as np
>>> from viqa import ImageArray
>>> img = np.random.rand(128, 128)
>>> img = ImageArray(img)
>>> img.describe(path="path/to", filename="image_statistics")

visualize(slices: Tuple[int, int, int], export_path=None, **kwargs) → None[source]¶

Visualize the image array.

If export_path is provided, the visualization is saved to the directory.

Parameters:

slices (Tuple[int, int, int]) – Slices for the x, y and z axis
export_path (str or os.PathLike, optional) – Path to the directory where the visualization should be saved
**kwargs (dict) – Additional keyword arguments for visualization. See viqa.utils.visualize_3d().

Raises:

ValueError – If the image is not 2D or 3D.

Warns:

UserWarning – If the image is 2D, the parameter slices will be ignored.

Examples

>>> import numpy as np
>>> from viqa import ImageArray
>>> img = np.random.rand(128, 128, 128)
>>> img = ImageArray(img)
>>> img.visualize(slices=(64, 64, 64))

T¶

View of the transposed array.

Same as self.transpose().

Examples

>>> import numpy as np
>>> a = np.array([[1, 2], [3, 4]])
>>> a
array([[1, 2],
       [3, 4]])
>>> a.T
array([[1, 3],
       [2, 4]])

>>> a = np.array([1, 2, 3, 4])
>>> a
array([1, 2, 3, 4])
>>> a.T
array([1, 2, 3, 4])

See also

transpose

all(axis=None, out=None, keepdims=False, *, where=True)¶

Returns True if all elements evaluate to True.

Refer to numpy.all for full documentation.

See also

numpy.all: equivalent function

any(axis=None, out=None, keepdims=False, *, where=True)¶

Returns True if any of the elements of a evaluate to True.

Refer to numpy.any for full documentation.

See also

numpy.any: equivalent function

argmax(axis=None, out=None, *, keepdims=False)¶

Return indices of the maximum values along the given axis.

Refer to numpy.argmax for full documentation.

See also

numpy.argmax: equivalent function

argmin(axis=None, out=None, *, keepdims=False)¶

Return indices of the minimum values along the given axis.

Refer to numpy.argmin for detailed documentation.

See also

numpy.argmin: equivalent function

argpartition(kth, axis=-1, kind='introselect', order=None)¶

Returns the indices that would partition this array.

Refer to numpy.argpartition for full documentation.

Added in version 1.8.0.

See also

numpy.argpartition: equivalent function

argsort(axis=-1, kind=None, order=None)¶

Returns the indices that would sort this array.

Refer to numpy.argsort for full documentation.

See also

numpy.argsort: equivalent function

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

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

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

base¶

Base object if memory is from some other object.

Examples

The base of an array that owns its memory is None:

>>> import numpy as np
>>> x = np.array([1,2,3,4])
>>> x.base is None
True

Slicing creates a view, whose memory is shared with x:

>>> y = x[2:]
>>> y.base is x
True

byteswap(inplace=False)¶

Swap the bytes of the array elements

Toggle between low-endian and big-endian data representation by returning a byteswapped array, optionally swapped in-place. Arrays of byte-strings are not swapped. The real and imaginary parts of a complex number are swapped individually.

Parameters:: inplace (bool, optional) – If True, swap bytes in-place, default is False.
Returns:: out – The byteswapped array. If inplace is True, this is a view to self.
Return type:: ndarray

Examples

>>> import numpy as np
>>> A = np.array([1, 256, 8755], dtype=np.int16)
>>> list(map(hex, A))
['0x1', '0x100', '0x2233']
>>> A.byteswap(inplace=True)
array([  256,     1, 13090], dtype=int16)
>>> list(map(hex, A))
['0x100', '0x1', '0x3322']

Arrays of byte-strings are not swapped

>>> A = np.array([b'ceg', b'fac'])
>>> A.byteswap()
array([b'ceg', b'fac'], dtype='|S3')

A.view(A.dtype.newbyteorder()).byteswap() produces an array with the same values but different representation in memory

>>> A = np.array([1, 2, 3])
>>> A.view(np.uint8)
array([1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0,
       0, 0], dtype=uint8)
>>> A.view(A.dtype.newbyteorder()).byteswap(inplace=True)
array([1, 2, 3])
>>> A.view(np.uint8)
array([0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0,
       0, 3], dtype=uint8)

choose(choices, out=None, mode='raise')¶

Use an index array to construct a new array from a set of choices.

Refer to numpy.choose for full documentation.

See also

numpy.choose: equivalent function

clip(min=None, max=None, out=None, **kwargs)¶

Return an array whose values are limited to [min, max]. One of max or min must be given.

Refer to numpy.clip for full documentation.

See also

numpy.clip: equivalent function

compress(condition, axis=None, out=None)¶

Return selected slices of this array along given axis.

Refer to numpy.compress for full documentation.

See also

numpy.compress: equivalent function

conj()¶

Complex-conjugate all elements.

Refer to numpy.conjugate for full documentation.

See also

numpy.conjugate: equivalent function

conjugate()¶

Return the complex conjugate, element-wise.

Refer to numpy.conjugate for full documentation.

See also

numpy.conjugate: equivalent function

copy(order='C')¶

Return a copy of the array.

Parameters:: order ({'C', 'F', 'A', 'K'}, optional) – Controls the memory layout of the copy. ‘C’ means C-order, ‘F’ means F-order, ‘A’ means ‘F’ if a is Fortran contiguous, ‘C’ otherwise. ‘K’ means match the layout of a as closely as possible. (Note that this function and numpy.copy() are very similar but have different default values for their order= arguments, and this function always passes sub-classes through.)

See also

numpy.copy: Similar function with different default behavior

numpy.copyto

Notes

This function is the preferred method for creating an array copy. The function numpy.copy() is similar, but it defaults to using order ‘K’, and will not pass sub-classes through by default.

Examples

>>> import numpy as np
>>> x = np.array([[1,2,3],[4,5,6]], order='F')

>>> y = x.copy()

>>> x.fill(0)

>>> x
array([[0, 0, 0],
       [0, 0, 0]])

>>> y
array([[1, 2, 3],
       [4, 5, 6]])

>>> y.flags['C_CONTIGUOUS']
True

For arrays containing Python objects (e.g. dtype=object), the copy is a shallow one. The new array will contain the same object which may lead to surprises if that object can be modified (is mutable):

>>> a = np.array([1, 'm', [2, 3, 4]], dtype=object)
>>> b = a.copy()
>>> b[2][0] = 10
>>> a
array([1, 'm', list([10, 3, 4])], dtype=object)

To ensure all elements within an object array are copied, use copy.deepcopy:

>>> import copy
>>> a = np.array([1, 'm', [2, 3, 4]], dtype=object)
>>> c = copy.deepcopy(a)
>>> c[2][0] = 10
>>> c
array([1, 'm', list([10, 3, 4])], dtype=object)
>>> a
array([1, 'm', list([2, 3, 4])], dtype=object)

ctypes¶

An object to simplify the interaction of the array with the ctypes module.

This attribute creates an object that makes it easier to use arrays when calling shared libraries with the ctypes module. The returned object has, among others, data, shape, and strides attributes (see Notes below) which themselves return ctypes objects that can be used as arguments to a shared library.

Parameters:: None
Returns:: c – Possessing attributes data, shape, strides, etc.
Return type:: Python object

See also

numpy.ctypeslib

Notes

Below are the public attributes of this object which were documented in “Guide to NumPy” (we have omitted undocumented public attributes, as well as documented private attributes):

_ctypes.data

A pointer to the memory area of the array as a Python integer. This memory area may contain data that is not aligned, or not in correct byte-order. The memory area may not even be writeable. The array flags and data-type of this array should be respected when passing this attribute to arbitrary C-code to avoid trouble that can include Python crashing. User Beware! The value of this attribute is exactly the same as: self._array_interface_['data'][0].

Note that unlike data_as, a reference won’t be kept to the array: code like ctypes.c_void_p((a + b).ctypes.data) will result in a pointer to a deallocated array, and should be spelt (a + b).ctypes.data_as(ctypes.c_void_p)

_ctypes.shape

A ctypes array of length self.ndim where the basetype is the C-integer corresponding to dtype('p') on this platform (see ~numpy.ctypeslib.c_intp). This base-type could be ctypes.c_int, ctypes.c_long, or ctypes.c_longlong depending on the platform. The ctypes array contains the shape of the underlying array.

Type:: (c_intp*self.ndim)

_ctypes.strides

A ctypes array of length self.ndim where the basetype is the same as for the shape attribute. This ctypes array contains the strides information from the underlying array. This strides information is important for showing how many bytes must be jumped to get to the next element in the array.

Type:: (c_intp*self.ndim)

_ctypes.data_as(obj)

Return the data pointer cast to a particular c-types object. For example, calling self._as_parameter_ is equivalent to self.data_as(ctypes.c_void_p). Perhaps you want to use the data as a pointer to a ctypes array of floating-point data: self.data_as(ctypes.POINTER(ctypes.c_double)).

The returned pointer will keep a reference to the array.

_ctypes.shape_as(obj): Return the shape tuple as an array of some other c-types type. For example: self.shape_as(ctypes.c_short).

_ctypes.strides_as(obj): Return the strides tuple as an array of some other c-types type. For example: self.strides_as(ctypes.c_longlong).

If the ctypes module is not available, then the ctypes attribute of array objects still returns something useful, but ctypes objects are not returned and errors may be raised instead. In particular, the object will still have the as_parameter attribute which will return an integer equal to the data attribute.

Examples

>>> import numpy as np
>>> import ctypes
>>> x = np.array([[0, 1], [2, 3]], dtype=np.int32)
>>> x
array([[0, 1],
       [2, 3]], dtype=int32)
>>> x.ctypes.data
31962608 # may vary
>>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint32))
<__main__.LP_c_uint object at 0x7ff2fc1fc200> # may vary
>>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint32)).contents
c_uint(0)
>>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint64)).contents
c_ulong(4294967296)
>>> x.ctypes.shape
<numpy._core._internal.c_long_Array_2 object at 0x7ff2fc1fce60> # may vary
>>> x.ctypes.strides
<numpy._core._internal.c_long_Array_2 object at 0x7ff2fc1ff320> # may vary

cumprod(axis=None, dtype=None, out=None)¶

Return the cumulative product of the elements along the given axis.

Refer to numpy.cumprod for full documentation.

See also

numpy.cumprod: equivalent function

cumsum(axis=None, dtype=None, out=None)¶

Return the cumulative sum of the elements along the given axis.

Refer to numpy.cumsum for full documentation.

See also

numpy.cumsum: equivalent function

data¶: Python buffer object pointing to the start of the array’s data.

diagonal(offset=0, axis1=0, axis2=1)¶

Return specified diagonals. In NumPy 1.9 the returned array is a read-only view instead of a copy as in previous NumPy versions. In a future version the read-only restriction will be removed.

Refer to numpy.diagonal() for full documentation.

See also

numpy.diagonal: equivalent function

dtype¶

Data-type of the array’s elements.

Warning

Setting arr.dtype is discouraged and may be deprecated in the future. Setting will replace the dtype without modifying the memory (see also ndarray.view and ndarray.astype).

Parameters:: None
Returns:: d
Return type:: numpy dtype object

See also

ndarray.astype: Cast the values contained in the array to a new data-type.
ndarray.view: Create a view of the same data but a different data-type.

numpy.dtype

Examples

>>> x
array([[0, 1],
       [2, 3]])
>>> x.dtype
dtype('int32')
>>> type(x.dtype)
<type 'numpy.dtype'>

dump(file)¶

Dump a pickle of the array to the specified file. The array can be read back with pickle.load or numpy.load.

Parameters:

file (str or Path) –

A string naming the dump file.

Changed in version 1.17.0: pathlib.Path objects are now accepted.

dumps()¶

Returns the pickle of the array as a string. pickle.loads will convert the string back to an array.

Parameters:: None

fill(value)¶

Fill the array with a scalar value.

Parameters:: value (scalar) – All elements of a will be assigned this value.

Examples

>>> import numpy as np
>>> a = np.array([1, 2])
>>> a.fill(0)
>>> a
array([0, 0])
>>> a = np.empty(2)
>>> a.fill(1)
>>> a
array([1.,  1.])

Fill expects a scalar value and always behaves the same as assigning to a single array element. The following is a rare example where this distinction is important:

>>> a = np.array([None, None], dtype=object)
>>> a[0] = np.array(3)
>>> a
array([array(3), None], dtype=object)
>>> a.fill(np.array(3))
>>> a
array([array(3), array(3)], dtype=object)

Where other forms of assignments will unpack the array being assigned:

>>> a[...] = np.array(3)
>>> a
array([3, 3], dtype=object)

flags¶

Information about the memory layout of the array.

C_CONTIGUOUS(C)¶: The data is in a single, C-style contiguous segment.

F_CONTIGUOUS(F)¶: The data is in a single, Fortran-style contiguous segment.

OWNDATA(O)¶: The array owns the memory it uses or borrows it from another object.

WRITEABLE(W)¶: The data area can be written to. Setting this to False locks the data, making it read-only. A view (slice, etc.) inherits WRITEABLE from its base array at creation time, but a view of a writeable array may be subsequently locked while the base array remains writeable. (The opposite is not true, in that a view of a locked array may not be made writeable. However, currently, locking a base object does not lock any views that already reference it, so under that circumstance it is possible to alter the contents of a locked array via a previously created writeable view onto it.) Attempting to change a non-writeable array raises a RuntimeError exception.

ALIGNED(A)¶: The data and all elements are aligned appropriately for the hardware.

WRITEBACKIFCOPY(X)¶: This array is a copy of some other array. The C-API function PyArray_ResolveWritebackIfCopy must be called before deallocating to the base array will be updated with the contents of this array.

FNC¶: F_CONTIGUOUS and not C_CONTIGUOUS.

FORC¶: F_CONTIGUOUS or C_CONTIGUOUS (one-segment test).

BEHAVED(B)¶: ALIGNED and WRITEABLE.

CARRAY(CA)¶: BEHAVED and C_CONTIGUOUS.

FARRAY(FA)¶: BEHAVED and F_CONTIGUOUS and not C_CONTIGUOUS.

Notes

The flags object can be accessed dictionary-like (as in a.flags['WRITEABLE']), or by using lowercased attribute names (as in a.flags.writeable). Short flag names are only supported in dictionary access.

Only the WRITEBACKIFCOPY, WRITEABLE, and ALIGNED flags can be changed by the user, via direct assignment to the attribute or dictionary entry, or by calling ndarray.setflags.

The array flags cannot be set arbitrarily:

WRITEBACKIFCOPY can only be set False.
ALIGNED can only be set True if the data is truly aligned.
WRITEABLE can only be set True if the array owns its own memory or the ultimate owner of the memory exposes a writeable buffer interface or is a string.

Arrays can be both C-style and Fortran-style contiguous simultaneously. This is clear for 1-dimensional arrays, but can also be true for higher dimensional arrays.

Even for contiguous arrays a stride for a given dimension arr.strides[dim] may be arbitrary if arr.shape[dim] == 1 or the array has no elements. It does not generally hold that self.strides[-1] == self.itemsize for C-style contiguous arrays or self.strides[0] == self.itemsize for Fortran-style contiguous arrays is true.

flat¶

A 1-D iterator over the array.

This is a numpy.flatiter instance, which acts similarly to, but is not a subclass of, Python’s built-in iterator object.

See also

flatten: Return a copy of the array collapsed into one dimension.

flatiter

Examples

>>> import numpy as np
>>> x = np.arange(1, 7).reshape(2, 3)
>>> x
array([[1, 2, 3],
       [4, 5, 6]])
>>> x.flat[3]
4
>>> x.T
array([[1, 4],
       [2, 5],
       [3, 6]])
>>> x.T.flat[3]
5
>>> type(x.flat)
<class 'numpy.flatiter'>

An assignment example:

>>> x.flat = 3; x
array([[3, 3, 3],
       [3, 3, 3]])
>>> x.flat[[1,4]] = 1; x
array([[3, 1, 3],
       [3, 1, 3]])

flatten(order='C')¶

Return a copy of the array collapsed into one dimension.

Parameters:: order ({'C', 'F', 'A', 'K'}, optional) – ‘C’ means to flatten in row-major (C-style) order. ‘F’ means to flatten in column-major (Fortran- style) order. ‘A’ means to flatten in column-major order if a is Fortran contiguous in memory, row-major order otherwise. ‘K’ means to flatten a in the order the elements occur in memory. The default is ‘C’.
Returns:: y – A copy of the input array, flattened to one dimension.
Return type:: ndarray

See also

ravel: Return a flattened array.
flat: A 1-D flat iterator over the array.

Examples

>>> import numpy as np
>>> a = np.array([[1,2], [3,4]])
>>> a.flatten()
array([1, 2, 3, 4])
>>> a.flatten('F')
array([1, 3, 2, 4])

getfield(dtype, offset=0)¶

Returns a field of the given array as a certain type.

A field is a view of the array data with a given data-type. The values in the view are determined by the given type and the offset into the current array in bytes. The offset needs to be such that the view dtype fits in the array dtype; for example an array of dtype complex128 has 16-byte elements. If taking a view with a 32-bit integer (4 bytes), the offset needs to be between 0 and 12 bytes.

Parameters:

dtype (str or dtype) – The data type of the view. The dtype size of the view can not be larger than that of the array itself.
offset (int) – Number of bytes to skip before beginning the element view.

Examples

>>> import numpy as np
>>> x = np.diag([1.+1.j]*2)
>>> x[1, 1] = 2 + 4.j
>>> x
array([[1.+1.j,  0.+0.j],
       [0.+0.j,  2.+4.j]])
>>> x.getfield(np.float64)
array([[1.,  0.],
       [0.,  2.]])

By choosing an offset of 8 bytes we can select the complex part of the array for our view:

>>> x.getfield(np.float64, offset=8)
array([[1.,  0.],
       [0.,  4.]])

imag¶

The imaginary part of the array.

Examples

>>> import numpy as np
>>> x = np.sqrt([1+0j, 0+1j])
>>> x.imag
array([ 0.        ,  0.70710678])
>>> x.imag.dtype
dtype('float64')

item(*args)¶

Copy an element of an array to a standard Python scalar and return it.

Parameters:

*args (Arguments (variable number and type)) –

none: in this case, the method only works for arrays with one element (a.size == 1), which element is copied into a standard Python scalar object and returned.
int_type: this argument is interpreted as a flat index into the array, specifying which element to copy and return.
tuple of int_types: functions as does a single int_type argument, except that the argument is interpreted as an nd-index into the array.

Returns:

z – A copy of the specified element of the array as a suitable Python scalar

Return type:

Standard Python scalar object

Notes

When the data type of a is longdouble or clongdouble, item() returns a scalar array object because there is no available Python scalar that would not lose information. Void arrays return a buffer object for item(), unless fields are defined, in which case a tuple is returned.

item is very similar to a[args], except, instead of an array scalar, a standard Python scalar is returned. This can be useful for speeding up access to elements of the array and doing arithmetic on elements of the array using Python’s optimized math.

Examples

>>> import numpy as np
>>> np.random.seed(123)
>>> x = np.random.randint(9, size=(3, 3))
>>> x
array([[2, 2, 6],
       [1, 3, 6],
       [1, 0, 1]])
>>> x.item(3)
1
>>> x.item(7)
0
>>> x.item((0, 1))
2
>>> x.item((2, 2))
1

For an array with object dtype, elements are returned as-is.

>>> a = np.array([np.int64(1)], dtype=object)
>>> a.item() #return np.int64
np.int64(1)

itemsize¶

Length of one array element in bytes.

Examples

>>> import numpy as np
>>> x = np.array([1,2,3], dtype=np.float64)
>>> x.itemsize
8
>>> x = np.array([1,2,3], dtype=np.complex128)
>>> x.itemsize
16

mT¶

View of the matrix transposed array.

The matrix transpose is the transpose of the last two dimensions, even if the array is of higher dimension.

Added in version 2.0.

Raises:: ValueError – If the array is of dimension less than 2.

Examples

>>> import numpy as np
>>> a = np.array([[1, 2], [3, 4]])
>>> a
array([[1, 2],
       [3, 4]])
>>> a.mT
array([[1, 3],
       [2, 4]])

>>> a = np.arange(8).reshape((2, 2, 2))
>>> a
array([[[0, 1],
        [2, 3]],

       [[4, 5],
        [6, 7]]])
>>> a.mT
array([[[0, 2],
        [1, 3]],

       [[4, 6],
        [5, 7]]])

max(axis=None, out=None, keepdims=False, initial=<no value>, where=True)¶

Return the maximum along a given axis.

Refer to numpy.amax for full documentation.

See also

numpy.amax: equivalent function

mean(axis=None, dtype=None, out=None, keepdims=False, *, where=True)¶

Returns the average of the array elements along given axis.

Refer to numpy.mean for full documentation.

See also

numpy.mean: equivalent function

min(axis=None, out=None, keepdims=False, initial=<no value>, where=True)¶

Return the minimum along a given axis.

Refer to numpy.amin for full documentation.

See also

numpy.amin: equivalent function

nbytes¶

Total bytes consumed by the elements of the array.

Notes

Does not include memory consumed by non-element attributes of the array object.

See also

sys.getsizeof: Memory consumed by the object itself without parents in case view. This does include memory consumed by non-element attributes.

Examples

>>> import numpy as np
>>> x = np.zeros((3,5,2), dtype=np.complex128)
>>> x.nbytes
480
>>> np.prod(x.shape) * x.itemsize
480

ndim¶

Number of array dimensions.

Examples

>>> import numpy as np
>>> x = np.array([1, 2, 3])
>>> x.ndim
1
>>> y = np.zeros((2, 3, 4))
>>> y.ndim
3

nonzero()¶

Return the indices of the elements that are non-zero.

Refer to numpy.nonzero for full documentation.

See also

numpy.nonzero: equivalent function

partition(kth, axis=-1, kind='introselect', order=None)¶

Partially sorts the elements in the array in such a way that the value of the element in k-th position is in the position it would be in a sorted array. In the output array, all elements smaller than the k-th element are located to the left of this element and all equal or greater are located to its right. The ordering of the elements in the two partitions on the either side of the k-th element in the output array is undefined.

Added in version 1.8.0.

Parameters:

kth (int or sequence of ints) –
Element index to partition by. The kth element value will be in its final sorted position and all smaller elements will be moved before it and all equal or greater elements behind it. The order of all elements in the partitions is undefined. If provided with a sequence of kth it will partition all elements indexed by kth of them into their sorted position at once.

Deprecated since version 1.22.0: Passing booleans as index is deprecated.
axis (int, optional) – Axis along which to sort. Default is -1, which means sort along the last axis.
kind ({'introselect'}, optional) – Selection algorithm. Default is ‘introselect’.
order (str 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 to be specified, but unspecified fields will still be used, in the order in which they come up in the dtype, to break ties.

See also

numpy.partition: Return a partitioned copy of an array.
argpartition: Indirect partition.
sort: Full sort.

Notes

See np.partition for notes on the different algorithms.

Examples

>>> import numpy as np
>>> a = np.array([3, 4, 2, 1])
>>> a.partition(3)
>>> a
array([2, 1, 3, 4]) # may vary

>>> a.partition((1, 3))
>>> a
array([1, 2, 3, 4])

prod()¶

a.prod(axis=None, dtype=None, out=None, keepdims=False,: initial=1, where=True)

Return the product of the array elements over the given axis

Refer to numpy.prod for full documentation.

See also

numpy.prod: equivalent function

put(indices, values, mode='raise')¶

Set a.flat[n] = values[n] for all n in indices.

Refer to numpy.put for full documentation.

See also

numpy.put: equivalent function

ravel([order])¶

Return a flattened array.

Refer to numpy.ravel for full documentation.

See also

numpy.ravel: equivalent function
ndarray.flat: a flat iterator on the array.

real¶

The real part of the array.

Examples

>>> import numpy as np
>>> x = np.sqrt([1+0j, 0+1j])
>>> x.real
array([ 1.        ,  0.70710678])
>>> x.real.dtype
dtype('float64')

See also

numpy.real: equivalent function

repeat(repeats, axis=None)¶

Repeat elements of an array.

Refer to numpy.repeat for full documentation.

See also

numpy.repeat: equivalent function

reshape(shape, /, *, order='C', copy=None)¶

Returns an array containing the same data with a new shape.

Refer to numpy.reshape for full documentation.

See also

numpy.reshape: equivalent function

Notes

Unlike the free function numpy.reshape, this method on ndarray allows the elements of the shape parameter to be passed in as separate arguments. For example, a.reshape(10, 11) is equivalent to a.reshape((10, 11)).

resize(new_shape, refcheck=True)¶

Change shape and size of array in-place.

Parameters:

new_shape (tuple of ints, or n ints) – Shape of resized array.
refcheck (bool, optional) – If False, reference count will not be checked. Default is True.

Return type:

None

Raises:

ValueError – If a does not own its own data or references or views to it exist, and the data memory must be changed. PyPy only: will always raise if the data memory must be changed, since there is no reliable way to determine if references or views to it exist.
SystemError – If the order keyword argument is specified. This behaviour is a bug in NumPy.

See also

resize: Return a new array with the specified shape.

Notes

This reallocates space for the data area if necessary.

Only contiguous arrays (data elements consecutive in memory) can be resized.

The purpose of the reference count check is to make sure you do not use this array as a buffer for another Python object and then reallocate the memory. However, reference counts can increase in other ways so if you are sure that you have not shared the memory for this array with another Python object, then you may safely set refcheck to False.

Examples

Shrinking an array: array is flattened (in the order that the data are stored in memory), resized, and reshaped:

>>> import numpy as np

>>> a = np.array([[0, 1], [2, 3]], order='C')
>>> a.resize((2, 1))
>>> a
array([[0],
       [1]])

>>> a = np.array([[0, 1], [2, 3]], order='F')
>>> a.resize((2, 1))
>>> a
array([[0],
       [2]])

Enlarging an array: as above, but missing entries are filled with zeros:

>>> b = np.array([[0, 1], [2, 3]])
>>> b.resize(2, 3) # new_shape parameter doesn't have to be a tuple
>>> b
array([[0, 1, 2],
       [3, 0, 0]])

Referencing an array prevents resizing…

>>> c = a
>>> a.resize((1, 1))
Traceback (most recent call last):
...
ValueError: cannot resize an array that references or is referenced ...

Unless refcheck is False:

>>> a.resize((1, 1), refcheck=False)
>>> a
array([[0]])
>>> c
array([[0]])

round(decimals=0, out=None)¶

Return a with each element rounded to the given number of decimals.

Refer to numpy.around for full documentation.

See also

numpy.around: equivalent function

searchsorted(v, side='left', sorter=None)¶

Find indices where elements of v should be inserted in a to maintain order.

For full documentation, see numpy.searchsorted

See also

numpy.searchsorted: equivalent function

setfield(val, dtype, offset=0)¶

Put a value into a specified place in a field defined by a data-type.

Place val into a’s field defined by dtype and beginning offset bytes into the field.

Parameters:

val (object) – Value to be placed in field.
dtype (dtype object) – Data-type of the field in which to place val.
offset (int, optional) – The number of bytes into the field at which to place val.

Return type:

None

See also

getfield

Examples

>>> import numpy as np
>>> x = np.eye(3)
>>> x.getfield(np.float64)
array([[1.,  0.,  0.],
       [0.,  1.,  0.],
       [0.,  0.,  1.]])
>>> x.setfield(3, np.int32)
>>> x.getfield(np.int32)
array([[3, 3, 3],
       [3, 3, 3],
       [3, 3, 3]], dtype=int32)
>>> x
array([[1.0e+000, 1.5e-323, 1.5e-323],
       [1.5e-323, 1.0e+000, 1.5e-323],
       [1.5e-323, 1.5e-323, 1.0e+000]])
>>> x.setfield(np.eye(3), np.int32)
>>> x
array([[1.,  0.,  0.],
       [0.,  1.,  0.],
       [0.,  0.,  1.]])

setflags(write=None, align=None, uic=None)¶

Set array flags WRITEABLE, ALIGNED, WRITEBACKIFCOPY, respectively.

These Boolean-valued flags affect how numpy interprets the memory area used by a (see Notes below). The ALIGNED flag can only be set to True if the data is actually aligned according to the type. The WRITEBACKIFCOPY flag can never be set to True. The flag WRITEABLE can only be set to True if the array owns its own memory, or the ultimate owner of the memory exposes a writeable buffer interface, or is a string. (The exception for string is made so that unpickling can be done without copying memory.)

Parameters:

write (bool, optional) – Describes whether or not a can be written to.
align (bool, optional) – Describes whether or not a is aligned properly for its type.
uic (bool, optional) – Describes whether or not a is a copy of another “base” array.

Notes

Array flags provide information about how the memory area used for the array is to be interpreted. There are 7 Boolean flags in use, only three of which can be changed by the user: WRITEBACKIFCOPY, WRITEABLE, and ALIGNED.

WRITEABLE (W) the data area can be written to;

ALIGNED (A) the data and strides are aligned appropriately for the hardware (as determined by the compiler);

WRITEBACKIFCOPY (X) this array is a copy of some other array (referenced by .base). When the C-API function PyArray_ResolveWritebackIfCopy is called, the base array will be updated with the contents of this array.

All flags can be accessed using the single (upper case) letter as well as the full name.

Examples

>>> import numpy as np
>>> y = np.array([[3, 1, 7],
...               [2, 0, 0],
...               [8, 5, 9]])
>>> y
array([[3, 1, 7],
       [2, 0, 0],
       [8, 5, 9]])
>>> y.flags
  C_CONTIGUOUS : True
  F_CONTIGUOUS : False
  OWNDATA : True
  WRITEABLE : True
  ALIGNED : True
  WRITEBACKIFCOPY : False
>>> y.setflags(write=0, align=0)
>>> y.flags
  C_CONTIGUOUS : True
  F_CONTIGUOUS : False
  OWNDATA : True
  WRITEABLE : False
  ALIGNED : False
  WRITEBACKIFCOPY : False
>>> y.setflags(uic=1)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
ValueError: cannot set WRITEBACKIFCOPY flag to True

shape¶

Tuple of array dimensions.

The shape property is usually used to get the current shape of an array, but may also be used to reshape the array in-place by assigning a tuple of array dimensions to it. As with numpy.reshape, one of the new shape dimensions can be -1, in which case its value is inferred from the size of the array and the remaining dimensions. Reshaping an array in-place will fail if a copy is required.

Warning

Setting arr.shape is discouraged and may be deprecated in the future. Using ndarray.reshape is the preferred approach.

Examples

>>> import numpy as np
>>> x = np.array([1, 2, 3, 4])
>>> x.shape
(4,)
>>> y = np.zeros((2, 3, 4))
>>> y.shape
(2, 3, 4)
>>> y.shape = (3, 8)
>>> y
array([[ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],
       [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],
       [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.]])
>>> y.shape = (3, 6)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
ValueError: total size of new array must be unchanged
>>> np.zeros((4,2))[::2].shape = (-1,)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
AttributeError: Incompatible shape for in-place modification. Use
`.reshape()` to make a copy with the desired shape.

See also

numpy.shape: Equivalent getter function.
numpy.reshape: Function similar to setting shape.
ndarray.reshape: Method similar to setting shape.

size¶

Number of elements in the array.

Equal to np.prod(a.shape), i.e., the product of the array’s dimensions.

Notes

a.size returns a standard arbitrary precision Python integer. This may not be the case with other methods of obtaining the same value (like the suggested np.prod(a.shape), which returns an instance of np.int_), and may be relevant if the value is used further in calculations that may overflow a fixed size integer type.

Examples

>>> import numpy as np
>>> x = np.zeros((3, 5, 2), dtype=np.complex128)
>>> x.size
30
>>> np.prod(x.shape)
30

sort(axis=-1, kind=None, order=None)¶

Sort an array in-place. Refer to numpy.sort for full documentation.

Parameters:

axis (int, optional) – Axis along which to sort. Default is -1, which means sort along the last axis.
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 datatype. The ‘mergesort’ option is retained for backwards compatibility.

Changed in version 1.15.0: The ‘stable’ option was added.
order (str 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.

See also

numpy.sort: Return a sorted copy of an array.
numpy.argsort: Indirect sort.
numpy.lexsort: Indirect stable sort on multiple keys.
numpy.searchsorted: Find elements in sorted array.
numpy.partition: Partial sort.

Notes

See numpy.sort for notes on the different sorting algorithms.

Examples

>>> import numpy as np
>>> a = np.array([[1,4], [3,1]])
>>> a.sort(axis=1)
>>> a
array([[1, 4],
       [1, 3]])
>>> a.sort(axis=0)
>>> a
array([[1, 3],
       [1, 4]])

Use the order keyword to specify a field to use when sorting a structured array:

>>> a = np.array([('a', 2), ('c', 1)], dtype=[('x', 'S1'), ('y', int)])
>>> a.sort(order='y')
>>> a
array([(b'c', 1), (b'a', 2)],
      dtype=[('x', 'S1'), ('y', '<i8')])

squeeze(axis=None)¶

Remove axes of length one from a.

Refer to numpy.squeeze for full documentation.

See also

numpy.squeeze: equivalent function

std(axis=None, dtype=None, out=None, ddof=0, keepdims=False, *, where=True)¶

Returns the standard deviation of the array elements along given axis.

Refer to numpy.std for full documentation.

See also

numpy.std: equivalent function

strides¶

Tuple of bytes to step in each dimension when traversing an array.

The byte offset of element (i[0], i[1], ..., i[n]) in an array a is:

offset = sum(np.array(i) * a.strides)

A more detailed explanation of strides can be found in The N-dimensional array (ndarray).

Warning

Setting arr.strides is discouraged and may be deprecated in the future. numpy.lib.stride_tricks.as_strided should be preferred to create a new view of the same data in a safer way.

Notes

Imagine an array of 32-bit integers (each 4 bytes):

x = np.array([[0, 1, 2, 3, 4],
              [5, 6, 7, 8, 9]], dtype=np.int32)

This array is stored in memory as 40 bytes, one after the other (known as a contiguous block of memory). The strides of an array tell us how many bytes we have to skip in memory to move to the next position along a certain axis. For example, we have to skip 4 bytes (1 value) to move to the next column, but 20 bytes (5 values) to get to the same position in the next row. As such, the strides for the array x will be (20, 4).

See also

numpy.lib.stride_tricks.as_strided

Examples

>>> import numpy as np
>>> y = np.reshape(np.arange(2*3*4), (2,3,4))
>>> y
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]]])
>>> y.strides
(48, 16, 4)
>>> y[1,1,1]
17
>>> offset=sum(y.strides * np.array((1,1,1)))
>>> offset/y.itemsize
17

>>> x = np.reshape(np.arange(5*6*7*8), (5,6,7,8)).transpose(2,3,1,0)
>>> x.strides
(32, 4, 224, 1344)
>>> i = np.array([3,5,2,2])
>>> offset = sum(i * x.strides)
>>> x[3,5,2,2]
813
>>> offset / x.itemsize
813

sum(axis=None, dtype=None, out=None, keepdims=False, initial=0, where=True)¶

Return the sum of the array elements over the given axis.

Refer to numpy.sum for full documentation.

See also

numpy.sum: equivalent function

swapaxes(axis1, axis2)¶

Return a view of the array with axis1 and axis2 interchanged.

Refer to numpy.swapaxes for full documentation.

See also

numpy.swapaxes: equivalent function

take(indices, axis=None, out=None, mode='raise')¶

Return an array formed from the elements of a at the given indices.

Refer to numpy.take for full documentation.

See also

numpy.take: equivalent function

tobytes(order='C')¶

Construct Python bytes containing the raw data bytes in the array.

Constructs Python bytes showing a copy of the raw contents of data memory. The bytes object is produced in C-order by default. This behavior is controlled by the order parameter.

Added in version 1.9.0.

Parameters:: order ({'C', 'F', 'A'}, optional) – Controls the memory layout of the bytes object. ‘C’ means C-order, ‘F’ means F-order, ‘A’ (short for Any) means ‘F’ if a is Fortran contiguous, ‘C’ otherwise. Default is ‘C’.
Returns:: s – Python bytes exhibiting a copy of a’s raw data.
Return type:: bytes

See also

frombuffer: Inverse of this operation, construct a 1-dimensional array from Python bytes.

Examples

>>> import numpy as np
>>> x = np.array([[0, 1], [2, 3]], dtype='<u2')
>>> x.tobytes()
b'\x00\x00\x01\x00\x02\x00\x03\x00'
>>> x.tobytes('C') == x.tobytes()
True
>>> x.tobytes('F')
b'\x00\x00\x02\x00\x01\x00\x03\x00'

tofile(fid, sep='', format='%s')¶

Write array to a file as text or binary (default).

Data is always written in ‘C’ order, independent of the order of a. The data produced by this method can be recovered using the function fromfile().

Parameters:

fid (file or str or Path) –
An open file object, or a string containing a filename.

Changed in version 1.17.0: pathlib.Path objects are now accepted.
sep (str) – Separator between array items for text output. If “” (empty), a binary file is written, equivalent to file.write(a.tobytes()).
format (str) – Format string for text file output. Each entry in the array is formatted to text by first converting it to the closest Python type, and then using “format” % item.

Notes

This is a convenience function for quick storage of array data. Information on endianness and precision is lost, so this method is not a good choice for files intended to archive data or transport data between machines with different endianness. Some of these problems can be overcome by outputting the data as text files, at the expense of speed and file size.

When fid is a file object, array contents are directly written to the file, bypassing the file object’s write method. As a result, tofile cannot be used with files objects supporting compression (e.g., GzipFile) or file-like objects that do not support fileno() (e.g., BytesIO).

tolist()¶

Return the array as an a.ndim-levels deep nested list of Python scalars.

Return a copy of the array data as a (nested) Python list. Data items are converted to the nearest compatible builtin Python type, via the ~numpy.ndarray.item function.

If a.ndim is 0, then since the depth of the nested list is 0, it will not be a list at all, but a simple Python scalar.

Parameters:: none
Returns:: y – The possibly nested list of array elements.
Return type:: object, or list of object, or list of list of object, or …

Notes

The array may be recreated via a = np.array(a.tolist()), although this may sometimes lose precision.

Examples

For a 1D array, a.tolist() is almost the same as list(a), except that tolist changes numpy scalars to Python scalars:

>>> import numpy as np
>>> a = np.uint32([1, 2])
>>> a_list = list(a)
>>> a_list
[1, 2]
>>> type(a_list[0])
<class 'numpy.uint32'>
>>> a_tolist = a.tolist()
>>> a_tolist
[1, 2]
>>> type(a_tolist[0])
<class 'int'>

Additionally, for a 2D array, tolist applies recursively:

>>> a = np.array([[1, 2], [3, 4]])
>>> list(a)
[array([1, 2]), array([3, 4])]
>>> a.tolist()
[[1, 2], [3, 4]]

The base case for this recursion is a 0D array:

>>> a = np.array(1)
>>> list(a)
Traceback (most recent call last):
  ...
TypeError: iteration over a 0-d array
>>> a.tolist()
1

tostring(order='C')¶

A compatibility alias for ~ndarray.tobytes, with exactly the same behavior.

Despite its name, it returns bytes not strs.

Deprecated since version 1.19.0.

trace(offset=0, axis1=0, axis2=1, dtype=None, out=None)¶

Return the sum along diagonals of the array.

Refer to numpy.trace for full documentation.

See also

numpy.trace: equivalent function

transpose(*axes)¶

Returns a view of the array with axes transposed.

Refer to numpy.transpose for full documentation.

Parameters:

axes (None, tuple of ints, or n ints) –

None or no argument: reverses the order of the axes.
tuple of ints: i in the j-th place in the tuple means that the array’s i-th axis becomes the transposed array’s j-th axis.
n ints: same as an n-tuple of the same ints (this form is intended simply as a “convenience” alternative to the tuple form).

Returns:

p – View of the array with its axes suitably permuted.

Return type:

ndarray

See also

transpose: Equivalent function.
ndarray.T: Array property returning the array transposed.
ndarray.reshape: Give a new shape to an array without changing its data.

Examples

>>> import numpy as np
>>> a = np.array([[1, 2], [3, 4]])
>>> a
array([[1, 2],
       [3, 4]])
>>> a.transpose()
array([[1, 3],
       [2, 4]])
>>> a.transpose((1, 0))
array([[1, 3],
       [2, 4]])
>>> a.transpose(1, 0)
array([[1, 3],
       [2, 4]])

>>> a = np.array([1, 2, 3, 4])
>>> a
array([1, 2, 3, 4])
>>> a.transpose()
array([1, 2, 3, 4])

var(axis=None, dtype=None, out=None, ddof=0, keepdims=False, *, where=True)¶

Returns the variance of the array elements, along given axis.

Refer to numpy.var for full documentation.

See also

numpy.var: equivalent function

view([dtype][, type])¶

New view of array with the same data.

Note

Passing None for dtype is different from omitting the parameter, since the former invokes dtype(None) which is an alias for dtype('float64').

Parameters:

dtype (data-type or ndarray sub-class, optional) – Data-type descriptor of the returned view, e.g., float32 or int16. Omitting it results in the view having the same data-type as a. This argument can also be specified as an ndarray sub-class, which then specifies the type of the returned object (this is equivalent to setting the type parameter).
type (Python type, optional) – Type of the returned view, e.g., ndarray or matrix. Again, omission of the parameter results in type preservation.

Notes

a.view() is used two different ways:

a.view(some_dtype) or a.view(dtype=some_dtype) constructs a view of the array’s memory with a different data-type. This can cause a reinterpretation of the bytes of memory.

a.view(ndarray_subclass) or a.view(type=ndarray_subclass) just returns an instance of ndarray_subclass that looks at the same array (same shape, dtype, etc.) This does not cause a reinterpretation of the memory.

For a.view(some_dtype), if some_dtype has a different number of bytes per entry than the previous dtype (for example, converting a regular array to a structured array), then the last axis of a must be contiguous. This axis will be resized in the result.

Changed in version 1.23.0: Only the last axis needs to be contiguous. Previously, the entire array had to be C-contiguous.

Examples

>>> import numpy as np
>>> x = np.array([(-1, 2)], dtype=[('a', np.int8), ('b', np.int8)])

Viewing array data using a different type and dtype:

>>> nonneg = np.dtype([("a", np.uint8), ("b", np.uint8)])
>>> y = x.view(dtype=nonneg, type=np.recarray)
>>> x["a"]
array([-1], dtype=int8)
>>> y.a
array([255], dtype=uint8)

Creating a view on a structured array so it can be used in calculations

>>> x = np.array([(1, 2),(3,4)], dtype=[('a', np.int8), ('b', np.int8)])
>>> xv = x.view(dtype=np.int8).reshape(-1,2)
>>> xv
array([[1, 2],
       [3, 4]], dtype=int8)
>>> xv.mean(0)
array([2.,  3.])

Making changes to the view changes the underlying array

>>> xv[0,1] = 20
>>> x
array([(1, 20), (3,  4)], dtype=[('a', 'i1'), ('b', 'i1')])

Using a view to convert an array to a recarray:

>>> z = x.view(np.recarray)
>>> z.a
array([1, 3], dtype=int8)

Views share data:

>>> x[0] = (9, 10)
>>> z[0]
np.record((9, 10), dtype=[('a', 'i1'), ('b', 'i1')])

Views that change the dtype size (bytes per entry) should normally be avoided on arrays defined by slices, transposes, fortran-ordering, etc.:

>>> x = np.array([[1, 2, 3], [4, 5, 6]], dtype=np.int16)
>>> y = x[:, ::2]
>>> y
array([[1, 3],
       [4, 6]], dtype=int16)
>>> y.view(dtype=[('width', np.int16), ('length', np.int16)])
Traceback (most recent call last):
    ...
ValueError: To change to a dtype of a different size, the last axis must be contiguous
>>> z = y.copy()
>>> z.view(dtype=[('width', np.int16), ('length', np.int16)])
array([[(1, 3)],
       [(4, 6)]], dtype=[('width', '<i2'), ('length', '<i2')])

However, views that change dtype are totally fine for arrays with a contiguous last axis, even if the rest of the axes are not C-contiguous:

>>> x = np.arange(2 * 3 * 4, dtype=np.int8).reshape(2, 3, 4)
>>> x.transpose(1, 0, 2).view(np.int16)
array([[[ 256,  770],
        [3340, 3854]],

       [[1284, 1798],
        [4368, 4882]],

       [[2312, 2826],
        [5396, 5910]]], dtype=int16)