How `numpy.array(order='F')` works

np_array_order.py

>>> np.array([[[0, 4], [2, 6]], [[1, 5], [3, 7]]], dtype='b')
array([[[0, 4],
        [2, 6]],
       [[1, 5],
        [3, 7]]], dtype=int8)
>>> ctypes.string_at(np.array([[[0, 4], [2, 6]], [[1, 5], [3, 7]]], dtype='b').ctypes.data, 8)  # .data.tobytes() doesn't work properly
b'\x00\x04\x02\x06\x01\x05\x03\x07'
>>> np.array([[[0, 4], [2, 6]], [[1, 5], [3, 7]]], dtype='b').__array_interface__
{'data': (23426096, False), 'strides': None, 'descr': [('', '|i1')], 'typestr': '|i1', 'shape': (2, 2, 2), 'version': 3}
>>> np.array([[[0, 4], [2, 6]], [[1, 5], [3, 7]]], dtype='b').flags
  C_CONTIGUOUS : True
  F_CONTIGUOUS : False
  OWNDATA : True
  WRITEABLE : True
  ALIGNED : True
  WRITEBACKIFCOPY : False
  UPDATEIFCOPY : False

>>> np.array([[[0, 4], [2, 6]], [[1, 5], [3, 7]]], dtype='b', order='F')
array([[[0, 4],
        [2, 6]],
       [[1, 5],
        [3, 7]]], dtype=int8)
>>> ctypes.string_at(np.array([[[0, 4], [2, 6]], [[1, 5], [3, 7]]], dtype='b', order='F').ctypes.data, 8)
b'\x00\x01\x02\x03\x04\x05\x06\x07'
>>> np.array([[[0, 4], [2, 6]], [[1, 5], [3, 7]]], dtype='b', order='F').__array_interface__
{'data': (23304720, False), 'strides': (1, 2, 4), 'descr': [('', '|i1')], 'typestr': '|i1', 'shape': (2, 2, 2), 'version': 3}
>>> np.array([[[0, 4], [2, 6]], [[1, 5], [3, 7]]], dtype='b', order='F').flags
  C_CONTIGUOUS : False
  F_CONTIGUOUS : True  # `order` does not configure it directly; it is just computed from the current shape and strides
  OWNDATA : True
  WRITEABLE : True
  ALIGNED : True
  WRITEBACKIFCOPY : False
  UPDATEIFCOPY : False

>>> np.array([[[0, 4], [2, 6]], [[1, 5], [3, 7]]], dtype='b', order='F').T
array([[[0, 1],
        [2, 3]],

       [[4, 5],
        [6, 7]]], dtype=int8)
>>> ctypes.string_at(np.array([[[0, 4], [2, 6]], [[1, 5], [3, 7]]], dtype='b', order='F').T.ctypes.data, 8)
b'\x00\x01\x02\x03\x04\x05\x06\x07'
>>> np.array([[[0, 4], [2, 6]], [[1, 5], [3, 7]]], dtype='b', order='F').T.__array_interface__
{'data': (23426096, False), 'strides': None, 'descr': [('', '|i1')], 'typestr': '|i1', 'shape': (2, 2, 2), 'version': 3}
>>> np.array([[[0, 4], [2, 6]], [[1, 5], [3, 7]]], dtype='b', order='F').T.flags
  C_CONTIGUOUS : True
  F_CONTIGUOUS : False
  OWNDATA : False
  WRITEABLE : True
  ALIGNED : True
  WRITEBACKIFCOPY : False
  UPDATEIFCOPY : False

np_order.py

import ctypes
import numpy as np
from numpy.lib import stride_tricks


def from_array_to_bytes(a):
    return ctypes.string_at(a.ctypes.data, a.nbytes)


def print_array(desc, a):
    print(desc + " ->")
    print("  " + str(a.tolist()))
    print("  underlying: {}, strides: {}, owndata: {: >5}, c: {: >5}, f:{: >5}, data: {: >15}".format(
        from_array_to_bytes(a),
        a.strides,
        str(a.flags.owndata),
        str(a.flags.c_contiguous),
        str(a.flags.f_contiguous),
        a.ctypes.data,
        ))


def main():
    a0 = np.array([[[0, 1], [2, 3]], [[4, 5], [6, 7]]], dtype="b")
    print_array("array(list)", a0)
    #print_array("array(list).view()", a0.view())
    #print_array("array(list).reshape((2, 2, 2)))", a0.reshape((2, 2, 2)))
    #print_array("array(list).reshape((2, 2, 2), order='f'))", a0.reshape((2, 2, 2), order='f'))
    print()

    a1 = np.array([[[0, 1], [2, 3]], [[4, 5], [6, 7]]], dtype="b", order="f")
    print_array("array(list, order='f')", a1)
    print()

    #b0 = np.frombuffer(b"\x00\x01\x02\x03\x04\x05\x06\x07", dtype="b")
    #print_array("frombuffer(bytes).reshape((2, 2, 2))", b0.reshape(2, 2, 2))
    #print_array("frombuffer(bytes).reshape((2, 2, 2)).view()", b0.reshape(2, 2, 2).view())
    #print_array("frombuffer(bytes).reshape((2, 2, 2), order='f')", b0.reshape(2, 2, 2, order='f'))
    #print_array("frombuffer(bytes).reshape((2, 2, 2)).reshape((2, 2, 2), order='f')", b0.reshape(2, 2, 2).reshape(2, 2, 2, order='f'))
    #print()

    c0 = np.array([np.array([[0, 1], [2, 3]], dtype='b'), np.array([[4, 5], [6, 7]], dtype='b')], dtype="b")
    print_array("array(list[ndarray(c), ndarray(c)])", c0)
    c1 = np.array([np.array([[0, 1], [2, 3]], dtype='b'), np.array([[4, 5], [6, 7]], dtype='b')], dtype="b", order='f')
    print_array("array(list[ndarray(c), ndarray(c)], order='f')", c1)
    c2 = np.array([np.array([[0, 1], [2, 3]], dtype='b', order='f'), np.array([[4, 5], [6, 7]], dtype='b')], dtype="b")
    print_array("array(list[ndarray(f), ndarray(c)])", c2)
    c3 = np.array([np.array([[0, 1], [2, 3]], dtype='b', order='f'), np.array([[4, 5], [6, 7]], dtype='b')], dtype="b", order='f')
    print_array("array(list[ndarray(f), ndarray(c)], order='f')", c3)
    #c4 = np.array([np.array([[0, 1], [2, 3]], dtype='b'), np.array([[4, 5], [6, 7]], dtype='b', order='f')], dtype="b", order='a')
    #print_array("array(list[ndarray(c), ndarray(f)], order='a')", c4)
    #c5 = np.array([np.array([[0, 1], [2, 3]], dtype='b'), np.array([[4, 5], [6, 7]], dtype='b', order='f')], dtype="b", order='k')
    #print_array("array(list[ndarray(c), ndarray(f)], order='k')", c5)
    c6 = np.array([np.array([[0, 1], [2, 3]], dtype='b', order='f'), np.array([[4, 5], [6, 7]], dtype='b', order='f')], dtype="b")
    print_array("array(list[ndarray(f), ndarray(f)])", c6)
    c7 = np.array([np.array([[0, 1], [2, 3]], dtype='b', order='f'), np.array([[4, 5], [6, 7]], dtype='b', order='f')], dtype="b", order='f')
    print_array("array(list[ndarray(f), ndarray(f)], order='f')", c7)
    print()

    c8 = np.stack([np.array([[0, 1], [2, 3]], dtype='b'), np.array([[4, 5], [6, 7]], dtype='b')])
    print_array("stack(list[ndarray(c), ndarray(c)])", c8)
    c9 = np.asfortranarray(np.stack([np.array([[0, 1], [2, 3]], dtype='b'), np.array([[4, 5], [6, 7]], dtype='b')]))
    print_array("asfortranarray(stack(list[ndarray(c), ndarray(c)]))", c9)
    print()

    c11 = np.stack([np.array([[0, 1], [2, 3]], dtype='b'), np.array([[4, 5], [6, 7]], dtype='b', order='f')])
    print_array("stack(list[ndarray(c), ndarray(f)])", c11)
    c12 = np.asfortranarray(np.stack([np.array([[0, 1], [2, 3]], dtype='b'), np.array([[4, 5], [6, 7]], dtype='b', order='f')]))
    print_array("asfortranarray(stack(list[ndarray(c), ndarray(f)]))", c12)
    print()

    c12 = np.stack([np.array([[0, 1], [2, 3]], dtype='b', order='f'), np.array([[4, 5], [6, 7]], dtype='b', order='f')])
    print_array("stack(list[ndarray(f), ndarray(f)])", c12)
    c13 = np.asfortranarray(np.stack([np.array([[0, 1], [2, 3]], dtype='b', order='f'), np.array([[4, 5], [6, 7]], dtype='b', order='f')]))
    print_array("asfortranarray(stack(list[ndarray(f), ndarray(f)]))", c13)
    print()

    c14 = np.stack([np.array([[0, 1], [2, 3]], dtype='b', order='f'), np.array([[4, 5], [6, 7]], dtype='b', order='f')], axis=-1)
    print_array("stack(list[ndarray(f), ndarray(f)], axis=-1)", c14)
    c15 = np.stack([np.array([[0, 1], [2, 3]], dtype='b', order='f'), np.array([[4, 5], [6, 7]], dtype='b', order='f')], axis=1)
    print_array("stack(list[ndarray(f), ndarray(f)], axis=1)", c15)
    print()

    d6 = [np.array([[0, 1], [2, 3]], dtype='b', order='c'), np.array([[4, 5], [6, 7]], dtype='b', order='c')]
    d7 = np.frombuffer(bytearray([0x00] * 8), dtype='b').reshape((2, 2, 2), order='C')
    print_array("concatenate(list[ndarray(c)[None], ndarray(c)[None]], axis=0)", d7)
    np.concatenate([e[None] for e in d6], axis=0, out=d7)
    print_array("concatenate(list[ndarray(c)[None], ndarray(c)[None]], axis=0)", d7)
    print()

    d8 = [np.array([[0, 1], [2, 3]], dtype='b', order='f'), np.array([[4, 5], [6, 7]], dtype='b', order='c')]
    d9 = np.frombuffer(bytearray([0x00] * 8), dtype='b').reshape((2, 2, 2), order='C')
    print_array("concatenate(list[ndarray(f)[None], ndarray(c)[None]], axis=0)", d9)
    np.concatenate([e[None] for e in d6], axis=0, out=d9)
    print_array("concatenate(list[ndarray(f)[None], ndarray(c)[None]], axis=0)", d9)
    print()

    d0 = [np.array([[0, 1], [2, 3]], dtype='b', order='f'), np.array([[4, 5], [6, 7]], dtype='b', order='f')]
    d1 = [e[None] for e in d0]
    d2 = np.frombuffer(bytearray([0x00] * 8), dtype='b').reshape((2, 2, 2), order='C')
    print_array("concatenate(list[ndarray(f)[None], ndarray(f)[None]], axis=0)", d2)
    np.concatenate(d1, axis=0, out=d2)
    print_array("concatenate(list[ndarray(f)[None], ndarray(f)[None]], axis=0)", d2)
    #d10 = np.ascontiguousarray(d2)
    #print_array("ascontiguoussrray(concatenate(list[ndarray(f)[None], ndarray(f)[None]], axis=0))", d10)
    #d11 = np.asfortranarray(d2)
    #print_array("asfortranarray(concatenate(list[ndarray(f)[None], ndarray(f)[None]], axis=0))", d11)
    print()

    #d3 = [e[:,None] for e in d0]
    #d4 = np.concatenate(d3, axis=1)
    #print_array("concatenate(list[ndarray(f)[:,None], ndarray(f)[:,None]], axis=1)", d4)
    #d5 = stride_tricks.as_strided(d4, (2, 2, 2), (1, 2, 4))
    #print_array("as_strided(concatenate(list[ndarray(f)[:,None], ndarray(f)[:,None]], axis=1), shape=(2, 2, 2), strides=(1, 2, 4))", d5)
    #print()


if __name__ == '__main__':
    main()