#!/usr/bin/env?python
#?-*-?coding:?utf-8?-*-

#
#?Authors:?Chiheb?Trabelsi?Olexa?Bilaniuk
#
#?Note:?The?implementation?of?complex?Batchnorm?is?based?on
#???????the?Keras?implementation?of?batch?Normalization
#???????available?here:
#???????https://github.com/fchollet/keras/blob/master/keras/layers/normalization.py

import?numpy?as?np
from?keras.layers?import?layer?InputSpec
from?keras?import?initializers?regularizers?constraints
import?keras.backend?as?K


def?sqrt_init（shape?dtype=None）:
????value?=?（1?/?K.sqrt（2））?*?K.ones（shape）
????return?value


def?sanitizedInitGet（init）:
????if?init?in?[“sqrt_init“]:
????????return?sqrt_init
????else:
????????return?initializers.get（init）
def?sanitizedInitSer（init）:
????if?init?in?[sqrt_init]:
????????return?“sqrt_init“
????else:
????????return?initializers.serialize（init）



def?complex_standardization（input_centred?Vrr?Vii?Vri
????????????????????????????layernorm=False?axis=-1）:
????
????ndim?=?K.ndim（input_centred）
????input_dim?=?K.shape（input_centred）[axis]?//?2
????variances_broadcast?=?[1]?*?ndim
????variances_broadcast[axis]?=?input_dim
????if?layernorm:
????????variances_broadcast[0]?=?K.shape（input_centred）[0]

????#?We?require?the?covariance?matrix‘s?inverse?square?root.?That?first?requires
????#?square?rooting?followed?by?inversion?（I?do?this?in?that?order?because?during
????#?the?computation?of?square?root?we?compute?the?determinant?we‘ll?need?for
????#?inversion?as?well）.

????#?tau?=?Vrr?+?Vii?=?Trace.?Guaranteed?>=?0?because?SPD
????tau?=?Vrr?+?Vii
????#?delta?=?（Vrr?*?Vii）?-?（Vri?**?2）?=?Determinant.?Guaranteed?>=?0?because?SPD
????delta?=?（Vrr?*?Vii）?-?（Vri?**?2）

????s?=?np.sqrt（delta）?#?Determinant?of?square?root?matrix
????t?=?np.sqrt（tau?+?2?*?s）

????#?The?square?root?matrix?could?now?be?explicitly?formed?as
????#???????[?Vrr+s?Vri???]
????#?（1/t）?[?Vir???Vii+s?]
????#?https://en.wikipedia.org/wiki/Square_root_of_a_2_by_2_matrix
????#?but?we?don‘t?need?to?do?this?immediately?since?we?can?also?simultaneously
????#?invert.?We?can?do?this?because?we‘ve?already?computed?the?determinant?of
????#?the?square?root?matrix?and?can?thus?invert?it?using?the?analytical
????#?solution?for?2x2?matrices
????#??????[?A?B?]?????????????[??D??-B?]
????#?inv（?[?C?D?]?）?=?（1/det）?[?-C???A?]
????#?http://mathworld.wolfram.com/MatrixInverse.html
????#?Thus?giving?us
????#???????????[??Vii+s??-Vri???]
????#?（1/s）（1/t）[?-Vir?????Vrr+s?]
????#?So?we?proceed?as?follows:

????inverse_st?=?1.0?/?（s?*?t）
????Wrr?=?（Vii?+?s）?*?inverse_st
????Wii?=?（Vrr?+?s）?*?inverse_st
????Wri?=?-Vri?*?inverse_st

????#?And?we?have?computed?the?inverse?square?root?matrix?W?=?sqrt（V）!
????#?Normalization.?We?multiply?x_normalized?=?W.x.

????#?The?returned?result?will?be?a?complex?standardized?input
????#?where?the?real?and?imaginary?parts?are?obtained?as?follows:
????#?x_real_normed?=?Wrr?*?x_real_centred?+?Wri?*?x_imag_centred
????#?x_imag_normed?=?Wri?*?x_real_centred?+?Wii?*?x_imag_centred

????broadcast_Wrr?=?K

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----

?????文件??????21518??2018-01-18?14:57??vgg19_retrain\complexnn\bn.py

?????文件??????43080??2018-01-26?17:08??vgg19_retrain\complexnn\conv.py

?????文件???????9107??2018-01-18?14:57??vgg19_retrain\complexnn\dense.py

?????文件???????5588??2018-01-26?15:12??vgg19_retrain\complexnn\fft.py

?????文件??????10779??2018-01-18?14:57??vgg19_retrain\complexnn\init.py

?????文件??????11239??2018-01-26?15:04??vgg19_retrain\complexnn\norm.py

?????文件???????4876??2018-01-18?14:57??vgg19_retrain\complexnn\pool.py

?????文件???????2186??2018-01-18?14:57??vgg19_retrain\complexnn\utils.py

?????文件????????861??2018-01-18?14:57??vgg19_retrain\complexnn\__init__.py

?????文件??????11139??2018-01-26?11:50??vgg19_retrain\complexnn\__pycache__\bn.cpython-36.pyc

?????文件??????31498??2018-01-26?17:08??vgg19_retrain\complexnn\__pycache__\conv.cpython-36.pyc

?????文件???????6604??2018-01-26?15:05??vgg19_retrain\complexnn\__pycache__\dense.cpython-36.pyc

?????文件???????5682??2018-01-26?15:14??vgg19_retrain\complexnn\__pycache__\fft.cpython-36.pyc

?????文件???????5963??2018-01-26?15:04??vgg19_retrain\complexnn\__pycache__\init.cpython-36.pyc

?????文件???????6497??2018-01-26?15:05??vgg19_retrain\complexnn\__pycache__\norm.cpython-36.pyc

?????文件???????4448??2018-01-26?15:14??vgg19_retrain\complexnn\__pycache__\pool.cpython-36.pyc

?????文件???????2750??2018-01-26?15:18??vgg19_retrain\complexnn\__pycache__\utils.cpython-36.pyc

?????文件???????1002??2018-01-25?15:44??vgg19_retrain\complexnn\__pycache__\__init__.cpython-36.pyc

?????文件??????11592??2018-02-28?15:53??vgg19_retrain\scripts\vgg.py

?????文件????4132109??2018-01-20?12:41??vgg19_retrain\vgg19_retrain_logs\events.out.tfevents.1516423255.DESKTOP-DJOM3UF

?????目錄??????????0??2018-01-26?17:08??vgg19_retrain\complexnn\__pycache__

?????目錄??????????0??2018-01-26?15:04??vgg19_retrain\complexnn

?????目錄??????????0??2018-01-26?15:40??vgg19_retrain\scripts

?????目錄??????????0??2018-01-20?12:40??vgg19_retrain\vgg19_retrain_logs

?????目錄??????????0??2018-01-26?14:44??vgg19_retrain

-----------?---------??----------?-----??----

??????????????4328518????????????????????25