# -*- coding: utf-8 -*-
"""
==========================================================================================
Granley et al. (2021): Effects of Biphasic Pulse Parameters with the BiphasicAxonMapModel
==========================================================================================

This example shows how to use the
:py:class:`~pulse2percept.models.BiphasicAxonMapModel` to model the effects of 
biphasic pulse train parameters phosphene appearance in an epiretinal
implant such as :py:class:`~pulse2percept.implants.ArgusII`. 

Biphasic pulse trains are a commonly used type of stimulus in visual prostheses. 
This model enhances the :py:class:`~pulse2percept.models.AxonMapModel` to reflect
the effects of the amplitude, frequency, and pulse duration on threshold,
phosphene size, brightness, and streak length, according to previous
psychophysical and electrophysiological studies.

The :py:class:`~pulse2percept.models.BiphasicAxonMapModel` shares the same underlying 
assumptions as the axon map model. Namely, an axon's sensitivity to electrical stimulation
is assumed to decay exponentially with...

*  distance along the axon from the soma (:math:`d_s`), with spatial decay
   constant :math:`\\lambda`,
*  distance from the stimulated electrode (:math:`d_e`), with spatial decay 
   constant :math:`\\rho`.

In the biphasic model, the radial decay rate :math:`\\rho` is scaled by :math:`F_{size}`,
the axonal decay rate :math:`\\lambda` is scaled by :math:`F_{streak}`, and the brightness 
contribution from each electrode is scaled by :math:`F_{bright}`. These 3 equations are called
effect models. The final equation for the brightness intensity for a pixel located at polar 
coordinates :math:`(r, \\theta)` is given by:

.. math::

    I =  \\max_{axon}\\sum_{elecs}F_\\mathrm{bright} \\exp\\left(\\frac{-d_{e}^2}{2\\rho^2 F_\\mathrm{size} } + 
            \\frac{-d_{s}^2}{2\\lambda^2 F_\\mathrm{streak} }\\right).


Basic Model Usage
-----------------
The biphasic axon map model can be instantiated and ran similarly to other models,
with the exception that all stimuli are required to be :py:class:`~pulse2percept.stimuli.BiphasicPulseTrain`
"""
# sphinx_gallery_thumbnail_number = 4

import matplotlib.pyplot as plt
import numpy as np
from pulse2percept.implants import ArgusII
from pulse2percept.models import BiphasicAxonMapModel
from pulse2percept.stimuli import BiphasicPulseTrain
model = BiphasicAxonMapModel(rho=200, axlambda=800)

##############################################################################
# Parameters you don't specify will take on default values. You can inspect
# all current model parameters as follows:

print(model)

##############################################################################
# The most important parameters are ``rho`` and ``axlambda``, which control the 
# radial and axonal current spread, respectively. The parameters ``a0``-``a9`` are 
# coefficients for the size, streak, and bright models, which will be discussed 
# later in this example. The biphasic axon map model supports both the default 
# cython engine and a faster, gpu-enabled jax engine.
#
# The rest of the parameters are shared with 
# :py:class:`~pulse2percept.models.AxonMapModel`. For full details on these 
# parameters, see the Axon Map Tutorial
#
#
# Next, build the model to perform expensive, one time calculations,
# and specify a visual prosthesis from the
# :py:mod:`~pulse2percept.implants` module. Models with an axon map are well 
# suited for epiretinal implants, such as Argus II.
model.build()
implant = ArgusII()

##############################################################################
# .. important ::
#
#     You need to build a model only once. After that, you can apply any number
#     of stimuli -- or even apply the model to different implants -- without
#     having to rebuild (which takes time).
#
#     However, if you change model parameters
#     (e.g., by directly setting ``model.a5 = 2``), you will have to
#     call ``model.build()`` again for your changes to take effect.
#
#
# You can visualize the location of the implant and the axon map

model.plot()
implant.plot()
plt.show()


##############################################################################
# As mentioned above, the Biphasic Axon Map Model only accepts 
# :py:class:`~pulse2percept.stimuli.BiphasicPulseTrain`
# stimuli with no :py:attr:`~pulse2percept.stimuli.BiphasicPulseTrain.delay_dur`. 
# The amplitude given to the BiphasicPulseTrain
# is interpreted as amplitude as a factor of threshold (i.e. an amp of 1 means 
# 1xTh)
#
# You can easily assign BiphasicPulseTrains to electrodes with a dictionary
# The following creates a train with 20Hz frequency, 1xTh amplitude, and 0.45ms
# pulse / phase duration.

implant.stim = {'A4' : BiphasicPulseTrain(20, 1, 0.45)}
implant.stim.plot()

##############################################################################
# Finally, you can predict the percept resulting from stimulation

percept = model.predict_percept(implant)
ax = percept.plot()
ax.set_title('Predicted percept')
plt.show()
##############################################################################
# Increasing the frequency will make phosphenes brighter
fig, axes = plt.subplots(1, 2, sharex=True, sharey=True)
implant.stim = {'A4' : BiphasicPulseTrain(50, 1, 0.45)}
new_percept = model.predict_percept(implant)
new_percept.plot(ax=axes[1])
percept.plot(ax=axes[0], vmax=new_percept.max())
axes[0].set_title("20 Hz")
axes[1].set_title("40 Hz")
plt.show()
##############################################################################
# Note that without setting vmax, matplotlib automatically rescales images to
# have the same max brightness and the difference isn't visible

##############################################################################
# Increasing amplitude increases both size and brightness
fig, axes = plt.subplots(1, 2, sharex=True, sharey=True)
implant.stim = {'A4' : BiphasicPulseTrain(20, 3, 0.45)}
new_percept = model.predict_percept(implant)
new_percept.plot(ax=axes[1])
percept.plot(ax=axes[0], vmax=new_percept.max())
axes[0].set_title("1xTh")
axes[1].set_title("3xTh")
plt.show()

##############################################################################
# Increasing pulse duration decreases threshold, thus indirectly causing an 
# increase in size and brightness (amp factor is increased)
fig, axes = plt.subplots(1, 2, sharex=True, sharey=True)
implant.stim = {'A4' : BiphasicPulseTrain(20, 1, 4)}
new_percept = model.predict_percept(implant)
new_percept.plot(ax=axes[1])
percept.plot(ax=axes[0], vmax=new_percept.max())
axes[0].set_title("0.45ms")
axes[1].set_title("4ms")
plt.show()

##############################################################################
# If you account for the change in threshold by decreasing amplitude, then 
# the only affect of increasing pulse duration is the streak length decreasing
fig, axes = plt.subplots(1, 2, sharex=True, sharey=True)
implant.stim = {'A4' : BiphasicPulseTrain(20, 0.023835, 20)}
new_percept = model.predict_percept(implant)
new_percept.plot(ax=axes[1])
percept.plot(ax=axes[0], vmax=new_percept.max())
axes[0].set_title("0.45ms")
axes[1].set_title("20ms, 0.02xTh")
plt.show()

#################################################################################
# This illustrates another important point: The amplitude used for the Biphasic
# model is relative to the threshold current at 0.45ms pulse duration. Since larger 
# pulse durations have been shown to reduce the threshold amplitude needed, the 
# 0.02xTh amplitude used in the previous plot still is able to produce a phosphene.

################################################################################
#
#
# Changing Effect Models
# ----------------------
# All of the 'effects' plotted above (e.g. size increasing with amplitude)
# are controlled by the effect models :math:`F_{bright}`, :math:`F_{size}`, and
# :math:`F_{streak}`. The variables 
# ``bright_model``, ``size_model``, and ``streak_model`` encode the 
# effects models.
# 
# These default to :py:class:`~pulse2percept.models.granley2021.DefaultBrightModel`,
# :py:class:`~pulse2percept.models.granley2021.DefaultSizeModel`, and 
# :py:class:`~pulse2percept.models.granley2021.DefaultStreakModel` respectively, which
# implement the simple scaling functions described in `Granley et al. (2021) <[Granley2021]>`_.
# 
#
# The coefficients ``a0``-``a9`` parametrize these effect models. While the default values
# are likely to work for most cases, they can be customized to be patient specific. 
# Notice how we only have to change the value given to the `BiphasicAxonMapModel`, 
# and it is automatically passed down to the effect models.
model.a5 = 0
print(model.size_model.a5)

##################################################################################
# For example, ``a0`` and ``a1`` control how threshold changed with pulse duration: 
# :math:`amp = (A_0*pdur + A_1)^{-1}*amp`. Thus, pulse duration threshold 
# scaling can easily be disabled by setting ``a0`` to 0 and ``a1`` to 1. If we increase 
# pulse duration like we did previously, we will now see that only streak length decreases, 
# and we no longer have to change amplitude to account for change in threshold
model = BiphasicAxonMapModel(rho=200, axlambda=800)
model.a0 = 0
model.a1 = 1
model.build()
fig, axes = plt.subplots(1, 2, sharex=True, sharey=True)
implant.stim = {'A4' : BiphasicPulseTrain(20, 1, 0.45)}
percept = model.predict_percept(implant)
implant.stim = {'A4' : BiphasicPulseTrain(20, 1, 20)}
new_percept = model.predict_percept(implant)
new_percept.plot(ax=axes[1])
percept.plot(ax=axes[0], vmax=new_percept.max())
axes[0].set_title("0.45ms")
axes[1].set_title("20ms")
plt.show()

##################################################################################
# Similarly, ``a2``-``a4`` control brightness scaling; ``a5``-``a6`` control size scaling, and
# ``a7``-``a9`` control streak length scaling. For more details on these parameters,
# see the effect models documentation, or [Granley2021]_ 
#
# Advanced Usage
# ----------------------
#
# Custom Effect Models
# =====================
# For most cases, using the provided, default implementation of the effect models
# will probably be enough. However, the effect models are completely modular, and 
# can be replaced by any python callable with the parameters frequency, amplitude, 
# and pulse duration. For example, we can easily change the model to no longer scale size
model = BiphasicAxonMapModel(rho=200, axlambda=800)
def size_modulation(freq, amp, pdur):
    return 1
model.size_model = size_modulation
model.build()

fig, axes = plt.subplots(1, 2, sharex=True, sharey=True)
implant.stim = {'A4' : BiphasicPulseTrain(20, 1, 0.45)}
percept = model.predict_percept(implant)
implant.stim = {'A4' : BiphasicPulseTrain(20, 3, 0.45)}
new_percept = model.predict_percept(implant)
new_percept.plot(ax=axes[1])
percept.plot(ax=axes[0], vmax=new_percept.max())
axes[0].set_title("1xTh")
axes[1].set_title("3xTh")
plt.show()
######################################################################################
# The stimuli with larger amplitude created a brighter, but equally-sized phosphene
#
#
# The effect models can even be a class, and can have its own parameters, 
# which can be shared with the overarching BiphasicAxonMapModel itself (e.g. an effect 
# model can depend on ``rho``, and if ``model.rho`` is changed, ``rho`` will also be changed in
# the effect model). For an example of this, 
# see :py:class:`~pulse2percept.models.granley2021.DefaultSizeModel` 
#
#
# If using custom effect models with jax, the effect models must be written for jax so they can
# be JIT compiled (i.e. using jax.numpy instead of numpy)

########################################################################################
# JAX Engine
# ============
#
# The default computational engine is cython, but an engine based on 
# `jax <https://github.com/google/jax>`_ is also provided. The jax engine is slightly faster on CPU
# and significantly faster on GPU, at the cost of increased memory usage. The jax-based model 
# can be used identically to the cython engine, but it also has some additional features
# and limitations. 
# 
# .. note ::
#
#     Jax functions are compiled the first time they are called. Thus, the first
#     `predict_percept` will be slow. Subsequent calls reuse the compiled and
#     optimized function, and are much faster
#
# One additional feature is the 
# `_predict_spatial_jax` function,
# which is a stripped, purely functional version of 
# `predict_percept` that operates on
# numpy arrays. This avoids the overhead of creating p2p stimulus and percept objects,
# and if used correctly, provides an additional speedup. 
#
# `_predict_spatial_jax` takes in 
# a (n_elecs, 3) numpy array specifying the frequency, amplitude, and pulse duration on
# each electrode, and two (n_elec) shaped arrays specifying the x and y locations of each
# electrode
model = BiphasicAxonMapModel(engine='jax')
model.build()
implant = ArgusII()
ex = np.array([implant[e].x for e in implant.electrodes])
ey = np.array([implant[e].y for e in implant.electrodes]) 
stim = np.zeros((60, 3))
stim[3] = [20, 1, 0.45]
percept = model._predict_spatial_jax(stim, ex, ey)
percept = np.array(percept).reshape(model.grid.shape)
plt.imshow(percept, cmap='gray')
plt.show()
##################################################################################################
# One other useful feature is the 
# `predict_percept_batched` function. This
# applies predict_percept to batches of input stimuli, using optimized matrix operations. See also 
# its faster, stripped version `_predict_spatial_batched`. This 
# function is only intended to be used if you are repeatedly simulating batches of percepts. 
# Since jax compiles each function the first time it is used, using this function only once
# for a singular group of stimuli will be noticably slower than repeatedly applying 
# `predict_percept`. However, splitting a very large set of stimuli into smaller batches and 
# using `predict_percept_batched` will be significantly faster than `predict_percept` on each
# individual stimuli.
#
# Note that this function consumes a large amount of memory, and may not run on systems or 
# GPUs with limited memory. 


# -*- coding: utf-8 -*-
"""
==========================================================================================
Granley et al. (2021): Effects of Biphasic Pulse Parameters with the BiphasicAxonMapModel
==========================================================================================

This example shows how to use the
:py:class:`~pulse2percept.models.BiphasicAxonMapModel` to model the effects of 
biphasic pulse train parameters phosphene appearance in an epiretinal
implant such as :py:class:`~pulse2percept.implants.ArgusII`. 

Biphasic pulse trains are a commonly used type of stimulus in visual prostheses. 
This model enhances the :py:class:`~pulse2percept.models.AxonMapModel` to reflect
the effects of the amplitude, frequency, and pulse duration on threshold,
phosphene size, brightness, and streak length, according to previous
psychophysical and electrophysiological studies.

The :py:class:`~pulse2percept.models.BiphasicAxonMapModel` shares the same underlying 
assumptions as the axon map model. Namely, an axon's sensitivity to electrical stimulation
is assumed to decay exponentially with...

*  distance along the axon from the soma (:math:`d_s`), with spatial decay
   constant :math:`\\lambda`,
*  distance from the stimulated electrode (:math:`d_e`), with spatial decay 
   constant :math:`\\rho`.

In the biphasic model, the radial decay rate :math:`\\rho` is scaled by :math:`F_{size}`,
the axonal decay rate :math:`\\lambda` is scaled by :math:`F_{streak}`, and the brightness 
contribution from each electrode is scaled by :math:`F_{bright}`. These 3 equations are called
effect models. The final equation for the brightness intensity for a pixel located at polar 
coordinates :math:`(r, \\theta)` is given by:

.. math::

    I =  \\max_{axon}\\sum_{elecs}F_\\mathrm{bright} \\exp\\left(\\frac{-d_{e}^2}{2\\rho^2 F_\\mathrm{size} } + 
            \\frac{-d_{s}^2}{2\\lambda^2 F_\\mathrm{streak} }\\right).


Basic Model Usage
-----------------
The biphasic axon map model can be instantiated and ran similarly to other models,
with the exception that all stimuli are required to be :py:class:`~pulse2percept.stimuli.BiphasicPulseTrain`
"""
# sphinx_gallery_thumbnail_number = 4

import matplotlib.pyplot as plt
import numpy as np
from pulse2percept.implants import ArgusII
from pulse2percept.models import BiphasicAxonMapModel
from pulse2percept.stimuli import BiphasicPulseTrain
model = BiphasicAxonMapModel(rho=200, axlambda=800)

##############################################################################
# Parameters you don't specify will take on default values. You can inspect
# all current model parameters as follows:

print(model)

##############################################################################
# The most important parameters are ``rho`` and ``axlambda``, which control the 
# radial and axonal current spread, respectively. The parameters ``a0``-``a9`` are 
# coefficients for the size, streak, and bright models, which will be discussed 
# later in this example. The biphasic axon map model supports both the default 
# cython engine and a faster, gpu-enabled jax engine.
#
# The rest of the parameters are shared with 
# :py:class:`~pulse2percept.models.AxonMapModel`. For full details on these 
# parameters, see the Axon Map Tutorial
#
#
# Next, build the model to perform expensive, one time calculations,
# and specify a visual prosthesis from the
# :py:mod:`~pulse2percept.implants` module. Models with an axon map are well 
# suited for epiretinal implants, such as Argus II.
model.build()
implant = ArgusII()

##############################################################################
# .. important ::
#
#     You need to build a model only once. After that, you can apply any number
#     of stimuli -- or even apply the model to different implants -- without
#     having to rebuild (which takes time).
#
#     However, if you change model parameters
#     (e.g., by directly setting ``model.a5 = 2``), you will have to
#     call ``model.build()`` again for your changes to take effect.
#
#
# You can visualize the location of the implant and the axon map

model.plot()
implant.plot()
plt.show()


##############################################################################
# As mentioned above, the Biphasic Axon Map Model only accepts 
# :py:class:`~pulse2percept.stimuli.BiphasicPulseTrain`
# stimuli with no :py:attr:`~pulse2percept.stimuli.BiphasicPulseTrain.delay_dur`. 
# The amplitude given to the BiphasicPulseTrain
# is interpreted as amplitude as a factor of threshold (i.e. an amp of 1 means 
# 1xTh)
#
# You can easily assign BiphasicPulseTrains to electrodes with a dictionary
# The following creates a train with 20Hz frequency, 1xTh amplitude, and 0.45ms
# pulse / phase duration.

implant.stim = {'A4' : BiphasicPulseTrain(20, 1, 0.45)}
implant.stim.plot()

##############################################################################
# Finally, you can predict the percept resulting from stimulation

percept = model.predict_percept(implant)
ax = percept.plot()
ax.set_title('Predicted percept')
plt.show()
##############################################################################
# Increasing the frequency will make phosphenes brighter
fig, axes = plt.subplots(1, 2, sharex=True, sharey=True)
implant.stim = {'A4' : BiphasicPulseTrain(50, 1, 0.45)}
new_percept = model.predict_percept(implant)
new_percept.plot(ax=axes[1])
percept.plot(ax=axes[0], vmax=new_percept.max())
axes[0].set_title("20 Hz")
axes[1].set_title("40 Hz")
plt.show()
##############################################################################
# Note that without setting vmax, matplotlib automatically rescales images to
# have the same max brightness and the difference isn't visible

##############################################################################
# Increasing amplitude increases both size and brightness
fig, axes = plt.subplots(1, 2, sharex=True, sharey=True)
implant.stim = {'A4' : BiphasicPulseTrain(20, 3, 0.45)}
new_percept = model.predict_percept(implant)
new_percept.plot(ax=axes[1])
percept.plot(ax=axes[0], vmax=new_percept.max())
axes[0].set_title("1xTh")
axes[1].set_title("3xTh")
plt.show()

##############################################################################
# Increasing pulse duration decreases threshold, thus indirectly causing an 
# increase in size and brightness (amp factor is increased)
fig, axes = plt.subplots(1, 2, sharex=True, sharey=True)
implant.stim = {'A4' : BiphasicPulseTrain(20, 1, 4)}
new_percept = model.predict_percept(implant)
new_percept.plot(ax=axes[1])
percept.plot(ax=axes[0], vmax=new_percept.max())
axes[0].set_title("0.45ms")
axes[1].set_title("4ms")
plt.show()

##############################################################################
# If you account for the change in threshold by decreasing amplitude, then 
# the only affect of increasing pulse duration is the streak length decreasing
fig, axes = plt.subplots(1, 2, sharex=True, sharey=True)
implant.stim = {'A4' : BiphasicPulseTrain(20, 0.023835, 20)}
new_percept = model.predict_percept(implant)
new_percept.plot(ax=axes[1])
percept.plot(ax=axes[0], vmax=new_percept.max())
axes[0].set_title("0.45ms")
axes[1].set_title("20ms, 0.02xTh")
plt.show()

#################################################################################
# This illustrates another important point: The amplitude used for the Biphasic
# model is relative to the threshold current at 0.45ms pulse duration. Since larger 
# pulse durations have been shown to reduce the threshold amplitude needed, the 
# 0.02xTh amplitude used in the previous plot still is able to produce a phosphene.

################################################################################
#
#
# Changing Effect Models
# ----------------------
# All of the 'effects' plotted above (e.g. size increasing with amplitude)
# are controlled by the effect models :math:`F_{bright}`, :math:`F_{size}`, and
# :math:`F_{streak}`. The variables 
# ``bright_model``, ``size_model``, and ``streak_model`` encode the 
# effects models.
# 
# These default to :py:class:`~pulse2percept.models.granley2021.DefaultBrightModel`,
# :py:class:`~pulse2percept.models.granley2021.DefaultSizeModel`, and 
# :py:class:`~pulse2percept.models.granley2021.DefaultStreakModel` respectively, which
# implement the simple scaling functions described in `Granley et al. (2021) <[Granley2021]>`_.
# 
#
# The coefficients ``a0``-``a9`` parametrize these effect models. While the default values
# are likely to work for most cases, they can be customized to be patient specific. 
# Notice how we only have to change the value given to the `BiphasicAxonMapModel`, 
# and it is automatically passed down to the effect models.
model.a5 = 0
print(model.size_model.a5)

##################################################################################
# For example, ``a0`` and ``a1`` control how threshold changed with pulse duration: 
# :math:`amp = (A_0*pdur + A_1)^{-1}*amp`. Thus, pulse duration threshold 
# scaling can easily be disabled by setting ``a0`` to 0 and ``a1`` to 1. If we increase 
# pulse duration like we did previously, we will now see that only streak length decreases, 
# and we no longer have to change amplitude to account for change in threshold
model = BiphasicAxonMapModel(rho=200, axlambda=800)
model.a0 = 0
model.a1 = 1
model.build()
fig, axes = plt.subplots(1, 2, sharex=True, sharey=True)
implant.stim = {'A4' : BiphasicPulseTrain(20, 1, 0.45)}
percept = model.predict_percept(implant)
implant.stim = {'A4' : BiphasicPulseTrain(20, 1, 20)}
new_percept = model.predict_percept(implant)
new_percept.plot(ax=axes[1])
percept.plot(ax=axes[0], vmax=new_percept.max())
axes[0].set_title("0.45ms")
axes[1].set_title("20ms")
plt.show()

##################################################################################
# Similarly, ``a2``-``a4`` control brightness scaling; ``a5``-``a6`` control size scaling, and
# ``a7``-``a9`` control streak length scaling. For more details on these parameters,
# see the effect models documentation, or [Granley2021]_ 
#
# Advanced Usage
# ----------------------
#
# Custom Effect Models
# =====================
# For most cases, using the provided, default implementation of the effect models
# will probably be enough. However, the effect models are completely modular, and 
# can be replaced by any python callable with the parameters frequency, amplitude, 
# and pulse duration. For example, we can easily change the model to no longer scale size
model = BiphasicAxonMapModel(rho=200, axlambda=800)
def size_modulation(freq, amp, pdur):
    return 1
model.size_model = size_modulation
model.build()

fig, axes = plt.subplots(1, 2, sharex=True, sharey=True)
implant.stim = {'A4' : BiphasicPulseTrain(20, 1, 0.45)}
percept = model.predict_percept(implant)
implant.stim = {'A4' : BiphasicPulseTrain(20, 3, 0.45)}
new_percept = model.predict_percept(implant)
new_percept.plot(ax=axes[1])
percept.plot(ax=axes[0], vmax=new_percept.max())
axes[0].set_title("1xTh")
axes[1].set_title("3xTh")
plt.show()
######################################################################################
# The stimuli with larger amplitude created a brighter, but equally-sized phosphene
#
#
# The effect models can even be a class, and can have its own parameters, 
# which can be shared with the overarching BiphasicAxonMapModel itself (e.g. an effect 
# model can depend on ``rho``, and if ``model.rho`` is changed, ``rho`` will also be changed in
# the effect model). For an example of this, 
# see :py:class:`~pulse2percept.models.granley2021.DefaultSizeModel` 
#
#
# If using custom effect models with jax, the effect models must be written for jax so they can
# be JIT compiled (i.e. using jax.numpy instead of numpy)

########################################################################################
# JAX Engine
# ============
#
# The default computational engine is cython, but an engine based on 
# `jax <https://github.com/google/jax>`_ is also provided. The jax engine is slightly faster on CPU
# and significantly faster on GPU, at the cost of increased memory usage. The jax-based model 
# can be used identically to the cython engine, but it also has some additional features
# and limitations. 
# 
# .. note ::
#
#     Jax functions are compiled the first time they are called. Thus, the first
#     `predict_percept` will be slow. Subsequent calls reuse the compiled and
#     optimized function, and are much faster
#
# One additional feature is the 
# `_predict_spatial_jax` function,
# which is a stripped, purely functional version of 
# `predict_percept` that operates on
# numpy arrays. This avoids the overhead of creating p2p stimulus and percept objects,
# and if used correctly, provides an additional speedup. 
#
# `_predict_spatial_jax` takes in 
# a (n_elecs, 3) numpy array specifying the frequency, amplitude, and pulse duration on
# each electrode, and two (n_elec) shaped arrays specifying the x and y locations of each
# electrode
model = BiphasicAxonMapModel(engine='jax')
model.build()
implant = ArgusII()
ex = np.array([implant[e].x for e in implant.electrodes])
ey = np.array([implant[e].y for e in implant.electrodes]) 
stim = np.zeros((60, 3))
stim[3] = [20, 1, 0.45]
percept = model._predict_spatial_jax(stim, ex, ey)
percept = np.array(percept).reshape(model.grid.shape)
plt.imshow(percept, cmap='gray')
plt.show()
##################################################################################################
# One other useful feature is the 
# `predict_percept_batched` function. This
# applies predict_percept to batches of input stimuli, using optimized matrix operations. See also 
# its faster, stripped version `_predict_spatial_batched`. This 
# function is only intended to be used if you are repeatedly simulating batches of percepts. 
# Since jax compiles each function the first time it is used, using this function only once
# for a singular group of stimuli will be noticably slower than repeatedly applying 
# `predict_percept`. However, splitting a very large set of stimuli into smaller batches and 
# using `predict_percept_batched` will be significantly faster than `predict_percept` on each
# individual stimuli.
#
# Note that this function consumes a large amount of memory, and may not run on systems or 
# GPUs with limited memory. 


# -*- coding: utf-8 -*- ========================================================================================== Granley et al. (2021): Effects of Biphasic Pulse Parameters with the BiphasicAxonMapModel ==========================================================================================  This example shows how to use the :py:class:`~pulse2percept.models.BiphasicAxonMapModel` to model the effects of  biphasic pulse train parameters phosphene appearance in an epiretinal implant such as :py:class:`~pulse2percept.implants.ArgusII`.   Biphasic pulse trains are a commonly used type of stimulus in visual prostheses.  This model enhances the :py:class:`~pulse2percept.models.AxonMapModel` to reflect the effects of the amplitude, frequency, and pulse duration on threshold, phosphene size, brightness, and streak length, according to previous psychophysical and electrophysiological studies.  The :py:class:`~pulse2percept.models.BiphasicAxonMapModel` shares the same underlying  assumptions as the axon map model. Namely, an axon's sensitivity to electrical stimulation is assumed to decay exponentially with...  *  distance along the axon from the soma (:math:`d_s`), with spatial decay    constant :math:`\\lambda`, *  distance from the stimulated electrode (:math:`d_e`), with spatial decay     constant :math:`\\rho`.  In the biphasic model, the radial decay rate :math:`\\rho` is scaled by :math:`F_{size}`, the axonal decay rate :math:`\\lambda` is scaled by :math:`F_{streak}`, and the brightness  contribution from each electrode is scaled by :math:`F_{bright}`. These 3 equations are called effect models. The final equation for the brightness intensity for a pixel located at polar  coordinates :math:`(r, \\theta)` is given by:  .. math::      I =  \\max_{axon}\\sum_{elecs}F_\\mathrm{bright} \\exp\\left(\\frac{-d_{e}^2}{2\\rho^2 F_\\mathrm{size} } +              \\frac{-d_{s}^2}{2\\lambda^2 F_\\mathrm{streak} }\\right).   Basic Model Usage ----------------- The biphasic axon map model can be instantiated and ran similarly to other models, with the exception that all stimuli are required to be :py:class:`~pulse2percept.stimuli.BiphasicPulseTrain` # sphinx_gallery_thumbnail_number = 4 ############################################################################## # Parameters you don't specify will take on default values. You can inspect # all current model parameters as follows: ############################################################################## # The most important parameters are ``rho`` and ``axlambda``, which control the # radial and axonal current spread, respectively. The parameters ``a0``-``a9`` are # coefficients for the size, streak, and bright models, which will be discussed # later in this example. The biphasic axon map model supports both the default # cython engine and a faster, gpu-enabled jax engine. # # The rest of the parameters are shared with # :py:class:`~pulse2percept.models.AxonMapModel`. For full details on these # parameters, see the Axon Map Tutorial # # # Next, build the model to perform expensive, one time calculations, # and specify a visual prosthesis from the # :py:mod:`~pulse2percept.implants` module. Models with an axon map are well # suited for epiretinal implants, such as Argus II. ############################################################################## # .. important :: # #     You need to build a model only once. After that, you can apply any number #     of stimuli -- or even apply the model to different implants -- without #     having to rebuild (which takes time). # #     However, if you change model parameters #     (e.g., by directly setting ``model.a5 = 2``), you will have to #     call ``model.build()`` again for your changes to take effect. # # # You can visualize the location of the implant and the axon map ############################################################################## # As mentioned above, the Biphasic Axon Map Model only accepts # :py:class:`~pulse2percept.stimuli.BiphasicPulseTrain` # stimuli with no :py:attr:`~pulse2percept.stimuli.BiphasicPulseTrain.delay_dur`. # The amplitude given to the BiphasicPulseTrain # is interpreted as amplitude as a factor of threshold (i.e. an amp of 1 means # 1xTh) # # You can easily assign BiphasicPulseTrains to electrodes with a dictionary # The following creates a train with 20Hz frequency, 1xTh amplitude, and 0.45ms # pulse / phase duration. ############################################################################## # Finally, you can predict the percept resulting from stimulation ############################################################################## # Increasing the frequency will make phosphenes brighter ############################################################################## # Note that without setting vmax, matplotlib automatically rescales images to # have the same max brightness and the difference isn't visible ############################################################################## # Increasing amplitude increases both size and brightness ############################################################################## # Increasing pulse duration decreases threshold, thus indirectly causing an # increase in size and brightness (amp factor is increased) ############################################################################## # If you account for the change in threshold by decreasing amplitude, then # the only affect of increasing pulse duration is the streak length decreasing ################################################################################# # This illustrates another important point: The amplitude used for the Biphasic # model is relative to the threshold current at 0.45ms pulse duration. Since larger # pulse durations have been shown to reduce the threshold amplitude needed, the # 0.02xTh amplitude used in the previous plot still is able to produce a phosphene. ################################################################################ # # # Changing Effect Models # ---------------------- # All of the 'effects' plotted above (e.g. size increasing with amplitude) # are controlled by the effect models :math:`F_{bright}`, :math:`F_{size}`, and # :math:`F_{streak}`. The variables # ``bright_model``, ``size_model``, and ``streak_model`` encode the # effects models. # # These default to :py:class:`~pulse2percept.models.granley2021.DefaultBrightModel`, # :py:class:`~pulse2percept.models.granley2021.DefaultSizeModel`, and # :py:class:`~pulse2percept.models.granley2021.DefaultStreakModel` respectively, which # implement the simple scaling functions described in `Granley et al. (2021) <[Granley2021]>`_. # # # The coefficients ``a0``-``a9`` parametrize these effect models. While the default values # are likely to work for most cases, they can be customized to be patient specific. # Notice how we only have to change the value given to the `BiphasicAxonMapModel`, # and it is automatically passed down to the effect models. ################################################################################## # For example, ``a0`` and ``a1`` control how threshold changed with pulse duration: # :math:`amp = (A_0*pdur + A_1)^{-1}*amp`. Thus, pulse duration threshold # scaling can easily be disabled by setting ``a0`` to 0 and ``a1`` to 1. If we increase # pulse duration like we did previously, we will now see that only streak length decreases, # and we no longer have to change amplitude to account for change in threshold ################################################################################## # Similarly, ``a2``-``a4`` control brightness scaling; ``a5``-``a6`` control size scaling, and # ``a7``-``a9`` control streak length scaling. For more details on these parameters, # see the effect models documentation, or [Granley2021]_ # # Advanced Usage # ---------------------- # # Custom Effect Models # ===================== # For most cases, using the provided, default implementation of the effect models # will probably be enough. However, the effect models are completely modular, and # can be replaced by any python callable with the parameters frequency, amplitude, # and pulse duration. For example, we can easily change the model to no longer scale size ###################################################################################### # The stimuli with larger amplitude created a brighter, but equally-sized phosphene # # # The effect models can even be a class, and can have its own parameters, # which can be shared with the overarching BiphasicAxonMapModel itself (e.g. an effect # model can depend on ``rho``, and if ``model.rho`` is changed, ``rho`` will also be changed in # the effect model). For an example of this, # see :py:class:`~pulse2percept.models.granley2021.DefaultSizeModel` # # # If using custom effect models with jax, the effect models must be written for jax so they can # be JIT compiled (i.e. using jax.numpy instead of numpy) ######################################################################################## # JAX Engine # ============ # # The default computational engine is cython, but an engine based on # `jax <https://github.com/google/jax>`_ is also provided. The jax engine is slightly faster on CPU # and significantly faster on GPU, at the cost of increased memory usage. The jax-based model # can be used identically to the cython engine, but it also has some additional features # and limitations. # # .. note :: # #     Jax functions are compiled the first time they are called. Thus, the first #     `predict_percept` will be slow. Subsequent calls reuse the compiled and #     optimized function, and are much faster # # One additional feature is the # `_predict_spatial_jax` function, # which is a stripped, purely functional version of # `predict_percept` that operates on # numpy arrays. This avoids the overhead of creating p2p stimulus and percept objects, # and if used correctly, provides an additional speedup. # # `_predict_spatial_jax` takes in # a (n_elecs, 3) numpy array specifying the frequency, amplitude, and pulse duration on # each electrode, and two (n_elec) shaped arrays specifying the x and y locations of each # electrode ################################################################################################## # One other useful feature is the # `predict_percept_batched` function. This # applies predict_percept to batches of input stimuli, using optimized matrix operations. See also # its faster, stripped version `_predict_spatial_batched`. This # function is only intended to be used if you are repeatedly simulating batches of percepts. # Since jax compiles each function the first time it is used, using this function only once # for a singular group of stimuli will be noticably slower than repeatedly applying # `predict_percept`. However, splitting a very large set of stimuli into smaller batches and # using `predict_percept_batched` will be significantly faster than `predict_percept` on each # individual stimuli. # # Note that this function consumes a large amount of memory, and may not run on systems or # GPUs with limited memory.