p83571920
/
mindspore
forked from mindspore-Ecosystem/mindspore
1
0
Fork 0
Code Issues Pull Requests Projects Releases Wiki Activity

add RMSProp optimizer

This commit is contained in:
zhaoting 2020-03-31 09:14:08 +08:00
parent 5c22c088bb
commit ed3c2d7229
10 changed files with 390 additions and 5 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

6
mindspore/ccsrc/transform/convert.cc
View File

@ -183,6 +183,8 @@ const char kNameDiagPart[] = "DiagPart";
const char kNameSpaceToBatch[] = "SpaceToBatch";
const char kNameBatchToSpace[] = "BatchToSpace";
const char kNameAtan2[] = "Atan2";
const char kNameApplyRMSProp[] = "ApplyRMSProp";
const char kNameApplyCenteredRMSProp[] = "ApplyCenteredRMSProp";
// -----------------OpAdapter initialization--------------
std::unordered_map<std::string, OpAdapterDescPtr> &DfGraphConvertor::get_adpt_map() {
@ -367,7 +369,9 @@ std::unordered_map<std::string, OpAdapterDescPtr> &DfGraphConvertor::get_adpt_ma
{string(kNameDiagPart), ADPT_DESC(DiagPart)},
{string(kNameSpaceToBatch), ADPT_DESC(SpaceToBatchD)},
{string(kNameBatchToSpace), ADPT_DESC(BatchToSpaceD)},
{string(kNameAtan2), ADPT_DESC(Atan2)}};
{string(kNameAtan2), ADPT_DESC(Atan2)},
{string(kNameApplyRMSProp), ADPT_DESC(ApplyRMSPropD)},
{string(kNameApplyCenteredRMSProp), ADPT_DESC(ApplyCenteredRMSProp)}};
#ifdef ENABLE_GE
adpt_map[string(kNamePrint)] = ADPT_DESC(Print);
#endif

16
mindspore/ccsrc/transform/op_declare.cc
View File

@ -1202,6 +1202,22 @@ INPUT_MAP(Atan2) = {{1, INPUT_DESC(x1)}, {2, INPUT_DESC(x2)}};
ATTR_MAP(Atan2) = EMPTY_ATTR_MAP;
OUTPUT_MAP(Atan2) = {{0, OUTPUT_DESC(y)}};
// ApplyRMSPropD
INPUT_MAP(ApplyRMSPropD) = {
{1, INPUT_DESC(var)}, {2, INPUT_DESC(ms)}, {3, INPUT_DESC(mom)}, {4, INPUT_DESC(grad)}, {5, INPUT_DESC(lr)}};
INPUT_ATTR_MAP(ApplyRMSPropD) = {{6, ATTR_DESC(rho, AnyTraits<float>())},
{7, ATTR_DESC(momentum, AnyTraits<float>())},
{8, ATTR_DESC(epsilon, AnyTraits<float>())}};
ATTR_MAP(ApplyRMSPropD) = {{"use_locking", ATTR_DESC(use_locking, AnyTraits<bool>())}};
OUTPUT_MAP(ApplyRMSPropD) = {{0, OUTPUT_DESC(var)}};
// ApplyCenteredRMSProp
INPUT_MAP(ApplyCenteredRMSProp) = {{1, INPUT_DESC(var)}, {2, INPUT_DESC(mg)}, {3, INPUT_DESC(ms)},
{4, INPUT_DESC(mom)}, {5, INPUT_DESC(grad)}, {6, INPUT_DESC(lr)},
{7, INPUT_DESC(rho)}, {8, INPUT_DESC(momentum)}, {9, INPUT_DESC(epsilon)}};
ATTR_MAP(ApplyCenteredRMSProp) = {{"use_locking", ATTR_DESC(use_locking, AnyTraits<bool>())}};
OUTPUT_MAP(ApplyCenteredRMSProp) = {{0, OUTPUT_DESC(var)}};
#ifdef ENABLE_GE
// Print
INPUT_MAP(Print) = EMPTY_INPUT_MAP;

6
mindspore/ccsrc/transform/op_declare.h
View File

@ -445,6 +445,12 @@ DECLARE_OP_ADAPTER(BatchToSpaceD)
DECLARE_OP_USE_OUTPUT(BatchToSpaceD)
DECLARE_OP_ADAPTER(Atan2)
DECLARE_OP_USE_OUTPUT(Atan2)
DECLARE_OP_ADAPTER(ApplyRMSPropD)
DECLARE_OP_USE_INPUT_ATTR(ApplyRMSPropD)
DECLARE_OP_USE_OUTPUT(ApplyRMSPropD)
DECLARE_OP_ADAPTER(ApplyCenteredRMSProp)
DECLARE_OP_USE_OUTPUT(ApplyCenteredRMSProp)
#ifdef ENABLE_GE
DECLARE_OP_ADAPTER(Print)
DECLARE_OP_USE_DYN_INPUT(Print)

3
mindspore/nn/optim/__init__.py
View File

@ -25,6 +25,7 @@ from .lamb import Lamb
from .sgd import SGD
from .lars import LARS
from .ftrl import FTRL
from .rmsprop import RMSProp
__all__ = ['Optimizer', 'Momentum', 'LARS', 'Adam', 'AdamWeightDecay',
'AdamWeightDecayDynamicLR', 'Lamb', 'SGD', 'FTRL']
'AdamWeightDecayDynamicLR', 'Lamb', 'SGD', 'FTRL', 'RMSProp']

187
mindspore/nn/optim/rmsprop.py Normal file
View File

@ -0,0 +1,187 @@
# Copyright 2020 Huawei Technologies Co., Ltd
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
# ============================================================================
"""rmsprop"""
from mindspore.ops import functional as F, composite as C, operations as P
from mindspore.common.initializer import initializer
from mindspore.common.parameter import Parameter
from mindspore._checkparam import ParamValidator as validator
import mindspore.common.dtype as mstype
from .optimizer import Optimizer, grad_scale
rmsprop_opt = C.MultitypeFuncGraph("rmsprop_opt")
centered_rmsprop_opt = C.MultitypeFuncGraph("rmsprop_opt")
@rmsprop_opt.register("Function", "Number", "Number", "Number", "Number", "Tensor", "Tensor", "Tensor", "Tensor")
def _rmsprop_opt(opt, learning_rate, decay, epsilon, momentum, weight, ms, mom, grad):
"""Apply rmsprop optimizer to the weight parameter."""
success = True
success = F.depend(success, opt(weight, ms, mom, grad, learning_rate, decay, momentum, epsilon))
return success
@rmsprop_opt.register("Function", "Tensor", "Number", "Number", "Number", "Tensor", "Tensor", "Tensor", "Tensor")
def _rmsprop_opt_dynamic_lr(opt, learning_rate, decay, epsilon, momentum, weight, ms, mom, grad):
"""Apply rmsprop optimizer to the weight parameter using dynamic learning rate."""
success = True
success = F.depend(success, opt(weight, ms, mom, grad, learning_rate, decay, momentum, epsilon))
return success
@centered_rmsprop_opt.register("Function", "Number", "Number", "Number", "Number", "Tensor", "Tensor", "Tensor",
"Tensor", "Tensor")
def _centered_rmsprop_opt(opt, learning_rate, decay, epsilon, momentum, weight, mg, ms, mom, grad):
"""Apply centered rmsprop optimizer to the weight parameter."""
success = True
success = F.depend(success, opt(weight, mg, ms, mom, grad, learning_rate, decay, momentum, epsilon))
return success
@centered_rmsprop_opt.register("Function", "Tensor", "Number", "Number", "Number", "Tensor", "Tensor", "Tensor",
"Tensor", "Tensor")
def _centered_rmsprop_opt_dynamic_lr(opt, learning_rate, decay, epsilon, momentum, weight, mg, ms, mom, grad):
"""Apply centered rmsprop optimizer to the weight parameter using dynamic learning rate."""
success = True
success = F.depend(success, opt(weight, mg, ms, mom, grad, learning_rate, decay, momentum, epsilon))
return success
class RMSProp(Optimizer):
"""
Implements Root Mean Squared Propagation (RMSProp) algorithm.
Note:
Update `params` according to the RMSProp algorithm.
The equation is as follows:
.. math::
s_{t} = \\rho s_{t-1} + (1 - \\rho)(\\nabla Q_{i}(w))^2
.. math::
m_{t} = \\beta m_{t-1} + \\frac{\\eta} {\\sqrt{s_{t} + \\epsilon}} \\nabla Q_{i}(w)
.. math::
w = w - m_{t}
The first equation calculates moving average of the squared gradient for
each weight. Then dividing the gradient by :math:`\\sqrt{ms_{t} + \\epsilon}`.
if centered is True:
.. math::
g_{t} = \\rho g_{t-1} + (1 - \\rho)\\nabla Q_{i}(w)
.. math::
s_{t} = \\rho s_{t-1} + (1 - \\rho)(\\nabla Q_{i}(w))^2
.. math::
m_{t} = \\beta m_{t-1} + \\frac{\\eta} {\\sqrt{s_{t} - g_{t}^2 + \\epsilon}} \\nabla Q_{i}(w)
.. math::
w = w - m_{t}
where, :math:`w` represents `params`, which will be updated.
:math:`g_{t}` is mean gradients, :math:`g_{t-1}` is the last moment of :math:`g_{t}`.
:math:`s_{t}` is the mean square gradients, :math:`s_{t-1}` is the last moment of :math:`s_{t}`,
:math:`m_{t}` is moment, the delta of `w`, :math:`m_{t-1}` is the last moment of :math:`m_{t}`.
:math:`\\rho` represents `decay`. :math:`\\beta` is the momentum term, represents `momentum`.
:math:`\\epsilon` is a smoothing term to avoid division by zero, represents `epsilon`.
:math:`\\eta` is learning rate, represents `learning_rate`. :math:`\\nabla Q_{i}(w)` is gradientse,
represents `gradients`.
Args:
params (list[Parameter]): A list of parameter, which will be updated. The element in `parameters`
should be class mindspore.Parameter.
learning_rate (Union[float, Tensor, Iterable]): A value for the learning rate. When the learning_rate is
Iterable or a Tensor and the dims of the Tensor is 1,
use dynamic learning rate, then the i-th step will
take the i-th value as the learning rate.
When the learning_rate is float or learning_rate is a Tensor
but the dims of the Tensor is 0, use fixed learning rate.
Other cases are not supported.
decay (float): Decay rate.
momentum (float): Hyperparameter of type float, means momentum for the moving average.
epsilon (float): Term added to the denominator to improve numerical stability. Should be greater than 0.
use_locking (bool): Enable a lock to protect the update of variable and accumlation tensors. Default: False.
centered (bool): If True, gradients are normalized by the estimated variance of the gradient. Default: False
loss_scale (float): A floating point value for the loss scale. Default: 1.0.
Inputs:
- **gradients** (tuple[Tensor]) - The gradients of `params`, the shape is the same as `params`.
Outputs:
Tensor[bool], the value is True.
Examples:
>>> net = Net()
>>> loss = nn.SoftmaxCrossEntropyWithLogits()
>>> opt = RMSProp(params=net.trainable_params(), learning_rate=lr)
>>> model = Model(net, loss, opt)
"""
def __init__(self, params, learning_rate=0.1, decay=0.9, momentum=0.0, epsilon=1e-10,
use_locking=False, centered=False, loss_scale=1.0):
super(RMSProp, self).__init__(learning_rate, params)
if isinstance(momentum, float) and momentum < 0.0:
raise ValueError("momentum should be at least 0.0, but got momentum {}".format(momentum))
if decay < 0.0:
raise ValueError("decay should be at least 0.0, but got dampening {}".format(decay))
self.decay = decay
self.epsilon = epsilon
validator.check_type("use_locking", use_locking, [bool])
validator.check_type("centered", centered, [bool])
self.centered = centered
if centered:
self.opt = P.ApplyCenteredRMSProp(use_locking)
self.mg = self.parameters.clone(prefix="mean_grad", init='zeros')
else:
self.opt = P.ApplyRMSProp(use_locking)
self.dynamic_lr = False
if not isinstance(learning_rate, float):
self.dynamic_lr = True
self.gather = P.GatherV2()
self.assignadd = P.AssignAdd()
self.global_step = Parameter(initializer(0, [1], mstype.int32), name="global_step")
self.axis = 0
self.momentum = momentum
self.ms = self.parameters.clone(prefix="mean_square", init='zeros')
self.moment = self.parameters.clone(prefix="moment", init='zeros')
self.hyper_map = C.HyperMap()
self.decay = decay
self.reciprocal_scale = 1.0 / loss_scale
def construct(self, gradients):
params = self.parameters
if self.reciprocal_scale != 1.0:
gradients = self.hyper_map(F.partial(grad_scale, self.reciprocal_scale), gradients)
if self.dynamic_lr:
lr = self.gather(self.learning_rate, self.global_step, self.axis)
F.control_depend(lr, self.assignadd(self.global_step, self.one))
else:
lr = self.learning_rate
if self.centered:
success = self.hyper_map(F.partial(centered_rmsprop_opt, self.opt, lr, self.decay, self.epsilon,
self.momentum), params, self.mg, self.ms, self.moment, gradients)
else:
success = self.hyper_map(F.partial(rmsprop_opt, self.opt, lr, self.decay, self.epsilon,
self.momentum), params, self.ms, self.moment, gradients)
return success

4
mindspore/ops/_grad/grad_math_ops.py
View File

@ -394,8 +394,8 @@ def _split_shape_index(input_shape, axis):
axis = tuple([axis])
reduction_indices = tuple([(i + rank) % rank for i in axis])
other_indices = tuple(set(range(rank)) - set(reduction_indices))
reduced_num = reduce(lambda x, y: x * y, [input_shape[i] for i in reduction_indices])
other_num = reduce(lambda x, y: x * y, [input_shape[i] for i in other_indices])
reduced_num = reduce(lambda x, y: x * y, [1] + [input_shape[i] for i in reduction_indices])
other_num = reduce(lambda x, y: x * y, [1] + [input_shape[i] for i in other_indices])
perm = reduction_indices + other_indices
return tuple([reduced_num, other_num]), perm

5
mindspore/ops/operations/__init__.py
View File

@ -65,7 +65,8 @@ from .nn_ops import (LSTM, SGD, Adam, ApplyMomentum, BatchNorm,
SmoothL1Loss, Softmax,
SoftmaxCrossEntropyWithLogits, ROIAlign,
SparseSoftmaxCrossEntropyWithLogits, Tanh,
TopK, BinaryCrossEntropy, SparseApplyAdagrad, LARSUpdate, ApplyFtrl)
TopK, BinaryCrossEntropy, SparseApplyAdagrad, LARSUpdate, ApplyFtrl,
ApplyRMSProp, ApplyCenteredRMSProp)
from .other_ops import Assign, IOU, BoundingBoxDecode, BoundingBoxEncode, CheckValid, MakeRefKey
@ -228,6 +229,8 @@ __all__ = [
"SpaceToBatch",
"BatchToSpace",
"Atan2",
"ApplyRMSProp",
"ApplyCenteredRMSProp"
]
__all__.sort()

152
mindspore/ops/operations/nn_ops.py
View File

@ -1359,6 +1359,158 @@ class SGD(PrimitiveWithInfer):
validator.check_typename("stat_dtype", stat_dtype, [mstype.float16, mstype.float32])
return parameters_dtype
class ApplyRMSProp(PrimitiveWithInfer):
"""
Optimizer that implements the Root Mean Square prop(RMSProp) algorithm.
Note:
Update `var` according to the RMSProp algorithm.
.. math::
s_{t} = \\rho s_{t-1} + (1 - \\rho)(\\nabla Q_{i}(w))^2
.. math::
m_{t} = \\beta m_{t-1} + \\frac{\\eta} {\\sqrt{s_{t} + \\epsilon}} \\nabla Q_{i}(w)
.. math::
w = w - m_{t}
where, :math:`w` represents `var`, which will be updated.
:math:`s_{t}` represents `mean_square`, :math:`s_{t-1}` is the last momentent of :math:`s_{t}`,
:math:`m_{t}` represents `moment`, :math:`m_{t-1}` is the last momentent of :math:`m_{t}`.
:math:`\\rho` represents `decay`. :math:`\\beta` is the momentum term, represents `momentum`.
:math:`\\epsilon` is a smoothing term to avoid division by zero, represents `epsilon`.
:math:`\\eta` represents `learning_rate`. :math:`\\nabla Q_{i}(w)` represents `grad`.
Args:
use_locking (bool): Enable a lock to protect the update of variable tensors. Default: False.
Inputs:
- **var** (Tensor) - Weights to be update.
- **mean_square** (Tensor) - Mean square gradients, must have the same type as `var`.
- **moment** (Tensor) - Delta of `var`, must have the same type as `var`.
- **grad** (Tensor) - Gradients, must have the same type as `var`.
- **learning_rate** (Union[Number, Tensor]) - Learning rate.
- **decay** (float) - Decay rate.
- **momentum** (float) - Momentum.
- **epsilon** (float) - Ridge term.
Outputs:
Tensor, parameters to be update.
Examples:
>>> net = Net()
>>> loss = nn.SoftmaxCrossEntropyWithLogits()
>>> opt = RMSProp(params=net.trainable_params(), learning_rate=learning_rate)
>>> model = Model(net, loss, opt)
"""
@prim_attr_register
def __init__(self, use_locking=False):
self.use_locking = validator.check_type("use_locking", use_locking, [bool])
def infer_shape(self, var_shape, mean_square_shape, moment_shape, grad_shape, learning_rate_shape, decay_shape,
momentum_shape, epsilon_shape):
validator.check_param_equal("var_shape", var_shape, "mean_square_shape", mean_square_shape)
validator.check_param_equal("var_shape", var_shape, "moment_shape", moment_shape)
validator.check_param_equal("var_shape", var_shape, "grad_shape", grad_shape)
return var_shape
def infer_dtype(self, var_dtype, mean_square_dtype, moment_dtype, grad_dtype, learning_rate_dtype, decay_dtype,
momentum_dtype, epsilon_dtype):
validator.check_subclass("var_dtype", var_dtype, mstype.tensor)
validator.check_subclass("mean_square_dtype", mean_square_dtype, mstype.tensor)
validator.check_subclass("moment_dtype", moment_dtype, mstype.tensor)
validator.check_subclass("grad_dtype", moment_dtype, mstype.tensor)
args = {"var_dtype": var_dtype, "mean_square_dtype": mean_square_dtype, "moment_dtype": moment_dtype,
"grad_dtype": grad_dtype}
validator.check_type_same(args, mstype.number_type)
args = {"learning_rate_dtype": learning_rate_dtype, "decay_dtype": decay_dtype,
'momentum_dtype': momentum_dtype, "epsilon_dtype": epsilon_dtype}
validator.check_type_same(args, [mstype.float16, mstype.float32])
return var_dtype
class ApplyCenteredRMSProp(PrimitiveWithInfer):
"""
Optimizer that implements the centered RMSProp algorithm.
Note:
Update `var` according to the centered RMSProp algorithm.
.. math::
g_{t} = \\rho g_{t-1} + (1 - \\rho)\\nabla Q_{i}(w)
.. math::
s_{t} = \\rho s_{t-1} + (1 - \\rho)(\\nabla Q_{i}(w))^2
.. math::
m_{t} = \\beta m_{t-1} + \\frac{\\eta} {\\sqrt{s_{t} - g_{t}^2 + \\epsilon}} \\nabla Q_{i}(w)
.. math::
w = w - m_{t}
where, :math:`w` represents `var`, which will be updated.
:math:`g_{t}` represents `mean_gradient`, :math:`g_{t-1}` is the last momentent of :math:`g_{t}`.
:math:`s_{t}` represents `mean_square`, :math:`s_{t-1}` is the last momentent of :math:`s_{t}`,
:math:`m_{t}` represents `moment`, :math:`m_{t-1}` is the last momentent of :math:`m_{t}`.
:math:`\\rho` represents `decay`. :math:`\\beta` is the momentum term, represents `momentum`.
:math:`\\epsilon` is a smoothing term to avoid division by zero, represents `epsilon`.
:math:`\\eta` represents `learning_rate`. :math:`\\nabla Q_{i}(w)` represents `grad`.
Args:
use_locking (bool): Enable a lock to protect the update of variable tensors. Default: False.
Inputs:
- **var** (Tensor) - Weights to be update.
- **mean_gradient** (Tensor) - Mean gradients, must have the same type as `var`.
- **mean_square** (Tensor) - Mean square gradients, must have the same type as `var`.
- **moment** (Tensor) - Delta of `var`, must have the same type as `var`.
- **grad** (Tensor) - Gradients, must have the same type as `var`.
- **learning_rate** (Union[Number, Tensor]) - Learning rate.
- **decay** (float) - Decay rate.
- **momentum** (float) - Momentum.
- **epsilon** (float) - Ridge term.
Outputs:
Tensor, parameters to be update.
Examples:
>>> net = Net()
>>> loss = nn.SoftmaxCrossEntropyWithLogits()
>>> opt = RMSProp(params=net.trainable_params(), learning_rate=learning_rate, centered=True)
>>> model = Model(net, loss, opt)
"""
@prim_attr_register
def __init__(self, use_locking=False):
self.use_locking = validator.check_type("use_locking", use_locking, [bool])
def infer_shape(self, var_shape, mean_gradient_shape, mean_square_shape, moment_shape, grad_shape,
learning_rate_shape, decay_shape, momentum_shape, epsilon_shape):
validator.check_param_equal("var_shape", var_shape, "mean_gradient_shape", mean_gradient_shape)
validator.check_param_equal("var_shape", var_shape, "mean_square_shape", mean_square_shape)
validator.check_param_equal("var_shape", var_shape, "moment_shape", moment_shape)
validator.check_param_equal("var_shape", var_shape, "grad_shape", grad_shape)
return var_shape
def infer_dtype(self, var_dtype, mean_gradient_dtype, mean_square_dtype, moment_dtype, grad_dtype,
learning_rate_dtype, rho_dtype, momentum_dtype, epsilon_dtype):
validator.check_subclass("var_dtype", var_dtype, mstype.tensor)
validator.check_subclass("mean_gradient_dtype", mean_gradient_dtype, mstype.tensor)
validator.check_subclass("mean_square_dtype", mean_square_dtype, mstype.tensor)
validator.check_subclass("moment_dtype", moment_dtype, mstype.tensor)
validator.check_subclass("grad_dtype", moment_dtype, mstype.tensor)
args = {"var_dtype": var_dtype, "mean_gradient_dtype": mean_gradient_dtype,
"mean_square_dtype": mean_square_dtype, "moment_dtype": moment_dtype, "grad_dtype": grad_dtype}
validator.check_type_same(args, mstype.number_type)
args = {"learning_rate_dtype": learning_rate_dtype, "rho_dtype": rho_dtype, 'momentum_dtype': momentum_dtype,
"epsilon_dtype": epsilon_dtype}
validator.check_type_same(args, [mstype.float16, mstype.float32])
return var_dtype
class LayerNorm(Primitive):
r"""

4
tests/mindspore_test_framework/utils/block_util.py
View File

@ -223,6 +223,10 @@ class InputOpNet(nn.Cell):
x = self.op(x1, x2, x3, x4, x5, self.c1)
return x
def construct5_c4(self, x1, x2, x3, x4, x5):
x = self.op(x1, x2, x3, x4, x5, self.c1, self.c2, self.c3, self.c4)
return x
def gen_net(op, input_num, training=True, desc_const=(), const_first=False, add_fake_input=False):
if isinstance(op, nn.Cell):
return op

12
tests/ut/python/ops/test_ops.py
View File

@ -805,6 +805,18 @@ test_case_nn_ops = [
'desc_inputs': [[3, 3], [3, 3], [3, 3], [3, 3]],
'desc_bprop': [3, 3],
'skip': ['backward']}),
('ApplyRMSProp', {
'block': P.ApplyRMSProp(),
'desc_const': [0.9, 0.0, 1e-10, 0.001],
'desc_inputs': [[3, 3], [3, 3], [3, 3], [3, 3]],
'desc_bprop': [3, 3],
'skip': ['backward']}),
('ApplyCenteredRMSProp', {
'block': P.ApplyCenteredRMSProp(),
'desc_const': [0.9, 0.0, 1e-10, 0.001],
'desc_inputs': [[3, 3], [3, 3], [3, 3], [3, 3], [3, 3]],
'desc_bprop': [3, 3],
'skip': ['backward']}),
]
test_case_array_ops = [