# Copyright 2020-2021 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.
# ============================================================================
"""math"""
import numpy as np
from mindspore.ops import operations as P
from mindspore.common.tensor import Tensor
from mindspore.common._decorator import deprecated
from mindspore.ops.primitive import constexpr
from mindspore.ops import functional as F
from ..cell import Cell
from ...common import dtype as mstype
from ..._checkparam import Validator as validator
__all__ = ['ReduceLogSumExp',
'Range',
'LGamma',
'DiGamma',
'IGamma',
'LBeta',
'MatMul',
'Moments',
'MatInverse',
'MatDet',
]
_BASE_LANCZOS_COEFF = 0.99999999999980993227684700473478
_LANCZOS_COEFFICIENTS = [676.520368121885098567009190444019,
-1259.13921672240287047156078755283,
771.3234287776530788486528258894,
-176.61502916214059906584551354,
12.507343278686904814458936853,
-0.13857109526572011689554707,
9.984369578019570859563e-6,
1.50563273514931155834e-7]
@constexpr
def _check_input_dtype(param_name, input_dtype, allow_dtypes, cls_name):
validator.check_type_name(param_name, input_dtype, allow_dtypes, cls_name)
[docs]class ReduceLogSumExp(Cell):
r"""
Reduces a dimension of a tensor by calculating exponential for all elements in the dimension,
then calculate logarithm of the sum.
.. math::
ReduceLogSumExp(x) = \log(\sum(e^x))
Args:
axis (Union[int, tuple(int), list(int)]) - The dimensions to reduce. Default: (), reduce all dimensions.
Only constant value is allowed.
keep_dims (bool): If True, keep these reduced dimensions and the length is 1.
If False, don't keep these dimensions.
Default : False.
Inputs:
- **x** (Tensor) - The input tensor. With float16 or float32 data type.
Outputs:
Tensor, has the same dtype as the `x`.
- If axis is (), and keep_dims is False,
the output is a 0-D tensor representing the sum of all elements in the input tensor.
- If axis is int, set as 2, and keep_dims is False,
the shape of output is :math:`(x_1, x_3, ..., x_R)`.
- If axis is tuple(int), set as (2, 3), and keep_dims is False,
the shape of output is :math:`(x_1, x_4, ..., x_R)`.
Raises:
TypeError: If `axis` is not one of int, list, tuple.
TypeError: If `keep_dims` is not bool.
TypeError: If dtype of `x` is neither float16 nor float32.
Supported Platforms:
``Ascend`` ``GPU`` ``CPU``
Examples:
>>> x = Tensor(np.random.randn(3, 4, 5, 6).astype(np.float32))
>>> op = nn.ReduceLogSumExp(1, keep_dims=True)
>>> output = op(x)
>>> print(output.shape)
(3, 1, 5, 6)
"""
def __init__(self, axis, keep_dims=False):
"""Initialize ReduceLogSumExp."""
super(ReduceLogSumExp, self).__init__()
validator.check_value_type('axis', axis, [int, list, tuple], self.cls_name)
validator.check_value_type('keep_dims', keep_dims, [bool], self.cls_name)
self.axis = axis
self.exp = P.Exp()
self.sum = P.ReduceSum(keep_dims)
self.log = P.Log()
self.max = P.ReduceMax()
def construct(self, x):
x_max = self.max(x)
exp = self.exp(x - x_max)
sumexp = self.sum(exp, self.axis)
logsumexp = self.log(sumexp)
return logsumexp + x_max
[docs]class Range(Cell):
r"""
Creates a sequence of numbers in range [start, limit) with step size delta.
The size of output is :math:`\left \lfloor \frac{limit-start}{delta} \right \rfloor + 1` and `delta` is the gap
between two values in the tensor.
.. math::
out_{i+1} = out_{i} +delta
Args:
start (Union[int, float]): If `limit` is `None`, the value acts as limit in the range and first entry
defaults to `0`. Otherwise, it acts as first entry in the range.
limit (Union[int, float]): Acts as upper limit of sequence. If `None`, defaults to the value of `start`
while set the first entry of the range to `0`. It can not be equal to `start`. Default: None.
delta (Union[int, float]): Increment of the range. It can not be equal to zero. Default: 1.
Outputs:
Tensor, the dtype is int if the dtype of `start`, `limit` and `delta` all are int. Otherwise, dtype is float.
Supported Platforms:
``Ascend`` ``GPU`` ``CPU``
Examples:
>>> net = nn.Range(1, 8, 2)
>>> output = net()
>>> print(output)
[1 3 5 7]
"""
def __init__(self, start, limit=None, delta=1):
"""Initialize Range."""
super(Range, self).__init__()
if delta == 0:
raise ValueError(f"For '{self.cls_name}', the 'delta' can not be zero.")
data = np.arange(start, limit, delta)
if data.dtype == np.float:
self.ms_dtype = mstype.float32
else:
self.ms_dtype = mstype.int32
self.result_tensor = Tensor(data, dtype=self.ms_dtype)
def construct(self):
return self.result_tensor
class LGamma(Cell):
r"""
Calculates LGamma using Lanczos' approximation referring to "A Precision Approximation of the Gamma Function".
The algorithm is:
.. math::
\begin{array}{ll} \\
lgamma(z + 1) = \frac{(\log(2) + \log(pi))}{2} + (z + 1/2) * log(t(z)) - t(z) + A(z) \\
t(z) = z + kLanczosGamma + 1/2 \\
A(z) = kBaseLanczosCoeff + \sum_{k=1}^n \frac{kLanczosCoefficients[i]}{z + k}
\end{array}
However, if the input is less than 0.5 use Euler's reflection formula:
.. math::
lgamma(x) = \log(pi) - lgamma(1-x) - \log(abs(sin(pi * x)))
And please note that
.. math::
lgamma(+/-inf) = +inf
Thus, the behaviour of LGamma follows:
- when x > 0.5, return log(Gamma(x))
- when x < 0.5 and is not an integer, return the real part of Log(Gamma(x)) where Log is the complex logarithm
- when x is an integer less or equal to 0, return +inf
- when x = +/- inf, return +inf
Inputs:
- **x** (Tensor) - The input tensor. Only float16, float32 are supported.
Outputs:
Tensor, has the same shape and dtype as the `x`.
Raises:
TypeError: If dtype of `x` is neither float16 nor float32.
Supported Platforms:
``Ascend`` ``GPU``
Examples:
>>> x = Tensor(np.array([2, 3, 4]).astype(np.float32))
>>> op = nn.LGamma()
>>> output = op(x)
>>> print(output)
[3.5762787e-07 6.9314754e-01 1.7917603e+00]
"""
def __init__(self):
"""Initialize LGamma."""
super(LGamma, self).__init__()
# const numbers
self.k_lanczos_gamma = 7
self.k_base_lanczos_coeff = _BASE_LANCZOS_COEFF
self.k_lanczos_coefficients = _LANCZOS_COEFFICIENTS
self.one_half = 0.5
self.one = 1
self.two = 2
self.inf = np.inf
self.pi = np.pi
self.log_2 = np.log(self.two)
self.log_pi = np.log(np.pi)
self.log_sqrt_two_pi = (self.log_2 + self.log_pi) / self.two
self.lanczos_gamma_plus_one_half = self.k_lanczos_gamma + 0.5
self.log_lanczos_gamma_plus_one_half = np.log(self.lanczos_gamma_plus_one_half)
# operations
self.log = P.Log()
self.log1p = P.Log1p()
self.abs = P.Abs()
self.shape = P.Shape()
self.dtype = P.DType()
self.fill = P.Fill()
self.floor = P.Floor()
self.equal = P.Equal()
self.greater = P.Greater()
self.less = P.Less()
self.lessequal = P.LessEqual()
self.select = P.Select()
self.sin = P.Sin()
self.isfinite = P.IsFinite()
def construct(self, x):
input_dtype = self.dtype(x)
_check_input_dtype("x", input_dtype, [mstype.float16, mstype.float32], self.cls_name)
infinity = self.fill(input_dtype, self.shape(x), self.inf)
need_to_reflect = self.less(x, 0.5)
neg_input = -x
z = self.select(need_to_reflect, neg_input, x - 1)
@constexpr
def _calculate_reflected_x(z, k_base_lanczos_coeff, k_lanczos_coefficients):
reflex_x = k_base_lanczos_coeff
for i in range(8):
product_ = k_lanczos_coefficients[i] / (z + i + 1)
reflex_x = product_ + reflex_x
return reflex_x
reflex_x = _calculate_reflected_x(z, self.k_base_lanczos_coeff, self.k_lanczos_coefficients)
t = z + self.lanczos_gamma_plus_one_half
log_t = self.log1p(z / self.lanczos_gamma_plus_one_half) + self.log_lanczos_gamma_plus_one_half
log_y = self.log(reflex_x) + (z + self.one_half - t / log_t) * log_t + self.log_sqrt_two_pi
abs_input = self.abs(x)
abs_frac_input = abs_input - self.floor(abs_input)
x = self.select(self.lessequal(x, 0.0), self.select(self.equal(abs_frac_input, 0.0), infinity, x), x)
reduced_frac_input = self.select(self.greater(abs_frac_input, 0.5),
1 - abs_frac_input, abs_frac_input)
reflection_denom = self.log(self.sin(self.pi * reduced_frac_input))
reflection = self.select(self.isfinite(reflection_denom),
-reflection_denom - log_y + self.log_pi, # pylint: disable=invalid-unary-operand-type
-reflection_denom) # pylint: disable=invalid-unary-operand-type
result = self.select(need_to_reflect, reflection, log_y)
return self.select(self.isfinite(x), result, infinity)
class DiGamma(Cell):
r"""
Calculates Digamma using Lanczos' approximation referring to "A Precision Approximation of the Gamma Function".
The algorithm is:
.. math::
\begin{array}{ll} \\
digamma(z + 1) = log(t(z)) + A'(z) / A(z) - kLanczosGamma / t(z) \\
t(z) = z + kLanczosGamma + 1/2 \\
A(z) = kBaseLanczosCoeff + \sum_{k=1}^n \frac{kLanczosCoefficients[i]}{z + k} \\
A'(z) = \sum_{k=1}^n \frac{kLanczosCoefficients[i]}{{z + k}^2}
\end{array}
However, if the input is less than 0.5 use Euler's reflection formula:
.. math::
digamma(x) = digamma(1 - x) - pi * cot(pi * x)
Inputs:
- **x** (Tensor[Number]) - The input tensor. Only float16, float32 are supported.
Outputs:
Tensor, has the same shape and dtype as the `x`.
Raises:
TypeError: If dtype of `x` is neither float16 nor float32.
Supported Platforms:
``Ascend`` ``GPU``
Examples:
>>> x = Tensor(np.array([2, 3, 4]).astype(np.float32))
>>> op = nn.DiGamma()
>>> output = op(x)
>>> print(output)
[0.42278463 0.92278427 1.2561178]
"""
def __init__(self):
"""Initialize DiGamma."""
super(DiGamma, self).__init__()
# const numbers
self.k_lanczos_gamma = 7
self.k_base_lanczos_coeff = _BASE_LANCZOS_COEFF
self.k_lanczos_coefficients = _LANCZOS_COEFFICIENTS
self.nan = np.nan
self.pi = np.pi
self.lanczos_gamma_plus_one_half = self.k_lanczos_gamma + 0.5
self.log_lanczos_gamma_plus_one_half = np.log(self.lanczos_gamma_plus_one_half)
# operations
self.log1p = P.Log1p()
self.abs = P.Abs()
self.shape = P.Shape()
self.dtype = P.DType()
self.fill = P.Fill()
self.floor = P.Floor()
self.equal = P.Equal()
self.less = P.Less()
self.select = P.Select()
self.sin = P.Sin()
self.cos = P.Cos()
self.logicaland = P.LogicalAnd()
def construct(self, x):
input_dtype = self.dtype(x)
_check_input_dtype("x", input_dtype, [mstype.float16, mstype.float32], self.cls_name)
need_to_reflect = self.less(x, 0.5)
neg_input = -x
z = self.select(need_to_reflect, neg_input, x - 1)
@constexpr
def _calculate_num_denom(z, k_base_lanczos_coeff, k_lanczos_coefficients):
num = 0
denom = k_base_lanczos_coeff
for i in range(8):
num = num - k_lanczos_coefficients[i] / ((z + i + 1) * (z + i + 1))
denom = denom + k_lanczos_coefficients[i] / (z + i + 1)
return num, denom
num, denom = _calculate_num_denom(z, self.k_base_lanczos_coeff, self.k_lanczos_coefficients)
t = z + self.lanczos_gamma_plus_one_half
log_t = self.log1p(z / self.lanczos_gamma_plus_one_half) + self.log_lanczos_gamma_plus_one_half
y = log_t + num / denom - self.k_lanczos_gamma / t
reduced_input = x + self.abs(self.floor(x + 0.5))
reflection = y - self.pi * self.cos(self.pi * reduced_input) / self.sin(self.pi * reduced_input)
real_result = self.select(need_to_reflect, reflection, y)
nan = self.fill(self.dtype(x), self.shape(x), np.nan)
return self.select(self.logicaland(self.less(x, 0), self.equal(x, self.floor(x))),
nan, real_result)
eps_fp32 = Tensor(np.finfo(np.float32).eps, mstype.float32)
def _while_helper_func(cond, body, vals):
while cond(vals).any():
vals = body(vals)
return vals
def _igamma_series(ax, x, a, enabled):
"""Helper function for computing Igamma using a power series."""
logicaland = P.LogicalAnd()
greater = P.Greater()
fill = P.Fill()
shape = P.Shape()
dtype = P.DType()
select = P.Select()
# If more data types are supported, this epsilon need to be selected.
epsilon = eps_fp32
def cond(vals):
enabled = vals[0]
return enabled
def body(vals):
enabled = vals[0]
r = vals[1]
c = vals[2]
ans = vals[3]
x = vals[4]
dc_da = vals[5]
dans_da = vals[6]
r = r + 1
dc_da = dc_da * (x / r) + (-1 * c * x) / (r * r)
dans_da = dans_da + dc_da
c = c * (x / r)
ans = ans + c
conditional = logicaland(enabled, greater(c / ans, epsilon))
return (conditional, select(enabled, r, vals[1]),
select(enabled, c, vals[2]), select(enabled, ans, vals[3]),
select(enabled, x, vals[4]), select(enabled, dc_da, vals[5]),
select(enabled, dans_da, vals[6]))
ones = fill(dtype(a), shape(a), 1)
zeros = fill(dtype(a), shape(a), 0)
vals = (enabled, a, ones, ones, x, zeros, zeros)
vals = _while_helper_func(cond, body, vals)
ans = vals[3]
return (ans * ax) / a
def _igammac_continued_fraction(ax, x, a, enabled):
"""Helper function for computing Igammac using a continued fraction."""
abs_x = P.Abs()
logicaland = P.LogicalAnd()
greater = P.Greater()
less = P.Less()
notequal = P.NotEqual()
fill = P.Fill()
shape = P.Shape()
dtype = P.DType()
select = P.Select()
# If more data types are supported, this epsilon need to be selected.
epsilon = eps_fp32
def cond(vals):
enabled = vals[0]
c = vals[5]
return logicaland(less(c, 2000), enabled)
def body(vals):
enabled = vals[0]
ans = vals[1]
t = vals[2]
y = vals[3]
z = vals[4]
c = vals[5]
pkm1 = vals[6]
qkm1 = vals[7]
pkm2 = vals[8]
qkm2 = vals[9]
dpkm2_da = vals[10]
dqkm2_da = vals[11]
dpkm1_da = vals[12]
dqkm1_da = vals[13]
dans_da = vals[14]
c = c + 1
y = y + 1
z = z + 2
yc = y * c
pk = pkm1 * z - pkm2 * yc
qk = qkm1 * z - qkm2 * yc
qk_is_nonzero = notequal(qk, 0)
r = pk / qk
t = select(qk_is_nonzero, abs_x((ans - r) / r), fill(dtype(t), shape(t), 1))
ans = select(qk_is_nonzero, r, ans)
dpk_da = dpkm1_da * z - pkm1 - dpkm2_da * yc + pkm2 * c
dqk_da = dqkm1_da * z - qkm1 - dqkm2_da * yc + qkm2 * c
dans_da_new = select(qk_is_nonzero, (dpk_da - ans * dqk_da) / qk, dans_da)
grad_conditional = select(qk_is_nonzero,
abs_x(dans_da_new - dans_da),
fill(dtype(dans_da), shape(dans_da), 1))
pkm2 = pkm1
pkm1 = pk
qkm2 = qkm1
qkm1 = qk
dpkm2_da = dpkm1_da
dqkm2_da = dqkm1_da
dpkm1_da = dpk_da
dqkm1_da = dqk_da
rescale = greater(abs_x(pk), 1 / epsilon)
pkm2 = select(rescale, pkm2 * epsilon, pkm2)
pkm1 = select(rescale, pkm1 * epsilon, pkm1)
qkm2 = select(rescale, qkm2 * epsilon, qkm2)
qkm1 = select(rescale, qkm1 * epsilon, qkm1)
dpkm2_da = select(rescale, dpkm2_da * epsilon, dpkm2_da)
dqkm2_da = select(rescale, dqkm2_da * epsilon, dqkm2_da)
dpkm1_da = select(rescale, dpkm1_da * epsilon, dpkm1_da)
dqkm1_da = select(rescale, dqkm1_da * epsilon, dqkm1_da)
conditional = logicaland(enabled, greater(grad_conditional, epsilon))
return (conditional, select(enabled, ans, vals[1]), select(enabled, t, vals[2]),
select(enabled, y, vals[3]), select(enabled, z, vals[4]),
c, select(enabled, pkm1, vals[6]),
select(enabled, qkm1, vals[7]), select(enabled, pkm2, vals[8]),
select(enabled, qkm2, vals[9]), select(enabled, dpkm2_da, vals[10]),
select(enabled, dqkm2_da, vals[11]), select(enabled, dpkm1_da, vals[12]),
select(enabled, dqkm1_da, vals[13]), select(enabled, dans_da_new, vals[14]))
y = 1 - a
z = x + y + 1
c = fill(dtype(x), shape(x), 0)
pkm2 = fill(dtype(x), shape(x), 1)
qkm2 = x
pkm1 = x + 1
qkm1 = z * x
ans = pkm1 / qkm1
t = fill(dtype(x), shape(x), 1)
dpkm2_da = fill(dtype(x), shape(x), 0)
dqkm2_da = fill(dtype(x), shape(x), 0)
dpkm1_da = fill(dtype(x), shape(x), 0)
dqkm1_da = -x
dans_da = (dpkm1_da - ans * dqkm1_da) / qkm1
vals = (enabled, ans, t, y, z, c, pkm1, qkm1, pkm2, qkm2, dpkm2_da, dqkm2_da, dpkm1_da, dqkm1_da, dans_da)
vals = _while_helper_func(cond, body, vals)
ans = vals[1]
return ans * ax
class IGamma(Cell):
r"""
Calculates lower regularized incomplete Gamma function.
The lower regularized incomplete Gamma function is defined as:
.. math::
P(a, x) = gamma(a, x) / Gamma(a) = 1 - Q(a, x)
where
.. math::
gamma(a, x) = \int_0^x t^{a-1} \exp^{-t} dt
is the lower incomplete Gamma function.
Above :math:`Q(a, x)` is the upper regularized complete Gamma function.
Inputs:
- **a** (Tensor) - The input tensor. With float32 data type. `a` should have
the same dtype with `x`.
- **x** (Tensor) - The input tensor. With float32 data type. `x` should have
the same dtype with `a`.
Outputs:
Tensor, has the same dtype as `a` and `x`.
Raises:
TypeError: If dtype of input x and a is not float16 nor float32,
or if x has different dtype with a.
Supported Platforms:
``Ascend`` ``GPU``
Examples:
>>> a = Tensor(np.array([2.0, 4.0, 6.0, 8.0]).astype(np.float32))
>>> x = Tensor(np.array([2.0, 3.0, 4.0, 5.0]).astype(np.float32))
>>> igamma = nn.IGamma()
>>> output = igamma(a, x)
>>> print (output)
[0.593994 0.35276785 0.21486944 0.13337152]
"""
def __init__(self):
"""Initialize IGamma."""
super(IGamma, self).__init__()
# const numbers
# If more data types are supported, this float max value need to be selected.
self.log_maxfloat32 = Tensor(np.log(np.finfo(np.float32).max), mstype.float32)
# operations
self.logicaland = P.LogicalAnd()
self.logicalor = P.LogicalOr()
self.logicalnot = P.LogicalNot()
self.equal = P.Equal()
self.greater = P.Greater()
self.less = P.Less()
self.neg = P.Neg()
self.log = P.Log()
self.exp = P.Exp()
self.select = P.Select()
self.zeroslike = P.ZerosLike()
self.fill = P.Fill()
self.shape = P.Shape()
self.dtype = P.DType()
self.lgamma = LGamma()
self.const = P.ScalarToArray()
self.cast = P.Cast()
def construct(self, a, x):
a_dtype = self.dtype(a)
x_dtype = self.dtype(x)
_check_input_dtype("a", a_dtype, [mstype.float32], self.cls_name)
_check_input_dtype("x", x_dtype, a_dtype, self.cls_name)
domain_error = self.logicalor(self.less(x, 0), self.less(a, 0))
use_igammac = self.logicaland(self.greater(x, 1), self.greater(x, a))
ax = a * self.log(x) - x - self.lgamma(a)
para_shape = self.shape(ax)
if para_shape != ():
broadcastto = P.BroadcastTo(para_shape)
x = broadcastto(x)
a = broadcastto(a)
x_is_zero = self.equal(x, 0)
log_maxfloat = self.log_maxfloat32
underflow = self.less(ax, self.neg(log_maxfloat))
ax = self.exp(ax)
enabled = self.logicalnot(self.logicalor(self.logicalor(x_is_zero, domain_error), underflow))
output = self.select(use_igammac,
1 - _igammac_continued_fraction(ax, x, a, self.logicaland(enabled, use_igammac)),
_igamma_series(ax, x, a, self.logicaland(enabled, self.logicalnot(use_igammac))))
output = self.select(x_is_zero, self.zeroslike(output), output)
output = self.select(domain_error, self.fill(self.dtype(a), self.shape(a), np.nan), output)
return output
class LBeta(Cell):
r"""
This method avoids the numeric cancellation by explicitly
decomposing lgamma into the Stirling approximation and an explicit log_gamma_correction, and cancelling
the large terms from the Striling analytically.
This is semantically equal to
.. math::
P(x, y) = lgamma(x) + lgamma(y) - lgamma(x + y).
The method is more accurate for arguments above 8. The reason for accuracy loss in the naive computation
is catastrophic cancellation between the lgammas.
Inputs:
- **x** (Tensor) - The input tensor. With float16 or float32 data type. `x` should have
the same dtype with `y`.
- **y** (Tensor) - The input tensor. With float16 or float32 data type. `y` should have
the same dtype with `x`.
Outputs:
Tensor, has the same dtype as `x` and `y`.
Raises:
TypeError: If dtype of `x` or `y` is neither float16 nor float32,
or if `x` has different dtype with `y`.
Supported Platforms:
``Ascend`` ``GPU``
Examples:
>>> x = Tensor(np.array([2.0, 4.0, 6.0, 8.0]).astype(np.float32))
>>> y = Tensor(np.array([2.0, 3.0, 14.0, 15.0]).astype(np.float32))
>>> lbeta = nn.LBeta()
>>> output = lbeta(y, x)
>>> print(output)
[-1.7917596 -4.094345 -12.000229 -14.754799]
"""
def __init__(self):
"""Initialize LBeta."""
super(LBeta, self).__init__()
# const numbers
self.log_2pi = np.log(2 * np.pi)
self.minimax_coeff = [-0.165322962780713e-02,
0.837308034031215e-03,
-0.595202931351870e-03,
0.793650666825390e-03,
-0.277777777760991e-02,
0.833333333333333e-01]
# operations
self.log = P.Log()
self.log1p = P.Log1p()
self.less = P.Less()
self.select = P.Select()
self.shape = P.Shape()
self.dtype = P.DType()
self.lgamma = LGamma()
self.const = P.ScalarToTensor()
def construct(self, x, y):
x_dtype = self.dtype(x)
y_dtype = self.dtype(y)
_check_input_dtype("x", x_dtype, [mstype.float16, mstype.float32], self.cls_name)
_check_input_dtype("y", y_dtype, x_dtype, self.cls_name)
x_plus_y = x + y
para_shape = self.shape(x_plus_y)
if para_shape != ():
broadcastto = P.BroadcastTo(para_shape)
x = broadcastto(x)
y = broadcastto(y)
comp_less = self.less(x, y)
x_min = self.select(comp_less, x, y)
y_max = self.select(comp_less, y, x)
@constexpr
def _log_gamma_correction(x, minimax_coeff):
inverse_x = 1. / x
inverse_x_squared = inverse_x * inverse_x
accum = minimax_coeff[0]
for i in range(1, 6):
accum = accum * inverse_x_squared + minimax_coeff[i]
return accum * inverse_x
log_gamma_correction_x = _log_gamma_correction(x_min, self.minimax_coeff)
log_gamma_correction_y = _log_gamma_correction(y_max, self.minimax_coeff)
log_gamma_correction_x_y = _log_gamma_correction(x_plus_y, self.minimax_coeff)
# Two large arguments case: y >= x >= 8.
log_beta_two_large = self.const(0.5 * self.log_2pi, x_dtype) - 0.5 * self.log(y_max) \
+ log_gamma_correction_x + log_gamma_correction_y - log_gamma_correction_x_y \
+ (x_min - 0.5) * self.log(x_min / (x_min + y_max)) - y_max * self.log1p(x_min / y_max)
cancelled_stirling = -1 * (x_min + y_max - 0.5) * self.log1p(x_min / y_max) - x_min * self.log(y_max) + x_min
correction = log_gamma_correction_y - log_gamma_correction_x_y
log_gamma_difference_big_y = correction + cancelled_stirling
# One large argument case: x < 8, y >= 8.
log_beta_one_large = self.lgamma(x_min) + log_gamma_difference_big_y
# Small arguments case: x <= y < 8.
log_beta_small = self.lgamma(x_min) + self.lgamma(y_max) - self.lgamma(x_min + y_max)
comp_xless8 = self.less(x_min, 8)
comp_yless8 = self.less(y_max, 8)
temp = self.select(comp_yless8, log_beta_small, log_beta_one_large)
return self.select(comp_xless8, temp, log_beta_two_large)
@constexpr
def get_broadcast_matmul_shape(x_shape, y_shape, prim_name=None):
"""get broadcast_matmul shape"""
msg_prefix = f"For '{prim_name}', the" if prim_name else "The"
if (len(x_shape) < 2) or (len(y_shape) < 2):
raise ValueError(f"{msg_prefix} length of 'x_shape' and 'y_shape' must be equal to or greater than 2, "
f"but got the length of 'x_shape': {len(x_shape)} and the length of 'y_shape': "
f"{len(y_shape)}.")
x_shape_batch = x_shape[:-2]
y_shape_batch = y_shape[:-2]
if x_shape_batch == y_shape_batch:
return x_shape, y_shape
x_len = len(x_shape)
y_len = len(y_shape)
length = x_len if x_len < y_len else y_len
broadcast_shape_back = []
for i in range(-length, -2):
if x_shape[i] == 1:
broadcast_shape_back.append(y_shape[i])
elif y_shape[i] == 1:
broadcast_shape_back.append(x_shape[i])
elif x_shape[i] == y_shape[i]:
broadcast_shape_back.append(x_shape[i])
else:
raise ValueError(f"{msg_prefix} 'x_shape[{i}]' must be equal to 1, or the 'y_shape[{i}]' must be equal "
f"to 1, or the 'x_shape[{i}]' must be equal to 'y_shape[{i}]', but got "
f"'x_shape[{i}]': {x_shape[i]}, 'y_shape[{i}]': {y_shape[i]}.")
broadcast_shape_front = y_shape[0: y_len - length] if length == x_len else x_shape[0: x_len - length]
x_broadcast_shape = broadcast_shape_front + tuple(broadcast_shape_back) + x_shape[-2:]
y_broadcast_shape = broadcast_shape_front + tuple(broadcast_shape_back) + y_shape[-2:]
return x_broadcast_shape, y_broadcast_shape
@constexpr
def check_col_row_equal(x1_shape, x2_shape, transpose_x1, transpose_x2, prim_name=None):
"""check col and row equal"""
msg_prefix = f"For '{prim_name}', the" if prim_name else "The"
if len(x1_shape) == 1:
transpose_x1 = False
x1_shape = (1,) + x1_shape
if len(x2_shape) == 1:
transpose_x2 = False
x2_shape = x2_shape + (1,)
x1_last = x1_shape[-2:]
x2_last = x2_shape[-2:]
x1_col = x1_last[not transpose_x1] # x1_col = x1_last[1] if (not transpose_a) else x1_last[0]
x2_row = x2_last[transpose_x2] # x2_row = x2_last[0] if (not transpose_b) else x2_last[1]
if x1_col != x2_row:
raise ValueError(f"{msg_prefix} column of matrix dimensions of 'x1' must be equal to "
f"the row of matrix dimensions of 'x2', but got 'x1_col' {x1_col} and 'x2_row' {x2_row}.")
def matmul_op_select(x1_shape, x2_shape, transpose_x1, transpose_x2):
"""select matmul op"""
x1_dim, x2_dim = len(x1_shape), len(x2_shape)
if x1_dim == 1 and x2_dim == 1:
matmul_op = P.Mul()
elif x1_dim <= 2 and x2_dim <= 2:
transpose_x1 = False if x1_dim == 1 else transpose_x1
transpose_x2 = False if x2_dim == 1 else transpose_x2
matmul_op = P.MatMul(transpose_x1, transpose_x2)
elif x1_dim == 1 and x2_dim > 2:
matmul_op = P.BatchMatMul(False, transpose_x2)
elif x1_dim > 2 and x2_dim == 1:
matmul_op = P.BatchMatMul(transpose_x1, False)
else:
matmul_op = P.BatchMatMul(transpose_x1, transpose_x2)
return matmul_op
[docs]class MatMul(Cell):
r"""
The nn.MatMul interface is deprecated, please use the :class:`mindspore.ops.matmul` instead.
Supported Platforms:
deprecated
"""
@deprecated('1.2', 'ops.matmul', False)
def __init__(self, transpose_x1=False, transpose_x2=False):
"""Initialize MatMul."""
super(MatMul, self).__init__()
validator.check_value_type('transpose_x1', transpose_x1, [bool], self.cls_name)
validator.check_value_type('transpose_x2', transpose_x2, [bool], self.cls_name)
self.transpose_x1 = transpose_x1
self.transpose_x2 = transpose_x2
self.shape_op = P.Shape()
self.expand_op = P.ExpandDims()
self.squeeze_left_op = P.Squeeze(-2)
self.squeeze_right_op = P.Squeeze(-1)
self.reduce_sum_op = P.ReduceSum(keep_dims=False)
def construct(self, x1, x2):
x1_shape = self.shape_op(x1)
x2_shape = self.shape_op(x2)
check_col_row_equal(x1_shape, x2_shape, self.transpose_x1, self.transpose_x2, self.cls_name)
matmul_op = matmul_op_select(x1_shape, x2_shape, self.transpose_x1, self.transpose_x2)
x1_dim, x2_dim = len(x1_shape), len(x2_shape)
if x1_dim == x2_dim and x2_dim == 1:
return self.reduce_sum_op(matmul_op(x1, x2), -1)
if x1_dim == 1:
x1 = self.expand_op(x1, 0)
x1_shape = self.shape_op(x1)
if x2_dim == 1:
x2 = self.expand_op(x2, 1)
x2_shape = self.shape_op(x2)
x1_broadcast_shape, x2_broadcast_shape = get_broadcast_matmul_shape(x1_shape, x2_shape)
x1_broadcast_to = P.BroadcastTo(x1_broadcast_shape)
x2_broadcast_to = P.BroadcastTo(x2_broadcast_shape)
if x1_broadcast_shape != x1_shape:
x1 = x1_broadcast_to(x1)
if x2_broadcast_shape != x2_shape:
x2 = x2_broadcast_to(x2)
matmul_broadcast = matmul_op(x1, x2)
if x1_dim == 1:
matmul_broadcast = self.squeeze_left_op(matmul_broadcast)
if x2_dim == 1:
matmul_broadcast = self.squeeze_right_op(matmul_broadcast)
return matmul_broadcast
[docs]class Moments(Cell):
"""
Calculate the mean and variance of the input `x` along the specified `axis`.
Args:
axis (Union[int, tuple(int)]): Calculates the mean and variance along the specified axis.
When the value is None, it means to calculate the mean and variance of all values of `x`. Default: None.
keep_dims (bool): If True, the calculation result will retain the dimension of `axis`,
and the dimensions of the mean and variance are the same as the input. If False or None,
the dimension of `axis` will be reduced. Default: None.
Inputs:
- **x** (Tensor) - Tensor of any dimension used to calculate the mean and variance.
Only float16 and float32 are supported.
Outputs:
- **mean** (Tensor) - The mean value of `x` on `axis`, with the same data type as input `x`.
- **variance** (Tensor) - The variance of `x` on `axis`, with the same data type as input `x`.
Raises:
TypeError: If `axis` is not one of int, tuple, None.
TypeError: If `keep_dims` is neither bool nor None.
TypeError: If dtype of `x` is neither float16 nor float32.
Supported Platforms:
``Ascend`` ``GPU`` ``CPU``
Examples:
>>> # case1: axis = 0, keep_dims=True
>>> x = Tensor(np.array([[[1, 2], [3, 4]], [[5, 6], [7, 8]]]), mindspore.float32)
>>> net = nn.Moments(axis=0, keep_dims=True)
>>> output = net(x)
>>> print(output)
(Tensor(shape=[1, 2, 2], dtype=Float32, value=
[[[ 3.00000000e+00, 4.00000000e+00],
[ 5.00000000e+00, 6.00000000e+00]]]), Tensor(shape=[1, 2, 2], dtype=Float32, value=
[[[ 4.00000000e+00, 4.00000000e+00],
[ 4.00000000e+00, 4.00000000e+00]]]))
>>> # case2: axis = 1, keep_dims=True
>>> net = nn.Moments(axis=1, keep_dims=True)
>>> output = net(x)
>>> print(output)
(Tensor(shape=[2, 1, 2], dtype=Float32, value=
[[[ 2.00000000e+00, 3.00000000e+00]],
[[ 6.00000000e+00, 7.00000000e+00]]]), Tensor(shape=[2, 1, 2], dtype=Float32, value=
[[[ 1.00000000e+00, 1.00000000e+00]],
[[ 1.00000000e+00, 1.00000000e+00]]]))
>>> # case3: axis = 2, keep_dims=None(default)
>>> net = nn.Moments(axis=2)
>>> output = net(x)
>>> print(output)
(Tensor(shape=[2, 2], dtype=Float32, value=
[[ 1.50000000e+00, 3.50000000e+00],
[ 5.50000000e+00, 7.50000000e+00]]), Tensor(shape=[2, 2], dtype=Float32, value=
[[ 2.50000000e-01, 2.50000000e-01],
[ 2.50000000e-01, 2.50000000e-01]]))
>>> # case4: axis = None(default), keep_dims=None(default)
>>> net = nn.Moments()
>>> output = net(x)
>>> print(output)
(Tensor(shape=[], dtype=Float32, value= 4.5), Tensor(shape=[], dtype=Float32, value= 5.25))
"""
def __init__(self, axis=None, keep_dims=None):
"""Initialize Moments."""
super(Moments, self).__init__()
if axis is None:
axis = ()
if isinstance(axis, tuple):
for idx, item in enumerate(axis):
validator.check_value_type("axis[%d]" % idx, item, [int], self.cls_name)
self.axis = validator.check_value_type('axis', axis, [int, tuple], self.cls_name)
if keep_dims is None:
keep_dims = False
self.keep_dims = validator.check_value_type('keep_dims', keep_dims, [bool], self.cls_name)
self.cast = P.Cast()
self.reduce_mean = P.ReduceMean(keep_dims=True)
self.square_diff = P.SquaredDifference()
self.squeeze = P.Squeeze(self.axis)
def construct(self, x):
tensor_dtype = F.dtype(x)
_check_input_dtype("input x", tensor_dtype, [mstype.float16, mstype.float32], self.cls_name)
if tensor_dtype == mstype.float16:
x = self.cast(x, mstype.float32)
mean = self.reduce_mean(x, self.axis)
variance = self.reduce_mean(self.square_diff(x, F.stop_gradient(mean)), self.axis)
if not self.keep_dims:
mean = self.squeeze(mean)
variance = self.squeeze(variance)
if tensor_dtype == mstype.float16:
mean = self.cast(mean, mstype.float16)
variance = self.cast(variance, mstype.float16)
return mean, variance
return mean, variance
class MatInverse(Cell):
"""
Calculates the inverse of Positive-Definite Hermitian matrix using Cholesky decomposition.
Inputs:
- **x** (Tensor[Number]) - The input tensor. It must be a positive-definite matrix.
With float16 or float32 data type.
Outputs:
Tensor, has the same dtype as the `x`.
Raises:
TypeError: If dtype of `x` is neither float16 nor float32.
Supported Platforms:
``GPU``
Examples:
>>> x = Tensor(np.array([[4, 12, -16], [12, 37, -43], [-16, -43, 98]]).astype(np.float32))
>>> op = nn.MatInverse()
>>> output = op(x)
>>> print(output)
[[49.36112 -13.555558 2.1111116]
[-13.555558 3.7777784 -0.5555557]
[2.1111116 -0.5555557 0.11111113]]
"""
def __init__(self):
"""Initialize MatInverse."""
super(MatInverse, self).__init__()
self.dtype = P.DType()
self.choleskytrsm = P.CholeskyTrsm()
self.matmul = MatMul(transpose_x1=True)
def construct(self, a):
input_dtype = self.dtype(a)
_check_input_dtype("input_a", input_dtype, [mstype.float16, mstype.float32], self.cls_name)
l_inverse = self.choleskytrsm(a)
a_inverse = self.matmul(l_inverse, l_inverse)
return a_inverse
class MatDet(Cell):
"""
Calculates the determinant of Positive-Definite Hermitian matrix using Cholesky decomposition.
Inputs:
- **x** (Tensor[Number]) - The input tensor. It must be a positive-definite matrix.
With float16 or float32 data type.
Outputs:
Tensor, has the same dtype as the `x`.
Raises:
TypeError: If dtype of `x` is neither float16 nor float32.
Supported Platforms:
``GPU``
Examples:
>>> x = Tensor(np.array([[4, 12, -16], [12, 37, -43], [-16, -43, 98]]).astype(np.float32))
>>> op = nn.MatDet()
>>> output = op(x)
>>> print(output)
35.999996
"""
def __init__(self):
"""Initialize MatDet."""
super(MatDet, self).__init__()
self.dtype = P.DType()
self.cholesky = P.Cholesky()
self.det_triangle = P.DetTriangle()
self.square = P.Square()
def construct(self, a):
input_dtype = self.dtype(a)
_check_input_dtype("input_a", input_dtype, [mstype.float16, mstype.float32], self.cls_name)
l = self.cholesky(a)
l_det = self.det_triangle(l)
a_det = self.square(l_det)
return a_det