# 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()
def construct(self, x):
exp = self.exp(x)
sumexp = self.sum(exp, self.axis)
logsumexp = self.log(sumexp)
return logsumexp
[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("The input of `delta` can not be equal to 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
[docs]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,
-reflection_denom)
result = self.select(need_to_reflect, reflection, log_y)
return self.select(self.isfinite(x), result, infinity)
[docs]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
[docs]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
[docs]class LBeta(Cell):
r"""
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. 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.
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):
"""get broadcast_matmul shape"""
if (len(x_shape) < 2) or (len(y_shape) < 2):
raise ValueError('For matmul, rank of x1 and x2 should be equal to or greater than 2, '
+ f'but got {x_shape} and {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"For MatMul, the x1_shape {x_shape} and x2_shape {y_shape} can not broadcast.")
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):
"""check col and row equal"""
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('The column of matrix dimensions of x1 should be equal to '
+ f'the row of matrix dimensions of x2, but got {x1_col} and {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"""
Multiplies matrix `x1` by matrix `x2`.
nn.MatMul will be deprecated in future versions. Please use ops.matmul instead.
- If both `x1` and `x2` are 1-dimensional, the dot product is returned.
- If the dimensions of `x1` and `x2` are all not greater than 2, the matrix-matrix product will
be returned. Note if one of 'x1' and 'x2' is 1-dimensional, the argument will first be
expanded to 2 dimension. After the matrix multiply, the expanded dimension will be removed.
- If at least one of `x1` and `x2` is N-dimensional (N>2), the none-matrix dimensions(batch) of inputs
will be broadcasted and must be broadcastable. Note if one of 'x1' and 'x2' is 1-dimensional,
the argument will first be expanded to 2 dimension and then the none-matrix dimensions will be broadcasted.
after the matrix multiply, the expanded dimension will be removed. For example,
if `x1` is a :math:`(j \times 1 \times n \times m)` tensor and
`x2` is b :math:`(k \times m \times p)` tensor, the output will be a :math:`(j \times k \times n \times p)`
tensor.
Args:
transpose_x1 (bool): If true, `a` is transposed before multiplication. Default: False.
transpose_x2 (bool): If true, `b` is transposed before multiplication. Default: False.
Inputs:
- **x1** (Tensor) - The first tensor to be multiplied.
- **x2** (Tensor) - The second tensor to be multiplied.
Outputs:
Tensor, the shape of the output tensor depends on the dimension of input tensors.
Raises:
TypeError: If `transpose_x1` or `transpose_x2` is not a bool.
ValueError: If the column of matrix dimensions of `x1` is not equal to
the row of matrix dimensions of `x2`.
Supported Platforms:
``Ascend`` ``GPU`` ``CPU``
Examples:
>>> net = nn.MatMul()
>>> x1 = Tensor(np.ones(shape=[3, 2, 3]), mindspore.float32)
>>> x2 = Tensor(np.ones(shape=[3, 4]), mindspore.float32)
>>> output = net(x1, x2)
>>> print(output.shape)
(3, 2, 4)
"""
@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)
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):
"""
Calculates the mean and variance of `x`.
Args:
axis (Union[int, tuple(int)]): Calculates the mean and variance along the specified axis. Default: None.
keep_dims (bool): If true, The dimension of mean and variance are identical with input's.
If false, don't keep these dimensions. Default: None.
Inputs:
- **x** (Tensor) - The tensor to be calculated. Only float16 and float32 are supported.
:math:`(N,*)` where :math:`*` means,any number of additional dimensions.
Outputs:
- **mean** (Tensor) - The mean of `x`, with the same date type as input `x`.
- **variance** (Tensor) - The variance of `x`, with the same date 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:
>>> x = Tensor(np.array([[[[1, 2, 3, 4], [3, 4, 5, 6]]]]), mindspore.float32)
>>> net = nn.Moments(axis=0, keep_dims=True)
>>> output = net(x)
>>> print(output)
(Tensor(shape=[1, 1, 2, 4], dtype=Float32, value=
[[[[ 1.00000000e+00, 2.00000000e+00, 3.00000000e+00, 4.00000000e+00],
[ 3.00000000e+00, 4.00000000e+00, 5.00000000e+00, 6.00000000e+00]]]]),
Tensor(shape=[1, 1, 2, 4], dtype=Float32, value=
[[[[ 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00],
[ 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00]]]]))
>>> net = nn.Moments(axis=1, keep_dims=True)
>>> output = net(x)
>>> print(output)
(Tensor(shape=[1, 1, 2, 4], dtype=Float32, value=
[[[[ 1.00000000e+00, 2.00000000e+00, 3.00000000e+00, 4.00000000e+00],
[ 3.00000000e+00, 4.00000000e+00, 5.00000000e+00, 6.00000000e+00]]]]),
Tensor(shape=[1, 1, 2, 4], dtype=Float32, value=
[[[[ 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00],
[ 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00]]]]))
>>> net = nn.Moments(axis=2, keep_dims=True)
>>> output = net(x)
>>> print(output)
(Tensor(shape=[1, 1, 1, 4], dtype=Float32, value=
[[[[ 2.00000000e+00, 3.00000000e+00, 4.00000000e+00, 5.00000000e+00]]]]),
Tensor(shape=[1, 1, 1, 4], dtype=Float32, value=
[[[[ 1.00000000e+00, 1.00000000e+00, 1.00000000e+00, 1.00000000e+00]]]]))
>>> net = nn.Moments(axis=3, keep_dims=True)
>>> output = net(x)
>>> print(output)
(Tensor(shape=[1, 1, 2, 1], dtype=Float32, value=
[[[[ 2.50000000e+00],
[ 4.50000000e+00]]]]), Tensor(shape=[1, 1, 2, 1], dtype=Float32, value=
[[[[ 1.25000000e+00],
[ 1.25000000e+00]]]]))
"""
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
[docs]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 0.11111111]]
"""
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
[docs]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