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作为一个张量计算库,算数操作是最基本的修养。PyTorch
中有一百来个算数操作算子。
PyTorch
中,Tensor 的逐元素操作可分为函数式操作和原位操作,在函数名中用 _
后缀区分了二者,比如 tensor.abs()
是一个函数式操作,不改变 tensor
而将改变体现在返回值中,而 tensor.abs_()
是一个原位操作,既修改了原 tensor
又将这个修改后的值返回。
这里的操作都是逐元素进行的,元素之间没有关联。基本上每个 API 都有函数式和原位两个版本,也有作为 torch
模块的函数的过程化编程和作为 Tensor
的方法的面向对象式编程,其实面向过程和面向对象的唯一区别是第一个参数。每个算子一共有至少三种写法。
算子名 | 说明 |
---|---|
abs | 计算 input 中每个元素的绝对值. |
absolute | Alias for torch.abs() |
acos | inverse cosine 大家熟悉的 arccos input . |
arccos | Alias for torch.acos() . |
acosh | inverse hyperbolic cosine of input . |
arccosh | Alias for torch.acosh() . |
add | Adds other , scaled by alpha , to input . |
addcdiv | Performs the element-wise division of tensor1 by tensor2 , multiply the result by the scalar value and add it to input . |
addcmul | Performs the element-wise multiplication of tensor1 by tensor2 , multiply the result by the scalar value and add it to input . |
angle | Computes the element-wise angle (in radians) of the given input tensor. |
asin | Returns a new tensor with the arcsine of the elements of input . |
arcsin | Alias for torch.asin() . |
asinh | Returns a new tensor with the inverse hyperbolic sine of the elements of input . |
arcsinh | Alias for torch.asinh() . |
atan | Returns a new tensor with the arctangent of the elements of input . |
arctan | Alias for torch.atan() . |
atanh | Returns a new tensor with the inverse hyperbolic tangent of the elements of input . |
arctanh | Alias for torch.atanh() . |
atan2 | Element-wise arctangent of \text{input}{i} / \text{other}{i}inputi/otheri with consideration of the quadrant. |
arctan2 | Alias for torch.atan2() . |
bitwise_not | Computes the bitwise NOT of the given input tensor. |
bitwise_and | Computes the bitwise AND of input and other . |
bitwise_or | Computes the bitwise OR of input and other . |
bitwise_xor | Computes the bitwise XOR of input and other . |
bitwise_left_shift | Computes the left arithmetic shift of input by other bits. |
bitwise_right_shift | Computes the right arithmetic shift of input by other bits. |
ceil | Returns a new tensor with the ceil of the elements of input , the smallest integer greater than or equal to each element. |
clamp | Clamps all elements in input into the range [ min , max ]. |
clip | Alias for torch.clamp() . |
conj_physical | Computes the element-wise conjugate of the given input tensor. |
copysign | Create a new floating-point tensor with the magnitude of input and the sign of other , elementwise. |
cos | Returns a new tensor with the cosine of the elements of input . |
cosh | Returns a new tensor with the hyperbolic cosine of the elements of input . |
deg2rad | Returns a new tensor with each of the elements of input converted from angles in degrees to radians. |
div | Divides each element of the input input by the corresponding element of other . |
divide | Alias for torch.div() . |
digamma | Alias for torch.special.digamma() . |
erf | Alias for torch.special.erf() . |
erfc | Alias for torch.special.erfc() . |
erfinv | Alias for torch.special.erfinv() . |
exp | Returns a new tensor with the exponential of the elements of the input tensor input . |
exp2 | Alias for torch.special.exp2() . |
expm1 | Alias for torch.special.expm1() . |
fake_quantize_per_channel_affine | Returns a new tensor with the data in input fake quantized per channel using scale , zero_point , quant_min and quant_max , across the channel specified by axis . |
fake_quantize_per_tensor_affine | Returns a new tensor with the data in input fake quantized using scale , zero_point , quant_min and quant_max . |
fix | Alias for torch.trunc() |
float_power | Raises input to the power of exponent , elementwise, in double precision. |
floor | Returns a new tensor with the floor of the elements of input , the largest integer less than or equal to each element. |
floor_divide | |
fmod | Applies C++’s std::fmod entrywise. |
frac | Computes the fractional portion of each element in input . |
frexp | Decomposes input into mantissa and exponent tensors such that
input
=
mantissa
×
2
exponent
\text{input} = \text{mantissa} \times 2^{\text{exponent}}
input=mantissa×2exponent. |
gradient | Estimates the gradient of a function g : R n → R g : \mathbb{R}^n \rightarrow \mathbb{R} g:Rn→R in one or more dimensions using the second-order accurate central differences method. |
imag | Returns a new tensor containing imaginary values of the self tensor. |
ldexp | Multiplies input by
2
other
2^\text{other}
2other. |
lerp | Does a linear interpolation of two tensors start (given by input ) and end based on a scalar or tensor weight and returns the resulting out tensor. |
lgamma | Computes the natural logarithm of the absolute value of the gamma function on input . |
log | Returns a new tensor with the natural logarithm of the elements of input . |
log10 | Returns a new tensor with the logarithm to the base 10 of the elements of input . |
log1p | Returns a new tensor with the natural logarithm of (1 + input ). |
log2 | Returns a new tensor with the logarithm to the base 2 of the elements of input . |
logaddexp | Logarithm of the sum of exponentiations of the inputs. |
logaddexp2 | Logarithm of the sum of exponentiations of the inputs in base-2. |
logical_and | Computes the element-wise logical AND of the given input tensors. |
logical_not | Computes the element-wise logical NOT of the given input tensor. |
logical_or | Computes the element-wise logical OR of the given input tensors. |
logical_xor | Computes the element-wise logical XOR of the given input tensors. |
logit | Alias for torch.special.logit() . |
hypot | Given the legs of a right triangle, return its hypotenuse. |
i0 | Alias for torch.special.i0() . |
igamma | Alias for torch.special.gammainc() . |
igammac | Alias for torch.special.gammaincc() . |
mul | Multiplies input by other . |
multiply | Alias for torch.mul() . |
mvlgamma | Alias for torch.special.multigammaln() . |
nan_to_num | Replaces NaN , positive infinity, and negative infinity values in input with the values specified by nan , posinf , and neginf , respectively. |
neg | Returns a new tensor with the negative of the elements of input . |
negative | Alias for torch.neg() |
nextafter | Return the next floating-point value after input towards other , elementwise. |
polygamma | Alias for torch.special.polygamma() . |
positive | Returns input . |
pow | Takes the power of each element in input with exponent and returns a tensor with the result. |
quantized_batch_norm | Applies batch normalization on a 4D (NCHW) quantized tensor. |
quantized_max_pool1d | Applies a 1D max pooling over an input quantized tensor composed of several input planes. |
quantized_max_pool2d | Applies a 2D max pooling over an input quantized tensor composed of several input planes. |
rad2deg | Returns a new tensor with each of the elements of input converted from angles in radians to degrees. |
real | Returns a new tensor containing real values of the self tensor. |
reciprocal | Returns a new tensor with the reciprocal of the elements of input |
remainder | Computes Python’s modulus operation entrywise. |
round | Rounds elements of input to the nearest integer. |
rsqrt | Returns a new tensor with the reciprocal of the square-root of each of the elements of input . |
sigmoid | Alias for torch.special.expit() . |
sign | Returns a new tensor with the signs of the elements of input . |
sgn | This function is an extension of torch.sign() to complex tensors. |
signbit | Tests if each element of input has its sign bit set (is less than zero) or not. |
sin | Returns a new tensor with the sine of the elements of input . |
sinc | Alias for torch.special.sinc() . |
sinh | Returns a new tensor with the hyperbolic sine of the elements of input . |
sqrt | Returns a new tensor with the square-root of the elements of input . |
square | Returns a new tensor with the square of the elements of input . |
sub | Subtracts other , scaled by alpha , from input . |
subtract | Alias for torch.sub() . |
tan | Returns a new tensor with the tangent of the elements of input . |
tanh | Returns a new tensor with the hyperbolic tangent of the elements of input . |
true_divide | Alias for torch.div() with rounding_mode=None . |
trunc | Returns a new tensor with the truncated integer values of the elements of input . |
xlogy | Alias for torch.special.xlogy() . |
除了上述函数,PyTorch
还为我们重载了 Tensor
的很多运算符,这些运算符都符合 Python 的语义。PyTorch
的开发者为了 be Pythonic 还是费了相当大心思的,这也是 PyTorch 能很好融入 Python 生态的原因。
运算符 | 说明 |
---|---|
+ | add |
- | sub |
* | mul |
/ | div |
// | truediv |
@ | matmul |
规约是函数式编程中的重要概念。
算子名 | 说明 |
---|---|
argmax | Returns the indices of the maximum value of all elements in the input tensor. |
argmin | Returns the indices of the minimum value(s) of the flattened tensor or along a dimension |
amax | Returns the maximum value of each slice of the input tensor in the given dimension(s) dim . |
amin | Returns the minimum value of each slice of the input tensor in the given dimension(s) dim . |
aminmax | Computes the minimum and maximum values of the input tensor. |
all | Tests if all elements in input evaluate to True. |
any | Tests if any element in input evaluates to True. |
max | Returns the maximum value of all elements in the input tensor. |
min | Returns the minimum value of all elements in the input tensor. |
dist | Returns the p-norm of (input - other ) |
logsumexp | Returns the log of summed exponentials of each row of the input tensor in the given dimension dim . |
mean | Returns the mean value of all elements in the input tensor. |
nanmean | Computes the mean of all non-NaN elements along the specified dimensions. |
median | Returns the median of the values in input . |
nanmedian | Returns the median of the values in input , ignoring NaN values. |
mode | Returns a namedtuple (values, indices) where values is the mode value of each row of the input tensor in the given dimension dim , i.e. a value which appears most often in that row, and indices is the index location of each mode value found. |
norm | Returns the matrix norm or vector norm of a given tensor. |
nansum | Returns the sum of all elements, treating Not a Numbers (NaNs) as zero. |
prod | Returns the product of all elements in the input tensor. |
quantile | Computes the q-th quantiles of each row of the input tensor along the dimension dim . |
nanquantile | This is a variant of torch.quantile() that “ignores” NaN values, computing the quantiles q as if NaN values in input did not exist. |
std | If unbiased is True , Bessel’s correction will be used. |
std_mean | If unbiased is True , Bessel’s correction will be used to calculate the standard deviation. |
sum | Returns the sum of all elements in the input tensor. |
unique | Returns the unique elements of the input tensor. |
unique_consecutive | Eliminates all but the first element from every consecutive group of equivalent elements. |
var | If unbiased is True , Bessel’s correction will be used. |
var_mean | If unbiased is True , Bessel’s correction will be used to calculate the variance. |
count_nonzero | Counts the number of non-zero values in the tensor input along the given dim . |
allclose | This function checks if all input and other satisfy the condition: |
---|---|
argsort | Returns the indices that sort a tensor along a given dimension in ascending order by value. |
eq | Computes element-wise equality |
equal | True if two tensors have the same size and elements, False otherwise. |
ge | Computes \text{input} \geq \text{other}input≥other element-wise. |
greater_equal | Alias for torch.ge() . |
gt | Computes \text{input} > \text{other}input>other element-wise. |
greater | Alias for torch.gt() . |
isclose | Returns a new tensor with boolean elements representing if each element of input is “close” to the corresponding element of other . |
isfinite | Returns a new tensor with boolean elements representing if each element is finite or not. |
isin | Tests if each element of elements is in test_elements . |
isinf | Tests if each element of input is infinite (positive or negative infinity) or not. |
isposinf | Tests if each element of input is positive infinity or not. |
isneginf | Tests if each element of input is negative infinity or not. |
isnan | Returns a new tensor with boolean elements representing if each element of input is NaN or not. |
isreal | Returns a new tensor with boolean elements representing if each element of input is real-valued or not. |
kthvalue | Returns a namedtuple (values, indices) where values is the k th smallest element of each row of the input tensor in the given dimension dim . |
le | Computes \text{input} \leq \text{other}input≤other element-wise. |
less_equal | Alias for torch.le() . |
lt | Computes \text{input} < \text{other}input<other element-wise. |
less | Alias for torch.lt() . |
maximum | Computes the element-wise maximum of input and other . |
minimum | Computes the element-wise minimum of input and other . |
fmax | Computes the element-wise maximum of input and other . |
fmin | Computes the element-wise minimum of input and other . |
ne | Computes \text{input} \neq \text{other}input=other element-wise. |
not_equal | Alias for torch.ne() . |
sort | Sorts the elements of the input tensor along a given dimension in ascending order by value. |
topk | Returns the k largest elements of the given input tensor along a given dimension. |
msort | Sorts the elements of the input tensor along its first dimension in ascending order by value. |
stft | Short-time Fourier transform (STFT). |
---|---|
istft | Inverse short time Fourier Transform. |
bartlett_window | Bartlett window function. |
blackman_window | Blackman window function. |
hamming_window | Hamming window function. |
hann_window | Hann window function. |
kaiser_window | Computes the Kaiser window with window length window_length and shape parameter beta . |
atleast_1d | Returns a 1-dimensional view of each input tensor with zero dimensions. |
---|---|
atleast_2d | Returns a 2-dimensional view of each input tensor with zero dimensions. |
atleast_3d | Returns a 3-dimensional view of each input tensor with zero dimensions. |
bincount | Count the frequency of each value in an array of non-negative ints. |
block_diag | Create a block diagonal matrix from provided tensors. |
broadcast_tensors | Broadcasts the given tensors according to Broadcasting semantics. |
broadcast_to | Broadcasts input to the shape shape . |
broadcast_shapes | Similar to broadcast_tensors() but for shapes. |
bucketize | Returns the indices of the buckets to which each value in the input belongs, where the boundaries of the buckets are set by boundaries . |
cartesian_prod | Do cartesian product of the given sequence of tensors. |
cdist | Computes batched the p-norm distance between each pair of the two collections of row vectors. |
clone | Returns a copy of input . |
combinations | Compute combinations of length rr of the given tensor. |
corrcoef | Estimates the Pearson product-moment correlation coefficient matrix of the variables given by the input matrix, where rows are the variables and columns are the observations. |
cov | Estimates the covariance matrix of the variables given by the input matrix, where rows are the variables and columns are the observations. |
cross | Returns the cross product of vectors in dimension dim of input and other . |
cummax | Returns a namedtuple (values, indices) where values is the cumulative maximum of elements of input in the dimension dim . |
cummin | Returns a namedtuple (values, indices) where values is the cumulative minimum of elements of input in the dimension dim . |
cumprod | Returns the cumulative product of elements of input in the dimension dim . |
cumsum | Returns the cumulative sum of elements of input in the dimension dim . |
diag | If input is a vector (1-D tensor), then returns a 2-D square tensor |
diag_embed | Creates a tensor whose diagonals of certain 2D planes (specified by dim1 and dim2 ) are filled by input . |
diagflat | If input is a vector (1-D tensor), then returns a 2-D square tensor |
diagonal | Returns a partial view of input with the its diagonal elements with respect to dim1 and dim2 appended as a dimension at the end of the shape. |
diff | Computes the n-th forward difference along the given dimension. |
einsum | Sums the product of the elements of the input operands along dimensions specified using a notation based on the Einstein summation convention. |
flatten | Flattens input by reshaping it into a one-dimensional tensor. |
flip | Reverse the order of a n-D tensor along given axis in dims. |
fliplr | Flip tensor in the left/right direction, returning a new tensor. |
flipud | Flip tensor in the up/down direction, returning a new tensor. |
kron | Computes the Kronecker product, denoted by \otimes⊗, of input and other . |
rot90 | Rotate a n-D tensor by 90 degrees in the plane specified by dims axis. |
gcd | Computes the element-wise greatest common divisor (GCD) of input and other . |
histc | Computes the histogram of a tensor. |
histogram | Computes a histogram of the values in a tensor. |
histogramdd | Computes a multi-dimensional histogram of the values in a tensor. |
meshgrid | Creates grids of coordinates specified by the 1D inputs in attr:tensors. |
lcm | Computes the element-wise least common multiple (LCM) of input and other . |
logcumsumexp | Returns the logarithm of the cumulative summation of the exponentiation of elements of input in the dimension dim . |
ravel | Return a contiguous flattened tensor. |
renorm | Returns a tensor where each sub-tensor of input along dimension dim is normalized such that the p-norm of the sub-tensor is lower than the value maxnorm |
repeat_interleave | Repeat elements of a tensor. |
roll | Roll the tensor input along the given dimension(s). |
searchsorted | Find the indices from the innermost dimension of sorted_sequence such that, if the corresponding values in values were inserted before the indices, when sorted, the order of the corresponding innermost dimension within sorted_sequence would be preserved. |
tensordot | Returns a contraction of a and b over multiple dimensions. |
trace | Returns the sum of the elements of the diagonal of the input 2-D matrix. |
tril | Returns the lower triangular part of the matrix (2-D tensor) or batch of matrices input , the other elements of the result tensor out are set to 0. |
tril_indices | Returns the indices of the lower triangular part of a row -by- col matrix in a 2-by-N Tensor, where the first row contains row coordinates of all indices and the second row contains column coordinates. |
triu | Returns the upper triangular part of a matrix (2-D tensor) or batch of matrices input , the other elements of the result tensor out are set to 0. |
triu_indices | Returns the indices of the upper triangular part of a row by col matrix in a 2-by-N Tensor, where the first row contains row coordinates of all indices and the second row contains column coordinates. |
vander | Generates a Vandermonde matrix. |
view_as_real | Returns a view of input as a real tensor. |
view_as_complex | Returns a view of input as a complex tensor. |
resolve_conj | Returns a new tensor with materialized conjugation if input ’s conjugate bit is set to True, else returns input . |
resolve_neg | Returns a new tensor with materialized negation if input ’s negative bit is set to True, else returns input . |
addbmm | Performs a batch matrix-matrix product of matrices stored in batch1 and batch2 , with a reduced add step (all matrix multiplications get accumulated along the first dimension). |
---|---|
addmm | Performs a matrix multiplication of the matrices mat1 and mat2 . |
addmv | Performs a matrix-vector product of the matrix mat and the vector vec . |
addr | Performs the outer-product of vectors vec1 and vec2 and adds it to the matrix input . |
baddbmm | Performs a batch matrix-matrix product of matrices in batch1 and batch2 . |
bmm | Performs a batch matrix-matrix product of matrices stored in input and mat2 . |
chain_matmul | Returns the matrix product of the NN 2-D tensors. |
cholesky | Computes the Cholesky decomposition of a symmetric positive-definite matrix AA or for batches of symmetric positive-definite matrices. |
cholesky_inverse | Computes the inverse of a symmetric positive-definite matrix AA using its Cholesky factor uu: returns matrix inv . |
cholesky_solve | Solves a linear system of equations with a positive semidefinite matrix to be inverted given its Cholesky factor matrix uu. |
dot | Computes the dot product of two 1D tensors. |
eig | Computes the eigenvalues and eigenvectors of a real square matrix. |
geqrf | This is a low-level function for calling LAPACK’s geqrf directly. |
ger | Alias of torch.outer() . |
inner | Computes the dot product for 1D tensors. |
inverse | Alias for torch.linalg.inv() |
det | Alias for torch.linalg.det() |
logdet | Calculates log determinant of a square matrix or batches of square matrices. |
slogdet | Alias for torch.linalg.slogdet() |
lstsq | Computes the solution to the least squares and least norm problems for a full rank matrix AA of size (m \times n)(m×n) and a matrix BB of size (m \times k)(m×k). |
lu | Computes the LU factorization of a matrix or batches of matrices A . |
lu_solve | Returns the LU solve of the linear system Ax = bA**x=b using the partially pivoted LU factorization of A from torch.lu() . |
lu_unpack | Unpacks the data and pivots from a LU factorization of a tensor into tensors L and U and a permutation tensor P such that LU_data, LU_pivots = (P @ L @ U).lu() . |
matmul | Matrix product of two tensors. |
matrix_power | Alias for torch.linalg.matrix_power() |
matrix_rank | Returns the numerical rank of a 2-D tensor. |
matrix_exp | Alias for torch.linalg.matrix_exp() . |
mm | Performs a matrix multiplication of the matrices input and mat2 . |
mv | Performs a matrix-vector product of the matrix input and the vector vec . |
orgqr | Alias for torch.linalg.householder_product() . |
ormqr | Computes the matrix-matrix multiplication of a product of Householder matrices with a general matrix. |
outer | Outer product of input and vec2 . |
pinverse | Alias for torch.linalg.pinv() |
qr | Computes the QR decomposition of a matrix or a batch of matrices input , and returns a namedtuple (Q, R) of tensors such that \text{input} = Q Rinput=QR with QQ being an orthogonal matrix or batch of orthogonal matrices and RR being an upper triangular matrix or batch of upper triangular matrices. |
svd | Computes the singular value decomposition of either a matrix or batch of matrices input . |
svd_lowrank | Return the singular value decomposition (U, S, V) of a matrix, batches of matrices, or a sparse matrix AA such that A \approx U diag(S) V^TA≈Udia**g(S)V**T. |
pca_lowrank | Performs linear Principal Component Analysis (PCA) on a low-rank matrix, batches of such matrices, or sparse matrix. |
symeig | This function returns eigenvalues and eigenvectors of a real symmetric or complex Hermitian matrix input or a batch thereof, represented by a namedtuple (eigenvalues, eigenvectors). |
lobpcg | Find the k largest (or smallest) eigenvalues and the corresponding eigenvectors of a symmetric positive definite generalized eigenvalue problem using matrix-free LOBPCG methods. |
trapz | Alias for torch.trapezoid() . |
trapezoid | Computes the trapezoidal rule along dim . |
cumulative_trapezoid | Cumulatively computes the trapezoidal rule along dim . |
triangular_solve | Solves a system of equations with a square upper or lower triangular invertible matrix AA and multiple right-hand sides bb. |
vdot | Computes the dot product of two 1D tensors. |
compiled_with_cxx11_abi | Returns whether PyTorch was built with _GLIBCXX_USE_CXX11_ABI=1 |
---|---|
result_type | Returns the torch.dtype that would result from performing an arithmetic operation on the provided input tensors. |
can_cast | Determines if a type conversion is allowed under PyTorch casting rules described in the type promotion documentation. |
promote_types | Returns the torch.dtype with the smallest size and scalar kind that is not smaller nor of lower kind than either type1 or type2. |
use_deterministic_algorithms | Sets whether PyTorch operations must use “deterministic” algorithms. |
are_deterministic_algorithms_enabled | Returns True if the global deterministic flag is turned on. |
is_deterministic_algorithms_warn_only_enabled | Returns True if the global deterministic flag is set to warn only. |
set_deterministic_debug_mode | Sets the debug mode for deterministic operations. |
get_deterministic_debug_mode | Returns the current value of the debug mode for deterministic operations. |
set_float32_matmul_precision | Sets the internal precision of float32 matrix multiplications. |
get_float32_matmul_precision | Returns the current value of float32 matrix multiplication precision. |
set_warn_always | When this flag is False (default) then some PyTorch warnings may only appear once per process. |
is_warn_always_enabled | Returns True if the global warn_always flag is turned on. |
_assert | A wrapper around Python’s assert which is symbolically traceable. |
PyTorch
的算子大多为异步惰性求值,尤其是 GPU 版本。
算子只定义了入口,真正的实现依赖于不同的后端,常用的有 cpu
、cuda
、mkldnn
、npu
等等。
知道这些的意义是,不用管这些,爱怎么编程就怎么编就可以了,PyTorch
引擎会帮你搞定一切的。
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