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from functools import partial
from typing import List, Optional, Tuple, Union
import torch
import torch._prims as prims
import torch._prims_common as utils
import torch._refs as refs
import torch._refs.linalg as linalg
from torch import Tensor
from torch._prims_common import (
check,
check_fp_or_complex,
check_is_matrix,
DimsType,
NumberType,
TensorLikeType,
)
from torch._prims_common.wrappers import out_wrapper
__all__ = [
"svd",
"vector_norm",
"matrix_norm",
"norm",
]
def check_norm_dtype(dtype: Optional[torch.dtype], x_dtype: torch.dtype, fn_name: str):
"""
Checks related to the dtype kwarg in `linalg.*norm` functions
"""
if dtype is not None:
check(
utils.is_float_dtype(dtype) or utils.is_complex_dtype(dtype),
lambda: f"{fn_name}: dtype should be floating point or complex. Got {dtype}",
)
check(
utils.is_complex_dtype(dtype) == utils.is_complex_dtype(x_dtype),
lambda: "{fn_name}: dtype should be {d} for {d} inputs. Got {dtype}".format(
fn_name=fn_name,
d="complex" if utils.is_complex_dtype(x_dtype) else "real",
dtype=dtype,
),
)
check(
utils.get_higher_dtype(dtype, x_dtype) == dtype,
lambda: f"{fn_name}: the dtype of the input ({x_dtype}) should be convertible "
"without narrowing to the specified dtype ({dtype})",
)
# Utilities should come BEFORE this import
from torch._decomp import register_decomposition
@register_decomposition(torch.ops.aten.linalg_vector_norm)
@out_wrapper(exact_dtype=True)
def vector_norm(
x: TensorLikeType,
ord: float = 2.0,
dim: Optional[DimsType] = None,
keepdim: bool = False,
*,
dtype: Optional[torch.dtype] = None,
) -> Tensor:
# Checks
check_fp_or_complex(x.dtype, "linalg.vector_norm")
if isinstance(dim, int):
dim = [dim] # type: ignore[assignment]
elif not isinstance(dim, List) and dim is not None:
# refs.amin just accepts List rather than DimType (Tuple)
dim = list(dim) # type: ignore[assignment]
if x.numel() == 0 and (ord < 0.0 or ord == float("inf")):
check(
dim is not None and len(dim) != 0,
lambda: f"linalg.vector_norm cannot compute the {ord} norm on an empty tensor "
"because the operation does not have an identity",
)
shape = x.shape
assert dim is not None # mypy does not seem to be able to see through check?
for d in dim:
check(
shape[d] != 0,
lambda: f"linalg.vector_norm cannot compute the {ord} norm on the "
f"dimension {d} because this dimension is empty and the "
"operation does not have an identity",
)
check_norm_dtype(dtype, x.dtype, "linalg.vector_norm")
computation_dtype, result_dtype = utils.reduction_dtypes(
x, utils.REDUCTION_OUTPUT_TYPE_KIND.COMPLEX_TO_FLOAT, dtype
)
to_result_dtype = partial(prims.convert_element_type, dtype=result_dtype)
# Implementation
if ord == 0.0:
return refs.sum(refs.ne(x, 0.0), dim=dim, keepdim=keepdim, dtype=result_dtype)
elif ord == float("inf"):
return to_result_dtype(refs.amax(torch.abs(x), dim=dim, keepdim=keepdim))
elif ord == float("-inf"):
return to_result_dtype(refs.amin(torch.abs(x), dim=dim, keepdim=keepdim))
else:
# From here on the computation dtype is important as the reduction is non-trivial
x = prims.convert_element_type(x, computation_dtype)
reduce_sum = partial(refs.sum, dim=dim, keepdim=keepdim)
if not (ord % 2.0 == 0.0 and utils.is_float_dtype(x.dtype)):
x = torch.abs(x)
return to_result_dtype(torch.pow(reduce_sum(torch.pow(x, ord)), 1.0 / ord))
def backshift_permutation(dim0, dim1, ndim):
# Auxiliary function for matrix_norm
# Computes the permutation that moves the two given dimensions to the back
ret = [i for i in range(ndim) if i != dim0 and i != dim1]
ret.extend((dim0, dim1))
return ret
def inverse_permutation(perm):
# Given a permutation, returns its inverse. It's equivalent to argsort on an array
return [i for i, j in sorted(enumerate(perm), key=lambda i_j: i_j[1])]
# CompositeImplicitAutograd
@out_wrapper(exact_dtype=True)
def matrix_norm(
A: TensorLikeType,
ord: Union[float, str] = "fro",
dim: DimsType = (-2, -1),
keepdim: bool = False,
*,
dtype: Optional[torch.dtype] = None,
) -> TensorLikeType:
# shape
check_is_matrix(A, "linalg.matrix_norm")
# dim
dim = utils.canonicalize_dims(A.ndim, dim)
if isinstance(dim, int):
dim = (dim,) # type: ignore[assignment]
check(len(dim) == 2, lambda: "linalg.matrix_norm: dim must be a 2-tuple. Got {dim}")
check(
dim[0] != dim[1],
lambda: "linalg.matrix_norm: dims must be different. Got ({dim[0]}, {dim[1]})",
)
# dtype arg
check_norm_dtype(dtype, A.dtype, "linalg.matrix_norm")
if isinstance(ord, str):
# ord
check(
ord in ("fro", "nuc"),
lambda: "linalg.matrix_norm: Order {ord} not supported.",
)
# dtype
check_fp_or_complex(
A.dtype, "linalg.matrix_norm", allow_low_precision_dtypes=ord != "nuc"
)
if ord == "fro":
return vector_norm(A, 2, dim, keepdim, dtype=dtype)
else: # ord == "nuc"
if dtype is not None:
A = prims.convert_element_type(A, dtype)
perm = backshift_permutation(dim[0], dim[1], A.ndim)
result = torch.sum(svdvals(prims.transpose(A, perm)), -1, keepdim)
if keepdim:
inv_perm = inverse_permutation(perm)
result = prims.transpose(torch.unsqueeze(result, -1), inv_perm)
return result
else:
# ord
abs_ord = abs(ord)
check(
abs_ord in (2, 1, float("inf")),
lambda: "linalg.matrix_norm: Order {ord} not supported.",
)
# dtype
check_fp_or_complex(
A.dtype, "linalg.matrix_norm", allow_low_precision_dtypes=ord != 2
)
max_min = partial(torch.amax if ord > 0.0 else torch.amin, keepdim=keepdim)
if abs_ord == 2.0:
if dtype is not None:
A = prims.convert_element_type(A, dtype)
perm = backshift_permutation(dim[0], dim[1], A.ndim)
result = max_min(svdvals(prims.transpose(A, perm)), dim=-1)
if keepdim:
inv_perm = inverse_permutation(perm)
result = prims.transpose(torch.unsqueeze(result, -1), inv_perm)
return result
else: # 1, -1, inf, -inf
dim0, dim1 = dim
if abs_ord == float("inf"):
dim0, dim1 = dim1, dim0
if not keepdim and (dim0 < dim1):
dim1 -= 1
return max_min(
vector_norm(A, 1.0, dim=dim0, keepdim=keepdim, dtype=dtype), dim1
)
# CompositeImplicitAutograd
@out_wrapper(exact_dtype=True)
def norm(
A: TensorLikeType,
ord: Optional[Union[float, str]] = None,
dim: Optional[DimsType] = None,
keepdim: bool = False,
*,
dtype: Optional[torch.dtype] = None,
) -> TensorLikeType:
if dim is not None:
if isinstance(dim, int):
dim = (dim,) # type: ignore[assignment]
check(
len(dim) in (1, 2),
lambda: "linalg.norm: If dim is specified, it must be of length 1 or 2. Got {dim}",
)
elif ord is not None:
check(
A.ndim in (1, 2),
lambda: "linalg.norm: If dim is not specified but ord is, the input must be 1D or 2D. Got {A.ndim}D",
)
if ord is not None and (
(dim is not None and len(dim) == 2) or (dim is None and A.ndim == 2)
):
if dim is None:
dim = (0, 1)
return matrix_norm(A, ord, dim, keepdim, dtype=dtype)
else:
if ord is None:
ord = 2.0
return vector_norm(A, ord, dim, keepdim, dtype=dtype)
# CompositeImplicitAutograd
@out_wrapper("U", "S", "Vh", exact_dtype=True)
def svd(A: TensorLikeType, full_matrices: bool = True) -> Tuple[Tensor, Tensor, Tensor]:
return prims.svd(A, full_matrices=full_matrices)
# CompositeImplicitAutograd
@out_wrapper(exact_dtype=True)
def svdvals(A: TensorLikeType) -> Tensor:
return svd(A, full_matrices=False)[1]
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