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LinearAlgebra.cpp
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LinearAlgebra.cpp
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#include <ATen/ATen.h>
#include <ATen/ExpandUtils.h>
#include <ATen/Dispatch.h>
#include <ATen/NativeFunctions.h>
#include <ATen/native/CPUBlas.h>
#include <ATen/native/LinearAlgebraUtils.h>
#include <ATen/native/ReduceOpsUtils.h>
#include <ATen/native/Resize.h>
#include <ATen/native/TensorIterator.h>
#include <ATen/native/LinearAlgebra.h>
#include <ATen/native/IndexingUtils.h>
#include <ATen/TensorUtils.h>
#include <ATen/Parallel.h>
#include <ATen/LegacyTHFunctionsCPU.h>
#include <ATen/core/grad_mode.h>
#include <functional>
#include <numeric>
#include <vector>
#include <limits>
#include <ATen/NamedTensorUtils.h>
#include <c10/util/variant.h>
namespace at {
namespace native {
DEFINE_DISPATCH(addr_stub);
// Helper function for det methods.
// For pivoted LU factorization A = P * L * U. Since we always have det(L) = 1,
// det(P) = \pm 1, this method returns a 3-tuple:
// (det(P), diag(U), info),
// where info helps us identify singular matrices.
static inline std::tuple<Tensor, Tensor> _lu_det_P_diag_U(const Tensor& self) {
Tensor pivs, lu, infos;
std::tie(lu, pivs, infos) = at::_lu_with_info(self, /*pivot=*/true, /*check_errors=*/false);
TORCH_CHECK(infos.ge(0).all().item<uint8_t>(), "Invalid argument passed to lu");
auto n = self.size(-1);
auto num_exchanges = (at::arange(1, n + 1, pivs.options()) != pivs)
.sum(-1, /*keepdim=*/false, /*dtype=*/at::kLong).fmod_(2);
auto u_diagonal = lu.diagonal(/*offset=*/0, /*dim1=*/-2, /*dim2=*/-1);
return std::tuple<Tensor, Tensor>(num_exchanges.mul_(-2).add_(1), u_diagonal);
}
// torch.linalg.det, alias for torch.det
Tensor linalg_det(const Tensor& self) {
return self.det();
}
Tensor det(const Tensor& self) {
squareCheckInputs(self);
TORCH_CHECK((at::isFloatingType(self.scalar_type()) || at::isComplexType(self.scalar_type())),
"Expected a floating point tensor as input");
Tensor det_P, diag_U;
std::tie(det_P, diag_U) = _lu_det_P_diag_U(self);
// complete_det is 0 when U is singular (U(i, i) = 0 for some i in [1, self.size(-1)]).
// The product accumulation takes care of this case, and hence no special case handling is required.
auto complete_det = diag_U.prod(-1).mul_(det_P);
return complete_det;
}
Tensor logdet(const Tensor& self) {
squareCheckInputs(self);
TORCH_CHECK((at::isFloatingType(self.scalar_type()) || at::isComplexType(self.scalar_type())),
"Expected a floating point tensor as input");
Tensor det_P, diag_U;
std::tie(det_P, diag_U) = _lu_det_P_diag_U(self);
Tensor det_sign = diag_U.sign().prod(-1).mul_(det_P);
// If det_sign > 0, diag_U.abs_().log_().sum(-1) gives logdet (this means U is not singular).
// If det_sign <= 0, then we get proper nan (when det < 0, i.e., det_sign) or -inf (when det = 0, i.e., U is singular).
// U is singular when U(i, i) = 0 for some i in [1, self.size(-1)].
Tensor logdet_vals = diag_U.abs_().log_().sum(-1);
if (self.dim() > 2) {
auto indices = toListOfOptionalTensors((det_sign < 0).nonzero_numpy());
logdet_vals.index_put_(std::move(indices), at::full({}, NAN, self.options()));
} else if (det_sign.item<double>() < 0) {
logdet_vals.fill_(NAN);
}
return logdet_vals;
}
std::tuple<Tensor, Tensor> linalg_slogdet(const Tensor& self) {
squareCheckInputs(self);
ScalarType t = self.scalar_type();
TORCH_CHECK(t == ScalarType::Double || t == ScalarType::Float || t == ScalarType::ComplexFloat || t == ScalarType::ComplexDouble,
"linalg_slogdet: expected a tensor of float, double, cfloat or cdouble types but got ", t);
Tensor det_P, diag_U;
std::tie(det_P, diag_U) = _lu_det_P_diag_U(self);
auto det_sign = diag_U.sgn().prod(-1).mul_(det_P);
// abslogdet_val is -inf if U is singular, in which case diag_U.abs_().log_().sum(-1) will return -inf.
// U is singular when U(i, i) = 0 for some i in [1, self.size(-1)].
// Since abslogdet_val cannot take nan, no special case handling is required.
// in-place abs is not supported for complex tensors
auto abslogdet_val = isComplexType(t) ? diag_U.abs().log_().sum(-1) : diag_U.abs_().log_().sum(-1);
return std::make_tuple(det_sign, abslogdet_val);
}
// TODO: implement _out variant avoiding copy and using already allocated storage directly
std::tuple<Tensor&, Tensor&> linalg_slogdet_out(const Tensor& input, Tensor& sign, Tensor& logabsdet) {
TORCH_CHECK(sign.scalar_type() == input.scalar_type(),
"sign dtype ", sign.scalar_type(), " does not match input dtype ", input.scalar_type());
ScalarType real_dtype = toValueType(typeMetaToScalarType(input.dtype()));
TORCH_CHECK(logabsdet.scalar_type() == real_dtype,
"logabsdet dtype ", logabsdet.scalar_type(), " does not match the expected dtype ", real_dtype);
TORCH_CHECK(sign.device() == input.device() && logabsdet.device() == input.device(),
"Expected sign, logabsdet and input to be on the same device, but found sign on ",
sign.device(), ", logabsdet on ", logabsdet.device(), " and input on ", input.device(), " instead.");
Tensor sign_tmp, logabsdet_tmp;
std::tie(sign_tmp, logabsdet_tmp) = at::linalg_slogdet(input);
at::native::resize_output(sign, sign_tmp.sizes());
sign.copy_(sign_tmp);
at::native::resize_output(logabsdet, logabsdet_tmp.sizes());
logabsdet.copy_(logabsdet_tmp);
return std::tuple<Tensor&, Tensor&>(sign, logabsdet);
}
std::tuple<Tensor, Tensor> slogdet(const Tensor& self) {
return at::linalg_slogdet(self);
}
Tensor linalg_pinv(const Tensor& input, const Tensor& rcond, bool hermitian) {
ScalarType t = input.scalar_type();
TORCH_CHECK((t == ScalarType::Double || t == ScalarType::Float || t == ScalarType::ComplexFloat || t == ScalarType::ComplexDouble)
&& input.dim() >= 2,
"linalg_pinv(", t, "{", input.sizes(), "}): expected a tensor with 2 or more dimensions "
"of float, double, cfloat or cdouble types");
TORCH_CHECK(rcond.device() == input.device(),
"Expected rcond and input to be on the same device, but found rcond on ",
rcond.device(), " and input on ", input.device(), " instead.");
TORCH_CHECK(!at::isComplexType(rcond.scalar_type()),
"linalg_pinv: rcond tensor of complex type is not supported.");
if (input.numel() == 0) {
// The implementation below uses operations that do not work for zero numel tensors
// therefore we need this early return for 'input.numel() == 0' case
auto input_sizes = input.sizes().vec();
std::swap(input_sizes[input.dim() - 1], input_sizes[input.dim() - 2]);
return at::empty(input_sizes, input.options());
}
// If not Hermitian use singular value decomposition, else use eigenvalue decomposition
if (!hermitian) {
Tensor U, S, V;
// TODO: replace input.svd with linalg_svd
// using linalg_svd breaks pytorch/xla, see https://github.com/pytorch/xla/issues/2755
std::tie(U, S, V) = input.svd();
Tensor max_val = at::narrow(S, /*dim=*/-1, /*start=*/0, /*length=*/1); // singular values are sorted in descending order
Tensor S_pseudoinv = at::where(S > (rcond.unsqueeze(-1) * max_val), S.reciprocal(), at::zeros({}, S.options())).to(input.dtype());
// computes V @ diag(S_pseudoinv) @ U.conj().T
return at::matmul(V * S_pseudoinv.unsqueeze(-2), U.conj().transpose(-2, -1));
} else {
Tensor S, U;
std::tie(S, U) = at::linalg_eigh(input);
// For Hermitian matrices, singular values equal to abs(eigenvalues)
Tensor S_abs = S.abs();
// eigenvalues are sorted in ascending order starting with negative values, we need a maximum value of abs(eigenvalues)
Tensor max_val = S_abs.amax(/*dim=*/-1, /*keepdim=*/true);
Tensor S_pseudoinv = at::where(S_abs > (rcond.unsqueeze(-1) * max_val), S.reciprocal(), at::zeros({}, S.options())).to(input.dtype());
// computes U @ diag(S_pseudoinv) @ U.conj().T
return at::matmul(U * S_pseudoinv.unsqueeze(-2), U.conj().transpose(-2, -1));
}
}
Tensor linalg_pinv(const Tensor& input, double rcond, bool hermitian) {
Tensor rcond_tensor = at::full({}, rcond, input.options().dtype(ScalarType::Double));
return at::linalg_pinv(input, rcond_tensor, hermitian);
}
// TODO: implement _out variant avoiding copy and using already allocated storage directly
Tensor& linalg_pinv_out(Tensor& result, const Tensor& input, const Tensor& rcond, bool hermitian) {
TORCH_CHECK(result.scalar_type() == input.scalar_type(),
"result dtype ", result.scalar_type(), " does not match the expected dtype ", input.scalar_type());
TORCH_CHECK(result.device() == input.device(),
"Expected result and input to be on the same device, but found result on ",
result.device(), " and input on ", input.device(), " instead.");
Tensor result_tmp = at::linalg_pinv(input, rcond, hermitian);
at::native::resize_output(result, result_tmp.sizes());
result.copy_(result_tmp);
return result;
}
Tensor& linalg_pinv_out(Tensor& result, const Tensor& input, double rcond, bool hermitian) {
Tensor rcond_tensor = at::full({}, rcond, input.options().dtype(ScalarType::Double));
return at::linalg_pinv_out(result, input, rcond_tensor, hermitian);
}
Tensor pinverse(const Tensor& self, double rcond) {
return at::linalg_pinv(self, rcond, /*hermitian=*/false);
}
Tensor& linalg_matrix_rank_out(Tensor& result, const Tensor& self, optional<double> tol, bool hermitian) {
TORCH_CHECK(result.scalar_type() == ScalarType::Long,
"result dtype ", result.scalar_type(), " does not match the expected dtype ", ScalarType::Long);
// Matrices or batch of matrices are allowed
TORCH_CHECK(self.dim() >= 2, "linalg_matrix_rank: Expected as input a matrix or a batch of matrices, but got a tensor of size: ", self.sizes());
// matrix_rank assigns a scalar value for each matrix in the batch so
// result's shape is equal to self.shape[0:self.ndim-2]
// for single matrix result_shape = {}
auto result_shape = IntArrayRef(self.sizes().cbegin(), self.sizes().cend()-2);
at::native::resize_output(result, result_shape);
// NumPy doesn't take into account possible input with no elements and it errors on max not defined for this case
// Let's output 0 for this case, since that kind of matrices have zero number of non-zero rows, hence rank is 0.
if (self.numel() == 0) {
result.fill_(0);
return result;
}
// We compute matrix rank as the number of singular or absolute eigen values above 'tol' threshold
Tensor S;
if (!hermitian) {
Tensor U, V;
// TODO: replace self.svd with linalg_svd
std::tie(U, S, V) = self.svd(/*some=*/true, /*compute_uv=*/false);
} else {
S = at::linalg_eigvalsh(self);
S = S.abs();
}
if (tol.has_value()) {
double tol_value = tol.value();
at::sum_out(result, S > tol_value, /*dim=*/-1);
} else {
ScalarType real_dtype = toValueType(typeMetaToScalarType(self.dtype()));
double tol_value = _get_epsilon(real_dtype) * std::max(self.size(-1), self.size(-2));
Tensor max_S = S.amax(/*dim=*/-1);
at::sum_out(result, S > max_S.mul_(tol_value).unsqueeze_(-1), /*dim=*/-1);
}
return result;
}
Tensor linalg_matrix_rank(const Tensor& self, optional<double> tol, bool hermitian) {
Tensor result = at::empty({0}, self.options().dtype(ScalarType::Long));
result = at::linalg_matrix_rank_out(result, self, tol, hermitian);
return result;
}
Tensor matrix_rank(const Tensor& self, double tol, bool symmetric) {
return at::linalg_matrix_rank(self, optional<double>(tol), symmetric);
}
Tensor matrix_rank(const Tensor& self, bool symmetric) {
return at::linalg_matrix_rank(self, c10::nullopt, symmetric);
}
static void check_1d(const Tensor& t, const char* arg, const char* fn) {
TORCH_CHECK(t.dim() == 1, fn, ": Expected 1-D argument ", arg, ", but got ", t.dim(), "-D");
}
static void check_addr_scalar(const ScalarType dtype,
const Scalar scalar,
const std::string& scalar_name) {
TORCH_CHECK(
!scalar.isBoolean() || dtype == ScalarType::Bool,
"Boolean ", scalar_name, " only supported for Boolean results.");
TORCH_CHECK(
isFloatingType(dtype) || isComplexType(dtype) || scalar.isIntegral(true),
"For integral input tensors, "
"argument ", scalar_name ," must not be a floating point number.");
}
static TensorIterator build_addr_iter(Tensor& result,
const Tensor& self,
const Tensor& vec1,
const Tensor& vec2) {
check_1d(vec1, "vec1", "addr");
check_1d(vec2, "vec2", "addr");
Tensor self_;
if (&result != &self) {
std::tie(self_) = expand_size(self, {vec1.size(0), vec2.size(0)}, "addr");
} else {
self_ = self;
}
TORCH_CHECK(
self_.dim() == 2,
"2D tensor expected, got ", self_.dim(), "D tensor for input"
);
TORCH_CHECK(
self_.size(0) == vec1.size(0) && self_.size(1) == vec2.size(0),
"size mismatch, input: ", self_.sizes(),
", v1: ", vec1.sizes(),
", v2: ", vec2.sizes()
);
auto iter = TensorIteratorConfig()
.set_check_mem_overlap(true)
.add_output(result)
.add_input(self_)
.add_input(vec1.reshape({vec1.size(0), 1}))
.add_input(vec2)
.allow_cpu_scalars(true)
.promote_inputs_to_common_dtype(true)
.cast_common_dtype_to_outputs(true)
.enforce_safe_casting_to_output(true)
.build();
return iter;
}
Tensor addr(const Tensor& self,
const Tensor& vec1, const Tensor& vec2,
Scalar beta, Scalar alpha) {
Tensor result;
auto iter = build_addr_iter(result, self, vec1, vec2);
check_addr_scalar(iter.dtype(), beta, "beta");
check_addr_scalar(iter.dtype(), alpha, "alpha");
addr_stub(iter.device_type(), iter, beta, alpha);
return iter.output();
}
Tensor& addr_(Tensor& self,
const Tensor& vec1, const Tensor& vec2,
Scalar beta, Scalar alpha) {
return at::addr_out(self, self, vec1, vec2, beta, alpha);
}
Tensor& addr_out(Tensor &result,
const Tensor& self,
const Tensor& vec1, const Tensor& vec2,
Scalar beta, Scalar alpha) {
auto iter = build_addr_iter(result, self, vec1, vec2);
check_addr_scalar(iter.dtype(), beta, "beta");
check_addr_scalar(iter.dtype(), alpha, "alpha");
addr_stub(iter.device_type(), iter, beta, alpha);
return result;
}
// The math_addr and math_addr_out functions support backends
// other than CPU and CUDA, such as XLA.
// They are implemented using the composition of existing ops
Tensor math_addr(const Tensor& self,
const Tensor& vec1, const Tensor& vec2,
Scalar beta, Scalar alpha) {
// when beta==0, values in self should be ignored,
// nans and infs in self should not propagate.
if (beta.toComplexDouble() == 0.0) {
if (alpha.toComplexDouble() == 1.0) {
return at::outer(vec1, vec2);
}
return alpha * at::outer(vec1, vec2);
}
if (beta.toComplexDouble() == 1.0) {
if (alpha.toComplexDouble() == 1.0) {
return self + at::outer(vec1, vec2);
}
return self + alpha * at::outer(vec1, vec2);
}
if (alpha.toComplexDouble() == 1.0) {
return beta * self + at::outer(vec1, vec2);
}
return beta * self + alpha * at::outer(vec1, vec2);
}
Tensor& math_addr_out(Tensor &result,
const Tensor& self,
const Tensor& vec1, const Tensor& vec2,
Scalar beta, Scalar alpha) {
auto addr_result = at::addr(self, vec1, vec2, beta, alpha);
// Validates safe casting
const auto result_dtype = addr_result.scalar_type();
TORCH_CHECK(canCast(result_dtype, result.scalar_type()),
"result type ", result_dtype,
" can't be cast to the desired output type ", result.scalar_type());
at::native::resize_output(result, addr_result.sizes().vec());
result.copy_(addr_result);
return result;
}
// torch.ger, alias for torch.outer
Tensor& ger_out(Tensor &result, const Tensor& self, const Tensor& vec2) {
TORCH_WARN("torch.ger is deprecated and will be removed in a future PyTorch release. "
"Use torch.outer instead.");
return at::outer_out(result, self, vec2);
}
Tensor ger(const Tensor& self, const Tensor& vec2) {
return self.outer(vec2);
}
Tensor& inner_out(Tensor& out, const Tensor& self, const Tensor& other) {
checkDeviceType("inner()", {out, self, other}, self.device().type());
// If either self or other is a scalar just multiply them
if (self.dim() == 0 || other.dim() == 0) {
at::mul_out(out, self, other);
return out;
}
// Last dimension should match (tensordot does not enforce this)
TORCH_CHECK(
self.size(-1) == other.size(-1),
"inner() the last dimension must match on both input tensors but got shapes ",
self.sizes(),
" and ",
other.sizes());
at::tensordot_out(out, self, other, -1, -1);
return out;
}
Tensor inner(const Tensor& self, const Tensor& other) {
checkDeviceType("inner()", {self, other}, self.device().type());
// If either self or other is a scalar just multiply them
if (self.dim() == 0 || other.dim() == 0) {
return self * other;
}
// Last dimension should match (tensordot does not enforce this)
TORCH_CHECK(
self.size(-1) == other.size(-1),
"inner() the last dimension must match on both input tensors but got shapes ",
self.sizes(),
" and ",
other.sizes());
return at::tensordot(self, other, -1, -1);
}
Tensor& outer_out(Tensor &result, const Tensor& self, const Tensor& vec2) {
check_1d(self, "self", "outer");
check_1d(vec2, "vec2", "outer");
// torch.outer is implemented as a composite op using reshape and mul
at::mul_out(result, self.reshape({self.size(0), 1}), vec2);
return result;
}
Tensor outer(const Tensor& self, const Tensor& vec2) {
check_1d(self, "self", "outer");
check_1d(vec2, "vec2", "outer");
return self.reshape({self.size(0), 1}) * vec2;
}
static void addmm_impl_cpu_(
Tensor &result, const Tensor &self, Tensor m1, Tensor m2, Scalar beta, Scalar alpha) {
TORCH_INTERNAL_ASSERT(self.dim() == 2 && m1.dim() == 2 && m2.dim() == 2);
// Array access is faster than .size(n) and .stride(n)
const auto self_sizes = self.sizes();
auto m1_strides = m1.strides();
auto m1_sizes = m1.sizes();
auto m2_strides = m2.strides();
auto m2_sizes = m2.sizes();
TORCH_CHECK(
m1_sizes[1] == m2_sizes[0], "mat1 and mat2 shapes cannot be multiplied (",
m1_sizes[0], "x", m1_sizes[1], " and ", m2_sizes[0], "x", m2_sizes[1], ")");
TORCH_CHECK(
self_sizes[0] == m1_sizes[0] && self_sizes[1] == m2_sizes[1],
"input shape is incompatible with matrix multiplication (",
m1_sizes[0], "x", m1_sizes[1], " @ ", m2_sizes[0], "x", m2_sizes[1], " != ",
self_sizes[0], "x", self_sizes[1], ")");
native::resize_(result, self_sizes);
const auto result_strides = result.strides();
const auto result_sizes = result.sizes();
if (result.numel() == 0) {
return;
}
if (beta.toComplexDouble() != 0.0 && !self.is_same(result)) {
result.copy_(self);
}
bool transpose_c = false;
Tensor c;
// Cast result as matrix a
if (result_strides[0] == 1 &&
(result_sizes[1] == 1 || result_strides[1] >= std::max(int64_t{1}, result_sizes[0]))) {
transpose_c = false;
c = result;
} else if (result_strides[1] == 1 &&
(result_sizes[0] == 1 || result_strides[0] >= std::max(int64_t{1}, result_sizes[1]))) {
std::swap(m1, m2);
std::swap(m1_sizes, m2_sizes);
std::swap(m1_strides, m2_strides);
transpose_c = true;
c = result;
} else {
transpose_c = false;
// make c FORTRAN contiguous
c = result.transpose(0, 1).contiguous().transpose_(0, 1);
}
const int64_t m = result_sizes[transpose_c ? 1 : 0];
const int64_t n = result_sizes[transpose_c ? 0 : 1];
const int64_t k = m1_sizes[transpose_c ? 0 : 1];
// Cast m1 as matrix a
bool transpose_a = false;
Tensor a;
/* Need lda >= max(1, (transpose_a ? k : m)) */
if (m1_strides[transpose_c ? 1 : 0] == 1 &&
m1_strides[transpose_c ? 0 : 1] >= std::max(int64_t{1}, m)) {
transpose_a = false;
a = m1;
} else if (m1_strides[transpose_c ? 0 : 1] == 1 &&
m1_strides[transpose_c ? 1 : 0] >= std::max(int64_t{1}, k)) {
transpose_a = true;
a = m1;
} else {
transpose_a = !transpose_c;
a = m1.clone(at::MemoryFormat::Contiguous);
}
// Cast m2 as matrix b
bool transpose_b = false;
Tensor b;
/* Need ldm2_ >= max(1, (transpose_m2 == 'n' ? k : n)) */
if (m2_strides[transpose_c ? 1 : 0] == 1 &&
m2_strides[transpose_c ? 0 : 1] >= std::max(int64_t{1}, k)) {
transpose_b = false;
b = m2;
} else if (m2_strides[transpose_c ? 0 : 1] == 1 &&
m2_strides[transpose_c ? 1 : 0] >= std::max(int64_t{1}, n)) {
transpose_b = true;
b = m2;
} else {
transpose_b = !transpose_c;
b = m2.clone(at::MemoryFormat::Contiguous);
}
const int64_t lda = a.strides()[(transpose_a == transpose_c) ? 1 : 0];
const int64_t ldb = b.strides()[(transpose_b == transpose_c) ? 1 : 0];
const int64_t ldc = c.strides()[transpose_c ? 0 : 1];
// Apply BLAS routine
AT_DISPATCH_ALL_TYPES_AND_COMPLEX_AND2(kHalf, kBFloat16,
result.scalar_type(), "addmm_impl_cpu_",
[&]{
at::native::cpublas::gemm(
transpose_a ? cpublas::Transpose : cpublas::NoTranspose,
transpose_b ? cpublas::Transpose : cpublas::NoTranspose,
m, n, k,
alpha.to<scalar_t>(),
a.data_ptr<scalar_t>(), lda,
b.data_ptr<scalar_t>(), ldb,
beta.to<scalar_t>(),
c.data_ptr<scalar_t>(), ldc);
});
if (!c.is_same(result)) {
result.copy_(c);
}
}
static void addbmm_impl_(
Tensor &result, const Tensor &self, const Tensor &batch1, const Tensor &batch2, Scalar beta, Scalar alpha) {
TORCH_CHECK(batch1.dim() == 3, "batch1 must be a 3D tensor");
TORCH_CHECK(batch2.dim() == 3, "batch2 must be a 3D tensor");
TORCH_CHECK(batch1.size(0) == batch2.size(0),
"batch1 and batch2 must have same number of batches, got ",
batch1.size(0), " and ", batch2.size(0));
TORCH_CHECK(batch1.size(2) == batch2.size(1),
"Incompatible matrix sizes for bmm (",
batch1.size(1), "x", batch1.size(2), " and ",
batch2.size(1), "x", batch2.size(2), ")");
const int64_t dim1 = batch1.size(1);
const int64_t dim2 = batch2.size(2);
TORCH_CHECK(self.size(0) == dim1 && self.size(1) == dim2,
"self tensor does not match matmul output shape");
result.resize_as_(self);
if (beta.to<c10::complex<double>>() != 0.0 && !self.is_same(result)) {
result.copy_(self);
}
const int64_t num_batches = batch1.size(0);
if (num_batches == 0) {
if (beta.to<c10::complex<double>>() != 0.0) {
result.mul_(beta);
} else {
result.zero_();
}
return;
}
for (int64_t batch = 0; batch < num_batches; ++batch) {
result.addmm_(batch1[batch], batch2[batch], beta, alpha);
beta = 1; // accumulate output once
}
}
Tensor& addbmm_out(Tensor& result, const Tensor& self, const Tensor& batch1, const Tensor& batch2, Scalar beta, Scalar alpha) {
Tensor b_self = std::get<0>(expand_size(self, {batch1.size(1), batch2.size(2)}, "addbmm_out"));
{
at::NoNamesGuard guard;
addbmm_impl_(result, b_self, batch1, batch2, beta, alpha);
}
at::namedinference::propagate_names_for_addmm(result, batch1, batch2, self);
return result;
}
Tensor &addbmm_(Tensor& self, const Tensor& batch1, const Tensor& batch2, Scalar beta, Scalar alpha) {
return native::addbmm_out(self, self, batch1, batch2, beta, alpha);
}
Tensor addbmm(const Tensor& self, const Tensor& batch1, const Tensor& batch2, Scalar beta, Scalar alpha) {
Tensor result = at::empty({0}, self.options());
return native::addbmm_out(result, self, batch1, batch2, beta, alpha);
}
Tensor& addmm_cpu_out(Tensor &result, const Tensor& self, const Tensor& mat1, const Tensor& mat2, Scalar beta, Scalar alpha) {
TORCH_CHECK(mat1.dim() == 2, "mat1 must be a matrix, got ", mat1.dim(), "-D tensor");
TORCH_CHECK(mat2.dim() == 2, "mat2 must be a matrix, got ", mat2.dim(), "-D tensor");
Tensor b_self = std::get<0>(expand_size(self, {mat1.sizes()[0], mat2.sizes()[1]}, "addmm_out"));
{
at::NoNamesGuard guard;
addmm_impl_cpu_(result, b_self, mat1, mat2, beta, alpha);
}
at::namedinference::propagate_names_for_addmm(result, mat1, mat2, self);
return result;
}
Tensor addmm_cpu(const Tensor& self, const Tensor& mat1, const Tensor& mat2, Scalar beta, Scalar alpha) {
Tensor result = at::empty({0}, self.options());
return addmm_cpu_out(result, self, mat1, mat2, beta, alpha);
}
Tensor &addmm_cpu_(Tensor& self, const Tensor& mat1, const Tensor& mat2, Scalar beta, Scalar alpha) {
return addmm_cpu_out(self, self, mat1, mat2, beta, alpha);
}
Tensor& mm_cpu_out(Tensor & result, const Tensor & self, const Tensor & mat2) {
TORCH_CHECK(self.dim() == 2, "self must be a matrix");
TORCH_CHECK(mat2.dim() == 2, "mat2 must be a matrix");
native::resize_(result, {self.sizes()[0], mat2.sizes()[1]});
return addmm_cpu_out(result, result, self, mat2, 0, 1);
}
Tensor mm_cpu(const Tensor & self, const Tensor & mat2) {
TORCH_CHECK(self.dim() == 2, "self must be a matrix");
TORCH_CHECK(mat2.dim() == 2, "mat2 must be a matrix");
Tensor result = at::empty({self.sizes()[0], mat2.sizes()[1]}, self.options());
return addmm_cpu_out(result, result, self, mat2, 0, 1);
}
template <typename scalar_t, bool is_bmm>
inline void baddbmm_cpu_kernel(const Tensor& result, const Tensor& self, const Tensor& mat2, Scalar beta_, Scalar alpha_) {
int64_t bs = result.size(0);
int64_t is = result.size(1);
int64_t js = result.size(2);
int64_t ks = self.size(2);
scalar_t alpha = alpha_.to<scalar_t>();
scalar_t beta = beta_.to<scalar_t>();
auto r0 = result.accessor<scalar_t, 3>();
auto s0 = self.accessor<scalar_t, 3>();
auto m0 = mat2.accessor<scalar_t, 3>();
int64_t grain_size = std::min(internal::GRAIN_SIZE / (is * js * ks), (int64_t)1);
parallel_for(0, bs, grain_size, [&](int64_t b_begin, int64_t b_end) {
for (int64_t b = b_begin; b < b_end; b++) {
auto r1 = r0[b];
auto s1 = s0[b];
auto m1 = m0[b];
for (int64_t i = 0; i < is; i++) {
auto r2 = r1[i];
auto s2 = s1[i];
for (int64_t j = 0; j < js; j++) {
scalar_t &r = r2[j];
if (is_bmm) {
r = 0;
for (int64_t k = 0; k < ks; k++) {
r += s2[k] * m1[k][j];
}
} else {
r *= beta;
for (int64_t k = 0; k < ks; k++) {
r += alpha * s2[k] * m1[k][j];
}
}
}
}
}
});
}
// This tries to apply some optimizations to bmm/baddbmm:
// - When the operand size is small, computation are parallelized over the batch
// dimension using OMP and naive matrix multiplication is applied.
// - When the operand size is larger than the threshold, if compiled with MKL, MKL's batch gemm is used.
// - Otherwise, we use a series of matrix multiplications.
// The threshold of 400 for the first has not been thoroughly benchmarked yet and may have room for further
// optimization, it likely depends on the characteristics of the CPU, MKL will be different from non-MKL etc.,
// but this seems to be a first starting point.
static inline Tensor& bmm_out_or_baddbmm_(Tensor& self_or_result, const Tensor& batch1, const Tensor& batch2, Scalar beta, Scalar alpha, bool is_bmm_out) {
// is_bmm_out: true for bmm_out, false for baddbmm_
// self_or_result is "self" for baddbmm_ and "result" for bmm_out
CheckedFrom c = (is_bmm_out ? "bmm" : "baddbmm");
auto checkOnCPU = [](const Tensor& t, CheckedFrom c) {
TORCH_CHECK(
!t.is_cuda(),
"Expect tensor to have CPU backend, but got tensor with ",
toString(t.options().backend()),
" Backend (while checking arguments for ",
c);
};
checkOnCPU(self_or_result, c);
checkOnCPU(batch1, c);
checkOnCPU(batch2, c);
checkDim(c, batch1, "batch1", /* pos */ 1, /* dim */ 3);
checkDim(c, batch2, "batch2", /* pos */ 2, /* dim */ 3);
const auto batch1_sizes = batch1.sizes();
const auto batch2_sizes = batch2.sizes();
int64_t bs = batch1_sizes[0];
int64_t contraction_size = batch1_sizes[2];
int64_t res_rows = batch1_sizes[1];
int64_t res_cols = batch2_sizes[2];
TORCH_CHECK(batch2_sizes[0] == bs && batch2_sizes[1] == contraction_size);
if (is_bmm_out) {
self_or_result.resize_({bs, res_rows, res_cols});
} else {
const auto self_sizes = self_or_result.sizes();
TORCH_CHECK(self_sizes[0] == bs && self_sizes[1] == res_rows && self_sizes[2] == res_cols);
}
// handle pathological cases that blas may not like
if (self_or_result.numel() == 0) {
return self_or_result;
} else if (contraction_size == 0) {
if (is_bmm_out || (beta.to<c10::complex<double>>() == 0.0)) {
return self_or_result.zero_();
} else {
return self_or_result.mul_(beta);
}
}
auto batch_items_contiguous_or_transposed = [&](const Tensor& t) {
const auto sizes = t.sizes();
const auto strides = t.strides();
return (strides[2] == 1 && strides[1] >= sizes[2])
|| (strides[1] == 1 && strides[2] >= sizes[1]);
};
if (contraction_size * res_rows * res_cols < 400) {
if (is_bmm_out) {
AT_DISPATCH_ALL_TYPES_AND_COMPLEX_AND2(kHalf, kBFloat16, batch1.scalar_type(), "bmm", [&] {
baddbmm_cpu_kernel<scalar_t, true>(self_or_result, batch1, batch2, beta, alpha);
});
} else {
AT_DISPATCH_ALL_TYPES_AND_COMPLEX_AND2(kHalf, kBFloat16, batch1.scalar_type(), "baddbmm", [&] {
baddbmm_cpu_kernel<scalar_t, false>(self_or_result, batch1, batch2, beta, alpha);
});
}
} else if (at::hasMKL() && ((
self_or_result.scalar_type() != kHalf &&
self_or_result.scalar_type() != kBFloat16 &&
at::native::is_floating_point(self_or_result)) ||
at::native::is_complex(self_or_result))
&& batch_items_contiguous_or_transposed(batch1)
&& batch_items_contiguous_or_transposed(batch2)
&& self_or_result.is_contiguous()) {
at::native::_baddbmm_mkl_(self_or_result, batch1, batch2, beta, alpha);
} else { // split along batch dimension
if (is_bmm_out) {
for (int64_t b = 0; b < bs; b++) {
auto r = self_or_result.select(0, b);
native::mm_cpu_out(r, batch1.select(0, b), batch2.select(0, b));
}
} else {
for (int64_t b = 0; b < bs; b++) {
self_or_result.select(0, b).addmm_(batch1.select(0, b), batch2.select(0, b), beta, alpha);
}
}
}
return self_or_result;
}
Tensor baddbmm_cpu(const Tensor& self, const Tensor& batch1, const Tensor& batch2, Scalar beta, Scalar alpha) {
Tensor result = at::empty({0}, self.options());
return at::native::baddbmm_out_cpu(result, self, batch1, batch2, beta, alpha);
}
Tensor& baddbmm_out_cpu(Tensor &result, const Tensor& self_, const Tensor& batch1, const Tensor& batch2, Scalar beta, Scalar alpha) {
Tensor self;
std::tie(self) = expand_size(self_, {batch1.size(0), batch1.size(1), batch2.size(2)}, "baddbmm");
result.resize_(self.sizes());
result.copy_(self);
return at::native::baddbmm__cpu(result, batch1, batch2, beta, alpha);
}
Tensor& baddbmm__cpu(Tensor& self, const Tensor& batch1, const Tensor& batch2, Scalar beta, Scalar alpha) {
return bmm_out_or_baddbmm_(self, batch1, batch2, beta, alpha, false);
}
Tensor bmm_cpu(const Tensor& self, const Tensor& mat2) {
Tensor result = at::empty({0}, self.options());
return at::native::bmm_out_cpu(result, self, mat2);
}
Tensor& bmm_out_cpu(Tensor &result, const Tensor& batch1, const Tensor& batch2) {
Scalar beta(0.0);
Scalar alpha(1.0);
{
NoNamesGuard guard;
bmm_out_or_baddbmm_(result, batch1, batch2, beta, alpha, true);
}
namedinference::propagate_names_if_nonempty(
result,
namedinference::compute_bmm_outnames(result, batch1, batch2));
return result;
}
Tensor& dot_out(Tensor& result, const Tensor& self, const Tensor& tensor) {
at::native::resize_output(result, {});
TORCH_CHECK(result.scalar_type() == self.scalar_type(),
"result dtype ", result.scalar_type(), " does not match self dtype ", self.scalar_type());
return result.fill_(self.dot(tensor));
}
Tensor& vdot_out(Tensor& result, const Tensor& self, const Tensor& other) {
at::native::resize_output(result, {});
TORCH_CHECK(result.scalar_type() == self.scalar_type(),
"result dtype ", result.scalar_type(), " does not match self dtype ", self.scalar_type());
return result.fill_(self.vdot(other));
}
/*
Matrix product of two Tensors.
The behavior depends on the dimensionality of the Tensors as follows:
- If both Tensors are 1-dimensional, the dot product (scalar) is returned.
- If both arguments are 2-dimensional, the matrix-matrix product is returned.
- If the first argument is 1-dimensional and the second argument is 2-dimensional,
a 1 is prepended to its dimension for the purpose of the matrix multiply.
After the matrix multiply, the prepended dimension is removed.
- If the first argument is 2-dimensional and the second argument is 1-dimensional,
the matrix-vector product is returned.
- If both arguments are at least 1-dimensional and at least one argument is
N-dimensional (where N > 2), then a batched matrix multiply is returned. If the first
argument is 1-dimensional, a 1 is prepended to its dimension for the purpose of the
batched matrix multiply and removed after. If the second argument is 1-dimensional, a
1 is appended to its dimension for the purpose of the batched matrix multiple and removed after.
The non-matrix (i.e. batch) dimensions are broadcasted (and thus
must be broadcastable). For example, if tensor1 is a (j x 1 x n x m) Tensor
and tensor2 is a (k x m x p) Tensor, the returned tensor will be an (j x k x n x p) Tensor.
*/
Tensor matmul(
c10::optional<Tensor> out_opt,
const Tensor& tensor1,
const Tensor& tensor2) {
NoNamesGuard guard;
auto dim_tensor1 = tensor1.dim();
auto dim_tensor2 = tensor2.dim();
auto has_out = out_opt.has_value();
Tensor out = out_opt.value_or(Tensor());
if (dim_tensor1 == 1 && dim_tensor2 == 1) {
return has_out ? at::native::dot_out(out, tensor1, tensor2) : tensor1.dot(tensor2);
} else if (dim_tensor1 == 2 && dim_tensor2 == 1) {
return has_out ? at::mv_out(out, tensor1, tensor2) : tensor1.mv(tensor2);
} else if (dim_tensor1 == 1 && dim_tensor2 == 2) {
return has_out ? at::mm_out(out, tensor1.unsqueeze(0), tensor2).squeeze_(0)
: tensor1.unsqueeze(0).mm(tensor2).squeeze_(0);
} else if (dim_tensor1 == 2 && dim_tensor2 == 2) {
return has_out ? at::mm_out(out, tensor1, tensor2) : tensor1.mm(tensor2);
} else if (dim_tensor1 >= 3 && (dim_tensor2 == 1 || dim_tensor2 == 2)) {
// optimization: use mm instead of bmm by folding tensor1's batch into
// its leading matrix dimension.
Tensor t2 = dim_tensor2 == 1 ? tensor2.unsqueeze(-1) : tensor2;
auto size1 = tensor1.sizes();
auto size2 = t2.sizes();
std::vector<int64_t> output_size;
output_size.insert(output_size.end(), size1.begin(), size1.end() - 1);
if (dim_tensor2 > 1) {
output_size.push_back(size2[dim_tensor2 - 1]);
}
// fold the batch into the first dimension
Tensor t1 = tensor1.contiguous().view({-1, size1[size1.size() - 1]});
Tensor output = has_out ? at::_unsafe_view(at::mm_out(out, t1, t2), output_size)
: at::_unsafe_view(t1.mm(t2), output_size);
return has_out ? out.set_(output) : output;
} else if ((dim_tensor1 == 1 || dim_tensor1 == 2) && dim_tensor2 >= 3) {
// optimization: transpose the inner dimensions of the arguments, call
// matmul on the swapped arguments, then transpose the inner dimensions
// of the result.
const int64_t n = dim_tensor1 == 2 ? tensor1.size(-2) : 1;
const int64_t m = tensor1.size(-1);
const int64_t p = tensor2.size(-1);
const Tensor t2_T = tensor2.transpose(-1, -2);
const Tensor t1_T = dim_tensor1 == 2 ? tensor1.t() : tensor1.reshape({n, m}).t();
const Tensor res_T = matmul(out_opt, t2_T, t1_T);
if (dim_tensor1 == 2) {
Tensor res = res_T.transpose(-1, -2).contiguous();
return has_out ? out.set_(res) : res;
}
else {
std::vector<int64_t> shape = tensor2.sizes().slice(0, dim_tensor2 - 2).vec();
shape.push_back(p);
Tensor res = res_T.reshape(shape).contiguous();
return has_out ? out.set_(res) : res;
}
} else if ((dim_tensor1 >= 1 && dim_tensor2 >= 1) && (dim_tensor1 >= 3 || dim_tensor2 >= 3)) {
// We are multiplying b1 x n x m1 by x2 x m2 x p (where b1 can be a list);
// we track m1 vs m2 separately even though they must match for nicer error messages
int64_t n = dim_tensor1 > 1 ? tensor1.size(-2) : 1;
int64_t m1 = tensor1.size(-1);
IntArrayRef batch_tensor1(tensor1.sizes().data(), std::max<int64_t>(dim_tensor1 - 2, 0));
int64_t m2 = dim_tensor2 > 1 ? tensor2.size(-2) : 1;
int64_t p = tensor2.size(-1);
IntArrayRef batch_tensor2(tensor2.sizes().data(), std::max<int64_t>(dim_tensor2 - 2, 0));
// expand the batch portion (i.e. cut off matrix dimensions and expand rest)
std::vector<int64_t> expand_batch_portion = infer_size(batch_tensor1, batch_tensor2);
std::vector<int64_t> tensor1_expand_size(expand_batch_portion);
tensor1_expand_size.insert(tensor1_expand_size.end(), {n, m1});
std::vector<int64_t> tensor2_expand_size(expand_batch_portion);
tensor2_expand_size.insert(tensor2_expand_size.end(), {m2, p});
const int64_t expand_batch_product =
prod_intlist(expand_batch_portion);
std::vector<int64_t> tensor1_bmm_view({expand_batch_product});
tensor1_bmm_view.insert(tensor1_bmm_view.end(), {n, m1});
std::vector<int64_t> tensor2_bmm_view({expand_batch_product});
tensor2_bmm_view.insert(tensor2_bmm_view.end(), {m2, p});
// flatten expanded batches
Tensor tensor1_expanded = tensor1.expand(tensor1_expand_size).contiguous().view(tensor1_bmm_view);
Tensor tensor2_expanded = tensor2.expand(tensor2_expand_size).contiguous().view(tensor2_bmm_view);
// reshape batches back into result
std::vector<int64_t> output_shape(expand_batch_portion);
if (dim_tensor1 > 1) {
output_shape.push_back(n);
}
if (dim_tensor2 > 1) {
output_shape.push_back(p);
}
Tensor output = has_out ? at::_unsafe_view(at::bmm_out(out, tensor1_expanded, tensor2_expanded), output_shape)
: at::_unsafe_view(tensor1_expanded.bmm(tensor2_expanded), output_shape);
return has_out ? out.set_(output) : output;
}
AT_ERROR("both arguments to matmul need to be at least 1D, but they are ",
dim_tensor1, "D and ", dim_tensor2, "D");
}
Tensor matmul(const Tensor & tensor1, const Tensor & tensor2) {
auto maybe_outnames = namedinference::compute_matmul_outnames(tensor1, tensor2);
auto result = at::native::matmul(c10::nullopt, tensor1, tensor2);
namedinference::propagate_names_if_nonempty(result, maybe_outnames);
return result;
}
Tensor& matmul_out(Tensor &result, const Tensor & tensor1, const Tensor & tensor2) {
auto maybe_outnames = namedinference::compute_matmul_outnames(tensor1, tensor2);
at::native::matmul(c10::optional<Tensor>(result), tensor1, tensor2);
namedinference::propagate_names_if_nonempty(result, maybe_outnames);
return result;
}
// helper methods for matrix_exp
namespace {