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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/Resize.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>
namespace at {
namespace native {
// 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=*/self.scalar_type()).fmod_(2);
// NB: the `.contiguous()` call is added due to the bug in `.prod()` as reported in
// issue #https://github.com/pytorch/pytorch/issues/34061
auto u_diagonal = lu.diagonal(/*offset=*/0, /*dim1=*/-2, /*dim2=*/-1).contiguous();
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) {
logdet_vals.index_put_((det_sign < 0).nonzero_numpy(), at::full({}, NAN, self.options()));
} else if (det_sign.item<double>() < 0) {
logdet_vals.fill_(NAN);
}
return logdet_vals;
}
std::tuple<Tensor, Tensor> slogdet(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);
auto det_sign = diag_U.sign().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.
auto abslogdet_val = diag_U.abs_().log_().sum(-1);
return std::make_tuple(det_sign, abslogdet_val);
}
Tensor pinverse(const Tensor& self, double rcond) {
TORCH_CHECK((at::isFloatingType(self.scalar_type()) || at::isComplexType(self.scalar_type())) && self.dim() >= 2,
"pinverse(", self.scalar_type(), "{", self.sizes(), "}): expected a tensor with 2 or more dimensions "
"of floating types");
if (self.numel() == 0) {
// Match NumPy
auto self_sizes = self.sizes().vec();
std::swap(self_sizes[self.dim() - 1], self_sizes[self.dim() - 2]);
return at::empty(self_sizes, self.options());
}
Tensor U, S, V;
std::tie(U, S, V) = self.svd();
Tensor max_val = at::narrow(S, /*dim=*/-1, /*start=*/0, /*length=*/1);
Tensor S_pseudoinv = at::where(S > rcond * max_val, S.reciprocal(), at::zeros({}, self.options()));
return at::matmul(V, at::matmul(S_pseudoinv.diag_embed(/*offset=*/0, /*dim1=*/-2, /*dim2=*/-1), U.transpose(-2, -1)));
}
static inline Tensor _matrix_rank_helper(const Tensor& self, bool symmetric) {
Tensor S;
if (!symmetric) {
Tensor U, V;
std::tie(U, S, V) = self.svd(/*some=*/true, /*compute_uv=*/false);
} else {
Tensor eigvecs;
std::tie(S, eigvecs) = self.symeig(/*eigenvectors=*/false);
S = S.abs();
}
return S;
}
Tensor matrix_rank(const Tensor& self, double tol, bool symmetric) {
TORCH_CHECK((at::isFloatingType(self.scalar_type()) || at::isComplexType(self.scalar_type())) && self.dim() == 2,
"matrix_rank(", self.scalar_type(), "{", self.sizes(), "}): expected a 2D tensor "
"of floating types");
Tensor S = _matrix_rank_helper(self, symmetric);
return (S > tol).sum();
}
Tensor matrix_rank(const Tensor& self, bool symmetric) {
TORCH_CHECK((at::isFloatingType(self.scalar_type()) || at::isComplexType(self.scalar_type())) && self.dim() == 2,
"matrix_rank(", self.scalar_type(), "{", self.sizes(), "}): expected a 2D tensor "
"of floating types");
Tensor S = _matrix_rank_helper(self, symmetric);
double tol = _get_epsilon(self.scalar_type()) * std::max(self.size(0), self.size(1));
return (S > S.max().mul_(tol)).sum();
}
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");
}
Tensor addr(const Tensor& self, const Tensor& vec1, const Tensor& vec2, Scalar beta, Scalar alpha) {
check_1d(vec1, "vec1", "addr");
check_1d(vec2, "vec2", "addr");
Tensor b_self;
std::tie(b_self) = expand_size(self, {vec1.size(0), vec2.size(0)}, "addr");
return at::_addr(b_self, vec1, vec2, beta, alpha);
}
Tensor& addr_(Tensor& self, const Tensor& vec1, const Tensor& vec2, Scalar beta, Scalar alpha) {
check_1d(vec1, "vec1", "addr");
check_1d(vec2, "vec2", "addr");
return at::_addr_(self, vec1, vec2, beta, alpha);
}
Tensor& addr_out(Tensor &result, const Tensor& self, const Tensor& vec1, const Tensor& vec2, Scalar beta, Scalar alpha) {
check_1d(vec1, "vec1", "addr");
check_1d(vec2, "vec2", "addr");
Tensor b_self;
std::tie(b_self) = expand_size(self, {vec1.size(0), vec2.size(0)}, "addr_out");
return at::_addr_out(result, b_self, vec1, vec2, beta, alpha);
}
Tensor& ger_out(Tensor &result, const Tensor& self, const Tensor& vec2) {
check_1d(self, "self", "ger");
check_1d(vec2, "vec2", "ger");
if (result.dim() != 2 || result.size(0) != self.size(0) || result.size(1) != vec2.size(0)) {
result.resize_({ self.size(0), vec2.size(0) });
}
// resize_ does the "broadcasting", don't need to broadcast again.
return at::_addr_out(result, result, self, vec2, Scalar(0), Scalar(1));
}
Tensor ger(const Tensor& self, const Tensor& vec2) {
Tensor result = at::empty({0}, self.options());
at::ger_out(result, self, vec2);
return result;
}
// torch.outer, alias for torch.ger
Tensor& outer_out(Tensor &result, const Tensor& self, const Tensor& vec2) {
return at::ger_out(result, self, vec2);
}
Tensor outer(const Tensor& self, const Tensor& vec2) {
return self.ger(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_cpu_(
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<double>() != 0.0 && !self.is_same(result)) {
result.copy_(self);
}
const int64_t num_batches = batch1.size(0);
for (int64_t batch = 0; batch < num_batches; ++batch) {
addmm_impl_cpu_(result, result, batch1[batch], batch2[batch], beta, alpha);
beta = 1; // accumulate output once
}
}
Tensor& addbmm_cpu_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_cpu_(result, b_self, batch1, batch2, beta, alpha);
}
at::namedinference::propagate_names_for_addmm(result, batch1, batch2, self);
return result;
}
Tensor &addbmm_cpu_(Tensor& self, const Tensor& batch1, const Tensor& batch2, Scalar beta, Scalar alpha) {
return addbmm_cpu_out(self, self, batch1, batch2, beta, alpha);
}
Tensor addbmm_cpu(const Tensor& self, const Tensor& batch1, const Tensor& batch2, Scalar beta, Scalar alpha) {
Tensor result = at::empty({0}, self.options());
return addbmm_cpu_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");
TensorArg self_arg(self_or_result, is_bmm_out ? "self" : "result", 0);
TensorArg b1_arg(batch1, "batch1", 1);
TensorArg b2_arg(batch2, "batch2", 2);
checkBackend(c, {self_or_result, batch1, batch2}, Backend::CPU);
checkDim(c, b1_arg, 3);
checkDim(c, b2_arg, 3);
int64_t bs = batch1.size(0);
checkSize(c, b2_arg, 0, bs);
int64_t contraction_size = batch1.size(2);
int64_t res_rows = batch1.size(1);
int64_t res_cols = batch2.size(2);
checkSize(c, b2_arg, 1, contraction_size);
if (is_bmm_out) {
self_or_result.resize_({bs, res_rows, res_cols});
} else {
checkSize(c, self_arg, 0, bs);
checkSize(c, self_arg, 1, res_rows);
checkSize(c, self_arg, 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) {
return self_or_result.zero_();
} else {
return self_or_result.mul_(beta);
}
}
auto batch_items_contiguous_or_transposed = [&](const Tensor& t) {
return (t.stride(2) == 1 && t.stride(1) >= t.size(2))
|| (t.stride(1) == 1 && t.stride(2) >= t.size(1));
};
if (contraction_size * res_rows * res_cols < 400) {
if (is_bmm_out) {
AT_DISPATCH_ALL_TYPES_AND_COMPLEX(batch1.scalar_type(), "bmm", [&] {
baddbmm_cpu_kernel<scalar_t, true>(self_or_result, batch1, batch2, beta, alpha);
});
} else {
AT_DISPATCH_ALL_TYPES_AND_COMPLEX(batch1.scalar_type(), "baddbmm", [&] {
baddbmm_cpu_kernel<scalar_t, false>(self_or_result, batch1, batch2, beta, alpha);
});
}
} else if (at::hasMKL() && (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});
int expand_batch_product = std::accumulate(expand_batch_portion.begin(), expand_batch_portion.end(),
1, std::multiplies<int64_t>());
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 {
template <typename scalar_t, int ROW, int COL>
using array2d = std::array<std::array<scalar_t, COL>, ROW>;
// we consider 6 Taylor expansions of degree
// 1, 2, 4, 8, 12, 18
constexpr int total_n_degs = 6;
Tensor operator_1_norm(const Tensor& tensor) {
return std::get<0>(tensor.abs().sum(-2).max(-1));
}
// Allocates a buffers of uninitialized or zero values
// of shape [n_copies, a.size()]
Tensor _allocate_buffer(const Tensor& a, int n_copies, bool is_zero = false) {
auto res = at::empty(
{n_copies, a.size(0), a.size(1), a.size(2)},
a.options().memory_format(at::MemoryFormat::Contiguous)
);
if (is_zero) {
res.zero_();
}
return res;
}
// Makes `buffer` to store `num_matrices` number of matrices needed for
// compute the matrix exponentials of different orders, i.e.
// first `num_matrices` matrices from the list l := {I, A, A^2, A^3, A^6}
// in a contiguous block of memory such that
// buffer[0, ...] = l[0], // I
// buffer[1, ...] = l[1], // A
// ...
// buffer[num_matrices - 1, ...] = l[num_matries - 1]
void _fill_matrix_powers(Tensor& buffer, const Tensor& a, int num_matrices) {
auto a_sizes_minus_last = a.sizes().vec();
a_sizes_minus_last.pop_back();
// fill I
buffer.select(0, 0).copy_(
at::diag_embed(
at::ones({1}, buffer.options())
.expand(a_sizes_minus_last)
)
);
// fill a
buffer.select(0, 1).copy_(a);
// fill a^2
if (2 <= num_matrices - 1) {
at::native::matmul(
buffer.select(0, 2), // out for a^2
buffer.select(0, 1),
buffer.select(0, 1)
);
}
// fill a^3
if (3 <= num_matrices - 1) {
at::native::matmul(
buffer.select(0, 3), // out for a^3
buffer.select(0, 1),
buffer.select(0, 2)
);
}
// fill a^6
if (4 <= num_matrices - 1) {
at::native::matmul(
buffer.select(0, 4),
buffer.select(0, 3),
buffer.select(0, 3)
);
}
}
inline Tensor _move_memory_if_cuda_input(
const Tensor& mem,
const Tensor& in
) {
return (in.device().type() == at::kCUDA)
? mem.to(at::device_of(in).value())
: mem;
}
// convert a 1D blob to a 2D Tensor of size [1, blob.size()]
// such that blob.device() == in.device())
// designed to be used with _compute_linear_combination
template <typename scalar_t>
inline Tensor _blob_to_Tensor(
std::initializer_list<scalar_t> blob,
const Tensor& in
) {
// we convert to void* expecitly because begin() returns
// a pointer to a constant.
// Blob is assumed to be a 1D array, that is why
// we also insert a fake dimension so that the result could directly
// be used in _compute_linear_combination
auto tensor = at::from_blob((void*)blob.begin(), blob.size(), in.dtype())
.unsqueeze(0);
return _move_memory_if_cuda_input(tensor, in);
}
// I + A
Tensor compute_T1(const Tensor& A) {
// 2 for {I, A}
auto As = _allocate_buffer(A, 2);
_fill_matrix_powers(As, A, 2);
return As.sum(0);
}
// I + A + A^2 / 2
Tensor compute_T2(const Tensor& A) {
auto As = _allocate_buffer(A, 3);
// 3 for {I, A, A^2}
_fill_matrix_powers(As, A, 3);
As.select(0, 2).div_(2.0);
return As.sum(0);
}
// I + A + A^2 * (I / 2 + A / 6 + A^2 / 24)
template <typename scalar_t>
Tensor compute_T4(const Tensor& A) {
auto As = _allocate_buffer(A, 4);
// 3 for {I, A, A^2}
_fill_matrix_powers(As, A, 3);
at::native::matmul(
// output for A^2 * (I / 2 + A / 6 + A^2 / 24)
As.select(0, 3),
// contains A^2
As.select(0, 2),
// computes (I / 2 + A / 6 + A^2 / 24)
at::native::_compute_linear_combination(
As.narrow(0, 0, 3),
_blob_to_Tensor<scalar_t>({1 / 2.0, 1 / 6.0, 1 / 24.0}, A)
)
);
// I + A + A^2 * (I / 2 + A / 6 + A^2 / 24)
return at::native::_compute_linear_combination(
As, _blob_to_Tensor<scalar_t>({1.0, 1.0, 0.0, 1.0}, A)
);
}
template <typename scalar_t>
Tensor compute_T8(const Tensor& A) {
constexpr scalar_t sqrt_177 = 0.1330413469565007072504e+2;
constexpr scalar_t x3 = 2. / 3.;
constexpr scalar_t x1 = x3 * ((1. + sqrt_177) / 88.);
constexpr scalar_t x2 = x3 * ((1. + sqrt_177) / 352.);
constexpr scalar_t x4 = (-271. + 29. * sqrt_177) / (315. * x3);
constexpr scalar_t x5 = (-11. + 11. * sqrt_177) / (1260. * x3);
constexpr scalar_t x6 = (-99. + 11. * sqrt_177) / (5040. * x3);
constexpr scalar_t x7 = (89. - sqrt_177) / (5040. * x3);
constexpr scalar_t y2 = (857. - 58. * sqrt_177) / 630.;
auto As = _allocate_buffer(A, 5);
// 3 for {I, A, A^2}
_fill_matrix_powers(As, A, 3);
// A4 = A2 * (x1 * A + x2 * A2)
at::native::matmul(
// output for A4
As.select(0, 3),
// As.select(0, 2) = A^2
As.select(0, 2),
at::native::_compute_linear_combination(
// extract {A, A^2} from As
As.narrow(0, 1, 2),
_blob_to_Tensor<scalar_t>({x1, x2}, A)
)
);
// A8 = (x3 * A2 + A4) * (x4 * I + x5 * A + x6 * A2 + x7 * A4)
at::native::matmul(
// output for A8
As.select(0, 4),
// x3 * A2 + A4
at::native::_compute_linear_combination(
As.narrow(0, 2, 2),
_blob_to_Tensor<scalar_t>({x3, 1.0}, A)
),
at::native::_compute_linear_combination(
As.narrow(0, 0, 4),
_blob_to_Tensor<scalar_t>({x4, x5, x6, x7}, A)
)
);
// return I + A + y2 * A2 + A8;
return at::native::_compute_linear_combination(
As,
_blob_to_Tensor<scalar_t>({1.0, 1.0, y2, 0.0, 1.0}, A)
);
}
template <typename scalar_t>
Tensor compute_T12(const Tensor& A) {
constexpr int num_prods = 4;
array2d<scalar_t, num_prods, num_prods> b = {{
{
9.0198e-16,
0.46932117595418237389,
-0.20099424927047284052,
-0.04623946134063071740
},
{
5.31597895759871264183,
1.19926790417132231573,
0.01179296240992997031,
0.01108844528519167989
},
{
0.18188869982170434744,
0.05502798439925399070,
0.09351590770535414968,
0.00610700528898058230
},
{
-2.0861320e-13,
-0.13181061013830184015,
-0.02027855540589259079,
-0.00675951846863086359
}
}};
// gather coefficients `b` from above into a tensor,
// and move them to device `device_of(A)`
auto bs = at::from_blob(
reinterpret_cast<void*>(&b),
{num_prods, num_prods},
{num_prods, 1},
A.dtype()
);
bs = _move_memory_if_cuda_input(bs, A);
auto As = _allocate_buffer(A, num_prods);
_fill_matrix_powers(As, A, num_prods);
auto Bs = at::native::_compute_linear_combination(As, bs);
// compute A6
Bs.select(0, 2).add_(at::native::matmul(
// tmp buffer for this matrix product
As.select(0, 0),
Bs.select(0, 3),
Bs.select(0, 3)
));
return Bs.select(0,0).add_(at::native::matmul(
// tmp buffer for this matrix product
As.select(0, 0),
Bs.select(0, 1).add_(Bs.select(0, 2)),
Bs.select(0, 2)
));
}
template <typename scalar_t>
Tensor compute_T18(const Tensor& A) {
constexpr int num_prods = 5;
array2d<scalar_t, num_prods, num_prods> b = {{
{
0.,
-1.00365581030144618291e-01,
-8.02924648241156932449e-03,
-8.92138498045729985177e-04,
0.
},
{
0.,
3.97849749499645077844e-01,
1.36783778460411720168e+00,
4.98289622525382669416e-01,
-6.37898194594723280150e-04
},
{
-1.09676396052962061844e+01,
1.68015813878906206114e+00,
5.71779846478865511061e-02,
-6.98210122488052056106e-03,
3.34975017086070470649e-05
},
{
-9.04316832390810593223e-02,
-6.76404519071381882256e-02,
6.75961301770459654925e-02,
2.95552570429315521194e-02,