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BatchLinearAlgebra.cpp
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BatchLinearAlgebra.cpp
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#include <ATen/ATen.h>
#include <ATen/CPUApplyUtils.h>
#include <ATen/Dispatch.h>
#include <ATen/NativeFunctions.h>
#include <ATen/ExpandUtils.h>
#include <ATen/native/LinearAlgebraUtils.h>
#include <ATen/native/cpu/zmath.h>
#include <ATen/Parallel.h>
#include <TH/TH.h> // for USE_LAPACK
#include <vector>
// First the required LAPACK implementations are registered here.
// A comment above the registered LAPACK routine suggest which batched
// linear algebra function uses that routine
#ifdef USE_LAPACK
// gesv
extern "C" void zgesv_(int *n, int *nrhs, std::complex<double> *a, int *lda, int *ipiv, std::complex<double> *b, int *ldb, int *info);
extern "C" void cgesv_(int *n, int *nrhs, std::complex<float> *a, int *lda, int *ipiv, std::complex<float> *b, int *ldb, int *info);
extern "C" void dgesv_(int *n, int *nrhs, double *a, int *lda, int *ipiv, double *b, int *ldb, int *info);
extern "C" void sgesv_(int *n, int *nrhs, float *a, int *lda, int *ipiv, float *b, int *ldb, int *info);
// getrf
extern "C" void zgetrf_(int *m, int *n, std::complex<double> *a, int *lda, int *ipiv, int *info);
extern "C" void cgetrf_(int *m, int *n, std::complex<float> *a, int *lda, int *ipiv, int *info);
extern "C" void dgetrf_(int *m, int *n, double *a, int *lda, int *ipiv, int *info);
extern "C" void sgetrf_(int *m, int *n, float *a, int *lda, int *ipiv, int *info);
// getri
extern "C" void zgetri_(int *n, std::complex<double> *a, int *lda, int *ipiv, std::complex<double> *work, int *lwork, int *info);
extern "C" void cgetri_(int *n, std::complex<float> *a, int *lda, int *ipiv, std::complex<float> *work, int *lwork, int *info);
extern "C" void dgetri_(int *n, double *a, int *lda, int *ipiv, double *work, int *lwork, int *info);
extern "C" void sgetri_(int *n, float *a, int *lda, int *ipiv, float *work, int *lwork, int *info);
// potrs
extern "C" void zpotrs_(char *uplo, int *n, int *nrhs, std::complex<double> *a, int *lda, std::complex<double> *b, int *ldb, int *info);
extern "C" void cpotrs_(char *uplo, int *n, int *nrhs, std::complex<float> *a, int *lda, std::complex<float> *b, int *ldb, int *info);
extern "C" void dpotrs_(char *uplo, int *n, int *nrhs, double *a, int *lda, double *b, int *ldb, int *info);
extern "C" void spotrs_(char *uplo, int *n, int *nrhs, float *a, int *lda, float *b, int *ldb, int *info);
// potrf
extern "C" void zpotrf_(char *uplo, int *n, std::complex<double> *a, int *lda, int *info);
extern "C" void cpotrf_(char *uplo, int *n, std::complex<float> *a, int *lda, int *info);
extern "C" void dpotrf_(char *uplo, int *n, double *a, int *lda, int *info);
extern "C" void spotrf_(char *uplo, int *n, float *a, int *lda, int *info);
// trtrs
extern "C" void ztrtrs_(char *uplo, char *trans, char *diag, int *n, int *nrhs, std::complex<double> *a, int *lda, std::complex<double> *b, int *ldb, int *info);
extern "C" void ctrtrs_(char *uplo, char *trans, char *diag, int *n, int *nrhs, std::complex<float> *a, int *lda, std::complex<float> *b, int *ldb, int *info);
extern "C" void dtrtrs_(char *uplo, char *trans, char *diag, int *n, int *nrhs, double *a, int *lda, double *b, int *ldb, int *info);
extern "C" void strtrs_(char *uplo, char *trans, char *diag, int *n, int *nrhs, float *a, int *lda, float *b, int *ldb, int *info);
// geqrf
extern "C" void zgeqrf_(int *m, int *n, std::complex<double> *a, int *lda, std::complex<double> *tau, std::complex<double> *work, int *lwork, int *info);
extern "C" void cgeqrf_(int *m, int *n, std::complex<float> *a, int *lda, std::complex<float> *tau, std::complex<float> *work, int *lwork, int *info);
extern "C" void dgeqrf_(int *m, int *n, double *a, int *lda, double *tau, double *work, int *lwork, int *info);
extern "C" void sgeqrf_(int *m, int *n, float *a, int *lda, float *tau, float *work, int *lwork, int *info);
// orgqr
extern "C" void zungqr_(int *m, int *n, int *k, std::complex<double> *a, int *lda, std::complex<double> *tau, std::complex<double> *work, int *lwork, int *info);
extern "C" void cungqr_(int *m, int *n, int *k, std::complex<float> *a, int *lda, std::complex<float> *tau, std::complex<float> *work, int *lwork, int *info);
extern "C" void dorgqr_(int *m, int *n, int *k, double *a, int *lda, double *tau, double *work, int *lwork, int *info);
extern "C" void sorgqr_(int *m, int *n, int *k, float *a, int *lda, float *tau, float *work, int *lwork, int *info);
// syev
extern "C" void dsyev_(char *jobz, char *uplo, int *n, double *a, int *lda, double *w, double *work, int *lwork, int *info);
extern "C" void ssyev_(char *jobz, char *uplo, int *n, float *a, int *lda, float *w, float *work, int *lwork, int *info);
// gesdd
extern "C" void zgesdd_(char *jobz, int *m, int *n, std::complex<double> *a, int *lda,
double *s, std::complex<double> *u, int *ldu, std::complex<double> *vt, int *ldvt, std::complex<double> *work, int *lwork, int *rwork, int *iwork, int *info);
extern "C" void cgesdd_(char *jobz, int *m, int *n, std::complex<float> *a, int *lda,
float *s, std::complex<float> *u, int *ldu, std::complex<float> *vt, int *ldvt, std::complex<float> *work, int *lwork, int *rwork, int *iwork, int *info);
extern "C" void dgesdd_(char *jobz, int *m, int *n, double *a, int *lda,
double *s, double *u, int *ldu, double *vt, int *ldvt, double *work, int *lwork, int *iwork, int *info);
extern "C" void sgesdd_(char *jobz, int *m, int *n, float *a, int *lda,
float *s, float *u, int *ldu, float *vt, int *ldvt, float *work, int *lwork, int *iwork, int *info);
// getrs
extern "C" void zgetrs_(char *trans, int *n, int *nrhs, std::complex<double> *a, int *lda, int *ipiv, std::complex<double> *b, int *ldb, int *info);
extern "C" void cgetrs_(char *trans, int *n, int *nrhs, std::complex<float> *a, int *lda, int *ipiv, std::complex<float> *b, int *ldb, int *info);
extern "C" void dgetrs_(char *trans, int *n, int *nrhs, double *a, int *lda, int *ipiv, double *b, int *ldb, int *info);
extern "C" void sgetrs_(char *trans, int *n, int *nrhs, float *a, int *lda, int *ipiv, float *b, int *ldb, int *info);
#endif
namespace at {
namespace native {
#ifdef USE_LAPACK
// Define the per-batch functions to be used in the main implementation of the batched
// linear algebra operations
template<class scalar_t>
void lapackSolve(int n, int nrhs, scalar_t *a, int lda, int *ipiv, scalar_t *b, int ldb, int *info);
template<class scalar_t>
void lapackLu(int m, int n, scalar_t *a, int lda, int *ipiv, int *info);
template<class scalar_t>
void lapackGetri(int n, scalar_t *a, int lda, int *ipiv, scalar_t *work, int lwork, int *info);
template<class scalar_t>
void lapackCholeskySolve(char uplo, int n, int nrhs, scalar_t *a, int lda, scalar_t *b, int ldb, int *info);
template<class scalar_t>
void lapackCholesky(char uplo, int n, scalar_t *a, int lda, int *info);
template<class scalar_t>
void lapackTriangularSolve(char uplo, char trans, char diag, int n, int nrhs, scalar_t *a, int lda, scalar_t *b, int ldb, int *info);
template<class scalar_t>
void lapackGeqrf(int m, int n, scalar_t *a, int lda, scalar_t *tau, scalar_t *work, int lwork, int *info);
template<class scalar_t>
void lapackOrgqr(int m, int n, int k, scalar_t *a, int lda, scalar_t *tau, scalar_t *work, int lwork, int *info);
template<class scalar_t>
void lapackSymeig(char jobz, char uplo, int n, scalar_t *a, int lda, scalar_t *w, scalar_t *work, int lwork, int *info);
template<class scalar_t, class value_t=scalar_t>
void lapackSvd(char jobz, int m, int n, scalar_t *a, int lda,
value_t *s, scalar_t *u, int ldu, scalar_t *vt, int ldvt, scalar_t *work, int lwork, int *rwork, int *iwork, int *info);
template<class scalar_t>
void lapackLuSolve(char trans, int n, int nrhs, scalar_t *a, int lda, int *ipiv, scalar_t *b, int ldb, int *info);
template<> void lapackSolve<std::complex<double>>(int n, int nrhs, std::complex<double> *a, int lda, int *ipiv, std::complex<double> *b, int ldb, int *info) {
zgesv_(&n, &nrhs, a, &lda, ipiv, b, &ldb, info);
}
template<> void lapackSolve<std::complex<float>>(int n, int nrhs, std::complex<float> *a, int lda, int *ipiv, std::complex<float> *b, int ldb, int *info) {
cgesv_(&n, &nrhs, a, &lda, ipiv, b, &ldb, info);
}
template<> void lapackSolve<double>(int n, int nrhs, double *a, int lda, int *ipiv, double *b, int ldb, int *info) {
dgesv_(&n, &nrhs, a, &lda, ipiv, b, &ldb, info);
}
template<> void lapackSolve<float>(int n, int nrhs, float *a, int lda, int *ipiv, float *b, int ldb, int *info) {
sgesv_(&n, &nrhs, a, &lda, ipiv, b, &ldb, info);
}
template<> void lapackGetri<std::complex<double>>(int n, std::complex<double> *a, int lda, int *ipiv, std::complex<double> *work, int lwork, int *info) {
zgetri_(&n, a, &lda, ipiv, work, &lwork, info);
}
template<> void lapackGetri<std::complex<float>>(int n, std::complex<float> *a, int lda, int *ipiv, std::complex<float> *work, int lwork, int *info) {
cgetri_(&n, a, &lda, ipiv, work, &lwork, info);
}
template<> void lapackGetri<double>(int n, double *a, int lda, int *ipiv, double *work, int lwork, int *info) {
dgetri_(&n, a, &lda, ipiv, work, &lwork, info);
}
template<> void lapackGetri<float>(int n, float *a, int lda, int *ipiv, float *work, int lwork, int *info) {
sgetri_(&n, a, &lda, ipiv, work, &lwork, info);
}
template<> void lapackLu<std::complex<double>>(int m, int n, std::complex<double> *a, int lda, int *ipiv, int *info) {
zgetrf_(&m, &n, a, &lda, ipiv, info);
}
template<> void lapackLu<std::complex<float>>(int m, int n, std::complex<float> *a, int lda, int *ipiv, int *info) {
cgetrf_(&m, &n, a, &lda, ipiv, info);
}
template<> void lapackLu<double>(int m, int n, double *a, int lda, int *ipiv, int *info) {
dgetrf_(&m, &n, a, &lda, ipiv, info);
}
template<> void lapackLu<float>(int m, int n, float *a, int lda, int *ipiv, int *info) {
sgetrf_(&m, &n, a, &lda, ipiv, info);
}
template<> void lapackCholeskySolve<std::complex<double>>(char uplo, int n, int nrhs, std::complex<double> *a, int lda, std::complex<double> *b, int ldb, int *info) {
zpotrs_(&uplo, &n, &nrhs, a, &lda, b, &ldb, info);
}
template<> void lapackCholeskySolve<std::complex<float>>(char uplo, int n, int nrhs, std::complex<float> *a, int lda, std::complex<float> *b, int ldb, int *info) {
cpotrs_(&uplo, &n, &nrhs, a, &lda, b, &ldb, info);
}
template<> void lapackCholeskySolve<double>(char uplo, int n, int nrhs, double *a, int lda, double *b, int ldb, int *info) {
dpotrs_(&uplo, &n, &nrhs, a, &lda, b, &ldb, info);
}
template<> void lapackCholeskySolve<float>(char uplo, int n, int nrhs, float *a, int lda, float *b, int ldb, int *info) {
spotrs_(&uplo, &n, &nrhs, a, &lda, b, &ldb, info);
}
template<> void lapackCholesky<std::complex<double>>(char uplo, int n, std::complex<double> *a, int lda, int *info) {
zpotrf_(&uplo, &n, a, &lda, info);
}
template<> void lapackCholesky<std::complex<float>>(char uplo, int n, std::complex<float> *a, int lda, int *info) {
cpotrf_(&uplo, &n, a, &lda, info);
}
template<> void lapackCholesky<double>(char uplo, int n, double *a, int lda, int *info) {
dpotrf_(&uplo, &n, a, &lda, info);
}
template<> void lapackCholesky<float>(char uplo, int n, float *a, int lda, int *info) {
spotrf_(&uplo, &n, a, &lda, info);
}
template<> void lapackTriangularSolve<std::complex<double>>(char uplo, char trans, char diag, int n, int nrhs, std::complex<double> *a, int lda, std::complex<double> *b, int ldb, int *info) {
ztrtrs_(&uplo, &trans, &diag, &n, &nrhs, a, &lda, b, &ldb, info);
}
template<> void lapackTriangularSolve<std::complex<float>>(char uplo, char trans, char diag, int n, int nrhs, std::complex<float> *a, int lda, std::complex<float> *b, int ldb, int *info) {
ctrtrs_(&uplo, &trans, &diag, &n, &nrhs, a, &lda, b, &ldb, info);
}
template<> void lapackTriangularSolve<double>(char uplo, char trans, char diag, int n, int nrhs, double *a, int lda, double *b, int ldb, int *info) {
dtrtrs_(&uplo, &trans, &diag, &n, &nrhs, a, &lda, b, &ldb, info);
}
template<> void lapackTriangularSolve<float>(char uplo, char trans, char diag, int n, int nrhs, float *a, int lda, float *b, int ldb, int *info) {
strtrs_(&uplo, &trans, &diag, &n, &nrhs, a, &lda, b, &ldb, info);
}
template<> void lapackGeqrf<std::complex<double>>(int m, int n, std::complex<double> *a, int lda, std::complex<double> *tau, std::complex<double> *work, int lwork, int *info) {
zgeqrf_(&m, &n, a, &lda, tau, work, &lwork, info);
}
template<> void lapackGeqrf<std::complex<float>>(int m, int n, std::complex<float> *a, int lda, std::complex<float> *tau, std::complex<float> *work, int lwork, int *info) {
cgeqrf_(&m, &n, a, &lda, tau, work, &lwork, info);
}
template<> void lapackGeqrf<double>(int m, int n, double *a, int lda, double *tau, double *work, int lwork, int *info) {
dgeqrf_(&m, &n, a, &lda, tau, work, &lwork, info);
}
template<> void lapackGeqrf<float>(int m, int n, float *a, int lda, float *tau, float *work, int lwork, int *info) {
sgeqrf_(&m, &n, a, &lda, tau, work, &lwork, info);
}
template<> void lapackOrgqr<std::complex<double>>(int m, int n, int k, std::complex<double> *a, int lda, std::complex<double> *tau, std::complex<double> *work, int lwork, int *info) {
zungqr_(&m, &n, &k, a, &lda, tau, work, &lwork, info);
}
template<> void lapackOrgqr<std::complex<float>>(int m, int n, int k, std::complex<float> *a, int lda, std::complex<float> *tau, std::complex<float> *work, int lwork, int *info) {
cungqr_(&m, &n, &k, a, &lda, tau, work, &lwork, info);
}
template<> void lapackOrgqr<double>(int m, int n, int k, double *a, int lda, double *tau, double *work, int lwork, int *info) {
dorgqr_(&m, &n, &k, a, &lda, tau, work, &lwork, info);
}
template<> void lapackOrgqr<float>(int m, int n, int k, float *a, int lda, float *tau, float *work, int lwork, int *info) {
sorgqr_(&m, &n, &k, a, &lda, tau, work, &lwork, info);
}
template<> void lapackSymeig<double>(char jobz, char uplo, int n, double *a, int lda, double *w, double *work, int lwork, int *info) {
dsyev_(&jobz, &uplo, &n, a, &lda, w, work, &lwork, info);
}
template<> void lapackSymeig<float>(char jobz, char uplo, int n, float *a, int lda, float *w, float *work, int lwork, int *info) {
ssyev_(&jobz, &uplo, &n, a, &lda, w, work, &lwork, info);
}
template<> void lapackSvd<std::complex<double>, double>(char jobz, int m, int n, std::complex<double> *a, int lda,
double *s, std::complex<double> *u, int ldu, std::complex<double> *vt, int ldvt, std::complex<double> *work, int lwork, int *rwork, int *iwork, int *info) {
zgesdd_(&jobz, &m, &n, a, &lda, s, u, &ldu, vt, &ldvt, work, &lwork, rwork, iwork, info);
}
template<> void lapackSvd<std::complex<float>, float>(char jobz, int m, int n, std::complex<float> *a, int lda,
float *s, std::complex<float> *u, int ldu, std::complex<float> *vt, int ldvt, std::complex<float> *work, int lwork, int *rwork, int *iwork, int *info) {
cgesdd_(&jobz, &m, &n, a, &lda, s, u, &ldu, vt, &ldvt, work, &lwork, rwork, iwork, info);
}
template<> void lapackSvd<double>(char jobz, int m, int n, double *a, int lda,
double *s, double *u, int ldu, double *vt, int ldvt, double *work, int lwork, int *rwork, int *iwork, int *info) {
dgesdd_(&jobz, &m, &n, a, &lda, s, u, &ldu, vt, &ldvt, work, &lwork, iwork, info);
}
template<> void lapackSvd<float>(char jobz, int m, int n, float *a, int lda,
float *s, float *u, int ldu, float *vt, int ldvt, float *work, int lwork, int *rwork, int *iwork, int *info) {
sgesdd_(&jobz, &m, &n, a, &lda, s, u, &ldu, vt, &ldvt, work, &lwork, iwork, info);
}
template<> void lapackLuSolve<std::complex<double>>(char trans, int n, int nrhs, std::complex<double> *a, int lda, int *ipiv, std::complex<double> *b, int ldb, int *info) {
zgetrs_(&trans, &n, &nrhs, a, &lda, ipiv, b, &ldb, info);
}
template<> void lapackLuSolve<std::complex<float>>(char trans, int n, int nrhs, std::complex<float> *a, int lda, int *ipiv, std::complex<float> *b, int ldb, int *info) {
cgetrs_(&trans, &n, &nrhs, a, &lda, ipiv, b, &ldb, info);
}
template<> void lapackLuSolve<double>(char trans, int n, int nrhs, double *a, int lda, int *ipiv, double *b, int ldb, int *info) {
dgetrs_(&trans, &n, &nrhs, a, &lda, ipiv, b, &ldb, info);
}
template<> void lapackLuSolve<float>(char trans, int n, int nrhs, float *a, int lda, int *ipiv, float *b, int ldb, int *info) {
sgetrs_(&trans, &n, &nrhs, a, &lda, ipiv, b, &ldb, info);
}
#endif
// Below of the definitions of the functions operating on a batch that are going to be dispatched
// in the main helper functions for the linear algebra operations
// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ solve ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
template<typename scalar_t>
static void apply_solve(Tensor& b, Tensor& A, std::vector<int64_t>& infos) {
#ifndef USE_LAPACK
AT_ERROR("solve: LAPACK library not found in compilation");
#else
auto A_data = A.data_ptr<scalar_t>();
auto b_data = b.data_ptr<scalar_t>();
auto A_mat_stride = matrixStride(A);
auto b_mat_stride = matrixStride(b);
auto batch_size = batchCount(A);
auto n = A.size(-2);
auto nrhs = b.size(-1);
auto ipiv = at::empty({n}, b.options().dtype(kInt));
auto ipiv_data = ipiv.data_ptr<int>();
int info;
for (int64_t i = 0; i < batch_size; i++) {
scalar_t* A_working_ptr = &A_data[i * A_mat_stride];
scalar_t* b_working_ptr = &b_data[i * b_mat_stride];
lapackSolve<scalar_t>(n, nrhs, A_working_ptr, n, ipiv_data, b_working_ptr, n, &info);
infos[i] = info;
if (info != 0) {
return;
}
}
#endif
}
std::tuple<Tensor, Tensor> _solve_helper_cpu(const Tensor& self, const Tensor& A) {
auto self_working_copy = cloneBatchedColumnMajor(self);
auto A_working_copy = cloneBatchedColumnMajor(A);
std::vector<int64_t> infos(batchCount(self), 0);
AT_DISPATCH_FLOATING_AND_COMPLEX_TYPES(self.scalar_type(), "solve_cpu", [&]{
apply_solve<scalar_t>(self_working_copy, A_working_copy, infos);
});
if (self.dim() > 2) {
batchCheckErrors(infos, "solve_cpu");
} else {
singleCheckErrors(infos[0], "solve_cpu");
}
return std::tuple<Tensor, Tensor>(self_working_copy, A_working_copy);
}
// Supports arbitrary batch dimensions for self and A
std::tuple<Tensor,Tensor> solve(const Tensor& self, const Tensor& A) {
TORCH_CHECK(self.dim() >= 2,
"B should have at least 2 dimensions, but has ", self.dim(), " dimensions instead");
TORCH_CHECK(A.dim() >= 2,
"A should have at least 2 dimensions, but has ", A.dim(), " dimensions instead");
Tensor self_broadcasted, A_broadcasted;
std::tie(self_broadcasted, A_broadcasted) = _linalg_broadcast_batch_dims(self, A, "solve");
return at::_solve_helper(self_broadcasted, A_broadcasted);
}
std::tuple<Tensor&,Tensor&> solve_out(Tensor& solution, Tensor& lu, const Tensor& self, const Tensor& A) {
Tensor solution_tmp, lu_tmp;
std::tie(solution_tmp, lu_tmp) = at::_solve_helper(self, A);
solution.resize_as_(solution_tmp).copy_(solution_tmp);
lu.resize_as_(lu_tmp).copy_(lu_tmp);
return std::tuple<Tensor&, Tensor&>(solution, lu);
}
// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ inverse ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
template <typename scalar_t>
static void apply_inverse(Tensor& self, std::vector<int64_t>& infos) {
#ifndef USE_LAPACK
AT_ERROR("inverse: LAPACK library not found in compilation");
#else
using value_t = typename ztype<scalar_t>::value_t;
auto self_data = self.data_ptr<scalar_t>();
auto self_matrix_stride = matrixStride(self);
auto batch_size = batchCount(self);
auto n = self.size(-2);
auto ipiv = at::empty({n}, self.options().dtype(kInt));
auto ipiv_data = ipiv.data_ptr<int>();
int info;
// Run once, first to get the optimum work size
// Since we deal with batches of matrices with the same dimensions, doing this outside
// the loop saves (batch_size - 1) workspace queries which would provide the same result
// and (batch_size - 1) calls to allocate and deallocate workspace using at::empty()
int lwork = -1;
scalar_t wkopt;
lapackGetri<scalar_t>(n, self_data, n, ipiv_data, &wkopt, lwork, &info);
lwork = static_cast<int>(real_impl<scalar_t, value_t>(wkopt));
Tensor work = at::empty({lwork}, self.options());
auto work_data = work.data_ptr<scalar_t>();
for (int64_t i = 0; i < batch_size; i++) {
scalar_t* self_working_ptr = &self_data[i * self_matrix_stride];
lapackLu<scalar_t>(n, n, self_working_ptr, n, ipiv_data, &info);
infos[i] = info;
if (info != 0) {
return;
}
// now compute the actual inverse
lapackGetri<scalar_t>(n, self_working_ptr, n, ipiv_data, work_data, lwork, &info);
infos[i] = info;
if (info != 0) {
return;
}
}
#endif
}
Tensor _inverse_helper_cpu(const Tensor& self) {
std::vector<int64_t> infos(batchCount(self), 0);
auto self_working_copy = cloneBatchedColumnMajor(self);
AT_DISPATCH_FLOATING_AND_COMPLEX_TYPES(self.scalar_type(), "inverse_cpu", [&]{
apply_inverse<scalar_t>(self_working_copy, infos);
});
if (self.dim() > 2) {
batchCheckErrors(infos, "inverse_cpu");
} else {
singleCheckErrors(infos[0], "inverse_cpu");
}
return self_working_copy;
}
Tensor inverse(const Tensor &self) {
if (self.size(-1) == 0) {
return at::empty_like(self, LEGACY_CONTIGUOUS_MEMORY_FORMAT);
}
squareCheckInputs(self);
return at::_inverse_helper(self);
}
Tensor& inverse_out(Tensor &result, const Tensor &self) {
if (self.size(-1) == 0) {
return result.resize_as_(self);
}
result.copy_(native::inverse(self));
return result;
}
// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ cholesky_solve ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
template<typename scalar_t>
static void apply_cholesky_solve(Tensor& b, Tensor& A, bool upper, std::vector<int64_t>& infos) {
#ifndef USE_LAPACK
AT_ERROR("cholesky_solve: LAPACK library not found in compilation");
#else
char uplo = upper ? 'U' : 'L';
auto A_data = A.data_ptr<scalar_t>();
auto b_data = b.data_ptr<scalar_t>();
auto A_mat_stride = matrixStride(A);
auto b_mat_stride = matrixStride(b);
auto batch_size = batchCount(A);
auto n = A.size(-2);
auto nrhs = b.size(-1);
int info;
for (int64_t i = 0; i < batch_size; i++) {
scalar_t* A_working_ptr = &A_data[i * A_mat_stride];
scalar_t* b_working_ptr = &b_data[i * b_mat_stride];
lapackCholeskySolve<scalar_t>(uplo, n, nrhs, A_working_ptr, n, b_working_ptr, n, &info);
infos[i] = info;
if (info != 0) {
return;
}
}
#endif
}
Tensor _cholesky_solve_helper_cpu(const Tensor& self, const Tensor& A, bool upper) {
auto self_working_copy = cloneBatchedColumnMajor(self);
auto A_working_copy = cloneBatchedColumnMajor(A);
std::vector<int64_t> infos(batchCount(self), 0);
AT_DISPATCH_FLOATING_AND_COMPLEX_TYPES(self.scalar_type(), "cholesky_solve_cpu", [&]{
apply_cholesky_solve<scalar_t>(self_working_copy, A_working_copy, upper, infos);
});
if (self.dim() > 2) {
batchCheckErrors(infos, "cholesky_solve_cpu");
} else {
singleCheckErrors(infos[0], "cholesky_solve_cpu");
}
return self_working_copy;
}
// Supports arbitrary batch dimensions for self and A
Tensor cholesky_solve(const Tensor& self, const Tensor& A, bool upper) {
TORCH_CHECK(self.dim() >= 2,
"b should have at least 2 dimensions, but has ", self.dim(), " dimensions instead");
TORCH_CHECK(A.dim() >= 2,
"u should have at least 2 dimensions, but has ", A.dim(), " dimensions instead");
Tensor self_broadcasted, A_broadcasted;
std::tie(self_broadcasted, A_broadcasted) = _linalg_broadcast_batch_dims(self, A, "cholesky_solve");
return at::_cholesky_solve_helper(self_broadcasted, A_broadcasted, upper);
}
Tensor& cholesky_solve_out(Tensor& result, const Tensor& self, const Tensor& A, bool upper) {
Tensor result_tmp;
result_tmp = at::_cholesky_solve_helper(self, A, upper);
result.resize_as_(result_tmp).copy_(result_tmp);
return result;
}
// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ cholesky ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
template<typename scalar_t>
static void apply_cholesky(Tensor& self, bool upper, std::vector<int64_t>& infos) {
#ifndef USE_LAPACK
AT_ERROR("cholesky: LAPACK library not found in compilation");
#else
char uplo = upper ? 'U' : 'L';
auto self_data = self.data_ptr<scalar_t>();
auto self_matrix_stride = matrixStride(self);
auto batch_size = batchCount(self);
auto n = self.size(-2);
int info;
for (int64_t i = 0; i < batch_size; i++) {
scalar_t* self_working_ptr = &self_data[i * self_matrix_stride];
lapackCholesky<scalar_t>(uplo, n, self_working_ptr, n, &info);
infos[i] = info;
if (info != 0) {
return;
}
}
#endif
}
Tensor _cholesky_helper_cpu(const Tensor& self, bool upper) {
std::vector<int64_t> infos(batchCount(self), 0);
auto self_working_copy = cloneBatchedColumnMajor(self);
AT_DISPATCH_FLOATING_AND_COMPLEX_TYPES(self.scalar_type(), "cholesky_cpu", [&]{
apply_cholesky<scalar_t>(self_working_copy, upper, infos);
});
if (self.dim() > 2) {
batchCheckErrors(infos, "cholesky_cpu");
} else {
singleCheckErrors(infos[0], "cholesky_cpu");
}
return self_working_copy;
}
Tensor cholesky(const Tensor &self, bool upper) {
if (self.size(-1) == 0) {
return at::empty_like(self, LEGACY_CONTIGUOUS_MEMORY_FORMAT);
}
squareCheckInputs(self);
auto raw_cholesky_output = at::_cholesky_helper(self, upper);
if (upper) {
return raw_cholesky_output.triu_();
} else {
return raw_cholesky_output.tril_();
}
}
Tensor& cholesky_out(Tensor &result, const Tensor &self, bool upper) {
if (self.size(-1) == 0) {
return result.resize_as_(self);
}
result.copy_(native::cholesky(self, upper));
return result;
}
// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ lu ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
template<typename scalar_t>
static void apply_lu(Tensor& self, Tensor& pivots, Tensor& infos) {
#ifndef USE_LAPACK
AT_ERROR("lu: LAPACK library not found in compilation");
#else
auto self_data = self.data_ptr<scalar_t>();
auto pivots_data = pivots.data_ptr<int>();
auto infos_data = infos.data_ptr<int>();
auto self_matrix_stride = matrixStride(self);
auto pivots_matrix_stride = pivots.size(-1);
auto batch_size = batchCount(self);
auto m = self.size(-2);
auto n = self.size(-1);
for (int64_t i = 0; i < batch_size; i++) {
scalar_t* self_working_ptr = &self_data[i * self_matrix_stride];
int* pivots_working_ptr = &pivots_data[i * pivots_matrix_stride];
int* infos_working_ptr = &infos_data[i];
lapackLu<scalar_t>(m, n, self_working_ptr, m, pivots_working_ptr, infos_working_ptr);
}
#endif
}
std::tuple<Tensor, Tensor, Tensor> _lu_with_info_cpu(const Tensor& self, bool pivot, bool check_errors) {
TORCH_CHECK(pivot, "lu without pivoting is not implemented on the CPU");
TORCH_CHECK(self.dim() >= 2,
"expected tensor with 2 or more dimensions, got size: ", self.sizes(),
" instead");
auto m = self.size(-2);
auto n = self.size(-1);
auto req_size = self.sizes().vec();
req_size.pop_back();
req_size.back() = std::min(m, n);
auto pivots_tensor = at::empty(req_size, self.options().dtype(kInt));
req_size.pop_back();
auto infos_tensor = at::zeros(req_size, self.options().dtype(kInt));
Tensor self_working_copy;
if (self.numel() == 0) {
self_working_copy = at::empty_like(self, LEGACY_CONTIGUOUS_MEMORY_FORMAT);
} else {
self_working_copy = cloneBatchedColumnMajor(self);
AT_DISPATCH_FLOATING_AND_COMPLEX_TYPES(self.scalar_type(), "lu_cpu", [&]{
apply_lu<scalar_t>(self_working_copy, pivots_tensor, infos_tensor);
});
}
if (check_errors) {
if (self.dim() > 2) {
batchCheckErrors(infos_tensor, "lu", /*allow_singular=*/true);
} else {
singleCheckErrors(infos_tensor.item<int64_t>(), "lu", /*allow_singular=*/true);
}
}
return std::make_tuple(self_working_copy, pivots_tensor, infos_tensor);
}
// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ triangular_solve ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
template<typename scalar_t>
static void apply_triangular_solve(Tensor& b, Tensor& A, bool upper, bool transpose, bool unitriangular) {
#ifndef USE_LAPACK
AT_ERROR("triangular_solve: LAPACK library not found in compilation");
#else
char uplo = upper ? 'U' : 'L';
char trans = transpose ? 'T' : 'N';
char diag = unitriangular ? 'U' : 'N';
auto A_data = A.data_ptr<scalar_t>();
auto b_data = b.data_ptr<scalar_t>();
auto A_mat_stride = matrixStride(A);
auto b_mat_stride = matrixStride(b);
auto batch_size = batchCount(A);
auto n = A.size(-2);
auto nrhs = b.size(-1);
int info;
for (int64_t i = 0; i < batch_size; i++) {
scalar_t* A_working_ptr = &A_data[i * A_mat_stride];
scalar_t* b_working_ptr = &b_data[i * b_mat_stride];
lapackTriangularSolve<scalar_t>(uplo, trans, diag, n, nrhs, A_working_ptr, n, b_working_ptr, n, &info);
}
#endif
}
std::tuple<Tensor, Tensor> _triangular_solve_helper_cpu(const Tensor& self, const Tensor& A,
bool upper, bool transpose, bool unitriangular) {
auto self_working_copy = cloneBatchedColumnMajor(self);
auto A_working_copy = cloneBatchedColumnMajor(A);
AT_DISPATCH_FLOATING_AND_COMPLEX_TYPES(self.scalar_type(), "triangular_solve_cpu", [&]{
apply_triangular_solve<scalar_t>(self_working_copy, A_working_copy, upper, transpose, unitriangular);
});
return std::tuple<Tensor, Tensor>(self_working_copy, A_working_copy);
}
// Supports arbitrary batch dimensions for self and A
std::tuple<Tensor, Tensor> triangular_solve(const Tensor& self, const Tensor& A,
bool upper, bool transpose, bool unitriangular) {
TORCH_CHECK(self.dim() >= 2,
"b should have at least 2 dimensions, but has ", self.dim(), " dimensions instead");
TORCH_CHECK(A.dim() >= 2,
"u should have at least 2 dimensions, but has ", A.dim(), " dimensions instead");
Tensor self_broadcasted, A_broadcasted;
std::tie(self_broadcasted, A_broadcasted) = _linalg_broadcast_batch_dims(self, A, "triangular_solve");
return at::_triangular_solve_helper(self_broadcasted, A_broadcasted, upper, transpose, unitriangular);
}
std::tuple<Tensor&, Tensor&> triangular_solve_out(Tensor& result, Tensor& clone_A, const Tensor& self, const Tensor& A,
bool upper, bool transpose, bool unitriangular) {
Tensor result_tmp, clone_A_tmp;
std::tie(result_tmp, clone_A_tmp) = at::_triangular_solve_helper(self, A, upper, transpose, unitriangular);
result.resize_as_(result_tmp).copy_(result_tmp);
clone_A.resize_as_(clone_A_tmp).copy_(clone_A_tmp);
return std::tuple<Tensor&, Tensor&>(result, clone_A);
}
// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ qr ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
template<typename scalar_t>
static void apply_geqrf(Tensor& self, Tensor& tau, int64_t m, int64_t n,
std::vector<int64_t>& infos) {
#ifndef USE_LAPACK
AT_ERROR("qr: LAPACK library not found in compilation");
#else
using value_t = typename ztype<scalar_t>::value_t;
auto self_data = self.data_ptr<scalar_t>();
auto tau_data = tau.data_ptr<scalar_t>();
auto self_matrix_stride = matrixStride(self);
auto tau_stride = tau.size(-1);
auto batch_size = batchCount(self);
int info;
// Run once, first to get the optimum work size.
// Since we deal with batches of matrices with the same dimensions, doing this outside
// the loop saves (batch_size - 1) workspace queries which would provide the same result
// and (batch_size - 1) calls to allocate and deallocate workspace using at::empty()
int lwork = -1;
scalar_t wkopt;
lapackGeqrf<scalar_t>(m, n, self_data, m, tau_data, &wkopt, lwork, &info);
lwork = static_cast<int>(real_impl<scalar_t, value_t>(wkopt));
Tensor work = at::empty({lwork}, self.options());
for (int64_t i = 0; i < batch_size; i++) {
scalar_t* self_working_ptr = &self_data[i * self_matrix_stride];
scalar_t* tau_working_ptr = &tau_data[i * tau_stride];
// now compute the actual R and TAU
lapackGeqrf<scalar_t>(m, n, self_working_ptr, m, tau_working_ptr, work.data_ptr<scalar_t>(), lwork, &info);
infos[i] = info;
if (info != 0) {
return;
}
}
#endif
}
template<typename scalar_t>
static void apply_orgqr(Tensor& self, const Tensor& tau, int64_t m, int64_t n_columns,
int64_t k, std::vector<int64_t>& infos) {
#ifndef USE_LAPACK
AT_ERROR("qr: LAPACK library not found in compilation");
#else
using value_t = typename ztype<scalar_t>::value_t;
auto self_data = self.data_ptr<scalar_t>();
auto tau_data = tau.data_ptr<scalar_t>();
auto self_matrix_stride = matrixStride(self);
auto tau_stride = tau.size(-1);
auto batch_size = batchCount(self);
int info;
// Run once, first to get the optimum work size.
// Since we deal with batches of matrices with the same dimensions, doing this outside
// the loop saves (batch_size - 1) workspace queries which would provide the same result
// and (batch_size - 1) calls to allocate and deallocate workspace using at::empty()
int lwork = -1;
scalar_t wkopt;
lapackOrgqr<scalar_t>(m, n_columns, k, self_data, m, tau_data, &wkopt, lwork, &info);
lwork = static_cast<int>(real_impl<scalar_t, value_t>(wkopt));
Tensor work = at::empty({lwork}, self.options());
for (int64_t i = 0; i < batch_size; i++) {
scalar_t* self_working_ptr = &self_data[i * self_matrix_stride];
scalar_t* tau_working_ptr = &tau_data[i * tau_stride];
// now compute the actual Q
lapackOrgqr<scalar_t>(m, n_columns, k, self_working_ptr, m, tau_working_ptr, work.data_ptr<scalar_t>(), lwork, &info);
infos[i] = info;
if (info != 0) {
return;
}
}
#endif
}
std::tuple<Tensor, Tensor> _qr_helper_cpu(const Tensor& self, bool some) {
std::vector<int64_t> infos(batchCount(self), 0);
int64_t m = self.size(-2), n = self.size(-1);
// Setup inputs for apply_geqrf
auto self_sizes = self.sizes().vec();
self_sizes.pop_back();
self_sizes[self.dim() - 2] = std::min(m, n);
auto tau_working_copy = at::empty(self_sizes, self.options());
Tensor q_working_copy;
// Setup input geometry for apply_orgqr
std::vector<int64_t> q_sizes, q_strides;
int64_t n_columns_q;
Tensor R;
std::tie(q_sizes, q_strides, n_columns_q) = _compute_geometry_for_Q(self, some);
// If there are no elements, then we simply return a pair of tensors of required dimensions
if (self.numel() == 0) {
// Fix the number of columns of q appropriately
q_sizes[self.dim() - 1] = n_columns_q;
q_working_copy = at::eye(q_sizes[self.dim() - 2], q_sizes[self.dim() - 1], self.options());
q_working_copy = q_working_copy.expand_as(q_working_copy);
// We repurpose the same q_sizes for R
// Fix the number of rows and columns of q_working_copy appropriately
q_sizes[self.dim() - 1] = n;
q_sizes[self.dim() - 2] = n_columns_q;
R = at::empty(q_sizes, self.options());
return std::make_tuple(q_working_copy, R);
}
// First perform GEQRF for R and TAU (the elementary reflectors)
// We will need to generate R from the upper triangular matrix from the
// matrix input to GEQRF.
q_working_copy = at::empty_strided(q_sizes, q_strides, self.options());
q_working_copy.narrow(-1, 0, n).copy_(self);
AT_DISPATCH_FLOATING_AND_COMPLEX_TYPES(self.scalar_type(), "qr_cpu", [&]{
apply_geqrf<scalar_t>(q_working_copy, tau_working_copy, m, n, infos);
});
if (self.dim() > 2) {
batchCheckErrors(infos, "qr_cpu");
} else {
singleCheckErrors(infos[0], "qr_cpu");
}
R = q_working_copy.slice(-2, 0, n_columns_q).slice(-1, 0, n).triu();
// Next perform ORGQR for Q using the results (both raw R and TAU) from GEQRF
AT_DISPATCH_FLOATING_AND_COMPLEX_TYPES(self.scalar_type(), "qr_cpu", [&]{
apply_orgqr<scalar_t>(q_working_copy, tau_working_copy, m, n_columns_q, std::min(m, n), infos);
});
if (self.dim() > 2) {
batchCheckErrors(infos, "qr_cpu");
} else {
singleCheckErrors(infos[0], "qr_cpu");
}
return std::make_tuple(q_working_copy.narrow(-1, 0, n_columns_q), R);
}
std::tuple<Tensor,Tensor> qr(const Tensor& self, bool some) {
TORCH_CHECK(self.dim() >= 2,
"self should have at least 2 dimensions, but has ", self.dim(), " dimensions instead");
return at::_qr_helper(self, some);
}
std::tuple<Tensor&,Tensor&> qr_out(Tensor& Q, Tensor& R, const Tensor& self, bool some) {
TORCH_CHECK(self.dim() >= 2,
"self should have at least 2 dimensions, but has ", self.dim(), " dimensions instead");
Tensor Q_tmp, R_tmp;
std::tie(Q_tmp, R_tmp) = at::_qr_helper(self, some);
Q.resize_as_(Q_tmp).copy_(Q_tmp);
R.resize_as_(R_tmp).copy_(R_tmp);
return std::tuple<Tensor&, Tensor&>(Q, R);
}
// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ symeig ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
template <typename scalar_t>
static void apply_symeig(Tensor& self, Tensor& eigvals, bool eigenvectors, bool upper, std::vector<int64_t>& infos) {
#ifndef USE_LAPACK
AT_ERROR("symeig: LAPACK library not found in compilation");
#else
using value_t = typename ztype<scalar_t>::value_t;
auto self_data = self.data_ptr<scalar_t>();
auto eigvals_data = eigvals.data_ptr<scalar_t>();
auto self_matrix_stride = matrixStride(self);
auto eigvals_stride = eigvals.size(-1);
auto batch_size = batchCount(self);
auto n = self.size(-1);
char uplo = upper ? 'U' : 'L';
char jobz = eigenvectors ? 'V' : 'N';
int info;
// Run once, first to get the optimum work size.
// Since we deal with batches of matrices with the same dimensions, doing this outside
// the loop saves (batch_size - 1) workspace queries which would provide the same result
// and (batch_size - 1) calls to allocate and deallocate workspace using at::empty()
int lwork = -1;
scalar_t wkopt;
lapackSymeig<scalar_t>(jobz, uplo, n, self_data, n, eigvals_data, &wkopt, lwork, &info);
lwork = static_cast<int>(real_impl<scalar_t, value_t>(wkopt));
Tensor work = at::empty({lwork}, self.options());
for (int64_t i = 0; i < batch_size; i++) {
scalar_t* self_working_ptr = &self_data[i * self_matrix_stride];
scalar_t* eigvals_working_ptr = &eigvals_data[i * eigvals_stride];
// now compute the eigenvalues and the eigenvectors (optionally)
lapackSymeig<scalar_t>(jobz, uplo, n, self_working_ptr, n, eigvals_working_ptr, work.data_ptr<scalar_t>(), lwork, &info);
infos[i] = info;
if (info != 0) {
return;
}
}
#endif
}
std::tuple<Tensor, Tensor> _symeig_helper_cpu(const Tensor& self, bool eigenvectors, bool upper) {
std::vector<int64_t> infos(batchCount(self), 0);
auto self_sizes = self.sizes().vec();
self_sizes.pop_back();
auto eigvals = at::empty(self_sizes, self.options());
if (self.numel() == 0) {
return std::tuple<Tensor, Tensor>(eigvals, at::empty_like(self, LEGACY_CONTIGUOUS_MEMORY_FORMAT));
}
auto self_working_copy = cloneBatchedColumnMajor(self);
AT_DISPATCH_FLOATING_TYPES(self.scalar_type(), "symeig_cpu", [&]{
apply_symeig<scalar_t>(self_working_copy, eigvals, eigenvectors, upper, infos);
});
if (self.dim() > 2) {
batchCheckErrors(infos, "symeig_cpu");
} else {
singleCheckErrors(infos[0], "symeig_cpu");
}
if (eigenvectors) {
return std::tuple<Tensor, Tensor>(eigvals, self_working_copy);
} else {
return std::tuple<Tensor, Tensor>(eigvals, at::empty({0}, self.options()));
}
}
std::tuple<Tensor, Tensor> symeig(const Tensor& self, bool eigenvectors, bool upper) {
squareCheckInputs(self);
return at::_symeig_helper(self, eigenvectors, upper);
}
std::tuple<Tensor&, Tensor&> symeig_out(Tensor& vals, Tensor& vecs, const Tensor& self, bool eigenvectors, bool upper) {
squareCheckInputs(self);
Tensor vals_tmp, vecs_tmp;
std::tie(vals_tmp, vecs_tmp) = at::_symeig_helper(self, eigenvectors, upper);
vals.resize_as_(vals_tmp).copy_(vals_tmp);
vecs.resize_as_(vecs_tmp).copy_(vecs_tmp);
return std::tuple<Tensor&, Tensor&>(vals, vecs);
}
// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ svd ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
template <typename scalar_t>
static void apply_svd(Tensor& self, Tensor& U, Tensor& S, Tensor& VT,
char jobz, std::vector<int64_t>& infos) {
#ifndef USE_LAPACK
AT_ERROR("svd: LAPACK library not found in compilation");
#else
using value_t = typename ztype<scalar_t>::value_t;
auto self_data = self.data_ptr<scalar_t>();
auto U_data = U.data_ptr<scalar_t>();
auto S_data = S.data_ptr<value_t>();
auto VT_data = VT.data_ptr<scalar_t>();
auto self_stride = matrixStride(self);
auto U_stride = matrixStride(U);
auto S_stride = S.size(-1);
auto VT_stride = matrixStride(VT);
auto batchsize = batchCount(self);
int info;
auto m = self.size(-2);
auto n = self.size(-1);
auto mn = std::min(m, n);
Tensor iwork = at::empty({8*mn}, at::kInt);
auto iwork_data = iwork.data_ptr<int>();
Tensor rwork;
int* rwork_data = nullptr;
if (isComplexType(at::typeMetaToScalarType(self.dtype()))) {
auto mx = std::max(m, n);
int64_t lrwork; // These settings are valid for on LAPACK 3.6+
if (jobz == 'N'){
lrwork = 7 * mn;
}else if (mx > 10 * mn){
lrwork = 7 * mn * mn + 7 * mn;
} else {
lrwork = std::max(7 * mn * mn + 7 * mn, 2 * mx * mn + 2 *mn * mn + mn);
}
rwork = at::empty({std::max(int64_t(1), lrwork)}, at::kInt);
rwork_data = rwork.data_ptr<int>();
}
// Run once, first to get the optimum work size.
// Since we deal with batches of matrices with the same dimensions, doing this outside
// the loop saves (batch_size - 1) workspace queries which would provide the same result
// and (batch_size - 1) calls to allocate and deallocate workspace using at::empty()
int lwork = -1;
scalar_t wkopt;
lapackSvd<scalar_t, value_t>(jobz, m, n, self_data, m, S_data, U_data, m, VT_data, n, &wkopt, lwork, rwork_data, iwork_data, &info);
lwork = static_cast<int>(real_impl<scalar_t, value_t>(wkopt));
Tensor work = at::empty({lwork}, self.options());
auto work_data = work.data_ptr<scalar_t>();
for (int64_t i = 0; i < batchsize; i++) {
scalar_t* self_working_ptr = &self_data[i * self_stride];
value_t* S_working_ptr = &S_data[i * S_stride];
scalar_t* U_working_ptr = &U_data[i * U_stride];
scalar_t* VT_working_ptr = &VT_data[i * VT_stride];
// Compute S, U (optionally) and VT (optionally)
lapackSvd<scalar_t, value_t>(jobz, m, n, self_working_ptr, m,
S_working_ptr, U_working_ptr, m, VT_working_ptr, n, work_data, lwork, rwork_data, iwork_data, &info);
infos[i] = info;
if (info != 0) {
return;
}
}
#endif
}
std::tuple<Tensor, Tensor, Tensor> _svd_helper_cpu(const Tensor& self, bool some, bool compute_uv) {
std::vector<int64_t> infos(batchCount(self), 0);
int64_t m = self.size(-2), n = self.size(-1);