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BatchLinearAlgebra.cpp
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#include <ATen/ATen.h>
#include <ATen/CPUApplyUtils.h>
#include <ATen/Dispatch.h>
#include <ATen/TensorMeta.h>
#include <ATen/NativeFunctions.h>
#include <ATen/ExpandUtils.h>
#include <ATen/native/BatchLinearAlgebra.h>
#include <ATen/native/LinearAlgebraUtils.h>
#include <ATen/native/Resize.h>
#include <ATen/native/cpu/zmath.h>
#include <ATen/Parallel.h>
#include <c10/util/irange.h>
#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
#if AT_BUILD_WITH_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);
// potri
extern "C" void zpotri_(char *uplo, int *n, std::complex<double> *a, int *lda, int *info);
extern "C" void cpotri_(char *uplo, int *n, std::complex<float> *a, int *lda, int *info);
extern "C" void dpotri_(char *uplo, int *n, double *a, int *lda, int *info);
extern "C" void spotri_(char *uplo, int *n, float *a, int *lda, 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);
// ormqr
extern "C" void zunmqr_(char *side, char *trans, int *m, int *n, int *k, std::complex<double> *a, int *lda, std::complex<double> *tau, std::complex<double> *c, int *ldc, std::complex<double> *work, int *lwork, int *info);
extern "C" void cunmqr_(char *side, char *trans, int *m, int *n, int *k, std::complex<float> *a, int *lda, std::complex<float> *tau, std::complex<float> *c, int *ldc, std::complex<float> *work, int *lwork, int *info);
extern "C" void dormqr_(char *side, char *trans, int *m, int *n, int *k, double *a, int *lda, double *tau, double *c, int *ldc, double *work, int *lwork, int *info);
extern "C" void sormqr_(char *side, char *trans, int *m, int *n, int *k, float *a, int *lda, float *tau, float *c, int *ldc, float *work, int *lwork, int *info);
// syev
extern "C" void zheev_(char *jobz, char *uplo, int *n, std::complex<double> *a, int *lda, double *w, std::complex<double> *work, int *lwork, double *rwork, int *info);
extern "C" void cheev_(char *jobz, char *uplo, int *n, std::complex<float> *a, int *lda, float *w, std::complex<float> *work, int *lwork, float *rwork, int *info);
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);
// syevd
extern "C" void zheevd_(char *jobz, char *uplo, int *n, std::complex<double> *a, int *lda, double *w, std::complex<double> *work, int *lwork, double *rwork, int *lrwork, int *iwork, int *liwork, int *info);
extern "C" void cheevd_(char *jobz, char *uplo, int *n, std::complex<float> *a, int *lda, float *w, std::complex<float> *work, int *lwork, float *rwork, int *lrwork, int *iwork, int *liwork, int *info);
extern "C" void dsyevd_(char *jobz, char *uplo, int *n, double *a, int *lda, double *w, double *work, int *lwork, int *iwork, int *liwork, int *info);
extern "C" void ssyevd_(char *jobz, char *uplo, int *n, float *a, int *lda, float *w, float *work, int *lwork, int *iwork, int *liwork, int *info);
// geev
extern "C" void dgeev_(char *jobvl, char *jobvr, int *n, double *a, int *lda, double *wr, double *wi, double* vl, int *ldvl, double *vr, int *ldvr, double *work, int *lwork, int *info);
extern "C" void sgeev_(char *jobvl, char *jobvr, int *n, float *a, int *lda, float *wr, float *wi, float* vl, int *ldvl, float *vr, int *ldvr, float *work, int *lwork, int *info);
extern "C" void cgeev_(char *jobvl, char *jobvr, int *n,
std::complex<float> *a, int *lda,
std::complex<float> *w,
std::complex<float> *vl, int *ldvl,
std::complex<float> *vr, int *ldvr,
std::complex<float> *work, int *lwork,
float *rwork,
int *info);
extern "C" void zgeev_(char *jobvl, char *jobvr, int *n,
std::complex<double> *a, int *lda,
std::complex<double> *w,
std::complex<double> *vl, int *ldvl,
std::complex<double> *vr, int *ldvr,
std::complex<double> *work, int *lwork,
double *rwork,
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, double *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, float *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);
// gels
extern "C" void zgels_(char *trans, int *m, int *n, int *nrhs,
std::complex<double> *a, int *lda, std::complex<double> *b, int *ldb,
std::complex<double> *work, int *lwork, int *info);
extern "C" void cgels_(char *trans, int *m, int *n, int *nrhs,
std::complex<float> *a, int *lda, std::complex<float> *b, int *ldb,
std::complex<float> *work, int *lwork, int *info);
extern "C" void dgels_(char *trans, int *m, int *n, int *nrhs,
double *a, int *lda, double *b, int *ldb,
double *work, int *lwork, int *info);
extern "C" void sgels_(char *trans, int *m, int *n, int *nrhs,
float *a, int *lda, float *b, int *ldb,
float *work, int *lwork, int *info);
// gelsd
extern "C" void zgelsd_(int *m, int *n, int *nrhs,
std::complex<double> *a, int *lda, std::complex<double> *b, int *ldb,
double *s, double *rcond, int *rank,
std::complex<double> *work, int *lwork, double *rwork, int *iwork, int *info);
extern "C" void cgelsd_(int *m, int *n, int *nrhs,
std::complex<float> *a, int *lda, std::complex<float> *b, int *ldb,
float *s, float *rcond, int *rank,
std::complex<float> *work, int *lwork, float *rwork, int *iwork, int *info);
extern "C" void dgelsd_(int *m, int *n, int *nrhs,
double *a, int *lda, double *b, int *ldb,
double *s, double *rcond, int *rank,
double *work, int *lwork, int *iwork, int *info);
extern "C" void sgelsd_(int *m, int *n, int *nrhs,
float *a, int *lda, float *b, int *ldb,
float *s, float *rcond, int *rank,
float *work, int *lwork, int *iwork, int *info);
// gelsy
extern "C" void zgelsy_(int *m, int *n, int *nrhs,
std::complex<double> *a, int *lda, std::complex<double> *b, int *ldb,
int *jpvt, double *rcond, int *rank,
std::complex<double> *work, int *lwork,
double *rwork, int *info);
extern "C" void cgelsy_(int *m, int *n, int *nrhs,
std::complex<float> * a, int *lda, std::complex<float> *b, int *ldb,
int *jpvt, float *rcond, int *rank,
std::complex<float> *work, int *lwork,
float *rwork, int *info);
extern "C" void dgelsy_(int *m, int *n, int *nrhs,
double *a, int *lda, double *b, int *ldb,
int *jpvt, double *rcond, int *rank,
double *work, int *lwork, int *info);
extern "C" void sgelsy_(int *m, int *n, int *nrhs,
float *a, int *lda, float *b, int *ldb,
int *jpvt, float *rcond, int *rank,
float *work, int *lwork, int *info);
// gelss
extern "C" void zgelss_(int *m, int *n, int *nrhs,
std::complex<double> *a, int *lda, std::complex<double> *b, int *ldb,
double *s, double *rcond, int *rank,
std::complex<double> *work, int *lwork,
double *rwork, int *info);
extern "C" void cgelss_(int *m, int *n, int *nrhs,
std::complex<float> *a, int *lda, std::complex<float> *b, int *ldb,
float *s, float *rcond, int *rank,
std::complex<float> *work, int *lwork,
float *rwork, int *info);
extern "C" void dgelss_(int *m, int *n, int *nrhs,
double *a, int *lda, double *b, int *ldb,
double *s, double *rcond, int *rank,
double *work, int *lwork, int *info);
extern "C" void sgelss_(int *m, int *n, int *nrhs,
float *a, int *lda, float *b, int *ldb,
float *s, float *rcond, int *rank,
float *work, int *lwork, int *info);
#endif
#if AT_BUILD_WITH_BLAS()
// trsm
extern "C" void ztrsm_(char *side, char *uplo, char *trans, char *diag, int *n, int *nrhs, std::complex<double> *alpha, std::complex<double> *a, int *lda, std::complex<double> *b, int *ldb);
extern "C" void ctrsm_(char *side, char *uplo, char *trans, char *diag, int *n, int *nrhs, std::complex<float> *alpha, std::complex<float> *a, int *lda, std::complex<float> *b, int *ldb);
extern "C" void dtrsm_(char *side, char *uplo, char *trans, char *diag, int *n, int *nrhs, double *alpha, double *a, int *lda, double *b, int *ldb);
extern "C" void strsm_(char *side, char *uplo, char *trans, char *diag, int *n, int *nrhs, float *alpha, float *a, int *lda, float *b, int *ldb);
#endif
namespace at {
namespace meta {
TORCH_META_FUNC(triangular_solve)(const Tensor& self, const Tensor& A, bool upper, bool transpose, bool unitriangular) {
TORCH_CHECK(self.dim() >= 2,
"torch.triangular_solve: Expected b to have at least 2 dimensions, but it has ", self.dim(), " dimensions instead");
TORCH_CHECK(A.dim() >= 2,
"torch.triangular_solve: Expected A to have at least 2 dimensions, but it has ", A.dim(), " dimensions instead");
at::native::linearSolveCheckInputs(self, A, "triangular_solve");
if (A.layout() == Layout::Strided) {
std::vector<int64_t> self_broadcast_size, A_broadcast_size;
std::tie(self_broadcast_size, A_broadcast_size) = at::native::_linalg_broadcast_batch_dims(self, A);
auto ndim = self_broadcast_size.size();
auto nrows = A.size(-2);
// make column major strides for BLAS
auto solution_strides = at::detail::defaultStrides(self_broadcast_size);
solution_strides[ndim - 2] = 1;
solution_strides[ndim - 1] = nrows;
set_output(0, self_broadcast_size, solution_strides, self.options(), {});
// make column major strides for BLAS
auto clone_A_strides = at::detail::defaultStrides(A_broadcast_size);
clone_A_strides[ndim - 2] = 1;
clone_A_strides[ndim - 1] = nrows;
set_output(1, A_broadcast_size, clone_A_strides, A.options(), {});
} else if (A.layout() == Layout::SparseCsr) {
// no broadcasting for non-strided layout
set_output(0, self.sizes(), {}, self.options(), {}); // make row major strides for Sparse BLAS
set_output(1, {0}, {}, self.options(), {}); // return 0-sized tensor
} else {
TORCH_INTERNAL_ASSERT(false, "triangular_solve: Got an unexpected layout.");
}
}
} // namespace meta
namespace native {
#if AT_BUILD_WITH_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 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, class value_t=scalar_t>
void lapackSymeig(char jobz, char uplo, int n, scalar_t *a, int lda, value_t *w, scalar_t *work, int lwork, value_t *rwork, 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, value_t *rwork, int *iwork, int *info);
template<> void lapackSolve<c10::complex<double>>(int n, int nrhs, c10::complex<double> *a, int lda, int *ipiv, c10::complex<double> *b, int ldb, int *info) {
zgesv_(&n, &nrhs, reinterpret_cast<std::complex<double>*>(a), &lda, ipiv, reinterpret_cast<std::complex<double>*>(b), &ldb, info);
}
template<> void lapackSolve<c10::complex<float>>(int n, int nrhs, c10::complex<float> *a, int lda, int *ipiv, c10::complex<float> *b, int ldb, int *info) {
cgesv_(&n, &nrhs, reinterpret_cast<std::complex<float>*>(a), &lda, ipiv, reinterpret_cast<std::complex<float>*>(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<c10::complex<double>>(int n, c10::complex<double> *a, int lda, int *ipiv, c10::complex<double> *work, int lwork, int *info) {
zgetri_(&n, reinterpret_cast<std::complex<double>*>(a), &lda, ipiv, reinterpret_cast<std::complex<double>*>(work), &lwork, info);
}
template<> void lapackGetri<c10::complex<float>>(int n, c10::complex<float> *a, int lda, int *ipiv, c10::complex<float> *work, int lwork, int *info) {
cgetri_(&n, reinterpret_cast<std::complex<float>*>(a), &lda, ipiv, reinterpret_cast<std::complex<float>*>(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<c10::complex<double>>(int m, int n, c10::complex<double> *a, int lda, int *ipiv, int *info) {
zgetrf_(&m, &n, reinterpret_cast<std::complex<double>*>(a), &lda, ipiv, info);
}
template<> void lapackLu<c10::complex<float>>(int m, int n, c10::complex<float> *a, int lda, int *ipiv, int *info) {
cgetrf_(&m, &n, reinterpret_cast<std::complex<float>*>(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<c10::complex<double>>(char uplo, int n, int nrhs, c10::complex<double> *a, int lda, c10::complex<double> *b, int ldb, int *info) {
zpotrs_(&uplo, &n, &nrhs, reinterpret_cast<std::complex<double>*>(a), &lda, reinterpret_cast<std::complex<double>*>(b), &ldb, info);
}
template<> void lapackCholeskySolve<c10::complex<float>>(char uplo, int n, int nrhs, c10::complex<float> *a, int lda, c10::complex<float> *b, int ldb, int *info) {
cpotrs_(&uplo, &n, &nrhs, reinterpret_cast<std::complex<float>*>(a), &lda, reinterpret_cast<std::complex<float>*>(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<c10::complex<double>>(char uplo, int n, c10::complex<double> *a, int lda, int *info) {
zpotrf_(&uplo, &n, reinterpret_cast<std::complex<double>*>(a), &lda, info);
}
template<> void lapackCholesky<c10::complex<float>>(char uplo, int n, c10::complex<float> *a, int lda, int *info) {
cpotrf_(&uplo, &n, reinterpret_cast<std::complex<float>*>(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 lapackCholeskyInverse<c10::complex<double>>(char uplo, int n, c10::complex<double> *a, int lda, int *info) {
zpotri_(&uplo, &n, reinterpret_cast<std::complex<double>*>(a), &lda, info);
}
template<> void lapackCholeskyInverse<c10::complex<float>>(char uplo, int n, c10::complex<float> *a, int lda, int *info) {
cpotri_(&uplo, &n, reinterpret_cast<std::complex<float>*>(a), &lda, info);
}
template<> void lapackCholeskyInverse<double>(char uplo, int n, double *a, int lda, int *info) {
dpotri_(&uplo, &n, a, &lda, info);
}
template<> void lapackCholeskyInverse<float>(char uplo, int n, float *a, int lda, int *info) {
spotri_(&uplo, &n, a, &lda, info);
}
template<> void lapackGeqrf<c10::complex<double>>(int m, int n, c10::complex<double> *a, int lda, c10::complex<double> *tau, c10::complex<double> *work, int lwork, int *info) {
zgeqrf_(&m, &n, reinterpret_cast<std::complex<double>*>(a), &lda, reinterpret_cast<std::complex<double>*>(tau), reinterpret_cast<std::complex<double>*>(work), &lwork, info);
}
template<> void lapackGeqrf<c10::complex<float>>(int m, int n, c10::complex<float> *a, int lda, c10::complex<float> *tau, c10::complex<float> *work, int lwork, int *info) {
cgeqrf_(&m, &n, reinterpret_cast<std::complex<float>*>(a), &lda, reinterpret_cast<std::complex<float>*>(tau), reinterpret_cast<std::complex<float>*>(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<c10::complex<double>>(int m, int n, int k, c10::complex<double> *a, int lda, c10::complex<double> *tau, c10::complex<double> *work, int lwork, int *info) {
zungqr_(&m, &n, &k, reinterpret_cast<std::complex<double>*>(a), &lda, reinterpret_cast<std::complex<double>*>(tau), reinterpret_cast<std::complex<double>*>(work), &lwork, info);
}
template<> void lapackOrgqr<c10::complex<float>>(int m, int n, int k, c10::complex<float> *a, int lda, c10::complex<float> *tau, c10::complex<float> *work, int lwork, int *info) {
cungqr_(&m, &n, &k, reinterpret_cast<std::complex<float>*>(a), &lda, reinterpret_cast<std::complex<float>*>(tau), reinterpret_cast<std::complex<float>*>(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 lapackOrmqr<c10::complex<double>>(char side, char trans, int m, int n, int k, c10::complex<double> *a, int lda, c10::complex<double> *tau, c10::complex<double> *c, int ldc, c10::complex<double> *work, int lwork, int *info) {
zunmqr_(&side, &trans, &m, &n, &k, reinterpret_cast<std::complex<double>*>(a), &lda, reinterpret_cast<std::complex<double>*>(tau), reinterpret_cast<std::complex<double>*>(c), &ldc, reinterpret_cast<std::complex<double>*>(work), &lwork, info);
}
template<> void lapackOrmqr<c10::complex<float>>(char side, char trans, int m, int n, int k, c10::complex<float> *a, int lda, c10::complex<float> *tau, c10::complex<float> *c, int ldc, c10::complex<float> *work, int lwork, int *info) {
cunmqr_(&side, &trans, &m, &n, &k, reinterpret_cast<std::complex<float>*>(a), &lda, reinterpret_cast<std::complex<float>*>(tau), reinterpret_cast<std::complex<float>*>(c), &ldc, reinterpret_cast<std::complex<float>*>(work), &lwork, info);
}
template<> void lapackOrmqr<double>(char side, char trans, int m, int n, int k, double *a, int lda, double *tau, double *c, int ldc, double *work, int lwork, int *info) {
dormqr_(&side, &trans, &m, &n, &k, a, &lda, tau, c, &ldc, work, &lwork, info);
}
template<> void lapackOrmqr<float>(char side, char trans, int m, int n, int k, float *a, int lda, float *tau, float *c, int ldc, float *work, int lwork, int *info) {
sormqr_(&side, &trans, &m, &n, &k, a, &lda, tau, c, &ldc, work, &lwork, info);
}
template<> void lapackSymeig<c10::complex<double>, double>(char jobz, char uplo, int n, c10::complex<double> *a, int lda, double *w, c10::complex<double> *work, int lwork, double *rwork, int *info) {
zheev_(&jobz, &uplo, &n, reinterpret_cast<std::complex<double>*>(a), &lda, w, reinterpret_cast<std::complex<double>*>(work), &lwork, rwork, info);
}
template<> void lapackSymeig<c10::complex<float>, float>(char jobz, char uplo, int n, c10::complex<float> *a, int lda, float *w, c10::complex<float> *work, int lwork, float *rwork, int *info) {
cheev_(&jobz, &uplo, &n, reinterpret_cast<std::complex<float>*>(a), &lda, w, reinterpret_cast<std::complex<float>*>(work), &lwork, rwork, info);
}
template<> void lapackSymeig<double>(char jobz, char uplo, int n, double *a, int lda, double *w, double *work, int lwork, double* rwork, int *info) {
(void)rwork; // unused
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, float* rwork, int *info) {
(void)rwork; // unused
ssyev_(&jobz, &uplo, &n, a, &lda, w, work, &lwork, info);
}
template<> void lapackSyevd<c10::complex<double>, double>(char jobz, char uplo, int n, c10::complex<double> *a, int lda, double *w, c10::complex<double> *work, int lwork, double *rwork, int lrwork, int *iwork, int liwork, int *info) {
zheevd_(&jobz, &uplo, &n, reinterpret_cast<std::complex<double>*>(a), &lda, w, reinterpret_cast<std::complex<double>*>(work), &lwork, rwork, &lrwork, iwork, &liwork, info);
}
template<> void lapackSyevd<c10::complex<float>, float>(char jobz, char uplo, int n, c10::complex<float> *a, int lda, float *w, c10::complex<float> *work, int lwork, float *rwork, int lrwork, int *iwork, int liwork, int *info) {
cheevd_(&jobz, &uplo, &n, reinterpret_cast<std::complex<float>*>(a), &lda, w, reinterpret_cast<std::complex<float>*>(work), &lwork, rwork, &lrwork, iwork, &liwork, info);
}
template<> void lapackSyevd<double>(char jobz, char uplo, int n, double *a, int lda, double *w, double *work, int lwork, double *rwork, int lrwork, int *iwork, int liwork, int *info) {
(void)rwork; // unused
(void)lrwork; // unused
dsyevd_(&jobz, &uplo, &n, a, &lda, w, work, &lwork, iwork, &liwork, info);
}
template<> void lapackSyevd<float>(char jobz, char uplo, int n, float *a, int lda, float *w, float *work, int lwork, float *rwork, int lrwork, int *iwork, int liwork, int *info) {
(void)rwork; // unused
(void)lrwork; // unused
ssyevd_(&jobz, &uplo, &n, a, &lda, w, work, &lwork, iwork, &liwork, info);
}
template<> void lapackEig<double>(char jobvl, char jobvr, int n, double *a, int lda, double *w, double* vl, int ldvl, double *vr, int ldvr, double *work, int lwork, double *rwork, int *info) {
// lapack [sd]geev wants to separate output arrays: wr and wi for the real
// and imaginary parts
double *wr = w;
double *wi = w + n;
(void)rwork; // unused
dgeev_(&jobvl, &jobvr, &n, a, &lda, wr, wi, vl, &ldvl, vr, &ldvr, work, &lwork, info);
}
template<> void lapackEig<float>(char jobvl, char jobvr, int n, float *a, int lda, float *w, float* vl, int ldvl, float *vr, int ldvr, float *work, int lwork, float *rwork, int *info) {
// lapack [sd]geev wants to separate output arrays: wr and wi for the real
// and imaginary parts
float *wr = w;
float *wi = w + n;
(void)rwork; // unused
sgeev_(&jobvl, &jobvr, &n, a, &lda, wr, wi, vl, &ldvl, vr, &ldvr, work, &lwork, info);
}
template<> void lapackEig<c10::complex<double>, double>(char jobvl, char jobvr, int n, c10::complex<double> *a, int lda, c10::complex<double> *w, c10::complex<double> *vl, int ldvl, c10::complex<double> *vr, int ldvr, c10::complex<double> *work, int lwork, double *rwork, int *info) {
zgeev_(&jobvl, &jobvr, &n,
reinterpret_cast<std::complex<double>*>(a), &lda,
reinterpret_cast<std::complex<double>*>(w),
reinterpret_cast<std::complex<double>*>(vl), &ldvl,
reinterpret_cast<std::complex<double>*>(vr), &ldvr,
reinterpret_cast<std::complex<double>*>(work), &lwork,
rwork, info);
}
template<> void lapackEig<c10::complex<float>, float>(char jobvl, char jobvr, int n, c10::complex<float> *a, int lda, c10::complex<float> *w, c10::complex<float> *vl, int ldvl, c10::complex<float> *vr, int ldvr, c10::complex<float> *work, int lwork, float *rwork, int *info) {
cgeev_(&jobvl, &jobvr, &n,
reinterpret_cast<std::complex<float>*>(a), &lda,
reinterpret_cast<std::complex<float>*>(w),
reinterpret_cast<std::complex<float>*>(vl), &ldvl,
reinterpret_cast<std::complex<float>*>(vr), &ldvr,
reinterpret_cast<std::complex<float>*>(work), &lwork,
rwork, info);
}
template<> void lapackSvd<c10::complex<double>, double>(char jobz, int m, int n, c10::complex<double> *a, int lda,
double *s, c10::complex<double> *u, int ldu, c10::complex<double> *vt, int ldvt, c10::complex<double> *work, int lwork, double *rwork, int *iwork, int *info) {
zgesdd_(&jobz, &m, &n, reinterpret_cast<std::complex<double>*>(a), &lda, s, reinterpret_cast<std::complex<double>*>(u), &ldu,
reinterpret_cast<std::complex<double>*>(vt), &ldvt, reinterpret_cast<std::complex<double>*>(work), &lwork, rwork, iwork, info);
}
template<> void lapackSvd<c10::complex<float>, float>(char jobz, int m, int n, c10::complex<float> *a, int lda,
float *s, c10::complex<float> *u, int ldu, c10::complex<float> *vt, int ldvt, c10::complex<float> *work, int lwork, float *rwork, int *iwork, int *info) {
cgesdd_(&jobz, &m, &n, reinterpret_cast<std::complex<float>*>(a), &lda, s, reinterpret_cast<std::complex<float>*>(u), &ldu,
reinterpret_cast<std::complex<float>*>(vt), &ldvt, reinterpret_cast<std::complex<float>*>(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, double *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, float *rwork, int *iwork, int *info) {
sgesdd_(&jobz, &m, &n, a, &lda, s, u, &ldu, vt, &ldvt, work, &lwork, iwork, info);
}
template<> void lapackLuSolve<c10::complex<double>>(char trans, int n, int nrhs, c10::complex<double> *a, int lda, int *ipiv, c10::complex<double> *b, int ldb, int *info) {
zgetrs_(&trans, &n, &nrhs, reinterpret_cast<std::complex<double>*>(a), &lda, ipiv, reinterpret_cast<std::complex<double>*>(b), &ldb, info);
}
template<> void lapackLuSolve<c10::complex<float>>(char trans, int n, int nrhs, c10::complex<float> *a, int lda, int *ipiv, c10::complex<float> *b, int ldb, int *info) {
cgetrs_(&trans, &n, &nrhs, reinterpret_cast<std::complex<float>*>(a), &lda, ipiv, reinterpret_cast<std::complex<float>*>(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);
}
template<> void lapackGels<c10::complex<double>>(
char trans, int m, int n, int nrhs,
c10::complex<double> *a, int lda, c10::complex<double> *b, int ldb,
c10::complex<double> *work, int lwork, int *info) {
zgels_(&trans, &m, &n, &nrhs,
reinterpret_cast<std::complex<double>*>(a), &lda,
reinterpret_cast<std::complex<double>*>(b), &ldb,
reinterpret_cast<std::complex<double>*>(work), &lwork, info);
}
template<> void lapackGels<c10::complex<float>>(
char trans, int m, int n, int nrhs,
c10::complex<float> *a, int lda, c10::complex<float> *b, int ldb,
c10::complex<float> *work, int lwork, int *info) {
cgels_(&trans, &m, &n, &nrhs,
reinterpret_cast<std::complex<float>*>(a), &lda,
reinterpret_cast<std::complex<float>*>(b), &ldb,
reinterpret_cast<std::complex<float>*>(work), &lwork, info);
}
template<> void lapackGels<double>(
char trans, int m, int n, int nrhs,
double *a, int lda, double *b, int ldb,
double *work, int lwork, int *info) {
dgels_(&trans, &m, &n, &nrhs,
a, &lda, b, &ldb, work, &lwork, info);
}
template<> void lapackGels<float>(
char trans, int m, int n, int nrhs,
float *a, int lda, float *b, int ldb,
float *work, int lwork, int *info) {
sgels_(&trans, &m, &n, &nrhs,
a, &lda, b, &ldb, work, &lwork, info);
}
template<> void lapackGelsd<c10::complex<double>, double>(
int m, int n, int nrhs,
c10::complex<double> *a, int lda, c10::complex<double> *b, int ldb,
double *s, double rcond, int *rank,
c10::complex<double> *work, int lwork,
double *rwork, int *iwork, int *info) {
zgelsd_(&m, &n, &nrhs,
reinterpret_cast<std::complex<double>*>(a), &lda,
reinterpret_cast<std::complex<double>*>(b), &ldb,
s, &rcond, rank,
reinterpret_cast<std::complex<double>*>(work), &lwork,
rwork, iwork, info);
}
template<> void lapackGelsd<c10::complex<float>, float>(
int m, int n, int nrhs,
c10::complex<float> *a, int lda, c10::complex<float> *b, int ldb,
float *s, float rcond, int *rank,
c10::complex<float> *work, int lwork,
float *rwork, int *iwork, int *info) {
cgelsd_(&m, &n, &nrhs,
reinterpret_cast<std::complex<float>*>(a), &lda,
reinterpret_cast<std::complex<float>*>(b), &ldb,
s, &rcond, rank,
reinterpret_cast<std::complex<float>*>(work), &lwork,
rwork, iwork, info);
}
template<> void lapackGelsd<double>(
int m, int n, int nrhs,
double *a, int lda, double *b, int ldb,
double *s, double rcond, int *rank,
double *work, int lwork,
double *rwork, int *iwork, int *info) {
dgelsd_(&m, &n, &nrhs,
a, &lda, b, &ldb,
s, &rcond, rank,
work, &lwork, iwork, info);
}
template<> void lapackGelsd<float>(
int m, int n, int nrhs,
float *a, int lda, float *b, int ldb,
float *s, float rcond, int *rank,
float *work, int lwork,
float *rwork, int *iwork, int *info) {
sgelsd_(&m, &n, &nrhs,
a, &lda, b, &ldb,
s, &rcond, rank,
work, &lwork, iwork, info);
}
template<> void lapackGelsy<c10::complex<double>, double>(
int m, int n, int nrhs,
c10::complex<double> *a, int lda, c10::complex<double> *b, int ldb,
int *jpvt, double rcond, int *rank,
c10::complex<double> *work, int lwork, double *rwork, int *info) {
zgelsy_(&m, &n, &nrhs,
reinterpret_cast<std::complex<double>*>(a), &lda,
reinterpret_cast<std::complex<double>*>(b), &ldb,
jpvt, &rcond, rank,
reinterpret_cast<std::complex<double>*>(work), &lwork,
rwork, info);
}
template<> void lapackGelsy<c10::complex<float>, float>(
int m, int n, int nrhs,
c10::complex<float> *a, int lda, c10::complex<float> *b, int ldb,
int *jpvt, float rcond, int *rank,
c10::complex<float> *work, int lwork, float *rwork, int *info) {
cgelsy_(&m, &n, &nrhs,
reinterpret_cast<std::complex<float>*>(a), &lda,
reinterpret_cast<std::complex<float>*>(b), &ldb,
jpvt, &rcond, rank,
reinterpret_cast<std::complex<float>*>(work), &lwork,
rwork, info);
}
template<> void lapackGelsy<double>(
int m, int n, int nrhs,
double *a, int lda, double *b, int ldb,
int *jpvt, double rcond, int *rank,
double *work, int lwork, double *rwork, int *info) {
dgelsy_(&m, &n, &nrhs,
a, &lda, b, &ldb,
jpvt, &rcond, rank,
work, &lwork, info);
}
template<> void lapackGelsy<float>(
int m, int n, int nrhs,
float *a, int lda, float *b, int ldb,
int *jpvt, float rcond, int *rank,
float *work, int lwork, float *rwork, int *info) {
sgelsy_(&m, &n, &nrhs,
a, &lda, b, &ldb,
jpvt, &rcond, rank,
work, &lwork, info);
}
template<> void lapackGelss<c10::complex<double>, double>(
int m, int n, int nrhs,
c10::complex<double> *a, int lda, c10::complex<double> *b, int ldb,
double *s, double rcond, int *rank,
c10::complex<double> *work, int lwork,
double *rwork, int *info
) {
zgelss_(&m, &n, &nrhs,
reinterpret_cast<std::complex<double>*>(a), &lda,
reinterpret_cast<std::complex<double>*>(b), &ldb,
s, &rcond, rank,
reinterpret_cast<std::complex<double>*>(work), &lwork,
rwork, info);
}
template<> void lapackGelss<c10::complex<float>, float>(
int m, int n, int nrhs,
c10::complex<float> *a, int lda, c10::complex<float> *b, int ldb,
float *s, float rcond, int *rank,
c10::complex<float> *work, int lwork,
float *rwork, int *info
) {
cgelss_(&m, &n, &nrhs,
reinterpret_cast<std::complex<float>*>(a), &lda,
reinterpret_cast<std::complex<float>*>(b), &ldb,
s, &rcond, rank,
reinterpret_cast<std::complex<float>*>(work), &lwork,
rwork, info);
}
template<> void lapackGelss<double>(
int m, int n, int nrhs,
double *a, int lda, double *b, int ldb,
double *s, double rcond, int *rank,
double *work, int lwork,
double *rwork, int *info) {
dgelss_(&m, &n, &nrhs,
a, &lda, b, &ldb,
s, &rcond, rank,
work, &lwork, info);
}
template<> void lapackGelss<float>(
int m, int n, int nrhs,
float *a, int lda, float *b, int ldb,
float *s, float rcond, int *rank,
float *work, int lwork,
float *rwork, int *info) {
sgelss_(&m, &n, &nrhs,
a, &lda, b, &ldb,
s, &rcond, rank,
work, &lwork, info);
}
#endif
#if AT_BUILD_WITH_BLAS()
template<> void blasTriangularSolve<c10::complex<double>>(char side, char uplo, char trans, char diag, int n, int nrhs, c10::complex<double> *a, int lda, c10::complex<double> *b, int ldb) {
std::complex<double> one{1., 0.};
ztrsm_(&side, &uplo, &trans, &diag, &n, &nrhs, &one, reinterpret_cast<std::complex<double>*>(a), &lda, reinterpret_cast<std::complex<double>*>(b), &ldb);
}
template<> void blasTriangularSolve<c10::complex<float>>(char side, char uplo, char trans, char diag, int n, int nrhs, c10::complex<float> *a, int lda, c10::complex<float> *b, int ldb) {
std::complex<float> one{1.f, 0.f};
ctrsm_(&side, &uplo, &trans, &diag, &n, &nrhs, &one, reinterpret_cast<std::complex<float>*>(a), &lda, reinterpret_cast<std::complex<float>*>(b), &ldb);
}
template<> void blasTriangularSolve<double>(char side, char uplo, char trans, char diag, int n, int nrhs, double *a, int lda, double *b, int ldb) {
auto one = 1.;
dtrsm_(&side, &uplo, &trans, &diag, &n, &nrhs, &one, a, &lda, b, &ldb);
}
template<> void blasTriangularSolve<float>(char side, char uplo, char trans, char diag, int n, int nrhs, float *a, int lda, float *b, int ldb) {
auto one = 1.f;
strsm_(&side, &uplo, &trans, &diag, &n, &nrhs, &one, a, &lda, b, &ldb);
}
#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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
/*
Computes the solution to a system of linear equations
A X = B,
where A is an n-by-n matrix and X and B are n-by-nrhs matrices.
Note that B is required to be a matrix, the usual, vector case, is obtained with nrhs = 1.
Above description is for non-batched input, the batched input is also supported.
This is an in-place routine, content of both A and b are overwritten.
'infos' is an int Tensor containing error codes for each matrix in the batched input.
For more information see LAPACK's documentation for GESV routine.
*/
template<typename scalar_t>
static void apply_solve(Tensor& b, Tensor& A, Tensor& infos) {
#if !AT_BUILD_WITH_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 lda = std::max<int64_t>(1, n);
auto ipiv = at::empty({lda}, b.options().dtype(kInt));
auto ipiv_data = ipiv.data_ptr<int>();
auto infos_data = infos.data_ptr<int>();
for (const auto i : c10::irange(batch_size)) {
scalar_t* A_working_ptr = &A_data[i * A_mat_stride];
scalar_t* b_working_ptr = &b_data[i * b_mat_stride];
int* info_working_ptr = &infos_data[i];
lapackSolve<scalar_t>(n, nrhs, A_working_ptr, lda, ipiv_data, b_working_ptr, lda, info_working_ptr);
}
#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);
// infos might not get filled for empty inputs therefore at::zeros is used instead of at::empty
auto infos = at::zeros({std::max<int64_t>(1, batchCount(self))}, self.options().dtype(kInt));
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.item().toInt(), "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_WARN_ONCE(
"torch.solve is deprecated in favor of torch.linalg.solve",
"and will be removed in a future PyTorch release.\n",
"torch.linalg.solve has its arguments reversed and does not return the LU factorization.\n",
"To get the LU factorization see torch.lu, which can be used with torch.lu_solve or torch.lu_unpack.\n",
"X = torch.solve(B, A).solution\n",
"should be replaced with\n",
"X = torch.linalg.solve(A, B)"
);
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(const Tensor& self, const Tensor& A, Tensor& solution, Tensor& lu) {
TORCH_WARN_ONCE(
"torch.solve is deprecated in favor of torch.linalg.solve",
"and will be removed in a future PyTorch release.\n",
"torch.linalg.solve has its arguments reversed and does not return the LU factorization.\n",
"To get the LU factorization see torch.lu, which can be used with torch.lu_solve or torch.lu_unpack.\n",
"X = torch.solve(B, A).solution\n",
"should be replaced with\n",
"X = torch.linalg.solve(A, B)"
);
checkSameDevice("solve", solution, self, "solution");
checkSameDevice("solve", lu, self, "lu");
checkLinalgCompatibleDtype("solve", solution, self, "solution");
checkLinalgCompatibleDtype("solve", lu, self, "lu");
Tensor solution_tmp, lu_tmp;
std::tie(solution_tmp, lu_tmp) = at::_solve_helper(self, A);
at::native::resize_output(solution, solution_tmp.sizes());
at::native::resize_output(lu, lu_tmp.sizes());
solution.copy_(solution_tmp);
lu.copy_(lu_tmp);
return std::tuple<Tensor&, Tensor&>(solution, lu);
}
// Solves a system of linear equations matmul(input, x) = other in-place
// LAPACK/MAGMA error codes are saved in 'infos' tensor, they are not checked here
static Tensor& linalg_solve_out_info(Tensor& result, Tensor& infos, const Tensor& input, const Tensor& other) {
checkSameDevice("linalg.solve", result, input);
checkSameDevice("linalg.solve", other, input, "other");
checkLinalgCompatibleDtype("linalg.solve", result, input);
TORCH_CHECK(input.scalar_type() == other.scalar_type(),
"input dtype ", input.scalar_type(), " does not match other dtype ", other.scalar_type());
squareCheckInputs(input, "linalg.solve");
TORCH_CHECK(other.dim() >= 1,
"other should have at least 1 dimension, but has ", other.dim(), " dimensions instead");
// Two types of 'other' tensors are supported:
// - 1-dimensional (1D) tensor or batch of 1D tensors (vector case)
// - 2-dimensional (2D) tensor or batch of 2D tensors (matrix case)
// original torch.solve supported only the matrix case, while NumPy works for both cases
// for the batched input we need to be able to distinguish them
bool vector_case = linalg_solve_is_vector_rhs(input, other);
bool is_batched_column_major = false;
if (vector_case) {
is_batched_column_major = result.is_contiguous();
} else if (!vector_case && result.dim() >= 2) {
is_batched_column_major = result.mT().is_contiguous();
}
// if 'other' is a batch of 2D tensors, then 'input' can be non-batched and will be broadcasted
auto expected_shape = IntArrayRef(input.sizes().data(), input.dim() - 1); // input.shape[:-1]
if (!vector_case && other.dim() > 2) {
expected_shape = other.sizes();
}
bool result_equal_expected_shape = result.sizes().equals(expected_shape);
bool result_input_same_type = (result.scalar_type() == input.scalar_type());
// if result is not empty and not in batched column major format
bool copy_needed = (result.numel() != 0 && !is_batched_column_major);
copy_needed |= !result_input_same_type; // or result does not have the same dtype as input
copy_needed |= (result.numel() != 0 && !result_equal_expected_shape); // or result does not have the expected shape
// we have to allocate a temporary tensor
if (copy_needed) {
Tensor result_tmp = at::empty({0}, input.options());
result_tmp = linalg_solve_out_info(result_tmp, infos, input, other);
at::native::resize_output(result, result_tmp.sizes());
result.copy_(result_tmp);
return result;
}
// else use result's storage directly
// we need to unsqueeze 'other' because 2-dimensional tensors are expected in the implementation
Tensor other_ = vector_case ? other.unsqueeze(-1) : other;
// _linalg_broadcast_batch_dims also includes linearSolveCheckInputs
// it checks for squareness of 'input' and 'shape' compatibility of 'other' and 'input'
Tensor other_broadcasted, input_broadcasted;
std::tie(other_broadcasted, input_broadcasted) = _linalg_broadcast_batch_dims(other_, input, "linalg.solve");
auto squeezed_other_broadcasted = at::squeeze(other_broadcasted, -1);
auto squeezed_result_shape = squeezed_other_broadcasted.sizes();
// if result has no elements we can modify it
if (result.numel() == 0) {
if (vector_case) {
result.resize_(squeezed_result_shape);
} else {
at::native::resize_as_(result, other_broadcasted.mT(), MemoryFormat::Contiguous);
result.transpose_(-2, -1);
}
}
auto expected_result_shape = vector_case ? squeezed_result_shape : other_broadcasted.sizes();
TORCH_INTERNAL_ASSERT(result.sizes().equals(expected_result_shape));
TORCH_INTERNAL_ASSERT(result.scalar_type() == input.scalar_type());
TORCH_INTERNAL_ASSERT(result.device() == input.device());
// result tensor must be in batched column major order (Fortran contiguous) for 2D inputs
// or C contiguous for 1D input
if (vector_case) {
TORCH_INTERNAL_ASSERT(result.is_contiguous());
} else {
TORCH_INTERNAL_ASSERT(result.mT().is_contiguous());
}
// for 1-dimensional 'other', we need to unsqueeze the result before passing to "apply_solve"
if (vector_case) {
result = result.unsqueeze_(-1);
}
// lu_stub+lu_solve_stub perform calculations in-place and 'result' must be a copy of 'other_broadcasted'
result.copy_(other_broadcasted);
auto input_working_copy = cloneBatchedColumnMajor(input_broadcasted);
TORCH_INTERNAL_ASSERT(infos.scalar_type() == kInt);
TORCH_INTERNAL_ASSERT(infos.device() == input.device());
infos.resize_({std::max<int64_t>(1, batchCount(input_broadcasted))});
// if input is empty infos might not get filled; make sure infos doesn't contain garbage then
if (input.numel() == 0) {
infos.fill_(0);
}
// compute the LU factorization of 'input_working_copy'
auto pivots_shape = IntArrayRef(input_broadcasted.sizes().data(), input_broadcasted.dim() - 2).vec(); // input_broadcasted.shape[:-2]
pivots_shape.push_back(std::min(input.size(-2), input.size(-1)));
Tensor pivots = at::empty(pivots_shape, input.options().dtype(kInt));
lu_stub(input.device().type(), input_working_copy, pivots, infos, /*compute_pivots=*/true);
// solve the linear system using the LU factorization
lu_solve_stub(input.device().type(), result, input_working_copy, pivots);
// for 1-dimensional 'other', we need to squeeze the result after "apply_solve"
if (vector_case) {
result = result.squeeze_(-1);
}
return result;
}
// Solves a system of linear equations matmul(input, x) = other in-place
Tensor& linalg_solve_out(const Tensor& input, const Tensor& other, Tensor& result) {
auto infos = at::empty({0}, input.options().dtype(kInt));
result = linalg_solve_out_info(result, infos, input, other);
// Now check LAPACK/MAGMA error codes
// batchCheckErrors(Tensor, char*) calls 'infos = infos.to(kCPU)'
bool vector_case = linalg_solve_is_vector_rhs(input, other);
if (vector_case ? result.dim() > 1 : result.dim() > 2) {
batchCheckErrors(infos, "linalg.solve");
} else {
singleCheckErrors(infos.item().toInt(), "linalg.solve");
}
return result;
}
// Solves a system of linear equations matmul(input, x) = other
Tensor linalg_solve(const Tensor& input, const Tensor& other) {
Tensor result = at::empty({0}, input.options());
result = at::linalg_solve_out(result, input, other);
return result;
}
// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ inverse ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
/*
Computes the inverse of n-by-n matrix 'self'
This is an in-place routine, it overwrites the content of 'self'.
'infos_lu' and 'infos_getri' are int Tensors containing error codes for each matrix in the batched input.
'infos_lu' is for holding lapackLU errors, and 'infos_getri' is for holding lapackGetri errors.
For more information see LAPACK's documentation for GETRI and GETRF routines.
*/
template <typename scalar_t>
static void apply_inverse(Tensor& self, Tensor& infos_lu, Tensor& infos_getri) {
#if !AT_BUILD_WITH_LAPACK()
AT_ERROR("inverse: LAPACK library not found in compilation");
#else
using value_t = typename c10::scalar_value_type<scalar_t>::type;
auto self_data = self.data_ptr<scalar_t>();