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BatchLinearAlgebra.cu
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BatchLinearAlgebra.cu
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#include <ATen/Context.h>
#include <ATen/cuda/CUDAContext.h>
#include <ATen/Dispatch.h>
#include <ATen/NativeFunctions.h>
#include <ATen/cuda/PinnedMemoryAllocator.h>
#include <ATen/cuda/CUDAApplyUtils.cuh>
#include <ATen/cuda/detail/IndexUtils.cuh>
#include <ATen/native/LinearAlgebraUtils.h>
#include <ATen/native/cuda/MiscUtils.h>
#include <THC/THC.h> // for USE_MAGMA
#ifdef USE_MAGMA
#include <magma.h>
#include <magma_types.h>
#endif
namespace at {
namespace native {
#ifdef USE_MAGMA
template<class scalar_t>
void magmaSolve(
magma_int_t n, magma_int_t nrhs, scalar_t* dA, magma_int_t ldda,
magma_int_t* ipiv, scalar_t* dB, magma_int_t lddb, magma_int_t* info);
template<class scalar_t>
void magmaSolveBatched(
magma_int_t n, magma_int_t nrhs, scalar_t** dA_array, magma_int_t ldda,
magma_int_t** dipiv_array, scalar_t** dB_array, magma_int_t lddb,
magma_int_t* dinfo_array, magma_int_t batch_count, const MAGMAQueue& magma_queue);
template<class scalar_t>
void magmaLu(
magma_int_t m, magma_int_t n, scalar_t* dA, magma_int_t ldda,
magma_int_t* ipiv, magma_int_t* info);
template<class scalar_t>
void magmaLuBatched(
magma_int_t m, magma_int_t n, scalar_t** dA_array, magma_int_t ldda,
magma_int_t** ipiv_array, magma_int_t* info_array, magma_int_t batchsize,
const MAGMAQueue& magma_queue);
template<class scalar_t>
void magmaLuNoPiv(
magma_int_t m, magma_int_t n, scalar_t* dA, magma_int_t ldda,
magma_int_t* info);
template<class scalar_t>
void magmaLuNoPivBatched(
magma_int_t m, magma_int_t n, scalar_t** dA_array, magma_int_t ldda,
magma_int_t* info_array, magma_int_t batchsize, const MAGMAQueue& magma_queue);
template<class scalar_t>
inline magma_int_t magmaGetriOptimalBlocksize(magma_int_t n);
template<class scalar_t>
void magmaGetri(
magma_int_t n, scalar_t* dA, magma_int_t ldda, magma_int_t* ipiv, scalar_t* dwork,
magma_int_t lwork, magma_int_t* info);
template<class scalar_t>
void magmaGetriBatched(
magma_int_t n, scalar_t** dA_array, magma_int_t ldda,
magma_int_t** ipiv_array, scalar_t** dinvA_array, magma_int_t lddia,
magma_int_t* info_array, magma_int_t batchsize, const MAGMAQueue& magma_queue);
template<class scalar_t>
void magmaCholeskySolve(
magma_uplo_t uplo, magma_int_t n, magma_int_t nrhs, scalar_t* dA, magma_int_t ldda,
scalar_t* dB, magma_int_t lddb, magma_int_t* info);
template<class scalar_t>
void magmaCholeskySolveBatched(
magma_uplo_t uplo, magma_int_t n, magma_int_t nrhs, scalar_t** dA_array, magma_int_t ldda,
scalar_t** dB_array, magma_int_t lddb, magma_int_t& info, magma_int_t batchsize, const MAGMAQueue& magma_queue);
template<class scalar_t>
void magmaCholesky(
magma_uplo_t uplo, magma_int_t n, scalar_t* dA,
magma_int_t ldda, magma_int_t* info);
template<class scalar_t>
void magmaCholeskyBatched(
magma_uplo_t uplo, magma_int_t n, scalar_t** dA_array, magma_int_t ldda,
magma_int_t* info_array, magma_int_t batchsize, const MAGMAQueue& magma_queue);
template<class scalar_t>
void magmaTriangularSolve(
magma_uplo_t uplo, magma_trans_t trans, magma_diag_t diag, magma_int_t m, magma_int_t n,
scalar_t* dA, magma_int_t ldda, scalar_t* dB, magma_int_t lddb);
template<class scalar_t>
void magmaTriangularSolveBatched(
magma_uplo_t uplo, magma_trans_t trans, magma_diag_t diag, magma_int_t m, magma_int_t n,
scalar_t** dA_array, magma_int_t ldda, scalar_t** dB_array, magma_int_t lddb, magma_int_t batchsize,
const MAGMAQueue& magma_queue);
template<class scalar_t>
inline magma_int_t magmaGeqrfOptimalBlocksize(magma_int_t m, magma_int_t n);
template<class scalar_t>
void magmaGeqrf(
magma_int_t m, magma_int_t n, scalar_t* dA, magma_int_t ldda,
scalar_t* tau, scalar_t* dT, magma_int_t* info, bool is_v2);
template<class scalar_t>
void magmaOrgqr(
magma_int_t m, magma_int_t n, magma_int_t k, scalar_t* dA,
magma_int_t ldda, scalar_t* tau, scalar_t* dT, magma_int_t nb, magma_int_t* info);
template<class scalar_t>
void magmaSymeig(
magma_vec_t jobz, magma_uplo_t uplo, magma_int_t n, scalar_t* dA, magma_int_t ldda,
scalar_t* w, scalar_t* wA, magma_int_t ldwa, scalar_t* work, magma_int_t lwork,
magma_int_t* iwork, magma_int_t liwork, magma_int_t* info);
template<class scalar_t>
void magmaSvd(
magma_vec_t jobz, magma_int_t m, magma_int_t n, scalar_t* A,
magma_int_t lda, scalar_t* s, scalar_t* U, magma_int_t ldu,
scalar_t* VT, magma_int_t ldvt, scalar_t* work, magma_int_t lwork,
magma_int_t* iwork, magma_int_t* info);
template<class scalar_t>
void magmaLuSolve(
magma_int_t n, magma_int_t nrhs, scalar_t* dA, magma_int_t ldda, magma_int_t* ipiv,
scalar_t* dB, magma_int_t lddb, magma_int_t* info);
template<class scalar_t>
void magmaLuSolveBatched(
magma_int_t n, magma_int_t nrhs, scalar_t** dA_array, magma_int_t ldda, magma_int_t** dipiv_array,
scalar_t** dB_array, magma_int_t lddb, magma_int_t& info,
magma_int_t batchsize, const MAGMAQueue& magma_queue);
template<>
void magmaSolve<double>(
magma_int_t n, magma_int_t nrhs, double* dA, magma_int_t ldda,
magma_int_t* ipiv, double* dB, magma_int_t lddb, magma_int_t* info) {
magma_dgesv_gpu(n, nrhs, dA, ldda, ipiv, dB, lddb, info);
}
template<>
void magmaSolve<float>(
magma_int_t n, magma_int_t nrhs, float* dA, magma_int_t ldda,
magma_int_t* ipiv, float* dB, magma_int_t lddb, magma_int_t* info) {
magma_sgesv_gpu(n, nrhs, dA, ldda, ipiv, dB, lddb, info);
}
template<>
void magmaSolveBatched<double>(
magma_int_t n, magma_int_t nrhs, double** dA_array, magma_int_t ldda,
magma_int_t** dipiv_array, double** dB_array, magma_int_t lddb,
magma_int_t* dinfo_array, magma_int_t batch_count, const MAGMAQueue& magma_queue) {
magma_dgesv_batched(n, nrhs, dA_array, ldda, dipiv_array, dB_array, lddb, dinfo_array, batch_count, magma_queue.get_queue());
}
template<>
void magmaSolveBatched<float>(
magma_int_t n, magma_int_t nrhs, float** dA_array, magma_int_t ldda,
magma_int_t** dipiv_array, float** dB_array, magma_int_t lddb,
magma_int_t* dinfo_array, magma_int_t batch_count, const MAGMAQueue& magma_queue) {
magma_sgesv_batched(n, nrhs, dA_array, ldda, dipiv_array, dB_array, lddb, dinfo_array, batch_count, magma_queue.get_queue());
}
template<>
void magmaLu<double>(
magma_int_t m, magma_int_t n, double* dA, magma_int_t ldda,
magma_int_t* ipiv, magma_int_t* info) {
magma_dgetrf_gpu(m, n, dA, ldda, ipiv, info);
}
template<>
void magmaLu<float>(
magma_int_t m, magma_int_t n, float* dA, magma_int_t ldda,
magma_int_t* ipiv, magma_int_t* info) {
magma_sgetrf_gpu(m, n, dA, ldda, ipiv, info);
}
template<>
void magmaLuBatched<double>(
magma_int_t m, magma_int_t n, double** dA_array, magma_int_t ldda,
magma_int_t** ipiv_array, magma_int_t* info_array, magma_int_t batchsize,
const MAGMAQueue& magma_queue) {
magma_dgetrf_batched(m, n, dA_array, ldda, ipiv_array, info_array, batchsize, magma_queue.get_queue());
}
template<>
void magmaLuBatched<float>(
magma_int_t m, magma_int_t n, float** dA_array, magma_int_t ldda,
magma_int_t** ipiv_array, magma_int_t* info_array, magma_int_t batchsize,
const MAGMAQueue& magma_queue) {
magma_sgetrf_batched(m, n, dA_array, ldda, ipiv_array, info_array, batchsize, magma_queue.get_queue());
}
template<>
void magmaLuNoPiv<double>(
magma_int_t m, magma_int_t n, double* dA, magma_int_t ldda,
magma_int_t* info) {
magma_dgetrf_nopiv_gpu(m, n, dA, ldda, info);
}
template<>
void magmaLuNoPiv<float>(
magma_int_t m, magma_int_t n, float* dA, magma_int_t ldda,
magma_int_t* info) {
magma_sgetrf_nopiv_gpu(m, n, dA, ldda, info);
}
template<>
void magmaLuNoPivBatched<double>(
magma_int_t m, magma_int_t n, double** dA_array, magma_int_t ldda,
magma_int_t* info_array, magma_int_t batchsize, const MAGMAQueue& magma_queue) {
magma_dgetrf_nopiv_batched(m, n, dA_array, ldda, info_array, batchsize, magma_queue.get_queue());
}
template<>
void magmaLuNoPivBatched<float>(
magma_int_t m, magma_int_t n, float** dA_array, magma_int_t ldda,
magma_int_t* info_array, magma_int_t batchsize, const MAGMAQueue& magma_queue) {
magma_sgetrf_nopiv_batched(m, n, dA_array, ldda, info_array, batchsize, magma_queue.get_queue());
}
template<>
inline magma_int_t magmaGetriOptimalBlocksize<double>(magma_int_t n) {
return magma_get_dgetri_nb(n);
}
template<>
inline magma_int_t magmaGetriOptimalBlocksize<float>(magma_int_t n) {
return magma_get_sgetri_nb(n);
}
template<>
void magmaGetri<double>(
magma_int_t n, double* dA, magma_int_t ldda, magma_int_t* ipiv, double* dwork,
magma_int_t lwork, magma_int_t* info) {
magma_dgetri_gpu(n, dA, ldda, ipiv, dwork, lwork, info);
}
template<>
void magmaGetri<float>(
magma_int_t n, float* dA, magma_int_t ldda, magma_int_t* ipiv, float* dwork,
magma_int_t lwork, magma_int_t* info) {
magma_sgetri_gpu(n, dA, ldda, ipiv, dwork, lwork, info);
}
template<>
void magmaGetriBatched<double>(
magma_int_t n, double** dA_array, magma_int_t ldda,
magma_int_t** ipiv_array, double** dinvA_array, magma_int_t lddia,
magma_int_t* info_array, magma_int_t batchsize, const MAGMAQueue& magma_queue) {
magma_dgetri_outofplace_batched(n, dA_array, ldda, ipiv_array, dinvA_array, lddia, info_array, batchsize, magma_queue.get_queue());
}
template<>
void magmaGetriBatched<float>(
magma_int_t n, float** dA_array, magma_int_t ldda,
magma_int_t** ipiv_array, float** dinvA_array, magma_int_t lddia,
magma_int_t* info_array, magma_int_t batchsize, const MAGMAQueue& magma_queue) {
magma_sgetri_outofplace_batched(n, dA_array, ldda, ipiv_array, dinvA_array, lddia, info_array, batchsize, magma_queue.get_queue());
}
template<>
void magmaCholeskySolve<double>(
magma_uplo_t uplo, magma_int_t n, magma_int_t nrhs, double* dA, magma_int_t ldda,
double* dB, magma_int_t lddb, magma_int_t* info) {
magma_dpotrs_gpu(uplo, n, nrhs, dA, ldda, dB, lddb, info);
}
template<>
void magmaCholeskySolve<float>(
magma_uplo_t uplo, magma_int_t n, magma_int_t nrhs, float* dA, magma_int_t ldda,
float* dB, magma_int_t lddb, magma_int_t* info) {
magma_spotrs_gpu(uplo, n, nrhs, dA, ldda, dB, lddb, info);
}
template<>
void magmaCholeskySolveBatched<double>(
magma_uplo_t uplo, magma_int_t n, magma_int_t nrhs, double** dA_array, magma_int_t ldda,
double** dB_array, magma_int_t lddb, magma_int_t& info, magma_int_t batchsize, const MAGMAQueue& magma_queue) {
info = magma_dpotrs_batched(uplo, n, nrhs, dA_array, ldda, dB_array, lddb, batchsize, magma_queue.get_queue());
}
template<>
void magmaCholeskySolveBatched<float>(
magma_uplo_t uplo, magma_int_t n, magma_int_t nrhs, float** dA_array, magma_int_t ldda,
float** dB_array, magma_int_t lddb, magma_int_t& info, magma_int_t batchsize, const MAGMAQueue& magma_queue) {
info = magma_spotrs_batched(uplo, n, nrhs, dA_array, ldda, dB_array, lddb, batchsize, magma_queue.get_queue());
}
template<>
void magmaCholesky<double>(
magma_uplo_t uplo, magma_int_t n, double* dA,
magma_int_t ldda, magma_int_t* info) {
magma_dpotrf_gpu(uplo, n, dA, ldda, info);
}
template<>
void magmaCholesky<float>(
magma_uplo_t uplo, magma_int_t n, float* dA,
magma_int_t ldda, magma_int_t* info) {
magma_spotrf_gpu(uplo, n, dA, ldda, info);
}
template<>
void magmaCholeskyBatched<double>(
magma_uplo_t uplo, magma_int_t n, double** dA_array, magma_int_t ldda,
magma_int_t* info_array, magma_int_t batchsize, const MAGMAQueue& magma_queue) {
magma_dpotrf_batched(uplo, n, dA_array, ldda, info_array, batchsize, magma_queue.get_queue());
}
template<>
void magmaCholeskyBatched<float>(
magma_uplo_t uplo, magma_int_t n, float** dA_array, magma_int_t ldda,
magma_int_t* info_array, magma_int_t batchsize, const MAGMAQueue& magma_queue) {
magma_spotrf_batched(uplo, n, dA_array, ldda, info_array, batchsize, magma_queue.get_queue());
}
template<>
void magmaTriangularSolve<double>(
magma_uplo_t uplo, magma_trans_t trans, magma_diag_t diag, magma_int_t m, magma_int_t n,
double* dA, magma_int_t ldda, double* dB, magma_int_t lddb) {
magma_dtrsm(MagmaLeft, uplo, trans, diag, m, n, 1, dA, ldda, dB, lddb);
}
template<>
void magmaTriangularSolve<float>(
magma_uplo_t uplo, magma_trans_t trans, magma_diag_t diag, magma_int_t m, magma_int_t n,
float* dA, magma_int_t ldda, float* dB, magma_int_t lddb) {
magma_strsm(MagmaLeft, uplo, trans, diag, m, n, 1, dA, ldda, dB, lddb);
}
template<>
void magmaTriangularSolveBatched<double>(
magma_uplo_t uplo, magma_trans_t trans, magma_diag_t diag, magma_int_t m, magma_int_t n,
double** dA_array, magma_int_t ldda, double** dB_array, magma_int_t lddb, magma_int_t batchsize,
const MAGMAQueue& magma_queue) {
magmablas_dtrsm_batched(MagmaLeft, uplo, trans, diag, m, n, 1, dA_array, ldda, dB_array, lddb, batchsize, magma_queue.get_queue());
}
template<>
void magmaTriangularSolveBatched<float>(
magma_uplo_t uplo, magma_trans_t trans, magma_diag_t diag, magma_int_t m, magma_int_t n,
float** dA_array, magma_int_t ldda, float** dB_array, magma_int_t lddb, magma_int_t batchsize,
const MAGMAQueue& magma_queue) {
magmablas_strsm_batched(MagmaLeft, uplo, trans, diag, m, n, 1, dA_array, ldda, dB_array, lddb, batchsize, magma_queue.get_queue());
}
template<>
inline magma_int_t magmaGeqrfOptimalBlocksize<double>(magma_int_t m, magma_int_t n) {
return magma_get_dgeqrf_nb(m, n);
}
template<>
inline magma_int_t magmaGeqrfOptimalBlocksize<float>(magma_int_t m, magma_int_t n) {
return magma_get_sgeqrf_nb(m, n);
}
template<>
void magmaGeqrf<double>(
magma_int_t m, magma_int_t n, double* dA, magma_int_t ldda,
double* tau, double* dT, magma_int_t* info, bool is_v2) {
if (!is_v2) {
magma_dgeqrf_gpu(m, n, dA, ldda, tau, dT, info);
} else {
magma_dgeqrf2_gpu(m, n, dA, ldda, tau, info);
}
}
template<>
void magmaGeqrf<float>(
magma_int_t m, magma_int_t n, float* dA, magma_int_t ldda,
float* tau, float* dT, magma_int_t* info, bool is_v2) {
if (!is_v2) {
magma_sgeqrf_gpu(m, n, dA, ldda, tau, dT, info);
} else {
magma_sgeqrf2_gpu(m, n, dA, ldda, tau, info);
}
}
template<>
void magmaOrgqr<double>(
magma_int_t m, magma_int_t n, magma_int_t k, double* dA, magma_int_t ldda,
double* tau, double* dT, magma_int_t nb, magma_int_t* info) {
magma_dorgqr_gpu(m, n, k, dA, ldda, tau, dT, nb, info);
}
template<>
void magmaOrgqr<float>(
magma_int_t m, magma_int_t n, magma_int_t k, float* dA, magma_int_t ldda,
float* tau, float* dT, magma_int_t nb, magma_int_t* info) {
magma_sorgqr_gpu(m, n, k, dA, ldda, tau, dT, nb, info);
}
template<>
void magmaSymeig<double>(
magma_vec_t jobz, magma_uplo_t uplo, magma_int_t n, double* dA, magma_int_t ldda,
double* w, double* wA, magma_int_t ldwa, double* work, magma_int_t lwork,
magma_int_t* iwork, magma_int_t liwork, magma_int_t* info) {
magma_dsyevd_gpu(jobz, uplo, n, dA, ldda, w, wA, ldwa, work, lwork, iwork, liwork, info);
}
template<>
void magmaSymeig<float>(
magma_vec_t jobz, magma_uplo_t uplo, magma_int_t n, float* dA, magma_int_t ldda,
float* w, float* wA, magma_int_t ldwa, float* work, magma_int_t lwork,
magma_int_t* iwork, magma_int_t liwork, magma_int_t* info) {
magma_ssyevd_gpu(jobz, uplo, n, dA, ldda, w, wA, ldwa, work, lwork, iwork, liwork, info);
}
template<>
void magmaSvd<double>(
magma_vec_t jobz, magma_int_t m, magma_int_t n, double* A,
magma_int_t lda, double* s, double* U, magma_int_t ldu,
double* VT, magma_int_t ldvt, double* work, magma_int_t lwork,
magma_int_t* iwork, magma_int_t* info) {
magma_dgesdd(jobz, m, n, A, lda, s, U, ldu, VT, ldvt, work, lwork, iwork, info);
}
template<>
void magmaSvd<float>(
magma_vec_t jobz, magma_int_t m, magma_int_t n, float* A,
magma_int_t lda, float* s, float* U, magma_int_t ldu,
float* VT, magma_int_t ldvt, float* work, magma_int_t lwork,
magma_int_t* iwork, magma_int_t* info) {
magma_sgesdd(jobz, m, n, A, lda, s, U, ldu, VT, ldvt, work, lwork, iwork, info);
}
template<>
void magmaLuSolve<double>(
magma_int_t n, magma_int_t nrhs, double* dA, magma_int_t ldda, magma_int_t* ipiv,
double* dB, magma_int_t lddb, magma_int_t* info) {
magma_dgetrs_gpu(MagmaNoTrans, n, nrhs, dA, ldda, ipiv, dB, lddb, info);
}
template<>
void magmaLuSolve<float>(
magma_int_t n, magma_int_t nrhs, float* dA, magma_int_t ldda, magma_int_t* ipiv,
float* dB, magma_int_t lddb, magma_int_t* info) {
magma_sgetrs_gpu(MagmaNoTrans, n, nrhs, dA, ldda, ipiv, dB, lddb, info);
}
template<>
void magmaLuSolveBatched<double>(
magma_int_t n, magma_int_t nrhs, double** dA_array, magma_int_t ldda, magma_int_t** dipiv_array,
double** dB_array, magma_int_t lddb, magma_int_t& info,
magma_int_t batchsize, const MAGMAQueue& magma_queue) {
info = magma_dgetrs_batched(MagmaNoTrans, n, nrhs, dA_array, ldda, dipiv_array, dB_array, lddb, batchsize, magma_queue.get_queue());
}
template<>
void magmaLuSolveBatched<float>(
magma_int_t n, magma_int_t nrhs, float** dA_array, magma_int_t ldda, magma_int_t** dipiv_array,
float** dB_array, magma_int_t lddb, magma_int_t& info,
magma_int_t batchsize, const MAGMAQueue& magma_queue) {
info = magma_sgetrs_batched(MagmaNoTrans, n, nrhs, dA_array, ldda, dipiv_array, dB_array, lddb, batchsize, magma_queue.get_queue());
}
#endif
#define ALLOCATE_ARRAY(name, type, size) \
auto storage_##name = pin_memory<type>(size); \
name = static_cast<type*>(storage_##name.data());
// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ solve ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
template <typename scalar_t>
static void apply_solve(Tensor& b, Tensor& A, std::vector<int64_t>& infos) {
#ifndef USE_MAGMA
AT_ERROR("solve: MAGMA library not found in "
"compilation. Please rebuild with MAGMA.");
#else
auto A_data = A.data_ptr<scalar_t>();
auto b_data = b.data_ptr<scalar_t>();
magma_int_t n = magma_int_cast(A.size(-2), "A.size(-2)");
magma_int_t nrhs = magma_int_cast(b.size(-1), "b.size(-1)");
if (b.dim() == 2) {
auto ipiv = at::empty({n}, at::kInt);
magma_int_t info = 0;
magmaSolve<scalar_t>(n, nrhs, A_data, n, ipiv.data_ptr<magma_int_t>(),
b_data, n, &info);
infos[0] = info;
} else {
auto A_mat_stride = matrixStride(A);
auto b_mat_stride = matrixStride(b);
magma_int_t batch_size = magma_int_cast(batchCount(A), "batchCount");
magma_int_t* info_array;
magma_int_t* ipiv_data;
magma_int_t** ipiv_array;
scalar_t** A_array;
scalar_t** b_array;
ALLOCATE_ARRAY(info_array, magma_int_t, batch_size);
ALLOCATE_ARRAY(ipiv_data, magma_int_t, batch_size * n);
ALLOCATE_ARRAY(ipiv_array, magma_int_t*, batch_size);
ALLOCATE_ARRAY(A_array, scalar_t*, batch_size);
ALLOCATE_ARRAY(b_array, scalar_t*, batch_size);
// Set up the created arrays
for (int64_t i = 0; i < batch_size; i++) {
A_array[i] = &A_data[i * A_mat_stride];
b_array[i] = &b_data[i * b_mat_stride];
ipiv_array[i] = &ipiv_data[i * n];
}
MAGMAQueue magma_queue(b.get_device());
constexpr int64_t batch_limit = 65535;
// Compute as many batches of 65535 possible
// The number of "mini"-batches are floor(batch_size / batch_limit)
// and these cover floor(batch_size / batch_limit) * batch_limit matrix solves
int64_t mini_batches = batch_size / batch_limit, mini_idx;
for (mini_idx = 0; mini_idx < mini_batches * batch_limit; mini_idx += batch_limit) {
scalar_t** A_array_cur = &A_array[mini_idx];
scalar_t** b_array_cur = &b_array[mini_idx];
magma_int_t** ipiv_array_cur = &ipiv_array[mini_idx];
magma_int_t* info_array_cur = &info_array[mini_idx];
magmaSolveBatched<scalar_t>(
n, nrhs, A_array_cur, n, ipiv_array_cur, b_array_cur, n,
info_array_cur, batch_limit, magma_queue);
}
// Compute whatever is left = batch_size - floor(batch_size / batch_limit) * batch_limit
// which concisely is equal to batch_size % batch_limit
if (batch_size % batch_limit != 0) {
magmaSolveBatched<scalar_t>(
n, nrhs, &A_array[mini_idx], n, &ipiv_array[mini_idx], &b_array[mini_idx], n,
&info_array[mini_idx], batch_size % batch_limit, magma_queue);
}
for (int64_t i = 0; i < batch_size; i++) {
infos[i] = info_array[i];
}
}
#endif
}
std::tuple<Tensor, Tensor> _solve_helper_cuda(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_TYPES(self.scalar_type(), "solve_cuda", [&]{
apply_solve<scalar_t>(self_working_copy, A_working_copy, infos);
});
if (self.dim() > 2) {
batchCheckErrors(infos, "solve_cuda");
} else {
singleCheckErrors(infos[0], "solve_cuda");
}
return std::tuple<Tensor, Tensor>(self_working_copy, A_working_copy);
}
// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ inverse ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
template <typename scalar_t>
static void apply_batched_inverse(Tensor& self, Tensor& self_inv, std::vector<int64_t>& infos) {
#ifndef USE_MAGMA
AT_ERROR("inverse: MAGMA library not found in "
"compilation. Please rebuild with MAGMA.");
#else
auto self_data = self.data_ptr<scalar_t>();
auto self_mat_stride = matrixStride(self);
auto self_inv_data = self_inv.data_ptr<scalar_t>();
auto self_inv_mat_stride = matrixStride(self_inv);
magma_int_t batch_size = magma_int_cast(batchCount(self), "batchCount");
magma_int_t n = magma_int_cast(self.size(-2), "self.size(-2)");
magma_int_t* info_array;
magma_int_t* ipiv_data;
magma_int_t** ipiv_array;
scalar_t** self_array;
scalar_t** self_inv_array;
ALLOCATE_ARRAY(info_array, magma_int_t, batch_size);
ALLOCATE_ARRAY(ipiv_data, magma_int_t, batch_size * n);
ALLOCATE_ARRAY(ipiv_array, magma_int_t*, batch_size);
ALLOCATE_ARRAY(self_array, scalar_t*, batch_size);
ALLOCATE_ARRAY(self_inv_array, scalar_t*, batch_size);
// Set up the created arrays
for (int64_t i = 0; i < batch_size; i++) {
self_array[i] = &self_data[i * self_mat_stride];
self_inv_array[i] = &self_inv_data[i * self_inv_mat_stride];
ipiv_array[i] = &ipiv_data[i * n];
}
MAGMAQueue magma_queue(self.get_device());
magmaLuBatched<scalar_t>(
n, n, self_array, n, ipiv_array, info_array,
batch_size, magma_queue);
constexpr int64_t batch_limit = 65535;
// Compute as many batches of 65535 possible
// The number of "mini"-batches are floor(batch_size / batch_limit)
// and these cover floor(batch_size / batch_limit) * batch_limit matrix solves
int64_t mini_batches = batch_size / batch_limit, mini_idx;
for (mini_idx = 0; mini_idx < mini_batches * batch_limit; mini_idx += batch_limit) {
scalar_t** self_array_cur = &self_array[mini_idx];
scalar_t** self_inv_array_cur = &self_inv_array[mini_idx];
magma_int_t** ipiv_array_cur = &ipiv_array[mini_idx];
magma_int_t* info_array_cur = &info_array[mini_idx];
magmaGetriBatched<scalar_t>(
n, self_array_cur, n, ipiv_array_cur, self_inv_array_cur,
n, info_array_cur, batch_limit, magma_queue);
}
// Compute whatever is left = batch_size - floor(batch_size / batch_limit) * batch_limit
// which concisely is equal to batch_size % batch_limit
if (batch_size % batch_limit != 0) {
magmaGetriBatched<scalar_t>(
n, &self_array[mini_idx], n, &ipiv_array[mini_idx], &self_inv_array[mini_idx],
n, &info_array[mini_idx], batch_size % batch_limit, magma_queue);
}
for (int64_t i = 0; i < batch_size; i++) {
infos[i] = info_array[i];
}
#endif
}
template <typename scalar_t>
static void apply_single_inverse(Tensor& self, int64_t& info) {
#ifndef USE_MAGMA
AT_ERROR("inverse: MAGMA library not found in "
"compilation. Please rebuild with MAGMA.");
#else
auto self_data = self.data_ptr<scalar_t>();
magma_int_t n = magma_int_cast(self.size(-2), "self.size(-2)");
magma_int_t lwork = n * magmaGetriOptimalBlocksize<scalar_t>(n);
magma_int_t info_tmp = 0;
Tensor ipiv = at::empty({n}, at::kInt);
Tensor dwork = at::empty({lwork}, self.options());
magmaLu<scalar_t>(n, n, self_data, n, ipiv.data_ptr<magma_int_t>(), &info_tmp);
if (info_tmp != 0) {
info = info_tmp;
return;
}
magmaGetri<scalar_t>(
n, self_data, n, ipiv.data_ptr<magma_int_t>(), dwork.data_ptr<scalar_t>(), lwork, &info_tmp);
info = info_tmp;
#endif
}
Tensor _inverse_helper_cuda(const Tensor& self) {
auto self_inv_working_copy = cloneBatchedColumnMajor(self);
if (self.dim() > 2) {
std::vector<int64_t> infos(batchCount(self), 0);
auto self_working_copy = cloneBatchedColumnMajor(self);
AT_DISPATCH_FLOATING_TYPES(self.scalar_type(), "inverse_cuda", [&]{
apply_batched_inverse<scalar_t>(
self_working_copy, self_inv_working_copy, infos);
});
batchCheckErrors(infos, "inverse_cuda");
} else {
int64_t info = 0;
AT_DISPATCH_FLOATING_TYPES(self.scalar_type(), "inverse_cuda", [&]{
apply_single_inverse<scalar_t>(self_inv_working_copy, info);
});
singleCheckErrors(info, "inverse_cuda");
}
return self_inv_working_copy;
}
// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ cholesky_solve ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
template <typename scalar_t>
static void apply_cholesky_solve(Tensor& b, Tensor& A, bool upper, int64_t& info) {
#ifndef USE_MAGMA
AT_ERROR("cholesky_solve: MAGMA library not found in "
"compilation. Please rebuild with MAGMA.");
#else
magma_uplo_t uplo = upper ? MagmaUpper : MagmaLower;
auto A_data = A.data_ptr<scalar_t>();
auto b_data = b.data_ptr<scalar_t>();
magma_int_t n = magma_int_cast(A.size(-2), "A.size(-2)");
magma_int_t nrhs = magma_int_cast(b.size(-1), "b.size(-1)");
int info_tmp = 0;
if (b.dim() == 2) {
magmaCholeskySolve<scalar_t>(uplo, n, nrhs, A_data, n,
b_data, n, &info_tmp);
info = info_tmp;
} else {
auto A_mat_stride = matrixStride(A);
auto b_mat_stride = matrixStride(b);
magma_int_t batch_size = magma_int_cast(batchCount(A), "batchCount");
scalar_t** A_array;
scalar_t** b_array;
ALLOCATE_ARRAY(A_array, scalar_t*, batch_size);
ALLOCATE_ARRAY(b_array, scalar_t*, batch_size);
// Set up the created arrays
for (int64_t i = 0; i < batch_size; i++) {
A_array[i] = &A_data[i * A_mat_stride];
b_array[i] = &b_data[i * b_mat_stride];
}
MAGMAQueue magma_queue(b.get_device());
constexpr int64_t batch_limit = 65535;
// Compute as many batches of 65535 possible
// The number of "mini"-batches are floor(batch_size / batch_limit)
// and these cover floor(batch_size / batch_limit) * batch_limit matrix solves
int64_t mini_batches = batch_size / batch_limit, mini_idx;
for (mini_idx = 0; mini_idx < mini_batches * batch_limit; mini_idx += batch_limit) {
scalar_t** A_array_cur = &A_array[mini_idx];
scalar_t** b_array_cur = &b_array[mini_idx];
magmaCholeskySolveBatched<scalar_t>(
uplo, n, nrhs, A_array_cur, n, b_array_cur, n,
info_tmp, batch_limit, magma_queue);
if (info_tmp != 0) {
break;
}
}
// Compute whatever is left = batch_size - floor(batch_size / batch_limit) * batch_limit
// which concisely is equal to batch_size % batch_limit
if (batch_size % batch_limit != 0 && info_tmp == 0) {
magmaCholeskySolveBatched<scalar_t>(
uplo, n, nrhs, &A_array[mini_idx], n, &b_array[mini_idx], n,
info_tmp, batch_size % batch_limit, magma_queue);
}
info = info_tmp;
}
#endif
}
Tensor _cholesky_solve_helper_cuda(const Tensor& self, const Tensor& A, bool upper) {
int64_t info = 0;
auto self_working_copy = cloneBatchedColumnMajor(self);
auto A_working_copy = cloneBatchedColumnMajor(A);
AT_DISPATCH_FLOATING_TYPES(self.scalar_type(), "cholesky_solve_cuda", [&]{
apply_cholesky_solve<scalar_t>(self_working_copy, A_working_copy, upper, info);
});
TORCH_CHECK(info == 0, "MAGMA cholesky_solve : invalid argument: ", -info);
return self_working_copy;
}
// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ cholesky ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
template <typename scalar_t>
static void apply_cholesky(Tensor& self, bool upper, std::vector<int64_t>& infos) {
#ifndef USE_MAGMA
AT_ERROR("cholesky: MAGMA library not found in "
"compilation. Please rebuild with MAGMA.");
#else
magma_uplo_t uplo = upper ? MagmaUpper : MagmaLower;
auto self_data = self.data_ptr<scalar_t>();
magma_int_t n = magma_int_cast(self.size(-2), "self.size(-2)");
if (self.dim() == 2) {
magma_int_t info = 0;
magmaCholesky<scalar_t>(uplo, n, self_data, n, &info);
infos[0] = info;
} else {
auto self_mat_stride = matrixStride(self);
magma_int_t batch_size = magma_int_cast(batchCount(self), "batchCount");
magma_int_t* info_array;
scalar_t** self_array;
ALLOCATE_ARRAY(info_array, magma_int_t, batch_size);
ALLOCATE_ARRAY(self_array, scalar_t*, batch_size);
// Set up the created arrays
for (int64_t i = 0; i < batch_size; i++) {
self_array[i] = &self_data[i * self_mat_stride];
}
MAGMAQueue magma_queue(self.get_device());
constexpr int64_t batch_limit = 262140;
// Compute as many batches of 262140 possible
// 262140 is the size of the largest batch of matrices that can be run with
// violating maximum kernel configuration
// The number of "mini"-batches are floor(batch_size / batch_limit)
// and these cover floor(batch_size / batch_limit) * batch_limit cholesky calls
int64_t mini_batches = batch_size / batch_limit, mini_idx;
for (mini_idx = 0; mini_idx < mini_batches * batch_limit; mini_idx += batch_limit) {
scalar_t** self_array_cur = &self_array[mini_idx];
magma_int_t* info_array_cur = &info_array[mini_idx];
magmaCholeskyBatched<scalar_t>(
uplo, n, self_array_cur, n, info_array_cur, batch_limit, magma_queue);
}
// Compute whatever is left = batch_size - floor(batch_size / batch_limit) * batch_limit
// which concisely is equal to batch_size % batch_limit
if (batch_size % batch_limit != 0) {
magmaCholeskyBatched<scalar_t>(
uplo, n, &self_array[mini_idx], n, &info_array[mini_idx], batch_size % batch_limit, magma_queue);
}
for (int64_t i = 0; i < batch_size; i++) {
infos[i] = info_array[i];
}
}
#endif
}
Tensor _cholesky_helper_cuda(const Tensor& self, bool upper) {
std::vector<int64_t> infos(batchCount(self), 0);
Tensor self_working_copy;
if (upper) {
self_working_copy = cloneBatchedColumnMajor(self.transpose(-1, -2));
} else {
self_working_copy = cloneBatchedColumnMajor(self);
}
AT_DISPATCH_FLOATING_TYPES(self.scalar_type(), "cholesky_cuda", [&]{
apply_cholesky<scalar_t>(self_working_copy, false, infos);
});
if (self.dim() > 2) {
batchCheckErrors(infos, "cholesky_cuda");
} else {
singleCheckErrors(infos[0], "cholesky_cuda");
}
if (upper) {
return self_working_copy.transpose(-1, -2);
} else {
return self_working_copy;
}
}
// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ lu ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
template <typename scalar_t>
static void apply_lu(Tensor& self, Tensor& pivots, Tensor& infos, bool get_pivots) {
#ifndef USE_MAGMA
AT_ERROR("lu: MAGMA library not found in "
"compilation. Please rebuild with MAGMA.");
#else
auto self_data = self.data_ptr<scalar_t>();
magma_int_t n = magma_int_cast(self.size(-1), "n");
if (self.dim() == 2) {
// If `pivots` is defined, then we have to compute them.
// magmaLu and magmaLuNoPiv use a hybrid CPU-GPU algorithm to compute
// the partially-pivoted LU decomposition with / without pivots.
// The driver routines magma_(d/s)getrf_(nopiv_)gpu accepts a tensor on the CPU for pivots.
// The data is later copied back to the appropriate output tensor.
Tensor info_tmp = at::zeros({}, at::kInt);
if (get_pivots) {
Tensor piv_tmp = at::empty({n}, at::kInt);
magmaLu<scalar_t>(
n, n, self_data, n, piv_tmp.data_ptr<magma_int_t>(), info_tmp.data_ptr<magma_int_t>());
pivots.copy_(piv_tmp);
} else {
magmaLuNoPiv<scalar_t>(n, n, self_data, n, info_tmp.data_ptr<magma_int_t>());
}
infos.copy_(info_tmp);
} else {
auto self_matrix_stride = matrixStride(self);
magma_int_t batch_size = magma_int_cast(batchCount(self), "batchCount");
scalar_t** self_array;
ALLOCATE_ARRAY(self_array, scalar_t*, batch_size);
// Set up the created arrays
for (int64_t i = 0; i < batch_size; i++) {
self_array[i] = &self_data[i * self_matrix_stride];
}
MAGMAQueue magma_queue(self.get_device());
// Same comment as in the case of single matrix above.
if (get_pivots) {
auto pivots_data = pivots.data_ptr<magma_int_t>();
auto pivots_matrix_stride = pivots.size(-1);
magma_int_t** pivots_array;
ALLOCATE_ARRAY(pivots_array, magma_int_t*, batch_size);
for (int64_t i = 0; i < batch_size; i++) {
pivots_array[i] = &pivots_data[i * pivots_matrix_stride];
}
magmaLuBatched<scalar_t>(
n, n, self_array, n, pivots_array,
infos.data_ptr<magma_int_t>(), batch_size, magma_queue);
} else {
magmaLuNoPivBatched<scalar_t>(
n, n, self_array, n, infos.data_ptr<magma_int_t>(),
batch_size, magma_queue);
}
}
#endif
}
std::tuple<Tensor, Tensor, Tensor> _lu_with_info_cuda(const Tensor& self, bool pivot, bool check_errors) {
TORCH_CHECK(self.dim() >= 2,
"expected tensor with 2 or more dimensions, got size: ", self.sizes(),
" instead");
squareCheckInputs(self);
auto req_size = self.sizes().vec();
req_size.pop_back();
Tensor pivots_tensor = at::arange(1, self.size(-1) + 1, self.options().dtype(at::kInt)).expand(req_size).contiguous();
req_size.pop_back();
auto infos_tensor = at::zeros(req_size, self.options().dtype(at::kInt));
Tensor self_working_copy;
if (self.numel() == 0) {
self_working_copy = at::empty_like(self);
} else {
self_working_copy = cloneBatchedColumnMajor(self);
AT_DISPATCH_FLOATING_TYPES(self.scalar_type(), "lu_cuda", [&]{
apply_lu<scalar_t>(self_working_copy, pivots_tensor, infos_tensor, pivot);
});
}
if (check_errors) {
if (self.dim() == 2) {
singleCheckErrors(infos_tensor.item<int64_t>(), "lu");
} else {
batchCheckErrors(infos_tensor, "lu");
}
}
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_MAGMA
AT_ERROR("triangular_solve: MAGMA library not found in "
"compilation. Please rebuild with MAGMA.");
#else
magma_uplo_t uplo = upper ? MagmaUpper : MagmaLower;
magma_trans_t trans = transpose ? MagmaTrans : MagmaNoTrans;
magma_diag_t diag = unitriangular ? MagmaUnit : MagmaNonUnit;
auto A_data = A.data_ptr<scalar_t>();
auto b_data = b.data_ptr<scalar_t>();
magma_int_t n = magma_int_cast(A.size(-2), "A.size(-2)");
magma_int_t nrhs = magma_int_cast(b.size(-1), "b.size(-1)");
magma_int_t batch_size = magma_int_cast(batchCount(A), "batchCount");
// batch_size == 1 implies that:
// 1. the RHS and LHS tensors have 2 dimensions, or
// 2. the RHS and LHS tensors have more than 2 dimensions but all batch dimensions are 1
if (batch_size == 1) {
magmaTriangularSolve<scalar_t>(uplo, trans, diag, n, nrhs, A_data, n, b_data, n);
} else {
auto A_mat_stride = matrixStride(A);
auto b_mat_stride = matrixStride(b);
scalar_t** A_array;
scalar_t** b_array;
ALLOCATE_ARRAY(A_array, scalar_t*, batch_size);
ALLOCATE_ARRAY(b_array, scalar_t*, batch_size);
// Set up the created arrays
for (int64_t i = 0; i < batch_size; i++) {
A_array[i] = &A_data[i * A_mat_stride];
b_array[i] = &b_data[i * b_mat_stride];
}
MAGMAQueue magma_queue(b.get_device());
constexpr int64_t batch_limit = 65535;
// Compute as many batches of 65535 possible
// The number of "mini"-batches are floor(batch_size / batch_limit)
// and these cover floor(batch_size / batch_limit) * batch_limit matrix solves
int64_t mini_batches = batch_size / batch_limit, mini_idx;
for (mini_idx = 0; mini_idx < mini_batches * batch_limit; mini_idx += batch_limit) {
scalar_t** A_array_cur = &A_array[mini_idx];
scalar_t** b_array_cur = &b_array[mini_idx];
magmaTriangularSolveBatched<scalar_t>(
uplo, trans, diag, n, nrhs, A_array_cur,
n, b_array_cur, n, batch_limit, magma_queue);
}
// Compute whatever is left = batch_size - floor(batch_size / batch_limit) * batch_limit
// which concisely is equal to batch_size % batch_limit
if (batch_size % batch_limit != 0) {
magmaTriangularSolveBatched<scalar_t>(
uplo, trans, diag, n, nrhs, &A_array[mini_idx],
n, &b_array[mini_idx], n, batch_size % batch_limit, magma_queue);
}
}
#endif
}
std::tuple<Tensor, Tensor> _triangular_solve_helper_cuda(const Tensor& self, const Tensor& A,
bool upper, bool transpose, bool unitriangular) {
auto self_working_copy = cloneBatchedColumnMajor(self);