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BatchLinearAlgebra.cpp
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BatchLinearAlgebra.cpp
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#define TORCH_ASSERT_ONLY_METHOD_OPERATORS
#include <ATen/core/Tensor.h>
#include <ATen/core/grad_mode.h>
#include <ATen/Dispatch.h>
#include <ATen/Parallel.h>
#include <ATen/TensorMeta.h>
#include <ATen/TensorOperators.h>
#include <ATen/TensorSubclassLikeUtils.h>
#include <ATen/native/BatchLinearAlgebra.h>
#include <ATen/native/LinearAlgebraUtils.h>
#include <ATen/native/Resize.h>
#include <ATen/native/cpu/zmath.h>
#include <c10/util/irange.h>
#include <utility>
#include <vector>
#ifndef AT_PER_OPERATOR_HEADERS
#include <ATen/Functions.h>
#include <ATen/NativeFunctions.h>
#else
#include <ATen/ops/_cholesky_solve_helper.h>
#include <ATen/ops/_cholesky_solve_helper_native.h>
#include <ATen/ops/_linalg_check_errors.h>
#include <ATen/ops/_linalg_check_errors_native.h>
#include <ATen/ops/_linalg_eigh.h>
#include <ATen/ops/_linalg_eigh_meta.h>
#include <ATen/ops/_linalg_eigh_native.h>
#include <ATen/ops/_linalg_eigvals.h>
#include <ATen/ops/_linalg_eigvals_native.h>
#include <ATen/ops/_linalg_solve_ex.h>
#include <ATen/ops/_linalg_solve_ex_meta.h>
#include <ATen/ops/_linalg_solve_ex_native.h>
#include <ATen/ops/_linalg_svd.h>
#include <ATen/ops/_linalg_svd_meta.h>
#include <ATen/ops/_linalg_svd_native.h>
#include <ATen/ops/_lu_with_info_native.h>
#include <ATen/ops/all.h>
#include <ATen/ops/arange.h>
#include <ATen/ops/cat.h>
#include <ATen/ops/cholesky.h>
#include <ATen/ops/cholesky_inverse.h>
#include <ATen/ops/cholesky_inverse_native.h>
#include <ATen/ops/cholesky_native.h>
#include <ATen/ops/cholesky_solve.h>
#include <ATen/ops/cholesky_solve_native.h>
#include <ATen/ops/clone.h>
#include <ATen/ops/complex.h>
#include <ATen/ops/cumprod.h>
#include <ATen/ops/empty.h>
#include <ATen/ops/empty_like.h>
#include <ATen/ops/geqrf.h>
#include <ATen/ops/geqrf_native.h>
#include <ATen/ops/inverse_native.h>
#include <ATen/ops/linalg_cholesky_ex.h>
#include <ATen/ops/linalg_cholesky_ex_meta.h>
#include <ATen/ops/linalg_cholesky_ex_native.h>
#include <ATen/ops/linalg_cholesky_native.h>
#include <ATen/ops/linalg_eig.h>
#include <ATen/ops/linalg_eig_native.h>
#include <ATen/ops/linalg_eigh_native.h>
#include <ATen/ops/linalg_eigvals.h>
#include <ATen/ops/linalg_eigvals_native.h>
#include <ATen/ops/linalg_eigvalsh_native.h>
#include <ATen/ops/linalg_householder_product.h>
#include <ATen/ops/linalg_householder_product_native.h>
#include <ATen/ops/linalg_inv.h>
#include <ATen/ops/linalg_inv_ex.h>
#include <ATen/ops/linalg_inv_ex_native.h>
#include <ATen/ops/linalg_inv_native.h>
#include <ATen/ops/linalg_ldl_factor_ex.h>
#include <ATen/ops/linalg_ldl_factor_ex_meta.h>
#include <ATen/ops/linalg_ldl_factor_ex_native.h>
#include <ATen/ops/linalg_ldl_factor_native.h>
#include <ATen/ops/linalg_ldl_solve_meta.h>
#include <ATen/ops/linalg_ldl_solve_native.h>
#include <ATen/ops/linalg_lstsq.h>
#include <ATen/ops/linalg_lstsq_native.h>
#include <ATen/ops/linalg_lu_factor_ex.h>
#include <ATen/ops/linalg_lu_factor_ex_meta.h>
#include <ATen/ops/linalg_lu_factor_ex_native.h>
#include <ATen/ops/linalg_lu_factor_native.h>
#include <ATen/ops/linalg_lu_meta.h>
#include <ATen/ops/linalg_lu_native.h>
#include <ATen/ops/linalg_lu_solve.h>
#include <ATen/ops/linalg_lu_solve_meta.h>
#include <ATen/ops/linalg_lu_solve_native.h>
#include <ATen/ops/linalg_qr.h>
#include <ATen/ops/linalg_qr_meta.h>
#include <ATen/ops/linalg_qr_native.h>
#include <ATen/ops/linalg_solve_ex.h>
#include <ATen/ops/linalg_solve_ex_native.h>
#include <ATen/ops/linalg_solve_native.h>
#include <ATen/ops/linalg_solve_triangular_native.h>
#include <ATen/ops/linalg_svd.h>
#include <ATen/ops/linalg_svd_native.h>
#include <ATen/ops/linalg_svdvals.h>
#include <ATen/ops/linalg_svdvals_native.h>
#include <ATen/ops/linalg_vander_native.h>
#include <ATen/ops/linalg_vecdot_native.h>
#include <ATen/ops/lu_solve_native.h>
#include <ATen/ops/lu_unpack.h>
#include <ATen/ops/lu_unpack_meta.h>
#include <ATen/ops/lu_unpack_native.h>
#include <ATen/ops/orgqr_native.h>
#include <ATen/ops/ormqr_native.h>
#include <ATen/ops/qr_native.h>
#include <ATen/ops/real.h>
#include <ATen/ops/resize_as_native.h>
#include <ATen/ops/sum.h>
#include <ATen/ops/svd_native.h>
#include <ATen/ops/triangular_solve_meta.h>
#include <ATen/ops/triangular_solve_native.h>
#include <ATen/ops/tril.h>
#include <ATen/ops/triu.h>
#include <ATen/ops/vdot.h>
#include <ATen/ops/zeros.h>
#endif
// 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()
// 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);
// 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);
// sytrf
extern "C" void dsytrf_(
char* uplo,
int* n,
double* a,
int* lda,
int* ipiv,
double* work,
int* lwork,
int* info);
extern "C" void ssytrf_(
char* uplo,
int* n,
float* a,
int* lda,
int* ipiv,
float* work,
int* lwork,
int* info);
extern "C" void zsytrf_(
char* uplo,
int* n,
std::complex<double>* a,
int* lda,
int* ipiv,
std::complex<double>* work,
int* lwork,
int* info);
extern "C" void csytrf_(
char* uplo,
int* n,
std::complex<float>* a,
int* lda,
int* ipiv,
std::complex<float>* work,
int* lwork,
int* info);
// hetrf
extern "C" void zhetrf_(
char* uplo,
int* n,
std::complex<double>* a,
int* lda,
int* ipiv,
std::complex<double>* work,
int* lwork,
int* info);
extern "C" void chetrf_(
char* uplo,
int* n,
std::complex<float>* a,
int* lda,
int* ipiv,
std::complex<float>* work,
int* lwork,
int* info);
// sytrs
extern "C" void dsytrs_(
char* uplo,
int* n,
int* nrhs,
double* a,
int* lda,
int* ipiv,
double* b,
int* ldb,
int* info);
extern "C" void ssytrs_(
char* uplo,
int* n,
int* nrhs,
float* a,
int* lda,
int* ipiv,
float* b,
int* ldb,
int* info);
extern "C" void zsytrs_(
char* uplo,
int* n,
int* nrhs,
std::complex<double>* a,
int* lda,
int* ipiv,
std::complex<double>* b,
int* ldb,
int* info);
extern "C" void csytrs_(
char* uplo,
int* n,
int* nrhs,
std::complex<float>* a,
int* lda,
int* ipiv,
std::complex<float>* b,
int* ldb,
int* info);
// hetrs
extern "C" void zhetrs_(
char* uplo,
int* n,
int* nrhs,
std::complex<double>* a,
int* lda,
int* ipiv,
std::complex<double>* b,
int* ldb,
int* info);
extern "C" void chetrs_(
char* uplo,
int* n,
int* nrhs,
std::complex<float>* a,
int* lda,
int* ipiv,
std::complex<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);
// 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);
// 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::meta {
TORCH_META_FUNC(linalg_ldl_factor_ex)
(const Tensor& self, bool hermitian, bool check_errors) {
at::native::squareCheckInputs(self, "torch.linalg.ldl_factor_ex");
at::native::checkFloatingOrComplex(self, "torch.linalg.ldl_factor_ex");
auto shape = self.sizes();
auto ndim = shape.size();
// prefer column major strides
auto ld_strides = at::native::batched_matrix_contiguous_strides(shape, /*f-contig=*/true);
set_output_strided(0, shape, ld_strides, self.options(), {}); // LD
set_output_contiguous(
1, shape.slice(0, ndim - 1), self.options().dtype(ScalarType::Int)); // pivots
set_output_contiguous(
2, shape.slice(0, ndim - 2), self.options().dtype(ScalarType::Int)); // info
}
TORCH_META_FUNC(linalg_ldl_solve)
(const Tensor& LD,
const Tensor& pivots,
const Tensor& B,
bool hermitian) {
at::native::squareCheckInputs(LD, "torch.linalg.ldl_solve");
at::native::checkFloatingOrComplex(LD, "torch.linalg.ldl_solve");
at::native::linearSolveCheckInputs(B, LD, "torch.linalg.ldl_solve");
TORCH_CHECK(
B.dim() >= 2,
"torch.linalg.ldl_solve: Expected B to have at least 2 dimensions, but it has ",
B.dim(),
" dimensions instead");
auto expected_pivots_shape = LD.sizes().slice(0, LD.dim() - 1);
TORCH_CHECK(
expected_pivots_shape.equals(pivots.sizes()),
"torch.linalg.ldl_solve: Expected LD.shape[:-1] and pivots.shape to be the same, but got pivots with shape ",
pivots.sizes(),
" instead");
// pivots is allowed to be any integer type
// LAPACK we use is 32-bit interface while cuSOLVER uses 64-bit interface for integers
TORCH_CHECK(
at::isIntegralType(pivots.scalar_type(), /*includeBool=*/false),
"torch.linalg.ldl_solve: Expected pivots to be integers. Got ",
pivots.scalar_type());
TORCH_CHECK(
LD.scalar_type() == B.scalar_type(),
"torch.linalg.ldl_solve: ",
"LD dtype",
LD.scalar_type(),
" does not match b dtype ",
B.scalar_type());
auto [B_broadcast_size, _] = at::native::_linalg_broadcast_batch_dims(B, LD);
// prefer column major strides
auto result_strides = at::native::batched_matrix_contiguous_strides(B_broadcast_size, /*column_major=*/true);
set_output_strided(0, B_broadcast_size, result_strides, B.options(), {});
}
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) {
auto [self_broadcast_size, A_broadcast_size] = at::native::_linalg_broadcast_batch_dims(self, A);
// make column major strides for BLAS
const auto solution_strides = at::native::batched_matrix_contiguous_strides(self_broadcast_size, /*f-contig=*/true);
set_output_raw_strided(0, self_broadcast_size, solution_strides, self.options(), {});
// make column major strides for BLAS
auto clone_A_strides = at::native::batched_matrix_contiguous_strides(A_broadcast_size, /*f_contig=*/true);
set_output_raw_strided(1, A_broadcast_size, clone_A_strides, A.options(), {});
} else if (A.layout() == Layout::SparseCsr || A.layout() == Layout::SparseBsr) {
// no broadcasting for non-strided layout
set_output_raw_strided(0, self.sizes(), {}, self.options(), {}); // make row major strides for Sparse BLAS
set_output_raw_strided(1, {0}, {}, self.options(), {}); // return 0-sized tensor
} else {
TORCH_INTERNAL_ASSERT(false, "triangular_solve: Got an unexpected layout.");
}
}
TORCH_META_FUNC(_linalg_solve_ex)(const Tensor& A,
const Tensor& B,
bool left,
bool check_errors) {
// dtype
at::native::checkFloatingOrComplex(A, "linalg.solve");
TORCH_CHECK(A.scalar_type() == B.scalar_type(),
"linalg.solve: Expected A and B to have the same dtype, but found A of type ",
A.scalar_type(), " and B of type ", B.scalar_type(), " instead");
// NumPy compat: Two types of 'B' tensors are supported:
// - 1D tensor or batch of 1D tensors (vector case)
// - 2D tensor or batch of 2D tensors (matrix case)
const bool vector_case = at::native::linalg_solve_is_vector_rhs(A, B);
auto B_ = vector_case ? B.unsqueeze(-1) : B;
// matrix shapes
at::native::checkInputsSolver(A, B_, /*left=*/left, "linalg.solve");
// Check that B can be broadcasted to the shape of A
auto B_broad_shape = std::get<0>(at::native::_linalg_broadcast_batch_dims(B_, A));
// We disallow the broadcasting of B as a vector when left=False as, in that case, A.shape = (*, 1, 1)
TORCH_CHECK(left || !vector_case, "linalg.solve: Vector broadcasting of the left hand side is not supported for left=False. In this case linalg.solve is equivalent to B / A.squeeze(-1)");
auto result_shape = vector_case ? IntArrayRef(B_broad_shape.data(), B_broad_shape.size() - 1)
: B_broad_shape;
auto result_strides = at::native::batched_matrix_contiguous_strides(result_shape, /*column_major=*/left);
set_output_strided(0, result_shape, result_strides, B.options(), {});
auto shape = A.sizes();
auto ndim = shape.size();
// LU
auto LU_strides = at::native::batched_matrix_contiguous_strides(shape, /*f-contig*=*/true);
set_output_strided(1, shape, LU_strides, A.options(), {});
// pivots
set_output_contiguous(2, shape.slice(0, ndim - 1), A.options().dtype(kInt));
// info
set_output_contiguous(3, shape.slice(0, ndim - 2), A.options().dtype(kInt));
}
TORCH_META_FUNC(linalg_inv_ex)(const Tensor& A, bool check_errors) {
at::native::squareCheckInputs(A, "linalg.inv");
at::native::checkFloatingOrComplex(A, "linalg.inv", /*allow_low_precision_dtypes*/false);
auto shape = A.sizes();
auto result_strides = at::native::batched_matrix_contiguous_strides(shape, /*f-contig*=*/true);
set_output_strided(0, shape, result_strides, A.options(), {});
set_output_contiguous(
1, shape.slice(0, shape.size() - 2), A.options().dtype(ScalarType::Int)); // info
}
TORCH_META_FUNC(linalg_lu_factor_ex)(const Tensor& A, bool pivot, bool check_errors) {
TORCH_CHECK(A.dim() >= 2, "torch.lu_factor: Expected tensor with 2 or more dimensions. Got size: ", A.sizes(), " instead");
auto sizes = A.sizes().vec();
const auto m = sizes.cend()[-2];
const auto n = sizes.cend()[-1];
// make column major strides for BLAS
auto LU_strides = at::native::batched_matrix_contiguous_strides(sizes, /*f-contig*=*/true);
set_output_strided(0, sizes, LU_strides, A.options(), {});
// Set sizes to the size of pivots
sizes.pop_back();
sizes.back() = std::min(m, n);
set_output_contiguous(1, sizes, A.options().dtype(kInt), {});
// Set sizes to the size of info
sizes.pop_back();
set_output_contiguous(2, sizes, A.options().dtype(kInt), {});
}
TORCH_META_FUNC(linalg_lu_solve)(const Tensor& LU,
const Tensor& pivots,
const Tensor& B,
bool left,
bool adjoint) {
// dtype
at::native::checkFloatingOrComplex(LU, "torch.linalg.lu_solve");
TORCH_CHECK(LU.scalar_type() == B.scalar_type(),
"linalg.lu_solve: Expected LU and B to have the same dtype, but found LU of type ",
LU.scalar_type(), " and B of type ", B.scalar_type(), " instead");
TORCH_CHECK(pivots.dtype() == at::kInt,
"linalg.lu_solve: pivots should be a Tensor of scalar type torch.int32");
// matrix shapes
at::native::squareCheckInputs(LU, "torch.linalg.lu_solve");
at::native::checkInputsSolver(LU, B, left, "linalg.lu_solve");
//
TORCH_CHECK(LU.size(-1) == pivots.size(-1),
"linalg.lu_solve: Number of pivots per batch should be same as the dimension of the matrix");
// batches
TORCH_CHECK(
LU.sizes().slice(0, LU.dim() - 1).equals(pivots.sizes()),
"linalg.lu_solve: Expected LU.shape[:-1] and pivots.shape to be the same, but got pivots with shape ",
pivots.sizes(), " instead");
// This one checks that B can be broadcasted to the shape of A
auto B_broadcast_size = std::get<0>(at::native::_linalg_broadcast_batch_dims(B, LU));
auto result_strides = at::native::batched_matrix_contiguous_strides(B_broadcast_size, /*column_major=*/left);
set_output_strided(0, B_broadcast_size, result_strides, B.options(), {});
}
TORCH_META_FUNC(linalg_cholesky_ex)(const Tensor& A,
bool upper,
bool check_errors) {
at::native::squareCheckInputs(A, "linalg.cholesky");
at::native::checkFloatingOrComplex(A, "linalg.cholesky");
auto A_shape = A.sizes();
auto ndim = A_shape.size();
// L
auto L_strides = at::native::batched_matrix_contiguous_strides(A_shape, /*f-contig*=*/true);
set_output_strided(0, A_shape, L_strides, A.options(), {});
// info
set_output_contiguous(1, A_shape.slice(0, ndim - 2), A.options().dtype(ScalarType::Int));
}
TORCH_META_FUNC(linalg_qr)(const Tensor& A,
c10::string_view mode) {
at::native::checkIsMatrix(A, "linalg.qr");
at::native::checkFloatingOrComplex(A, "linalg.qr");
auto [compute_q, reduced_mode] = at::native::_parse_qr_mode(mode);
auto A_shape = A.sizes().vec();
const auto m = A_shape.cend()[-2];
const auto n = A_shape.cend()[-1];
const auto k = std::min(m, n);
if (compute_q) {
auto Q_shape = A_shape;
Q_shape.end()[-1] = reduced_mode ? k : m;
auto Q_strides = at::native::batched_matrix_contiguous_strides(Q_shape, /*f-contig*=*/true);
set_output_strided(0, Q_shape, Q_strides, A.options(), {});
} else {
set_output_raw_strided(0, {0}, {}, A.options(), {});
}
// For readability
auto R_shape = std::move(A_shape);
R_shape.end()[-2] = (reduced_mode || !compute_q) ? k : m;
auto R_strides = at::native::batched_matrix_contiguous_strides(R_shape, /*f-contig*=*/true);
set_output_strided(1, R_shape, R_strides, A.options(), {});
}
TORCH_META_FUNC(_linalg_svd)(const Tensor& A,
bool full_matrices,
bool compute_uv,
std::optional<c10::string_view> driver) {
at::native::checkIsMatrix(A, "linalg.svd");
at::native::checkFloatingOrComplex(A, "linalg.svd");
auto sizes = A.sizes().vec();
const auto m = sizes.cend()[-2];
const auto n = sizes.cend()[-1];
const auto k = std::min(m, n);
// Prepare sizes for U
if (compute_uv) {
sizes.back() = full_matrices ? m : k;
auto U_strides = at::native::batched_matrix_contiguous_strides(sizes, /*f-contig*=*/true);
set_output_strided(0, sizes, U_strides, A.options(), {});
// Prepare sizes for Vh
sizes.end()[-2] = full_matrices ? n : k;
sizes.end()[-1] = n;
// We need to distinguish the cuSOLVER case, as the cuSOLVER algorithms we use
// expect F-contig matrices, but they compute V rather than Vh
const bool use_cusolver = at::native::svd_uses_cusolver(A);
auto Vh_strides = at::native::batched_matrix_contiguous_strides(sizes, /*f-contig*=*/!use_cusolver);
set_output_strided(2, sizes, Vh_strides, A.options(), {});
} else {
set_output_raw_strided(0, {0}, {}, A.options(), {});
set_output_raw_strided(2, {0}, {}, A.options(), {});
}
// Prepare sizes for S. S is always real, even when A is complex.
sizes.pop_back();
sizes.end()[-1] = k;
set_output_contiguous(1, sizes, A.options().dtype(c10::toRealValueType(A.scalar_type())), {});
}
TORCH_META_FUNC(lu_unpack)(const Tensor& LU, const Tensor& pivots, bool unpack_data, bool unpack_pivots) {
TORCH_CHECK(LU.dim() >= 2, "torch.lu_unpack: Expected tensor with 2 or more dimensions. Got size: ", LU.sizes(), " instead");
if (unpack_pivots) {
TORCH_CHECK(pivots.scalar_type() == at::kInt,
"torch.lu_unpack: LU_pivots is expected to be a contiguous tensor of torch.int32 dtype.\n"
"Note: this function is intended to be used with the output produced by torch.linalg.lu_factor");
}
auto sizes = LU.sizes().vec();
const auto m = sizes.cend()[-2];
const auto n = sizes.cend()[-1];
const auto k = std::min(m, n);
// P.shape[-2:] == (m, m) (or size zero if pivot == False)
sizes.end()[-1] = m;
if (unpack_pivots) {
set_output_raw_strided(0, sizes, {}, LU.options(), {});
} else {
set_output_raw_strided(0, {0}, {}, LU.options(), {});
}
if (unpack_data) {
// L.shape[-2:] == (m, k)
sizes.end()[-1] = k;
set_output_raw_strided(1, sizes, {}, LU.options(), {});
// U.shape[-2:] == (k, n)
sizes.end()[-2] = k;
sizes.end()[-1] = n;
set_output_raw_strided(2, sizes, {}, LU.options(), {});
} else {
set_output_raw_strided(1, {0}, {}, LU.options(), {});
set_output_raw_strided(2, {0}, {}, LU.options(), {});
}
}
TORCH_META_FUNC(_linalg_eigh)(const Tensor& A,
c10::string_view uplo,
bool compute_v) {
at::native::squareCheckInputs(A, "linalg.eigh");
at::native::checkUplo(uplo);
auto shape = A.sizes().vec();
if (compute_v) {
// eigenvectors
auto V_strides = at::native::batched_matrix_contiguous_strides(shape, /*f-contig*=*/true);
set_output_strided(1, shape, V_strides, A.options(), {});
} else {
set_output_raw_strided(1, {0}, {}, A.options(), {});
}
// eigenvalues
shape.pop_back();
set_output_contiguous(0, shape, A.options().dtype(c10::toRealValueType(A.scalar_type())), {});
}
TORCH_META_FUNC(linalg_lu)(const Tensor& A, bool pivot) {
TORCH_CHECK(A.dim() >= 2, "linalg.lu: Expected tensor with 2 or more dimensions. Got size: ", A.sizes(), " instead");
auto sizes = A.sizes().vec();
const auto m = sizes.cend()[-2];
const auto n = sizes.cend()[-1];
const auto k = std::min(m, n);
// P.shape[-2:] == (m, m) (or size zero if pivot == False)
sizes.end()[-1] = m;
if (pivot) {
set_output_raw_strided(0, sizes, {}, A.options(), {});
} else {
set_output_raw_strided(0, {0}, {}, A.options(), {});
}
// L.shape[-2:] == (m, k)
sizes.end()[-1] = k;
set_output_raw_strided(1, sizes, {}, A.options(), {});
// U.shape[-2:] == (k, n)
sizes.end()[-2] = k;
sizes.end()[-1] = n;
set_output_raw_strided(2, sizes, {}, A.options(), {});
}
} // namespace at::meta
namespace at::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 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<> 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 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 ? w + n : nullptr;
(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 ? w + n : nullptr;
(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 lapackLdlSymmetric<double>(
char uplo,
int n,
double* a,
int lda,
int* ipiv,
double* work,
int lwork,
int* info) {
dsytrf_(&uplo, &n, a, &lda, ipiv, work, &lwork, info);
}
template <>
void lapackLdlSymmetric<float>(
char uplo,
int n,
float* a,
int lda,