linalg.hpp File Reference

#include "Type.hpp"
#include "cytnx_error.hpp"
#include "Tensor.hpp"
#include "Storage.hpp"
#include "UniTensor.hpp"
#include "Scalar.hpp"
#include "LinOp.hpp"
#include <functional>

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Namespaces
namespace	cytnx
namespace	cytnx::linalg
	linear algebra related functions.

Functions
cytnx::UniTensor	cytnx::operator+ (const cytnx::UniTensor &Lt, const cytnx::UniTensor &Rt)
	The addtion operator between two UniTensor.
template<class T >
cytnx::UniTensor	cytnx::operator+ (const T &lc, const cytnx::UniTensor &Rt)
	The addtion operator between a template type and a UniTensor.
template<class T >
cytnx::UniTensor	cytnx::operator+ (const cytnx::UniTensor &Lt, const T &rc)
	The addtion operator between a UniTensor and a template type.
cytnx::UniTensor	cytnx::operator- (const cytnx::UniTensor &Lt, const cytnx::UniTensor &Rt)
	The subtraction operator between two UniTensor.
template<class T >
cytnx::UniTensor	cytnx::operator- (const T &lc, const cytnx::UniTensor &Rt)
	The subtraction operator between a template type and a UniTensor.
template<class T >
cytnx::UniTensor	cytnx::operator- (const cytnx::UniTensor &Lt, const T &rc)
	The subtraction operator between a UniTensor and a template type.
cytnx::UniTensor	cytnx::operator* (const cytnx::UniTensor &Lt, const cytnx::UniTensor &Rt)
	The multiplication operator between two UniTensor.
template<class T >
cytnx::UniTensor	cytnx::operator* (const T &lc, const cytnx::UniTensor &Rt)
	The multiplication operator between a template type and a UniTensor.
template<class T >
cytnx::UniTensor	cytnx::operator* (const cytnx::UniTensor &Lt, const T &rc)
	The multiplication operator between a UniTensor and a template type.
cytnx::UniTensor	cytnx::operator/ (const cytnx::UniTensor &Lt, const cytnx::UniTensor &Rt)
	The division operator between two UniTensor.
template<class T >
cytnx::UniTensor	cytnx::operator/ (const T &lc, const cytnx::UniTensor &Rt)
	The division operator between a template type and a UniTensor.
template<class T >
cytnx::UniTensor	cytnx::operator/ (const cytnx::UniTensor &Lt, const T &rc)
	The division operator between a UniTensor and a template type.
cytnx::UniTensor	cytnx::operator% (const cytnx::UniTensor &Lt, const cytnx::UniTensor &Rt)
	The modulo operator between two UniTensor.
template<class T >
cytnx::UniTensor	cytnx::operator% (const T &lc, const cytnx::UniTensor &Rt)
	The modulo operator between a template type and a UniTensor.
template<class T >
cytnx::UniTensor	cytnx::operator% (const cytnx::UniTensor &Lt, const T &rc)
	The modulo operator between a UniTensor and a template type.
cytnx::UniTensor	cytnx::linalg::Add (const cytnx::UniTensor &Lt, const cytnx::UniTensor &Rt)
	The addtion function between two UniTensor.
template<class T >
cytnx::UniTensor	cytnx::linalg::Add (const T &lc, const cytnx::UniTensor &Rt)
	The addtion function between a template type and a UniTensor.
template<class T >
cytnx::UniTensor	cytnx::linalg::Add (const cytnx::UniTensor &Lt, const T &rc)
	The addtion function between a UniTensor and a template type.
cytnx::UniTensor	cytnx::linalg::Sub (const cytnx::UniTensor &Lt, const cytnx::UniTensor &Rt)
	The subtraction function between two UniTensor.
template<class T >
cytnx::UniTensor	cytnx::linalg::Sub (const T &lc, const cytnx::UniTensor &Rt)
	The subtraction function between a UniTensor and a template type.
template<class T >
cytnx::UniTensor	cytnx::linalg::Sub (const cytnx::UniTensor &Lt, const T &rc)
	The subtraction function between a UniTensor and a template type.
cytnx::UniTensor	cytnx::linalg::Mul (const cytnx::UniTensor &Lt, const cytnx::UniTensor &Rt)
	The multiplication function between two UniTensor.
template<class T >
cytnx::UniTensor	cytnx::linalg::Mul (const T &lc, const cytnx::UniTensor &Rt)
	The multiplication function between a UniTensor and a template type.
template<class T >
cytnx::UniTensor	cytnx::linalg::Mul (const cytnx::UniTensor &Lt, const T &rc)
	The multiplication function between a UniTensor and a template type.
cytnx::UniTensor	cytnx::linalg::Div (const cytnx::UniTensor &Lt, const cytnx::UniTensor &Rt)
	The division function between two UniTensor.
template<class T >
cytnx::UniTensor	cytnx::linalg::Div (const T &lc, const cytnx::UniTensor &Rt)
	The division function between a UniTensor and a template type.
template<class T >
cytnx::UniTensor	cytnx::linalg::Div (const cytnx::UniTensor &Lt, const T &rc)
	The division function between a UniTensor and a template type.
cytnx::UniTensor	cytnx::linalg::Mod (const cytnx::UniTensor &Lt, const cytnx::UniTensor &Rt)
	element-wise modulo
template<class T >
cytnx::UniTensor	cytnx::linalg::Mod (const T &lc, const cytnx::UniTensor &Rt)
	The modulo function between a UniTensor and a template type.
template<class T >
cytnx::UniTensor	cytnx::linalg::Mod (const cytnx::UniTensor &Lt, const T &rc)
	The modulo function between a UniTensor and a template type.
std::vector< cytnx::UniTensor >	cytnx::linalg::Svd (const cytnx::UniTensor &Tin, const bool &is_UvT=true)
	Perform Singular-Value decomposition on a UniTensor using divide-and-conquer method.
std::vector< cytnx::UniTensor >	cytnx::linalg::Gesvd (const cytnx::UniTensor &Tin, const bool &is_U=true, const bool &is_vT=true)
	Perform Singular-Value decomposition on a UniTensor using ?gesvd method.
std::vector< cytnx::UniTensor >	cytnx::linalg::Svd_truncate (const cytnx::UniTensor &Tin, const cytnx_uint64 &keepdim, const double &err=0, const bool &is_UvT=true, const bool &return_err=false)
	Perform Singular-Value decomposition on a UniTensor with truncation.
std::vector< cytnx::UniTensor >	cytnx::linalg::Gesvd_truncate (const cytnx::UniTensor &Tin, const cytnx_uint64 &keepdim, const double &err=0, const bool &is_U=true, const bool &is_vT=true, const bool &return_err=false)
	Perform Singular-Value decomposition on a UniTensor with truncation.
std::vector< cytnx::UniTensor >	cytnx::linalg::Hosvd (const cytnx::UniTensor &Tin, const std::vector< cytnx_uint64 > &mode, const bool &is_core=true, const bool &is_Ls=false, const std::vector< cytnx_int64 > &trucate_dim=std::vector< cytnx_int64 >())
template<typename T >
cytnx::UniTensor	cytnx::linalg::ExpH (const cytnx::UniTensor &Tin, const T &a, const T &b=0)
	Perform the exponential function on a UniTensor, which the blocks are Hermitian matrix.
template<typename T >
cytnx::UniTensor	cytnx::linalg::ExpM (const cytnx::UniTensor &Tin, const T &a, const T &b=0)
	Perform the exponential function on a UniTensor.
cytnx::UniTensor	cytnx::linalg::ExpH (const cytnx::UniTensor &Tin)
	Perform the exponential function on a UniTensor, which the blocks are Hermitian matrix.
cytnx::UniTensor	cytnx::linalg::ExpM (const cytnx::UniTensor &Tin)
	Perform the exponential function on a UniTensor.
cytnx::UniTensor	cytnx::linalg::Trace (const cytnx::UniTensor &Tin, const cytnx_int64 &a=0, const cytnx_int64 &b=1)
cytnx::UniTensor	cytnx::linalg::Trace (const cytnx::UniTensor &Tin, const std::string &a, const std::string &b)
	Perform trace over two legs of a UniTensor.
cytnx::UniTensor	cytnx::linalg::Trace (const cytnx::UniTensor &Tin, const cytnx_int64 &a=0, const cytnx_int64 &b=1, const bool &by_label=false)
std::vector< cytnx::UniTensor >	cytnx::linalg::Qr (const cytnx::UniTensor &Tin, const bool &is_tau=false)
	Perform the QR decomposition on a UniTensor.
std::vector< cytnx::UniTensor >	cytnx::linalg::Qdr (const cytnx::UniTensor &Tin, const bool &is_tau=false)
	Perform the QDR decomposition on a UniTensor.
UniTensor	cytnx::linalg::Pow (const UniTensor &Tin, const double &p)
	take power p on all the elements in UniTensor.
void	cytnx::linalg::Pow_ (UniTensor &Tin, const double &p)
	Take power p on all the elements in UniTensor, inplacely.
Tensor	cytnx::linalg::Add (const Tensor &Lt, const Tensor &Rt)
template<class T >
Tensor	cytnx::linalg::Add (const T &lc, const Tensor &Rt)
	The addition function for Tensor.
template<class T >
Tensor	cytnx::linalg::Add (const Tensor &Lt, const T &rc)
	The addition function for Tensor.
void	cytnx::linalg::iAdd (Tensor &Lt, const Tensor &Rt)
	The addition function for Tensor, inplacely.
Tensor	cytnx::linalg::Sub (const Tensor &Lt, const Tensor &Rt)
	The subtraction function for Tensor.
template<class T >
Tensor	cytnx::linalg::Sub (const T &lc, const Tensor &Rt)
	The subtraction function for Tensor.
template<class T >
Tensor	cytnx::linalg::Sub (const Tensor &Lt, const T &rc)
	The subtraction function for Tensor.
void	cytnx::linalg::iSub (Tensor &Lt, const Tensor &Rt)
	The subtraction function for Tensot, inplscely.
Tensor	cytnx::linalg::Mul (const Tensor &Lt, const Tensor &Rt)
	The multiplication function for Tensor.
template<class T >
Tensor	cytnx::linalg::Mul (const T &lc, const Tensor &Rt)
	The multiplication function for Tensor.
template<class T >
Tensor	cytnx::linalg::Mul (const Tensor &Lt, const T &rc)
	The multiplication function for Tensor.
void	cytnx::linalg::iMul (Tensor &Lt, const Tensor &Rt)
	The multiplication function for Tensor, inplacely.
Tensor	cytnx::linalg::Div (const Tensor &Lt, const Tensor &Rt)
	The division function for Tensor.
template<class T >
Tensor	cytnx::linalg::Div (const T &lc, const Tensor &Rt)
	The division function for Tensor.
template<class T >
Tensor	cytnx::linalg::Div (const Tensor &Lt, const T &rc)
	The division function for Tensor.
void	cytnx::linalg::iDiv (Tensor &Lt, const Tensor &Rt)
	The inplace division function for Tensor, inplacely.
Tensor	cytnx::linalg::Mod (const Tensor &Lt, const Tensor &Rt)
	The mod function for Tensor.
template<class T >
Tensor	cytnx::linalg::Mod (const T &lc, const Tensor &Rt)
	The mod function for Tensor.
template<class T >
Tensor	cytnx::linalg::Mod (const Tensor &Lt, const T &rc)
	The mod function for Tensor.
Tensor	cytnx::linalg::Cpr (const Tensor &Lt, const Tensor &Rt)
	The comparison function for Tensor.
template<class T >
Tensor	cytnx::linalg::Cpr (const T &lc, const Tensor &Rt)
	The comparison function for Tensor.
template<class T >
Tensor	cytnx::linalg::Cpr (const Tensor &Lt, const T &rc)
	The comparison function for Tensor.
Tensor	cytnx::linalg::Norm (const Tensor &Tl)
	Calculate the norm of a tensor.
Tensor	cytnx::linalg::Det (const Tensor &Tl)
	Calculate the determinant of a tensor.
std::vector< Tensor >	cytnx::linalg::Svd (const Tensor &Tin, const bool &is_UvT=true)
	Perform Singular-Value decomposition on a rank-2 Tensor (a matrix).
std::vector< Tensor >	cytnx::linalg::Gesvd (const Tensor &Tin, const bool &is_U=true, const bool &is_vT=true)
	Perform Singular-Value decomposition on a rank-2 Tensor (a matrix).
std::vector< Tensor >	cytnx::linalg::Svd_truncate (const Tensor &Tin, const cytnx_uint64 &keepdim, const double &err=0, const bool &is_UvT=true, const bool &return_err=false)
	Perform the truncate Singular-Value decomposition on a rank-2 Tensor (a matrix).
std::vector< Tensor >	cytnx::linalg::Gesvd_truncate (const Tensor &Tin, const cytnx_uint64 &keepdim, const double &err=0, const bool &is_U=true, const bool &is_vT=true, const bool &return_err=false)
	Perform the truncate Singular-Value decomposition on a rank-2 Tensor (a matrix).
std::vector< Tensor >	cytnx::linalg::Hosvd (const Tensor &Tin, const std::vector< cytnx_uint64 > &mode, const bool &is_core=true, const bool &is_Ls=false, const std::vector< cytnx_int64 > &trucate_dim=std::vector< cytnx_int64 >())
std::vector< Tensor >	cytnx::linalg::Qr (const Tensor &Tin, const bool &is_tau=false)
	Perform QR decomposition on a rank-2 Tensor.
std::vector< Tensor >	cytnx::linalg::Qdr (const Tensor &Tin, const bool &is_tau=false)
	Perform QDR decomposition on a rank-2 Tensor.
std::vector< Tensor >	cytnx::linalg::Eigh (const Tensor &Tin, const bool &is_V=true, const bool &row_v=false)
	eigen-value decomposition for Hermitian matrix
std::vector< Tensor >	cytnx::linalg::Eig (const Tensor &Tin, const bool &is_V=true, const bool &row_v=false)
	eigen-value decomposition for generic square matrix
Tensor	cytnx::linalg::Trace (const Tensor &Tn, const cytnx_uint64 &axisA=0, const cytnx_uint64 &axisB=1)
	perform trace over index.
Tensor	cytnx::linalg::Min (const Tensor &Tn)
	get the minimum element.
Tensor	cytnx::linalg::Max (const Tensor &Tn)
	get the maximum element.
Tensor	cytnx::linalg::Sum (const Tensor &Tn)
	get the sum of all the elements.
Tensor	cytnx::linalg::Matmul (const Tensor &TL, const Tensor &TR)
	perform matrix multiplication on two tensors.
Tensor	cytnx::linalg::Matmul_dg (const Tensor &Tl, const Tensor &Tr)
	perform matrix multiplication on two Tensors with one rank-1 and the other rank-2 where the rank-1 represent the diagonal elements of the specific tensor.
Tensor	cytnx::linalg::InvM (const Tensor &Tin)
	Matrix inverse.
void	cytnx::linalg::InvM_ (Tensor &Tin)
	inplace matrix inverse.
Tensor	cytnx::linalg::Inv (const Tensor &Tin, const double &clip)
	Element-wise inverse with clip.
void	cytnx::linalg::Inv_ (Tensor &Tin, const double &clip)
	inplace perform Element-wise inverse with clip.
Tensor	cytnx::linalg::Conj (const Tensor &Tin)
	Conjugate all the element in Tensor.
void	cytnx::linalg::Conj_ (Tensor &Tin)
	inplace perform Conjugate on all the element in Tensor.
Tensor	cytnx::linalg::Exp (const Tensor &Tin)
	Exponential all the element in Tensor.
Tensor	cytnx::linalg::Expf (const Tensor &Tin)
	Exponential all the element in Tensor.
void	cytnx::linalg::Exp_ (Tensor &Tin)
	inplace perform Exponential on all the element in Tensor.
void	cytnx::linalg::Expf_ (Tensor &Tin)
	inplace perform Exponential on all the element in Tensor.
Tensor	cytnx::linalg::Pow (const Tensor &Tin, const double &p)
	take power p on all the elements in Tensor.
void	cytnx::linalg::Pow_ (Tensor &Tin, const double &p)
	inplace perform power on all the elements in Tensor.
Tensor	cytnx::linalg::Abs (const Tensor &Tin)
	Elementwise absolute value.
void	cytnx::linalg::Abs_ (Tensor &Tin)
	inplace perform elementwiase absolute value. @This is just a inplace version of Abs. The input Tensor Tin will be modified.
Tensor	cytnx::linalg::Diag (const Tensor &Tin)
	return a diagonal tensor with diagonal elements provided as Tin.
Tensor	cytnx::linalg::Tensordot (const Tensor &Tl, const Tensor &Tr, const std::vector< cytnx_uint64 > &idxl, const std::vector< cytnx_uint64 > &idxr, const bool &cacheL=false, const bool &cacheR=false)
	perform tensor dot by sum out the indices assigned of two Tensors.
Tensor	cytnx::linalg::Tensordot_dg (const Tensor &Tl, const Tensor &Tr, const std::vector< cytnx_uint64 > &idxl, const std::vector< cytnx_uint64 > &idxr, const bool &diag_L)
	perform tensor dot by sum out the indices assigned of two Tensors, with either one of them to be a rank-2 diagonal tensor represented by a rank-2 tensor.
Tensor	cytnx::linalg::Outer (const Tensor &Tl, const Tensor &Tr)
	perform outer produces of two rank-1 Tensor.
Tensor	cytnx::linalg::Kron (const Tensor &Tl, const Tensor &Tr, const bool &Tl_pad_left=false, const bool &Tr_pad_left=false)
	perform kronecker produces of two Tensor.
Tensor	cytnx::linalg::Directsum (const Tensor &T1, const Tensor &T2, const std::vector< cytnx_uint64 > &shared_axes)
	perform directsum of two Tensor.
Tensor	cytnx::linalg::Vectordot (const Tensor &Tl, const Tensor &Tr, const bool &is_conj=false)
	perform inner product of vectors
Tensor	cytnx::linalg::Dot (const Tensor &Tl, const Tensor &Tr)
	dot product of two arrays.
std::vector< Tensor >	cytnx::linalg::Tridiag (const Tensor &Diag, const Tensor &Sub_diag, const bool &is_V=true, const bool &is_row=false, bool throw_excp=false)
	perform diagonalization of symmetric tri-diagnoal matrix.
template<typename T >
Tensor	cytnx::linalg::ExpH (const Tensor &in, const T &a, const T &b=0)
	perform matrix exponential for Hermitian matrix
Tensor	cytnx::linalg::ExpH (const Tensor &in)
template<typename T >
Tensor	cytnx::linalg::ExpM (const Tensor &in, const T &a, const T &b=0)
	perform matrix exponential for generic matrix
Tensor	cytnx::linalg::ExpM (const Tensor &in)
	perform matrix exponential for generic matrix
std::vector< Tensor >	cytnx::linalg::Arnoldi (LinOp *Hop, const Tensor &Tin=Tensor(), const std::string which="LM", const cytnx_uint64 &maxiter=10000, const cytnx_double &cvg_crit=1.0e-9, const cytnx_uint64 &k=1, const bool &is_V=true, const bool &verbose=false)
	perform Arnoldi for matrices or linear function.
std::vector< Tensor >	cytnx::linalg::Lanczos (LinOp *Hop, const Tensor &Tin=Tensor(), const std::string method="Gnd", const double &CvgCrit=1.0e-14, const unsigned int &Maxiter=10000, const cytnx_uint64 &k=1, const bool &is_V=true, const bool &is_row=false, const cytnx_uint32 &max_krydim=0, const bool &verbose=false)
	perform Lanczos for hermitian/symmetric matrices or linear function.
std::vector< UniTensor >	cytnx::linalg::Lanczos (LinOp *Hop, const UniTensor &Tin=UniTensor(), const std::string method="Gnd", const double &CvgCrit=1.0e-14, const unsigned int &Maxiter=10000, const cytnx_uint64 &k=1, const bool &is_V=true, const bool &is_row=false, const cytnx_uint32 &max_krydim=4, const bool &verbose=false)
	perform Lanczos for hermitian/symmetric matrices or linear function.
std::vector< Tensor >	cytnx::linalg::Lanczos_ER (LinOp *Hop, const cytnx_uint64 &k=1, const bool &is_V=true, const cytnx_uint64 &maxiter=10000, const double &CvgCrit=1.0e-14, const bool &is_row=false, const Tensor &Tin=Tensor(), const cytnx_uint32 &max_krydim=4, const bool &verbose=false)
	perform Lanczos for hermitian/symmetric matrices or linear function.
std::vector< Tensor >	cytnx::linalg::Lanczos_Gnd (LinOp *Hop, const double &CvgCrit=1.0e-14, const bool &is_V=true, const Tensor &Tin=Tensor(), const bool &verbose=false, const unsigned int &Maxiter=100000)
	perform Lanczos for hermitian/symmetric matrices or linear function to get ground state and lowest eigen value
std::vector< UniTensor >	cytnx::linalg::Lanczos_Gnd_Ut (LinOp *Hop, const UniTensor &Tin, const double &CvgCrit=1.0e-14, const bool &is_V=true, const bool &verbose=false, const unsigned int &Maxiter=100000)
	perform Lanczos for hermitian/symmetric matrices or linear function to get ground state and lowest eigen value
std::vector< Tensor >	cytnx::linalg::Lstsq (const Tensor &A, const Tensor &b, const float &rcond=-1)
	Return the least-squares solution to a linear matrix equation.
Tensor	cytnx::linalg::Axpy (const Scalar &a, const Tensor &x, const Tensor &y=Tensor())
	Blas Axpy, performing \( a\textbf{x} + \textbf{y} \), inplacely.
void	cytnx::linalg::Axpy_ (const Scalar &a, const Tensor &x, Tensor &y)
	Blas Axpy, performing \( \textbf{y} = a\textbf{x} + \textbf{y} \), inplacely.
Tensor	cytnx::linalg::Ger (const Tensor &x, const Tensor &y, const Scalar &a=Scalar())
	Blas Ger, performing return = a*vec(x)*vec(y)^T.
void	cytnx::linalg::Gemm_ (const Scalar &a, const Tensor &x, const Tensor &y, const Scalar &b, Tensor &c)
	Blas Gemm, performing \( \textbf{c} = a\textbf{x}\textbf{y} + b\textbf{c} \), inplacely.
Tensor	cytnx::linalg::Gemm (const Scalar &a, const Tensor &x, const Tensor &y)
	Blas Gemm, performing \( a\textbf{x}\textbf{y} -> \) return.
Tensor	cytnx::operator+ (const Tensor &Lt, const Tensor &Rt)
	The addition operator for Tensor.
template<class T >
Tensor	cytnx::operator+ (const T &lc, const Tensor &Rt)
	The addition operator between a template type and Tensor.
template<class T >
Tensor	cytnx::operator+ (const Tensor &Lt, const T &rc)
	The addition operator between Tensor and a template type.
Tensor	cytnx::operator- (const Tensor &Lt, const Tensor &Rt)
	The subtraction operator for Tensor.
template<class T >
Tensor	cytnx::operator- (const T &lc, const Tensor &Rt)
	The subtraction operator between a template type and Tensor.
template<class T >
Tensor	cytnx::operator- (const Tensor &Lt, const T &rc)
	The subtraction operator between Tensor and a template type.
Tensor	cytnx::operator* (const Tensor &Lt, const Tensor &Rt)
	The multiplication operator for Tensor.
template<class T >
Tensor	cytnx::operator* (const T &lc, const Tensor &Rt)
	The multiplication operator between a template type and Tensor.
template<class T >
Tensor	cytnx::operator* (const Tensor &Lt, const T &rc)
	The multiplication operator between Tensor and a template type.
Tensor	cytnx::operator/ (const Tensor &Lt, const Tensor &Rt)
	The division operator for Tensor.
template<class T >
Tensor	cytnx::operator/ (const T &lc, const Tensor &Rt)
	The division operator between a template type and Tensor.
template<class T >
Tensor	cytnx::operator/ (const Tensor &Lt, const T &rc)
	The division operator between Tensor and a template type.
Tensor	cytnx::operator% (const Tensor &Lt, const Tensor &Rt)
	The mode operator for Tensor.
template<class T >
Tensor	cytnx::operator% (const T &lc, const Tensor &Rt)
	The mode operator between a template type and Tensor.
template<class T >
Tensor	cytnx::operator% (const Tensor &Lt, const T &rc)
	The mode operator between Tensor and a template type.
Tensor	cytnx::operator== (const Tensor &Lt, const Tensor &Rt)
	The comparison operator for Tensor.
template<class T >
Tensor	cytnx::operator== (const T &lc, const Tensor &Rt)
	The comparison operator between a template type and Tensor.
template<class T >
Tensor	cytnx::operator== (const Tensor &Lt, const T &rc)
	The comparison operator between Tensor and a template type.