Definition of Matrix types. More...
#include <type_traits>#include <sstream>#include "plumbing/defs.h"#include "datatypes/cmplx.h"#include "datatypes/array.h"#include "datatypes/diagonal_matrix.h"#include "datatypes/matrix_linalg.h"
Go to the source code of this file.
Classes | |
| struct | svd_result< M > |
| type to store the return combo of svd: {U, D, V} where U and V are nxn unitary / orthogonal, and D is real diagonal singular value matrices. More... | |
| struct | eigen_result< M > |
| type to store the return value of eigen_hermitean(): {E, U} where E is nxn DiagonalMatrix containing eigenvalues and U nxn unitary matrix, with eigenvector columns More... | |
| class | Matrix_t< n, m, T, Mtype > |
| The main \( n \times m \) matrix type template Matrix_t. This is a base class type for "useful" types which are derived from this. More... | |
| class | Matrix< n, m, T > |
| \( n \times m \) Matrix class which defines matrix operations. More... | |
Namespaces | |
| namespace | hila |
| Implement hila::swap for gauge fields. | |
Typedefs | |
| template<int n, typename T > | |
| using | Vector = Matrix< n, 1, T > |
| Vector is defined as 1-column Matrix. | |
| template<int n, typename T > | |
| using | RowVector = Matrix< 1, n, T > |
| RowVector is a 1-row Matrix. | |
| template<int n, typename T > | |
| using | SquareMatrix = Matrix< n, n, T > |
| Square matrix is defined as alias with special case of Matrix<n,n,T> | |
Functions | |
| template<typename Mtype , std::enable_if_t< Mtype::is_matrix(), int > = 0> | |
| auto | transpose (const Mtype &arg) |
| Return transposed Matrix or Vector. | |
| template<typename Mtype , std::enable_if_t< Mtype::is_matrix(), int > = 0> | |
| auto | conj (const Mtype &arg) |
| Return conjugate Matrix or Vector. | |
| template<typename Mtype , std::enable_if_t< Mtype::is_matrix(), int > = 0> | |
| auto | adjoint (const Mtype &arg) |
| Return adjoint Matrix. | |
| template<typename Mtype , std::enable_if_t< Mtype::is_matrix(), int > = 0> | |
| auto | dagger (const Mtype &arg) |
| Return dagger of Matrix. | |
| template<typename Mtype , std::enable_if_t< Mtype::is_matrix(), int > = 0> | |
| auto | abs (const Mtype &arg) |
| Return absolute value Matrix or Vector. | |
| template<typename Mtype , std::enable_if_t< Mtype::is_matrix(), int > = 0> | |
| auto | trace (const Mtype &arg) |
| Return trace of square Matrix. | |
| template<typename Mtype , std::enable_if_t< Mtype::is_matrix(), int > = 0> | |
| auto | real (const Mtype &arg) |
| Return real of Matrix or Vector. | |
| template<typename Mtype , std::enable_if_t< Mtype::is_matrix(), int > = 0> | |
| auto | imag (const Mtype &arg) |
| Return imaginary of Matrix or Vector. | |
| template<typename Mtype1 , typename Mtype2 , std::enable_if_t< Mtype1::is_matrix() &&Mtype2::is_matrix(), int > = 0, typename Rtype = hila::mat_x_mat_type<Mtype1, Mtype2>, std::enable_if_t<!std::is_same< Mtype1, Rtype >::value, int > = 0> | |
| Rtype | operator+ (const Mtype1 &a, const Mtype2 &b) |
| Addition operator. | |
| template<typename Mtype1 , typename Mtype2 , std::enable_if_t< Mtype1::is_matrix() &&Mtype2::is_matrix(), int > = 0, typename Rtype = hila::mat_x_mat_type<Mtype1, Mtype2>> | |
| Rtype | operator- (const Mtype1 &a, const Mtype2 &b) |
| Subtraction operator. | |
| template<typename Mt1 , typename Mt2 , std::enable_if_t< Mt1::is_matrix() &&Mt2::is_matrix() &&!std::is_same< Mt1, Mt2 >::value, int > = 0, typename R = hila::type_mul<hila::number_type<Mt1>, hila::number_type<Mt2>>, int n = Mt1::rows(), int m = Mt2::columns()> | |
| Matrix< n, m, R > | operator* (const Mt1 &a, const Mt2 &b) |
| Multiplication operator. | |
| template<typename Mt , typename S , std::enable_if_t<(Mt::is_matrix() &&hila::is_complex_or_arithmetic< S >::value), int > = 0, typename Rt = hila::mat_scalar_type<Mt, S>> | |
| Rt | operator/ (const Mt &mat, const S &rhs) |
| Division operator. | |
| template<typename Mtype1 , typename Mtype2 , std::enable_if_t< Mtype1::is_matrix() &&Mtype2::is_matrix(), int > = 0> | |
| auto | mul_trace (const Mtype1 &a, const Mtype2 &b) |
| Returns trace of product of two matrices. | |
| template<typename Mt , std::enable_if_t< Mt::is_matrix() &&Mt::is_square(), int > = 0> | |
| void | mult (const Mt &a, const Mt &b, Mt &res) |
| compute product of two square matrices and write result to existing matrix | |
| template<int n, int m, typename T , typename MT > | |
| std::ostream & | operator<< (std::ostream &strm, const Matrix_t< n, m, T, MT > &A) |
| Stream operator. | |
| template<int n, int m, typename T , typename MT > | |
| std::string | hila::to_string (const Matrix_t< n, m, T, MT > &A, int prec=8, char separator=' ') |
| Converts Matrix_t object to string. | |
| template<int n, int m, typename T , typename MT > | |
| std::string | hila::prettyprint (const Matrix_t< n, m, T, MT > &A, int prec=8) |
| Formats Matrix_t object in a human readable way. | |
| template<typename Mt , std::enable_if_t< Mt::is_matrix(), int > = 0> | |
| auto | squarenorm (const Mt &rhs) |
| Returns square norm of Matrix. | |
| template<typename Mt , std::enable_if_t< Mt::is_matrix(), int > = 0> | |
| auto | norm (const Mt &rhs) |
| Returns vector norm of Matrix. | |
| template<int n, int m, typename T , typename MT > | |
| Matrix_t< n, m, T, MT > | exp (const Matrix_t< n, m, T, MT > &mat, const int order=20) |
| Calculate exp of a square matrix. | |
| template<int n, int m, typename T , typename MT > | |
| void | chexp (const Matrix_t< n, m, T, MT > &mat, Matrix_t< n, m, T, MT > &omat, Matrix_t< n, m, T, MT >(&pl)[n+1]) |
| Calculate exp of a square matrix. | |
| template<int n, int m, typename T , typename MT > | |
| Matrix_t< n, m, T, MT > | chsexp (const Matrix_t< n, m, T, MT > &mat) |
| Calculate exp of a square matrix. | |
Detailed Description
Definition of Matrix types.
This file contains base matrix type Matrix_t which defines all general matrix type operations Matrix types are Matrix, Vector, RowVector, SquareMatrix of which Matrix is defined as a class and the rest are special cases of the Matrix class.
Definition in file matrix.h.
Function Documentation
◆ abs()
|
inline |
Return absolute value Matrix or Vector.
Wrapper around Matrix::abs
Can be called as:
- Template Parameters
-
Mtype Matrix type
- Parameters
-
arg Object to compute absolute value of
- Returns
- auto Mtype absolute value Matrix or Vector
◆ adjoint()
|
inline |
Return adjoint Matrix.
Wrapper around Matrix::adjoint
Can be called as:
- Template Parameters
-
Mtype Matrix type
- Parameters
-
arg Object to compute adjoint of
- Returns
- auto Mtype adjoint matrix
◆ chexp()
|
inline |
Calculate exp of a square matrix.
Computation is done using iterative Cayley-Hamilton (cf. from arXiv:2404.07704)
- Parameters
-
mat Matrix to compute exponential for omat Matrix to which exponential of mat gets stored (optional) pl array of n+1 temporary nxn Matrices (optional)
- Returns
- void (if omat is provided) or Matrix_t<n,m,T,MT>
◆ chsexp()
|
inline |
Calculate exp of a square matrix.
Computation is done using iterative Cayley-Hamilton (cf. from arXiv:2404.07704) with minimal temporary storage
- Parameters
-
mat Matrix to compute exponential for
- Returns
- Matrix_t<n, m, T, MT>
◆ conj()
|
inline |
Return conjugate Matrix or Vector.
Wrapper around Matrix::conj
Can be called as:
- Template Parameters
-
Mtype Matrix type
- Parameters
-
arg Object to be conjugated
- Returns
- auto Mtype conjugated matrix
◆ dagger()
|
inline |
Return dagger of Matrix.
Wrapper around Matrix::adjoint
Same as adjoint
- Template Parameters
-
Mtype Matrix type
- Parameters
-
arg Object to compute dagger of
- Returns
- auto Mtype dagger matrix
◆ exp()
|
inline |
Calculate exp of a square matrix.
Computes up to certain order given as argument
Evaluation is done as:
\begin{align} \exp(H) &= 1 + H + \frac{H^2}{2!} + \frac{H^2}{2!} + \frac{H^3}{3!} \\ &= 1 + H\cdot(1 + (\frac{H}{2})\cdot (1 + (\frac{H}{3})\cdot(...))) \end{align}
Done backwards in order to reduce accumulation of errors
- Parameters
-
mat Matrix to compute exponential for order order to compute exponential to
- Returns
- Matrix_t<n, m, T, MT>
◆ imag()
|
inline |
Return imaginary of Matrix or Vector.
Wrapper around Matrix::imag
Can be called as:
- Template Parameters
-
Mtype Matrix type
- Parameters
-
arg Object to compute imag part of
- Returns
- auto Mtype imag part of arg
◆ mul_trace()
|
inline |
Returns trace of product of two matrices.
Wrapper around Matrix::mul_trace in the form
- Returns
- auto Resulting trace
◆ mult()
|
inline |
◆ norm()
|
inline |
◆ operator*()
|
inline |
Multiplication operator.
Multiplication type depends on the original types of the multiplied matrices. Defined for the following operations.
Standard matrix multiplication where LHS columns must match RHS rows
RowVector * Vector / Vector * RowVector:
Defined as standard dot product between vectors as long as vectors are of same length
Vector * RowVector is same as outer product which is equivalent to a matrix multiplication
Matrix * Scalar / Scalar * Matrix:
Multiplication operator between Matrix and Scalar are defined in the usual way (element wise)
- Returns
- Matrix<n, m, R>
◆ operator+()
|
inline |
Addition operator.
Defined for the following operations
Addition operator between matrices is defined in the usual way (element wise).
NOTE: Matrices must share same dimensionality.
Scalar + Matrix / Matrix + Scalar:
Addition operator between matrix and scalar is defined in the usual way, where the scalar is added to the diagonal elements.
NOTE: Exact definition exist in overloaded functions that can be viewed in source code.
\( M + 2 = M + 2\cdot\mathbb{1} \)
- Parameters
-
a Left matrix or scalar b Right matrix or scalar
- Returns
- Rtype Return matrix of compatible type between Mtype1 and Mtype2
◆ operator-()
|
inline |
Subtraction operator.
Defined for the following operations
Subtraction operator between matrices is defined in the usual way (element wise).
NOTE: Matrices must share same dimensionality.
Scalar - Matrix / Matrix - Scalar:
Subtraction operator between matrix and scalar is defined in the usual way, where the scalar is subtracted from the diagonal elements.
NOTE: Exact definition exist in overloaded functions that can be viewed in source code.
\( M - 2 = M - 2\cdot\mathbb{1} \)
- Parameters
-
a Left matrix or scalar b Right matrix or scalar
- Returns
- Rtype Return matrix of compatible type between Mtype1 and Mtype2
◆ operator/()
|
inline |
Division operator.
Defined for following operations
__ Matrix / Scalar: __
Division operator between Matrix and Scalar are defined in the usual way (element wise)
- Template Parameters
-
Mt Matrix type S Scalar type
- Parameters
-
mat Matrix to divide scalar with rhs Scalar to divide with
- Returns
- Rt Resulting Matrix
◆ operator<<()
| std::ostream & operator<< | ( | std::ostream & | strm, |
| const Matrix_t< n, m, T, MT > & | A | ||
| ) |
◆ real()
|
inline |
Return real of Matrix or Vector.
Wrapper around Matrix::real
Can be called as:
- Template Parameters
-
Mtype Matrix type
- Parameters
-
arg Object to compute real part of
- Returns
- auto Mtype real part of arg
◆ squarenorm()
|
inline |
Returns square norm of Matrix.
Wrapper around Matrix::squarenorm - sum of squared elements
Can be called as:
- Template Parameters
-
Mt Matrix type
- Parameters
-
rhs Matrix to compute square norm of
- Returns
- auto
◆ trace()
|
inline |
Return trace of square Matrix.
Wrapper around Matrix::trace
Can be called as:
- Template Parameters
-
Mtype Matrix type
- Parameters
-
arg Object to compute trace of
- Returns
- auto Trace of Matrix
◆ transpose()
|
inline |
Return transposed Matrix or Vector.
Wrapper around Matrix::transpose
Can be called as:
- Template Parameters
-
Mtype Matrix type
- Parameters
-
arg Object to be transposed
- Returns
- auto Mtype transposed matrix
