uni20::linalg::backends::cpu Namespace Reference

Functions
template uni20::DenseMatrix< double >	matrix_exponential (uni20::DenseMatrix< double > const &, double)
template uni20::DenseMatrix< uni20::complex< double > >	matrix_exponential (uni20::DenseMatrix< double > const &, uni20::complex< double >)
template uni20::DenseMatrix< float >	matrix_exponential (uni20::DenseMatrix< float > const &, float)
template uni20::DenseMatrix< uni20::complex< float > >	matrix_exponential (uni20::DenseMatrix< float > const &, uni20::complex< float >)
template uni20::DenseMatrix< long double >	matrix_exponential (uni20::DenseMatrix< long double > const &, long double)
template uni20::DenseMatrix< uni20::complex< long double > >	matrix_exponential (uni20::DenseMatrix< long double > const &, uni20::complex< long double >)
template<uni20::RealOrComplex Scalar>
uni20::DenseMatrix< uni20::complex< uni20::make_real_t< Scalar > > >	matrix_exponential (uni20::DenseMatrix< Scalar > const &matrix, uni20::complex< uni20::make_real_t< Scalar > > t)
	Compute a complex-coefficient matrix exponential, promoting real matrices to complex output.
template<uni20::RealOrComplex Scalar>
uni20::DenseMatrix< Scalar >	matrix_exponential (uni20::DenseMatrix< Scalar > const &matrix, uni20::make_real_t< Scalar > t)
	Compute the matrix exponential using the adaptive scaling-and-squaring algorithm.
template uni20::DenseMatrix< uni20::complex< double > >	matrix_exponential (uni20::DenseMatrix< uni20::complex< double > > const &, double)
template uni20::DenseMatrix< uni20::complex< double > >	matrix_exponential (uni20::DenseMatrix< uni20::complex< double > > const &, uni20::complex< double >)
template uni20::DenseMatrix< uni20::complex< float > >	matrix_exponential (uni20::DenseMatrix< uni20::complex< float > > const &, float)
template uni20::DenseMatrix< uni20::complex< float > >	matrix_exponential (uni20::DenseMatrix< uni20::complex< float > > const &, uni20::complex< float >)
template uni20::DenseMatrix< uni20::complex< long double > >	matrix_exponential (uni20::DenseMatrix< uni20::complex< long double > > const &, long double)
template uni20::DenseMatrix< uni20::complex< long double > >	matrix_exponential (uni20::DenseMatrix< uni20::complex< long double > > const &, uni20::complex< long double >)

Function Documentation

matrix_exponential() [1/14]

template uni20::DenseMatrix< double > uni20::linalg::backends::cpu::matrix_exponential	(	uni20::DenseMatrix< double > const &	,
		double
	)

matrix_exponential() [2/14]

template uni20::DenseMatrix< uni20::complex< double > > uni20::linalg::backends::cpu::matrix_exponential	(	uni20::DenseMatrix< double > const &	,
		uni20::complex< double >
	)

matrix_exponential() [3/14]

template uni20::DenseMatrix< float > uni20::linalg::backends::cpu::matrix_exponential	(	uni20::DenseMatrix< float > const &	,
		float
	)

matrix_exponential() [4/14]

template uni20::DenseMatrix< uni20::complex< float > > uni20::linalg::backends::cpu::matrix_exponential	(	uni20::DenseMatrix< float > const &	,
		uni20::complex< float >
	)

matrix_exponential() [5/14]

template uni20::DenseMatrix< long double > uni20::linalg::backends::cpu::matrix_exponential	(	uni20::DenseMatrix< long double > const &	,
		long double
	)

matrix_exponential() [6/14]

template uni20::DenseMatrix< uni20::complex< long double > > uni20::linalg::backends::cpu::matrix_exponential	(	uni20::DenseMatrix< long double > const &	,
		uni20::complex< long double >
	)

matrix_exponential() [7/14]

template<uni20::RealOrComplex Scalar>

uni20::DenseMatrix< uni20::complex< uni20::make_real_t< Scalar > > > uni20::linalg::backends::cpu::matrix_exponential	(	uni20::DenseMatrix< Scalar > const &	matrix,
		uni20::complex< uni20::make_real_t< Scalar > >	t
	)

Compute a complex-coefficient matrix exponential, promoting real matrices to complex output.

This overload evaluates \(\exp(t A)\) for complex t. If matrix is real, the result is promoted to a complex dense matrix. If matrix is already complex, the result remains complex.

Template Parameters

Scalar

Real or complex matrix element type.

Parameters

matrix	Dense matrix whose exponential will be evaluated.
t	Complex multiplier applied to matrix before exponentiation.

Returns

The complex matrix exponential of \(\exp(t \cdot \text{matrix})\).

matrix_exponential() [8/14]

template<uni20::RealOrComplex Scalar>

uni20::DenseMatrix< Scalar > uni20::linalg::backends::cpu::matrix_exponential	(	uni20::DenseMatrix< Scalar > const &	matrix,
		uni20::make_real_t< Scalar >	t
	)

Compute the matrix exponential using the adaptive scaling-and-squaring algorithm.

Follows the Pad\'e-based scaling and squaring strategy of Higham (2005) and Al-Mohy & Higham (2011). The routine automatically selects between Pad\'e degrees {3, 5, 7, 9, 13} based on matrix norms.

Template Parameters

Scalar

Dense matrix element type; may be real or complex in single, double, or extended precision.

Parameters

matrix	Dense matrix whose exponential will be evaluated.
t	Scalar multiplier applied to matrix before exponentiation.

Returns

The matrix exponential of \(\exp(t \cdot \text{matrix})\).

matrix_exponential() [9/14]

template uni20::DenseMatrix< uni20::complex< double > > uni20::linalg::backends::cpu::matrix_exponential	(	uni20::DenseMatrix< uni20::complex< double > > const &	,
		double
	)

matrix_exponential() [10/14]

template uni20::DenseMatrix< uni20::complex< double > > uni20::linalg::backends::cpu::matrix_exponential	(	uni20::DenseMatrix< uni20::complex< double > > const &	,
		uni20::complex< double >
	)

matrix_exponential() [11/14]

template uni20::DenseMatrix< uni20::complex< float > > uni20::linalg::backends::cpu::matrix_exponential	(	uni20::DenseMatrix< uni20::complex< float > > const &	,
		float
	)

matrix_exponential() [12/14]

template uni20::DenseMatrix< uni20::complex< float > > uni20::linalg::backends::cpu::matrix_exponential	(	uni20::DenseMatrix< uni20::complex< float > > const &	,
		uni20::complex< float >
	)

matrix_exponential() [13/14]

template uni20::DenseMatrix< uni20::complex< long double > > uni20::linalg::backends::cpu::matrix_exponential	(	uni20::DenseMatrix< uni20::complex< long double > > const &	,
		long double
	)

matrix_exponential() [14/14]

template uni20::DenseMatrix< uni20::complex< long double > > uni20::linalg::backends::cpu::matrix_exponential	(	uni20::DenseMatrix< uni20::complex< long double > > const &	,
		uni20::complex< long double >
	)