Generate test data

Generate test data. More...

Functions
template<typename T >
matrix::COO< T >	monolish::util::asym_band_matrix (const int M, const int N, const int W, const T diag_val, const T Uval, const T Lval)
	create asymmetric band matrix More...
template<typename T >
matrix::COO< T >	monolish::util::band_matrix (const int M, const int N, const int W, const T diag_val, const T val)
	create band matrix More...
template<typename T >
matrix::COO< T >	monolish::util::eye (const int M)
	create band matrix More...
template<typename T >
matrix::COO< T >	monolish::util::frank_matrix (const int &M)
	create Frank matrix More...
template<typename T >
T	monolish::util::frank_matrix_eigenvalue (const int &M, const int &N)
	Nth eigenvalue from the bottom of MxM Frank matrix. More...
template<typename T >
matrix::COO< T >	monolish::util::laplacian_matrix_1D (const int &M)
	create 1D Laplacian matrix More...
template<typename T >
T	monolish::util::laplacian_matrix_1D_eigenvalue (const int &M, int N)
	Nth smallest eigenvalue of 1D Laplacian matrix. More...
template<typename T >
matrix::COO< T >	monolish::util::laplacian_matrix_2D_5p (const int M, const int N)
	create two dimensional Laplacian matrix using the five point central difference scheme More...
template<typename T >
matrix::COO< T >	monolish::util::random_structure_matrix (const int M, const int N, const int nnzrow, const T val)
	create random structure matrix (column number is decided by random) More...
template<typename T >
void	monolish::util::random_vector (vector< T > &vec, const T min, const T max)
	create random vector More...
template<typename T >
void	monolish::util::random_vector (vector< T > &vec, const T min, const T max, const std::uint32_t seed)
	create random vector with random seed More...
template<typename T >
matrix::COO< T >	monolish::util::toeplitz_plus_hankel_matrix (const int &M, T a0, T a1, T a2)
	create Toeplitz-plus-Hankel matrix More...
template<typename T >
T	monolish::util::toeplitz_plus_hankel_matrix_eigenvalue (const int &M, int N, T a0, T a1, T a2, T b0, T b1, T b2)
	Nth smallest eigenvalue of GEVP Ax=lBx of Toeplitz-plus-Hankel matrixes A, B. More...
template<typename T >
matrix::COO< T >	monolish::util::tridiagonal_toeplitz_matrix (const int &M, T a, T b)
	create tridiagonal Toeplitz matrix More...
template<typename T >
T	monolish::util::tridiagonal_toeplitz_matrix_eigenvalue (const int &M, int N, T a, T b)
	Nth smallest eigenvalue of MxM tridiagonal Toeplitz matrix. More...

Detailed Description

Generate test data.

Function Documentation

asym_band_matrix()

template<typename T >

matrix::COO<T> monolish::util::asym_band_matrix	(	const int	M,
		const int	N,
		const int	W,
		const T	diag_val,
		const T	Uval,
		const T	Lval
	)

create asymmetric band matrix

Parameters

M	# of Row
N	# of col.
W	half-bandwidth (bandwidth is 2*W+1)
diag_val	value of diagonal elements
Uval	value of upper non-diagonal elements
Lval	value of lower non-diagonal elements

Note

• # of computation: M*W
• Multi-threading: false
• GPU acceleration: false

band_matrix()

template<typename T >

matrix::COO<T> monolish::util::band_matrix	(	const int	M,
		const int	N,
		const int	W,
		const T	diag_val,
		const T	val
	)

create band matrix

Parameters

M	# of Row
N	# of col.
W	half-bandwidth (bandwidth is 2*W+1)
diag_val	value of diagonal elements
val	value of non-diagonal elements

Note

• # of computation: M*W
• Multi-threading: false
• GPU acceleration: false

eye()

template<typename T >

matrix::COO<T> monolish::util::eye

(

const int

M

)

create band matrix

Parameters

M	# of Row and col.

Note

• # of computation: M
• Multi-threading: false
• GPU acceleration: false

frank_matrix()

template<typename T >

matrix::COO<T> monolish::util::frank_matrix

(

const int &

M

)

create Frank matrix

Parameters

M	# of row and col

Note

• # of computation: M^2
• Multi-threading: false
• GPU acceleration: false

frank_matrix_eigenvalue()

template<typename T >

T monolish::util::frank_matrix_eigenvalue	(	const int &	M,
		const int &	N
	)

Nth eigenvalue from the bottom of MxM Frank matrix.

Parameters

M	dimension of Frank matrix
N	#-th eigenvalue from the bottom

Note

• # of computation: O(1)
• Multi-threading: false
• GPU acceleration: false

laplacian_matrix_1D()

template<typename T >

matrix::COO<T> monolish::util::laplacian_matrix_1D

(

const int &

M

)

create 1D Laplacian matrix

Parameters

M	# of row and col

Note

• # of computation: M
• Multi-threading: false
• GPU acceleration: false

laplacian_matrix_1D_eigenvalue()

template<typename T >

T monolish::util::laplacian_matrix_1D_eigenvalue	(	const int &	M,
		int	N
	)

Nth smallest eigenvalue of 1D Laplacian matrix.

Parameters

M	dimension of tridiagonal Toeplitz matrix
N	#-th eigenvalue from the bottom

Note

• # of computation: O(1)
• Multi-threading: false
• GPU acceleration: false

laplacian_matrix_2D_5p()

template<typename T >

matrix::COO<T> monolish::util::laplacian_matrix_2D_5p	(	const int	M,
		const int	N
	)

create two dimensional Laplacian matrix using the five point central difference scheme

Parameters

M	# of grid point
N	# of grid point

Note

• # of computation: N*M
• Multi-threading: false
• GPU acceleration: false

random_structure_matrix()

template<typename T >

matrix::COO<T> monolish::util::random_structure_matrix	(	const int	M,
		const int	N,
		const int	nnzrow,
		const T	val
	)

create random structure matrix (column number is decided by random)

Parameters

M	# of Row
N	# of col.
nnzrow	non-zero elements per row
val	value of elements

Note

• # of computation: M*nnzrow
• Multi-threading: false
• GPU acceleration: false

random_vector() [1/2]

template<typename T >

void monolish::util::random_vector	(	vector< T > &	vec,
		const T	min,
		const T	max
	)

create random vector

Parameters

vec	allocated vector
min	min. of random
max	min. of random

Note

the ramdom number generator is random generator is mt19937

• # of computation: N
• Multi-threading: true
• GPU acceleration: false

random_vector() [2/2]

template<typename T >

void monolish::util::random_vector	(	vector< T > &	vec,
		const T	min,
		const T	max,
		const std::uint32_t	seed
	)

create random vector with random seed

Parameters

vec	allocated vector
min	min. of random
max	min. of random
seed	random seed

Note

the ramdom number generator is random generator is mt19937

• # of computation: N
• Multi-threading: false
• GPU acceleration: false

toeplitz_plus_hankel_matrix()

template<typename T >

matrix::COO<T> monolish::util::toeplitz_plus_hankel_matrix	(	const int &	M,
		T	a0,
		T	a1,
		T	a2
	)

create Toeplitz-plus-Hankel matrix

Parameters

M	# of row and col
a0	value of diagonal elements
a1	value of next-to-diagonal elements
a2	value of second-next-to-diagonal elements

Note

• taken from arxiv:2007.08130
• (0, 0) and (M-1, M-1) elements are modified to a0-a2
• both A and B of the GEVP have same structure
• Multi-threading: false
• GPU acceleration: false

toeplitz_plus_hankel_matrix_eigenvalue()

template<typename T >

T monolish::util::toeplitz_plus_hankel_matrix_eigenvalue	(	const int &	M,
		int	N,
		T	a0,
		T	a1,
		T	a2,
		T	b0,
		T	b1,
		T	b2
	)

Nth smallest eigenvalue of GEVP Ax=lBx of Toeplitz-plus-Hankel matrixes A, B.

Parameters

M	dimension of Toeplitz-plus-Hankel marices
N	#-th eigenvalue from the bottom
a0,a1,a2	value of Toeplitz-plus-Hankel matrix A
b0,b1,b2	value of TOeplitz-plus-Hankel matrix B

Note

• # of computation: O(1)
• Multi-threading: false
• GPU acceleration: false

tridiagonal_toeplitz_matrix()

template<typename T >

matrix::COO<T> monolish::util::tridiagonal_toeplitz_matrix	(	const int &	M,
		T	a,
		T	b
	)

create tridiagonal Toeplitz matrix

Parameters

M	# of row and col
a	value of diagonal elements
b	value of next-to-diagonal elements

Note

• # of computation: M
• Multi-threading: false
• GPU acceleration: false

tridiagonal_toeplitz_matrix_eigenvalue()

template<typename T >

T monolish::util::tridiagonal_toeplitz_matrix_eigenvalue	(	const int &	M,
		int	N,
		T	a,
		T	b
	)

Nth smallest eigenvalue of MxM tridiagonal Toeplitz matrix.

Parameters

M	dimension of tridiagonal Toeplitz matrix
N	#-th eigenvalue from the bottom
a	value of diagonal elements
b	value of next-to-diagonal elements

Note

• # of computation: O(1)
• Multi-threading: false
• GPU acceleration: false