Special Matrices


Functions
vec	itpp::ones (int size)
	A float vector of ones.
bvec	itpp::ones_b (int size)
	A Binary vector of ones.
ivec	itpp::ones_i (int size)
	A Int vector of ones.
cvec	itpp::ones_c (int size)
	A float Complex vector of ones.
mat	itpp::ones (int rows, int cols)
	A float (rows,cols)-matrix of ones.
bmat	itpp::ones_b (int rows, int cols)
	A Binary (rows,cols)-matrix of ones.
imat	itpp::ones_i (int rows, int cols)
	A Int (rows,cols)-matrix of ones.
cmat	itpp::ones_c (int rows, int cols)
	A Double Complex (rows,cols)-matrix of ones.
vec	itpp::zeros (int size)
	A Double vector of zeros.
bvec	itpp::zeros_b (int size)
	A Binary vector of zeros.
ivec	itpp::zeros_i (int size)
	A Int vector of zeros.
cvec	itpp::zeros_c (int size)
	A Double Complex vector of zeros.
mat	itpp::zeros (int rows, int cols)
	A Double (rows,cols)-matrix of zeros.
bmat	itpp::zeros_b (int rows, int cols)
	A Binary (rows,cols)-matrix of zeros.
imat	itpp::zeros_i (int rows, int cols)
	A Int (rows,cols)-matrix of zeros.
cmat	itpp::zeros_c (int rows, int cols)
	A Double Complex (rows,cols)-matrix of zeros.
mat	itpp::eye (int size)
	A Double (size,size) unit matrix.
bmat	itpp::eye_b (int size)
	A Binary (size,size) unit matrix.
imat	itpp::eye_i (int size)
	A Int (size,size) unit matrix.
cmat	itpp::eye_c (int size)
	A Double Complex (size,size) unit matrix.
template<class T>
void	itpp::eye (int size, Mat< T > &m)
	A non-copying version of the eye function.
vec	itpp::impulse (int size)
	Impulse vector.
vec	itpp::linspace (double from, double to, int length=100)
	Linspace (works in the same way as the matlab version).
imat	itpp::hadamard (int size)
	A 2^size by 2^size Hadamard matrix.
imat	itpp::jacobsthal (int p)
	Jacobsthal matrix.
imat	itpp::conference (int n)
	Conference matrix.
cmat	itpp::toeplitz (const cvec &c, const cvec &r)
	Computes the Hermitian Toeplitz matrix.
cmat	itpp::toeplitz (const cvec &c)
	Computes the Hermitian Toeplitz matrix.
mat	itpp::toeplitz (const vec &c, const vec &r)
	Computes the Hermitian Toeplitz matrix.
mat	itpp::toeplitz (const vec &c)
	Computes the Hermitian Toeplitz matrix.

Detailed Description

Function Documentation

vec itpp::ones ( int size )

A float vector of ones.

Referenced by itpp::GMM::GMM(), itpp::gmmtrain(), itpp::GMM::init_from_vq(), itpp::Rice_Fading_Generator::init_MEDS(), and itpp::roots().

bvec itpp::ones_b ( int size )

A Binary vector of ones.

Referenced by itpp::graycode().

ivec itpp::ones_i ( int size )

A Int vector of ones.

Referenced by itpp::Modulator_NCD::map_demod(), and itpp::Modulator_NRD::map_demod().

cvec itpp::ones_c ( int size )

A float Complex vector of ones.

Referenced by itpp::roots().

mat itpp::ones	(	int	rows,
		int	cols
	)

A float (rows,cols)-matrix of ones.

bmat itpp::ones_b	(	int	rows,
		int	cols
	)

A Binary (rows,cols)-matrix of ones.

imat itpp::ones_i	(	int	rows,
		int	cols
	)

A Int (rows,cols)-matrix of ones.

cmat itpp::ones_c	(	int	rows,
		int	cols
	)

A Double Complex (rows,cols)-matrix of ones.

bvec itpp::zeros_b ( int size )

A Binary vector of zeros.

Referenced by itpp::CRC_Code::check_parity(), itpp::Extended_Golay::decode(), itpp::BCH::decode(), itpp::GF2mat::get_col(), itpp::GF2mat::get_row(), itpp::graycode(), and itpp::CRC_Code::parity().

ivec itpp::zeros_i ( int size )

A Int vector of zeros.

Referenced by itpp::GF2mat::T_fact().

cvec itpp::zeros_c ( int size )

A Double Complex vector of zeros.

Referenced by itpp::arma_estimator(), itpp::TDL_Channel::filter_known_channel(), itpp::IFFT_Fading_Generator::generate_Jakes(), and itpp::roots().

mat itpp::zeros	(	int	rows,
		int	cols
	)

A Double (rows,cols)-matrix of zeros.

bmat itpp::zeros_b	(	int	rows,
		int	cols
	)

A Binary (rows,cols)-matrix of zeros.

imat itpp::zeros_i	(	int	rows,
		int	cols
	)

A Int (rows,cols)-matrix of zeros.

cmat itpp::zeros_c	(	int	rows,
		int	cols
	)

A Double Complex (rows,cols)-matrix of zeros.

mat itpp::eye ( int size )

A Double (size,size) unit matrix.

bmat itpp::eye_b ( int size )

A Binary (size,size) unit matrix.

Referenced by itpp::Extended_Golay::decode(), itpp::Extended_Golay::Extended_Golay(), and itpp::permutation_matrix().

imat itpp::eye_i ( int size )

A Int (size,size) unit matrix.

cmat itpp::eye_c ( int size )

A Double Complex (size,size) unit matrix.

template<class T>

void itpp::eye	(	int	size,
		Mat< T > &	m
	)			`[inline]`

A non-copying version of the eye function.

vec itpp::impulse ( int size )

Impulse vector.

Definition at line 107 of file specmat.cpp.

vec itpp::linspace	(	double	from,
		double	to,
		int	points = `100`
	)

Linspace (works in the same way as the matlab version).

Definition at line 114 of file specmat.cpp.

Referenced by itpp::arma_estimator(), itpp::freqz(), itpp::IFFT_Fading_Generator::generate_Jakes(), itpp::Rice_Fading_Generator::init_MEDS(), itpp::sqtrain(), and itpp::xcorr().

imat itpp::hadamard ( int size )

A 2^size by 2^size Hadamard matrix.

Definition at line 133 of file specmat.cpp.

References it_assert1, itpp::levels2bits(), itpp::pow2(), and itpp::pow2i().

imat itpp::jacobsthal ( int p )

Jacobsthal matrix.

Constructs an p by p matrix Q where p is a prime (not checked). The elements in Q {qij} is given by qij=X(j-i), where X(x) is the Legendre symbol given as:

X(x)=0 if x is a multiple of p,
X(x)=1 if x is a quadratic residue modulo p,
X(x)=-1 if x is a quadratic nonresidue modulo p.

See Wicker "Error Control Systems for digital communication and storage", p. 134 for more information on these topics. Do not check that p is a prime.

Definition at line 156 of file specmat.cpp.

Referenced by itpp::conference().

imat itpp::conference ( int n )

Conference matrix.

Constructs an n by n matrix C, where n=p^m+1=2 (mod 4) and p is a odd prime (not checked). This code only work with m=1, that is n=p+1 and p odd prime. The valid sizes of n is then n=6, 14, 18, 30, 38, ... (and not 10, 26, ...). C has the property that C*C'=(n-1)I, that is it has orthogonal rows and columns in the same way as Hadamard matricies. However, one element in each row (on the diagonal) is zeros. The others are {-1,+1}.

For more details see pp. 55-58 in MacWilliams & Sloane "The theory of error correcting codes", North-Holland, 1977.

Definition at line 180 of file specmat.cpp.

References it_assert1, and itpp::jacobsthal().

cmat itpp::toeplitz	(	const cvec &	c,
		const cvec &	r
	)

Computes the Hermitian Toeplitz matrix.

Return the Toeplitz matrix constructed given the first column C, and (optionally) the first row R. If the first element of C is not the same as the first element of R, the first element of C is used. If the second argument is omitted, the first row is taken to be the same as the first column.

A square Toeplitz matrix has the form:

          c(0)    r(1)     r(2)   ...   r(n)
          c(1)*   c(0)     r(1)        r(n-1)
          c(2)*   c(1)*    c(0)        r(n-2)
           .                             .
           .                             .
           .                             .

          c(n)*  c(n-1)*  c(n-2)* ...   c(0)

Definition at line 194 of file specmat.cpp.

References itpp::conj(), it_assert, and itpp::reshape().

Referenced by itpp::arma_estimator(), and itpp::modified_yule_walker().

cmat itpp::toeplitz ( const cvec & c )

Computes the Hermitian Toeplitz matrix.

Definition at line 214 of file specmat.cpp.

References itpp::conj(), and itpp::reshape().