Special Matrices
[Base Module]

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).
vec	itpp::zigzag_space (double t0, double t1, int K=5)
	Zig-zag space function (variation on linspace).
imat	itpp::hadamard (int size)
	Hadamard matrix.
imat	itpp::jacobsthal (int p)
	Jacobsthal matrix.
imat	itpp::conference (int n)
	Conference matrix.
template<typename Num_T >
const Mat< Num_T >	itpp::toeplitz (const Vec< Num_T > &c, const Vec< Num_T > &r)
	Generate Toeplitz matrix from two vectors c and r.
template<typename Num_T >
const Mat< Num_T >	itpp::toeplitz (const Vec< Num_T > &c)
	Generate symmetric Toeplitz matrix from vector c.
template<>
const cmat	itpp::toeplitz (const cvec &c)
	Generate symmetric Toeplitz matrix from vector c (complex valued).

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Function Documentation

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.

References it_assert_debug, and itpp::jacobsthal().

imat itpp::hadamard

(

int

size

)

Hadamard matrix.

This function constructs a size by size Hadammard matrix, where size is a power of 2.

References itpp::ceil_i(), it_assert, itpp::log2(), 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.

Referenced by itpp::conference().

template<typename Num_T >

const Mat<Num_T> itpp::toeplitz	(	const Vec< Num_T > &	c,
		const Vec< Num_T > &	r
	)			[inline]

Generate Toeplitz matrix from two vectors c and r.

Returns 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 and a symmetric (Hermitian) Toeplitz matrix is created.

An example 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)
 * 

Author:

Adam Piatyszek

References itpp::min(), and itpp::Vec< Num_T >::size().

vec itpp::zigzag_space	(	double	t0,
		double	t1,
		int	K = 5
	)

Zig-zag space function (variation on linspace).

This function is a variation on linspace(). It traverses the points in different order. For example

zigzag_space(-5,5,3)

gives the vector

[-5 5 0 -2.5 2.5 -3.75 -1.25 1.25 3.75]

and

zigzag_space(-5,5,4)

gives the vector

[-5 5 0 -2.5 2.5 -3.75 -1.25 1.25 3.75 -4.375 -3.125 -1.875 -0.625 0.625 1.875 3.125 4.375]

and so on.

I.e. the function samples the interval [t0,t1] with finer and finer density and with points uniformly distributed over the interval, rather than from left to right (as does linspace).

The result is a vector of length 1+2^K.

References it_assert, itpp::length(), itpp::linspace(), and itpp::zeros().