toeplitz.c File Reference

Toeplitz matrix related functions. More...

#include <math.h>
#include "toeplitz.h"

Go to the source code of this file.

Functions

void toeplitz_gershgorin (const T *t, unsigned int n, T *low, T *up)
void toeplitz_mult (int n, const T *t, const T *x, T *y)
void levinson (unsigned int n, T td, const T *t0, const T *b0, T *x)


Detailed Description

Toeplitz matrix related functions.

Author:
Leandro GraciĆ” Gil, leagragi@inf.upv.es
Date:
18/11/08

Definition in file toeplitz.c.


Function Documentation

void levinson ( unsigned int  n,
td,
const T *  t0,
const T *  b0,
T *  x 
)

Solve system toeplitz(r0) * x = b0 where r0 defines a symmetric positive-definite Toeplitz matrix.

Parameters:
n Size of r0, b0 and x vectors.
td Main diagonal element of the symmetric Toeplitz matrix.
t0 Rest of the symmetric Toeplitz matrix data in vector form.
b0 Right-hand side vector data.
x Result vector.
Note:
If matrix is not positive-definite the algorithm can still converge.

Definition at line 97 of file toeplitz.c.

void toeplitz_gershgorin ( const T *  t,
unsigned int  n,
T *  low,
T *  up 
)

Calculate Gershgorin disc for a given Toeplitz symmetric matrix.

Parameters:
t Vector defining a symmetric Toeplitz matrix.
n Size of vector t.
low Lower bound of the Gershgorin disc interval.
up Upper bound of the Gershgorin disc interval.

Definition at line 42 of file toeplitz.c.

void toeplitz_mult ( int  n,
const T *  t,
const T *  x,
T *  y 
)

Calculate y = toeplitz(t) * x matrix-vector product where t is in vector form.

Parameters:
n Size of t and x, y vectors.
t Data of the symmetric Toeplitz matrix in vector form.
x Data of the input vector.
y Data of the destination vector. Will be overwritten with the result.

Definition at line 70 of file toeplitz.c.


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