Functions
Using these poles	make (s-a) terms %Each row corresponds to a partial fraction model at one frequency Asys

:	wSimFreqs ()

	res (:, 2)

	res (:, 3)

	res (:, 4)

Determine residues for	sigma (s) function %ctilde

Variables
	function [residues, ctilde, Asim, residual]

Number of poles to use in fit	numPoles = length(poles)

Turn this into a	matrix

Turn this into a with identical frequencies along the rows	Sk = 1j*repmat(wSimFreqs(:),1,numPoles)

anorm are the complex starting current poles Here we create a matrix with identical poles down the columns	P = repmat(poles,numFreqs,1)

To ensure residues come in perfect conjugate	pairs

To ensure residues come in perfect conjugate we form A as	A = [ANorm + AConj, 1jANorm - 1jAConj]

How many vectors are we fitting	numVec = size(freqData,1)*size(freqData,2)

	numVar = numPoles + 2

The partial fraction expansions consits of	terms

	AsimFull = Asim

	freqDataFull = freqData

	b = freqData(:)

Obtain iteration resiudes for model	x = A\b

	res = x(1:numVar)

	residues = res(:)

	ctilde = x(end/2+2:end)

	residual = norm(A*x-b)

Check fit	H = simPoleResidueRemainder(wSimFreqs/2*pi, poles, residues)

Function Documentation

◆ make()

Using these poles make ( s- a )

◆ res() [1/3]

res	(	:	,
		2
	)

◆ res() [2/3]

res	(	:	,
		3
	)

◆ res() [3/3]

res	(	:	,
		4
	)

◆ sigma()

Determine residues for sigma ( s )

◆ wSimFreqs()

: wSimFreqs ( )

virtual

Variable Documentation

◆ A

Add the partial fraction terms for the sigma function A = [ANorm + AConj, 1j*ANorm - 1j*AConj]

Definition at line 28 of file getResidues.m.

◆ AsimFull

AsimFull = Asim

Definition at line 40 of file getResidues.m.

◆ b

b = freqData(:)

Definition at line 47 of file getResidues.m.

◆ ctilde

ctilde = x(end/2+2:end)

Definition at line 59 of file getResidues.m.

◆ freqDataFull

freqDataFull = freqData

Definition at line 41 of file getResidues.m.

◆ function

function[residues, ctilde, Asim, residual]

Initial value:

= getResidues(poles, freqData, wSimFreqs)
%GETRESIDUES Determines the residues of a rational model fit to frequency
%domain matrix (note that this is true VectorFitting)
%   This function is for use with vector fitting. It simulates a rational
%   model (in adjusted partial fraction form) and determines the resdiues
%   required to fit a function signma(s) using least squares. This can then 
%   in turn be used to update the poles of the rational model for the next 
%   iteration.
    
    % Total number of frequency points
    numFreqs = length(wSimFreqs)

Definition at line 1 of file getResidues.m.

◆ H

Check fit H = simPoleResidueRemainder(wSimFreqs/2*pi, poles, residues)

Definition at line 64 of file getResidues.m.

◆ matrix

Turn this into a matrix

Definition at line 16 of file getResidues.m.

◆ numPoles

Number of poles to use in fit numPoles = length(poles)

Definition at line 14 of file getResidues.m.

◆ numVar

numVar = numPoles + 2

Definition at line 32 of file getResidues.m.

◆ numVec

How many vectors are we fitting numVec = size(freqData,1)*size(freqData,2)

Definition at line 31 of file getResidues.m.

◆ P

anorm are the complex starting current poles Here we create a matrix with identical poles down the columns P = repmat(poles,numFreqs,1)

Definition at line 21 of file getResidues.m.

◆ pairs

To ensure residues come in perfect conjugate pairs

Definition at line 27 of file getResidues.m.

◆ res

res = x(1:numVar)

Definition at line 51 of file getResidues.m.

◆ residual

residual = norm(A*x-b)

Definition at line 61 of file getResidues.m.

◆ residues

residues = res(:)

Definition at line 55 of file getResidues.m.

◆ Sk

Turn this into a with identical frequencies along the rows Sk = 1j*repmat(wSimFreqs(:),1,numPoles)

Definition at line 17 of file getResidues.m.

◆ terms

The partial fraction expansions consits of terms

Definition at line 34 of file getResidues.m.

◆ x

Obtain iteration resiudes for model x = A\b

Definition at line 50 of file getResidues.m.

Functions

Variables