java.lang.Object
- java.lang.Thread
- - gov.nih.mipav.model.algorithms.AlgorithmBase
  - - gov.nih.mipav.model.algorithms.filters.PseudoPolarFourierTransform

All Implemented Interfaces:

java.awt.event.ActionListener, java.awt.event.WindowListener, java.lang.Runnable, java.util.EventListener
```
public class PseudoPolarFourierTransform
extends AlgorithmBase
```
Author:

ilb This is a port of MATLAB code in the ppft2 download package by Yoel Shkolnisky. The Magic Square code used in testing is derived from the code in the article Magic Square by A. Riazi. The article states that the article has no explicit license attached to it. References: 1.) Pseudo-Polar and Discrete Radon Transforms Software Package Documentation by Yoel Shkolnisky February 19, 2003. 2.) DIRECT INVERSION OF THE THREE-DIMENSIONAL PSEUDO-POLAR FOURIER TRANSFORM AMIR AVERBUCH, GIL SHABAT, AND YOEL SHKOLNISKY SIAM J. SCI. COMPUT. 2016 Society for Industrial and Applied Mathematics Vol. 38, No. 2, pp. A1100-A1120 3.) A FRAMEWORK FOR DISCRETE INTEGRAL TRANSFORMATIONS I - THE PSEUDO-POLAR FOURIER TRANSFORM A. AVERBUCH, R.R. COIFMAN, D.L. DONOHO, M. ISRAELI, AND Y. SHKOLNISKY 4.) Y. Keller, Y. Shkolnisky, and A. Averbuch. Volume registration using the 3-D pseudo-polar Fourier transform. IEEE Transactions on Signal Processing, 54(11):4323-4331, 2006.

Nested Class Summary

Nested Classes
Modifier and Type Class Description

private class PseudoPolarFourierTransform.indexValueComparator

private class PseudoPolarFourierTransform.indexValueItem
- Nested classes/interfaces inherited from class java.lang.Thread
  java.lang.Thread.State, java.lang.Thread.UncaughtExceptionHandler

Field Summary

Fields
Modifier and Type Field Description

private ViewUserInterface UI
- Fields inherited from class gov.nih.mipav.model.algorithms.AlgorithmBase
  destFlag, destImage, image25D, mask, maxProgressValue, minProgressValue, multiThreadingEnabled, nthreads, progress, progressModulus, progressStep, runningInSeparateThread, separable, srcImage, threadStopped
- Fields inherited from class java.lang.Thread
  MAX_PRIORITY, MIN_PRIORITY, NORM_PRIORITY

Constructor Summary

Constructors
Constructor Description

PseudoPolarFourierTransform()

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method	Description
`private double[][]`	`adjCfrft(double[][] x, double alpha)`
`private double[][]`	`adjE(double[][] v)`
`private double[][]`	`adjF(double[][] y)`
`private double[][]`	`adjGKN(double[][] w, int k)`
`private double[][]`	`adjInvF(double[][] v)`
`private double[][][]`	`adjPPFT(double[][][] pp1, double[][][] pp2)`
`private double[][]`	`adjRadon(double[][] r1, double[][] r2)`
`private double[][]`	`adjU(double[][] v)`
`private double[][][][]`	`applyppftfilter(double[][][][] X, double[][][][] filter)`
`private double[][]`	`cdft(double[] x)`
`private double[][]`	`cdft(double[][] x)`
`private double[][][]`	`cdft2(double[][] x)`
`private double[][][]`	`cdft2(double[][][] x)`
`private double[][][][]`	`cdft3(double[][][] x)`
`private double[][][][]`	`cdft3(double[][][][] x)`
`private double[][]`	`cfft(double[][] x)`
`private double[][][]`	`cfft2(double[][][] x)`
`private double[][][][]`	`cfft3(double[][][][] x)`
`private double[][]`	`cfrft(double[][] x, double alpha)`
`private double[][]`	`cfrftV2(double[][] x, double alpha)`
`private double[][][]`	`cfrftV3(double[][][] x, double alpha, double[][][] PQ, double[][][] PZ, int k)`
`private void`	`cfrftV3_precomp(double[][][] PQ, double[][][] PZ, int m, double[] alpha)`
`private void`	`CG(double[][][][] Y, int[] flag, double[] relres, int[] iter, double[] absres, boolean ref, double[][][][] X, double[][][][] filt, double ErrTol, int MaxIts, double[][][][] guess, boolean verbose, double[][][][] RefY)`
`private void`	`CG(double[][][] Y, int[] flag, double[] relres, int[] iter, double[] absres, double[][][] X, double ErrTol, int MaxIts, double[][][] guess, boolean verbose, double[][][] RefY)`
`private double[]`	`chebzeros(int n)`
`private int`	`checkInput(double[][][] pp1, double[][][] pp2)`
`private double[][]`	`ChirpZ(double[][] x, double[] A, double[] W, int M)`
`private void`	`compare(double[][] c1, double[][] c2)`
`private double[]`	`compC(int n, int j, int type)`
`private double[]`	`compD(int n, int j, int type)`
`private int[]`	`createArray(int lower, int upper)`
`private double[]`	`dirichlet(double[] t, int m)`
`private void`	`DoublyEvenMagicSquare(int[][] matrix, int n)`
`private void`	`equals(double[][][][][] v1, double[][][][][] v2, double eps, boolean[] ok, double[] error)`
`private void`	`equals(double[][][][] v1, double[][][][] v2, double eps, boolean[] ok, double[] error)`
`private double[][]`	`fastfmmresample(double[][] f, double[] yin, double[] xin, double[] dj, double[] cl, double EPS)`
`private double[][][]`	`fftshift(double[][][] in)`
`private double[][][][]`	`fftshift(double[][][][] in)`
`private double[][]`	`fftshift1d(double[][] x)`
`private void`	`fippft3(double[][][][] Y, int[] flag, double[] residual, int[] iter, double[][][][][] pp, double ErrTol, int MaxIts, boolean verbose)`
`private boolean`	`floateq(double[] x, double[] y)`
`private boolean`	`floateq(double x, double y)`
`private double[][][][]`	`FPtP(double[][][][] X, double[][][][] H)`
`private double[][]`	`frft(double[][] x, double alpha)`
`private java.lang.String`	`getppfiltname(int n)`
`private double[][]`	`GKN(double[][] x, int k)`
`private double[][]`	`GKN3(double[][] x, int k)`
`private int`	`hiIdx(int n)`
`private double`	`I1(double[][][] im, int n, double x, int v, int w)`
`private double`	`I1(double[][] im, int n, int u, double y)`
`private double`	`I2(double[][][] im, int n, int u, double y, int w)`
`private double`	`I2(double[][] im, int n, double x, int v)`
`private double`	`I3(double[][][] im, int n, int u, int v, double z)`
`private double[][]`	`icdft(double[][] x)`
`private double[][]`	`icfft(double[][] x)`
`private double[][][]`	`icfft2(double[][][] x)`
`private double[][][][]`	`icfft3(double[][][][] x)`
`private double[][][]`	`ifftshift(double[][][] in)`
`private double[][][][]`	`ifftshift(double[][][][] in)`
`private double[][]`	`ifftshift1d(double[][] x)`
`private double[][]`	`invDecimatedFreqs(double[][][] fim)`
`private double[]`	`ip(double[][][][][] a, double[][][][][] b)`
`private double[]`	`ip(double[][][][] a, double[][][][] b)`
`private double[]`	`ip(double[][][] a, double[][][] b)`
`private double`	`ip(double[][] a, double[][] b)`
`private void`	`ippft(double[][][] Y, int[] flag, double[] residual, int[] iter, double[][][] pp1, double[][][] pp2, double ErrTol, int MaxIts, boolean verbose)`
`private void`	`ippft3(double[][][][] Y, int[] flag, double[] residual, int[] iter, double[][][][][] pp, double ErrTol, int MaxIts, boolean verbose)`
`private void`	`ippft3_ref(double[][][][] Y, int[] flag, double[] residual, int[] iter, double[][][][][] pp, double ErrTol, int MaxIts, boolean verbose)`
`private void`	`ippftconsts(double[][][] c, double[][][] d, int n)`
`private double[][]`	`ippftd(double[][][] pp1, double[][][] pp2, double EPS)`
`private void`	`ippftprecomp(int n)`
`private void`	`iRadon(double[][][] Y, int[] flag, double[] residual, int[] iter, double[][][] res1, double[][][] res2, double ErrTol, int MaxIts, boolean verbose)`
`private void`	`iradon3(double[][][][] Y, int[] flag, double[] residual, int[] iter, double[][][][] res, double ErrTol, int MaxIts, boolean verbose)`
`private void`	`loadConsts(double[][][] c, double[][][] d, int n)`
`void`	`loadppftfilter(int[] precond, double[][][][] filter, java.lang.String fname, boolean verbose)`
`private double`	`log2(double input)`
`private int`	`lowIdx(int n)`
`private int[][]`	`MagicSquare(int n)`
`private double[][][][]`	`makeppftfilter(int n, int precond)`
`private int`	`matlab_mod(int j, int n)`
`private double`	`mult(int k, double alpha, int n)`
`private int`	`N(int k, int s)`
`private double[][][][]`	`nufft_3d(double[][][][] alpha, double[][] omega, int M)`
`private double[][][][]`	`nufft3dauxmx(int n, int M, int m, int q, int[] mu, double[] Px, double[] Py, double[] Pz, double[][] alpha)`
`private void`	`OddMagicSquare(int[][] matrix, int n)`
`private double[][][]`	`OptimizedAdjPPFT(double[][][] pp1, double[][][] pp2)`
`private void`	`OptimizedPPFT(double[][][] res1, double[][][] res2, double[][][] im)`
`private double[][]`	`optimizedtansum(double[][] alphain, double[] xin, double[] yin, double eps)`
`private void`	`PPFT(double[][][] res1, double[][][] res2, double[][][] im)`
`private double[][][][][]`	`ppft3(double[][][][] im)`
`private double[][][][][]`	`ppft3_ref(double[][][][] im)`
`private double[][][]`	`PrecondAdjPPFT(double[][][] pp1, double[][][] pp2)`
`private double[][][][]`	`precondadjppft3(double[][][][][] pp)`
`private double[][][][]`	`precondadjppft3_ref(double[][][][][] pp)`
`private void`	`prepConstC(double[][][] c, int n)`
`private void`	`prepConstD(double[][][] d, int n)`
`private double[][][]`	`PtP(double[][][] X)`
`private double[][][][]`	`PtP3(double[][][][] X)`
`private double[][][][]`	`PtP3_ref(double[][][][] X)`
`private void`	`Radon(double[][] res1, double[][] res2, double[][] im)`
`private double[][][][]`	`Radon3(double[][][][] im)`
`private double[][]`	`recover(double[][] fu, double[][] u, int j, int type, double[] dj, double[] cl, double EPS)`
`private void`	`reportResult(java.lang.String testMsg, boolean res, double err)`
`private void`	`reportResult(java.lang.String testMsg, int n, boolean res, double err, double t1, double t2)`
`void`	`runAlgorithm()`	Starts the program.
`private void`	`runTest(double[][][][] pp, double ErrTol, int MaxIts, double[][][] ref, java.lang.String description, boolean verbose, boolean trueimage)`
`private void`	`runTest(double[][][] pp1, double[][][] pp2, double ErrTol, int MaxIts, double[][] ref, java.lang.String description, boolean verbose, boolean trueimage)`
`private void`	`runTest(int n, double[][][][][] pp, double ErrTol, int MaxIts, double[][][][] ref, boolean verbose, boolean doippt3_ref)`
`private void`	`saveppftfilter(int precond, double[][][][] filter, java.lang.String fname)`
`private void`	`SinglyEvenMagicSquare(int[][] matrix, int n)`
`private double[][]`	`slowChirp(double[][] x, double[] A, double[] W, int M)`
`private void`	`slowPPFT(double[][][] res1, double[][][] res2, double[][][] im)`
`private double[][][][][]`	`slowppft3(double[][][][] im)`
`private void`	`slowRadon(double[][] res1, double[][] res2, double[][] im)`
`private double[][][][]`	`slowradon3(double[][][][] im)`
`void`	`testAdj()`
`void`	`testCfft()`
`void`	`testChirp()`
`void`	`testippft()`
`void`	`testippft3()`
`void`	`testIRadon()`
`void`	`testiRadon3()`
`void`	`testOptimizedAdjPPFT()`
`void`	`testppft3()`
`void`	`testppft3_ref()`
`void`	`testprecondAdjPPFT3(boolean ref)`
`void`	`testRadon()`
`private void`	`topinv(double[][] m1, double[][] m2, double[][] m3, double[][] m4, double[][] c, double[][] r)`
`private double[][]`	`topinvmul(double[][] D1, double[][] D2, double[][] D3, double[][] D4, double[][] v)`
`private double[][]`	`topmul(double[][] D, double[][] v)`
`private double[][]`	`topprep(double[][] c, double[][] r)`
`private void`	`topprepinv(double[][] D1, double[][] D2, double[][] D3, double[][] D4, double[][] m1, double[][] m2, double[][] m3, double[][] m4)`
`private double[][]`	`topsol(double[][] c, double[][] rin, double[][] y)`
`private int[]`	`toUnaliasedCoord(int[] aCoord, int[] N)`
`private int`	`toUnaliasedIdx(int idx, int n)`
`private double[]`	`trigPoly(double[][][][] im, double ox, double oy, double oz)`
`private double[]`	`trigPoly(double[][][] im, double xi1, double xi2)`
`boolean`	`verifyImage(double[][][][] im)`
`private int`	`verifyPP(double[][][][][] pp)`
`private double`	`zabs(double zr, double zi)`	zabs computes the absolute value or magnitude of a double precision complex variable zr + j*zi.
`private void`	`zdiv(double ar, double ai, double br, double bi, double[] cr, double[] ci)`	complex divide c = a/b.
`private void`	`zexp(double ar, double ai, double[] br, double[] bi)`	complex exponential function b = exp(a).
`private void`	`zlog(double ar, double ai, double[] br, double[] bi, int[] ierr)`	complex logarithm b = clog(a).
`private void`	`zpow(double zr, double zi, double a, double[] br, double[] bi, int[] ierr)`	b = z*a = exp(alog(z))

Methods inherited from class gov.nih.mipav.model.algorithms.AlgorithmBase
actionPerformed, addListener, addProgressChangeListener, calculateImageSize, calculatePrincipleAxis, computeElapsedTime, computeElapsedTime, convertIntoFloat, delinkProgressToAlgorithm, delinkProgressToAlgorithmMulti, displayError, errorCleanUp, finalize, fireProgressStateChanged, fireProgressStateChanged, fireProgressStateChanged, fireProgressStateChanged, fireProgressStateChanged, generateProgressValues, getDestImage, getElapsedTime, getMask, getMaxProgressValue, getMinProgressValue, getNumberOfThreads, getProgress, getProgressChangeListener, getProgressChangeListeners, getProgressModulus, getProgressStep, getProgressValues, getSrcImage, isCompleted, isImage25D, isMultiThreadingEnabled, isRunningInSeparateThread, isThreadStopped, linkProgressToAlgorithm, linkProgressToAlgorithm, makeProgress, notifyListeners, removeListener, removeProgressChangeListener, run, setCompleted, setImage25D, setMask, setMaxProgressValue, setMinProgressValue, setMultiThreadingEnabled, setNumberOfThreads, setProgress, setProgressModulus, setProgressStep, setProgressValues, setProgressValues, setRunningInSeparateThread, setSrcImage, setStartTime, setThreadStopped, startMethod, windowActivated, windowClosed, windowClosing, windowDeactivated, windowDeiconified, windowIconified, windowOpened

Methods inherited from class java.lang.Thread
activeCount, checkAccess, clone, countStackFrames, currentThread, dumpStack, enumerate, getAllStackTraces, getContextClassLoader, getDefaultUncaughtExceptionHandler, getId, getName, getPriority, getStackTrace, getState, getThreadGroup, getUncaughtExceptionHandler, holdsLock, interrupt, interrupted, isAlive, isDaemon, isInterrupted, join, join, join, onSpinWait, resume, setContextClassLoader, setDaemon, setDefaultUncaughtExceptionHandler, setName, setPriority, setUncaughtExceptionHandler, sleep, sleep, start, stop, suspend, toString, yield

Methods inherited from class java.lang.Object
equals, getClass, hashCode, notify, notifyAll, wait, wait, wait

Field Detail
- UI
```
private ViewUserInterface UI
```

Constructor Detail
- PseudoPolarFourierTransform
```
public PseudoPolarFourierTransform()
```

Method Detail

runAlgorithm
```
public void runAlgorithm()
```
Starts the program.

Specified by:

runAlgorithm in class AlgorithmBase

testCfft
```
public void testCfft()
```

testChirp
```
public void testChirp()
```

compare

private void compare(double[][] c1,
                     double[][] c2)

testippft
```
public void testippft()
```

MagicSquare

private int[][] MagicSquare(int n)

OddMagicSquare

private void OddMagicSquare(int[][] matrix,
                            int n)

DoublyEvenMagicSquare

private void DoublyEvenMagicSquare(int[][] matrix,
                                   int n)

SinglyEvenMagicSquare

private void SinglyEvenMagicSquare(int[][] matrix,
                                   int n)

testOptimizedAdjPPFT
```
public void testOptimizedAdjPPFT()
```

testAdj
```
public void testAdj()
```

testRadon
```
public void testRadon()
```

testIRadon
```
public void testIRadon()
```

runTest

private void runTest(double[][][] pp1,
                     double[][][] pp2,
                     double ErrTol,
                     int MaxIts,
                     double[][] ref,
                     java.lang.String description,
                     boolean verbose,
                     boolean trueimage)

testppft3
```
public void testppft3()
```

reportResult

private void reportResult(java.lang.String testMsg,
                          int n,
                          boolean res,
                          double err,
                          double t1,
                          double t2)

testppft3_ref
```
public void testppft3_ref()
```

reportResult

private void reportResult(java.lang.String testMsg,
                          boolean res,
                          double err)

testprecondAdjPPFT3

public void testprecondAdjPPFT3(boolean ref)

testippft3
```
public void testippft3()
```

runTest

private void runTest(int n,
                     double[][][][][] pp,
                     double ErrTol,
                     int MaxIts,
                     double[][][][] ref,
                     boolean verbose,
                     boolean doippt3_ref)

testiRadon3
```
public void testiRadon3()
```

runTest

private void runTest(double[][][][] pp,
                     double ErrTol,
                     int MaxIts,
                     double[][][] ref,
                     java.lang.String description,
                     boolean verbose,
                     boolean trueimage)

equals

private void equals(double[][][][][] v1,
                    double[][][][][] v2,
                    double eps,
                    boolean[] ok,
                    double[] error)

equals

private void equals(double[][][][] v1,
                    double[][][][] v2,
                    double eps,
                    boolean[] ok,
                    double[] error)

lowIdx
```
private int lowIdx(int n)
```

hiIdx
```
private int hiIdx(int n)
```

toUnaliasedIdx

private int toUnaliasedIdx(int idx,
                           int n)

cdft

private double[][] cdft(double[] x)

cdft

private double[][] cdft(double[][] x)

cdft2

private double[][][] cdft2(double[][] x)

cdft2

private double[][][] cdft2(double[][][] x)

cdft3

private double[][][][] cdft3(double[][][] x)

cdft3

private double[][][][] cdft3(double[][][][] x)

icdft

private double[][] icdft(double[][] x)

fftshift1d

private double[][] fftshift1d(double[][] x)

ifftshift1d

private double[][] ifftshift1d(double[][] x)

cfft

private double[][] cfft(double[][] x)

icfft

private double[][] icfft(double[][] x)

fftshift

private double[][][] fftshift(double[][][] in)

ifftshift

private double[][][] ifftshift(double[][][] in)

fftshift

private double[][][][] fftshift(double[][][][] in)

ifftshift

private double[][][][] ifftshift(double[][][][] in)

cfft2

private double[][][] cfft2(double[][][] x)

icfft2

private double[][][] icfft2(double[][][] x)

cfft3

private double[][][][] cfft3(double[][][][] x)

icfft3

private double[][][][] icfft3(double[][][][] x)

frft

private double[][] frft(double[][] x,
                        double alpha)

cfrft

private double[][] cfrft(double[][] x,
                         double alpha)

log2
```
private double log2(double input)
```

cfrftV2

private double[][] cfrftV2(double[][] x,
                           double alpha)

zabs
```
private double zabs(double zr,
                    double zi)
```
zabs computes the absolute value or magnitude of a double precision complex variable zr + j*zi.

Parameters:

zr - double

zi - double

Returns:

double

zpow

private void zpow(double zr,
                  double zi,
                  double a,
                  double[] br,
                  double[] bi,
                  int[] ierr)

b = z**a = exp(a*log(z))

Parameters:: zr -; zi -; a -; br -; bi -; ierr -

zlog

private void zlog(double ar,
                  double ai,
                  double[] br,
                  double[] bi,
                  int[] ierr)

complex logarithm b = clog(a).

Parameters:: ar - double; ai - double; br - double[]; bi - double[]; ierr - int[] ierr = 0, normal return ierr = 1, z = cmplx(0.0, 0.0)

zexp

private void zexp(double ar,
                  double ai,
                  double[] br,
                  double[] bi)

complex exponential function b = exp(a).

Parameters:: ar - double; ai - double; br - double[]; bi - double[]

zdiv

private void zdiv(double ar,
                  double ai,
                  double br,
                  double bi,
                  double[] cr,
                  double[] ci)

complex divide c = a/b.

Parameters:: ar - double; ai - double; br - double; bi - double; cr - double[]; ci - double[]

ChirpZ

private double[][] ChirpZ(double[][] x,
                          double[] A,
                          double[] W,
                          int M)

slowChirp

private double[][] slowChirp(double[][] x,
                             double[] A,
                             double[] W,
                             int M)

iRadon

private void iRadon(double[][][] Y,
                    int[] flag,
                    double[] residual,
                    int[] iter,
                    double[][][] res1,
                    double[][][] res2,
                    double ErrTol,
                    int MaxIts,
                    boolean verbose)

iradon3

private void iradon3(double[][][][] Y,
                     int[] flag,
                     double[] residual,
                     int[] iter,
                     double[][][][] res,
                     double ErrTol,
                     int MaxIts,
                     boolean verbose)

fippft3

private void fippft3(double[][][][] Y,
                     int[] flag,
                     double[] residual,
                     int[] iter,
                     double[][][][][] pp,
                     double ErrTol,
                     int MaxIts,
                     boolean verbose)

ippft3_ref

private void ippft3_ref(double[][][][] Y,
                        int[] flag,
                        double[] residual,
                        int[] iter,
                        double[][][][][] pp,
                        double ErrTol,
                        int MaxIts,
                        boolean verbose)

ippft3

private void ippft3(double[][][][] Y,
                    int[] flag,
                    double[] residual,
                    int[] iter,
                    double[][][][][] pp,
                    double ErrTol,
                    int MaxIts,
                    boolean verbose)

ippft

private void ippft(double[][][] Y,
                   int[] flag,
                   double[] residual,
                   int[] iter,
                   double[][][] pp1,
                   double[][][] pp2,
                   double ErrTol,
                   int MaxIts,
                   boolean verbose)

CG

private void CG(double[][][] Y,
                int[] flag,
                double[] relres,
                int[] iter,
                double[] absres,
                double[][][] X,
                double ErrTol,
                int MaxIts,
                double[][][] guess,
                boolean verbose,
                double[][][] RefY)

CG

private void CG(double[][][][] Y,
                int[] flag,
                double[] relres,
                int[] iter,
                double[] absres,
                boolean ref,
                double[][][][] X,
                double[][][][] filt,
                double ErrTol,
                int MaxIts,
                double[][][][] guess,
                boolean verbose,
                double[][][][] RefY)

dirichlet

private double[] dirichlet(double[] t,
                           int m)

toUnaliasedCoord

private int[] toUnaliasedCoord(int[] aCoord,
                               int[] N)

verifyImage

public boolean verifyImage(double[][][][] im)

adjF

private double[][] adjF(double[][] y)

chebzeros
```
private double[] chebzeros(int n)
```

fastfmmresample

private double[][] fastfmmresample(double[][] f,
                                   double[] yin,
                                   double[] xin,
                                   double[] dj,
                                   double[] cl,
                                   double EPS)

optimizedtansum

private double[][] optimizedtansum(double[][] alphain,
                                   double[] xin,
                                   double[] yin,
                                   double eps)

floateq

private boolean floateq(double x,
                        double y)

floateq

private boolean floateq(double[] x,
                        double[] y)

topsol

private double[][] topsol(double[][] c,
                          double[][] rin,
                          double[][] y)

topinv

private void topinv(double[][] m1,
                    double[][] m2,
                    double[][] m3,
                    double[][] m4,
                    double[][] c,
                    double[][] r)

topmul

private double[][] topmul(double[][] D,
                          double[][] v)

topinvmul

private double[][] topinvmul(double[][] D1,
                             double[][] D2,
                             double[][] D3,
                             double[][] D4,
                             double[][] v)

topprep

private double[][] topprep(double[][] c,
                           double[][] r)

topprepinv

private void topprepinv(double[][] D1,
                        double[][] D2,
                        double[][] D3,
                        double[][] D4,
                        double[][] m1,
                        double[][] m2,
                        double[][] m3,
                        double[][] m4)

invDecimatedFreqs

private double[][] invDecimatedFreqs(double[][][] fim)

ippftconsts

private void ippftconsts(double[][][] c,
                         double[][][] d,
                         int n)

prepConstD

private void prepConstD(double[][][] d,
                        int n)

N

private int N(int k,
              int s)

createArray

private int[] createArray(int lower,
                          int upper)

compD

private double[] compD(int n,
                       int j,
                       int type)

prepConstC

private void prepConstC(double[][][] c,
                        int n)

compC

private double[] compC(int n,
                       int j,
                       int type)

ippftprecomp
```
private void ippftprecomp(int n)
```

ippftd

private double[][] ippftd(double[][][] pp1,
                          double[][][] pp2,
                          double EPS)

checkInput

private int checkInput(double[][][] pp1,
                       double[][][] pp2)

loadConsts

private void loadConsts(double[][][] c,
                        double[][][] d,
                        int n)

recover

private double[][] recover(double[][] fu,
                           double[][] u,
                           int j,
                           int type,
                           double[] dj,
                           double[] cl,
                           double EPS)

adjGKN

private double[][] adjGKN(double[][] w,
                          int k)

adjU

private double[][] adjU(double[][] v)

adjE

private double[][] adjE(double[][] v)

adjCfrft

private double[][] adjCfrft(double[][] x,
                            double alpha)

adjInvF

private double[][] adjInvF(double[][] v)

adjPPFT

private double[][][] adjPPFT(double[][][] pp1,
                             double[][][] pp2)

PrecondAdjPPFT

private double[][][] PrecondAdjPPFT(double[][][] pp1,
                                    double[][][] pp2)

OptimizedAdjPPFT

private double[][][] OptimizedAdjPPFT(double[][][] pp1,
                                      double[][][] pp2)

adjRadon

private double[][] adjRadon(double[][] r1,
                            double[][] r2)

ip

private double ip(double[][] a,
                  double[][] b)

ip

private double[] ip(double[][][] a,
                    double[][][] b)

ip

private double[] ip(double[][][][] a,
                    double[][][][] b)

ip

private double[] ip(double[][][][][] a,
                    double[][][][][] b)

GKN

private double[][] GKN(double[][] x,
                       int k)

GKN3

private double[][] GKN3(double[][] x,
                        int k)

PPFT

private void PPFT(double[][][] res1,
                  double[][][] res2,
                  double[][][] im)

OptimizedPPFT

private void OptimizedPPFT(double[][][] res1,
                           double[][][] res2,
                           double[][][] im)

slowPPFT

private void slowPPFT(double[][][] res1,
                      double[][][] res2,
                      double[][][] im)

slowppft3

private double[][][][][] slowppft3(double[][][][] im)

trigPoly

private double[] trigPoly(double[][][] im,
                          double xi1,
                          double xi2)

trigPoly

private double[] trigPoly(double[][][][] im,
                          double ox,
                          double oy,
                          double oz)

Radon

private void Radon(double[][] res1,
                   double[][] res2,
                   double[][] im)

Radon3

private double[][][][] Radon3(double[][][][] im)

slowRadon

private void slowRadon(double[][] res1,
                       double[][] res2,
                       double[][] im)

slowradon3

private double[][][][] slowradon3(double[][][][] im)

I1

private double I1(double[][] im,
                  int n,
                  int u,
                  double y)

I1

private double I1(double[][][] im,
                  int n,
                  double x,
                  int v,
                  int w)

I2

private double I2(double[][] im,
                  int n,
                  double x,
                  int v)

I2

private double I2(double[][][] im,
                  int n,
                  int u,
                  double y,
                  int w)

I3

private double I3(double[][][] im,
                  int n,
                  int u,
                  int v,
                  double z)

PtP

private double[][][] PtP(double[][][] X)

cfrftV3_precomp

private void cfrftV3_precomp(double[][][] PQ,
                             double[][][] PZ,
                             int m,
                             double[] alpha)

cfrftV3

private double[][][] cfrftV3(double[][][] x,
                             double alpha,
                             double[][][] PQ,
                             double[][][] PZ,
                             int k)

ppft3

private double[][][][][] ppft3(double[][][][] im)

ppft3_ref

private double[][][][][] ppft3_ref(double[][][][] im)

precondadjppft3

private double[][][][] precondadjppft3(double[][][][][] pp)

precondadjppft3_ref

private double[][][][] precondadjppft3_ref(double[][][][][] pp)

verifyPP

private int verifyPP(double[][][][][] pp)

mult

private double mult(int k,
                    double alpha,
                    int n)

PtP3

private double[][][][] PtP3(double[][][][] X)

PtP3_ref

private double[][][][] PtP3_ref(double[][][][] X)

getppfiltname

private java.lang.String getppfiltname(int n)

saveppftfilter

private void saveppftfilter(int precond,
                            double[][][][] filter,
                            java.lang.String fname)

loadppftfilter

public void loadppftfilter(int[] precond,
                           double[][][][] filter,
                           java.lang.String fname,
                           boolean verbose)

makeppftfilter

private double[][][][] makeppftfilter(int n,
                                      int precond)

nufft_3d

private double[][][][] nufft_3d(double[][][][] alpha,
                                double[][] omega,
                                int M)

matlab_mod

private int matlab_mod(int j,
                       int n)

nufft3dauxmx

private double[][][][] nufft3dauxmx(int n,
                                    int M,
                                    int m,
                                    int q,
                                    int[] mu,
                                    double[] Px,
                                    double[] Py,
                                    double[] Pz,
                                    double[][] alpha)

FPtP

private double[][][][] FPtP(double[][][][] X,
                            double[][][][] H)

applyppftfilter

private double[][][][] applyppftfilter(double[][][][] X,
                                       double[][][][] filter)

Modifier and Type	Class	Description
`private class`	`PseudoPolarFourierTransform.indexValueComparator`
`private class`	`PseudoPolarFourierTransform.indexValueItem`

Class PseudoPolarFourierTransform

Nested Class Summary

Nested classes/interfaces inherited from class java.lang.Thread

Field Summary

Fields inherited from class gov.nih.mipav.model.algorithms.AlgorithmBase

Fields inherited from class java.lang.Thread

Constructor Summary

Method Summary

Methods inherited from class gov.nih.mipav.model.algorithms.AlgorithmBase

Methods inherited from class java.lang.Thread

Methods inherited from class java.lang.Object

Field Detail

UI

Constructor Detail

PseudoPolarFourierTransform

Method Detail

runAlgorithm

testCfft

testChirp

compare

testippft

MagicSquare

OddMagicSquare

DoublyEvenMagicSquare

SinglyEvenMagicSquare

testOptimizedAdjPPFT

testAdj

testRadon

testIRadon

runTest

testppft3

reportResult

testppft3_ref

reportResult

testprecondAdjPPFT3

testippft3

runTest

testiRadon3

runTest

equals

equals

lowIdx

hiIdx

toUnaliasedIdx

cdft

cdft

cdft2

cdft2

cdft3

cdft3

icdft

fftshift1d

ifftshift1d

cfft

icfft

fftshift

ifftshift

fftshift

ifftshift

cfft2

icfft2

cfft3

icfft3

frft

cfrft

log2

cfrftV2

zabs

zpow

zlog

zexp

zdiv

ChirpZ

slowChirp

iRadon

iradon3

fippft3

ippft3_ref

ippft3

ippft