package be.tarsos.dsp.wavelet.lift;

/**
 
* <p>
 
* HaarWavelet transform extended with a polynomial interpolation step
 
* </p>
 
* <p>
 
* This wavelet transform extends the HaarWavelet transform with a polynomial
 
* wavelet function.
 
* </p>
 
* <p>
 
* The polynomial wavelet uses 4-point polynomial interpolation to "predict" an
 
* odd point from four even point values.
 
* </p>
 
* <p>
 
* This class extends the HaarWavelet transform with an interpolation stage
 
* which follows the predict and update stages of the HaarWavelet transform. The
 
* predict value is calculated from the even points, which in this case are the
 
* smoothed values calculated by the scaling function (e.g., the averages of the
 
* even and odd values).
 
* </p>
 
*
 
* <p>
 
* The predict value is subtracted from the current odd value, which is the
 
* result of the HaarWavelet wavelet function (e.g., the difference between the
 
* odd value and the even value). This tends to result in large odd values after
 
* the interpolation stage, which is a weakness in this algorithm.
 
* </p>
 
*
 
* <p>
 
* This algorithm was suggested by Wim Sweldens' tutorial <i>Building Your Own
 
* Wavelets at Home</i>.
 
* </p>
 
*
 
* </p>
 
*
 
* <pre>
 
*
   
<a href=" http://www.bearcave.com/misl/misl_tech/wavelets/lifting/index.html">
 
*
   
http://www.bearcave.com/misl/misl_tech/wavelets/lifting/index.html</a>
 
* </pre>
 
*
 
* <h4>
 
* Copyright and Use</h4>
 
*
 
* <p>
 
* You may use this source code without limitation and without fee as long as
 
* you include:
 
* </p>
 
* <blockquote> This software was written and is copyrighted by Ian Kaplan, Bear
 
* Products International, www.bearcave.com, 2001. </blockquote>
 
* <p>
 
* This software is provided "as is", without any warrenty or claim as to its
 
* usefulness. Anyone who uses this source code uses it at their own risk. Nor
 
* is any support provided by Ian Kaplan and Bear Products International.
 
* <p>
 
* Please send any bug fixes or suggested source changes to:
 
*
 
* <pre>
 
*
      
iank@bearcave.com
 
* </pre>
 
*
 
* @author Ian Kaplan
 
*/

public class HaarWithPolynomialInterpolationWavelet extends HaarWavelet {
	
final static int numPts = 4;
	
private PolynomialInterpolation fourPt;

	
/**
	 
* HaarWithPolynomialInterpolationWavelet class constructor
	 
*/
	
public HaarWithPolynomialInterpolationWavelet() {
		
fourPt = new PolynomialInterpolation();
	
}

	
/**
	 
* <p>
	 
* Copy four points or <i>N</i> (which ever is less) data points from
	 
* <i>vec</i> into <i>d</i> These points are the "known" points used in the
	 
* polynomial interpolation.
	 
* </p>
	 
*
 

	 
* @param vec
	 
*
            
the input data set on which the wavelet is calculated
	 
* @param d
	 
*
            
an array into which <i>N</i> data points, starting at
	 
*
            
<i>start</i> are copied.
	 
* @param N
	 
*
            
the number of polynomial interpolation points
	 
* @param start
	 
*
            
the index in <i>vec</i> from which copying starts
	 
*/

	
private void fill(float vec[], float d[], int N, int start) {
		
int n = numPts;
		
if (n > N)
			
n = N;
		
int end = start + n;
		
int j = 0;

		
for (int i = start; i < end; i++) {
			
d[j] = vec[i];
			
j++;
		
}
	
} // fill

	
/**
	 
* <p>
	 
* Predict an odd point from the even points, using 4-point polynomial
	 
* interpolation.
	 
* </p>
	 
* <p>
	 
* The four points used in the polynomial interpolation are the even points.
	 
* We pretend that these four points are located at the x-coordinates
	 
* 0,1,2,3. The first odd point interpolated will be located between the
	 
* first and second even point, at 0.5. The next N-3 points are located at
	 
* 1.5 (in the middle of the four points). The last two points are located
	 
* at 2.5 and 3.5. For complete documentation see
	 
* </p>
	 
*
 

	 
* <pre>
	 
*
   
<a href=" http://www.bearcave.com/misl/misl_tech/wavelets/lifting/index.html">
	 
*
   
http://www.bearcave.com/misl/misl_tech/wavelets/lifting/index.html</a>
	 
* </pre>
	 
*
 

	 
* <p>
	 
* The difference between the predicted (interpolated) value and the actual
	 
* odd value replaces the odd value in the forward transform.
	 
* </p>
	 
*
 

	 
* <p>
	 
* As the recursive steps proceed, N will eventually be 4 and then 2. When N
	 
* = 4, linear interpolation is used. When N = 2, HaarWavelet interpolation
	 
* is used (the prediction for the odd value is that it is equal to the even
	 
* value).
	 
* </p>
	 
*
 

	 
* @param vec
	 
*
            
the input data on which the forward or inverse transform is
	 
*
            
calculated.
	 
* @param N
	 
*
            
the area of vec over which the transform is calculated
	 
* @param direction
	 
*
            
forward or inverse transform
	 
*/

	
protected void interp(float[] vec, int N, int direction) {
		
int half = N >> 1;
		
float d[] = new float[numPts];

		
// int k = 42;

		
for (int i = 0; i < half; i++) {
			
float predictVal;

			
if (i == 0) {
				
if (half == 1) {
					
// e.g., N == 2, and we use HaarWavelet interpolation
					
predictVal = vec[0];
				
} else {
					
fill(vec, d, N, 0);
					
predictVal = fourPt.interpPoint(0.5f, half, d);
				
}
			
} else if (i == 1) {
				
predictVal = fourPt.interpPoint(1.5f, half, d);
			
} else if (i == half - 2) {
				
predictVal = fourPt.interpPoint(2.5f, half, d);
			
} else if (i == half - 1) {
				
predictVal = fourPt.interpPoint(3.5f, half, d);
			
} else {
				
fill(vec, d, N, i - 1);
				
predictVal = fourPt.interpPoint(1.5f, half, d);
			
}

			
int j = i + half;
			
if (direction == forward) {
				
vec[j] = vec[j] - predictVal;
			
} else if (direction == inverse) {
				
vec[j] = vec[j] + predictVal;
			
} else {
				
System.out
						
.println
("PolynomialWavelets::predict: bad direction value");
			
}
		
}
	
} // interp

	
/**
	 
* <p>
	 
* HaarWavelet transform extened with polynomial interpolation forward
	 
* transform.
	 
* </p>
	 
* <p>
	 
* This version of the forwardTrans function overrides the function in the
	 
* LiftingSchemeBaseWavelet base class. This function introduces an extra
	 
* polynomial interpolation stage at the end of the transform.
	 
* </p>
	 
*/

	
public void forwardTrans(float[] vec) {
		
final int N = vec.length;

		
for (int n = N; n > 1; n = n >> 1) {
			
split(vec, n);
			
predict(vec, n, forward);
			
update(vec, n, forward);
			
interp(vec, n, forward);
		
} // for
	
} // forwardTrans

	
/**
	 
* <p>
	 
* HaarWavelet transform extened with polynomial interpolation inverse
	 
* transform.
	 
* </p>
	 
* <p>
	 
* This version of the inverseTrans function overrides the function in the
	 
* LiftingSchemeBaseWavelet base class. This function introduces an inverse
	 
* polynomial interpolation stage at the start of the inverse transform.
	 
* </p>
	 
*/

	
public void inverseTrans(float[] vec) {
		
final int N = vec.length;

		
for (int n = 2; n <= N; n = n << 1) {
			
interp(vec, n, inverse);
			
update(vec, n, inverse);
			
predict(vec, n, inverse);
			
merge(vec, n);
		
}
	
} // inverseTrans

} // HaarWithPolynomialInterpolationWavelet