/*
 * $RCSfile: SynWTFilterFloatLift9x7.java,v $
 * $Revision: 1.1 $
 * $Date: 2005/02/11 05:02:34 $
 * $State: Exp $
 *
 * Class:                   SynWTFilterFloatLift9x7
 *
 * Description:             A synthetizing wavelet filter implementing the
 *                          lifting 9x7 transform.
 *
 *
 *
 * COPYRIGHT:
 *
 * This software module was originally developed by Raphaël Grosbois and
 * Diego Santa Cruz (Swiss Federal Institute of Technology-EPFL); Joel
 * Askelöf (Ericsson Radio Systems AB); and Bertrand Berthelot, David
 * Bouchard, Félix Henry, Gerard Mozelle and Patrice Onno (Canon Research
 * Centre France S.A) in the course of development of the JPEG2000
 * standard as specified by ISO/IEC 15444 (JPEG 2000 Standard). This
 * software module is an implementation of a part of the JPEG 2000
 * Standard. Swiss Federal Institute of Technology-EPFL, Ericsson Radio
 * Systems AB and Canon Research Centre France S.A (collectively JJ2000
 * Partners) agree not to assert against ISO/IEC and users of the JPEG
 * 2000 Standard (Users) any of their rights under the copyright, not
 * including other intellectual property rights, for this software module
 * with respect to the usage by ISO/IEC and Users of this software module
 * or modifications thereof for use in hardware or software products
 * claiming conformance to the JPEG 2000 Standard. Those intending to use
 * this software module in hardware or software products are advised that
 * their use may infringe existing patents. The original developers of
 * this software module, JJ2000 Partners and ISO/IEC assume no liability
 * for use of this software module or modifications thereof. No license
 * or right to this software module is granted for non JPEG 2000 Standard
 * conforming products. JJ2000 Partners have full right to use this
 * software module for his/her own purpose, assign or donate this
 * software module to any third party and to inhibit third parties from
 * using this software module for non JPEG 2000 Standard conforming
 * products. This copyright notice must be included in all copies or
 * derivative works of this software module.
 *
 * Copyright (c) 1999/2000 JJ2000 Partners.
 *  */

package jj2000.j2k.wavelet.synthesis;


/**
 * This class inherits from the synthesis wavelet filter definition for int
 * data. It implements the inverse wavelet transform specifically for the 9x7
 * filter. The implementation is based on the lifting scheme.
 *
 * <P>See the SynWTFilter class for details such as normalization, how to
 * split odd-length signals, etc. In particular, this method assumes that the
 * low-pass coefficient is computed first.
 *
 * @see SynWTFilter
 * @see SynWTFilterFloat
 * */
public class SynWTFilterFloatLift9x7 extends SynWTFilterFloat {
    
    /** The value of the first lifting step coefficient */
    public final static float ALPHA = -1.586134342f;

    /** The value of the second lifting step coefficient */
    public final static float BETA = -0.05298011854f;

    /** The value of the third lifting step coefficient */
    public final static float GAMMA = 0.8829110762f;

    /** The value of the fourth lifting step coefficient */
    public final static float DELTA = 0.4435068522f;

    /** The value of the low-pass subband normalization factor */
    public final static float KL = 0.8128930655f;

    /** The value of the high-pass subband normalization factor */
    public final static float KH = 1.230174106f;
    
    /**
     * An implementation of the synthetize_lpf() method that works on int
     * data, for the inverse 9x7 wavelet transform using the lifting
     * scheme. See the general description of the synthetize_lpf() method in
     * the SynWTFilter class for more details.
     *
     * <P>The low-pass and high-pass subbands are normalized by respectively a
     * factor of 1/KL and a factor of 1/KH
     *
     * <P>The coefficients of the first lifting step are [-DELTA 1 -DELTA]. 
     *
     * <P>The coefficients of the second lifting step are [-GAMMA 1 -GAMMA].
     * 
     * <P>The coefficients of the third lifting step are [-BETA 1 -BETA]. 
     *
     * <P>The coefficients of the fourth lifting step are [-ALPHA 1 -ALPHA].
     *
     * @param lowSig This is the array that contains the low-pass input
     * signal.
     *
     * @param lowOff This is the index in lowSig of the first sample to
     * filter.
     *
     * @param lowLen This is the number of samples in the low-pass input
     * signal to filter.
     *
     * @param lowStep This is the step, or interleave factor, of the low-pass
     * input signal samples in the lowSig array.
     *
     * @param highSig This is the array that contains the high-pass input
     * signal.
     *
     * @param highOff This is the index in highSig of the first sample to
     * filter.
     *
     * @param highLen This is the number of samples in the high-pass input
     * signal to filter.
     *
     * @param highStep This is the step, or interleave factor, of the
     * high-pass input signal samples in the highSig array.
     *
     * @param outSig This is the array where the output signal is placed. It
     * should be long enough to contain the output signal.
     *
     * @param outOff This is the index in outSig of the element where to put
     * the first output sample.
     *
     * @param outStep This is the step, or interleave factor, of the output
     * samples in the outSig array.
     *
     * @see SynWTFilter#synthetize_lpf
     * */
    public
        void synthetize_lpf(float[] lowSig,int lowOff,int lowLen,int lowStep,
                            float[] highSig,int highOff,int highLen,
                            int highStep,
                            float[] outSig, int outOff, int outStep) {
                        
        int i;
        int outLen = lowLen + highLen; //Length of the output signal
        int iStep = 2*outStep; //Upsampling in outSig
        int ik; //Indexing outSig
        int lk; //Indexing lowSig
        int hk; //Indexing highSig
        
        // Generate intermediate low frequency subband
        float sample = 0;

        //Initialize counters
        lk = lowOff;
        hk = highOff;
        ik = outOff;
        
        //Handle tail boundary effect. Use symmetric extension
        if(outLen>1) {
            outSig[ik] = lowSig[lk]/KL - 2*DELTA*highSig[hk]/KH;
        }
        else {
            outSig[ik] = lowSig[lk];
        }
        
        lk += lowStep;
        hk += highStep;
        ik += iStep;
        
        //Apply lifting step to each "inner" sample
        for(i=2; i<outLen-1; i+=2, ik+=iStep, lk+=lowStep, hk+=highStep) {
            outSig[ik] = lowSig[lk]/KL - 
                DELTA*(highSig[hk-highStep] + highSig[hk])/KH;
        }
        
        //Handle head boundary effect if input signal has odd length
        if(outLen%2 == 1) {
            if(outLen>2){
                outSig[ik] = lowSig[lk]/KL - 
                2*DELTA*highSig[hk-highStep]/KH;
            }
        }
        
        // Generate intermediate high frequency subband
         
        //Initialize counters
        lk = lowOff;
        hk = highOff;
        ik = outOff + outStep;

        //Apply lifting step to each "inner" sample
        for(i = 1; i<outLen-1; i+=2, ik+=iStep, hk+=highStep, lk+=lowStep) {
            outSig[ik] = highSig[hk]/KH - 
                GAMMA*(outSig[ik-outStep] + outSig[ik+outStep]);
        }

        //Handle head boundary effect if output signal has even length
        if(outLen % 2 == 0) {
            outSig[ik] = highSig[hk]/KH - 2*GAMMA*outSig[ik-outStep];
        }       

        // Generate even samples (inverse low-pass filter)
        
        //Initialize counters
        ik = outOff;
 
        //Handle tail boundary effect
        //If access the overlap then perform the lifting step.
        if(outLen>1) {
            outSig[ik] -= 2*BETA*outSig[ik+outStep];
        }
        ik += iStep;
 
        //Apply lifting step to each "inner" sample
        for(i=2; i<outLen-1; i+=2, ik+=iStep) {
            outSig[ik] -= BETA*(outSig[ik-outStep] + outSig[ik+outStep]);
        }
        
        //Handle head boundary effect if input signal has odd length
        if(outLen%2 == 1 && outLen>2) {
            outSig[ik] -= 2*BETA*outSig[ik-outStep];
        }

        // Generate odd samples (inverse high pass-filter)
         
        //Initialize counters
        ik = outOff + outStep;

        //Apply first lifting step to each "inner" sample
        for(i=1; i<outLen-1; i+=2, ik+=iStep) {           
            outSig[ik] -= ALPHA*(outSig[ik-outStep] + outSig[ik+outStep]);
        }

        //Handle head boundary effect if input signal has even length
        if(outLen%2 == 0) {
            outSig[ik] -= 2*ALPHA*outSig[ik-outStep];
        }
    }
    
    /**
     * An implementation of the synthetize_hpf() method that works on int
     * data, for the inverse 9x7 wavelet transform using the lifting
     * scheme. See the general description of the synthetize_hpf() method in
     * the SynWTFilter class for more details.
     *
     * <P>The low-pass and high-pass subbands are normalized by respectively
     * a factor of 1/KL and a factor of 1/KH   
     *
     * <P>The coefficients of the first lifting step are [-DELTA 1 -DELTA]. 
     *
     * <P>The coefficients of the second lifting step are [-GAMMA 1 -GAMMA].
     * 
     * <P>The coefficients of the third lifting step are [-BETA 1 -BETA]. 
     *
     * <P>The coefficients of the fourth lifting step are [-ALPHA 1 -ALPHA].
     *
     * @param lowSig This is the array that contains the low-pass
     * input signal.
     *
     * @param lowOff This is the index in lowSig of the first sample to
     * filter.
     *
     * @param lowLen This is the number of samples in the low-pass input
     * signal to filter.
     *
     * @param lowStep This is the step, or interleave factor, of the low-pass
     * input signal samples in the lowSig array.
     *
     * @param highSig This is the array that contains the high-pass input
     * signal.
     *
     * @param highOff This is the index in highSig of the first sample to
     * filter.
     *
     * @param highLen This is the number of samples in the high-pass input
     * signal to filter.
     *
     * @param highStep This is the step, or interleave factor, of the
     * high-pass input signal samples in the highSig array.
     *
     * @param outSig This is the array where the output signal is placed. It
     * should be long enough to contain the output signal.
     *
     * @param outOff This is the index in outSig of the element where to put
     * the first output sample.
     *
     * @param outStep This is the step, or interleave factor, of the output
     * samples in the outSig array.
     *
     * @see SynWTFilter#synthetize_hpf
     * */
    public
        void synthetize_hpf(float[] lowSig,int lowOff,int lowLen,int lowStep,
                            float[] highSig,int highOff,int highLen,
                            int highStep,float[] outSig,int outOff,
                            int outStep) {
                        
        int i;
        int outLen = lowLen + highLen; //Length of the output signal
        int iStep = 2*outStep; //Upsampling in outSig
        int ik; //Indexing outSig
        int lk; //Indexing lowSig
        int hk; //Indexing highSig
        
        // Initialize counters
        lk = lowOff;
        hk = highOff;
        
        if(outLen!=1) {
            int outLen2 = outLen>>1;
            // "Inverse normalize" each sample
            for(i=0; i<outLen2; i++) {
                lowSig[lk] /= KL;
                highSig[hk] /= KH;
                lk += lowStep;  
                hk += highStep;
            } 
            // "Inverse normalise" last high pass coefficient
            if(outLen%2==1) {
                highSig[hk] /= KH;
            }
        } else {
            // Normalize for Nyquist gain
            highSig[highOff] /= 2;
        }
        
        // Generate intermediate low frequency subband
        
        //Initialize counters
        lk = lowOff;
        hk = highOff;
        ik = outOff + outStep;
        
        //Apply lifting step to each "inner" sample
        for(i=1; i<outLen-1; i+=2 ) {
            outSig[ik] = lowSig[lk] - 
                DELTA*(highSig[hk] + highSig[hk+highStep]);
            ik += iStep;
            lk += lowStep;
            hk += highStep;
        }
        
        if(outLen%2==0 && outLen>1) {
            //Use symmetric extension
            outSig[ik] = lowSig[lk] - 2*DELTA*highSig[hk];
        }
        
        // Generate intermediate high frequency subband
         
        //Initialize counters
        hk = highOff;
        ik = outOff;
        
        if(outLen>1) {
            outSig[ik] = highSig[hk] - 2*GAMMA*outSig[ik+outStep];
        } else {
            outSig[ik] = highSig[hk];
        }
            
        ik += iStep;
        hk += highStep;
            
        //Apply lifting step to each "inner" sample
        for(i=2; i<outLen-1; i+=2 ) {
            outSig[ik] = highSig[hk] - 
                GAMMA*(outSig[ik-outStep] + outSig[ik+outStep]);
            ik += iStep;
            hk += highStep;
        }

        //Handle head boundary effect if output signal has even length
        if(outLen%2==1 && outLen>1) {
            //Use symmetric extension
            outSig[ik] = highSig[hk] - 2*GAMMA*outSig[ik-outStep];
        }        

        // Generate even samples (inverse low-pass filter)

        //Initialize counters
        ik = outOff + outStep;
    
        //Apply lifting step to each "inner" sample
        for(i=1; i<outLen-1; i+=2 ) {
            outSig[ik] -= BETA*(outSig[ik-outStep] + outSig[ik+outStep]);
            ik += iStep;
        }
        
        if(outLen%2==0 && outLen>1) { 
            // symmetric extension.
            outSig[ik] -= 2*BETA*outSig[ik-outStep];
        }
        
        // Generate odd samples (inverse high pass-filter)
         
        //Initialize counters
        ik = outOff;

        if(outLen>1) {
            // symmetric extension.
            outSig[ik] -= 2*ALPHA*outSig[ik+outStep];
        }
        ik += iStep;
        
        //Apply first lifting step to each "inner" sample
        for(i=2; i<outLen-1 ; i+=2) { 
            outSig[ik] -= ALPHA*(outSig[ik-outStep] + outSig[ik+outStep]);
            ik += iStep;
        }
        
        //Handle head boundary effect if input signal has even length
        if((outLen%2==1) && (outLen>1)) {
            //Use symmetric extension 
            outSig[ik] -= 2*ALPHA*outSig[ik-outStep];
        }
    }
    
    /**
     * Returns the negative support of the low-pass analysis filter. That is
     * the number of taps of the filter in the negative direction.
     *
     * @return 2
     * */
    public int getAnLowNegSupport() {
        return 4;
    }

    /**
     * Returns the positive support of the low-pass analysis filter. That is
     * the number of taps of the filter in the negative direction.
     *
     * @return The number of taps of the low-pass analysis filter in the
     * positive direction
     * */
    public int getAnLowPosSupport() {
        return 4;
    }

    /**
     * Returns the negative support of the high-pass analysis filter. That is
     * the number of taps of the filter in the negative direction.
     *
     * @return The number of taps of the high-pass analysis filter in
     * the negative direction
     * */
    public int getAnHighNegSupport() {
        return 3;
    }

    /**
     * Returns the positive support of the high-pass analysis filter. That is
     * the number of taps of the filter in the negative direction.
     *
     * @return The number of taps of the high-pass analysis filter in the
     * positive direction
     * */
    public int getAnHighPosSupport() {
        return 3;
    }

    /**
     * Returns the negative support of the low-pass synthesis filter. That is
     * the number of taps of the filter in the negative direction.
     *
     * <P>A MORE PRECISE DEFINITION IS NEEDED
     *
     * @return The number of taps of the low-pass synthesis filter in the
     * negative direction
     * */
    public int getSynLowNegSupport() {
        return 3;
    }

    /**
     * Returns the positive support of the low-pass synthesis filter. That is
     * the number of taps of the filter in the negative direction.
     *
     * <P>A MORE PRECISE DEFINITION IS NEEDED
     *
     * @return The number of taps of the low-pass synthesis filter in the
     * positive direction
     * */
    public int getSynLowPosSupport() {
        return 3;
    }

    /**
     * Returns the negative support of the high-pass synthesis filter. That is
     * the number of taps of the filter in the negative direction.
     *
     * <P>A MORE PRECISE DEFINITION IS NEEDED
     *
     * @return The number of taps of the high-pass synthesis filter in the
     * negative direction
     * */
    public int getSynHighNegSupport() {
        return 4;
    }

    /**
     * Returns the positive support of the high-pass synthesis filter. That is
     * the number of taps of the filter in the negative direction.
     *
     * <P>A MORE PRECISE DEFINITION IS NEEDED
     *
     * @return The number of taps of the high-pass synthesis filter in the
     * positive direction
     * */
    public int getSynHighPosSupport() {
        return 4;
    }

    /**
     * Returns the implementation type of this filter, as defined in this
     * class, such as WT_FILTER_INT_LIFT, WT_FILTER_FLOAT_LIFT,
     * WT_FILTER_FLOAT_CONVOL.
     *
     * @return WT_FILTER_INT_LIFT.
     * */
    public int getImplType() {
        return WT_FILTER_FLOAT_LIFT;
    }

    /**
     * Returns the reversibility of the filter. A filter is considered
     * reversible if it is suitable for lossless coding.
     *
     * @return true since the 9x7 is reversible, provided the appropriate
     * rounding is performed.
     * */
    public boolean isReversible() {
        return false; 
    }
    
    /**
     * Returns true if the wavelet filter computes or uses the
     * same "inner" subband coefficient as the full frame wavelet transform,
     * and false otherwise. In particular, for block based transforms with 
     * reduced overlap, this method should return false. The term "inner"
     * indicates that this applies only with respect to the coefficient that 
     * are not affected by image boundaries processings such as symmetric
     * extension, since there is not reference method for this.
     *
     * <P>The result depends on the length of the allowed overlap when
     * compared to the overlap required by the wavelet filter. It also
     * depends on how overlap processing is implemented in the wavelet
     * filter.
     *
     * @param tailOvrlp This is the number of samples in the input
     * signal before the first sample to filter that can be used for
     * overlap.
     *
     * @param headOvrlp This is the number of samples in the input
     * signal after the last sample to filter that can be used for
     * overlap.
     *
     * @param inLen This is the lenght of the input signal to filter.The
     * required number of samples in the input signal after the last sample
     * depends on the length of the input signal.
     *
     * @return true if both overlaps are greater than 2, and correct 
     * processing is applied in the analyze() method.
     *
     *
     *
     */
    public boolean isSameAsFullWT(int tailOvrlp, int headOvrlp, int inLen) {
        
        //If the input signal has even length.
        if(inLen % 2 == 0) {
            if(tailOvrlp >= 2 && headOvrlp >= 1) return true;
            else return false;
        }
        //Else if the input signal has odd length.
        else {
            if(tailOvrlp >= 2 && headOvrlp >= 2) return true;
            else return false;
        }
    }

    /** 
     * Returns a string of information about the synthesis wavelet filter
     *
     * @return wavelet filter type.
     *
     *
     */
    public String toString(){
        return "w9x7 (lifting)";
    }
}