annotate maths/MathUtilities.cpp @ 418:d583feeeed7a

Add L^p norms, doc, tests

/* -*- c-basic-offset: 4 indent-tabs-mode: nil -*-  vi:set ts=8 sts=4 sw=4: */

/*
    QM DSP Library

    Centre for Digital Music, Queen Mary, University of London.
    This file 2005-2006 Christian Landone.

    This program is free software; you can redistribute it and/or
    modify it under the terms of the GNU General Public License as
    published by the Free Software Foundation; either version 2 of the
    License, or (at your option) any later version.  See the file
    COPYING included with this distribution for more information.
*/

#include "MathUtilities.h"

#include <iostream>
#include <algorithm>
#include <vector>
#include <cmath>

using namespace std;

double MathUtilities::mod(double x, double y)
{
    double a = floor( x / y );

    double b = x - ( y * a );
    return b;
}

double MathUtilities::princarg(double ang)
{
    double ValOut;

    ValOut = mod( ang + M_PI, -2 * M_PI ) + M_PI;

    return ValOut;
}

void MathUtilities::getAlphaNorm(const double *data, int len, int alpha, double* ANorm)
{
    int i;
    double temp = 0.0;
    double a=0.0;
	
    for( i = 0; i < len; i++)
    {
	temp = data[ i ];
		
	a  += ::pow( fabs(temp), double(alpha) );
    }
    a /= ( double )len;
    a = ::pow( a, ( 1.0 / (double) alpha ) );

    *ANorm = a;
}

double MathUtilities::getAlphaNorm( const vector <double> &data, int alpha )
{
    int i;
    int len = data.size();
    double temp = 0.0;
    double a=0.0;
	
    for( i = 0; i < len; i++)
    {
	temp = data[ i ];
	a  += ::pow( fabs(temp), double(alpha) );
    }
    a /= ( double )len;
    a = ::pow( a, ( 1.0 / (double) alpha ) );

    return a;
}

double MathUtilities::round(double x)
{
    if (x < 0) {
        return -floor(-x + 0.5);
    } else {
        return floor(x + 0.5);
    }
}

double MathUtilities::median(const double *src, int len)
{
    if (len == 0) return 0;
    
    vector<double> scratch;
    for (int i = 0; i < len; ++i) scratch.push_back(src[i]);
    sort(scratch.begin(), scratch.end());

    int middle = len/2;
    if (len % 2 == 0) {
        return (scratch[middle] + scratch[middle - 1]) / 2;
    } else {
        return scratch[middle];
    }
}

double MathUtilities::sum(const double *src, int len)
{
    int i ;
    double retVal =0.0;

    for(  i = 0; i < len; i++)
    {
	retVal += src[ i ];
    }

    return retVal;
}

double MathUtilities::mean(const double *src, int len)
{
    double retVal =0.0;

    if (len == 0) return 0;

    double s = sum( src, len );
	
    retVal =  s  / (double)len;

    return retVal;
}

double MathUtilities::mean(const vector<double> &src,
                           int start,
                           int count)
{
    double sum = 0.;
	
    if (count == 0) return 0;
    
    for (int i = 0; i < (int)count; ++i)
    {
        sum += src[start + i];
    }

    return sum / count;
}

void MathUtilities::getFrameMinMax(const double *data, int len, double *min, double *max)
{
    int i;
    double temp = 0.0;

    if (len == 0) {
        *min = *max = 0;
        return;
    }
	
    *min = data[0];
    *max = data[0];

    for( i = 0; i < len; i++)
    {
	temp = data[ i ];

	if( temp < *min )
	{
	    *min =  temp ;
	}
	if( temp > *max )
	{
	    *max =  temp ;
	}
		
    }
}

int MathUtilities::getMax( double* pData, int Length, double* pMax )
{
	int index = 0;
	int i;
	double temp = 0.0;
	
	double max = pData[0];

	for( i = 0; i < Length; i++)
	{
		temp = pData[ i ];

		if( temp > max )
		{
			max =  temp ;
			index = i;
		}
		
   	}

	if (pMax) *pMax = max;


	return index;
}

int MathUtilities::getMax( const vector<double> & data, double* pMax )
{
	int index = 0;
	int i;
	double temp = 0.0;
	
	double max = data[0];

	for( i = 0; i < int(data.size()); i++)
	{
		temp = data[ i ];

		if( temp > max )
		{
			max =  temp ;
			index = i;
		}
		
   	}

	if (pMax) *pMax = max;


	return index;
}

void MathUtilities::circShift( double* pData, int length, int shift)
{
	shift = shift % length;
	double temp;
	int i,n;

	for( i = 0; i < shift; i++)
	{
		temp=*(pData + length - 1);

		for( n = length-2; n >= 0; n--)
		{
			*(pData+n+1)=*(pData+n);
		}

        *pData = temp;
    }
}

int MathUtilities::compareInt (const void * a, const void * b)
{
  return ( *(int*)a - *(int*)b );
}

void MathUtilities::normalise(double *data, int length, NormaliseType type)
{
    switch (type) {

    case NormaliseNone: return;

    case NormaliseUnitSum:
    {
        double sum = 0.0;
        for (int i = 0; i < length; ++i) {
            sum += data[i];
        }
        if (sum != 0.0) {
            for (int i = 0; i < length; ++i) {
                data[i] /= sum;
            }
        }
    }
    break;

    case NormaliseUnitMax:
    {
        double max = 0.0;
        for (int i = 0; i < length; ++i) {
            if (fabs(data[i]) > max) {
                max = fabs(data[i]);
            }
        }
        if (max != 0.0) {
            for (int i = 0; i < length; ++i) {
                data[i] /= max;
            }
        }
    }
    break;

    }
}

void MathUtilities::normalise(vector<double> &data, NormaliseType type)
{
    switch (type) {

    case NormaliseNone: return;

    case NormaliseUnitSum:
    {
        double sum = 0.0;
        for (int i = 0; i < (int)data.size(); ++i) sum += data[i];
        if (sum != 0.0) {
            for (int i = 0; i < (int)data.size(); ++i) data[i] /= sum;
        }
    }
    break;

    case NormaliseUnitMax:
    {
        double max = 0.0;
        for (int i = 0; i < (int)data.size(); ++i) {
            if (fabs(data[i]) > max) max = fabs(data[i]);
        }
        if (max != 0.0) {
            for (int i = 0; i < (int)data.size(); ++i) data[i] /= max;
        }
    }
    break;

    }
}

double MathUtilities::getLpNorm(const vector<double> &data, int p)
{
    double tot = 0.0;
    for (int i = 0; i < int(data.size()); ++i) {
        tot += abs(pow(data[i], p));
    }
    return pow(tot, 1.0 / p);
}

vector<double> MathUtilities::normaliseLp(const vector<double> &data,
                                               int p,
                                               double threshold)
{
    int n = int(data.size());
    if (n == 0 || p == 0) return data;
    double norm = getLpNorm(data, p);
    if (norm < threshold) {
        return vector<double>(n, 1.0 / pow(n, 1.0 / p)); // unit vector
    }
    vector<double> out(n);
    for (int i = 0; i < n; ++i) {
        out[i] = data[i] / norm;
    }
    return out;
}
    
void MathUtilities::adaptiveThreshold(vector<double> &data)
{
    int sz = int(data.size());
    if (sz == 0) return;

    vector<double> smoothed(sz);
	
    int p_pre = 8;
    int p_post = 7;

    for (int i = 0; i < sz; ++i) {

        int first = max(0,      i - p_pre);
        int last  = min(sz - 1, i + p_post);

        smoothed[i] = mean(data, first, last - first + 1);
    }

    for (int i = 0; i < sz; i++) {
        data[i] -= smoothed[i];
        if (data[i] < 0.0) data[i] = 0.0;
    }
}

bool
MathUtilities::isPowerOfTwo(int x)
{
    if (x < 1) return false;
    if (x & (x-1)) return false;
    return true;
}

int
MathUtilities::nextPowerOfTwo(int x)
{
    if (isPowerOfTwo(x)) return x;
    if (x < 1) return 1;
    int n = 1;
    while (x) { x >>= 1; n <<= 1; }
    return n;
}

int
MathUtilities::previousPowerOfTwo(int x)
{
    if (isPowerOfTwo(x)) return x;
    if (x < 1) return 1;
    int n = 1;
    x >>= 1;
    while (x) { x >>= 1; n <<= 1; }
    return n;
}

int
MathUtilities::nearestPowerOfTwo(int x)
{
    if (isPowerOfTwo(x)) return x;
    int n0 = previousPowerOfTwo(x), n1 = nextPowerOfTwo(x);
    if (x - n0 < n1 - x) return n0;
    else return n1;
}

double
MathUtilities::factorial(int x)
{
    if (x < 0) return 0;
    double f = 1;
    for (int i = 1; i <= x; ++i) {
	f = f * i;
    }
    return f;
}

int
MathUtilities::gcd(int a, int b)
{
    int c = a % b;
    if (c == 0) {
        return b;
    } else {
        return gcd(b, c);
    }
}