/* ICA.c
 *
 * Copyright (C) 2010-2011 David Weenink
 *
 * 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.
 *
 * This program is distributed in the hope that it will be useful, but
 * WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
 * General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program; if not, write to the Free Software
 * Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
 */

/*
  djmw 20101202 Initial version
  djmw 20110304 Thing_new
*/

#include "ICA.h"
#include "Interpreter.h"
#include "NUM2.h"
#include "PCA.h"
#include "SVD.h"

// matrix multiply R = V*C*V', V is nrv x ncv, C is ncv x ncv, R is nrv x nrv
static void NUMdmatrices_multiply_VCVp (double **r, double **v, long nrv, long ncv, double **c, int csym)
{
	for (long i = 1; i <= nrv; i++)
	{
		long jstart = csym ? i : 1;
		for (long j = jstart; j <= nrv; j++)
		{
			// V_ik C_kl V'_lj = V_ik C_kl V_jl
			double vcv = 0;
			for (long k = 1; k <= ncv; k++)
			{
				for (long l = 1; l <= ncv; l++) { vcv += v[i][k] * c[k][l] * v[j][l]; }
			}
			r[i][j] = vcv;
			if (csym) r[j][i] = vcv;
		}
	}
}

// matrix multiply R = V'*C*V, V is nrv x ncv, C is ncv x ncv, R is nrv x nrv
static void NUMdmatrices_multiply_VpCV (double **r, double **v, long nrv, long ncv, double **c, int csym)
{
	for (long i = 1; i <= ncv; i++)
	{
		long jstart = csym ? i : 1;
		for (long j = jstart; j <= ncv; j++)
		{
			// V'_ik C_kl V_lj = V_ki C_kl V_lj
			double vcv = 0;
			for (long k = 1; k <= nrv; k++)
			{
				for (long l = 1; l <= ncv; l++) { vcv += v[k][i] * c[k][l] * v[l][j]; }
			}
			r[i][j] = vcv;
			if (csym) r[j][i] = vcv;
		}
	}
}

// matrix multiply V*C, V is nrv x ncv, C is ncv x ncc, R is nrv x ncc;
static void NUMdmatrices_multiply_VC (double **r, double **v, long nrv, long ncv, double **c, long ncc)
{
	for (long i = 1; i <= nrv; i++)
	{
		for (long j = 1; j <= ncc; j++)
		{
			// V_ik C_kj
			double vc = 0;
			for (long k = 1; k <= ncv; k++) { vc += v[i][k] * c[k][j]; }
			r[i][j] = vc;
		}
	}
}

// matrix multiply V'*C, V is nrv x ncv, C is nrv x ncc, R is ncv x ncc;
static void NUMdmatrices_multiply_VpC (double **r, double **v, long nrv, long ncv, double **c, long ncc)
{
	for (long i = 1; i <= ncv; i++)
	{
		for (long j = 1; j <= ncc; j++)
		{
			// V'_ik C_kj
			double vc = 0;
			for (long k = 1; k <= nrv; k++) { vc += v[k][i] * c[k][j]; }
			r[i][j] = vc;
		}
	}
}

// D += scalef * M * M', M = nrm x ncm, D is nrm x nrm
static void NUMdmatrices_multiplyScaleAdd (double **r, double **m, long nrm, long ncm, double scalef)
{
	for (long i = 1; i <= nrm; i++)
	{
		for (long j = 1; j <= nrm; j++)
		{
			// M_ik M'_kj = M_ik M_jk
			double mm = 0;
			for (long k = 1; k <= ncm; k++) { mm += m[i][k] * m[j][k]; }
			r[i][j] += scalef * mm;
		}
	}
}

/*
	d = diag(diag(W'*C0*W));
	W = W*d^(-1/2);

	D_ij = W'_ik C_kl W_lj => D_ii = W_ki C_kl W_li
*/
static void NUMdmatrix_normalizeColumnVectors (double **w, long nrw, long ncw, double **c)
{
	for (long i = 1; i <= ncw; i++)
	{
		double di = 0;
		for (long k = 1; k <= ncw; k++)
			for (long l = 1; l <= nrw; l++) { di += w[k][i] * c[k][l] * w[l][i]; }
		di = 1 / sqrt (di);
		for (long j = 1; j <= nrw; j++) { w[j][i] *= di; }
	}
}

static double NUMdmatrix_diagonalityMeasure (double **v, long dimension)
{
	double dmsq = 0;
	if (dimension < 2) return 0;
	for (long i = 1; i <= dimension; i++)
	{
		for (long j = 1; j <= dimension; j++)
		{
			if (i != j) { dmsq += v[i][j] * v[i][j]; }
		}
	}
	return dmsq / (dimension * (dimension -1 ));
}

static double NUMdmatrix_diagonalityIndex (double **v, long dimension)
{
	double dindex = 0;
	for (long irow = 1; irow <= dimension; irow++)
	{
		double rowmax = fabs(v[irow][1]), rowsum = 0;
		for (long icol = 2; icol <= dimension; icol++)
		{
			if (fabs (v[irow][icol]) > rowmax) rowmax = fabs (v[irow][icol]);
		}
		for (long icol = 1; icol <= dimension; icol++)
		{
			rowsum += fabs (v[irow][icol]) / rowmax;
		}
		dindex += rowsum - 1;
	}
	for (long icol = 1; icol <= dimension; icol++)
	{
		double colmax = fabs(v[icol][1]), colsum = 0;
		for (long irow = 2; irow <= dimension; irow++)
		{
			if (fabs (v[irow][icol]) > colmax) colmax = fabs (v[irow][icol]);
		}
		for (long irow = 1; irow <= dimension; irow++)
		{
			colsum += fabs (v[irow][icol]) / colmax;
		}
		dindex += colsum - 1;
	}
	return dindex;
}

/*
	This routine is modeled after qdiag.m from Andreas Ziehe, Pavel Laskov, Guido Nolte, Klaus-Robert Müller,
	A Fast Algorithm for Joint Diagonalization with Non-orthogonal Transformations and its Application to
	Blind Source Separation, Journal of Machine Learning Research 5 (2004), 777–800.
*/
static void Diagonalizer_and_CrossCorrelationTables_ffdiag (Diagonalizer me, CrossCorrelationTables thee, long maxNumberOfIterations, double delta)
{
	try {
		long iter = 0, dimension = my numberOfRows;
		double **v = my data;

		autoCrossCorrelationTables ccts = CrossCorrelationTables_and_Diagonalizer_diagonalize (thee, me);
		autoNUMmatrix<double> w (1, dimension, 1, dimension);
		autoNUMmatrix<double> vnew (1, dimension, 1, dimension);
		autoNUMmatrix<double> cc (1, dimension, 1, dimension);
		
		for (long i = 1; i<= dimension; i++) { w[i][i] = 1; }

		MelderInfo_open ();
		double dm_new = CrossCorrelationTables_getDiagonalityMeasure (ccts.peek(), NULL, 0, 0);
		MelderInfo_writeLine5 (L"\nIteration ", Melder_integer (iter), L":  ", Melder_double (dm_new), 
			L" (= diagonality measurement)");

		double dm_old, theta = 1 ;
		do
		{
			dm_old = dm_new;
			for (long i = 1; i <= dimension; i++)
			{
				for (long j = i + 1; j <= dimension; j++)
				{
					double zii = 0, zij = 0, zjj = 0, yij = 0, yji = 0; // zij = zji
					for (long k = 1; k <= ccts -> size; k++)
					{
						CrossCorrelationTable ct = (CrossCorrelationTable) ccts -> item [k];
						zii += ct -> data[i][i] * ct -> data[i][i];
						zij += ct -> data[i][i] * ct -> data[j][j];
						zjj += ct -> data[j][j] * ct -> data[j][j];
						yij += ct -> data[j][j] * ct -> data[i][j];
						yji += ct -> data[i][i] * ct -> data[i][j];
					}
					double denom = zjj * zii - zij * zij;
					if (denom != 0)
					{
						w[i][j] = (zij * yji - zii * yij) / denom;
						w[j][i] = (zij * yij - zjj * yji) / denom;
					}
				}
			}
			double norma = 0;
			for (long i = 1; i <= dimension; i++)
			{
				double normai = 0;
				for (long j = 1; j <= dimension; j++)
				{
					if (i != j) { normai += fabs (w[i][j]); }
				}
				if (normai > norma) norma = normai;
			}
			// evaluate the norm
			if (norma > theta)
			{
				double normf = 0;
				for (long i = 1; i <= dimension; i++)
					for (long j = 1; j <= dimension; j++)
						if (i != j) normf += w[i][j] * w[i][j];
				double scalef = theta / sqrt (normf);
				for (long i = 1; i <= dimension; i++)
				{
					for (long j = 1; j <= dimension; j++)
					{
						if (i != j) { w[i][j] *= scalef; }
					}
				}
			}
			// update V
			NUMdmatrix_copyElements (v, vnew.peek(), 1, dimension, 1, dimension);
			NUMdmatrices_multiply_VC (v, w.peek(), dimension, dimension, vnew.peek(), dimension);
			for (long k = 1; k <= ccts -> size; k++)
			{
				CrossCorrelationTable ct = (CrossCorrelationTable) ccts -> item[k];
				NUMdmatrix_copyElements (ct -> data, cc.peek(), 1, dimension, 1, dimension);
				NUMdmatrices_multiply_VCVp (ct -> data, w.peek(), dimension, dimension, cc.peek(), 1);
			}
			dm_new = CrossCorrelationTables_getDiagonalityMeasure (ccts.peek(), 0, 0, 0);
			iter++;
			MelderInfo_writeLine5 (L"\nIteration ", Melder_integer (iter), L":  ", Melder_double (dm_new), L" (= diagonality measurement)");
		} while (fabs((dm_old - dm_new) / dm_new) > delta && iter < maxNumberOfIterations);
		MelderInfo_close ();
	} catch (MelderError) { MelderInfo_close (); rethrow; }
}

/*
	The folowing two routine are modeled after qdiag.m from
	R. Vollgraf and K. Obermayer, Quadratic Optimization for Simultaneous
	Matrix Diagonalization, IEEE Transaction on Signal Processing, 2006,
*/

static void update_one_column (CrossCorrelationTables me, double **d, double *wp, double *wvec, double scalef, double *work)
{
	long dimension = ((CrossCorrelationTable)(my item[1])) -> numberOfColumns;

	for (long ic = 2; ic <= my size; ic++) // exclude C0
	{
		SSCP cov = (SSCP) my item[ic];
		double **c = cov -> data;
		// m1 = C * wvec
		for (long i = 1; i <= dimension; i++)
		{
			double r = 0;
			for (long j = 1; j <= dimension; j++) { r += c[i][j] * wvec[j]; }
			work[i] = r;
		}
		// D = D +/- 2*p(t)*(m1*m1');
		for (long i = 1; i <= dimension; i++)
		{
			for (long j = 1; j <= dimension; j++)
			{
				d[i][j] += 2 * scalef * wp[ic] * work[i] * work[j];
			}
		}
	}
}

static void Diagonalizer_and_CrossCorrelationTable_qdiag (Diagonalizer me, CrossCorrelationTables thee, double *cweights, long maxNumberOfIterations, double delta)
{
	try {
		CrossCorrelationTable c0 = (CrossCorrelationTable) thy item[1];
		double **w = my data;
		long dimension = c0 -> numberOfColumns;

		autoEigen eigen = Thing_new (Eigen);
		autoCrossCorrelationTables ccts = (CrossCorrelationTables) Data_copy (thee);
		autoNUMmatrix<double> pinv (1, dimension, 1, dimension);
		autoNUMmatrix<double> d (1, dimension, 1, dimension);
		autoNUMmatrix<double> p (1, dimension, 1, dimension);
		autoNUMmatrix<double> m1 (1, dimension, 1, dimension);
		autoNUMmatrix<double> wc (1, dimension, 1, dimension);
		autoNUMvector<double> wvec (1, dimension);
		autoNUMvector<double> wnew (1, dimension);
		autoNUMvector<double> mvec (1, dimension);

		for (long i = 1; i <= dimension; i++) // Transpose W
			for (long j = 1; j <= dimension; j++) { wc[i][j] = w[j][i]; }

		// d = diag(diag(W'*C0*W));
		// W = W*d^(-1/2);

		NUMdmatrix_normalizeColumnVectors (wc.peek(), dimension, dimension, c0 -> data);

		// scale eigenvectors for sphering
		// [vb,db] = eig(C0);
		// P = db^(-1/2)*vb';

		Eigen_initFromSymmetricMatrix (eigen.peek(), c0 -> data, dimension);
		for (long i = 1; i <= dimension; i++)
		{
			if (eigen -> eigenvalues[i] < 0) Melder_throw ("Covariance matrix not positive definite.");
			double scalef = 1 / sqrt (eigen -> eigenvalues[i]);
			for (long j = 1; j <= dimension; j++)
			{
				p[dimension - i + 1][j] = scalef * eigen -> eigenvectors[i][j];
			}
		}

		// P*C[i]*P'

		for (long ic = 1; ic <= thy size; ic++)
		{
			CrossCorrelationTable cov1 = (CrossCorrelationTable) thy item[ic];
			CrossCorrelationTable cov2 = (CrossCorrelationTable) ccts -> item[ic];
			NUMdmatrices_multiply_VCVp (cov2 -> data, p.peek(), dimension, dimension, cov1 -> data, 1);
		}

		// W = P'\W == inv(P') * W

		NUMpseudoInverse (p.peek(), dimension, dimension, pinv.peek(), 0);

		NUMdmatrices_multiply_VpC (w, pinv.peek(), dimension, dimension, wc.peek(), dimension);

		// initialisation for order KN^3

		for (long ic = 2; ic <= thy size; ic++)
		{
			CrossCorrelationTable cov = (CrossCorrelationTable) ccts -> item[ic];
			// C * W
			NUMdmatrices_multiply_VC (m1.peek(), cov -> data, dimension, dimension, w, dimension);
			// D += scalef * M1*M1'
			NUMdmatrices_multiplyScaleAdd (d.peek(), m1.peek(), dimension, dimension, 2 * cweights[ic]);
		}

		long iter = 0;
		double delta_w;
		MelderInfo_open ();
		do
		{
			// the standard diagonality measure is rather expensive to calculate so we compare the norms of
			// differences of eigenvectors.

			delta_w = 0;
			for (long kol = 1; kol <= dimension; kol++)
			{
				for (long i = 1; i <= dimension; i++) { wvec[i] = w[i][kol]; }

				update_one_column (ccts.peek(), d.peek(), cweights, wvec.peek(), -1, mvec.peek());

				Eigen_initFromSymmetricMatrix (eigen.peek(), d.peek(), dimension);

				// Eigenvalues already sorted; get eigenvector of smallest !

				for (long i = 1; i <= dimension; i++) { wnew[i] = eigen -> eigenvectors[dimension][i]; }

				update_one_column (ccts.peek(), d.peek(), cweights, wnew.peek(), 1, mvec.peek());
				for (long i = 1; i <= dimension; i++) { w[i][kol] = wnew[i]; }

				// compare norms of eigenvectors. We have to compare ||wvec +/- w_new|| because eigenvectors
				//  may change sign.

				double normp = 0, normm = 0;
				for (long j = 1; j <= dimension; j++)
				{
					double dm = wvec[j] - wnew[j], dp = wvec[j] + wnew[j];
					normp += dm * dm; normm += dp * dp;
				}

				normp = normp < normm ? normp : normm;
				normp = sqrt (normp);
				delta_w = normp > delta_w ? normp : delta_w;
			}
			iter++;
			MelderInfo_writeLine5 (L"\nIteration ", Melder_integer (iter), L":  ", Melder_double (delta_w), L" (= vector norm difference)");
		} while (delta_w > delta && iter < maxNumberOfIterations);

		// Revert the sphering W = P'*W;
		// Take transpose to make W*C[i]W' diagonal instead of W'*C[i]*W => (P'*W)'=W'*P
		// Calculate the "real" diagonality measure

		NUMdmatrix_copyElements (w, wc.peek(), 1, dimension, 1, dimension);
		NUMdmatrices_multiply_VpC (w, wc.peek(), dimension, dimension, p.peek(), dimension); // W = W'*P: final result

		double dm = CrossCorrelationTables_and_Diagonalizer_getDiagonalityMeasure (thee, me, cweights, 1, thy size);
		MelderInfo_writeLine5 (L"\nDiagonality measure: ", Melder_double (dm), L" after ", Melder_integer (iter),
		L" iterations.");
		MelderInfo_close ();
	} catch (MelderError) {MelderInfo_close (); rethrowm (me, ": not improved."); }
}

void MixingMatrix_and_CrossCorrelationTables_improveUnmixing (MixingMatrix me, CrossCorrelationTables thee, long maxNumberOfIterations, double tol, int method)
{
	try {
		autoDiagonalizer him = MixingMatrix_to_Diagonalizer (me);
		Diagonalizer_and_CrossCorrelationTables_improveDiagonality (him.peek(), thee, maxNumberOfIterations, tol, method);
		NUMpseudoInverse (his data, his numberOfRows, his numberOfColumns, my data, 0);
	} catch (MelderError) { rethrow; }
}

/*
	This is for multi-channel "sounds" like EEG signals.
	The cross-correlation between channel i and channel j is defined as
		sum(k=1..nsamples, (z[i][k] - mean[i])(z[j][k + tau] - mean[j]))*samplingTime
*/
CrossCorrelationTable Sound_to_CrossCorrelationTable (Sound me, double startTime, double endTime, double lagTime)
{
	try {
		if (endTime <= startTime) { startTime = my xmin; endTime = my xmax; }
		long ndelta = lagTime / my dx;
		long i1 = Sampled_xToNearestIndex (me, startTime);
		if (i1 < 1) i1 = 1;
		long i2 = Sampled_xToNearestIndex (me, endTime);
		if (i2 > my nx) i2 = my nx;
		i2 -= ndelta;
		long nsamples = i2 - i1 + 1;
		if (nsamples <= my ny) Melder_throw ("Not enough samples");
		autoCrossCorrelationTable thee = CrossCorrelationTable_create (my ny);
		double **data = my z;

		for (long ichan = 1; ichan <= my ny; ichan++)
		{
			double *z = my z[ichan];
			double sum = 0;
			for (long k = i1; k <= i2; k++) sum += z[k];
			thy centroid[ichan] = sum / nsamples;
		}

		double *mean = thy centroid;

		for (long i = 1; i <= my ny; i++)
		{
			for (long j = i; j <= my ny; j++)
			{
				double cc = 0;
				for (long k = i1; k <= i2; k++) { cc += (data[i][k] - mean[i]) * (data[j][k + ndelta] - mean[j]); }
				thy data[j][i] = thy data[i][j] = cc * my dx;
			}
		}

		thy numberOfObservations = nsamples;

		return thee.transfer();
	} catch (MelderError) { rethrowmzero (me, ": CrossCorrelationTable not created."); }
}

CrossCorrelationTables Sound_to_CrossCorrelationTables (Sound me, double startTime, double endTime, double lagTime, long ncovars)
{
	try {
		if (lagTime < my dx) lagTime = my dx;
		if (startTime + ncovars * lagTime > endTime) Melder_throw ("Lag time too large.");
		if (endTime <= startTime) { startTime = my xmin; endTime = my xmax; }
		autoCrossCorrelationTables thee = CrossCorrelationTables_create ();
		for (long i = 1; i <= ncovars; i++)
		{
			double lag = (i - 1) * lagTime;
			autoCrossCorrelationTable ct = Sound_to_CrossCorrelationTable (me, startTime, endTime, lag);
			Collection_addItem (thee.peek(), ct.transfer());
		}
		return thee.transfer();
	} catch (MelderError) { rethrowmzero (me, ": no CrossCorrelationTables created."); }
}

Sound Sound_to_Sound_BSS (Sound me, double startTime, double endTime, long ncovars, double lagTime, long maxNumberOfIterations, double tol, int method)
{
	try {
		autoMixingMatrix him = Sound_to_MixingMatrix (me, startTime, endTime, ncovars, lagTime, maxNumberOfIterations, tol, method);
		autoSound thee = Sound_and_MixingMatrix_unmix (me, him.peek());
		return thee.transfer();
	} catch (MelderError) { rethrowmzero (me, ": not separated."); }
}

PCA Sound_to_PCA (Sound me, double startTime, double endTime)
{
	try {
		autoCrossCorrelationTable thee = Sound_to_CrossCorrelationTable (me, startTime, endTime, 0);
		autoPCA him = SSCP_to_PCA (thee.peek());
		return him.transfer();
	} catch (MelderError) { rethrowmzero (me, ": no PCA created."); }
}

/************************ Diagonalizer **********************************/

class_methods (Diagonalizer, TableOfReal)
{
	class_methods_end
}

Diagonalizer Diagonalizer_create (long dimension)
{
	try {
		autoDiagonalizer me = Thing_new (Diagonalizer);
		TableOfReal_init (me.peek(), dimension, dimension); therror
		for (long i = 1; i <= dimension; i++) { my data[i][i] = 1; }
		return me.transfer();
	} catch (MelderError) { rethrowmzero ("Diagonalizer not created."); }
}


/************************ MixingMatrix **********************************/

class_methods (MixingMatrix, TableOfReal)
{
	class_methods_end
}

MixingMatrix MixingMatrix_create (long numberOfChannels, long numberOfComponents)
{
	try {
		autoMixingMatrix me = Thing_new (MixingMatrix);
		TableOfReal_init (me.peek(), numberOfChannels, numberOfComponents); therror
		MixingMatrix_initializeRandom (me.peek());
		return me.transfer();
	} catch (MelderError) { rethrowmzero ("MixingMatrix not created."); }
}

MixingMatrix MixingMatrix_createSimple (long numberOfChannels, long numberOfComponents, wchar_t *elements)
{
	try {
		long inum = 1, ntokens = Melder_countTokens (elements);
		if (ntokens == 0) Melder_throw ("No matrix elements.");
		long nwanted = numberOfChannels * numberOfComponents;

		autoMixingMatrix me = MixingMatrix_create (numberOfChannels, numberOfComponents);

		// Construct the full matrix from the elements
		double number;
		for (wchar_t *token = Melder_firstToken (elements); token != NULL && inum <= ntokens; token = Melder_nextToken (), inum++)
		{
			long irow = (inum - 1) / numberOfComponents + 1;
			long icol = (inum - 1) % numberOfComponents + 1;
			if (! Interpreter_numericExpression (0, token, &number)) Melder_throw 
				(L"Item ", inum, L" \"", token, L"\"is not a number.");

			my data[irow][icol] = number;
		}
		if (ntokens < nwanted)
		{
			for (long i = inum; i <= nwanted; i++)
			{
				long irow = (inum - 1) / numberOfComponents + 1;
				long icol = (inum - 1) % numberOfComponents + 1;
				my data[irow][icol] = number; // repeat the last number given!
			}
		}
		return me.transfer();
	} catch (MelderError) { rethrowmzero ("MixingMatrix not created."); }
}

void MixingMatrix_initializeRandom (MixingMatrix me)
{
	for (long i = 1; i <= my numberOfRows; i++)
	{
		for (long j = 1; j <= my numberOfColumns; j++)
		{
			my data[i][j] = NUMrandomGauss (0, 1);
		}
	}
}

/***************** Diagonalizer & MixingMatrix *************************/


Diagonalizer MixingMatrix_to_Diagonalizer (MixingMatrix me)
{
	try {
		if (my numberOfRows != my numberOfColumns) Melder_throw ("The number of channels and the number of components must be equal.");
		autoDiagonalizer thee = Diagonalizer_create (my numberOfRows);
		NUMpseudoInverse (my data, my numberOfRows, my numberOfColumns, thy data, 0);
		return thee.transfer();
	} catch (MelderError) { rethrowmzero (me, ": no Diagonalizer created."); }
}

MixingMatrix Diagonalizer_to_MixingMatrix (Diagonalizer me)
{
	try {
		autoMixingMatrix thee = MixingMatrix_create (my numberOfRows, my numberOfColumns);
		NUMpseudoInverse (my data, my numberOfRows, my numberOfColumns, thy data, 0);
		return thee.transfer();
	} catch (MelderError) { rethrowmzero (me, ": no MixingMatrix created."); }
}

/********************* Sound & MixingMatrix ************************************/

Sound Sound_and_MixingMatrix_mix (Sound me, MixingMatrix thee)
{
	try {
		if (my ny != thy numberOfRows) Melder_throw ("The MixingMatrix and the Sound must have the same number of channels.");
		autoSound him = Sound_create (my ny, my xmin, my xmax, my nx, my dx, my x1);
		for (long i = 1; i <= thy numberOfRows; i++)
		{
			for (long j = 1; j <= my nx; j++)
			{
				double mix = 0;
				for (long k = 1; k <= my ny; k++) { mix += thy data[i][k] * my z[k][j]; }
				his z[i][j] = mix;
			}
		}
		return him.transfer();
	} catch (MelderError) { rethrowmzero (me, ": not mixed."); }
}

Sound Sound_and_MixingMatrix_unmix (Sound me, MixingMatrix thee)
{
	try {
		if (my ny != thy numberOfRows) Melder_throw ("The MixingMatrix and the Sound must have the same number of channels.");

		autoNUMmatrix<double> minv (1, thy numberOfColumns, 1, thy numberOfRows);
		NUMpseudoInverse (thy data, thy numberOfRows, thy numberOfColumns, minv.peek(), 0);
		autoSound him = Sound_create (my ny, my xmin, my xmax, my nx, my dx, my x1);
		for (long i = 1; i <= thy numberOfColumns; i++)
		{
			for (long j = 1; j <= my nx; j++)
			{
				double s = 0;
				for (long k = 1; k <= my ny; k++) { s += minv[i][k] * my z[k][j]; }
				his z[i][j] = s;
			}
		}
		return him.transfer();
	} catch (MelderError) { rethrowmzero (me, ": not unmixed."); }
}

MixingMatrix Sound_to_MixingMatrix (Sound me, double startTime, double endTime, long ncovars, double lagTime, long maxNumberOfIterations, double tol, int method)
{
	try {
		autoCrossCorrelationTables ccs = Sound_to_CrossCorrelationTables (me, startTime, endTime, lagTime, ncovars); 
		autoMixingMatrix thee = MixingMatrix_create (my ny, my ny);
		MixingMatrix_and_CrossCorrelationTables_improveUnmixing (thee.peek(), ccs.peek(), maxNumberOfIterations, tol, method);
		return thee.transfer();
	} catch (MelderError) { rethrowmzero (me, ": no MixingMatrix created."); }
}

MixingMatrix TableOfReal_to_MixingMatrix (TableOfReal me)
{
	try {
		if (my numberOfColumns != my numberOfRows) Melder_throw ("Number of rows and columns must be equal.");
		autoMixingMatrix thee = (MixingMatrix) Data_copy (me);
		Thing_overrideClass (thee.peek(), classMixingMatrix);
		return thee.transfer();
	} catch (MelderError) { rethrowmzero (me, ": not converted to MixingMatrix."); }
}

/************* CrossCorrelationTable *****************************/

static void classCrossCorrelationTable_info (I)
{
	iam (CrossCorrelationTable);
	classSSCP -> info (me);
	double dm = CrossCorrelationTable_getDiagonalitymeasure (me);
	MelderInfo_writeLine2 (L"Diagonality measure: ", Melder_double (dm));
}

class_methods (CrossCorrelationTable, SSCP)
{
	class_method_local (CrossCorrelationTable, info)
	class_methods_end
}

CrossCorrelationTable CrossCorrelationTable_create (long dimension)
{
	try {
		autoCrossCorrelationTable me = Thing_new (CrossCorrelationTable);
		SSCP_init (me.peek(), dimension, dimension);
		return me.transfer();
	} catch (MelderError) { rethrowmzero ("CrossCorrelationTable not created."); }
}

CrossCorrelationTable CrossCorrelationTable_createSimple (wchar_t *covars, wchar_t *centroid, long numberOfSamples)
{
	try {
		long dimension = Melder_countTokens (centroid);
		long ncovars = Melder_countTokens (covars);
		long ncovars_wanted = dimension * (dimension + 1) / 2;
		if (ncovars != ncovars_wanted) Melder_throw ("The number of matrix elements and the number of "
		"centroid elements are not in concordance. There should be \"d(d+1)/2\" matrix values and \"d\" centroid values.");

		autoCrossCorrelationTable me = CrossCorrelationTable_create (dimension);

		// Construct the full matrix from the upper-diagonal elements

		long inum = 1, irow = 1;
		for (wchar_t *token = Melder_firstToken (covars); token != NULL && inum <= ncovars_wanted; token = Melder_nextToken (), inum++)
		{
			double number;
			long nmissing = (irow - 1) * irow / 2;
			long inumc = inum + nmissing;
			irow = (inumc - 1) / dimension + 1;
			long icol = ((inumc - 1) % dimension) + 1;
			if (! Interpreter_numericExpression (NULL, token, &number)) Melder_throw 
				("Item ", inum, L" \"", token, L"\"is not a number.");
			my data[irow][icol] = my data[icol][irow] = number;
			if (icol == dimension) irow++;
		}

		inum = 1;
		for (wchar_t *token = Melder_firstToken (centroid); token != NULL && inum <= dimension; token = Melder_nextToken (), inum++)
		{
			double number;
			if (! Interpreter_numericExpression (NULL, token, &number)) Melder_throw 
				(L"Item ", inum, L" \"", token, L"\"is not a number.");
			my centroid[inum] = number;
		}
		my numberOfObservations = numberOfSamples;
		return me.transfer();
	} catch (MelderError) { rethrowmzero ("CrossCorrelationTable not created."); }
}

double CrossCorrelationTable_getDiagonalitymeasure (CrossCorrelationTable me)
{
	return NUMdmatrix_diagonalityMeasure (my data, my numberOfColumns);
}

/************* CrossCorrelationTables *****************************/

static void classCrossCorrelationTables_info (I)
{
	iam (CrossCorrelationTables);
	classOrdered -> info (me);
	CrossCorrelationTable thee = (CrossCorrelationTable) my item[1];
	MelderInfo_writeLine2 (L"  Number of rows and columns: ", Melder_integer (thy numberOfRows));
	for (long i = 1; i <= my size; i++)
	{
		double dm = CrossCorrelationTable_getDiagonalitymeasure ((CrossCorrelationTable) my item[i]);
		MelderInfo_writeLine4 (L"Diagonality measure for item ", Melder_integer (i), L": ", Melder_double (dm));
	}
}

class_methods (CrossCorrelationTables, Ordered)
{
	class_method_local (CrossCorrelationTables, info)
	class_methods_end
}

CrossCorrelationTables CrossCorrelationTables_create (void)
{
	try {
		autoCrossCorrelationTables me = Thing_new (CrossCorrelationTables);
		Ordered_init (me.peek(), classCrossCorrelationTable, 30);
		return me.transfer();
	} catch (MelderError) { rethrowmzero ("CrossCorrelationTables not created."); }
}

double CrossCorrelationTables_getDiagonalityMeasure (CrossCorrelationTables me, double *w, long start, long end)
{
	if (start >= end) { start = 1; end = my size; }
	if (start < 1) start = 1;
	if (end > my size) end = my size;
	long ntables = end - start + 1;
	long dimension = ((Covariance)(my item[1]))-> numberOfColumns;
	double dmsq = 0;
	for (long k = start; k <= end; k++)
	{
		CrossCorrelationTable thee = (CrossCorrelationTable) my item[k];
		double dmksq = NUMdmatrix_diagonalityMeasure (thy data, dimension);
		dmsq += w == NULL ? dmksq / ntables : dmksq * w[k];
	}
	return dmsq;
}

/************************** CrossCorrelationTables & Diagonalizer *******************************/

double CrossCorrelationTables_and_Diagonalizer_getDiagonalityMeasure (CrossCorrelationTables me, Diagonalizer thee, double *w, long start, long end)
{
	try {
		autoCrossCorrelationTables him = CrossCorrelationTables_and_Diagonalizer_diagonalize (me, thee);
		double dm = CrossCorrelationTables_getDiagonalityMeasure (him.peek(), w, start, end);
		return dm;
	} catch (MelderError) { rethrowzero; }
}

CrossCorrelationTable CrossCorrelationTable_and_Diagonalizer_diagonalize (CrossCorrelationTable me, Diagonalizer thee)
{
	try {
		if (my numberOfRows != thy numberOfRows) Melder_throw ("The CrossCorrelationTable and the Diagonalizer matrix dimensions must be equal.");
		autoCrossCorrelationTable him = CrossCorrelationTable_create (my numberOfColumns);
		NUMdmatrices_multiply_VCVp (his data, thy data, my numberOfColumns, my numberOfColumns, my data, 1);
		return him.transfer();
	} catch (MelderError) { rethrowmzero ("CrossCorrelationTable not diagonalized."); }
}

CrossCorrelationTables CrossCorrelationTables_and_Diagonalizer_diagonalize (CrossCorrelationTables me, Diagonalizer thee)
{
	try {
		autoCrossCorrelationTables him = CrossCorrelationTables_create ();
		for (long i = 1; i <= my size; i++)
		{
			CrossCorrelationTable item = (CrossCorrelationTable) my item[i];
			autoCrossCorrelationTable ct = CrossCorrelationTable_and_Diagonalizer_diagonalize (item, thee);
			Collection_addItem (him.peek(), ct.transfer());
		}
		return him.transfer();
	} catch (MelderError) { rethrowmzero ("CrossCorrelationTables not diagonalized."); }
}

Diagonalizer CrossCorrelationTables_to_Diagonalizer (CrossCorrelationTables me, long maxNumberOfIterations, double tol, int method)
{
	try {
		CrossCorrelationTable him = (CrossCorrelationTable) my item[1];
		autoDiagonalizer thee = Diagonalizer_create (his numberOfColumns);
		Diagonalizer_and_CrossCorrelationTables_improveDiagonality (thee.peek(), me, maxNumberOfIterations, tol, method);
		return thee.transfer();
	} catch (MelderError) { rethrowmzero ("Diagonalizer not created from CrossCorrelationTables."); };
}

void Diagonalizer_and_CrossCorrelationTables_improveDiagonality (Diagonalizer me, CrossCorrelationTables thee, long maxNumberOfIterations, double tol, int method)
{
	try {
		if (method == 1)
		{
			autoNUMvector<double> cweights (1, thy size);
			for (long i = 1; i <= thy size; i++) { cweights[i] = 1.0 / thy size; }
			Diagonalizer_and_CrossCorrelationTable_qdiag (me, thee, cweights.peek(), maxNumberOfIterations, tol);
		}
		else
		{
			Diagonalizer_and_CrossCorrelationTables_ffdiag (me, thee, maxNumberOfIterations, tol);
		}
	} catch (MelderError) { rethrow; }
}

Sound Sound_and_PCA_to_Sound_pc (Sound me, PCA thee, long numberOfComponents, int whiten)
{
	try {
		if (my ny != thy dimension) Melder_throw ("The number of channels of the sound and the dimension of the PCA must be equal.");
		if (numberOfComponents > my ny) numberOfComponents = my ny;

		autoSound him = Sound_create (numberOfComponents, my xmin, my xmax, my nx, my dx, my x1);
		for (long i = 1; i <= his ny; i++)
		{
			double scalef = whiten ? 1 / sqrt (thy eigenvalues[i]) : 1;
			for (long j = 1; j <= his nx; j++)
			{
				double s = 0;
				for (long k = 1; k <= my ny; k++) { s += thy eigenvectors[i][k] * my z[k][j]; }
				his z[i][j] = s * scalef;
			}
		}
		return him.transfer();
	} catch (MelderError) { rethrowmzero ("Sound not created."); }
}

/*
 * Generate n different cct's that have a common diagonalizer.
 */
CrossCorrelationTables CrossCorrelationTables_createTestSet (long dimension, long n, int firstPositiveDefinite, double sigma)
{
	try {
		// Start with a square matrix with random gaussian elements and make its singular value decomposition UDV'
		// The V matrix will be the common diagonalizer matrix that we use.

		autoNUMmatrix<double> d (1, dimension, 1, dimension);
		for (long i = 1; i <= dimension; i++) // Generate the rotation matrix
		{
			for (long j = 1; j <= dimension; j++) { d[i][j] = NUMrandomGauss (0, 1); }
		}
		autoNUMmatrix<double> v (1, dimension, 1, dimension);
		autoSVD svd = SVD_create_d (d.peek(), dimension, dimension);
		autoCrossCorrelationTables me = CrossCorrelationTables_create ();

		for (long i = 1; i <= dimension; i++)
		{
			for (long j = 1; j <= dimension; j++) { d[i][j] = 0; }
		}

		// Start with a diagonal matrix D and calculate V'DV

		for (long k = 1; k <= n; k++)
		{
			autoCrossCorrelationTable ct = CrossCorrelationTable_create (dimension);
			Collection_addItem (me.peek(), ct.transfer());
			double low = k == 1 && firstPositiveDefinite ? 0.1 : -1;
			for (long i = 1; i <= dimension; i++)
			{
				d[i][i] = NUMrandomUniform (low, 1);
			}
			for (long i = 1; i <= dimension; i++)
			{
				for (long j = 1; j <= dimension; j++)
				{
					v[i][j] = NUMrandomGauss (svd -> v[i][j], sigma);
				}
			}
			// we need V'DV, however our V has eigenvectors row-wise -> VDV'
			NUMdmatrices_multiply_VCVp (ct -> data, v.peek(), dimension, dimension, d.peek(), 1);
		}
		return me.transfer();
	} catch (MelderError) { rethrowmzero ("CrossCorrelationTables test set not created."); }
}

static int Sound_and_MixingMatrix_improveUnmixing_fica (Sound me, MixingMatrix thee, long maxNumberOfIterations, double tol, int method)
{
	try {
	long iter = 0;
		if (my ny != thy numberOfColumns) Melder_throw ("Dimensions do not agree.");
		autoNUMmatrix<double> x (NUMdmatrix_copy (my z, 1, my ny, 1, my nx), 1, 1);
		do
		{
			iter++;
		} while (/*fabs((dm_old - dm_new) / dm_new) > tol &&*/ iter < maxNumberOfIterations);
		return 1;
	} catch (MelderError) { rethrowzero; }
}

/* End of file ICA.cpp 987*/
