/* Eigen.c
 *
 * Copyright (C) 1993-2005 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 20010719
 djmw 20020402 GPL header.
 djmw 20030701 Modified sorting in Eigen_initFromSquareRootPair.
 djmw 20030703 Added Eigens_alignEigenvectors.
 djmw 20030708 Corrected syntax error in Eigens_alignEigenvectors.
 djmw 20030812 Corrected memory bug in Eigen_initFromSymmetricMatrix.
 djmw 20030825 Removed praat_USE_LAPACK external variable.
 djmw 20031101 Documentation
 djmw 20031107 Moved NUMdmatrix_transpose to NUM2.c
 djmw 20031210 Added rowLabels to Eigen_drawEigenvector and Eigen_and_Strings_drawEigenvector
 djmw 20030322 Extra test in Eigen_initFromSquareRootPair. 
 djmw 20040329 Added fractionOfTotal  and cumulative parameters in Eigen_drawEigenvalues_scree.
 djmw 20040622 Less horizontal labels in Eigen_drawEigenvector.
 djmw 20050706 Shortened horizontal offsets in Eigen_drawEigenvalues from 1 to 0.5
 djmw 20051204 Eigen_initFromSquareRoot adapted for nrows < ncols
*/

#include "Eigen.h"
#include "NUMmachar.h"
#include "NUMlapack.h"
#include "NUMclapack.h"
#include "NUM2.h"
#include "SVD.h"

#include "oo_DESTROY.h"
#include "Eigen_def.h"
#include "oo_COPY.h"
#include "Eigen_def.h"
#include "oo_EQUAL.h"
#include "Eigen_def.h"
#include "oo_WRITE_ASCII.h"
#include "Eigen_def.h"
#include "oo_READ_ASCII.h"
#include "Eigen_def.h"
#include "oo_WRITE_BINARY.h"
#include "Eigen_def.h"
#include "oo_READ_BINARY.h"
#include "Eigen_def.h"
#include "oo_DESCRIPTION.h"
#include "Eigen_def.h"

#define MAX(m,n) ((m) > (n) ? (m) : (n))
#define MIN(m,n) ((m) < (n) ? (m) : (n))
#define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;}

extern machar_Table NUMfpp;

static void Graphics_ticks (Graphics g, double min, double max, int hasNumber,
	int hasTick, int hasDottedLine, int integers)
{
	double range = max - min, scale = 1, tick = min, dtick = 1;

	if (range == 0)
	{
		return;
	}
	else if (range > 1)
	{
		while (range / scale > 10) scale *= 10;
		range /= scale;
	}
	else
	{
		while (range / scale < 10) scale /= 10;
		range *= scale;
	}

	if (range < 3) dtick = 0.5; 
	dtick *= scale;	
	tick = dtick * floor (min / dtick);
	if (tick < min) tick += dtick;
	while (tick <= max)
	{
		double num = integers ? floor (tick + 0.5) : tick;
		Graphics_markBottom (g, num, hasNumber, hasTick, hasDottedLine, NULL);
		tick += dtick;
	}
}

class_methods (Eigen, Data)
	class_method_local (Eigen, destroy)
	class_method_local (Eigen, description)
	class_method_local (Eigen, copy)
	class_method_local (Eigen, equal)
	class_method_local (Eigen, writeAscii)
	class_method_local (Eigen, readAscii)
	class_method_local (Eigen, writeBinary)
	class_method_local (Eigen, readBinary)
class_methods_end

int Eigen_init (I, long numberOfEigenvalues, long dimension)
{
	iam (Eigen);
	my numberOfEigenvalues = numberOfEigenvalues;
	my dimension = dimension;
	if (! (my eigenvalues = NUMdvector (1, numberOfEigenvalues)) ||
		! (my eigenvectors = NUMdmatrix (1, numberOfEigenvalues, 
			1, dimension))) return 0;
	return 1;
}

/*
	Solve: (A'A - lambda)x = 0 for eigenvalues lambda and eigenvectors x.
	svd(A) = UDV' => A'A = (UDV')'(UDV') = VD^2V'
	(VD^2V'-lambda)x = 0 => (D^2 - lambda)V'x = 0 => solution V'x = I => x = V
	Eigenvectors: the columns of the matrix V
	Eigenvalues: D_i^2
*/
int Eigen_initFromSquareRoot (I, double **a, long numberOfRows, long numberOfColumns)
{
	iam (Eigen);
	SVD svd;
	long i, j, k, numberOfZeroed, numberOfEigenvalues;
	long nsv = MIN (numberOfRows, numberOfColumns);
	
	my dimension = numberOfColumns;
	if (! (svd = SVD_create_d (a, numberOfRows, numberOfColumns))) return 0;
	
	/*
		Make sv's that are too small zero. These values occur automatically 
		when the rank of A'A < numberOfColumns. This could occur when for
		example numberOfRows <= numberOfColumns. 
		(n points in  an n-dimensional space define maximally an n-1 
		dimensional surface for which we maximally need an n-1 dimensional
		basis.)
	*/

	numberOfZeroed = SVD_zeroSmallSingularValues (svd, 0);

	numberOfEigenvalues = nsv - numberOfZeroed;

	if (! Eigen_init (me, numberOfEigenvalues, numberOfColumns)) goto end;

	for (k = 0, i = 1; i <= nsv; i++)
	{
		double t = svd -> d[i];
		if (t > 0)
		{
			my eigenvalues[++k] = t * t;
			for (j = 1; j <= numberOfColumns; j++)
			{
				my eigenvectors[k][j] = svd -> v[j][i];
			}
		}
	}

	Eigen_sort (me);
	
end:
	forget (svd);
	return ! Melder_hasError ();
}

int Eigen_initFromSquareRootPair (I, double **a, long numberOfRows,
	long numberOfColumns, double **b, long numberOfRows_b)
{
	iam (Eigen);
	char *proc = "Eigen_initFromSquareRootPair";
	double *u = NULL, *v = NULL, *work = NULL, **ac = NULL, **bc = NULL;
	double *alpha = NULL, *beta = NULL, **q = NULL, maxsv2 = -10;
	char jobu = 'N', jobv = 'N', jobq = 'Q';
	long i, ii, j = 0, k, ll, m = numberOfRows, n = numberOfColumns, p = numberOfRows_b;
	long lda = m, ldb = p, ldu = lda, ldv = ldb, ldq = n;
	long lwork = MAX (MAX (3*n, m), p) + n, *iwork = NULL, info;

/*	Melder_assert (numberOfRows >= numberOfColumns || numberOfRows_b >= numberOfColumns);*/

	my dimension = numberOfColumns;

	if (((alpha = NUMdvector (1, n)) == NULL) ||
		((beta = NUMdvector (1, n)) == NULL) ||
		((q = NUMdmatrix (1, n, 1, n)) == NULL) ||
		((work = NUMdvector (1, lwork)) == NULL) ||
		((iwork = NUMlvector (1, n)) == NULL) ||
		((ac = NUMdmatrix_transpose (a, numberOfRows,numberOfColumns)) == NULL) ||
		((bc = NUMdmatrix_transpose (b, numberOfRows_b,numberOfColumns)) == NULL)) goto end;

	(void) NUMlapack_dggsvd (&jobu, &jobv, &jobq, &m, &n, &p, &k, &ll,
		&ac[1][1], &lda, &bc[1][1], &ldb, &alpha[1], &beta[1], u, &ldu,
		v, &ldv, &q[1][1], &ldq, &work[1], &iwork[1], &info);

	if (info != 0)
	{
		(void) Melder_error ("%: Returned status code from NUMlapack_dggsvd: %d", proc, info);
		goto end;
	}

	/*
		Calculate the eigenvalues (alpha[i]/beta[i])^2 and store in alpha[i].
	*/

	maxsv2 = -1;
	for (i = k + 1; i <= k + ll; i++)
	{
		double t = alpha[i] / beta[i];
		alpha[i] = t * t;
		if (alpha[i] > maxsv2) maxsv2 = alpha[i]; 
	}

	/*
		Deselect the eigenvalues < eps * max_eigenvalue.
	*/

	for (n = 0, i = k + 1; i <= k + ll; i++)
	{
		if (alpha[i] < NUMfpp -> eps * maxsv2)
		{
			n++; alpha[i] = -1;
		}
	}

	if (ll - n < 1)
	{
		(void) Melder_error ("%s: No eigenvectors can be found. Matrix too singular.", proc);
		goto end;
	}
	
	if (! Eigen_init (me, ll - n, numberOfColumns)) goto end;

	for (i = k+1, ii = 0; i <= k+ll; i++)
	{
		if (alpha[i] == -1) continue;

		my eigenvalues[++ii] = alpha[i];
		for (j = 1; j <= numberOfColumns; j++)
		{
			my eigenvectors[ii][j] = q[i][j];
		}
	}

	Eigen_sort (me);

	NUMnormalizeRows_d (my eigenvectors, my numberOfEigenvalues, numberOfColumns, 1);

end:

	NUMdmatrix_free (bc, 1, 1);
	NUMdmatrix_free (ac, 1, 1);
	NUMlvector_free (iwork, 1);
	NUMdvector_free (work, 1);
	NUMdmatrix_free (q, 1, 1);
	NUMdvector_free (beta, 1);
	NUMdvector_free (alpha, 1);

	return ! Melder_hasError();
}

int Eigen_initFromSymmetricMatrix_f (I, float **a, long n)
{
	iam (Eigen);
	double **m;
	long i, j;
	int status;

	m = NUMdmatrix (1, n, 1, n);
	if (m == NULL) return 0;
	for (i = 1; i <= n; i++)
	{
		for (j = 1; j <= n; j++) m[i][j] = a[i][j];
	}
	status = Eigen_initFromSymmetricMatrix (me, m, n);
	NUMdmatrix_free (m, 1, 1);
	return status;
}

int Eigen_initFromSymmetricMatrix (I, double **a, long n)
{
	iam (Eigen);
	double *work, wt[1], temp;
	char jobz = 'V', uplo = 'U';
	long  i, j, lwork = -1, info;
	
	my dimension = my numberOfEigenvalues = n;
	
	if (my eigenvectors == NULL && ! Eigen_init (me, n, n)) return 0;
		
	NUMdmatrix_copyElements (a, my eigenvectors, 1, n, 1, n);
		
	/*
		Get size of work array
	*/
			
	(void) NUMlapack_dsyev (&jobz, &uplo, &n, &my eigenvectors[1][1], &n, 
			&my eigenvalues[1], wt, &lwork, &info);
	if (info != 0) return 0;
	
	lwork = wt[0];
	work = NUMdvector (1, lwork);
	if (work == NULL) return 0;
		
	(void) NUMlapack_dsyev (&jobz, &uplo, &n, &my eigenvectors[1][1], &n, 
		&my eigenvalues[1], &work[1], &lwork, &info);
	NUMdvector_free (work, 1);
	if (info != 0) return 0;
		
	/*
		We want descending order instead of ascending.
	*/
		
	for (i = 1; i <= n / 2; i++)
	{
		long ilast = n - i + 1;
			 
		SWAP(my eigenvalues[i], my eigenvalues[ilast])
		for (j = 1; j <= n; j++)
		{
			SWAP(my eigenvectors[i][j], my eigenvectors[ilast][j])
		}	
	}

	return 1;
}

Eigen Eigen_create (long numberOfEigenvalues, long dimension)
{
	Eigen me = new (Eigen);
	
	if (! me || ! Eigen_init (me, numberOfEigenvalues, dimension)) forget (me);
	return me;
}

long Eigen_getNumberOfEigenvectors (I)
{
	iam (Eigen);
	return my numberOfEigenvalues;
}

double Eigen_getEigenvectorElement (I, long ivec, long element)
{
	iam (Eigen);
	if (ivec > my numberOfEigenvalues || element < 1 || element > my dimension) return NUMundefined;
	return my eigenvectors[ivec][element];
}

long Eigen_getDimensionOfComponents (I)
{
	iam (Eigen);
	return my dimension;
}

double Eigen_getSumOfEigenvalues (I, long from, long to)
{
	iam (Eigen); 
	double sum = 0;
	long i; 
	
	if (from < 1) from = 1;
	if (to < 1) to = my numberOfEigenvalues;
	if (to > my numberOfEigenvalues || from > to) return NUMundefined;
	for (i = from; i <= to; i++)
	{
		sum += my eigenvalues[i];
	}
	return sum;
}

double Eigen_getCumulativeContributionOfComponents (I, long from, long to)
{
	iam (Eigen);
	long i;
	double partial = 0, sum = 0;
	
	if (to == 0) to = my numberOfEigenvalues;
	if (from > 0 && to <= my numberOfEigenvalues && from <= to)
	{
		for (i = 1; i <= my numberOfEigenvalues; i++)
		{
			sum += my eigenvalues[i];
			if (i >= from && i <= to) partial += my eigenvalues[i];
		}
	}
	return sum > 0 ? partial / sum : 0;

}

long Eigen_getDimensionOfFraction (I, double fraction)
{
	iam (Eigen); 
	long n;
	double p, sum = Eigen_getSumOfEigenvalues (me, 0, 0);
	
	if (sum == 0) return 1;
	
	n = 1; p = my eigenvalues[1];
	while (p / sum < fraction && n < my numberOfEigenvalues)
	{
		p += my eigenvalues[++n];
	}
	return n;
}

void Eigen_sort (I)
{
	iam (Eigen); 
	long i, j, k;
	double temp, *e = my eigenvalues, **v = my eigenvectors;
			
    for (i = 1; i < my numberOfEigenvalues; i++)
    {
        double emax = e[k=i];
        for (j = i + 1; j <= my numberOfEigenvalues; j++)
		{
			if (e[j] > emax) emax = e[k=j];
		}
		if (k != i)
        {
			/*
				Swap eigenvalues and eigenvectors
			*/
			
			SWAP (e[i], e[k]) 
            for (j = 1; j <= my dimension; j++)
			{
				SWAP (v[i][j], v[k][j])
			}
        }
    }
}

void Eigen_invertEigenvector (I, long ivec)
{
	iam (Eigen); long j;

	if (ivec < 1 || ivec > my numberOfEigenvalues) return;

	for (j = 1; j <= my dimension; j++)
	{
		my eigenvectors[ivec][j] = - my eigenvectors[ivec][j];
	}
}

void Eigen_drawEigenvalues (I, Graphics g, long first, long last, double ymin, double ymax,
	int fractionOfTotal, int cumulative, double size_mm, const char *mark, int garnish)
{
	iam (Eigen); 
	double xmin = first, xmax = last, scale = 1, sumOfEigenvalues = 0;
	long i;

	if (first < 1) first = 1;
	if (last < 1 || last > my numberOfEigenvalues) last = my numberOfEigenvalues;
	if (last <= first )
	{
		first = 1; last = my numberOfEigenvalues;
	}
	xmin = first - 0.5; xmax = last + 0.5;
	if (fractionOfTotal || cumulative)
	{
		sumOfEigenvalues = Eigen_getSumOfEigenvalues (me, 0, 0);
		if (sumOfEigenvalues <= 0)  sumOfEigenvalues = 1;
		scale = sumOfEigenvalues;
	}
	if (ymax <= ymin)
	{
		ymax = Eigen_getSumOfEigenvalues (me, (cumulative ? 1 : first), first) / scale;
		ymin = Eigen_getSumOfEigenvalues (me, (cumulative ? 1 : last), last) / scale;
		if (ymin > ymax)
		{
			double tmp = ymin; ymin = ymax; ymax = tmp;
		}
	}
	Graphics_setInner (g);
	Graphics_setWindow (g, xmin, xmax, ymin, ymax);
	for (i = first; i <= last; i++)
	{
		double accu = Eigen_getSumOfEigenvalues (me, (cumulative ? 1 : i), i);
		Graphics_mark (g, i, accu / scale, size_mm, mark);
	}
	Graphics_unsetInner (g);
	if (garnish)
	{
    	Graphics_drawInnerBox (g);
		Graphics_textLeft (g, 1, fractionOfTotal ? (cumulative ? "Cumulative fractional eigenvalue" : "Fractional eigenvalue") :
			(cumulative ? "Cumulative eigenvalue" : "Eigenvalue"));
		Graphics_ticks (g, first, last, 1, 1, 0, 1);
    	Graphics_marksLeft (g, 2, 1, 1, 0);
		Graphics_textBottom (g, 1, "Index");
	}
}

void Eigen_drawEigenvector (I, Graphics g, long ivec, long first, long last,
	double ymin, double ymax, int weigh, double size_mm, const char *mark,
	int connect, char **rowLabels, int garnish)
{
	iam (Eigen); 
	long i; 
	double xmin = first, xmax = last, *vec, w;
	
	if (ivec < 1 || ivec > my numberOfEigenvalues) return;
	
	if (last <= first )
	{
		first = 1; last = my dimension;
		xmin = 0.5; xmax = last + 0.5;
	}
	vec = my eigenvectors[ivec];
	w = weigh ? sqrt (my eigenvalues[ivec]) : 1;
	/*
		If ymax < ymin the eigenvector will automatically be drawn inverted.
	*/
	
	if (ymax == ymin)
	{
		NUMdvector_extrema (vec, first, last, &ymin, &ymax);
		ymax *= w; ymin *= w;
	}
	Graphics_setInner (g);
	Graphics_setWindow (g, xmin, xmax, ymin, ymax);
	
	for (i = first; i <= last; i++)
	{
		Graphics_mark (g, i, w * vec[i], size_mm, mark);
		if (connect && i > first) Graphics_line (g, i - 1, w * vec[i-1], i, w * vec[i]);
	}
	Graphics_unsetInner (g);
	if (garnish)
	{
		Graphics_markBottom (g, first, 0, 1, 0, rowLabels ? rowLabels[first] : Melder_integer (first));
		Graphics_markBottom (g, last, 0, 1, 0, rowLabels ? rowLabels[last] : Melder_integer (last));
    	Graphics_drawInnerBox (g);
    	if (ymin * ymax < 0) Graphics_markLeft (g, 0.0, 1, 1, 1, NULL);
    	Graphics_marksLeft (g, 2, 1, 1, 0);
		if (rowLabels == NULL) Graphics_textBottom (g, 1, "Element number");
	}
}

int Eigens_alignEigenvectors (Ordered me)
{
	Eigen e1, e2;
	long i, j, k, nev1, dimension;
	double **evec1, **evec2;
	
	if (my size < 2) return 1;
	
	e1 = my item[1];
	evec1 = e1 -> eigenvectors;
	nev1 = e1 -> numberOfEigenvalues;
	dimension = e1 -> dimension;
	
	for (i = 2; i <= my size; i++)
	{
		e2 = my item[i];
		if (e2 -> dimension != dimension)
		{
			 return Melder_error ("Eigens_alignEigenvectors: The dimension of the "
			 	"eigenvectors must be equal (Object %d offending).", i);
		}
	}
	
	/*
		Correlate eigenvectors. 
		If r < 0 then mirror the eigenvector.
	*/
	
	for (i = 2; i <= my size; i++)
	{
		e2 = my item[i];
		evec2 = e2 -> eigenvectors;
		
		for (j = 1; j <= MIN (nev1, e2 -> numberOfEigenvalues); j++)
		{
			double ip = 0;
			for (k = 1; k <= dimension; k++)
			{
				ip += evec1[j][k] * evec2[j][k];
			}
			if (ip < 0)
			{
				for (k = 1; k <= dimension; k++) evec2[j][k] = - evec2[j][k];
			}
		}
	}
	return 1;
}

static int Eigens_getAnglesBetweenSubspaces (I, thou, long ivec_from, long ivec_to, double *angles_degrees)
{
	iam (Eigen); thouart (Eigen);
	SVD svd = NULL;
	long i, j, k, nvectors = ivec_to - ivec_from + 1;
	long nmin = my numberOfEigenvalues < thy numberOfEigenvalues ? my numberOfEigenvalues : thy numberOfEigenvalues;
	double **c = NULL;
	int status = 0;
		
	if (my dimension != thy dimension)
		return Melder_error ("The eigenvectors must have the same dimension.");
	if (ivec_from > ivec_to || ivec_from< 1 || ivec_to > nmin)
		return Melder_error ("Eigenvector range too large.");
	
	c = NUMdmatrix (1, nvectors, 1, nvectors);
	if (c == NULL) goto end;

	/* 
		Algorithm 12.4.3 Golub & van Loan
		Because we deal with eigenvectors we don't have to do the QR-decomposition,
			the columns in the Q's are the eigenvectors. 
		Compute C.
	*/
	
	for (i = 1; i <= nvectors; i++)
	{
		for (j = 1; j <= nvectors; j++)
		{
			for (k = 1; k <= my dimension; k++)
			{
				c[i][j] += my eigenvectors[ivec_from+i-1][k] * thy eigenvectors[ivec_from+j-1][k];
			}
		}
	}
	svd = SVD_create_d (c, nvectors, nvectors);
	if (svd == NULL) goto end;
	for (i = 1; i <= nvectors; i++)
	{
		angles_degrees[i] = acos (svd -> d[i]) * 180 / NUMpi;
	}
	forget (svd);
	status = 1;
		
end:
	
	NUMdmatrix_free (c, 1, 1);
	return status;	

}

double Eigens_getAngleBetweenEigenplanes_degrees (I, thou)
{
	iam (Eigen); thouart (Eigen);
	double angles_degrees[3];

	if (! Eigens_getAnglesBetweenSubspaces (me, thee, 1, 2, angles_degrees)) return NUMundefined;
	return angles_degrees[2];
}

/*double Eigens_getAngleBetweenEigenplanes_degrees (I, thou)
{
	iam (Eigen); thouart (Eigen);
	SVD svd = NULL;
	double **c = NULL, angle_degrees = NUMundefined;;
	long i, j, k, nvectors = my numberOfEigenvalues > 1 && thy numberOfEigenvalues > 1 ? 2 : 1;
	
	if (my dimension != thy dimension)
	{
		Melder_warning ("The eigenvectors must have the same dimension.");
		return NUMundefined;
	}
	
	c = NUMdmatrix (1, nvectors, 1, nvectors);
	if (c == NULL) goto end;

	for (i = 1; i <= nvectors; i++)
	{
		for (j = 1; j <= nvectors; j++)
		{
			for (k = 1; k <= my dimension; k++)
			{
				c[i][j] += my eigenvectors[i][k] * thy eigenvectors[j][k];
			}
		}
	}
	svd = SVD_create_d (c, nvectors, nvectors);
	if (svd == NULL) goto end;
	
	angle_degrees = acos (svd -> d[2]) * 180 / NUMpi;
	forget (svd);
		
end:
	
	NUMdmatrix_free (c, 1, 1);
	return angle_degrees;	
}*/

#undef MAX
#undef MIN
#undef SWAP

/* End of file Eigen.c */