/*
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;
}
autoMelderProgress progress (U"Simultaneous diagonalization of many CrossCorrelationTables...");
double dm_new = CrossCorrelationTables_getDiagonalityMeasure (ccts.peek(), nullptr, 0, 0);
try {
double dm_old, theta = 1, dm_start = dm_new;
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
NUMmatrix_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];
NUMmatrix_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++;
Melder_progress ((double) iter / (double) maxNumberOfIterations, U"Iteration: ", iter, U", measure: ", dm_new, U"\n fractional measure: ", dm_new / dm_start);
} while (fabs ((dm_old - dm_new) / dm_new) > delta && iter < maxNumberOfIterations);
} catch (MelderError) {
Melder_clearError ();
}
} catch (MelderError) {
Melder_throw (me, U" & ", thee, U": no joint diagonalization (ffdiag).");
}
}
double CrossCorrelationTables_and_Diagonalizer_getDiagonalityMeasure (CrossCorrelationTables me, Diagonalizer thee, double *w, long start, long end) {
autoCrossCorrelationTables him = CrossCorrelationTables_and_Diagonalizer_diagonalize (me, thee);
double dm = CrossCorrelationTables_getDiagonalityMeasure (him.peek(), w, start, end);
return dm;
}
Diagonalizer d = FIRST (Diagonalizer); double dm = CrossCorrelationTables_and_Diagonalizer_getDiagonalityMeasure (ccts, d, 0, GET_INTEGER (L"First table"), GET_INTEGER (L"Last table")); Melder_information (Melder_double (dm), L" (= average sum of squared off-diagonal elements)"); END DIRECT (CrossCorrelationTable_and_Diagonalizer_diagonalize) CrossCorrelationTable cct = FIRST (CrossCorrelationTable); Diagonalizer d = FIRST (Diagonalizer); praat_new (CrossCorrelationTable_and_Diagonalizer_diagonalize (cct, d), cct->name, L"_", d->name); END DIRECT (CrossCorrelationTables_and_Diagonalizer_diagonalize) CrossCorrelationTables ccts = FIRST (CrossCorrelationTables); Diagonalizer d = FIRST (Diagonalizer); praat_new (CrossCorrelationTables_and_Diagonalizer_diagonalize (ccts, d), ccts->name, L"_", d->name); END FORM (CrossCorrelationTables_and_MixingMatrix_improveUnmixing, L"", 0) LABEL (L"", L"Iteration parameters") NATURAL (L"Maximum number of iterations", L"100") POSITIVE (L"Tolerance", L"0.001") OPTIONMENU (L"Diagonalization method", 2) OPTION (L"qdiag") OPTION (L"ffdiag") OK DO MixingMatrix mm = FIRST (MixingMatrix); CrossCorrelationTables ccts = FIRST (CrossCorrelationTables); MixingMatrix_and_CrossCorrelationTables_improveUnmixing (mm, ccts, GET_INTEGER (L"Maximum number of iterations"), GET_REAL (L"Tolerance"), GET_INTEGER (L"Diagonalization method"));
