SVD SVD_create_d (double **m, long numberOfRows, long numberOfColumns) {
try {
autoSVD me = SVD_create (numberOfRows, numberOfColumns);
SVD_svd_d (me.peek(), m);
return me.transfer();
} catch (MelderError) {
Melder_throw ("SVD not created from vector.");
}
}
static void NUMmaximizeCongruence (double **b, double **a, long nr, long nc, double **t, long maximumNumberOfIterations, double tolerance) {
long numberOfIterations = 0;
Melder_assert (nr > 0 && nc > 0);
Melder_assert (t);
if (nc == 1) {
t[1][1] = 1; return;
}
autoNUMmatrix<double> c (1, nc, 1, nc);
autoNUMmatrix<double> w (1, nc, 1, nc);
autoNUMmatrix<double> u (1, nc, 1, nc);
autoNUMvector<double> evec (1, nc);
autoSVD svd = SVD_create (nc, nc);
// Steps 1 & 2: C = A'A and W = A'B
double checkc = 0, checkw = 0;
for (long i = 1; i <= nc; i++) {
for (long j = 1; j <= nc; j++) {
for (long k = 1; k <= nr; k++) {
c[i][j] += a[k][i] * a[k][j];
w[i][j] += a[k][i] * b[k][j];
}
checkc += c[i][j]; checkw += w[i][j];
}
}
if (checkc == 0.0 || checkw == 0.0) {
Melder_throw (U"NUMmaximizeCongruence: we cannot rotate a zero matrix.");
}
// Scale W by (diag(B'B))^-1/2
for (long j = 1; j <= nc; j++) {
double scale = 0.0;
for (long k = 1; k <= nr; k++) {
scale += b[k][j] * b[k][j];
}
if (scale > 0.0) {
scale = 1.0 / sqrt (scale);
}
for (long i = 1; i <= nc; i++) {
w[i][j] *= scale;
}
}
// Step 3: largest eigenvalue of C
evec[1] = 1.0;
double rho, f, f_old;
NUMdominantEigenvector (c.peek(), nc, evec.peek(), &rho, 1.0e-6);
do_steps45 (w.peek(), t, c.peek(), nc, &f);
do {
for (long j = 1; j <= nc; j++) {
// Step 7.a
double p = 0.0;
for (long k = 1; k <= nc; k++) {
for (long i = 1; i <= nc; i++) {
p += t[k][j] * c[k][i] * t[i][j];
}
}
// Step 7.b
double q = 0.0;
for (long k = 1; k <= nc; k++) {
q += w[k][j] * t[k][j];
}
// Step 7.c
if (q == 0.0) {
for (long i = 1; i <= nc; i++) {
u[i][j] = 0.0;
}
} else {
double ww = 0.0;
for (long k = 1; k <= nc; k++) {
ww += w[k][j] * w[k][j];
}
for (long i = 1; i <= nc; i++) {
double ct = 0.0;
for (long k = 1; k <= nc; k++) {
ct += c[i][k] * t[k][j];
}
u[i][j] = (q * (ct - rho * t[i][j]) / p - 2.0 * ww * t[i][j] / q - w[i][j]) / sqrt (p);
}
}
}
// Step 8
SVD_svd_d (svd.get(), u.peek());
// Step 9
for (long i = 1; i <= nc; i++) {
for (long j = 1; j <= nc; j++) {
t[i][j] = 0.0;
for (long k = 1; k <= nc; k++) {
t[i][j] -= svd -> u[i][k] * svd -> v[j][k];
}
}
}
numberOfIterations++;
f_old = f;
// Steps 10 & 11 equal steps 4 & 5
do_steps45 (w.peek(), t, c.peek(), nc, &f);
} while (fabs (f_old - f) / f_old > tolerance && numberOfIterations < maximumNumberOfIterations);
}
