static autoPCA NUMdmatrix_to_PCA (double **m, long numberOfRows, long numberOfColumns, bool byColumns) {
try {
if (! NUMdmatrix_hasFiniteElements(m, 1, numberOfRows, 1, numberOfColumns)) {
Melder_throw (U"At least one of the matrix elements is not finite or undefined.");
}
if (NUMfrobeniusnorm (numberOfRows, numberOfColumns, m) == 0.0) {
Melder_throw (U"All values in your table are zero.");
}
autoNUMmatrix<double> mcopy;
long numberOfRows2, numberOfColumns2;
if (byColumns) {
if (numberOfColumns < numberOfRows) {
Melder_warning (U"The number of columns in your table is less than the number of rows. ");
}
numberOfRows2 = numberOfColumns, numberOfColumns2 = numberOfRows;
mcopy.reset (1, numberOfRows2, 1, numberOfColumns2);
for (long i = 1; i <= numberOfRows2; i ++) { // transpose
for (long j = 1; j <= numberOfColumns2; j++) {
mcopy [i] [j] = m [j] [i];
}
}
} else {
if (numberOfRows < numberOfColumns) {
Melder_warning (U"The number of rows in your table is less than the number of columns. ");
}
numberOfRows2 = numberOfRows, numberOfColumns2 = numberOfColumns;
mcopy.reset (1, numberOfRows2, 1, numberOfColumns2);
NUMmatrix_copyElements<double>(m, mcopy.peek(), 1, numberOfRows2, 1, numberOfColumns2);
}
autoPCA thee = Thing_new (PCA);
thy centroid = NUMvector<double> (1, numberOfColumns2);
NUMcentreColumns (mcopy.peek(), 1, numberOfRows2, 1, numberOfColumns2, thy centroid);
Eigen_initFromSquareRoot (thee.get(), mcopy.peek(), numberOfRows2, numberOfColumns2);
thy labels = NUMvector<char32 *> (1, numberOfColumns2);
PCA_setNumberOfObservations (thee.get(), numberOfRows2);
/*
The covariance matrix C = A'A / (N-1). However, we have calculated
the eigenstructure for A'A. This has no consequences for the
eigenvectors, but the eigenvalues have to be divided by (N-1).
*/
for (long i = 1; i <= thy numberOfEigenvalues; i++) {
thy eigenvalues [i] /= (numberOfRows2 - 1);
}
return thee;
} catch (MelderError) {
Melder_throw (U"No PCA created from ", byColumns ? U"columns." : U"rows.");
}
}
autoDiscriminant TableOfReal_to_Discriminant (TableOfReal me) {
try {
autoDiscriminant thee = Thing_new (Discriminant);
long dimension = my numberOfColumns;
if (! NUMdmatrix_hasFiniteElements(my data, 1, my numberOfRows, 1, my numberOfColumns)) {
Melder_throw (U"At least one of the table's elements is not finite or undefined.");
}
if (! TableOfReal_hasRowLabels (me)) {
Melder_throw (U"At least one of the rows has no label.");
}
autoTableOfReal mew = TableOfReal_sortOnlyByRowLabels (me);
if (! TableOfReal_hasColumnLabels (mew.get())) {
TableOfReal_setSequentialColumnLabels (mew.get(), 0, 0, U"c", 1, 1);
}
thy groups = TableOfReal_to_SSCPList_byLabel (mew.get());
thy total = TableOfReal_to_SSCP (mew.get(), 0, 0, 0, 0);
if ((thy numberOfGroups = thy groups -> size) < 2) {
Melder_throw (U"Number of groups must be greater than one.");
}
TableOfReal_centreColumns_byRowLabel (mew.get());
// Overall centroid and apriori probabilities and costs.
autoNUMvector<double> centroid (1, dimension);
autoNUMmatrix<double> between (1, thy numberOfGroups, 1, dimension);
thy aprioriProbabilities = NUMvector<double> (1, thy numberOfGroups);
thy costs = NUMmatrix<double> (1, thy numberOfGroups, 1, thy numberOfGroups);
double sum = 0, scale;
for (long k = 1; k <= thy numberOfGroups; k ++) {
SSCP m = thy groups->at [k];
sum += scale = SSCP_getNumberOfObservations (m);
for (long j = 1; j <= dimension; j ++) {
centroid [j] += scale * m -> centroid [j];
}
}
for (long j = 1; j <= dimension; j ++) {
centroid [j] /= sum;
}
for (long k = 1; k <= thy numberOfGroups; k ++) {
SSCP m = thy groups->at [k];
scale = SSCP_getNumberOfObservations (m);
thy aprioriProbabilities[k] = scale / my numberOfRows;
for (long j = 1; j <= dimension; j ++) {
between [k] [j] = sqrt (scale) * (m -> centroid [j] - centroid [j]);
}
}
// We need to solve B'B.x = lambda W'W.x, where B'B and W'W are the between and within covariance matrices.
// We do not calculate these covariance matrices directly from the data but instead use the GSVD to solve for
// the eigenvalues and eigenvectors of the equation.
thy eigen = Thing_new (Eigen);
Eigen_initFromSquareRootPair (thy eigen.get(), between.peek(), thy numberOfGroups, dimension, mew -> data, my numberOfRows);
// Default priors and costs
for (long igroup = 1; igroup <= thy numberOfGroups; igroup ++) {
for (long jgroup = igroup + 1; jgroup <= thy numberOfGroups; jgroup ++) {
thy costs [igroup] [jgroup] = thy costs [jgroup] [igroup] = 1.0;
}
}
return thee;
} catch (MelderError) {
Melder_throw (me, U": Discriminant not created.");
}
}
autoCCA TableOfReal_to_CCA (TableOfReal me, long ny) {
try {
long n = my numberOfRows, nx = my numberOfColumns - ny;
if (ny < 1 || ny > my numberOfColumns - 1) {
Melder_throw (U"Dimension of first part not correct.");
}
if (ny > nx) {
Melder_throw (U"The dimension of the dependent part (", ny, U") must be less than or equal to "
"the dimension of the independent part (", nx, U").");
}
if (n < ny) {
Melder_throw (U"The number of observations must be larger then ", ny, U".");
}
if (! NUMdmatrix_hasFiniteElements (my data, 1, my numberOfRows, 1, my numberOfColumns)) {
Melder_throw (U"At least one of the table's elements is not finite or undefined.");;
}
// Use svd as (temporary) storage, and copy data
autoSVD svdy = SVD_create (n, ny);
autoSVD svdx = SVD_create (n, nx);
for (long i = 1; i <= n; i++) {
for (long j = 1; j <= ny; j++) {
svdy -> u[i][j] = my data[i][j];
}
for (long j = 1; j <= nx; j++) {
svdx -> u[i][j] = my data[i][ny + j];
}
}
double **uy = svdy -> u;
double **vy = svdy -> v;
double **ux = svdx -> u;
double **vx = svdx -> v;
double fnormy = NUMfrobeniusnorm (n, ny, uy);
double fnormx = NUMfrobeniusnorm (n, nx, ux);
if (fnormy == 0.0 || fnormx == 0.0) {
Melder_throw (U"One of the parts of the table contains only zeros.");
}
// Centre the data and svd it.
NUMcentreColumns (uy, 1, n, 1, ny, nullptr);
NUMcentreColumns (ux, 1, n, 1, nx, nullptr);
SVD_compute (svdy.get());
SVD_compute (svdx.get());
long numberOfZeroedy = SVD_zeroSmallSingularValues (svdy.get(), 0.0);
long numberOfZeroedx = SVD_zeroSmallSingularValues (svdx.get(), 0.0);
// Form the matrix C = ux' uy (use svd-object storage)
autoSVD svdc = SVD_create (nx, ny);
double **uc = svdc -> u;
double **vc = svdc -> v;
for (long i = 1; i <= nx; i ++) {
for (long j = 1; j <= ny; j ++) {
double t = 0.0;
for (long q = 1; q <= n; q ++) {
t += ux [q] [i] * uy [q] [j];
}
uc [i] [j] = t;
}
}
SVD_compute (svdc.get());
long numberOfZeroedc = SVD_zeroSmallSingularValues (svdc.get(), 0.0);
long numberOfCoefficients = ny - numberOfZeroedc;
autoCCA thee = CCA_create (numberOfCoefficients, ny, nx);
thy yLabels = strings_to_Strings (my columnLabels, 1, ny);
thy xLabels = strings_to_Strings (my columnLabels, ny + 1, my numberOfColumns);
double **evecy = thy y -> eigenvectors;
double **evecx = thy x -> eigenvectors;
thy numberOfObservations = n;
/*
Y = Vy * inv(Dy) * Vc
X = Vx * inv(Dx) * Uc
For the eigenvectors we want a row representation:
colums(Y) = rows(Y') = rows(Vc' * inv(Dy) * Vy')
colums(X) = rows(X') = rows(Uc' * inv(Dx) * Vx')
rows(Y') = evecy[i][j] = Vc[k][i] * Vy[j][k] / Dy[k]
rows(X') = evecx[i][j] = Uc[k][i] * Vx[j][k] / Dx[k]
*/
for (long i = 1; i <= numberOfCoefficients; i ++) {
double ccc = svdc -> d [i];
thy y -> eigenvalues [i] = thy x -> eigenvalues [i] = ccc * ccc;
for (long j = 1; j <= ny; j ++) {
double t = 0.0;
for (long q = 1; q <= ny - numberOfZeroedy; q ++) {
t += vc [q] [i] * vy [j] [q] / svdy -> d [q];
}
evecy [i] [j] = t;
}
for (long j = 1; j <= nx; j ++) {
double t = 0.0;
for (long q = 1; q <= nx - numberOfZeroedx; q ++) {
t += uc [q] [i] * vx [j] [q] / svdx -> d [q];
}
evecx [i] [j] = t;
}
}
// Normalize eigenvectors.
NUMnormalizeRows (thy y -> eigenvectors, numberOfCoefficients, ny, 1);
NUMnormalizeRows (thy x -> eigenvectors, numberOfCoefficients, nx, 1);
Melder_assert (thy x -> dimension == thy xLabels -> numberOfStrings &&
thy y -> dimension == thy yLabels -> numberOfStrings);
return thee;
} catch (MelderError) {
Melder_throw (me, U": CCA not created.");
}
}
