// Optimization function for hypersphere and lower-diagonal algorithm
private static Matrix hypersphereOptimize(Matrix targetMatrix, Matrix currentRoot, bool lowerDiagonal)
{
int i, j, k, size = targetMatrix.rows();
Matrix result = new Matrix(currentRoot);
Vector variance = new Vector(size);
for (i = 0; i < size; i++)
{
variance[i] = Math.Sqrt(targetMatrix[i, i]);
}
if (lowerDiagonal)
{
Matrix approxMatrix = result * Matrix.transpose(result);
result = MatrixUtilities.CholeskyDecomposition(approxMatrix, true);
for (i = 0; i < size; i++)
{
for (j = 0; j < size; j++)
{
result[i, j] /= Math.Sqrt(approxMatrix[i, i]);
}
}
}
else
{
for (i = 0; i < size; i++)
{
for (j = 0; j < size; j++)
{
result[i, j] /= variance[i];
}
}
}
ConjugateGradient optimize = new ConjugateGradient();
EndCriteria endCriteria = new EndCriteria(100, 10, 1e-8, 1e-8, 1e-8);
HypersphereCostFunction costFunction = new HypersphereCostFunction(targetMatrix, variance, lowerDiagonal);
NoConstraint constraint = new NoConstraint();
// hypersphere vector optimization
if (lowerDiagonal)
{
Vector theta = new Vector(size * (size - 1) / 2);
const double eps = 1e-16;
for (i = 1; i < size; i++)
{
for (j = 0; j < i; j++)
{
theta[i * (i - 1) / 2 + j] = result[i, j];
if (theta[i * (i - 1) / 2 + j] > 1 - eps)
{
theta[i * (i - 1) / 2 + j] = 1 - eps;
}
if (theta[i * (i - 1) / 2 + j] < -1 + eps)
{
theta[i * (i - 1) / 2 + j] = -1 + eps;
}
for (k = 0; k < j; k++)
{
theta[i * (i - 1) / 2 + j] /= Math.Sin(theta[i * (i - 1) / 2 + k]);
if (theta[i * (i - 1) / 2 + j] > 1 - eps)
{
theta[i * (i - 1) / 2 + j] = 1 - eps;
}
if (theta[i * (i - 1) / 2 + j] < -1 + eps)
{
theta[i * (i - 1) / 2 + j] = -1 + eps;
}
}
theta[i * (i - 1) / 2 + j] = Math.Acos(theta[i * (i - 1) / 2 + j]);
if (j == i - 1)
{
if (result[i, i] < 0)
{
theta[i * (i - 1) / 2 + j] = -theta[i * (i - 1) / 2 + j];
}
}
}
}
Problem p = new Problem(costFunction, constraint, theta);
optimize.minimize(p, endCriteria);
theta = p.currentValue();
result.fill(1);
for (i = 0; i < size; i++)
{
for (k = 0; k < size; k++)
{
if (k > i)
{
result[i, k] = 0;
}
else
{
for (j = 0; j <= k; j++)
{
if (j == k && k != i)
{
result[i, k] *= Math.Cos(theta[i * (i - 1) / 2 + j]);
}
else if (j != i)
{
result[i, k] *= Math.Sin(theta[i * (i - 1) / 2 + j]);
}
}
}
}
}
}
else
{
Vector theta = new Vector(size * (size - 1));
const double eps = 1e-16;
for (i = 0; i < size; i++)
{
for (j = 0; j < size - 1; j++)
{
theta[j * size + i] = result[i, j];
if (theta[j * size + i] > 1 - eps)
{
theta[j * size + i] = 1 - eps;
}
if (theta[j * size + i] < -1 + eps)
{
theta[j * size + i] = -1 + eps;
}
for (k = 0; k < j; k++)
{
theta[j * size + i] /= Math.Sin(theta[k * size + i]);
if (theta[j * size + i] > 1 - eps)
{
theta[j * size + i] = 1 - eps;
}
if (theta[j * size + i] < -1 + eps)
{
theta[j * size + i] = -1 + eps;
}
}
theta[j * size + i] = Math.Acos(theta[j * size + i]);
if (j == size - 2)
{
if (result[i, j + 1] < 0)
{
theta[j * size + i] = -theta[j * size + i];
}
}
}
}
Problem p = new Problem(costFunction, constraint, theta);
optimize.minimize(p, endCriteria);
theta = p.currentValue();
result.fill(1);
for (i = 0; i < size; i++)
{
for (k = 0; k < size; k++)
{
for (j = 0; j <= k; j++)
{
if (j == k && k != size - 1)
{
result[i, k] *= Math.Cos(theta[j * size + i]);
}
else if (j != size - 1)
{
result[i, k] *= Math.Sin(theta[j * size + i]);
}
}
}
}
}
for (i = 0; i < size; i++)
{
for (j = 0; j < size; j++)
{
result[i, j] *= variance[i];
}
}
return(result);
}
// Optimization function for hypersphere and lower-diagonal algorithm
private static Matrix hypersphereOptimize(Matrix targetMatrix, Matrix currentRoot, bool lowerDiagonal)
{
int i,j,k,size = targetMatrix.rows();
Matrix result = new Matrix(currentRoot);
Vector variance = new Vector(size);
for (i=0; i<size; i++){
variance[i]=Math.Sqrt(targetMatrix[i,i]);
}
if (lowerDiagonal) {
Matrix approxMatrix = result*Matrix.transpose(result);
result = MatrixUtilities.CholeskyDecomposition(approxMatrix, true);
for (i=0; i<size; i++) {
for (j=0; j<size; j++) {
result[i,j]/=Math.Sqrt(approxMatrix[i,i]);
}
}
} else {
for (i=0; i<size; i++) {
for (j=0; j<size; j++) {
result[i,j]/=variance[i];
}
}
}
ConjugateGradient optimize = new ConjugateGradient();
EndCriteria endCriteria = new EndCriteria(100, 10, 1e-8, 1e-8, 1e-8);
HypersphereCostFunction costFunction = new HypersphereCostFunction(targetMatrix, variance, lowerDiagonal);
NoConstraint constraint = new NoConstraint();
// hypersphere vector optimization
if (lowerDiagonal) {
Vector theta = new Vector(size * (size-1)/2);
const double eps=1e-16;
for (i=1; i<size; i++) {
for (j=0; j<i; j++) {
theta[i*(i-1)/2+j]=result[i,j];
if (theta[i*(i-1)/2+j]>1-eps)
theta[i*(i-1)/2+j]=1-eps;
if (theta[i*(i-1)/2+j]<-1+eps)
theta[i*(i-1)/2+j]=-1+eps;
for (k=0; k<j; k++) {
theta[i*(i-1)/2+j] /= Math.Sin(theta[i*(i-1)/2+k]);
if (theta[i*(i-1)/2+j]>1-eps)
theta[i*(i-1)/2+j]=1-eps;
if (theta[i*(i-1)/2+j]<-1+eps)
theta[i*(i-1)/2+j]=-1+eps;
}
theta[i*(i-1)/2+j] = Math.Acos(theta[i*(i-1)/2+j]);
if (j==i-1) {
if (result[i,i]<0)
theta[i*(i-1)/2+j]=-theta[i*(i-1)/2+j];
}
}
}
Problem p = new Problem(costFunction, constraint, theta);
optimize.minimize(p, endCriteria);
theta = p.currentValue();
result.fill(1);
for (i=0; i<size; i++) {
for (k=0; k<size; k++) {
if (k>i) {
result[i,k]=0;
} else {
for (j=0; j<=k; j++) {
if (j == k && k!=i)
result[i,k] *= Math.Cos(theta[i*(i-1)/2+j]);
else if (j!=i)
result[i,k] *= Math.Sin(theta[i*(i-1)/2+j]);
}
}
}
}
} else {
Vector theta = new Vector(size * (size-1));
const double eps=1e-16;
for (i=0; i<size; i++) {
for (j=0; j<size-1; j++) {
theta[j*size+i]=result[i,j];
if (theta[j*size+i]>1-eps)
theta[j*size+i]=1-eps;
if (theta[j*size+i]<-1+eps)
theta[j*size+i]=-1+eps;
for (k=0;k<j;k++) {
theta[j*size+i] /= Math.Sin(theta[k*size+i]);
if (theta[j*size+i]>1-eps)
theta[j*size+i]=1-eps;
if (theta[j*size+i]<-1+eps)
theta[j*size+i]=-1+eps;
}
theta[j*size+i] = Math.Acos(theta[j*size+i]);
if (j==size-2) {
if (result[i,j+1]<0)
theta[j*size+i]=-theta[j*size+i];
}
}
}
Problem p = new Problem(costFunction, constraint, theta);
optimize.minimize(p, endCriteria);
theta=p.currentValue();
result.fill(1);
for (i = 0; i < size; i++) {
for (k=0; k<size; k++) {
for (j=0; j<=k; j++) {
if (j == k && k!=size-1)
result[i,k] *= Math.Cos(theta[j*size+i]);
else if (j!=size-1)
result[i,k] *= Math.Sin(theta[j*size+i]);
}
}
}
}
for (i=0; i<size; i++) {
for (j=0; j<size; j++) {
result[i,j]*=variance[i];
}
}
return result;
}