public void Subtract(double p, QuadraticModel Q)
{
f -= p * Q.f;
for (int i = 0; i < g.Length; i++)
{
g[i] -= p * Q.g[i];
for (int j = 0; j <= i; j++)
{
h[i][j] -= p * Q.h[i][j];
}
}
}
private void Initialize(MultiFunctor f, IReadOnlyList <double> x, double s)
{
// Allocate storage
d = x.Count;
int m = (d + 1) * (d + 2) / 2;
origin = new double[d];
points = new double[m][];
for (int i = 0; i < m; i++)
{
points[i] = new double[d];
}
values = new double[m];
polynomials = new QuadraticModel[m];
for (int i = 0; i < m; i++)
{
polynomials[i] = new QuadraticModel(d);
}
// Start with x as the origin.
x.CopyTo(origin, 0);
// The first interpolation point is the origin.
x.CopyTo(points[0], 0);
values[0] = f.Evaluate(points[0]);
// Compute 2d more interpolation points one step along each axis.
int k = 0;
for (int i = 0; i < d; i++)
{
k++;
x.CopyTo(points[k], 0);
points[k][i] += s;
double plusValue = f.Evaluate(points[k]);
values[k] = plusValue;
k++;
x.CopyTo(points[k], 0);
points[k][i] -= s;
double minusValue = f.Evaluate(points[k]);
values[k] = minusValue;
}
// Compute d(d+1)/2 more interpolation points at the corners.
for (int i = 0; i < d; i++)
{
for (int j = 0; j < i; j++)
{
k++;
x.CopyTo(points[k], 0);
points[k][i] += s;
points[k][j] += s;
double cornerValue = f.Evaluate(points[k]);
values[k] = cornerValue;
}
}
double s1 = 1.0 / s;
double s2 = s1 * s1;
// Compute the Lagrange polynomial for each point
k = 0;
for (int i = 0; i < d; i++)
{
k++;
polynomials[2 * i + 1].g[i] = 0.5 * s1;
polynomials[2 * i + 1].h[i][i] = 0.5 * s2;
k++;
polynomials[2 * i + 2].g[i] = -0.5 * s1;
polynomials[2 * i + 2].h[i][i] = 0.5 * s2;
}
for (int i = 0; i < d; i++)
{
for (int j = 0; j < i; j++)
{
k++;
polynomials[k].h[i][j] = s2;
polynomials[2 * i + 1].h[i][j] -= s2;
polynomials[2 * j + 1].h[i][j] -= s2;
}
}
polynomials[0].f = 1.0;
for (int l = 1; l < m; l++)
{
for (int i = 0; i < d; i++)
{
polynomials[0].g[i] -= polynomials[l].g[i];
for (int j = 0; j <= i; j++)
{
polynomials[0].h[i][j] -= polynomials[l].h[i][j];
}
}
}
// Compute the total interpolating polynomial.
total = new QuadraticModel(d);
for (int l = 0; l < m; l++)
{
total.f += values[l] * polynomials[l].f;
for (int i = 0; i < d; i++)
{
total.g[i] += values[l] * polynomials[l].g[i];
for (int j = 0; j <= i; j++)
{
total.h[i][j] += values[l] * polynomials[l].h[i][j];
}
}
}
// Find the minimum point.
minValueIndex = 0;
for (int i = 1; i < m; i++)
{
if (values[i] < values[minValueIndex])
{
minValueIndex = i;
}
}
// move the origin to the minimum point
double[] z = new double[d];
for (int i = 0; i < z.Length; i++)
{
z[i] = points[minValueIndex][i] - origin[i];
}
ShiftOrigin(z);
// compute badnesses
//badnesses = new double[points.Length];
//for (int i = 0; i < points.Length; i++) {
// badnesses[i] = ComputeBadressAbsolute(points[i], values[i]);
//}
}
public void Subtract(double p, QuadraticModel Q)
{
f -= p * Q.f;
for (int i = 0; i < g.Length; i++) {
g[i] -= p * Q.g[i];
for (int j = 0; j <= i; j++) {
h[i][j] -= p * Q.h[i][j];
}
}
}
private void Initialize(MultiFunctor f, IList<double> x, double s)
{
// Allocate storage
d = x.Count;
int m = (d + 1) * (d + 2) / 2;
origin = new double[d];
points = new double[m][];
for (int i = 0; i < m; i++) points[i] = new double[d];
values = new double[m];
polynomials = new QuadraticModel[m];
for (int i = 0; i < m; i++) polynomials[i] = new QuadraticModel(d);
// Start with x as the origin.
x.CopyTo(origin, 0);
// The first interpolation point is the origin.
x.CopyTo(points[0], 0);
values[0] = f.Evaluate(points[0]);
// Compute 2d more interpolation points one step along each axis.
int k = 0;
for (int i = 0; i < d; i++) {
k++;
x.CopyTo(points[k], 0);
points[k][i] += s;
double plusValue = f.Evaluate(points[k]);
values[k] = plusValue;
k++;
x.CopyTo(points[k], 0);
points[k][i] -= s;
double minusValue = f.Evaluate(points[k]);
values[k] = minusValue;
}
// Compute d(d+1)/2 more interpolation points at the corners.
for (int i = 0; i < d; i++) {
for (int j = 0; j < i; j++) {
k++;
x.CopyTo(points[k], 0);
points[k][i] += s;
points[k][j] += s;
double cornerValue = f.Evaluate(points[k]);
values[k] = cornerValue;
}
}
double s1 = 1.0 / s;
double s2 = s1 * s1;
// Compute the Lagrange polynomial for each point
k = 0;
for (int i = 0; i < d; i++) {
k++;
polynomials[2 * i + 1].g[i] = 0.5 * s1;
polynomials[2 * i + 1].h[i][i] = 0.5 * s2;
k++;
polynomials[2 * i + 2].g[i] = -0.5 * s1;
polynomials[2 * i + 2].h[i][i] = 0.5 * s2;
}
for (int i = 0; i < d; i++) {
for (int j = 0; j < i; j++) {
k++;
polynomials[k].h[i][j] = s2;
polynomials[2 * i + 1].h[i][j] -= s2;
polynomials[2 * j + 1].h[i][j] -= s2;
}
}
polynomials[0].f = 1.0;
for (int l = 1; l < m; l++) {
for (int i = 0; i < d; i++) {
polynomials[0].g[i] -= polynomials[l].g[i];
for (int j = 0; j <= i; j++) {
polynomials[0].h[i][j] -= polynomials[l].h[i][j];
}
}
}
// Compute the total interpolating polynomial.
total = new QuadraticModel(d);
for (int l = 0; l < m; l++) {
total.f += values[l] * polynomials[l].f;
for (int i = 0; i < d; i++) {
total.g[i] += values[l] * polynomials[l].g[i];
for (int j = 0; j <= i; j++) {
total.h[i][j] += values[l] * polynomials[l].h[i][j];
}
}
}
// Find the minimum point.
minValueIndex = 0;
for (int i = 1; i < m; i++) {
if (values[i] < values[minValueIndex]) minValueIndex = i;
}
// move the origin to the minimum point
double[] z = new double[d];
for (int i = 0; i < z.Length; i++) z[i] = points[minValueIndex][i] - origin[i];
ShiftOrigin(z);
// compute badnesses
//badnesses = new double[points.Length];
//for (int i = 0; i < points.Length; i++) {
// badnesses[i] = ComputeBadressAbsolute(points[i], values[i]);
//}
}