public void testRegression()
{
//("Testing linear least-squares regression...");
//SavedSettings backup;
const int nr = 100000;
var rng = new InverseCumulativeRng <MersenneTwisterUniformRng, InverseCumulativeNormal>(
new MersenneTwisterUniformRng(1234u));
List <Func <double, double> > v = new List <Func <double, double> >();
v.Add(x => 1.0);
v.Add(x => x);
v.Add(x => x * x);
v.Add(Math.Sin);
List <Func <double, double> > w = new List <Func <double, double> >(v);
w.Add(x => x * x);
for (int k = 0; k < 3; ++k)
{
int i;
double[] a = { rng.next().value,
rng.next().value,
rng.next().value,
rng.next().value };
List <double> x = new InitializedList <double>(nr), y = new InitializedList <double>(nr);
for (i = 0; i < nr; ++i)
{
x[i] = rng.next().value;
// regression in y = a_1 + a_2*x + a_3*x^2 + a_4*sin(x) + eps
y[i] = a[0] * v[0](x[i]) + a[1] * v[1](x[i]) + a[2] * v[2](x[i])
+ a[3] * v[3](x[i]) + rng.next().value;
}
LinearLeastSquaresRegression m = new LinearLeastSquaresRegression(x, y, v);
for (i = 0; i < v.Count; ++i)
{
if (m.standardErrors()[i] > tolerance)
{
Assert.Fail("Failed to reproduce linear regression coef."
+ "\n error: " + m.standardErrors()[i]
+ "\n tolerance: " + tolerance);
}
if (Math.Abs(m.coefficients()[i] - a[i]) > 3 * m.error()[i])
{
Assert.Fail("Failed to reproduce linear regression coef."
+ "\n calculated: " + m.coefficients()[i]
+ "\n error: " + m.standardErrors()[i]
+ "\n expected: " + a[i]);
}
}
m = new LinearLeastSquaresRegression(x, y, w);
double[] ma = { m.coefficients()[0], m.coefficients()[1], m.coefficients()[2] + m.coefficients()[4], m.coefficients()[3] };
double[] err = { m.standardErrors()[0], m.standardErrors()[1],
Math.Sqrt(m.standardErrors()[2] * m.standardErrors()[2]
+ m.standardErrors()[4] * m.standardErrors()[4]),
m.standardErrors()[3] };
for (i = 0; i < v.Count; ++i)
{
if (Math.Abs(ma[i] - a[i]) > 3 * err[i])
{
Assert.Fail("Failed to reproduce linear regression coef."
+ "\n calculated: " + ma[i]
+ "\n error: " + err[i]
+ "\n expected: " + a[i]);
}
}
}
}
public void testMultiDimRegression()
{
//BOOST_MESSAGE("Testing linear least-squares regression...");
//SavedSettings backup;
const int nr=100000;
const int dims = 4;
const double tolerance = 0.01;
var rng = new InverseCumulativeRng<MersenneTwisterUniformRng,InverseCumulativeNormal>(
new MersenneTwisterUniformRng(1234u));
List<Func<Vector, double>> v = new List<Func<Vector,double>>();
v.Add(xx => 1.0);
for (int i = 0; i < dims; ++i) {
int jj = i; // c# delegate work-around vs. boost bind; jj has to be evaluted before add delegate to the list
v.Add(vv => vv[jj]);
}
Vector coeff = new Vector(v.Count);
for (int i=0; i < v.Count; ++i)
coeff[i] = rng.next().value;
List<double> y = new InitializedList<double>(nr, 0.0);
List<Vector> x = new InitializedList<Vector>(nr);
for (int i=0; i < nr; ++i) {
x[i] = new Vector(dims);
for (int j = 0; j < dims; ++j) {
x[i][j] = rng.next().value;
}
for (int j=0; j < v.Count; ++j) {
y[i] += coeff[j]*v[j](x[i]);
}
y[i] += rng.next().value;
}
LinearLeastSquaresRegression<Vector> m = new LinearLeastSquaresRegression<Vector>(x, y, v);
for (int i=0; i < v.Count; ++i) {
if (m.standardErrors()[i] > tolerance) {
Assert.Fail("Failed to reproduce linear regression coef."
+ "\n error: " + m.standardErrors()[i]
+ "\n tolerance: " + tolerance);
}
if (Math.Abs(m.coefficients()[i]-coeff[i]) > 3*tolerance) {
Assert.Fail("Failed to reproduce linear regression coef."
+ "\n calculated: " + m.coefficients()[i]
+ "\n error: " + m.standardErrors()[i]
+ "\n expected: " + coeff[i]);
}
}
}
public void testMultiDimRegression()
{
//BOOST_MESSAGE("Testing linear least-squares regression...");
//SavedSettings backup;
const int nr = 100000;
const int dims = 4;
const double tolerance = 0.01;
var rng = new InverseCumulativeRng <MersenneTwisterUniformRng, InverseCumulativeNormal>(
new MersenneTwisterUniformRng(1234u));
List <Func <Vector, double> > v = new List <Func <Vector, double> >();
v.Add(xx => 1.0);
for (int i = 0; i < dims; ++i)
{
int jj = i; // c# delegate work-around vs. boost bind; jj has to be evaluted before add delegate to the list
v.Add(vv => vv[jj]);
}
Vector coeff = new Vector(v.Count);
for (int i = 0; i < v.Count; ++i)
{
coeff[i] = rng.next().value;
}
List <double> y = new InitializedList <double>(nr, 0.0);
List <Vector> x = new InitializedList <Vector>(nr);
for (int i = 0; i < nr; ++i)
{
x[i] = new Vector(dims);
for (int j = 0; j < dims; ++j)
{
x[i][j] = rng.next().value;
}
for (int j = 0; j < v.Count; ++j)
{
y[i] += coeff[j] * v[j](x[i]);
}
y[i] += rng.next().value;
}
LinearLeastSquaresRegression <Vector> m = new LinearLeastSquaresRegression <Vector>(x, y, v);
for (int i = 0; i < v.Count; ++i)
{
if (m.standardErrors()[i] > tolerance)
{
Assert.Fail("Failed to reproduce linear regression coef."
+ "\n error: " + m.standardErrors()[i]
+ "\n tolerance: " + tolerance);
}
if (Math.Abs(m.coefficients()[i] - coeff[i]) > 3 * tolerance)
{
Assert.Fail("Failed to reproduce linear regression coef."
+ "\n calculated: " + m.coefficients()[i]
+ "\n error: " + m.standardErrors()[i]
+ "\n expected: " + coeff[i]);
}
}
}
public void testRegression()
{
//("Testing linear least-squares regression...");
//SavedSettings backup;
const int nr=100000;
var rng = new InverseCumulativeRng<MersenneTwisterUniformRng,InverseCumulativeNormal>(
new MersenneTwisterUniformRng(1234u));
List<Func<double, double>> v = new List<Func<double,double>>();
v.Add(x => 1.0);
v.Add(x => x);
v.Add(x => x*x);
v.Add(Math.Sin);
List<Func<double, double>> w = new List<Func<double,double>>(v);
w.Add(x => x*x);
for (int k=0; k<3; ++k) {
int i;
double[] a = { rng.next().value,
rng.next().value,
rng.next().value,
rng.next().value};
List<double> x = new InitializedList<double>(nr), y = new InitializedList<double>(nr);
for (i=0; i<nr; ++i) {
x[i] = rng.next().value;
// regression in y = a_1 + a_2*x + a_3*x^2 + a_4*sin(x) + eps
y[i] = a[0]*v[0](x[i]) + a[1]*v[1](x[i]) + a[2]*v[2](x[i])
+ a[3]*v[3](x[i]) + rng.next().value;
}
LinearLeastSquaresRegression m = new LinearLeastSquaresRegression(x, y, v);
for (i=0; i<v.Count; ++i) {
if (m.standardErrors()[i] > tolerance) {
Assert.Fail("Failed to reproduce linear regression coef."
+ "\n error: " + m.standardErrors()[i]
+ "\n tolerance: " + tolerance);
}
if (Math.Abs(m.coefficients()[i]-a[i]) > 3*m.error()[i]) {
Assert.Fail("Failed to reproduce linear regression coef."
+ "\n calculated: " + m.coefficients()[i]
+ "\n error: " + m.standardErrors()[i]
+ "\n expected: " + a[i]);
}
}
m = new LinearLeastSquaresRegression(x, y, w);
double[] ma = { m.coefficients()[0], m.coefficients()[1], m.coefficients()[2] + m.coefficients()[4], m.coefficients()[3] };
double[] err = {m.standardErrors()[0], m.standardErrors()[1],
Math.Sqrt( m.standardErrors()[2]*m.standardErrors()[2]
+m.standardErrors()[4]*m.standardErrors()[4]),
m.standardErrors()[3]};
for (i = 0; i < v.Count; ++i) {
if (Math.Abs(ma[i] - a[i]) > 3 * err[i]) {
Assert.Fail("Failed to reproduce linear regression coef."
+ "\n calculated: " + ma[i]
+ "\n error: " + err[i]
+ "\n expected: " + a[i]);
}
}
}
}