/// <summary>Divides the polynomial by the given polynomial and stores the remainder in <paramref name="remainder"/>.</summary>
public void Divide(Polynomial value, out Polynomial remainder)
{
if (value == null)
{
throw new ArgumentNullException();
}
double mainFactor = 1 / value.coefficients[value.Degree]; // this should catch division by zero
double[] remain = new double[Length];
ArrayUtility.FastCopy(coefficients, remain, Length);
int i = Degree;
for (int end = Degree - value.Degree; i > end; i--)
{
coefficients[i] = 0;
}
for (; i >= 0; i--)
{
double quot = remain[value.Degree + i] * mainFactor;
coefficients[i] = quot;
for (int j = value.Degree + i - 1; j >= i; j--)
{
remain[j] -= quot * value.coefficients[j - i];
}
}
for (i = value.Degree; i <= Degree; i++)
{
remain[i] = 0;
}
remainder = new Polynomial(remain, false);
Degree -= value.Degree;
}
/// <inheritdoc/>
public void EvaluateJacobian(double[] input, Matrix matrix)
{
if (input == null || matrix == null)
{
throw new ArgumentNullException();
}
function.Evaluate(input, output);
ArrayUtility.FastCopy(input, input2, input.Length);
for (int x = 0; x < input2.Length; x++)
{
double arg = input[x], h = arg * factor;
if (h == 0)
{
h = factor;
}
input2[x] = arg + h; // this trick ensures that the value of h added to the input value is exactly the same as the value of h used
h = input2[x] - arg; // in the divisor later. essentially, it eliminates a source of error caused by the difference of precision
function.Evaluate(input2, output2);
input2[x] = arg;
for (int y = 0; y < output.Length; y++)
{
matrix[y, x] = (output2[y] - output[y]) / h;
}
}
}
Polynomial(double[] coefficients, int length, int degree)
{
double[] array = new double[length];
ArrayUtility.FastCopy(coefficients, array, degree + 1);
this.coefficients = array;
Degree = degree;
}
void Initialize(double[] coefficients, bool clone)
{
int degree = coefficients.Length; // find the degree of the polynomial
while (degree > 0 && coefficients[--degree] == 0)
{
}
// if the array is substantially larger than needed or we have to clone it, then reallocate it
if (clone || coefficients.Length - degree > 5 && degree <= coefficients.Length / 2)
{
double[] array = new double[degree + 1];
ArrayUtility.FastCopy(coefficients, array, array.Length);
coefficients = array;
}
this.coefficients = coefficients;
Degree = degree;
}
/// <inheritdoc/>
public void EvaluateGradient(double[] input, double[] gradient)
{
if (input == null || gradient == null)
{
throw new ArgumentNullException();
}
double value = function.Evaluate(input);
ArrayUtility.FastCopy(input, input2, input.Length);
for (int x = 0; x < input2.Length; x++)
{
double arg = input[x], h = arg * factor;
if (h == 0)
{
h = factor;
}
input2[x] = arg + h; // this trick ensures that the value of h added to the input value is exactly the same as the value of h used
h = input2[x] - arg; // in the divisor later. essentially, it eliminates a source of error caused by the difference of precision
double value2 = function.Evaluate(input2);
input2[x] = arg;
gradient[x] = (value2 - value) / h;
}
}
/// <summary>Returns an array containing the coefficients of the polynomial. The coefficients will be returned in the same format as
/// that accepted by the <see cref="Polynomial(double[])"/> constructor. That is, the first value will be the constant term, the second
/// value will be the linear term, etc.
/// </summary>
public double[] ToArray()
{
double[] array = new double[Length];
ArrayUtility.FastCopy(coefficients, array, Length);
return(array);
}
/// <summary>Copies the coefficients of the polynomial into the array at the given index. The coefficients will be written in the same
/// format as that accepted by the <see cref="Polynomial(double[])"/> constructor. That is, the first value will be the constant term,
/// the second value will be the linear term, etc.
/// </summary>
public void CopyTo(double[] array, int index)
{
Utility.ValidateRange(array, index, Length);
ArrayUtility.FastCopy(coefficients, 0, array, index, Length);
}
/// <summary>Copies data from another vector into this one.</summary>
public void Assign(Vector other)
{
ValidateSameSize(other);
ArrayUtility.FastCopy(other.data, data, data.Length);
}
void Initialize(double[] data, int index, int length)
{
Utility.ValidateRange(data, index, length);
this.data = new double[length];
ArrayUtility.FastCopy(data, index, this.data, 0, length);
}
/// <summary>Returns an array containing a copy of the components from the vector.</summary>
public double[] ToArray()
{
double[] array = new double[Size];
ArrayUtility.FastCopy(data, array, array.Length);
return(array);
}
/// <summary>Copies the elements of the vector into an array at the given index.</summary>
public void CopyTo(double[] array, int index)
{
Utility.ValidateRange(array, index, Size);
ArrayUtility.FastCopy(data, 0, array, index, data.Length);
}