public static VectorR Transform(VectorR v, MatrixR m)
{
VectorR result = new VectorR(v.GetSize());
if (!m.IsSquared())
{
throw new ArgumentOutOfRangeException(
"Dimension", m.GetRows(), "The matrix must be squared!");
}
if (m.GetRows() != v.GetSize())
{
throw new ArgumentOutOfRangeException(
"Size", v.GetSize(), "The size of the vector must be equal"
+ "to the number of rows of the matrix!");
}
for (int i = 0; i < m.GetRows(); i++)
{
result[i] = 0.0;
for (int j = 0; j < m.GetCols(); j++)
{
result[i] += v[j] * m[j, i];
}
}
return(result);
}
public MatrixR GetTranspose()
{
MatrixR m = this;
m.Transpose();
return(m);
}
public static MatrixR Minor(MatrixR m, int row, int col)
{
MatrixR mm = new MatrixR(m.GetRows() - 1, m.GetCols() - 1);
int ii = 0, jj = 0;
for (int i = 0; i < m.GetRows(); i++)
{
if (i == row)
{
continue;
}
jj = 0;
for (int j = 0; j < m.GetCols(); j++)
{
if (j == col)
{
continue;
}
mm[ii, jj] = m[i, j];
jj++;
}
ii++;
}
return(mm);
}
public MatrixR Clone()
{
// returns a deep copy of the matrix
MatrixR m = new MatrixR(matrix);
m.matrix = (double[, ])matrix.Clone();
return(m);
}
public static MatrixR Inverse(MatrixR m)
{
if (Determinant(m) == 0)
{
throw new DivideByZeroException(
"Cannot inverse a matrix with a zero determinant!");
}
return(Adjoint(m) / Determinant(m));
}
public static bool CompareDimension(MatrixR m1, MatrixR m2)
{
if (m1.GetRows() == m2.GetRows() && m1.GetCols() == m2.GetCols())
{
return(true);
}
else
{
return(false);
}
}
public static MatrixR operator /(double d, MatrixR m)
{
MatrixR result = new MatrixR(m.GetRows(), m.GetCols());
for (int i = 0; i < m.GetRows(); i++)
{
for (int j = 0; j < m.GetCols(); j++)
{
result[i, j] = d / m[i, j];
}
}
return(result);
}
public void Transpose()
{
MatrixR m = new MatrixR(Cols, Rows);
for (int i = 0; i < Rows; i++)
{
for (int j = 0; j < Cols; j++)
{
m[j, i] = matrix[i, j];
}
}
this = m;
}
public static VectorR LinearRegression(double[] xarray, double[] yarray, ModelFunction[] f, out double sigma)
{
int m = f.Length;
MatrixR A = new MatrixR(m, m);
VectorR b = new VectorR(m);
int n = xarray.Length;
for (int k = 0; k < m; k++)
{
b[k] = 0.0;
for (int i = 0; i < n; i++)
{
b[k] += f[k](xarray[i]) * yarray[i];
}
}
for (int j = 0; j < m; j++)
{
for (int k = 0; k < m; k++)
{
A[j, k] = 0.0;
for (int i = 0; i < n; i++)
{
A[j, k] += f[j](xarray[i]) * f[k](xarray[i]);
}
}
}
//LinearSystem ls = new LinearSystem();
//VectorR coef = ls.GaussJordan(A, b);
VectorR coef = GaussJordan(A, b);
// Calculate the standard deviation:
double s = 0.0;
for (int i = 0; i < n; i++)
{
double s1 = 0.0;
for (int j = 0; j < m; j++)
{
s1 += coef[j] * f[j](xarray[i]);
}
s += (yarray[i] - s1) * (yarray[i] - s1);
}
sigma = Math.Sqrt(s / (n - m));
return(coef);
}
public MatrixR Identity()
{
MatrixR m = new MatrixR(Rows, Cols);
for (int i = 0; i < Rows; i++)
{
for (int j = 0; j < Cols; j++)
{
if (i == j)
{
m[i, j] = 1;
}
}
}
return(m);
}
public static VectorR PolynomialFit(double[] xarray, double[] yarray, int m, out double sigma)
{
m++;
MatrixR A = new MatrixR(m, m);
VectorR b = new VectorR(m);
int n = xarray.Length;
for (int k = 0; k < m; k++)
{
b[k] = 0.0;
for (int i = 0; i < n; i++)
{
b[k] += Math.Pow(xarray[i], k) * yarray[i];
}
}
for (int j = 0; j < m; j++)
{
for (int k = 0; k < m; k++)
{
A[j, k] = 0.0;
for (int i = 0; i < n; i++)
{
A[j, k] += Math.Pow(xarray[i], j + k);
}
}
}
VectorR coef = GaussJordan(A, b);
// Calculate the standard deviation:
double s = 0.0;
for (int i = 0; i < n; i++)
{
double s1 = 0.0;
for (int j = 0; j < m; j++)
{
s1 += coef[j] * Math.Pow(xarray[i], j);
}
s += (yarray[i] - s1) * (yarray[i] - s1);
}
sigma = Math.Sqrt(s / (n - m));
return(coef);
}
public static VectorR GaussJordan(MatrixR A, VectorR b)
{
Triangulate(A, b);
int n = b.GetSize();
VectorR x = new VectorR(n);
for (int i = n - 1; i >= 0; i--)
{
double d = A[i, i];
if (Math.Abs(d) < 1.0e-500)
{
throw new ArgumentException("Diagonal element is too small!");
}
x[i] = (b[i] - VectorR.DotProduct(A.GetRowVector(i), x)) / d;
}
return(x);
}
public static MatrixR Adjoint(MatrixR m)
{
if (!m.IsSquared())
{
throw new ArgumentOutOfRangeException(
"Dimension", m.GetRows(), "The matrix must be squared!");
}
MatrixR ma = new MatrixR(m.GetRows(), m.GetCols());
for (int i = 0; i < m.GetRows(); i++)
{
for (int j = 0; j < m.GetCols(); j++)
{
ma[i, j] = Math.Pow(-1, i + j) * (Determinant(Minor(m, i, j)));
}
}
return(ma.GetTranspose());
}
public static MatrixR operator -(MatrixR m1, MatrixR m2)
{
if (!MatrixR.CompareDimension(m1, m2))
{
throw new ArgumentOutOfRangeException(
"Dimension", m1, "The dimensions of two matrices must be the same!");
}
MatrixR result = new MatrixR(m1.GetRows(), m1.GetCols());
for (int i = 0; i < m1.GetRows(); i++)
{
for (int j = 0; j < m1.GetCols(); j++)
{
result[i, j] = m1[i, j] - m2[i, j];
}
}
return(result);
}
public static MatrixR Transform(VectorR v1, VectorR v2)
{
if (v1.GetSize() != v2.GetSize())
{
throw new ArgumentOutOfRangeException(
"v1", v1.GetSize(), "The vectors must have the same size!");
}
MatrixR result = new MatrixR(v1.GetSize(), v1.GetSize());
for (int i = 0; i < v1.GetSize(); i++)
{
for (int j = 0; j < v1.GetSize(); j++)
{
result[j, i] = v1[i] * v2[j];
}
}
return(result);
}
private static double Pivot(MatrixR A, VectorR b, int q)
{
int n = b.GetSize();
int i = q;
double d = 0.0;
for (int j = q; j < n; j++)
{
double dd = Math.Abs(A[j, q]);
if (dd > d)
{
d = dd;
i = j;
}
}
if (i > q)
{
A.GetRowSwap(q, i);
b.GetSwap(q, i);
}
return(A[q, q]);
}
public static double Determinant(MatrixR m)
{
double result = 0.0;
if (!m.IsSquared())
{
throw new ArgumentOutOfRangeException(
"Dimension", m.GetRows(), "The matrix must be squared!");
}
if (m.GetRows() == 1)
{
result = m[0, 0];
}
else
{
for (int i = 0; i < m.GetRows(); i++)
{
result += Math.Pow(-1, i) * m[0, i] * Determinant(MatrixR.Minor(m, 0, i));
}
}
return(result);
}
private static void Triangulate(MatrixR A, VectorR b)
{
int n = A.GetRows();
VectorR v = new VectorR(n);
for (int i = 0; i < n - 1; i++)
{
double d = Pivot(A, b, i);
if (Math.Abs(d) < 1.0e-500)
{
throw new ArgumentException("Diagonal element is too small!");
}
for (int j = i + 1; j < n; j++)
{
double dd = A[j, i] / d;
for (int k = i + 1; k < n; k++)
{
A[j, k] -= dd * A[i, k];
}
b[j] -= dd * b[i];
}
}
}
public static MatrixR operator *(MatrixR m1, MatrixR m2)
{
if (m1.GetCols() != m2.GetRows())
{
throw new ArgumentOutOfRangeException(
"Columns", m1, "The numbers of columns of the first matrix must be equal to" +
" the number of rows of the second matrix!");
}
MatrixR result = new MatrixR(m1.GetRows(), m2.GetCols());
VectorR v1 = new VectorR(m1.GetCols());
VectorR v2 = new VectorR(m2.GetRows());
for (int i = 0; i < m1.GetRows(); i++)
{
v1 = m1.GetRowVector(i);
for (int j = 0; j < m2.GetCols(); j++)
{
v2 = m2.GetColVector(j);
result[i, j] = VectorR.DotProduct(v1, v2);
}
}
return(result);
}
public MatrixR(MatrixR m)
{
Rows = m.GetRows();
Cols = m.GetCols();
matrix = m.matrix;
}
public bool Equals(MatrixR m)
{
return(matrix == m.matrix);
}