public MatrixC(MatrixC m)
{
Rows = m.GetRows();
Cols = m.GetCols();
matrix = m.matrix;
}
/// <summary>
/// Implementation Convex optimization using ADMM( Stephen Boyd, Stanford) It is essentially least squares fitting with non-negativity constraints
/// An ANOVA computation is added below for significance testing although this implementation is NOT VALIDATED
/// The matrix is any reference matrix (database) and y is the experimental data. The result is a vector of coefficients for the model
/// </summary>
/// <param name="matrix"></param>
/// <param name="y"></param>
/// <returns></returns>
public VectorC MatchLibraryMatrix(MatrixC matrix, VectorC y)
{
#region ADMM (Alternating direction method of multipliers)
//regularized matrix version of least squares
//x = (A'*A)*A'*b
//rho, the wiggle factor
double rho = .001;
//Ax = b where x is the prediction, b is the experimental and A is the reference database matrix
// A = x^t*x
var A = matrix.Transpose() * matrix;
//b = xt*y
MatrixC y1 = new MatrixC(matrix.GetRows(), 1);
y1.ReplaceCol(y, 0);
var temp1 = matrix.Transpose() * y1;
VectorC b = new VectorC(temp1.GetRows());
for(int i = 0; i < temp1.GetRows();i++)
{
b[i] = temp1[i,0];
}
//create identity matrix
var I = A.Identity();
//A' = (A + rho*I)
var Aprime = MatrixC.Inverse(A + (rho * I));
double[] components = new double[b.GetSize()];
//add zeros to vectors
for (int i = 0; i < b.GetSize(); i++)
{
components[i] = 0;
}
VectorC u = new VectorC(components); //accululated error in the negative direction
VectorC z = new VectorC(components); //non-negative version of x
VectorC x = new VectorC(components); //regularized least squares
u = u.Clone();
z = z.Clone();
x = x.Clone();
double sumSquares = 0;
for (int i = 0; i < 1500; i++)
{
x = MatrixC.Transform(Aprime, (b + rho * (z - u)));
//for each element in x + u
//z = (x + u);
for (int j = 0; j < x.GetSize(); j++)
{
var temp = x[j] + u[j];
if (temp > 0)
{
z[j] = temp;
}
else
{
z[j] = 0;
}
}
if (i == 1499)
{
int test11 = 0;
}
//for each element in x - z
// u = u + (x - z);
for (int k = 0; k < u.GetSize(); k++)
{
u[k] = u[k] + (x[k] - z[k]);
}
//calculate RMS error
for (int ii = 0; ii < x.GetSize(); ii++)
{
sumSquares += (x[ii] - z[ii])*(x[ii] - z[ii]);
}
var RMS = Math.Sqrt(sumSquares / x.GetSize());
if (RMS < .001)
{
break;
}
}
#endregion
#region ANOVA
//Matrix yMatrix = Matrix.Create(y);
//Matrix database = (m.Transpose()*m).GetInverse()*m.Transpose();
////ADMM
//var predicted = m*z;
////Hat matrix. The hat matrix is used to reduce overfitting by finding outliers
////inv(x'*x)*x'*x'
//var hatMatrix = (m*(m.Transpose()*m).GetInverse())*m.Transpose();
////J matrix square matrix of ones
//Matrix JMatrix = Matrix.Create(hatMatrix.ColumnCount, hatMatrix.RowCount);
//for (int i = 0; i < JMatrix.ColumnCount; i++)
//{
// for (int j = 0; j < JMatrix.RowCount; j++)
// {
// JMatrix[i, j] = 1;
// }
//}
////SSr (2000 is the observations or m/z in our case)
////y'*[H - (1/n)J]*y
//var SSr = Y.Transpose()*((hatMatrix - (1/2000)*JMatrix))*Y;
////Mean Square Regression
//var MSR = SSr/matrix.GetLongLength(1);
////Identity matrix
//// The following constructs a nxn identity matrix:
//DenseMatrix identityMatrix = DenseMatrix.GetIdentity(2001);
////SSE
////y'*[I-H]*y
//var SSe = Y.Transpose()*(identityMatrix - hatMatrix)*Y;
//double MSquareRegression = MSR[0, 0];
////Mean Square Error
//var MSE = SSe/(2000 - (matrix.GetLongLength(1) + 1));
//double MSquareError = MSE[0, 0];
////F-statistic
////The fstat conducts a hypothesis test. It simply says, is there at least one coefficient that
////id different than zero?
//var f = MSquareRegression/MSquareError;
////get covariance matrix
//var C = MSquareError*(m.Transpose()*m).GetInverse();
////get diangonal
//var d = C.GetDiagonal();
////conduct t-test for all coefficients (vectorResult for OLS)
//for (int i = 0; i < z.Length; i++)
//{
// double tTest = z[i]/Math.Sqrt(d[i]);
//}
////populate correlation scores (vectorResult for OLS)
//for (int i = 0; i < z.Length; i++)
//{
//}
#endregion
return z;
}
public static VectorC Transform(VectorC v, MatrixC m)
{
VectorC result = new VectorC(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 static MatrixC Minor(MatrixC m, int row, int col)
{
MatrixC mm = new MatrixC(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 static double Determinant(MatrixC 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(MatrixC.Minor(m, 0, i));
}
}
return result;
}
public static bool CompareDimension(MatrixC m1, MatrixC m2)
{
if (m1.GetRows() == m2.GetRows() && m1.GetCols() == m2.GetCols())
return true;
else
return false;
}
public static MatrixC Adjoint(MatrixC m)
{
if (!m.IsSquared())
{
throw new ArgumentOutOfRangeException(
"Dimension", m.GetRows(), "The matrix must be squared!");
}
MatrixC ma = new MatrixC(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();
}
