/**
* Gauss-Seidel scaling for a sparse matrix:
* <br>AScaled = U.A.V, with A mxn matrix, U, V diagonal.
* Returns the two scaling matrices
* <br>U[i,i] = base^x[i], i=0,...,m
* <br>V[i,i] = base^y[i], i=0,...,n
*
* @see Gajulapalli, Lasdon "Scaling Sparse Matrices for Optimization Algorithms", algorithms 1 and 2
*/
public void GetMatrixScalingFactors(CompressedColumnStorage <double> A, out double[] U, out double[] V)
{
int m = A.RowCount;
int n = A.ColumnCount;
double log10_b = Math.Log10(basis);
//Setup for Gauss-Seidel Iterations
int[] R = new int[m];
int[] C = new int[n];
double[] t = new double[1];
double[] a = new double[m];
double[] b = new double[n];
// bool[,] Z = new bool[m, n];
foreach (var e in A.EnumerateIndexed())
{
var i = e.Item1;
var j = e.Item2;
var aij = e.Item3;
R[i] = R[i] + 1;
C[j] = C[j] + 1;
// Z[i, j] = true;
t[0] = -(Math.Log10(Math.Abs(aij)) / log10_b + 0.5);
a[i] = a[i] + t[0];
b[j] = b[j] + t[0];
}
for (int i = 0; i < m; i++)
{
a[i] = a[i] / ((double)R[i]);
}
for (int j = 0; j < n; j++)
{
b[j] = b[j] / ((double)C[j]);
}
int[] xx = new int[m];
int[] yy = new int[n];
int[] previousXX = null;
int[] previousYY = null;
bool stopX = false;
bool stopY = false;
int maxIteration = 5;
int l = 0;
for (l = 0; l <= maxIteration && !(stopX && stopY); l++)
{
double[] tt = new double[m];
Array.Copy(a, 0, tt, 0, m);
for (int i = 0; i < m; i++)
{
for (int j = 0; j < n; j++)
{
if (/*Z[i, j]*/ true)
{
tt[i] = tt[i] - ((double)yy[j]) / ((double)R[i]);
}
}
}
for (int k = 0; k < m; k++)
{
xx[k] = (int)Math.Round(tt[k]);
}
if (previousXX == null)
{
previousXX = xx;
}
else
{
bool allEquals = true;
for (int k = 0; k < m && allEquals; k++)
{
allEquals = (xx[k] == previousXX[k]);
}
stopX = allEquals;
previousXX = xx;
}
tt = new double[n];
Array.Copy(b, 0, tt, 0, n);
for (int i = 0; i < m; i++)
{
for (int j = 0; j < n; j++)
{
if (/*Z[i, j])*/ true)
{
tt[j] = tt[j] - ((double)xx[i]) / ((double)C[j]);
}
}
}
for (int k = 0; k < n; k++)
{
yy[k] = (int)Math.Round(tt[k]);
}
if (previousYY == null)
{
previousYY = yy;
}
else
{
bool allEquals = true;
for (int k = 0; k < n && allEquals; k++)
{
allEquals = (yy[k] == previousYY[k]);
}
stopY = allEquals;
previousYY = yy;
}
}
U = new double[m];
V = new double[n];
var maxabs = 10;
for (int k = 0; k < m; k++)
{
xx[k] = Math.Min(maxabs, Math.Max(-maxabs, xx[k]));
U[k] = Math.Pow(basis, xx[k]);
}
for (int k = 0; k < n; k++)
{
yy[k] = Math.Min(maxabs, Math.Max(-maxabs, yy[k]));
V[k] = Math.Pow(basis, yy[k]);
}
}