/// <summary>
/// Computes the Frobenius norm of the symmetric and non-symmetric parts of A,
/// number of matching elements in symmetry and relative symmetry match.
/// </summary>
private void SymmetryInfo()
{
int n = S.ColumnCount;
var ax = S.Values;
var ap = S.RowPointers;
var ai = S.ColumnIndices;
var B = A.Transpose().Storage as SparseCompressedRowMatrixStorage <T>;
var bx = B.Values;
var bp = B.RowPointers;
var bi = B.ColumnIndices;
int i, j1, k1, k2, j2;
int nnz, k1max, k2max;
double st, fnorm;
double fas = 0.0;
double fan = 0.0;
int imatch = 0;
nnz = ap[n] - ap[0];
st = 0.0;
for (i = 0; i < n; ++i)
{
k1 = ap[i];
k2 = bp[i];
k1max = ap[i + 1];
k2max = bp[i + 1];
while (k1 < k1max && k2 < k2max)
{
j1 = ai[k1];
j2 = bi[k2];
if (j1 == j2)
{
fas += math.Sum2(ax[k1], bx[k2]);
fan += math.Difference2(ax[k1], bx[k2]);
st += math.Square(ax[k1]);
imatch++;
}
k1++;
k2++;
if (j1 < j2)
{
k2--;
}
if (j1 > j2)
{
k1--;
}
}
}
fas *= 0.25;
fan *= 0.25;
if (imatch == nnz)
{
st = 0.0;
}
else
{
fnorm = FrobeniusNorm(B);
st = (fnorm * fnorm - st) * 0.5;
if (st < 0.0)
{
st = 0.0;
}
}
var info = this.StorageInfo;
info.ElementsInSymmetry = imatch;
info.FrobeniusNormSymPart = Math.Sqrt(fas + st);
info.FrobeniusNormNonSymPart = fan < 0.0 ? 0.0 : Math.Sqrt(fan + st);
}