public static MatrixSparseLinkedList operator -(MatrixSparseLinkedList matrix1, MatrixSparseLinkedList matrix2)
{
MatrixSparseLinkedList matrix3 = new MatrixSparseLinkedList();
matrix3.InitializeMatrix(matrix1.n);
AddMatrix_ToExistingMatrix(ref matrix3, matrix1);
SubtractMatrix_FromExistingMatrix(ref matrix3, matrix2);
return(matrix3);
}
public static MatrixSparseLinkedList MultiplyMatrix_ByMatrix(MatrixSparseLinkedList Matrix1, MatrixSparseLinkedList Matrix2)
{
MatrixSparseLinkedList NewMatrix = new MatrixSparseLinkedList();
NewMatrix.InitializeMatrix(Matrix1.n);
MatrixSparseLinkedList A = Matrix1;
int NumberOfRows_A = A.n;
MatrixSparseLinkedList B = Matrix2;
int NumberOfRows_B = B.n;
for (int i = 0; i < NumberOfRows_A; i++)
{
if (!A.Rows[i].RowNotPopulated)
{
MatrixElement E_A = A.Rows[i].FirsElement;
while (E_A.NotLastItem)
{
for (int j = 0; j < NumberOfRows_B; j++)
{
if (!B.Rows[j].RowNotPopulated)
{
MatrixElement E_B = B.Rows[j].FirsElement;
while (E_B.NotLastItem)
{
NewMatrix.AddToMatrixElement(i, E_B.Index, E_A.Value * E_B.Value);
E_B = E_B.NextItem;
}
NewMatrix.AddToMatrixElement(i, E_B.Index, E_A.Value * E_B.Value);
}
}
E_A = E_A.NextItem;
}
for (int j = 0; j < NumberOfRows_B; j++)
{
if (!B.Rows[j].RowNotPopulated)
{
MatrixElement E_B = B.Rows[j].FirsElement;
while (E_B.NotLastItem)
{
NewMatrix.AddToMatrixElement(i, E_B.Index, E_A.Value * E_B.Value);
E_B = E_B.NextItem;
}
NewMatrix.AddToMatrixElement(i, E_B.Index, E_A.Value * E_B.Value);
}
}
}
}
return(NewMatrix);
}
public static void MultiplyScalar_ByExistingMatrix(ref MatrixSparseLinkedList ExistingMatrix, double Scalar)
{
MatrixSparseLinkedList A = ExistingMatrix;
int NumberOfRows = A.n;
for (int i = 0; i < NumberOfRows; i++)
{
if (!A.Rows[i].RowNotPopulated)
{
MatrixElement E = A.Rows[i].FirsElement;
while (E.NotLastItem)
{
E.Value *= Scalar;
E = E.NextItem;
}
E.Value *= Scalar;
}
}
}
public static void SubtractMatrix_FromExistingMatrix(ref MatrixSparseLinkedList ExistingMatrix, MatrixSparseLinkedList MatrixToSubtract)
{
MatrixSparseLinkedList A = MatrixToSubtract;
int NumberOfRows = A.n;
for (int i = 0; i < NumberOfRows; i++)
{
if (!A.Rows[i].RowNotPopulated)
{
MatrixElement E = A.Rows[i].FirsElement;
while (E.NotLastItem)
{
ExistingMatrix.AddToMatrixElement(i, E.Index, -E.Value);
E = E.NextItem;
}
ExistingMatrix.AddToMatrixElement(i, E.Index, -E.Value);
}
}
}
public Vector ATx_Symmetric(MatrixSparseLinkedList A, Vector x)
{
//Calculate the product y = A^T x
int NumberOfRows = A.n;
Vector y = new Vector(NumberOfRows);
for (int i = 0; i < NumberOfRows; i++)
{
MatrixElement StartElement = A.Rows[i].FirsElement;
double xi = x.Values[i];
int index;
while (StartElement.NotLastItem)
{
index = StartElement.Index;
y.Values[index] += StartElement.Value * xi;
StartElement = StartElement.NextItem;
}
index = StartElement.Index;
y.Values[index] += StartElement.Value * xi;
}
return(y);
}
public static MatrixSparseLinkedList MultiplyScalar_ByMatrix(MatrixSparseLinkedList Matrix1, double Scalar)
{
MatrixSparseLinkedList A = Matrix1;
int NumberOfRows = A.n;
MatrixSparseLinkedList NewMatrix = new MatrixSparseLinkedList();
NewMatrix.InitializeMatrix(NumberOfRows);
for (int i = 0; i < NumberOfRows; i++)
{
if (!A.Rows[i].RowNotPopulated)
{
MatrixElement E = A.Rows[i].FirsElement;
while (E.NotLastItem)
{
NewMatrix.AddToMatrixElement(i, E.Index, E.Value * Scalar);
E = E.NextItem;
}
NewMatrix.AddToMatrixElement(i, E.Index, E.Value * Scalar);
}
}
return(NewMatrix);
}
public Vector Ax_Parallel(MatrixSparseLinkedList A, Vector x)
{
//Calculate the product y = A x
int NumberOfRows = A.n;
Vector y = new Vector(NumberOfRows);
Parallel.For(0, NumberOfRows, i =>
{
MatrixElement StartElement = A.Rows[i].FirsElement;
double temp = 0.0D;
int index;
while (StartElement.NotLastItem)
{
index = StartElement.Index;
temp += StartElement.Value * x.Values[index];
StartElement = StartElement.NextItem;
}
index = StartElement.Index;
temp += StartElement.Value * x.Values[index];
y.Values[i] = temp;
});
return(y);
}
public static Vector MultiplyExistingMatrix_ByVector(ref MatrixSparseLinkedList ExistingMatrix, Vector V)
{
Vector NewVector = new Vector(ExistingMatrix.n);
MatrixSparseLinkedList A = ExistingMatrix;
int NumberOfRows = A.n;
for (int i = 0; i < NumberOfRows; i++)
{
double Temp = 0.0D;
if (!A.Rows[i].RowNotPopulated)
{
MatrixElement E = A.Rows[i].FirsElement;
while (E.NotLastItem)
{
Temp += E.Value * V.Values[E.Index];
E = E.NextItem;
}
Temp += E.Value * V.Values[E.Index];
}
NewVector.Values[i] = Temp;
}
return(NewVector);
}
public Vector SolveUsingSingularValueDecomposition(Vector RHS, out double ConditionNumber, out Vector W, out MatrixSparseLinkedList V)
{
MatrixSparseLinkedList A = this;
//Matrix V;
//Vector W;
SingularValueDecomposition(ref A, out W, out V);
Vector x = ATx_Symmetric(A, RHS);
int n = x.Values.Length;
for (int i = 0; i < n; i++)
{
if (W.Values[i] == 0.0D)
{
x.Values[i] = 0.0D;
}
else
{
x.Values[i] /= W.Values[i];
}
}
x = Ax(V, x);
double Max = W.Max();
double Min = W.Min();
if (Min == 0.0D)
{
ConditionNumber = 1.0E100;
}
else
{
ConditionNumber = Max / Min;
}
return(x);
}
public void SingularValueDecomposition(ref MatrixSparseLinkedList A, out Vector W, out MatrixSparseLinkedList V)
{
//Adaptation of singular value decomposition from Numerical Recipes
// A = U W V^T
// Replaces A with U
int m, mp, n, np, NMAX;
m = A.n;
n = A.n;
mp = m;
np = n;
MatrixSparseLinkedList a = A;
V = new MatrixSparseLinkedList();
V.InitializeMatrix(n);
MatrixSparseLinkedList v = V;
double[] w = new double[np];
NMAX = np;
int l = 0;
int nm = 0;
int i, its, j, jj, k;
double anorm, c, f, g, h, s, scale, x, y, z;
double[] rv1 = new double[NMAX];
g = 0.0d;
scale = 0.0d;
anorm = 0.0d;
for (i = 0; i < n; i++)
{
l = i + 2;
rv1[i] = scale * g;
g = 0.0d;
s = 0.0d;
scale = 0.0d;
if (i < m)
{
for (k = i; k < m; k++)
{
scale += Math.Abs(a.GetMatrixElement(k, i));
}
if (scale != 0.0d)
{
for (k = i; k < m; k++)
{
double temp = a.GetMatrixElement(k, i);
temp /= scale;
s += temp * temp;
}
f = a.GetMatrixElement(i, i);
g = -FortranSign(Math.Sqrt(s), f);
h = f * g - s;
a.SetMatrixElement(i, i, f - g);
for (j = l - 1; j < n; j++)
{
s = 0.0d;
for (k = i; k < m; k++)
{
MatrixRow TempRow = Rows[k];
s += a.GetElementValueInRow(ref TempRow, i) * a.GetElementValueInRow(ref TempRow, j);
}
f = s / h;
for (k = i; k < m; k++)
{
MatrixRow TempRow = Rows[k];
a.AddToElementInRow(ref TempRow, j, f * a.GetElementValueInRow(ref TempRow, i));
}
}
for (k = i; k < m; k++)
{
double temp = a.GetMatrixElement(k, i);
temp *= scale;
a.SetMatrixElement(k, i, temp);
}
}
}
w[i] = scale * g;
g = 0.0d;
s = 0.0d;
scale = 0.0d;
if ((i + 1 <= m) && (i + 1 != n))
{
MatrixRow TempRowI = Rows[i];
MatrixElement ElementLMinus1 = a.GetElementInRowOrClosestAfter(ref TempRowI, l - 1);
MatrixElement StartElement = ElementLMinus1;
if (StartElement != null)
{
while (StartElement.NotLastItem)
{
scale += Math.Abs(StartElement.Value);
StartElement = StartElement.NextItem;
}
scale += Math.Abs(StartElement.Value);
if (scale != 0.0d)
{
StartElement = ElementLMinus1;
while (StartElement.NotLastItem)
{
StartElement.Value /= scale;
s += StartElement.Value * StartElement.Value;
StartElement = StartElement.NextItem;
}
StartElement.Value /= scale;
s += StartElement.Value * StartElement.Value;
if (ElementLMinus1.Index == l - 1)
{
f = ElementLMinus1.Value;
g = -FortranSign(Math.Sqrt(s), f);
h = f * g - s;
ElementLMinus1.Value = f - g;
}
else
{
f = 0.0;
g = -FortranSign(Math.Sqrt(s), f);
h = -s;
a.AddToElementInRow(ref TempRowI, l - 1, f - g);
ElementLMinus1 = a.GetElementInRowOrClosestAfter(ref TempRowI, l - 1);
}
for (k = l - 1; k < n; k++)
{
rv1[k] = a.GetElementValueInRow(ref ElementLMinus1, k) / h;
}
for (j = l - 1; j < m; j++)
{
s = 0.0d;
MatrixRow TempRowJ = Rows[j];
MatrixElement ElementRowJLMinus1 = a.GetElementInRowOrClosestAfter(ref TempRowJ, l - 1);
MatrixElement StartElementJ = ElementRowJLMinus1;
for (k = l - 1; k < n; k++)
{
s += a.GetElementValueInRow(ref ElementRowJLMinus1, k) * a.GetElementValueInRow(ref ElementLMinus1, k);
}
for (k = l - 1; k < n; k++)
{
a.AddToElementInRow(ref ElementRowJLMinus1, k, s * rv1[k]);
}
}
StartElement = ElementLMinus1;
while (StartElement.NotLastItem)
{
StartElement.Value *= scale;
StartElement = StartElement.NextItem;
}
StartElement.Value *= scale;
}
}
}
anorm = Math.Max(anorm, (Math.Abs(w[i]) + Math.Abs(rv1[i])));
}
for (i = n - 1; i > -1; i--)
{
MatrixRow VRowI = V.Rows[i];
if (i < n - 1)
{
if (g != 0.0d)
{
MatrixRow ARowI = Rows[i];
double AIl = a.GetElementValueInRow(ref ARowI, l);
MatrixElement StartElement = a.GetElementInRowOrClosestBefore(ref ARowI, l);
for (j = l; j < n; j++)
{
double temp = (a.GetElementValueInRow(ref StartElement, j) / AIl) / g;
V.SetMatrixElement(j, i, temp);
}
for (j = l; j < n; j++)
{
s = 0.0d;
for (k = l; k < n; k++)
{
s += a.GetElementValueInRow(ref StartElement, k) * V.GetMatrixElement(k, j);
}
for (k = l; k < n; k++)
{
V.AddToMatrixElement(k, j, s * V.GetMatrixElement(k, i));
}
}
}
for (j = l; j < n; j++)
{
V.DeleteMatrixElement(i, j);
V.DeleteMatrixElement(j, i);
}
}
V.SetMatrixElement(i, i, 1.0D);
g = rv1[i];
l = i;
}
for (i = Math.Min(m, n) - 1; i > -1; i--)
{
l = i + 1;
g = w[i];
for (j = l; j < n; j++)
{
a.DeleteMatrixElement(i, j);
}
if (g != 0.0d)
{
g = 1.0d / g;
for (j = l; j < n; j++)
{
s = 0.0d;
for (k = l; k < m; k++)
{
s += a.GetMatrixElement(k, i) * a.GetMatrixElement(k, j);
}
f = (s / a.GetMatrixElement(i, i)) * g;
for (k = i; k < m; k++)//i was l
{
double temp = f * a.GetMatrixElement(k, i);
a.AddToMatrixElement(k, j, temp);
}
}
for (j = i; j < m; j++)
{
double temp = a.GetMatrixElement(j, i) * g;
a.SetMatrixElement(j, i, temp);
}
}
else
{
for (j = i; j < m; j++)
{
a.DeleteMatrixElement(j, i);
}
}
a.AddToMatrixElement(i, i, 1.0D);
}
for (k = n - 1; k > -1; k--)
{
for (its = 0; its < 30; its++)
{
for (l = k; l > -1; l--)
{
nm = l - 1;
if ((Math.Abs(rv1[l]) + anorm) == anorm)
{
goto L2;
}
if ((Math.Abs(w[nm]) + anorm) == anorm)
{
goto L1;
}
}
L1 : c = 0.0d;
s = 1.0d;
for (i = l; i < k + 1; i++)
{
f = s * rv1[i];
rv1[i] *= c;
if ((Math.Abs(f) + anorm) == anorm)
{
goto L2;
}
g = w[i];
h = PYTHAG(f, g);
w[i] = h;
h = 1.0d / h;
c = (g * h);
s = -(f * h);
for (j = 0; j < m; j++)
{
y = a.GetMatrixElement(j, nm);
z = a.GetMatrixElement(j, i);
a.SetMatrixElement(j, nm, (y * c) + (z * s));
a.SetMatrixElement(j, i, -(y * s) + (z * c));
}
}
L2 : z = w[k];
if (l == k)
{
if (z < 0.0d)
{
w[k] = -z;
for (j = 0; j < n; j++)
{
MatrixElement VJK = V.GetElementInRow(ref V.Rows[j], k);
if (VJK != null)
{
VJK.Value = -VJK.Value;
}
// V.SetMatrixElement(j, k, -V.GetMatrixElement(j, k));
}
}
goto L3;
}
if (its == 29)
{
Console.Write("no convergence in svdcmp");
}
x = w[l];
nm = k - 1;
y = w[nm];
g = rv1[nm];
h = rv1[k];
f = ((y - z) * (y + z) + (g - h) * (g + h)) / (2.0d * h * y);
g = PYTHAG(f, 1.0d);
f = ((x - z) * (x + z) + h * ((y / (f + FortranSign(g, f))) - h)) / x;
c = 1.0d;
s = 1.0d;
for (j = l; j < nm; j++)
{
i = j + 1;
g = rv1[i];
y = w[i];
h = s * g;
g = c * g;
z = PYTHAG(f, h);
rv1[j] = z;
c = f / z;
s = h / z;
f = (x * c) + (g * s);
g = -(x * s) + (g * c);
h = y * s;
y = y * c;
for (jj = 0; jj < n; jj++)
{
x = V.GetMatrixElement(jj, j);
z = V.GetMatrixElement(jj, i);
V.SetMatrixElement(jj, j, (x * c) + (z * s));
V.SetMatrixElement(jj, i, -(x * s) + (z * c));
}
z = PYTHAG(f, h);
w[j] = z;
if (z != 0.0d)
{
z = 1.0d / z;
c = f * z;
s = h * z;
}
f = (c * g) + (s * y);
x = -(s * g) + (c * y);
for (jj = 0; jj < m; jj++)
{
y = a.GetMatrixElement(jj, j);
z = a.GetMatrixElement(jj, i);
a.SetMatrixElement(jj, j, (y * c) + (z * s));
a.SetMatrixElement(jj, i, -(y * s) + (z * c));
}
}
rv1[l] = 0.0d;
rv1[k] = f;
w[k] = x;
}
L3 : continue;
}
W = new Vector();
W.Values = w;
}