/// <summary>
/// Copies the matrix.
/// </summary>
/// <returns>An independent copy of the matrix.</returns>
public SparseSquareMatrix Copy()
{
// a simple, slow solution is to create an empty sparse matrix with the same dimension and call
// set element for each entry; but this moves along each linked list many times
// we would like to just move along, say, each row, just once, copying the elements we find
// but that isn't simple, because we need to store pointers to the next in row and next in column,
// which we don't have on hand as we create the element
// dealing with the next in row is easy: just keep a reference to the last one we do and
// set its pointer to the next in row when we create the next element in the row
// dealing with the next in column is harder; we need to know what is above it in the column,
// but that was created a long time ago when we were dealing with a previous row.
// to solve this problem, we use auxiluary storage: a N-element array that stores that last
// element created in each column. when we create a new element, we hook it up to the previous
// element stored in that array, then put the new element in the array
SparseMatrixElement[] copyRows = new SparseMatrixElement[dimension];
SparseMatrixElement[] copyColumns = new SparseMatrixElement[dimension];
SparseMatrixElement[] lastInColumn = new SparseMatrixElement[dimension];
for (int r = 0; r < dimension; r++)
{
SparseMatrixElement element = rows[r];
SparseMatrixElement lastInRow = null;
while (element != null)
{
// create a copy of the element
SparseMatrixElement copyElement = new SparseMatrixElement(element.Row, element.Column, element.Value);
// hook it up to the previous one in the row (and store it for the next one)
if (lastInRow != null)
{
lastInRow.NextInRow = copyElement;
}
else
{
copyRows[r] = copyElement;
}
lastInRow = copyElement;
// hook it up to the previous one in the column (and store it for the next one)
if (lastInColumn[element.Column] != null)
{
lastInColumn[element.Column].NextInColumn = copyElement;
}
else
{
copyColumns[element.Column] = copyElement;
}
lastInColumn[element.Column] = copyElement;
// move to the next element in the row
element = element.NextInRow;
}
}
SparseSquareMatrix copy = new SparseSquareMatrix(dimension, copyRows, copyColumns, fill);
return(copy);
}
public void SparseSquareMatrixCopy()
{
SparseSquareMatrix A = new SparseSquareMatrix(5);
A[1, 1] = 1.0;
A[3, 1] = 2.0;
A[1, 3] = 3.0;
A[3, 3] = 4.0;
A[2, 4] = 5.0;
// make a copy
SparseSquareMatrix AC = A.Copy();
// test that the copy agrees
Assert.IsTrue(AC.Dimension == A.Dimension);
Assert.IsTrue(AC.FillCount == A.FillCount);
Assert.IsTrue(AC[2, 2] == A[2, 2]);
Assert.IsTrue(AC[3, 3] == A[3, 3]);
// test the copy's independence
A[3, 3] += 1.0;
Assert.IsTrue(AC[3,3] != A[3,3]);
A[1, 3] = 0.0;
Assert.IsTrue(AC[1, 3] != A[1, 3]);
Assert.IsTrue(AC.FillCount != A.FillCount);
}
public void SparseSquareMatrixAgreement()
{
int d = 6;
SparseSquareMatrix A = new SparseSquareMatrix(d);
SquareMatrix B = new SquareMatrix(d);
Random rng = new Random(1);
for (int i = 0; i < 2 * d; i++) {
int r = (int) Math.Floor(rng.NextDouble() * d);
int c = (int) Math.Floor(rng.NextDouble() * d);
A[r, c] = 2.0 * rng.NextDouble() - 1.0;
B[r, c] = A[r, c];
}
RowVector u = new RowVector(d);
ColumnVector v = new ColumnVector(d);
for (int i = 0; i < d; i++) {
u[i] = 2.0 * rng.NextDouble() - 1.0;
v[i] = 2.0 * rng.NextDouble() - 1.0;
}
RowVector uA = u * A;
RowVector uB = u * B;
Assert.IsTrue(TestUtilities.IsNearlyEqual(uA, uB));
ColumnVector Av = A * v;
ColumnVector Bv = B * v;
Assert.IsTrue(TestUtilities.IsNearlyEqual(Av, Bv));
}
public SparseSquareMatrix CreateRandomSparseSquareMatrix(int dim, int fill, Random rng)
{
SparseSquareMatrix S = new SparseSquareMatrix(dim);
for (int i = 0; i < fill; i++) {
int r = (int)Math.Floor(rng.NextDouble() * dim);
int c = (int)Math.Floor(rng.NextDouble() * dim);
S[r, c] = 2.0 * rng.NextDouble() - 1.0;
}
return (S);
}
/// <summary>
/// Multiplies a sparse matrix by a real scalar.
/// </summary>
/// <param name="alpha">The scalar value.</param>
/// <param name="A">The sparse matrix.</param>
/// <returns>The product sparse matrix.</returns>
public static SparseSquareMatrix operator *(double alpha, SparseSquareMatrix A)
{
if (A == null)
{
throw new ArgumentNullException("A");
}
SparseSquareMatrix aA = A.Copy();
if (alpha == 0.0)
{
return(aA);
}
for (int r = 0; r < aA.dimension; r++)
{
SparseMatrixElement element = aA.rows[r];
while (element != null)
{
element.Value = alpha * element.Value;
// handle the case where alpha != 0, but alpha * element.Value underflows to zero
element = element.NextInRow;
}
}
return(aA);
}
public void SparseSquareMatrixManipulation()
{
// 0 0 0 0 0 0
// 0 1 0 0 4 0
// 0 5 0 0 0 0
// 0 0 0 0 0 0
// 3 2 0 0 6 0
// 0 0 0 0 0 0
SparseSquareMatrix S = new SparseSquareMatrix(6);
Assert.IsTrue(S.Dimension == 6);
Assert.IsTrue(S.FillCount == 0);
Assert.IsTrue(S.FillFraction == 0.0);
// assign values
S[1, 1] = 1.0;
S[4, 1] = 2.0;
S[4, 0] = 3.0;
S[1, 4] = 4.0;
S[2, 1] = 5.0;
S[4, 4] = 6.0;
Assert.IsTrue(S[1, 1] == 1.0);
Assert.IsTrue(S[4, 1] == 2.0);
Assert.IsTrue(S.FillCount == 6);
Assert.IsTrue(TestUtilities.IsNearlyEqual(S.FillFraction, 6.0 / 36.0));
// change a value
S[4, 4] = 7.0;
Assert.IsTrue(S[4, 4] == 7.0);
Assert.IsTrue(S.FillCount == 6);
// remove a value
S[4, 1] = 0.0;
Assert.IsTrue(S[4, 1] == 0.0);
Assert.IsTrue(S.FillCount == 5);
}
public void SparseSquareMatrixSolutionAgreement()
{
Random rng = new Random(2);
int n = 16;
//for (int n = 8; n < 100; n+= 11) {
// create dense and sparse matrices with the same entries
SquareMatrix M = new SquareMatrix(n);
SparseSquareMatrix S = new SparseSquareMatrix(n);
for (int r = 0; r < n; r++) {
for (int c = 0; c < n; c++) {
if (rng.NextDouble() < 0.5) {
M[r, c] = rng.NextDouble();
S[r, c] = M[r, c];
}
}
}
// pick a RHS
ColumnVector b = new ColumnVector(n);
for (int i = 0; i < n; i++) b[i] = rng.NextDouble();
// solve each
ColumnVector Mx = M.LUDecomposition().Solve(b);
ColumnVector Sx = S.Solve(b);
// the solutions should be the same
Assert.IsTrue(TestUtilities.IsNearlyEqual(Mx, Sx, TestUtilities.TargetPrecision * 100.0));
//}
}
public void SparseSquareMatrixPotential()
{
// An 2D electrostatic boundary value problem in cartesian coordinates
// A square of length n, with specified constant potentials on each wall
// Discritized Laplace equation is
// u_{x,y-1} + u_{x+1,y} + u_{x,y+1} + u_{x-1,y} - 4 u_{x,y} = 0
// Number interior points sequentially row-wise i.e. i = x + n * y
// Points nearest the walls will pick up a boundary value, which because it is not a variable we move to the RHS
// Points closer to the interior pick up no boundary value, so their RHS is zero
int n = 100;
double pn = 0.0; double pe = 1.0; double ps = 0.0; double pw = 1.0;
SparseSquareMatrix A = new SparseSquareMatrix(n * n);
ColumnVector b = new ColumnVector(n * n);
// set up A and b
for (int y = 0; y < n; y++) {
for (int x = 0; x < n; x++) {
int i = x + n * y;
// center value
A[i, i] = 4.0;
// north
if (y == 0) {
b[i] += pn;
} else {
int j = x + n * (y - 1);
A[i, j] = -1.0;
}
// east
if (x == (n-1)) {
b[i] += pe;
} else {
int j = (x + 1) + n * y;
A[i, j] = -1.0;
}
// south
if (y == (n-1)) {
b[i] += ps;
} else {
int j = x + n * (y + 1);
A[i, j] = -1.0;
}
// west
if (x == 0) {
b[i] += pw;
} else {
int j = (x - 1) + n * y;
A[i, j] = -1.0;
}
}
}
ColumnVector u = A.Solve(b);
for (int y = 0; y < 10; y++) {
for (int x = 0; x < 10; x++) {
int i = x + n * y;
Console.Write("{0} ", u[i]);
}
Console.WriteLine();
}
Console.WriteLine(PotentialSolution(1, 2, n));
}
/// <summary>
/// Copies the matrix.
/// </summary>
/// <returns>An independent copy of the matrix.</returns>
public SparseSquareMatrix Copy()
{
// a simple, slow solution is to create an empty sparse matrix with the same dimension and call
// set element for each entry; but this moves along each linked list many times
// we would like to just move along, say, each row, just once, copying the elements we find
// but that isn't simple, because we need to store pointers to the next in row and next in column,
// which we don't have on hand as we create the element
// dealing with the next in row is easy: just keep a reference to the last one we do and
// set its pointer to the next in row when we create the next element in the row
// dealing with the next in column is harder; we need to know what is above it in the column,
// but that was created a long time ago when we were dealing with a previous row.
// to solve this problem, we use auxiluary storage: a N-element array that stores that last
// element created in each column. when we create a new element, we hook it up to the previous
// element stored in that array, then put the new element in the array
SparseMatrixElement[] copyRows = new SparseMatrixElement[dimension];
SparseMatrixElement[] copyColumns = new SparseMatrixElement[dimension];
SparseMatrixElement[] lastInColumn = new SparseMatrixElement[dimension];
for (int r = 0; r < dimension; r++) {
SparseMatrixElement element = rows[r];
SparseMatrixElement lastInRow = null;
while (element != null) {
// create a copy of the element
SparseMatrixElement copyElement = new SparseMatrixElement(element.Row, element.Column, element.Value);
// hook it up to the previous one in the row (and store it for the next one)
if (lastInRow != null) {
lastInRow.NextInRow = copyElement;
} else {
copyRows[r] = copyElement;
}
lastInRow = copyElement;
// hook it up to the previous one in the column (and store it for the next one)
if (lastInColumn[element.Column] != null) {
lastInColumn[element.Column].NextInColumn = copyElement;
} else {
copyColumns[element.Column] = copyElement;
}
lastInColumn[element.Column] = copyElement;
// move to the next element in the row
element = element.NextInRow;
}
}
SparseSquareMatrix copy = new SparseSquareMatrix(dimension, copyRows, copyColumns, fill);
return (copy);
}