/// <inheritdoc />
public override void Add(double alpha, double beta, CompressedColumnStorage <double> other,
CompressedColumnStorage <double> result)
{
if (other == null)
{
throw new ArgumentNullException(nameof(other));
}
if (result == null)
{
throw new ArgumentNullException(nameof(result));
}
int p, j, nz = 0;
int m = this.rows;
int n = this.columns;
// check inputs
if (m != other.RowCount || n != other.ColumnCount)
{
throw new ArgumentException(Resources.MatrixDimensions, nameof(other));
}
// Workspace
var w = new int[m];
var x = new double[m];
// Allocate result: (anz + bnz) is an upper bound
var ci = result.ColumnPointers;
var cj = result.RowIndices;
var cx = result.Values;
for (j = 0; j < n; j++)
{
ci[j] = nz; // column j of C starts here
nz = this.Scatter(j, alpha, w, x, j + 1, result, nz); // alpha*A(:,j)
nz = other.Scatter(j, beta, w, x, j + 1, result, nz); // beta*B(:,j)
for (p = ci[j]; p < nz; p++)
{
cx[p] = x[cj[p]];
}
}
// Finalize the last column
ci[n] = nz;
if (AutoTrimStorage)
{
// Remove extra space.
result.Resize(0);
}
Helper.SortIndices(result);
}
/// <summary>
/// Adds two matrices, C = alpha*A + beta*B, where A is current instance.
/// </summary>
/// <param name="alpha">Scalar factor for A, current instance.</param>
/// <param name="beta">Scalar factor for B, other instance.</param>
/// <param name="other">The matrix added to this instance.</param>
/// <param name="result">Contains the sum.</param>
/// <remarks>
/// The (result) matrix has to be fully initialized and provide enough space for
/// the nonzero entries of the sum. An upper bound is the sum of the nonzeros count
/// of (this) and (other).
/// </remarks>
public override void Add(Complex alpha, Complex beta, CompressedColumnStorage <Complex> other,
CompressedColumnStorage <Complex> result)
{
int p, j, nz = 0;
int m = this.rowCount;
int n = this.columnCount;
// check inputs
if (m != other.RowCount || n != other.ColumnCount)
{
throw new ArgumentException(Resources.MatrixDimensions);
}
// Workspace
var w = new int[m];
var x = new Complex[m];
// Allocate result: (anz + bnz) is an upper bound
var ci = result.ColumnPointers;
var cj = result.RowIndices;
var cx = result.Values;
for (j = 0; j < n; j++)
{
ci[j] = nz; // column j of C starts here
nz = this.Scatter(j, alpha, w, x, j + 1, result, nz); // alpha*A(:,j)
nz = other.Scatter(j, beta, w, x, j + 1, result, nz); // beta*B(:,j)
for (p = ci[j]; p < nz; p++)
{
cx[p] = x[cj[p]];
}
}
// Finalize the last column
ci[n] = nz;
// Remove extra space
result.Resize(0);
result.SortIndices();
}
/// <summary>
/// [L,U,pinv] = lu(A, [q lnz unz]). lnz and unz can be guess.
/// </summary>
private void Factorize(CompressedColumnStorage <Complex> A, double tol, IProgress <double> progress)
{
int[] q = S.q;
int i;
int lnz = S.lnz;
int unz = S.unz;
this.L = CompressedColumnStorage <Complex> .Create(n, n, lnz);
this.U = CompressedColumnStorage <Complex> .Create(n, n, unz);
this.pinv = new int[n];
// Workspace
var x = this.temp;
var xi = new int[2 * n];
for (i = 0; i < n; i++)
{
// No rows pivotal yet.
pinv[i] = -1;
}
lnz = unz = 0;
int ipiv, top, p, col;
Complex pivot;
double a, t;
int[] li, ui;
int[] lp = L.ColumnPointers;
int[] up = U.ColumnPointers;
Complex[] lx, ux;
double current = 0.0;
double step = n / 100.0;
// Now compute L(:,k) and U(:,k)
for (int k = 0; k < n; k++)
{
// Progress reporting.
if (k >= current)
{
current += step;
if (progress != null)
{
progress.Report(k / (double)n);
}
}
// Triangular solve
lp[k] = lnz; // L(:,k) starts here
up[k] = unz; // U(:,k) starts here
if (lnz + n > L.Values.Length)
{
L.Resize(2 * L.Values.Length + n);
}
if (unz + n > U.Values.Length)
{
U.Resize(2 * U.Values.Length + n);
}
li = L.RowIndices;
ui = U.RowIndices;
lx = L.Values;
ux = U.Values;
col = q != null ? (q[k]) : k;
top = SolveSp(L, A, col, xi, x, pinv, true); // x = L\A(:,col)
// Find pivot
ipiv = -1;
a = -1;
for (p = top; p < n; p++)
{
i = xi[p]; // x(i) is nonzero
if (pinv[i] < 0) // Row i is not yet pivotal
{
if ((t = Complex.Abs(x[i])) > a)
{
a = t; // Largest pivot candidate so far
ipiv = i;
}
}
else // x(i) is the entry U(pinv[i],k)
{
ui[unz] = pinv[i];
ux[unz++] = x[i];
}
}
if (ipiv == -1 || a <= 0.0)
{
throw new Exception("No pivot element found.");
}
if (pinv[col] < 0 && Complex.Abs(x[col]) >= a * tol)
{
ipiv = col;
}
// Divide by pivot
pivot = x[ipiv]; // the chosen pivot
ui[unz] = k; // last entry in U(:,k) is U(k,k)
ux[unz++] = pivot;
pinv[ipiv] = k; // ipiv is the kth pivot row
li[lnz] = ipiv; // first entry in L(:,k) is L(k,k) = 1
lx[lnz++] = 1.0;
for (p = top; p < n; p++) // L(k+1:n,k) = x / pivot
{
i = xi[p];
if (pinv[i] < 0) // x(i) is an entry in L(:,k)
{
li[lnz] = i; // save unpermuted row in L
lx[lnz++] = x[i] / pivot; // scale pivot column
}
x[i] = 0.0; // x [0..n-1] = 0 for next k
}
}
// Finalize L and U
lp[n] = lnz;
up[n] = unz;
li = L.RowIndices; // fix row indices of L for final pinv
for (p = 0; p < lnz; p++)
{
li[p] = pinv[li[p]];
}
// Remove extra space from L and U
L.Resize(0);
U.Resize(0);
}
/// <inheritdoc />
public override void Multiply(CompressedColumnStorage <double> other, CompressedColumnStorage <double> result)
{
if (other == null)
{
throw new ArgumentNullException(nameof(other));
}
if (result == null)
{
throw new ArgumentNullException(nameof(result));
}
int p, j, nz = 0;
int[] cp, ci;
double[] cx;
int m = this.rows;
int n = other.ColumnCount;
int anz = this.NonZerosCount;
int bnz = other.NonZerosCount;
if (this.ColumnCount != other.RowCount)
{
throw new ArgumentException(Resources.MatrixDimensions, nameof(other));
}
if ((m > 0 && this.ColumnCount == 0) || (other.RowCount == 0 && n > 0))
{
throw new Exception(Resources.InvalidDimensions);
}
if (result.RowCount != m || result.ColumnCount != n)
{
throw new ArgumentException(Resources.InvalidDimensions, nameof(result));
}
var bp = other.ColumnPointers;
var bi = other.RowIndices;
var bx = other.Values;
// Workspace
var w = new int[m];
var x = new double[m];
cp = result.ColumnPointers;
for (j = 0; j < n; j++)
{
if (nz + m > result.Values.Length)
{
// Might throw out of memory exception.
result.Resize(2 * (result.Values.Length) + m);
}
ci = result.RowIndices;
cx = result.Values; // C.i and C.x may be reallocated
cp[j] = nz; // column j of C starts here
for (p = bp[j]; p < bp[j + 1]; p++)
{
nz = this.Scatter(bi[p], bx[p], w, x, j + 1, result, nz);
}
for (p = cp[j]; p < nz; p++)
{
cx[p] = x[ci[p]];
}
}
cp[n] = nz; // finalize the last column of C
if (AutoTrimStorage)
{
// Remove extra space.
result.Resize(0);
}
Helper.SortIndices(result);
}
/// <summary>
/// Trim row indices and values array of the storage to the exact size (non-zeros count).
/// </summary>
/// <typeparam name="T"></typeparam>
/// <param name="storage">The sparse matrix.</param>
public static void TrimStorage <T>(CompressedColumnStorage <T> storage)
where T : struct, IEquatable <T>, IFormattable
{
storage.Resize(0);
}