/// <summary>
/// Links vector elements.
/// </summary>
/// <param name="vector">The vector.</param>
/// <param name="row">The row variable.</param>
private void LinkElement(ISparseVector <T> vector, Bridge <int> row)
{
var loc = Solver.ExternalToInternal(new MatrixLocation(row.Local, row.Local));
// Do we need to create an element?
var local_elt = vector.FindElement(loc.Row);
if (local_elt == null)
{
// Check if solving will result in an element
var first = vector.GetFirstInVector();
if (first == null || first.Index > Solver.Size - Solver.Degeneracy)
{
return;
}
local_elt = vector.GetElement(loc.Row);
}
if (local_elt == null)
{
return;
}
var parent_elt = Parent.Solver.GetElement(row.Global);
_elements.Add(new Bridge <Element <T> >(local_elt, parent_elt));
}
private void Count(ISparseMatrix <T> matrix, ISparseVector <T> rhs, int step, int max)
{
ISparseMatrixElement <T> element;
// Get the first element in the vector
var rhsElement = rhs.GetFirstInVector();
// Generate Markowitz row count
for (var i = max; i >= step; i--)
{
// Set count to -1 initially to remove count due to pivot element
var count = -1;
element = matrix.GetFirstInRow(i);
while (element != null && element.Column < step)
{
element = element.Right;
}
while (element != null) // We want to count the elements outside the limit as well
{
count++;
element = element.Right;
}
// Include elements on the Rhs vector
while (rhsElement != null && rhsElement.Index < step)
{
rhsElement = rhsElement.Below;
}
if (rhsElement != null && rhsElement.Index == i)
{
count++;
}
_markowitzRow[i] = Math.Min(count, _maxMarkowitzCount);
}
// Generate Markowitz column count
for (var i = step; i <= max; i++)
{
// Set count to -1 initially to remove count due to pivot element
var count = -1;
element = matrix.GetFirstInColumn(i);
while (element != null && element.Row < step)
{
element = element.Below;
}
while (element != null)
{
count++;
element = element.Below;
}
_markowitzColumn[i] = Math.Min(count, _maxMarkowitzCount);
}
}
/// <summary>
/// MPI-parallel 2-norm
/// </summary>
static public double drnm2 <TX>(int N, TX x, int incx, MPI_Comm comm) where TX : IList <double>
{
double locRes = 0;
double[] dx = x as double[];
if (dx != null)
{
// double[] - implementation
locRes = BLAS.dnrm2(N, dx, incx);
locRes = locRes * locRes;
}
else
{
ISparseVector <double> spx = x as ISparseVector <double>;
if (spx != null)
{
// sparse implementation
foreach (var entry in spx.SparseStruct)
{
int m = entry.Key % incx;
if (m != 0)
{
// entry is skipped by x-increment
continue;
}
double xi = entry.Value;
locRes += xi * xi;
}
}
else
{
// default implementation
for (int n = 0; n < N; n++)
{
double xi = x[n * incx];
locRes += xi * xi;
}
}
}
double globRes = double.NaN;
unsafe {
csMPI.Raw.Allreduce((IntPtr)(&locRes), (IntPtr)(&globRes), 1, csMPI.Raw._DATATYPE.DOUBLE, csMPI.Raw._OP.SUM, comm);
}
return(Math.Sqrt(globRes));
}
/// <summary>
/// Setup the pivot strategy.
/// </summary>
/// <param name="matrix">The matrix.</param>
/// <param name="rhs">The right-hand side vector.</param>
/// <param name="eliminationStep">The current elimination step.</param>
/// <param name="max">The maximum row/column index.</param>
/// <exception cref="ArgumentNullException">
/// Thrown if <paramref name="matrix"/> or <paramref name="rhs"/> is <c>null</c>.
/// </exception>
public void Setup(ISparseMatrix <T> matrix, ISparseVector <T> rhs, int eliminationStep, int max)
{
matrix.ThrowIfNull(nameof(matrix));
rhs.ThrowIfNull(nameof(rhs));
// Initialize Markowitz row, column and product vectors if necessary
if (_markowitzRow == null || _markowitzRow.Length != matrix.Size + 1)
{
Initialize(matrix);
}
Count(matrix, rhs, eliminationStep, max);
Products(eliminationStep, max);
}
/// <summary>
/// blas dscal: <paramref name="X"/> = <paramref name="X"/>*<paramref name="alpha"/>;
/// </summary>
static public void dscal <T>(int N, double alpha, T X, int incx) where T : IList <double>
{
ISparseVector <double> spx = X as ISparseVector <double>;
double[] arx = X as double[];
if (arx != null)
{
// double - array -> use BLAS
// ++++++++++++++++++++++++++
BLAS.dscal(N, alpha, arx, incx);
return;
}
if (spx != null)
{
// sparce vector -> compute only nonzero entries
// +++++++++++++++++++++++++++++++++++++++++++++
int[] idx = new int[spx.NonZeros];
spx.SparseStruct.Keys.CopyTo(idx, 0);
foreach (int i in idx)
{
int m = i % incx;
if (m != 0)
{
// entry is skipped by x-increment
continue;
}
spx[i] *= alpha;
}
return;
}
{
// reference version
// +++++++++++++++++
for (int i = 0; i < N; i += incx)
{
X[i] *= alpha;
}
}
}
/// <summary>
/// MPI - parallel scalar product
/// </summary>
static public double ddot <TX, TY>(int N, TX x, int incx, TY y, int incy, MPI.Wrappers.MPI_Comm comm)
where TX : IList <double>
where TY : IList <double>
{
if (incx * x.Count < N)
{
throw new ArgumentException("vector too short.", "x");
}
if (incy * y.Count < N)
{
throw new ArgumentException("vector too short.", "y");
}
double locRes = 0;
double[] dx = x as double[];
double[] dy = y as double[];
if (dx != null && dy != null)
{
// use dnese BLAS
locRes = BLAS.ddot(N, dx, incx, dy, incy);
}
else
{
ISparseVector <double> spx = x as ISparseVector <double>;
ISparseVector <double> spy = y as ISparseVector <double>;
IList <double> _y = y;
if (spy != null)
{
if (spx == null || spy.Sparsity < spx.Sparsity)
{
// y is sparser than x, use y !
spx = spy;
spy = null;
_y = x;
x = default(TX);
y = default(TY);
int buffy = incx;
incx = incy;
incy = buffy;
}
}
if (spx != null)
{
// sparse implementation
foreach (var entry in spx.SparseStruct)
{
int m = entry.Key % incx;
if (m != 0)
{
// entry is skipped by x-increment
continue;
}
int n = entry.Key / incx;
locRes += entry.Value * _y[n * incy];
}
}
else
{
// default IList<double> - implementation
for (int n = 0; n < N; n++)
{
locRes += x[n * incx] * y[n * incy];
}
}
}
double globRes = double.NaN;
unsafe {
csMPI.Raw.Allreduce((IntPtr)(&locRes), (IntPtr)(&globRes), 1, csMPI.Raw._DATATYPE.DOUBLE, csMPI.Raw._OP.SUM, comm);
}
return(globRes);
}
/// <summary>
/// blas daxpy: <paramref name="Y"/> = <paramref name="Y"/> + <paramref name="alpha"/>*<paramref name="X"/>;
/// </summary>
static public void daxpy <TX, TY>(int N,
double alpha, TX X, int INCX,
TY Y, int INCY)
where TX : IList <double>
where TY : IList <double>
{
if (object.ReferenceEquals(X, Y))
{
// while formally there is no problem that this should work, it seems much more likely
// that it's a bug.
throw new ArgumentException("Illegal use: reference-equality of input vectors -- this might be a mis-use instead of intention.");
}
{
// sparse vector branch
// ++++++++++++++++++++
ISparseVector <double> spx = X as ISparseVector <double>;
if (spx != null)
{
foreach (var entry in spx.SparseStruct)
{
int m = entry.Key % INCX;
if (m != 0)
{
// entry is skipped by x-increment
continue;
}
int n = entry.Key / INCX;
double xi = entry.Value;
Y[n * INCY] += xi * alpha;
}
return;
}
}
{
// both arrays-branch -> use BLAS
// ++++++++++++++++++++++++++++++
double[] _XasDouble = X as double[];
double[] _YasDouble = Y as double[];
if (_XasDouble != null && _YasDouble != null)
{
BLAS.daxpy(N, alpha, _XasDouble, INCX, _YasDouble, INCY);
return;
}
}
{
// default branch
// ++++++++++++++
for (int n = 0; n < N; n++)
{
Y[n * INCY] += X[n * INCX] * alpha;
}
return;
}
}
/// <summary>
/// Move the pivot to the diagonal for this elimination step.
/// </summary>
/// <param name="matrix">The matrix.</param>
/// <param name="rhs">The right-hand side vector.</param>
/// <param name="pivot">The pivot element.</param>
/// <param name="eliminationStep">The elimination step.</param>
/// <remarks>
/// This is done by swapping the rows and columns of the diagonal and that of the pivot.
/// </remarks>
/// <exception cref="ArgumentNullException">
/// Thrown if <paramref name="matrix"/>, <paramref name="rhs"/> or <paramref name="pivot"/> is <c>null</c>.
/// </exception>
public void MovePivot(ISparseMatrix <T> matrix, ISparseVector <T> rhs, ISparseMatrixElement <T> pivot, int eliminationStep)
{
matrix.ThrowIfNull(nameof(matrix));
rhs.ThrowIfNull(nameof(rhs));
pivot.ThrowIfNull(nameof(pivot));
// If we haven't setup, just skip
if (_markowitzProduct == null)
{
return;
}
int oldProduct;
var row = pivot.Row;
var col = pivot.Column;
// If the pivot is a singleton, then we just consumed it
if (_markowitzProduct[row] == 0 || _markowitzProduct[col] == 0)
{
Singletons--;
}
// Exchange rows
if (row != eliminationStep)
{
// Swap row Markowitz numbers
var tmp = _markowitzRow[row];
_markowitzRow[row] = _markowitzRow[eliminationStep];
_markowitzRow[eliminationStep] = tmp;
// Update the Markowitz product
oldProduct = _markowitzProduct[row];
_markowitzProduct[row] = _markowitzRow[row] * _markowitzColumn[row];
if (oldProduct == 0)
{
if (_markowitzProduct[row] != 0)
{
Singletons--;
}
}
else
{
if (_markowitzProduct[row] == 0)
{
Singletons++;
}
}
}
// Exchange columns
if (col != eliminationStep)
{
// Swap column Markowitz numbers
var tmp = _markowitzColumn[col];
_markowitzColumn[col] = _markowitzColumn[eliminationStep];
_markowitzColumn[eliminationStep] = tmp;
// Update the Markowitz product
oldProduct = _markowitzProduct[col];
_markowitzProduct[col] = _markowitzRow[col] * _markowitzColumn[col];
if (oldProduct == 0)
{
if (_markowitzProduct[col] != 0)
{
Singletons--;
}
}
else
{
if (_markowitzProduct[col] == 0)
{
Singletons++;
}
}
}
// Also update the moved pivot
oldProduct = _markowitzProduct[eliminationStep];
_markowitzProduct[eliminationStep] = _markowitzRow[eliminationStep] * _markowitzColumn[eliminationStep];
if (oldProduct == 0)
{
if (_markowitzProduct[eliminationStep] != 0)
{
Singletons--;
}
}
else
{
if (_markowitzProduct[eliminationStep] == 0)
{
Singletons++;
}
}
}