public virtual DoubleMatrix1D Assign(Cern.Jet.Math.Mult mult)
{
for (int i = Size; --i >= 0;)
{
this[i] = mult.Apply(this[i]);
}
return(this);
}
public void Solve(DoubleMatrix2D B)
{
int CUT_OFF = 10;
//algebra.property().checkRectangular(LU);
int m = M;
int n = N;
if (B.Rows != m)
{
throw new ArgumentException("Matrix row dimensions must agree.");
}
if (!this.IsNonsingular)
{
throw new ArgumentException("Matrix is singular.");
}
// right hand side with pivoting
// Matrix Xmat = B.getMatrix(piv,0,nx-1);
if (this.work1 == null || this.work1.Length < m)
{
this.work1 = new int[m];
}
//if (this.work2 == null || this.work2.Length < m) this.work2 = new int[m];
Algebra.PermuteRows(B, this.piv, this.work1);
if (m * n == 0)
{
return; // nothing to do
}
int nx = B.Columns;
//precompute and cache some views to avoid regenerating them time and again
DoubleMatrix1D[] Brows = new DoubleMatrix1D[n];
for (int k = 0; k < n; k++)
{
Brows[k] = B.ViewRow(k);
}
// transformations
Cern.Jet.Math.Mult div = Cern.Jet.Math.Mult.Div(0);
Cern.Jet.Math.PlusMult minusMult = Cern.Jet.Math.PlusMult.MinusMult(0);
IntArrayList nonZeroIndexes = new IntArrayList(); // sparsity
DoubleMatrix1D Browk = Cern.Colt.Matrix.DoubleFactory1D.Dense.Make(nx); // blocked row k
// Solve L*Y = B(piv,:)
for (int k = 0; k < n; k++)
{
// blocking (make copy of k-th row to localize references)
Browk.Assign(Brows[k]);
// sparsity detection
int maxCardinality = nx / CUT_OFF; // == heuristic depending on speedup
Browk.GetNonZeros(nonZeroIndexes, null, maxCardinality);
int cardinality = nonZeroIndexes.Count;
Boolean sparse = (cardinality < maxCardinality);
for (int i = k + 1; i < n; i++)
{
//for (int j = 0; j < nx; j++) B[i][j] -= B[k][j]*LU[i][k];
//for (int j = 0; j < nx; j++) B.set(i,j, B.Get(i,j) - B.Get(k,j)*LU.Get(i,k));
minusMult.Multiplicator = -LU[i, k];
if (minusMult.Multiplicator != 0)
{
if (sparse)
{
Brows[i].Assign(Browk, minusMult, nonZeroIndexes);
}
else
{
Brows[i].Assign(Browk, minusMult);
}
}
}
}
// Solve U*B = Y;
for (int k = n - 1; k >= 0; k--)
{
// for (int j = 0; j < nx; j++) B[k][j] /= LU[k][k];
// for (int j = 0; j < nx; j++) B.set(k,j, B.Get(k,j) / LU.Get(k,k));
div.Multiplicator = 1 / LU[k, k];
Brows[k].Assign(div);
// blocking
if (Browk == null)
{
Browk = Cern.Colt.Matrix.DoubleFactory1D.Dense.Make(B.Columns);
}
Browk.Assign(Brows[k]);
// sparsity detection
int maxCardinality = nx / CUT_OFF; // == heuristic depending on speedup
Browk.GetNonZeros(nonZeroIndexes, null, maxCardinality);
int cardinality = nonZeroIndexes.Count;
Boolean sparse = (cardinality < maxCardinality);
//Browk.GetNonZeros(nonZeroIndexes,null);
//Boolean sparse = nonZeroIndexes.Count < nx/10;
for (int i = 0; i < k; i++)
{
// for (int j = 0; j < nx; j++) B[i][j] -= B[k][j]*LU[i][k];
// for (int j = 0; j < nx; j++) B.set(i,j, B.Get(i,j) - B.Get(k,j)*LU.Get(i,k));
minusMult.Multiplicator = -LU[i, k];
if (minusMult.Multiplicator != 0)
{
if (sparse)
{
Brows[i].Assign(Browk, minusMult, nonZeroIndexes);
}
else
{
Brows[i].Assign(Browk, minusMult);
}
}
}
}
}
public void Decompose(DoubleMatrix2D A)
{
int CUT_OFF = 10;
// setup
LU = A;
int m = A.Rows;
int n = A.Columns;
// setup pivot vector
if (this.piv == null || this.piv.Length != m)
{
this.piv = new int[m];
}
for (int i = m; --i >= 0;)
{
piv[i] = i;
}
pivsign = 1;
if (m * n == 0)
{
LU = LU;
return; // nothing to do
}
//precompute and cache some views to avoid regenerating them time and again
DoubleMatrix1D[] LUrows = new DoubleMatrix1D[m];
for (int i = 0; i < m; i++)
{
LUrows[i] = LU.ViewRow(i);
}
IntArrayList nonZeroIndexes = new IntArrayList(); // sparsity
DoubleMatrix1D LUcolj = LU.ViewColumn(0).Like(); // blocked column j
Cern.Jet.Math.Mult multFunction = Cern.Jet.Math.Mult.CreateInstance(0);
// Outer loop.
for (int j = 0; j < n; j++)
{
// blocking (make copy of j-th column to localize references)
LUcolj.Assign(LU.ViewColumn(j));
// sparsity detection
int maxCardinality = m / CUT_OFF; // == heuristic depending on speedup
LUcolj.GetNonZeros(nonZeroIndexes, null, maxCardinality);
int cardinality = nonZeroIndexes.Count;
Boolean sparse = (cardinality < maxCardinality);
// Apply previous transformations.
for (int i = 0; i < m; i++)
{
int kmax = System.Math.Min(i, j);
double s;
if (sparse)
{
s = LUrows[i].ZDotProduct(LUcolj, 0, kmax, nonZeroIndexes);
}
else
{
s = LUrows[i].ZDotProduct(LUcolj, 0, kmax);
}
double before = LUcolj[i];
double after = before - s;
LUcolj[i] = after; // LUcolj is a copy
LU[i, j] = after; // this is the original
if (sparse)
{
if (before == 0 && after != 0)
{ // nasty bug fixed!
int pos = nonZeroIndexes.BinarySearch(i);
pos = -pos - 1;
nonZeroIndexes.Insert(pos, i);
}
if (before != 0 && after == 0)
{
nonZeroIndexes.Remove(nonZeroIndexes.BinarySearch(i));
}
}
}
// Find pivot and exchange if necessary.
int p = j;
if (p < m)
{
double max = System.Math.Abs(LUcolj[p]);
for (int i = j + 1; i < m; i++)
{
double v = System.Math.Abs(LUcolj[i]);
if (v > max)
{
p = i;
max = v;
}
}
}
if (p != j)
{
LUrows[p].Swap(LUrows[j]);
int k = piv[p]; piv[p] = piv[j]; piv[j] = k;
pivsign = -pivsign;
}
// Compute multipliers.
double jj;
if (j < m && (jj = LU[j, j]) != 0.0)
{
multFunction.Multiplicator = 1 / jj;
LU.ViewColumn(j).ViewPart(j + 1, m - (j + 1)).Assign(multFunction);
}
}
LU = LU;
}
