/// <summary>
/// Linear algebraic matrix-matrix multiplication; <tt>C = alpha * A x B + beta*C</tt>.
/// </summary>
/// <param name="b">
/// The econd source matrix.
/// </param>
/// <param name="c">
/// The matrix where results are to be stored. Set this parameter to <tt>null</tt> to indicate that a new result matrix shall be constructed.
/// </param>
/// <param name="alpha">
/// The alpha.
/// </param>
/// <param name="beta">
/// The beta.
/// </param>
/// <param name="transposeA">
/// Whether A must be transposed.
/// </param>
/// <param name="transposeB">
/// Whether B must be transposed.
/// </param>
/// <returns>
/// C (for convenience only).
/// </returns>
/// <exception cref="ArgumentOutOfRangeException">
/// If <tt>B.rows() != A.columns()</tt>.
/// </exception>
/// <exception cref="ArgumentException">
/// If <tt>C.rows() != A.rows() || C.columns() != B.columns()</tt>.
/// </exception>
/// <exception cref="ArithmeticException">
/// If <tt>A == C || B == C</tt>.
/// </exception>
public override DoubleMatrix2D ZMult(DoubleMatrix2D b, DoubleMatrix2D c, double alpha, double beta, bool transposeA, bool transposeB)
{
// overriden for performance only
if (transposeA)
{
return(ViewDice().ZMult(b, c, alpha, beta, false, transposeB));
}
if (b is SparseDoubleMatrix2D)
{
// exploit quick sparse mult
// A*B = (B' * A')'
if (c == null)
{
return(b.ZMult(this, null, alpha, beta, !transposeB, true).ViewDice());
}
b.ZMult(this, c.ViewDice(), alpha, beta, !transposeB, true);
return(c);
}
if (transposeB)
{
return(ZMult(b.ViewDice(), c, alpha, beta, false, false));
}
int m = Rows;
int n = Columns;
int p = b.Columns;
if (c == null)
{
c = new DenseDoubleMatrix2D(m, p);
}
if (!(c is DenseDoubleMatrix2D))
{
return(base.ZMult(b, c, alpha, beta, false, false));
}
if (b.Rows != n)
{
throw new ArgumentOutOfRangeException("b", "Matrix2D inner dimensions must agree:" + this + ", " + b);
}
if (c.Rows != m || c.Columns != p)
{
throw new ArgumentException("Incompatible result matrix: " + this + ", " + b + ", " + c);
}
if (this == c || b == c)
{
throw new ArgumentException("Matrices must not be identical");
}
var bb = (DenseDoubleMatrix2D)b;
var cc = (DenseDoubleMatrix2D)c;
double[] aElems = Elements;
double[] bElems = bb.Elements;
double[] cElems = cc.Elements;
if (aElems == null || bElems == null || cElems == null)
{
throw new ApplicationException();
}
int cA = ColumnStride;
int cB = bb.ColumnStride;
int cC = cc.ColumnStride;
int rA = RowStride;
int rB = bb.RowStride;
int rC = cc.RowStride;
/*
* A is blocked to hide memory latency
* xxxxxxx B
* xxxxxxx
* xxxxxxx
* A
* xxx xxxxxxx C
* xxx xxxxxxx
* --- -------
* xxx xxxxxxx
* xxx xxxxxxx
* --- -------
* xxx xxxxxxx
*/
const int BLOCK_SIZE = 30000;
int m_optimal = (BLOCK_SIZE - n) / (n + 1);
if (m_optimal <= 0)
{
m_optimal = 1;
}
int blocks = m / m_optimal;
int rr = 0;
if (m % m_optimal != 0)
{
blocks++;
}
for (; --blocks >= 0;)
{
int jB = bb.Index(0, 0);
int indexA = Index(rr, 0);
int jC = cc.Index(rr, 0);
rr += m_optimal;
if (blocks == 0)
{
m_optimal += m - rr;
}
for (int j = p; --j >= 0;)
{
int iA = indexA;
int iC = jC;
for (int i = m_optimal; --i >= 0;)
{
int kA = iA;
int kB = jB;
double s = 0;
/*
* // not unrolled:
* for (int k = n; --k >= 0;) {
* //s += getQuick(i,k) * B.getQuick(k,j);
* s += AElems[kA] * BElems[kB];
* kB += rB;
* kA += cA;
* }
*/
// loop unrolled
kA -= cA;
kB -= rB;
for (int k = n % 4; --k >= 0;)
{
s += aElems[kA += cA] * bElems[kB += rB];
}
for (int k = n / 4; --k >= 0;)
{
s += (aElems[kA += cA] * bElems[kB += rB]) +
(aElems[kA += cA] * bElems[kB += rB]) +
(aElems[kA += cA] * bElems[kB += rB]) +
(aElems[kA += cA] * bElems[kB += rB]);
}
cElems[iC] = (alpha * s) + (beta * cElems[iC]);
iA += rA;
iC += rC;
}
jB += cB;
jC += cC;
}
}
return(c);
}
public override DoubleMatrix2D ZMult(DoubleMatrix2D B, DoubleMatrix2D C, double alpha, double beta, Boolean transposeA, Boolean transposeB)
{
if (transposeB)
{
B = B.ViewDice();
}
int m = Rows;
int n = Columns;
if (transposeA)
{
m = Columns;
n = Rows;
}
int p = B.Columns;
Boolean ignore = (C == null);
if (C == null)
{
C = new DenseDoubleMatrix2D(m, p);
}
if (B.Rows != n)
{
throw new ArgumentException("Matrix2D inner dimensions must agree:" + ToStringShort() + ", " + (transposeB ? B.ViewDice() : B).ToStringShort());
}
if (C.Rows != m || C.Columns != p)
{
throw new ArgumentException("Incompatibel result matrix: " + ToStringShort() + ", " + (transposeB ? B.ViewDice() : B).ToStringShort() + ", " + C.ToStringShort());
}
if (this == C || B == C)
{
throw new ArgumentException("Matrices must not be identical");
}
if (!ignore)
{
C.Assign(F1.Mult(beta));
}
// cache views
DoubleMatrix1D[] Brows = new DoubleMatrix1D[n];
for (int i = n; --i >= 0;)
{
Brows[i] = B.ViewRow(i);
}
DoubleMatrix1D[] Crows = new DoubleMatrix1D[m];
for (int i = m; --i >= 0;)
{
Crows[i] = C.ViewRow(i);
}
ForEachNonZero(
new Cern.Colt.Function.IntIntDoubleFunction((i, j, value) =>
{
var fun = F2.PlusMult(value * alpha);
//fun.multiplicator = value * alpha;
if (!transposeA)
{
Crows[i].Assign(Brows[j], fun);
}
else
{
Crows[j].Assign(Brows[i], fun);
}
return(value);
}
));
return(C);
}
public override DoubleMatrix2D ZMult(DoubleMatrix2D B, DoubleMatrix2D C, double alpha, double beta, Boolean transposeA, Boolean transposeB)
{
if (transposeB)
{
B = B.ViewDice();
}
int m = Rows;
int n = Columns;
if (transposeA)
{
m = Columns;
n = Rows;
}
int p = B.Columns;
Boolean ignore = (C == null);
if (C == null)
{
C = new DenseDoubleMatrix2D(m, p);
}
if (B.Rows != n)
{
throw new ArgumentException(String.Format(Cern.LocalizedResources.Instance().Exception_Matrix2DInnerDimensionMustAgree, ToStringShort(), (transposeB ? B.ViewDice() : B).ToStringShort()));
}
if (C.Rows != m || C.Columns != p)
{
throw new ArgumentException(String.Format(Cern.LocalizedResources.Instance().Exception_IncompatibleResultMatrix, ToStringShort(), (transposeB ? B.ViewDice() : B).ToStringShort(), C.ToStringShort()));
}
if (this == C || B == C)
{
throw new ArgumentException(Cern.LocalizedResources.Instance().Exception_MatricesMustNotBeIdentical);
}
if (!ignore)
{
C.Assign(F1.Mult(beta));
}
// cache views
DoubleMatrix1D[] Brows = new DoubleMatrix1D[n];
for (int i = n; --i >= 0;)
{
Brows[i] = B.ViewRow(i);
}
DoubleMatrix1D[] Crows = new DoubleMatrix1D[m];
for (int i = m; --i >= 0;)
{
Crows[i] = C.ViewRow(i);
}
ForEachNonZero(
new Cern.Colt.Function.IntIntDoubleFunction((i, j, value) =>
{
var fun = F2.PlusMult(value * alpha);
//fun.multiplicator = value * alpha;
if (!transposeA)
{
Crows[i].Assign(Brows[j], fun);
}
else
{
Crows[j].Assign(Brows[i], fun);
}
return(value);
}
));
return(C);
}
public override DoubleMatrix2D ZMult(DoubleMatrix2D B, DoubleMatrix2D C, double alpha, double beta, Boolean transposeA, Boolean transposeB)
{
if (transposeB)
{
B = B.ViewDice();
}
int m = Rows;
int n = Columns;
if (transposeA)
{
m = Columns;
n = Rows;
}
int p = B.Columns;
Boolean ignore = (C == null);
if (C == null)
{
C = new DenseDoubleMatrix2D(m, p);
}
if (B.Rows != n)
{
throw new ArgumentException(String.Format(Cern.LocalizedResources.Instance().Exception_Matrix2DInnerDimensionMustAgree, ToStringShort(), (transposeB ? B.ViewDice() : B).ToStringShort()));
}
if (C.Rows != m || C.Columns != p)
{
throw new ArgumentException(String.Format(Cern.LocalizedResources.Instance().Exception_IncompatibleResultMatrix, ToStringShort(), (transposeB ? B.ViewDice() : B).ToStringShort(), C.ToStringShort()));
}
if (this == C || B == C)
{
throw new ArgumentException(Cern.LocalizedResources.Instance().Exception_MatricesMustNotBeIdentical);
}
if (!ignore)
{
C.Assign(F1.Mult(beta));
}
// cache views
DoubleMatrix1D[] Brows = new DoubleMatrix1D[n];
for (int i = n; --i >= 0;)
{
Brows[i] = B.ViewRow(i);
}
DoubleMatrix1D[] Crows = new DoubleMatrix1D[m];
for (int i = m; --i >= 0;)
{
Crows[i] = C.ViewRow(i);
}
int[] idx = Indexes.ToArray();
double[] vals = Values.ToArray();
for (int i = Starts.Length - 1; --i >= 0;)
{
int low = Starts[i];
for (int k = Starts[i + 1]; --k >= low;)
{
int j = idx[k];
var fun = F2.PlusMult(vals[k] * alpha);
//fun.Multiplicator = vals[k] * alpha;
if (!transposeA)
{
Crows[i].Assign(Brows[j], fun);
}
else
{
Crows[j].Assign(Brows[i], fun);
}
}
}
return(C);
}