/// <summary>
/// Multiplies two matrices and updates another with the result. <c>c = alpha*op(a)*op(b) + beta*c</c>
/// </summary>
/// <param name="transposeA">How to transpose the <paramref name="a"/> matrix.</param>
/// <param name="transposeB">How to transpose the <paramref name="b"/> matrix.</param>
/// <param name="alpha">The value to scale <paramref name="a"/> matrix.</param>
/// <param name="a">The a matrix.</param>
/// <param name="rowsA">The number of rows in the <paramref name="a"/> matrix.</param>
/// <param name="columnsA">The number of columns in the <paramref name="a"/> matrix.</param>
/// <param name="b">The b matrix</param>
/// <param name="rowsB">The number of rows in the <paramref name="b"/> matrix.</param>
/// <param name="columnsB">The number of columns in the <paramref name="b"/> matrix.</param>
/// <param name="beta">The value to scale the <paramref name="c"/> matrix.</param>
/// <param name="c">The c matrix.</param>
public virtual void MatrixMultiplyWithUpdate(Transpose transposeA, Transpose transposeB, Complex alpha, Complex[] a, int rowsA, int columnsA, Complex[] b, int rowsB, int columnsB, Complex beta, Complex[] c)
{
int m; // The number of rows of matrix op(A) and of the matrix C.
int n; // The number of columns of matrix op(B) and of the matrix C.
int k; // The number of columns of matrix op(A) and the rows of the matrix op(B).
// First check some basic requirement on the parameters of the matrix multiplication.
if (a == null)
{
throw new ArgumentNullException("a");
}
if (b == null)
{
throw new ArgumentNullException("b");
}
if ((int) transposeA > 111 && (int) transposeB > 111)
{
if (rowsA != columnsB)
{
throw new ArgumentOutOfRangeException();
}
if (columnsA*rowsB != c.Length)
{
throw new ArgumentOutOfRangeException();
}
m = columnsA;
n = rowsB;
k = rowsA;
}
else if ((int) transposeA > 111)
{
if (rowsA != rowsB)
{
throw new ArgumentOutOfRangeException();
}
if (columnsA*columnsB != c.Length)
{
throw new ArgumentOutOfRangeException();
}
m = columnsA;
n = columnsB;
k = rowsA;
}
else if ((int) transposeB > 111)
{
if (columnsA != columnsB)
{
throw new ArgumentOutOfRangeException();
}
if (rowsA*rowsB != c.Length)
{
throw new ArgumentOutOfRangeException();
}
m = rowsA;
n = rowsB;
k = columnsA;
}
else
{
if (columnsA != rowsB)
{
throw new ArgumentOutOfRangeException();
}
if (rowsA*columnsB != c.Length)
{
throw new ArgumentOutOfRangeException();
}
m = rowsA;
n = columnsB;
k = columnsA;
}
if (alpha.IsZero() && beta.IsZero())
{
Array.Clear(c, 0, c.Length);
return;
}
// Check whether we will be overwriting any of our inputs and make copies if necessary.
// TODO - we can don't have to allocate a completely new matrix when x or y point to the same memory
// as result, we can do it on a row wise basis. We should investigate this.
Complex[] adata;
if (ReferenceEquals(a, c))
{
adata = (Complex[]) a.Clone();
}
else
{
adata = a;
}
Complex[] bdata;
if (ReferenceEquals(b, c))
{
bdata = (Complex[]) b.Clone();
}
else
{
bdata = b;
}
if (beta.IsZero())
{
Array.Clear(c, 0, c.Length);
}
else if (!beta.IsOne())
{
ScaleArray(beta, c, c);
}
if (alpha.IsZero())
{
return;
}
CacheObliviousMatrixMultiply(transposeA, transposeB, alpha, adata, 0, 0, bdata, 0, 0, c, 0, 0, m, n, k, m, n, k, true);
}
/// <summary>
/// Multiples two matrices. <c>result = x * y</c>
/// </summary>
/// <param name="x">The x matrix.</param>
/// <param name="rowsX">The number of rows in the x matrix.</param>
/// <param name="columnsX">The number of columns in the x matrix.</param>
/// <param name="y">The y matrix.</param>
/// <param name="rowsY">The number of rows in the y matrix.</param>
/// <param name="columnsY">The number of columns in the y matrix.</param>
/// <param name="result">Where to store the result of the multiplication.</param>
/// <remarks>This is a simplified version of the BLAS GEMM routine with alpha
/// set to 1.0 and beta set to 0.0, and x and y are not transposed.</remarks>
public virtual void MatrixMultiply(Complex[] x, int rowsX, int columnsX, Complex[] y, int rowsY, int columnsY, Complex[] result)
{
// First check some basic requirement on the parameters of the matrix multiplication.
if (x == null)
{
throw new ArgumentNullException("x");
}
if (y == null)
{
throw new ArgumentNullException("y");
}
if (result == null)
{
throw new ArgumentNullException("result");
}
if (rowsX*columnsX != x.Length)
{
throw new ArgumentException("x.Length != xRows * xColumns");
}
if (rowsY*columnsY != y.Length)
{
throw new ArgumentException("y.Length != yRows * yColumns");
}
if (columnsX != rowsY)
{
throw new ArgumentException("xColumns != yRows");
}
if (rowsX*columnsY != result.Length)
{
throw new ArgumentException("xRows * yColumns != result.Length");
}
// Check whether we will be overwriting any of our inputs and make copies if necessary.
// TODO - we can don't have to allocate a completely new matrix when x or y point to the same memory
// as result, we can do it on a row wise basis. We should investigate this.
Complex[] xdata;
if (ReferenceEquals(x, result))
{
xdata = (Complex[]) x.Clone();
}
else
{
xdata = x;
}
Complex[] ydata;
if (ReferenceEquals(y, result))
{
ydata = (Complex[]) y.Clone();
}
else
{
ydata = y;
}
Array.Clear(result, 0, result.Length);
CacheObliviousMatrixMultiply(Transpose.DontTranspose, Transpose.DontTranspose, Complex.One, xdata, 0, 0, ydata, 0, 0, result, 0, 0, rowsX, columnsY, columnsX, rowsX, columnsY, columnsX, true);
}
/// <summary>
/// Multiples two matrices. <c>result = x * y</c>
/// </summary>
/// <param name="x">The x matrix.</param>
/// <param name="xRows">The number of rows in the x matrix.</param>
/// <param name="xColumns">The number of columns in the x matrix.</param>
/// <param name="y">The y matrix.</param>
/// <param name="yRows">The number of rows in the y matrix.</param>
/// <param name="yColumns">The number of columns in the y matrix.</param>
/// <param name="result">Where to store the result of the multiplication.</param>
/// <remarks>This is a simplified version of the BLAS GEMM routine with alpha
/// set to 1.0 and beta set to 0.0, and x and y are not transposed.</remarks>
public void MatrixMultiply(Complex[] x, int xRows, int xColumns, Complex[] y, int yRows, int yColumns, Complex[] result)
{
// First check some basic requirement on the parameters of the matrix multiplication.
if (x == null)
{
throw new ArgumentNullException("x");
}
if (y == null)
{
throw new ArgumentNullException("y");
}
if (result == null)
{
throw new ArgumentNullException("result");
}
if (xRows * xColumns != x.Length)
{
throw new ArgumentException("x.Length != xRows * xColumns");
}
if (yRows * yColumns != y.Length)
{
throw new ArgumentException("y.Length != yRows * yColumns");
}
if (xColumns != yRows)
{
throw new ArgumentException("xColumns != yRows");
}
if (xRows * yColumns != result.Length)
{
throw new ArgumentException("xRows * yColumns != result.Length");
}
// Check whether we will be overwriting any of our inputs and make copies if necessary.
// TODO - we can don't have to allocate a completely new matrix when x or y point to the same memory
// as result, we can do it on a row wise basis. We should investigate this.
Complex[] xdata;
if (ReferenceEquals(x, result))
{
xdata = (Complex[]) x.Clone();
}
else
{
xdata = x;
}
Complex[] ydata;
if (ReferenceEquals(y, result))
{
ydata = (Complex[]) y.Clone();
}
else
{
ydata = y;
}
// Start the actual matrix multiplication.
// TODO - For small matrices we should get rid of the parallelism because of startup costs.
// Perhaps the following implementations would be a good one
// http://blog.feradz.com/2009/01/cache-efficient-matrix-multiplication/
MatrixMultiplyWithUpdate(Transpose.DontTranspose, Transpose.DontTranspose, Complex.One, x, xRows, xColumns, y, yRows, yColumns, Complex.Zero, result);
}
private ComplexMatrix(int rows, int columns, Complex[] entries)
{
this.rows = rows;
this.columns = columns;
this.entries = (Complex[])entries.Clone();
}
/// <summary>
/// Multiplies two matrices and updates another with the result. <c>c = alpha*op(a)*op(b) + beta*c</c>
/// </summary>
/// <param name="transposeA">How to transpose the <paramref name="a"/> matrix.</param>
/// <param name="transposeB">How to transpose the <paramref name="b"/> matrix.</param>
/// <param name="alpha">The value to scale <paramref name="a"/> matrix.</param>
/// <param name="a">The a matrix.</param>
/// <param name="aRows">The number of rows in the <paramref name="a"/> matrix.</param>
/// <param name="aColumns">The number of columns in the <paramref name="a"/> matrix.</param>
/// <param name="b">The b matrix</param>
/// <param name="bRows">The number of rows in the <paramref name="b"/> matrix.</param>
/// <param name="bColumns">The number of columns in the <paramref name="b"/> matrix.</param>
/// <param name="beta">The value to scale the <paramref name="c"/> matrix.</param>
/// <param name="c">The c matrix.</param>
public void MatrixMultiplyWithUpdate(Transpose transposeA, Transpose transposeB, Complex alpha, Complex[] a,
int aRows, int aColumns, Complex[] b, int bRows, int bColumns, Complex beta, Complex[] c)
{
// Choose nonsensical values for the number of rows and columns in c; fill them in depending
// on the operations on a and b.
int cRows = -1;
int cColumns = -1;
// First check some basic requirement on the parameters of the matrix multiplication.
if (a == null)
{
throw new ArgumentNullException("a");
}
if (b == null)
{
throw new ArgumentNullException("b");
}
if ((int)transposeA > 111 && (int)transposeB > 111)
{
if (aRows != bColumns)
{
throw new ArgumentOutOfRangeException();
}
if (aColumns * bRows != c.Length)
{
throw new ArgumentOutOfRangeException();
}
cRows = aColumns;
cColumns = bRows;
}
else if ((int)transposeA > 111)
{
if (aRows != bRows)
{
throw new ArgumentOutOfRangeException();
}
if (aColumns * bColumns != c.Length)
{
throw new ArgumentOutOfRangeException();
}
cRows = aColumns;
cColumns = bColumns;
}
else if ((int)transposeB > 111)
{
if (aColumns != bColumns)
{
throw new ArgumentOutOfRangeException();
}
if (aRows * bRows != c.Length)
{
throw new ArgumentOutOfRangeException();
}
cRows = aRows;
cColumns = bRows;
}
else
{
if (aColumns != bRows)
{
throw new ArgumentOutOfRangeException();
}
if (aRows * bColumns != c.Length)
{
throw new ArgumentOutOfRangeException();
}
cRows = aRows;
cColumns = bColumns;
}
if (alpha == 0.0 && beta == 0.0)
{
Array.Clear(c, 0, c.Length);
return;
}
// Check whether we will be overwriting any of our inputs and make copies if necessary.
// TODO - we can don't have to allocate a completely new matrix when x or y point to the same memory
// as result, we can do it on a row wise basis. We should investigate this.
Complex[] adata;
if (ReferenceEquals(a, c))
{
adata = (Complex[])a.Clone();
}
else
{
adata = a;
}
Complex[] bdata;
if (ReferenceEquals(b, c))
{
bdata = (Complex[])b.Clone();
}
else
{
bdata = b;
}
if (alpha == 1.0)
{
if (beta == 0.0)
{
if ((int)transposeA > 111 && (int)transposeB > 111)
{
Parallel.For(0, aColumns, j =>
{
int jIndex = j * cRows;
for (int i = 0; i != bRows; i++)
{
int iIndex = i * aRows;
Complex s = 0;
for (int l = 0; l != bColumns; l++)
{
s += adata[iIndex + l] * bdata[l * bRows + j];
}
c[jIndex + i] = s;
}
});
}
else if ((int)transposeA > 111)
{
Parallel.For(0, bColumns, j =>
{
int jcIndex = j * cRows;
int jbIndex = j * bRows;
for (int i = 0; i != aColumns; i++)
{
int iIndex = i * aRows;
Complex s = 0;
for (int l = 0; l != aRows; l++)
{
s += adata[iIndex + l] * bdata[jbIndex + l];
}
c[jcIndex + i] = s;
}
});
}
else if ((int)transposeB > 111)
{
Parallel.For(0, bRows, j =>
{
int jIndex = j * cRows;
for (int i = 0; i != aRows; i++)
{
Complex s = 0;
for (int l = 0; l != aColumns; l++)
{
s += adata[l * aRows + i] * bdata[l * bRows + j];
}
c[jIndex + i] = s;
}
});
}
else
{
Parallel.For(0, bColumns, j =>
{
int jcIndex = j * cRows;
int jbIndex = j * bRows;
for (int i = 0; i != aRows; i++)
{
Complex s = 0;
for (int l = 0; l != aColumns; l++)
{
s += adata[l * aRows + i] * bdata[jbIndex + l];
}
c[jcIndex + i] = s;
}
});
}
}
else
{
if ((int)transposeA > 111 && (int)transposeB > 111)
{
Parallel.For(0, aColumns, j =>
{
int jIndex = j * cRows;
for (int i = 0; i != bRows; i++)
{
int iIndex = i * aRows;
Complex s = 0;
for (int l = 0; l != bColumns; l++)
{
s += adata[iIndex + l] * bdata[l * bRows + j];
}
c[jIndex + i] = c[jIndex + i] * beta + s;
}
});
}
else if ((int)transposeA > 111)
{
Parallel.For(0, bColumns, j =>
{
int jcIndex = j * cRows;
int jbIndex = j * bRows;
for (int i = 0; i != aColumns; i++)
{
int iIndex = i * aRows;
Complex s = 0;
for (int l = 0; l != aRows; l++)
{
s += adata[iIndex + l] * bdata[jbIndex + l];
}
c[jcIndex + i] = s + c[jcIndex + i] * beta;
}
});
}
else if ((int)transposeB > 111)
{
Parallel.For(0, bRows, j =>
{
int jIndex = j * cRows;
for (int i = 0; i != aRows; i++)
{
Complex s = 0;
for (int l = 0; l != aColumns; l++)
{
s += adata[l * aRows + i] * bdata[l * bRows + j];
}
c[jIndex + i] = s + c[jIndex + i] * beta;
}
});
}
else
{
Parallel.For(0, bColumns, j =>
{
int jcIndex = j * cRows;
int jbIndex = j * bRows;
for (int i = 0; i != aRows; i++)
{
Complex s = 0;
for (int l = 0; l != aColumns; l++)
{
s += adata[l * aRows + i] * bdata[jbIndex + l];
}
c[jcIndex + i] = s + c[jcIndex + i] * beta;
}
});
}
}
}
else
{
if ((int)transposeA > 111 && (int)transposeB > 111)
{
Parallel.For(0, aColumns, j =>
{
int jIndex = j * cRows;
for (int i = 0; i != bRows; i++)
{
int iIndex = i * aRows;
Complex s = 0;
for (int l = 0; l != bColumns; l++)
{
s += adata[iIndex + l] * bdata[l * bRows + j];
}
c[jIndex + i] = c[jIndex + i] * beta + alpha * s;
}
});
}
else if ((int)transposeA > 111)
{
Parallel.For(0, bColumns, j =>
{
int jcIndex = j * cRows;
int jbIndex = j * bRows;
for (int i = 0; i != aColumns; i++)
{
int iIndex = i * aRows;
Complex s = 0;
for (int l = 0; l != aRows; l++)
{
s += adata[iIndex + l] * bdata[jbIndex + l];
}
c[jcIndex + i] = alpha * s + c[jcIndex + i] * beta;
}
});
}
else if ((int)transposeB > 111)
{
Parallel.For(0, bRows, j =>
{
int jIndex = j * cRows;
for (int i = 0; i != aRows; i++)
{
Complex s = 0;
for (int l = 0; l != aColumns; l++)
{
s += adata[l * aRows + i] * bdata[l * bRows + j];
}
c[jIndex + i] = alpha * s + c[jIndex + i] * beta;
}
});
}
else
{
Parallel.For(0, bColumns, j =>
{
int jcIndex = j * cRows;
int jbIndex = j * bRows;
for (int i = 0; i != aRows; i++)
{
Complex s = 0;
for (int l = 0; l != aColumns; l++)
{
s += adata[l * aRows + i] * bdata[jbIndex + l];
}
c[jcIndex + i] = alpha * s + c[jcIndex + i] * beta;
}
});
}
}
}