Math.NET Numerics
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using System;
using System.Collections.Generic;
using BenchmarkDotNet.Attributes;
using MathNet.Numerics;
using MathNet.Numerics.LinearAlgebra;
using MathNet.Numerics.Providers.LinearAlgebra;
using MathNet.Numerics.Providers.LinearAlgebra.Mkl;
using MathNet.Numerics.Threading;
namespace Benchmark.LinearAlgebra
{
public class DenseMatrixProduct
{
readonly Dictionary<string, Matrix<double>> _data = new Dictionary<string, Matrix<double>>();
readonly ILinearAlgebraProvider _managed;
readonly ILinearAlgebraProvider _mkl;
readonly ILinearAlgebraProvider _experimental;
[Params(8, 64, 128)]
public int M { get; set; }
[Params(8, 64, 128)]
public int N { get; set; }
static string Key(int m, int n)
{
return $"{m}x{n}";
}
public DenseMatrixProduct()
{
foreach (var m in new[] {8, 64, 128})
foreach (var n in new[] {8, 64, 128})
{
var key = Key(m, n);
_data[key] = Matrix<double>.Build.Random(m, n);
}
Control.NativeProviderPath = @"..\..\..\..\out\MKL\Windows\";
_managed = new ManagedLinearAlgebraProvider();
_mkl = new MklLinearAlgebraProvider();
_experimental = new ExperimentalProvider();
_managed.InitializeVerify();
_mkl.InitializeVerify();
_experimental.InitializeVerify();
//Verify();
}
private void Verify()
{
M = 8;
N = 8;
var resultMkl = MathNet().ToRowArrays();
var resultManaged = MathNetManaged().ToRowArrays();
var resultExperimental = MathNetExperimental().ToRowArrays();
for (int i = 0; i < 8; i++)
{
for (int j = 0; j < 8; j++)
{
if (!resultMkl[i][j].AlmostEqual(resultManaged[i][j], 1e-14))
{
throw new Exception($"Managed [{i}][{j}] {resultManaged[i][j]} != {resultMkl[i][j]}");
}
if (!resultMkl[i][j].AlmostEqual(resultExperimental[i][j], 1e-14))
{
throw new Exception($"Experimental [{i}][{j}] {resultExperimental[i][j]} != {resultMkl[i][j]}");
}
}
}
}
[Setup]
public void Setup()
{
}
[Benchmark(OperationsPerInvoke = 1)]
public Matrix<double> MathNet()
{
Control.LinearAlgebraProvider = _mkl;
return _data[Key(M, N)].TransposeAndMultiply(_data[Key(M, N)]);
}
[Benchmark(OperationsPerInvoke = 1)]
public Matrix<double> MathNetManaged()
{
Control.LinearAlgebraProvider = _managed;
return _data[Key(M, N)].TransposeAndMultiply(_data[Key(M, N)]);
}
[Benchmark(OperationsPerInvoke = 1)]
public Matrix<double> MathNetExperimental()
{
Control.LinearAlgebraProvider = _experimental;
return _data[Key(M, N)].TransposeAndMultiply(_data[Key(M, N)]);
}
public class SafeProvider : ManagedLinearAlgebraProvider
{
public override void MatrixMultiply(
double[] x, int rowsX, int columnsX, double[] y, int rowsY, int columnsY, double[] result)
{
if (rowsX + columnsY <= Control.MaxDegreeOfParallelism)
{
for (int i = 0; i < rowsX; ++i)
{
for (int j = 0; j < columnsY; ++j)
{
var jrowsY = j*rowsY;
double sum = 0.0;
for (int k = 0; k < columnsX; ++k)
{
sum += x[k*rowsX + i]*y[jrowsY + k];
}
result[j*rowsX + i] = sum;
}
}
return;
}
double[] xdata;
if (ReferenceEquals(x, result))
{
xdata = (double[]) x.Clone();
}
else
{
xdata = x;
}
double[] ydata;
if (ReferenceEquals(y, result))
{
ydata = (double[]) y.Clone();
}
else
{
ydata = y;
}
Array.Clear(result, 0, result.Length);
CacheObliviousMatrixMultiply(xdata, 0, 0, ydata, 0, 0, result, 0, 0, rowsX, columnsY, columnsX, rowsX,
columnsY, columnsX, 0);
}
public override void MatrixMultiplyWithUpdate(
Transpose transposeA, Transpose transposeB, double alpha, double[] a, int rowsA, int columnsA,
double[] b,
int rowsB, int columnsB, double beta, double[] c)
{
if (transposeA == Transpose.DontTranspose && transposeB == Transpose.DontTranspose && alpha == 1.0 &&
beta == 0.0)
{
MatrixMultiply(a, rowsA, columnsA, b, rowsB, columnsB, c);
return;
}
base.MatrixMultiplyWithUpdate(transposeA, transposeB, alpha, a, rowsA, columnsA, b, rowsB, columnsB,
beta, c);
}
static void CacheObliviousMatrixMultiply(
double[] matrixA, int shiftArow, int shiftAcol, double[] matrixB, int shiftBrow, int shiftBcol,
double[] result, int shiftCrow, int shiftCcol, int m, int n, int k, int constM, int constN, int constK,
int level)
{
if (m + n <= Control.MaxDegreeOfParallelism)
{
for (var m1 = 0; m1 < m; m1++)
{
var matArowPos = m1 + shiftArow;
var matCrowPos = m1 + shiftCrow;
for (var n1 = 0; n1 < n; ++n1)
{
var boffset = ((n1 + shiftBcol)*constK) + shiftBrow;
double sum = 0;
for (var k1 = 0; k1 < k; ++k1)
{
sum += matrixA[((k1 + shiftAcol)*constM) + matArowPos]*matrixB[boffset + k1];
}
result[((n1 + shiftCcol)*constM) + matCrowPos] += sum;
}
}
return;
}
// divide and conquer
int m2 = m/2, n2 = n/2, k2 = k/2;
level++;
if (level <= 2)
{
CommonParallel.Invoke(
() =>
CacheObliviousMatrixMultiply(matrixA, shiftArow, shiftAcol, matrixB, shiftBrow, shiftBcol,
result, shiftCrow, shiftCcol, m2, n2, k2, constM, constN, constK, level),
() =>
CacheObliviousMatrixMultiply(matrixA, shiftArow, shiftAcol, matrixB, shiftBrow,
shiftBcol + n2,
result, shiftCrow, shiftCcol + n2, m2, n - n2, k2, constM, constN, constK, level),
() =>
CacheObliviousMatrixMultiply(matrixA, shiftArow + m2, shiftAcol, matrixB, shiftBrow,
shiftBcol,
result, shiftCrow + m2, shiftCcol, m - m2, n2, k2, constM, constN, constK, level),
() =>
CacheObliviousMatrixMultiply(matrixA, shiftArow + m2, shiftAcol, matrixB, shiftBrow,
shiftBcol + n2, result, shiftCrow + m2, shiftCcol + n2, m - m2, n - n2, k2, constM,
constN,
constK, level));
CommonParallel.Invoke(
() =>
CacheObliviousMatrixMultiply(matrixA, shiftArow, shiftAcol + k2, matrixB, shiftBrow + k2,
shiftBcol, result, shiftCrow, shiftCcol, m2, n2, k - k2, constM, constN, constK, level),
() =>
CacheObliviousMatrixMultiply(matrixA, shiftArow, shiftAcol + k2, matrixB, shiftBrow + k2,
shiftBcol + n2, result, shiftCrow, shiftCcol + n2, m2, n - n2, k - k2, constM, constN,
constK, level),
() =>
CacheObliviousMatrixMultiply(matrixA, shiftArow + m2, shiftAcol + k2, matrixB,
shiftBrow + k2,
shiftBcol, result, shiftCrow + m2, shiftCcol, m - m2, n2, k - k2, constM, constN, constK,
level),
() =>
CacheObliviousMatrixMultiply(matrixA, shiftArow + m2, shiftAcol + k2, matrixB,
shiftBrow + k2,
shiftBcol + n2, result, shiftCrow + m2, shiftCcol + n2, m - m2, n - n2, k - k2, constM,
constN, constK, level));
}
else
{
CacheObliviousMatrixMultiply(matrixA, shiftArow, shiftAcol, matrixB, shiftBrow, shiftBcol, result,
shiftCrow, shiftCcol, m2, n2, k2, constM, constN, constK, level);
CacheObliviousMatrixMultiply(matrixA, shiftArow, shiftAcol, matrixB, shiftBrow, shiftBcol + n2,
result,
shiftCrow, shiftCcol + n2, m2, n - n2, k2, constM, constN, constK, level);
CacheObliviousMatrixMultiply(matrixA, shiftArow, shiftAcol + k2, matrixB, shiftBrow + k2, shiftBcol,
result, shiftCrow, shiftCcol, m2, n2, k - k2, constM, constN, constK, level);
CacheObliviousMatrixMultiply(matrixA, shiftArow, shiftAcol + k2, matrixB, shiftBrow + k2,
shiftBcol + n2,
result, shiftCrow, shiftCcol + n2, m2, n - n2, k - k2, constM, constN, constK, level);
CacheObliviousMatrixMultiply(matrixA, shiftArow + m2, shiftAcol, matrixB, shiftBrow, shiftBcol,
result,
shiftCrow + m2, shiftCcol, m - m2, n2, k2, constM, constN, constK, level);
CacheObliviousMatrixMultiply(matrixA, shiftArow + m2, shiftAcol, matrixB, shiftBrow, shiftBcol + n2,
result, shiftCrow + m2, shiftCcol + n2, m - m2, n - n2, k2, constM, constN, constK, level);
CacheObliviousMatrixMultiply(matrixA, shiftArow + m2, shiftAcol + k2, matrixB, shiftBrow + k2,
shiftBcol,
result, shiftCrow + m2, shiftCcol, m - m2, n2, k - k2, constM, constN, constK, level);
CacheObliviousMatrixMultiply(matrixA, shiftArow + m2, shiftAcol + k2, matrixB, shiftBrow + k2,
shiftBcol + n2, result, shiftCrow + m2, shiftCcol + n2, m - m2, n - n2, k - k2, constM, constN,
constK, level);
}
}
}
public unsafe class UnsafeProvider : ManagedLinearAlgebraProvider
{
public override void MatrixMultiply(
double[] x, int rowsX, int columnsX, double[] y, int rowsY, int columnsY, double[] result)
{
if (rowsX + columnsY <= Control.ParallelizeOrder)
{
fixed (double* resultPtr = &result[0])
fixed (double* xPtr = &x[0])
fixed (double* yPtr = &y[0])
{
double* a = xPtr;
double* c = resultPtr;
for (int i = 0; i < rowsX; ++i)
{
double* b = yPtr;
double* cj = c;
for (int j = 0; j < columnsY; ++j)
{
double sum = 0.0;
for (int k = 0; k < columnsX; ++k)
{
sum += a[k*rowsX]*b[k];
}
*cj = sum;
cj += rowsX;
b += rowsY;
}
a++;
c++;
}
}
return;
}
double[] xdata;
if (ReferenceEquals(x, result))
{
xdata = (double[]) x.Clone();
}
else
{
xdata = x;
}
double[] ydata;
if (ReferenceEquals(y, result))
{
ydata = (double[]) y.Clone();
}
else
{
ydata = y;
}
Array.Clear(result, 0, result.Length);
CacheObliviousMatrixMultiply(xdata, 0, 0, ydata, 0, 0, result, 0, 0, rowsX, columnsY, columnsX, rowsX,
columnsY, columnsX, 0);
}
public override void MatrixMultiplyWithUpdate(
Transpose transposeA, Transpose transposeB, double alpha, double[] a, int rowsA, int columnsA,
double[] b,
int rowsB, int columnsB, double beta, double[] c)
{
if (transposeA == Transpose.DontTranspose && transposeB == Transpose.DontTranspose && alpha == 1.0 &&
beta == 0.0)
{
MatrixMultiply(a, rowsA, columnsA, b, rowsB, columnsB, c);
return;
}
base.MatrixMultiplyWithUpdate(transposeA, transposeB, alpha, a, rowsA, columnsA, b, rowsB, columnsB,
beta, c);
}
static void CacheObliviousMatrixMultiply(
double[] matrixA, int shiftArow, int shiftAcol, double[] matrixB, int shiftBrow, int shiftBcol,
double[] result, int shiftCrow, int shiftCcol, int m, int n, int k, int constM, int constN, int constK,
int level)
{
if (m + n <= Control.ParallelizeOrder)
{
fixed (double* resultPtr = &result[0])
fixed (double* aPtr = &matrixA[0])
fixed (double* bPtr = &matrixB[0])
{
double* a = aPtr + shiftArow;
double* c = resultPtr + shiftCrow;
for (var m1 = 0; m1 < m; m1++)
{
for (var n1 = 0; n1 < n; ++n1)
{
double* b = bPtr + (n1 + shiftBcol)*constK + shiftBrow;
double sum = 0;
for (var k1 = 0; k1 < k; ++k1)
{
sum += a[((k1 + shiftAcol)*constM)]*b[k1];
}
c[((n1 + shiftCcol)*constM)] += sum;
}
a++;
c++;
}
}
return;
}
// divide and conquer
int m2 = m/2, n2 = n/2, k2 = k/2;
level++;
if (level <= 2)
{
CommonParallel.Invoke(
() =>
CacheObliviousMatrixMultiply(matrixA, shiftArow, shiftAcol, matrixB, shiftBrow, shiftBcol,
result, shiftCrow, shiftCcol, m2, n2, k2, constM, constN, constK, level),
() =>
CacheObliviousMatrixMultiply(matrixA, shiftArow, shiftAcol, matrixB, shiftBrow,
shiftBcol + n2,
result, shiftCrow, shiftCcol + n2, m2, n - n2, k2, constM, constN, constK, level),
() =>
CacheObliviousMatrixMultiply(matrixA, shiftArow + m2, shiftAcol, matrixB, shiftBrow,
shiftBcol,
result, shiftCrow + m2, shiftCcol, m - m2, n2, k2, constM, constN, constK, level),
() =>
CacheObliviousMatrixMultiply(matrixA, shiftArow + m2, shiftAcol, matrixB, shiftBrow,
shiftBcol + n2, result, shiftCrow + m2, shiftCcol + n2, m - m2, n - n2, k2, constM,
constN,
constK, level));
CommonParallel.Invoke(
() =>
CacheObliviousMatrixMultiply(matrixA, shiftArow, shiftAcol + k2, matrixB, shiftBrow + k2,
shiftBcol, result, shiftCrow, shiftCcol, m2, n2, k - k2, constM, constN, constK, level),
() =>
CacheObliviousMatrixMultiply(matrixA, shiftArow, shiftAcol + k2, matrixB, shiftBrow + k2,
shiftBcol + n2, result, shiftCrow, shiftCcol + n2, m2, n - n2, k - k2, constM, constN,
constK, level),
() =>
CacheObliviousMatrixMultiply(matrixA, shiftArow + m2, shiftAcol + k2, matrixB,
shiftBrow + k2,
shiftBcol, result, shiftCrow + m2, shiftCcol, m - m2, n2, k - k2, constM, constN, constK,
level),
() =>
CacheObliviousMatrixMultiply(matrixA, shiftArow + m2, shiftAcol + k2, matrixB,
shiftBrow + k2,
shiftBcol + n2, result, shiftCrow + m2, shiftCcol + n2, m - m2, n - n2, k - k2, constM,
constN, constK, level));
}
else
{
CacheObliviousMatrixMultiply(matrixA, shiftArow, shiftAcol, matrixB, shiftBrow, shiftBcol, result,
shiftCrow, shiftCcol, m2, n2, k2, constM, constN, constK, level);
CacheObliviousMatrixMultiply(matrixA, shiftArow, shiftAcol, matrixB, shiftBrow, shiftBcol + n2,
result,
shiftCrow, shiftCcol + n2, m2, n - n2, k2, constM, constN, constK, level);
CacheObliviousMatrixMultiply(matrixA, shiftArow, shiftAcol + k2, matrixB, shiftBrow + k2, shiftBcol,
result, shiftCrow, shiftCcol, m2, n2, k - k2, constM, constN, constK, level);
CacheObliviousMatrixMultiply(matrixA, shiftArow, shiftAcol + k2, matrixB, shiftBrow + k2,
shiftBcol + n2,
result, shiftCrow, shiftCcol + n2, m2, n - n2, k - k2, constM, constN, constK, level);
CacheObliviousMatrixMultiply(matrixA, shiftArow + m2, shiftAcol, matrixB, shiftBrow, shiftBcol,
result,
shiftCrow + m2, shiftCcol, m - m2, n2, k2, constM, constN, constK, level);
CacheObliviousMatrixMultiply(matrixA, shiftArow + m2, shiftAcol, matrixB, shiftBrow, shiftBcol + n2,
result, shiftCrow + m2, shiftCcol + n2, m - m2, n - n2, k2, constM, constN, constK, level);
CacheObliviousMatrixMultiply(matrixA, shiftArow + m2, shiftAcol + k2, matrixB, shiftBrow + k2,
shiftBcol,
result, shiftCrow + m2, shiftCcol, m - m2, n2, k - k2, constM, constN, constK, level);
CacheObliviousMatrixMultiply(matrixA, shiftArow + m2, shiftAcol + k2, matrixB, shiftBrow + k2,
shiftBcol + n2, result, shiftCrow + m2, shiftCcol + n2, m - m2, n - n2, k - k2, constM, constN,
constK, level);
}
}
}
public class ExperimentalProvider : ManagedLinearAlgebraProvider
{
public override void MatrixMultiply(
double[] x, int rowsX, int columnsX, double[] y, int rowsY, int columnsY, double[] result)
{
MatrixMultiplyWithUpdate(Transpose.DontTranspose, Transpose.DontTranspose, 1.0, x, rowsX, columnsX, y,
rowsY,
columnsY, 0.0, result);
}
public override void MatrixMultiplyWithUpdate(
Transpose transposeA, Transpose transposeB, double alpha, double[] a, int rowsA, int columnsA,
double[] b,
int rowsB, int columnsB, double beta, double[] c)
{
if (a == null)
{
throw new ArgumentNullException(nameof(a));
}
if (b == null)
{
throw new ArgumentNullException(nameof(b));
}
if (c == null)
{
throw new ArgumentNullException(nameof(c));
}
if (transposeA != Transpose.DontTranspose)
{
var swap = rowsA;
rowsA = columnsA;
columnsA = swap;
}
if (transposeB != Transpose.DontTranspose)
{
var swap = rowsB;
rowsB = columnsB;
columnsB = swap;
}
if (columnsA != rowsB)
{
throw new ArgumentOutOfRangeException($"columnsA ({columnsA}) != rowsB ({rowsB})");
}
if (rowsA * columnsA != a.Length)
{
throw new ArgumentOutOfRangeException($"rowsA ({rowsA}) * columnsA ({columnsA}) != a.Length ({a.Length})");
}
if (rowsB * columnsB != b.Length)
{
throw new ArgumentOutOfRangeException($"rowsB ({rowsB}) * columnsB ({columnsB}) != b.Length ({b.Length})");
}
if (rowsA * columnsB != c.Length)
{
throw new ArgumentOutOfRangeException($"rowsA ({rowsA}) * columnsB ({columnsB}) != c.Length ({c.Length})");
}
// handle degenerate cases
if (beta == 0.0)
{
Array.Clear(c, 0, c.Length);
}
else if (beta != 1.0)
{
ScaleArray(beta, c, c);
}
if (alpha == 0.0)
{
return;
}
// Extract column arrays
var columnDataB = new double[columnsB][];
for (int i = 0; i < columnDataB.Length; i++)
{
columnDataB[i] = GetColumn(transposeB, i, rowsB, columnsB, b);
}
var shouldNotParallelize = rowsA + columnsB + columnsA < Control.ParallelizeOrder || Control.MaxDegreeOfParallelism < 2;
if (shouldNotParallelize)
{
var row = new double[columnsA];
for (int i = 0; i < rowsA; i++)
{
GetRow(transposeA, i, rowsA, columnsA, a, row);
for (int j = 0; j < columnsB; j++)
{
var col = columnDataB[j];
double sum = 0;
for (int ii = 0; ii < row.Length; ii++)
{
sum += row[ii] * col[ii];
}
c[j * rowsA + i] += alpha * sum;
}
}
}
else
{
CommonParallel.For(0, rowsA, 1, (u, v) =>
{
var row = new double[columnsA];
for (int i = u; i < v; i++)
{
GetRow(transposeA, i, rowsA, columnsA, a, row);
for (int j = 0; j < columnsB; j++)
{
var column = columnDataB[j];
double sum = 0;
for (int ii = 0; ii < row.Length; ii++)
{
sum += row[ii] * column[ii];
}
c[j * rowsA + i] += alpha * sum;
}
}
});
}
}
/// <summary>
/// Assumes that <paramref name="numRows"/> and <paramref name="numCols"/> have already been transposed.
/// </summary>
static void GetRow(Transpose transpose, int rowindx, int numRows, int numCols, double[] matrix, double[] row)
{
if (transpose == Transpose.DontTranspose)
{
for (int i = 0; i < numCols; i++)
{
row[i] = matrix[(i * numRows) + rowindx];
}
}
else
{
Array.Copy(matrix, rowindx * numCols, row, 0, numCols);
}
}
/// <summary>
/// Assumes that <paramref name="numRows"/> and <paramref name="numCols"/> have already been transposed.
/// </summary>
static double[] GetColumn(Transpose transpose, int colindx, int numRows, int numCols, double[] matrix)
{
var ret = new double[numRows];
if (transpose == Transpose.DontTranspose)
{
Array.Copy(matrix, colindx * numRows, ret, 0, numRows);
}
else
{
for (int i = 0; i < numRows; i++)
{
ret[i] = matrix[(i * numCols) + colindx];
}
}
return ret;
}
}
}
}