public static void MultiplyTrafoTest0() // two summation indices (k,r)
{
foreach (int K in new int[] { 210 }) // test unrolling and standard path
{
int I = 120;
int M = 43;
MultidimensionalArray A = MultidimensionalArray.Create(I, K, 2 * M);
MultidimensionalArray B = MultidimensionalArray.Create(2 * M, K);;
Console.WriteLine("number of operands in A: " + A.Length);
Console.WriteLine("number of operands in B: " + B.Length);
int[] mTrafo = new int[M];
MultidimensionalArray ResTst1 = MultidimensionalArray.Create(I, M);
MultidimensionalArray ResTst2 = MultidimensionalArray.Create(I, M);
MultidimensionalArray ResChck = MultidimensionalArray.Create(I, M);
// fill operands with random values
Random rnd = new Random();
A.ApplyAll(x => rnd.NextDouble());
B.ApplyAll(x => rnd.NextDouble());
ResTst1.ApplyAll(x => rnd.NextDouble());
ResChck.Set(ResTst1);
ResTst2.Set(ResTst1);
for (int m = 0; m < M; m++)
{
mTrafo[m] = rnd.Next(2 * M);
//mTrafo[m] = m;
Debug.Assert(mTrafo[m] < 2 * M);
}
double alpha = 0.67;
double beta = 1.3;
var mp1 = MultidimensionalArray.MultiplyProgram.Compile("im", "ikT(m)", "T(m)k", true);
var mp2 = MultidimensionalArray.MultiplyProgram.Compile("im", "T(m)k", "ikT(m)", true);
// tensorized multiplication:
Stopwatch TenMult = new Stopwatch();
TenMult.Start();
ResTst1.Multiply(alpha, A, B, beta, ref mp1, mTrafo);
TenMult.Stop();
ResTst2.Multiply(alpha, B, A, beta, ref mp2, mTrafo);
Console.WriteLine("runtime of tensorized multiplication: " + TenMult.ElapsedMilliseconds + " millisec.");
// comparison code
Stopwatch RefMult = new Stopwatch();
RefMult.Start();
double errSum = 0;
for (int i = 0; i < I; i++)
{
for (int m = 0; m < M; m++)
{
int m_trf = mTrafo[m];
// summation:
double sum = 0;
for (int k = 0; k < K; k++)
{
sum += A[i, k, m_trf] * B[m_trf, k];
}
ResChck[i, m] = sum * alpha + ResChck[i, m] * beta;
errSum += Math.Abs(ResTst1[i, m] - ResChck[i, m]);
errSum += Math.Abs(ResTst2[i, m] - ResChck[i, m]);
}
}
RefMult.Stop();
Console.WriteLine("runtime of loop multiplication: " + RefMult.ElapsedMilliseconds + " millisec.");
Console.WriteLine("total error: " + errSum);
double thres = 1.0e-6;
Assert.IsTrue(errSum < thres);
}
}
public static void MultiplyTest3() // two summation indices (k,r)
{
foreach (int K in new int[] { 2, 21 }) // test unrolling and standard path
{
int I = 12;
int M = 43;
int N = 63;
int R = 21;
MultidimensionalArray A = MultidimensionalArray.Create(I, R, K, M);
MultidimensionalArray B = MultidimensionalArray.Create(I, K, N, R);
Console.WriteLine("number of operands in A: " + A.Length);
Console.WriteLine("number of operands in B: " + B.Length);
MultidimensionalArray ResTst1 = MultidimensionalArray.Create(I, M, N);
MultidimensionalArray ResTst2 = MultidimensionalArray.Create(I, M, N);
MultidimensionalArray ResChck = MultidimensionalArray.Create(I, M, N);
// fill operands with random values
Random rnd = new Random();
A.ApplyAll(x => rnd.NextDouble());
B.ApplyAll(x => rnd.NextDouble());
ResTst1.ApplyAll(x => rnd.NextDouble());
ResChck.Set(ResTst1);
ResTst2.Set(ResTst1);
double alpha = 0.67;
double beta = 1.3;
// tensorized multiplication:
Stopwatch TenMult = new Stopwatch();
TenMult.Start();
ResTst1.Multiply(alpha, A, B, beta, "imn", "irkm", "iknr");
TenMult.Stop();
ResTst2.Multiply(alpha, B, A, beta, "imn", "iknr", "irkm");
Console.WriteLine("runtime of tensorized multiplication: " + TenMult.ElapsedMilliseconds + " millisec.");
// comparison code
Stopwatch RefMult = new Stopwatch();
RefMult.Start();
double errSum = 0;
for (int i = 0; i < I; i++)
{
for (int n = 0; n < N; n++)
{
for (int m = 0; m < M; m++)
{
// summation:
double sum = 0;
for (int r = 0; r < R; r++)
{
for (int k = 0; k < K; k++)
{
sum += A[i, r, k, m] * B[i, k, n, r];
}
}
ResChck[i, m, n] = sum * alpha + ResChck[i, m, n] * beta;
errSum += Math.Abs(ResTst1[i, m, n] - ResChck[i, m, n]);
errSum += Math.Abs(ResTst2[i, m, n] - ResChck[i, m, n]);
}
}
}
RefMult.Stop();
Console.WriteLine("runtime of loop multiplication: " + RefMult.ElapsedMilliseconds + " millisec.");
Console.WriteLine("total error: " + errSum);
double thres = 1.0e-6;
Assert.IsTrue(errSum < thres);
}
}
