public static double Det(MatrixExpression a)
{
var m = a.Evaluate();
if (a is MatrixInput)
{
m = Copy(m);
}
var ipiv = Pool.Int.Rent(m.Rows);
ThrowHelper.Check(Lapack.getrf(Layout.ColMajor, m.Rows, m.Rows, m.Array, m.Rows, ipiv));
Pool.Int.Return(ipiv);
double r = m[0, 0];
for (int i = 1; i < m.Rows; i++)
{
r *= m[i, i];
}
m.Dispose();
return(-r);
}
private static void Main()
{
CompareTimeDot(10);
CompareTimeDot(100);
CompareTimeDot(100000);
CompareTimeLU();
void CompareTimeDot(int size)
{
var sw = new Stopwatch();
(var x, var y) = GenerateVector();
WriteLine($"Calc dot product by raw C# : size = {size}");
sw.Reset();
var res = 0.0;
for (var i = 0; i < LoopDot; i++)
{
sw.Start();
res = Dot(x, y);
sw.Stop();
}
WriteLine($"Result : {res}\tTime : {sw.Elapsed / (double) LoopDot}");
WriteLine($"Calc dot product by BLAS : size = {size}");
sw.Reset();
for (var i = 0; i < LoopDot; i++)
{
sw.Start();
res = Blas1.dot(size, x, 1, y, 1);
sw.Stop();
}
WriteLine($"Result : {res}\tTime : {sw.Elapsed / (double) LoopDot}\n");
(double[] x, double[] y) GenerateVector()
{
x = new double[size];
y = new double[size];
for (var i = 0; i < size; i++)
{
x[i] = 1.0;
y[i] = 1.0;
}
return(x, y);
}
}
void CompareTimeLU()
{
const int M = 49;
const int N = M * M;
const double h = 1.0 / (M + 1);
const double Heat = 4.0;
var aBase = new double[N * N];
var bBase = new double[N];
var ipiv = new int[N];
for (var i = 1; i <= M; i++)
{
for (var j = 1; j <= M; j++)
{
var k = (j - 1) * M + i - 1;
aBase[k * N + k] = 4.0 / (h * h);
if (i > 1)
{
var kl = k - 1;
aBase[kl * N + k] = -1.0 / (h * h);
}
if (i < M)
{
var kr = k + 1;
aBase[kr * N + k] = -1.0 / (h * h);
}
if (j > 1)
{
var kd = k - M;
aBase[kd * N + k] = -1.0 / (h * h);
}
if (j < M)
{
var ku = k + M;
aBase[ku * N + k] = -1.0 / (h * h);
}
bBase[k] = Heat;
}
}
var sw = new Stopwatch();
WriteLine("Calc Poisson eq by raw C#");
sw.Reset();
var res = new double[bBase.Length];
for (var i = 0; i < LoopLU; i++)
{
Blas1.copy(aBase.Length, aBase, 1, out var a, 1);
Blas1.copy(bBase.Length, bBase, 1, out var b, 1);
sw.Start();
Decomp(N, N, a, ipiv);
Solve(N, N, a, b, ipiv);
sw.Stop();
if (i == LoopLU - 1)
{
Blas1.copy(b.Length, b, 1, res, 1);
}
}
WriteLine($"Result : {res[((M + 1) / 2 - 1) * M + M + 1]}\tTime : {sw.Elapsed / (double) LoopLU}");
WriteLine("Calc Poisson eq by LAPACK");
sw.Reset();
for (var i = 0; i < LoopLU; i++)
{
Blas1.copy(aBase.Length, aBase, 1, out var a, 1);
Blas1.copy(bBase.Length, bBase, 1, out var b, 1);
sw.Start();
Lapack.getrf(LapackLayout.RowMajor, N, N, a, N, ipiv);
Lapack.getrs(LapackLayout.RowMajor, LapackTranspose.NoTrans, N, 1, a, N, ipiv, b, 1);
sw.Stop();
if (i == LoopLU - 1)
{
Blas1.copy(b.Length, b, 1, res, 1);
}
}
WriteLine($"Result : {res[((M + 1) / 2 - 1) * M + M + 1]}\tTime : {sw.Elapsed / (double) LoopLU}");
}
}
