// reference:
// https://github.com/xianyi/OpenBLAS/blob/develop/reference/dlaswpf.f
/// <summary>
/// [dlaswp] Swaps rows on the matrix A.
/// </summary>
/// <typeparam name="T"></typeparam>
/// <param name="a"></param>
/// <param name="colstart"></param>
/// <param name="collength"></param>
/// <param name="ipiv"></param>
/// <remarks> The columns between <c>[colstart, colstart + collength)</c> </remarks>
public static void SwapRows <T>(MutableNdArray <T> a, int colstart, int collength, ReadOnlySpan <int> ipiv)
{
Guard.AssertArgumentRange(0 <= colstart, "0 <= colstart");
Guard.AssertArgumentRange(colstart + collength < a.Shape[1], "colstart + collength < a.Shape[1]");
if (a is RawNdArray <T> xa)
{
using var alloc = new AllocationSlim <T>(collength);
var tmp = alloc.Memory.Slice(0, collength);
var c = a.Shape[1];
for (var i = 0; i < ipiv.Length; ++i)
{
if (i == ipiv[i])
{
continue;
}
var row1 = xa.Entity.Buffer.Slice(c * ipiv[i] + colstart, collength);
var row2 = xa.Entity.Buffer.Slice(c * i + colstart, collength);
VectorOperation.Identity(row1, tmp);
VectorOperation.Identity(row2, row1);
VectorOperation.Identity(tmp, row2);
}
}
else
{
for (var i = 0; i < ipiv.Length; ++i)
{
if (i == ipiv[i])
{
continue;
}
for (var j = colstart; j < colstart + collength; ++j)
{
var tmp = a[i, j];
a[i, j] = a[ipiv[i], j];
a[ipiv[i], j] = tmp;
}
}
}
}
// reference:
// https://github.com/xianyi/OpenBLAS/blob/develop/reference/dtrsmf.f
/// <summary>
/// [dtrsm] Solves one of the matrix equations:
/// <list type="bullet">
/// <item>
/// <term><c>(side, transa) = (Left, None)</c></term>
/// <description><c>A * X = alpha * B</c></description>
/// </item>
/// <item>
/// <term><c>(side, transa) = (Right, None)</c></term>
/// <description><c>X * A = alpha * B</c></description>
/// </item>
/// </list>
/// </summary>
/// <typeparam name="T"></typeparam>
/// <param name="side"></param>
/// <param name="uplo"></param>
/// <param name="diag"> <c>true</c> if <paramref name="a"/> is a unit triangular; otherwise, <c>false</c>. </param>
/// <param name="alpha"></param>
/// <param name="a"></param>
/// <param name="b"></param>
public static void SolveTriangleMatrix <T>(OperandSide side, TriangleKind uplo, bool diag, T alpha, INdArray <T> a, MutableNdArray <T> b)
{
if (ValueTrait.Equals(alpha, Zero <T>()))
{
VectorOperation.Identity(NdArray.Zeros <T>(b.Shape), b);
return;
}
switch ((side, uplo))
{
case (OperandSide.Left, TriangleKind.Upper): SolveTriangleMatrixLU(diag, alpha, a, b); break;
case (OperandSide.Left, TriangleKind.Lower): SolveTriangleMatrixLL(diag, alpha, a, b); break;
case (OperandSide.Right, TriangleKind.Upper): SolveTriangleMatrixRU(diag, alpha, a, b); break;
case (OperandSide.Right, TriangleKind.Lower): SolveTriangleMatrixRL(diag, alpha, a, b); break;
default:
Guard.ThrowArgumentError("Invalid configs.");
break;
}
}