/// <summary>
/// Calculates inverse matrix.
/// </summary>
/// <typeparam name="T"></typeparam>
/// <param name="ndArray"></param>
/// <returns></returns>
public static NdArray <T> Inverse <T>(this INdArray <T> ndArray)
{
Guard.AssertShapeMatch((bool)(ndArray.Rank == 2 & ndArray.Shape[0] == ndArray.Shape[1]), "ndArray.Rank == 2 & ndArray.Shape[0] == ndArray.Shape[1]");
var b = Identity <T>((int)ndArray.Shape[0]);
var(l, u, perms) = NdLinAlg.LUWithPermutationsLegacy <T>(ndArray);
var xx = NdArray.CreateMutable(new T[b.Shape[0], b.Shape[1]]);
var x = xx.Entity;
var row = b.Shape[0];
var col = b.Shape[1];
for (var j = 0; j < col; ++j)
{
var bj = b[Range.Whole, new Index(j, false)];
var xj = xx[Range.Whole, new Index(j, false)];
SolveCore(l, u, perms, bj, xj);
}
for (var k = perms.Count - 1; k >= 0; --k)
{
var(p, q) = perms[k];
for (var i = 0; i < row; ++i)
{
Span <int> idx1 = stackalloc int[] { i, p };
Span <int> idx2 = stackalloc int[] { i, q };
InternalUtils.Exchange(ref x[idx1], ref x[idx2]);
}
}
for (var k = perms.Count - 1; k >= 0; --k)
{
var(p, q) = perms[k];
for (var i = 0; i < row; ++i)
{
Span <int> idx1 = stackalloc int[] { i, p };
Span <int> idx2 = stackalloc int[] { i, q };
InternalUtils.Exchange(ref x[idx1], ref x[idx2]);
}
}
return(xx.MoveToImmutable());
}
