internal static Matrix TryBuildingMatrix(List <Entity> elements)
{
if (!elements.Any())
{
return(MathS.Vector(elements.ToArray()));
}
var first = elements.First();
if (first is not Matrix {
IsVector : true
} firstVec)
{
return(MathS.Vector(elements.ToArray()));
}
var tb = new MatrixBuilder(firstVec.RowCount);
foreach (var row in elements)
{
if (row is not Matrix {
IsVector: true
} rowVec)
{
return(MathS.Vector(elements.ToArray()));
}
if (rowVec.RowCount != firstVec.RowCount)
{
return(MathS.Vector(elements.ToArray()));
}
tb.Add(rowVec);
}
return(tb.ToMatrix() ?? throw new AngouriBugException("Should've been checked already"));
}
[Fact] public void WithElementVector2()
{
var v = MathS.ZeroVector(5);
Assert.Equal(MathS.Vector(0, 0, 5, 6, 0), v.WithElement(2, 5).WithElement(3, 6));
Assert.Equal(MathS.Vector(0, 0, 0, 0, 0), v);
}
[Fact] public void WithElementVector1()
{
var v = MathS.Vector(1, 2, 3);
Assert.Equal(5, v.WithElement(2, 5)[2]);
Assert.Equal(MathS.Vector(1, 2, 3), v);
}
public void ScalarProduct1()
{
var a = MathS.Vector(1, 2, 3);
var b = MathS.Vector(1, 2, 4);
var scalar = a.T * b;
Assert.Equal(17, scalar.EvalNumerical());
}
public void TransposeVector()
{
var a = MathS.Vector(1, 2);
Assert.Equal(1, a[0]);
Assert.Equal(2, a[1]);
Assert.Equal(1, a.T[0, 0]);
Assert.Equal(2, a.T[0, 1]);
}
public void TransposeImmutability()
{
var a = MathS.Vector(1, 2);
var aT = MathS.Matrix(new Entity[, ] {
{ 1, 2 }
});
Assert.Equal(aT, a.T);
var origin = MathS.Vector(1, 2);
Assert.Equal(origin, a);
}
[Fact] public void WithColumnMatrix1()
{
var m = MathS.I_4.WithColumn(2, MathS.Vector(1, 2, 3, 4));
Assert.Equal(
MathS.Matrix(new Entity[, ]
{
{ 1, 0, 1, 0 },
{ 0, 1, 2, 0 },
{ 0, 0, 3, 0 },
{ 0, 0, 4, 1 }
}),
m);
}
[Fact] public void WithRowMatrix1()
{
var m = MathS.I_4.WithRow(2, MathS.Vector(1, 2, 3, 4).T);
Assert.Equal(
MathS.Matrix(new Entity[, ]
{
{ 1, 0, 0, 0 },
{ 0, 1, 0, 0 },
{ 1, 2, 3, 4 },
{ 0, 0, 0, 1 }
}),
m);
}
[Fact] public void WithColumnMatrix2()
{
var m = MathS.IdentityMatrix(5)
.WithColumn(2, MathS.Vector(1, 2, 3, 4, 5))
.WithColumn(4, MathS.Vector(1, 3, 5, 9, 1))
.WithColumn(4, MathS.Vector(5, 6, 7, 8, 9));
Assert.Equal(
MathS.Matrix(new Entity[, ]
{
{ 1, 0, 1, 0, 5 },
{ 0, 1, 2, 0, 6 },
{ 0, 0, 3, 0, 7 },
{ 0, 0, 4, 1, 8 },
{ 0, 0, 5, 0, 9 }
}),
m);
}
[Fact] public void WithRowMatrix2()
{
var m = MathS.IdentityMatrix(5)
.WithRow(2, MathS.Vector(1, 2, 3, 4, 5).T)
.WithRow(4, MathS.Vector(1, 3, 5, 9, 1).T)
.WithRow(4, MathS.Vector(5, 6, 7, 8, 9).T);
Assert.Equal(
MathS.Matrix(new Entity[, ]
{
{ 1, 0, 0, 0, 0 },
{ 0, 1, 0, 0, 0 },
{ 1, 2, 3, 4, 5 },
{ 0, 0, 0, 1, 0 },
{ 5, 6, 7, 8, 9 }
}),
m);
}
public void TransposeDoubleOperationVector()
{
var a = MathS.Vector(1, 2);
Assert.Equal(a, a.T.T);
}
[Fact] public void ZeroVector() => Assert.Equal(MathS.Vector(0, 0, 0, 0), MathS.ZeroVector(4));
[Fact] public void LeftScalarDivisionUnsuccessfulInnerSimplified() => Assert.Equal(2 / MathS.Vector(3, 4), (2 / MathS.Vector(3, 4)).InnerSimplified);
[Fact] public void LeftScalarDivisionUnsuccessfulEvaled() => Assert.Equal(2 / MathS.Vector(3, 4), (2 / MathS.Vector(3, 4)).Evaled);
[Fact] public void MatrixAddition1() => Assert.Equal(MathS.Vector(3, 2), MathS.Vector(1, 2) + MathS.Vector(2, 0));
[Fact] public void WithColumnVector() => Assert.Equal(MathS.Vector(1, 2, 3), MathS.ZeroVector(3).WithColumn(0, MathS.Vector(1, 2, 3)));
[Fact] public void RightScalarDivision()
=> Assert.Equal(MathS.Vector("1.5", 2), (MathS.Vector(3, 4) / 2).InnerSimplified);
[Fact] public void RightScalarMulitiplication() => Assert.Equal(MathS.Vector(6, 8), (MathS.Vector(3, 4) * 2).InnerSimplified);
[Fact] public void UnsuccessfulMatrixSubtraction2InnerSimplified() => Assert.Equal(MathS.Vector(1, 2) - (Entity)MathS.Vector(2, 0, 3), (MathS.Vector(1, 2) - (Entity)MathS.Vector(2, 0, 3)).InnerSimplified);
[Fact] public void MatrixSubtraction1() => Assert.Equal(MathS.Vector(-1, 2), MathS.Vector(1, 2) - MathS.Vector(2, 0));
[Fact] public void UnsuccessfulMatrixAddition2Evaled() => Assert.Equal(MathS.Vector(1, 2) + (Entity)MathS.Vector(2, 0, 3), (MathS.Vector(1, 2) + (Entity)MathS.Vector(2, 0, 3)).Evaled);
/// <summary> /// Converts a given sequence of elements into a vector, /// which is a one-column matrix /// </summary> public static Matrix ToVector(this IEnumerable <Entity> elements) => MathS.Vector(elements.ToArray());
[Fact] public void WithRowVector() => Assert.Equal(MathS.Vector(0, 0, 3, 0), MathS.ZeroVector(4).WithRow(2, MathS.Vector(3)));
[Fact] public void VectorSingle() =>
Test(@"\begin{bmatrix}x\end{bmatrix}", MathS.Vector(x));
[Fact] public void LeftScalarSubtraction() => Assert.Equal(MathS.Vector(-1, -2), (2 - MathS.Vector(3, 4)).InnerSimplified);
[Fact] public void RightScalarSubtraction() => Assert.Equal(MathS.Vector(1, 2), (MathS.Vector(3, 4) - 2).InnerSimplified);
[Fact] public void LeftScalarAddition() => Assert.Equal(MathS.Vector(5, 6), (2 + MathS.Vector(3, 4)).InnerSimplified);
[Fact] public void MatrixMultiplication1() => Assert.Equal(MathS.Vector(1, -1), H * MathS.Vector(0, 1));
[Fact] public void RightScalarAddition() => Assert.Equal(MathS.Vector(5, 6), (MathS.Vector(3, 4) + 2).InnerSimplified);
[Fact] public void Vector() =>
Test(@"\begin{bmatrix}11 & 12 & 21 & 22 & 31 & 32\end{bmatrix}", MathS.Vector(11, 12, 21, 22, 31, 32).T);