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Symmetric3x3Wide.cs
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Symmetric3x3Wide.cs
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using System.Numerics;
using System.Runtime.CompilerServices;
namespace BepuUtilities
{
/// <summary>
/// Stores the lower left triangle (including diagonal) of a 3x3 matrix. Useful for symmetric matrices (and sometimes antisymmetric matrices).
/// </summary>
public struct Symmetric3x3Wide
{
/// <summary>
/// First row, first column of the matrix.
/// </summary>
public Vector<float> XX;
/// <summary>
/// Second row, first column of the matrix.
/// </summary>
public Vector<float> YX;
/// <summary>
/// Second row, second column of the matrix.
/// </summary>
public Vector<float> YY;
/// <summary>
/// Third row, first column of the matrix.
/// </summary>
public Vector<float> ZX;
/// <summary>
/// Third row, second column of the matrix.
/// </summary>
public Vector<float> ZY;
/// <summary>
/// Third row, third column of the matrix.
/// </summary>
public Vector<float> ZZ;
/// <summary>
/// Inverts the matrix as if it is a symmetric matrix where M32 == M23, M13 == M31, and M21 == M12.
/// </summary>
/// <param name="m">Symmetric matrix to invert.</param>
/// <param name="inverse">Inverse of the symmetric matrix.</param>
//[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static void Invert(in Symmetric3x3Wide m, out Symmetric3x3Wide inverse)
{
var xx = m.YY * m.ZZ - m.ZY * m.ZY;
var yx = m.ZY * m.ZX - m.ZZ * m.YX;
var zx = m.YX * m.ZY - m.ZX * m.YY;
var determinantInverse = Vector<float>.One / (xx * m.XX + yx * m.YX + zx * m.ZX);
var yy = m.ZZ * m.XX - m.ZX * m.ZX;
var zy = m.ZX * m.YX - m.XX * m.ZY;
var zz = m.XX * m.YY - m.YX * m.YX;
inverse.XX = xx * determinantInverse;
inverse.YX = yx * determinantInverse;
inverse.ZX = zx * determinantInverse;
inverse.YY = yy * determinantInverse;
inverse.ZY = zy * determinantInverse;
inverse.ZZ = zz * determinantInverse;
}
/// <summary>
/// Adds the components of two symmetric matrices together.
/// </summary>
/// <param name="a">First matrix to add.</param>
/// <param name="b">Second matrix to add.</param>
/// <param name="result">Sum of the two input matrices.</param>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static void Add(in Symmetric3x3Wide a, in Symmetric3x3Wide b, out Symmetric3x3Wide result)
{
result.XX = a.XX + b.XX;
result.YX = a.YX + b.YX;
result.YY = a.YY + b.YY;
result.ZX = a.ZX + b.ZX;
result.ZY = a.ZY + b.ZY;
result.ZZ = a.ZZ + b.ZZ;
}
/// <summary>
/// Adds the components of two symmetric matrices together.
/// </summary>
/// <param name="a">First matrix to add.</param>
/// <param name="b">Second matrix to add.</param>
/// <returns>Sum of the two input matrices.</returns>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static Symmetric3x3Wide operator +(in Symmetric3x3Wide a, in Symmetric3x3Wide b)
{
Symmetric3x3Wide result;
result.XX = a.XX + b.XX;
result.YX = a.YX + b.YX;
result.YY = a.YY + b.YY;
result.ZX = a.ZX + b.ZX;
result.ZY = a.ZY + b.ZY;
result.ZZ = a.ZZ + b.ZZ;
return result;
}
/// <summary>
/// Subtracts one symmetric matrix's components from another.
/// </summary>
/// <param name="a">Matrix to be subtracted from.</param>
/// <param name="b">Matrix to subtract from the first matrix.</param>
/// <param name="result">Result of a - b.</param>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static void Subtract(in Symmetric3x3Wide a, in Symmetric3x3Wide b, out Symmetric3x3Wide result)
{
result.XX = a.XX - b.XX;
result.YX = a.YX - b.YX;
result.YY = a.YY - b.YY;
result.ZX = a.ZX - b.ZX;
result.ZY = a.ZY - b.ZY;
result.ZZ = a.ZZ - b.ZZ;
}
/// <summary>
/// Subtracts one symmetric matrix's components from another.
/// </summary>
/// <param name="a">Matrix to be subtracted from.</param>
/// <param name="b">Matrix to subtract from the first matrix.</param>
/// <returns>Result of a - b.</returns>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static Symmetric3x3Wide operator -(in Symmetric3x3Wide a, in Symmetric3x3Wide b) //TODO: without in decoration, this had some really peculiar codegen in .net 6 preview 5.
{
Symmetric3x3Wide result;
result.XX = a.XX - b.XX;
result.YX = a.YX - b.YX;
result.YY = a.YY - b.YY;
result.ZX = a.ZX - b.ZX;
result.ZY = a.ZY - b.ZY;
result.ZZ = a.ZZ - b.ZZ;
return result;
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static void Scale(in Symmetric3x3Wide m, in Vector<float> scale, out Symmetric3x3Wide result)
{
result.XX = m.XX * scale;
result.YX = m.YX * scale;
result.YY = m.YY * scale;
result.ZX = m.ZX * scale;
result.ZY = m.ZY * scale;
result.ZZ = m.ZZ * scale;
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static Symmetric3x3Wide operator *(in Symmetric3x3Wide m, in Vector<float> scale) //TODO: without in decoration, this had some really peculiar codegen in .net 6 preview 5.
{
Symmetric3x3Wide result;
result.XX = m.XX * scale;
result.YX = m.YX * scale;
result.YY = m.YY * scale;
result.ZX = m.ZX * scale;
result.ZY = m.ZY * scale;
result.ZZ = m.ZZ * scale;
return result;
}
//If you ever need a triangular invert, a couple of options:
//For matrices of the form:
//[ 1 0 0 ]
//[ YX 1 0 ]
//[ ZX ZY 1 ]
//The inverse is simply:
// [ 1 0 0 ]
//M^-1 = [ -YX 1 0 ]
// [ YX * ZY - ZX -ZY 1 ]
//For a matrix with an arbitrary diagonal (that's still invertible):
// [ 1/XX 0 0 ]
//M^-1 = [ -YX/(XX*YY) 1/M22 0 ]
// [ -(YY*ZX - YX*ZY)/(XX*YY*ZZ) -ZY/(YY*ZZ) 1/ZZ ]
//And with some refiddling, you could make all the denominators the same to avoid repeated divisions.
/// <summary>
/// Computes skewSymmetric(v) * m * transpose(skewSymmetric(v)) for a symmetric matrix m. Assumes that the input and output matrices do not overlap.
/// </summary>
/// <param name="m">Symmetric matrix.</param>
/// <param name="v">Vector to create the skew symmetric matrix from to act as the sandwich bread.</param>
/// <param name="sandwich">Result of skewSymmetric(v) * m * transpose(skewSymmetric(v)).</param>
/// <remarks>This operation might have a formal name that isn't skew sandwich. But that's okay, its real name is skew sandwich.</remarks>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static void SkewSandwichWithoutOverlap(in Vector3Wide v, in Symmetric3x3Wide m, out Symmetric3x3Wide sandwich)
{
//27 muls, 15 adds.
var xzy = v.X * m.ZY;
var yzx = v.Y * m.ZX;
var zyx = v.Z * m.YX;
var ixx = yzx - zyx;
var ixy = v.Y * m.ZY - v.Z * m.YY;
var ixz = v.Y * m.ZZ - v.Z * m.ZY;
var iyx = v.Z * m.XX - v.X * m.ZX;
var iyy = zyx - xzy;
var iyz = v.Z * m.ZX - v.X * m.ZZ;
var izx = v.X * m.YX - v.Y * m.XX;
var izy = v.X * m.YY - v.Y * m.YX;
var izz = xzy - yzx;
sandwich.XX = v.Y * ixz - v.Z * ixy;
sandwich.YX = v.Y * iyz - v.Z * iyy;
sandwich.YY = v.Z * iyx - v.X * iyz;
sandwich.ZX = v.Y * izz - v.Z * izy;
sandwich.ZY = v.Z * izx - v.X * izz;
sandwich.ZZ = v.X * izy - v.Y * izx;
}
/// <summary>
/// Computes v * m * transpose(v) for a symmetric matrix m. Assumes that the input and output do not overlap.
/// </summary>
/// <param name="v">Vector acting as the sandwich bread.</param>
/// <param name="m">Succulent interior symmetric matrix.</param>
/// <param name="sandwich">Result of v * m * transpose(v) for a symmetric matrix m.</param>
/// <remarks>Since I called the other one a skew sandwich, I really don't have a choice in the naming convention anymore.</remarks>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static void VectorSandwich(in Vector3Wide v, in Symmetric3x3Wide m, out Vector<float> sandwich)
{
//This isn't actually fewer flops than the equivalent explicit operation, but it does avoid some struct locals and it's a pretty common operation.
//(And at the moment, avoiding struct locals is unfortunately helpful for codegen reasons.)
var x = v.X * m.XX + v.Y * m.YX + v.Z * m.ZX;
var y = v.X * m.YX + v.Y * m.YY + v.Z * m.ZY;
var z = v.X * m.ZX + v.Y * m.ZY + v.Z * m.ZZ;
sandwich = x * v.X + y * v.Y + z * v.Z;
}
/// <summary>
/// Computes rT * m * r for a symmetric matrix m and a rotation matrix R.
/// </summary>
/// <param name="r">Rotation matrix to use as the sandwich bread.</param>
/// <param name="m">Succulent interior symmetric matrix.</param>
/// <param name="sandwich">Result of v * m * transpose(v) for a symmetric matrix m.</param>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static void RotationSandwich(in Matrix3x3Wide r, in Symmetric3x3Wide m, out Symmetric3x3Wide sandwich)
{
var ixx = r.X.X * m.XX + r.Y.X * m.YX + r.Z.X * m.ZX;
var ixy = r.X.X * m.YX + r.Y.X * m.YY + r.Z.X * m.ZY;
var ixz = r.X.X * m.ZX + r.Y.X * m.ZY + r.Z.X * m.ZZ;
var iyx = r.X.Y * m.XX + r.Y.Y * m.YX + r.Z.Y * m.ZX;
var iyy = r.X.Y * m.YX + r.Y.Y * m.YY + r.Z.Y * m.ZY;
var iyz = r.X.Y * m.ZX + r.Y.Y * m.ZY + r.Z.Y * m.ZZ;
var izx = r.X.Z * m.XX + r.Y.Z * m.YX + r.Z.Z * m.ZX;
var izy = r.X.Z * m.YX + r.Y.Z * m.YY + r.Z.Z * m.ZY;
var izz = r.X.Z * m.ZX + r.Y.Z * m.ZY + r.Z.Z * m.ZZ;
sandwich.XX = ixx * r.X.X + ixy * r.Y.X + ixz * r.Z.X;
sandwich.YX = iyx * r.X.X + iyy * r.Y.X + iyz * r.Z.X;
sandwich.YY = iyx * r.X.Y + iyy * r.Y.Y + iyz * r.Z.Y;
sandwich.ZX = izx * r.X.X + izy * r.Y.X + izz * r.Z.X;
sandwich.ZY = izx * r.X.Y + izy * r.Y.Y + izz * r.Z.Y;
sandwich.ZZ = izx * r.X.Z + izy * r.Y.Z + izz * r.Z.Z;
}
/// <summary>
/// Computes result = a * b, assuming that b represents a symmetric 3x3 matrix. Assumes that input parameters and output result do not overlap.
/// </summary>
/// <param name="a">First matrix of the pair to multiply.</param>
/// <param name="b">Matrix to be reinterpreted as symmetric for the multiply.</param>
/// <param name="result">Result of multiplying a * b.</param>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static void MultiplyWithoutOverlap(in Matrix2x3Wide a, in Symmetric3x3Wide b, out Matrix2x3Wide result)
{
result.X.X = a.X.X * b.XX + a.X.Y * b.YX + a.X.Z * b.ZX;
result.X.Y = a.X.X * b.YX + a.X.Y * b.YY + a.X.Z * b.ZY;
result.X.Z = a.X.X * b.ZX + a.X.Y * b.ZY + a.X.Z * b.ZZ;
result.Y.X = a.Y.X * b.XX + a.Y.Y * b.YX + a.Y.Z * b.ZX;
result.Y.Y = a.Y.X * b.YX + a.Y.Y * b.YY + a.Y.Z * b.ZY;
result.Y.Z = a.Y.X * b.ZX + a.Y.Y * b.ZY + a.Y.Z * b.ZZ;
}
/// <summary>
/// Computes result = a * b, assuming that b represents a symmetric 3x3 matrix. Assumes that input parameters and output result do not overlap.
/// </summary>
/// <param name="a">First matrix of the pair to multiply.</param>
/// <param name="b">Matrix to be reinterpreted as symmetric for the multiply.</param>
/// <returns>Result of multiplying a * b.</returns>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static Matrix2x3Wide operator *(in Matrix2x3Wide a, in Symmetric3x3Wide b) //TODO: without in decoration, this had some really peculiar codegen in .net 6 preview 5.
{
Matrix2x3Wide result;
result.X.X = a.X.X * b.XX + a.X.Y * b.YX + a.X.Z * b.ZX;
result.X.Y = a.X.X * b.YX + a.X.Y * b.YY + a.X.Z * b.ZY;
result.X.Z = a.X.X * b.ZX + a.X.Y * b.ZY + a.X.Z * b.ZZ;
result.Y.X = a.Y.X * b.XX + a.Y.Y * b.YX + a.Y.Z * b.ZX;
result.Y.Y = a.Y.X * b.YX + a.Y.Y * b.YY + a.Y.Z * b.ZY;
result.Y.Z = a.Y.X * b.ZX + a.Y.Y * b.ZY + a.Y.Z * b.ZZ;
return result;
}
/// <summary>
/// Computes result = a * b, assuming that b represents a symmetric 3x3 matrix. Assumes that input parameters and output result do not overlap.
/// </summary>
/// <param name="a">First matrix of the pair to multiply.</param>
/// <param name="b">Matrix to be reinterpreted as symmetric for the multiply.</param>
/// <param name="result">Result of multiplying a * b.</param>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static void MultiplyWithoutOverlap(in Matrix3x3Wide a, in Symmetric3x3Wide b, out Matrix3x3Wide result)
{
result.X.X = a.X.X * b.XX + a.X.Y * b.YX + a.X.Z * b.ZX;
result.X.Y = a.X.X * b.YX + a.X.Y * b.YY + a.X.Z * b.ZY;
result.X.Z = a.X.X * b.ZX + a.X.Y * b.ZY + a.X.Z * b.ZZ;
result.Y.X = a.Y.X * b.XX + a.Y.Y * b.YX + a.Y.Z * b.ZX;
result.Y.Y = a.Y.X * b.YX + a.Y.Y * b.YY + a.Y.Z * b.ZY;
result.Y.Z = a.Y.X * b.ZX + a.Y.Y * b.ZY + a.Y.Z * b.ZZ;
result.Z.X = a.Z.X * b.XX + a.Z.Y * b.YX + a.Z.Z * b.ZX;
result.Z.Y = a.Z.X * b.YX + a.Z.Y * b.YY + a.Z.Z * b.ZY;
result.Z.Z = a.Z.X * b.ZX + a.Z.Y * b.ZY + a.Z.Z * b.ZZ;
}
/// <summary>
/// Computes result = a * b, assuming that b represents a symmetric 3x3 matrix. Assumes that input parameters and output result do not overlap.
/// </summary>
/// <param name="a">First matrix of the pair to multiply.</param>
/// <param name="b">Matrix to be reinterpreted as symmetric for the multiply.</param>
/// <returns>Result of multiplying a * b.</returns>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static Matrix3x3Wide operator *(in Matrix3x3Wide a, in Symmetric3x3Wide b) //TODO: without in decoration, this had some really peculiar codegen in .net 6 preview 5.
{
Matrix3x3Wide result;
result.X.X = a.X.X * b.XX + a.X.Y * b.YX + a.X.Z * b.ZX;
result.X.Y = a.X.X * b.YX + a.X.Y * b.YY + a.X.Z * b.ZY;
result.X.Z = a.X.X * b.ZX + a.X.Y * b.ZY + a.X.Z * b.ZZ;
result.Y.X = a.Y.X * b.XX + a.Y.Y * b.YX + a.Y.Z * b.ZX;
result.Y.Y = a.Y.X * b.YX + a.Y.Y * b.YY + a.Y.Z * b.ZY;
result.Y.Z = a.Y.X * b.ZX + a.Y.Y * b.ZY + a.Y.Z * b.ZZ;
result.Z.X = a.Z.X * b.XX + a.Z.Y * b.YX + a.Z.Z * b.ZX;
result.Z.Y = a.Z.X * b.YX + a.Z.Y * b.YY + a.Z.Z * b.ZY;
result.Z.Z = a.Z.X * b.ZX + a.Z.Y * b.ZY + a.Z.Z * b.ZZ;
return result;
}
/// <summary>
/// Computes result = a * b, assuming that a represents a symmetric 3x3 matrix. Assumes that input parameters and output result do not overlap.
/// </summary>
/// <param name="a">Matrix to be reinterpreted as symmetric for the multiply.</param>
/// <param name="b">Second matrix of the pair to multiply.</param>
/// <param name="result">Result of multiplying a * b.</param>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static void Multiply(in Symmetric3x3Wide a, in Matrix3x3Wide b, out Matrix3x3Wide result)
{
result.X.X = a.XX * b.X.X + a.YX * b.Y.X + a.ZX * b.Z.X;
result.X.Y = a.XX * b.X.Y + a.YX * b.Y.Y + a.ZX * b.Z.Y;
result.X.Z = a.XX * b.X.Z + a.YX * b.Y.Z + a.ZX * b.Z.Z;
result.Y.X = a.YX * b.X.X + a.YY * b.Y.X + a.ZY * b.Z.X;
result.Y.Y = a.YX * b.X.Y + a.YY * b.Y.Y + a.ZY * b.Z.Y;
result.Y.Z = a.YX * b.X.Z + a.YY * b.Y.Z + a.ZY * b.Z.Z;
result.Z.X = a.ZX * b.X.X + a.ZY * b.Y.X + a.ZZ * b.Z.X;
result.Z.Y = a.ZX * b.X.Y + a.ZY * b.Y.Y + a.ZZ * b.Z.Y;
result.Z.Z = a.ZX * b.X.Z + a.ZY * b.Y.Z + a.ZZ * b.Z.Z;
}
/// <summary>
/// Computes result = a * b, assuming that a represents a symmetric 3x3 matrix. Assumes that input parameters and output result do not overlap.
/// </summary>
/// <param name="a">Matrix to be reinterpreted as symmetric for the multiply.</param>
/// <param name="b">Second matrix of the pair to multiply.</param>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static Matrix3x3Wide operator *(in Symmetric3x3Wide a, in Matrix3x3Wide b) //TODO: without in decoration, this had some really peculiar codegen in .net 6 preview 5.
{
Matrix3x3Wide result;
result.X.X = a.XX * b.X.X + a.YX * b.Y.X + a.ZX * b.Z.X;
result.X.Y = a.XX * b.X.Y + a.YX * b.Y.Y + a.ZX * b.Z.Y;
result.X.Z = a.XX * b.X.Z + a.YX * b.Y.Z + a.ZX * b.Z.Z;
result.Y.X = a.YX * b.X.X + a.YY * b.Y.X + a.ZY * b.Z.X;
result.Y.Y = a.YX * b.X.Y + a.YY * b.Y.Y + a.ZY * b.Z.Y;
result.Y.Z = a.YX * b.X.Z + a.YY * b.Y.Z + a.ZY * b.Z.Z;
result.Z.X = a.ZX * b.X.X + a.ZY * b.Y.X + a.ZZ * b.Z.X;
result.Z.Y = a.ZX * b.X.Y + a.ZY * b.Y.Y + a.ZZ * b.Z.Y;
result.Z.Z = a.ZX * b.X.Z + a.ZY * b.Y.Z + a.ZZ * b.Z.Z;
return result;
}
/// <summary>
/// Computes result = a * transpose(b).
/// </summary>
/// <param name="a">Matrix to multiply with the transposed matrix.</param>
/// <param name="b">Matrix to transpose and concatenate with the first matrix.</param>
/// <param name="result">Result of a * transpose(b).</param>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static void MultiplyByTransposed(in Symmetric3x3Wide a, in Matrix3x3Wide b, out Matrix3x3Wide result)
{
result.X.X = a.XX * b.X.X + a.YX * b.X.Y + a.ZX * b.X.Z;
result.X.Y = a.XX * b.Y.X + a.YX * b.Y.Y + a.ZX * b.Y.Z;
result.X.Z = a.XX * b.Z.X + a.YX * b.Z.Y + a.ZX * b.Z.Z;
result.Y.X = a.YX * b.X.X + a.YY * b.X.Y + a.ZY * b.X.Z;
result.Y.Y = a.YX * b.Y.X + a.YY * b.Y.Y + a.ZY * b.Y.Z;
result.Y.Z = a.YX * b.Z.X + a.YY * b.Z.Y + a.ZY * b.Z.Z;
result.Z.X = a.ZX * b.X.X + a.ZY * b.X.Y + a.ZZ * b.X.Z;
result.Z.Y = a.ZX * b.Y.X + a.ZY * b.Y.Y + a.ZZ * b.Y.Z;
result.Z.Z = a.ZX * b.Z.X + a.ZY * b.Z.Y + a.ZZ * b.Z.Z;
}
/// <summary>
/// Computes result = transpose(a * transpose(b)).
/// </summary>
/// <param name="a">Matrix to multiply with the transposed matrix.</param>
/// <param name="b">Matrix to transpose and concatenate with the first matrix.</param>
/// <param name="result">Result of transpose(a * transpose(b)).</param>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static void MultiplyByTransposed(in Symmetric3x3Wide a, in Matrix2x3Wide b, out Matrix2x3Wide result)
{
result.X.X = a.XX * b.X.X + a.YX * b.X.Y + a.ZX * b.X.Z;
result.Y.X = a.XX * b.Y.X + a.YX * b.Y.Y + a.ZX * b.Y.Z;
result.X.Y = a.YX * b.X.X + a.YY * b.X.Y + a.ZY * b.X.Z;
result.Y.Y = a.YX * b.Y.X + a.YY * b.Y.Y + a.ZY * b.Y.Z;
result.X.Z = a.ZX * b.X.X + a.ZY * b.X.Y + a.ZZ * b.X.Z;
result.Y.Z = a.ZX * b.Y.X + a.ZY * b.Y.Y + a.ZZ * b.Y.Z;
}
/// <summary>
/// Computes m * t * mT for a symmetric matrix t and a matrix m.
/// </summary>
/// <param name="m">Matrix to use as the sandwich bread.</param>
/// <param name="t">Succulent interior symmetric matrix.</param>
/// <param name="result">Result of m * t * mT for a symmetric matrix t.</param>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static void MatrixSandwich(in Matrix2x3Wide m, in Symmetric3x3Wide t, out Symmetric2x2Wide result)
{
var ixx = m.X.X * t.XX + m.X.Y * t.YX + m.X.Z * t.ZX;
var ixy = m.X.X * t.YX + m.X.Y * t.YY + m.X.Z * t.ZY;
var ixz = m.X.X * t.ZX + m.X.Y * t.ZY + m.X.Z * t.ZZ;
var iyx = m.Y.X * t.XX + m.Y.Y * t.YX + m.Y.Z * t.ZX;
var iyy = m.Y.X * t.YX + m.Y.Y * t.YY + m.Y.Z * t.ZY;
var iyz = m.Y.X * t.ZX + m.Y.Y * t.ZY + m.Y.Z * t.ZZ;
result.XX = ixx * m.X.X + ixy * m.X.Y + ixz * m.X.Z;
result.YX = iyx * m.X.X + iyy * m.X.Y + iyz * m.X.Z;
result.YY = iyx * m.Y.X + iyy * m.Y.Y + iyz * m.Y.Z;
}
/// <summary>
/// Computes result = a * b, where a = transpose(b) * M for some symmetric matrix M.
/// </summary>
/// <param name="a">Some matrix equal to transpose(b) * M for some symmetric matrix M.</param>
/// <param name="b">Matrix used to sandwich the original matrix M.</param>
/// <param name="result">Complete result of transpose(b) * M * b.</param>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static void CompleteMatrixSandwich(in Matrix3x3Wide a, in Matrix3x3Wide b, out Symmetric3x3Wide result)
{
//The only benefit of these 'completion' functions is knowing that the final result is symmetric, so there's no need to compute some of the results.
//Other than that, it's equivalent to a 3x3 multiply.
result.XX = a.X.X * b.X.X + a.X.Y * b.Y.X + a.X.Z * b.Z.X;
result.YX = a.Y.X * b.X.X + a.Y.Y * b.Y.X + a.Y.Z * b.Z.X;
result.YY = a.Y.X * b.X.Y + a.Y.Y * b.Y.Y + a.Y.Z * b.Z.Y;
result.ZX = a.Z.X * b.X.X + a.Z.Y * b.Y.X + a.Z.Z * b.Z.X;
result.ZY = a.Z.X * b.X.Y + a.Z.Y * b.Y.Y + a.Z.Z * b.Z.Y;
result.ZZ = a.Z.X * b.X.Z + a.Z.Y * b.Y.Z + a.Z.Z * b.Z.Z;
}
/// <summary>
/// Computes result = tranpose(a) * b, where a = transpose(transpose(b) * M) for some symmetric matrix M. In other words, we're just treating matrix a as a 3x2 matrix.
/// </summary>
/// <param name="a">Some matrix equal to transpose(b) * M for some symmetric matrix M.</param>
/// <param name="b">Matrix used to sandwich the original matrix M.</param>
/// <param name="result">Complete result of transpose(b) * M * b.</param>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static void CompleteMatrixSandwich(in Matrix2x3Wide a, in Matrix2x3Wide b, out Symmetric3x3Wide result)
{
result.XX = a.X.X * b.X.X + a.Y.X * b.Y.X;
result.YX = a.X.Y * b.X.X + a.Y.Y * b.Y.X;
result.YY = a.X.Y * b.X.Y + a.Y.Y * b.Y.Y;
result.ZX = a.X.Z * b.X.X + a.Y.Z * b.Y.X;
result.ZY = a.X.Z * b.X.Y + a.Y.Z * b.Y.Y;
result.ZZ = a.X.Z * b.X.Z + a.Y.Z * b.Y.Z;
}
/// <summary>
/// Computes result = a * transpose(b), where a = b * M for some symmetric matrix M.
/// </summary>
/// <param name="a">Some matrix equal to b * M for some symmetric matrix M.</param>
/// <param name="b">Matrix used to sandwich the original matrix M, to be transposed.</param>
/// <param name="result">Complete result of b * M * transpose(b).</param>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static void CompleteMatrixSandwichByTranspose(in Matrix3x3Wide a, in Matrix3x3Wide b, out Symmetric3x3Wide result)
{
result.XX = a.X.X * b.X.X + a.X.Y * b.X.Y + a.X.Z * b.X.Z;
result.YX = a.Y.X * b.X.X + a.Y.Y * b.X.Y + a.Y.Z * b.X.Z;
result.YY = a.Y.X * b.Y.X + a.Y.Y * b.Y.Y + a.Y.Z * b.Y.Z;
result.ZX = a.Z.X * b.X.X + a.Z.Y * b.X.Y + a.Z.Z * b.X.Z;
result.ZY = a.Z.X * b.Y.X + a.Z.Y * b.Y.Y + a.Z.Z * b.Y.Z;
result.ZZ = a.Z.X * b.Z.X + a.Z.Y * b.Z.Y + a.Z.Z * b.Z.Z;
}
/// <summary>
/// Computes result = transpose(a) * b, where b = M * a for some symmetric matrix M.
/// </summary>
/// <param name="a">Matrix used to sandwich the original matrix M.</param>
/// <param name="b">Some matrix equal to M * a for some symmetric matrix M.</param>
/// <param name="result">Complete result of transpose(a) * M * a.</param>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static void CompleteMatrixSandwichTranspose(in Matrix3x3Wide a, in Matrix3x3Wide b, out Symmetric3x3Wide result)
{
result.XX = a.X.X * b.X.X + a.Y.X * b.Y.X + a.Z.X * b.Z.X;
result.YX = a.X.Y * b.X.X + a.Y.Y * b.Y.X + a.Z.Y * b.Z.X;
result.YY = a.X.Y * b.X.Y + a.Y.Y * b.Y.Y + a.Z.Y * b.Z.Y;
result.ZX = a.X.Z * b.X.X + a.Y.Z * b.Y.X + a.Z.Z * b.Z.X;
result.ZY = a.X.Z * b.X.Y + a.Y.Z * b.Y.Y + a.Z.Z * b.Z.Y;
result.ZZ = a.X.Z * b.X.Z + a.Y.Z * b.Y.Z + a.Z.Z * b.Z.Z;
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static void TransformWithoutOverlap(in Vector3Wide v, in Symmetric3x3Wide m, out Vector3Wide result)
{
result.X = v.X * m.XX + v.Y * m.YX + v.Z * m.ZX;
result.Y = v.X * m.YX + v.Y * m.YY + v.Z * m.ZY;
result.Z = v.X * m.ZX + v.Y * m.ZY + v.Z * m.ZZ;
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static Vector3Wide operator *(in Vector3Wide v, in Symmetric3x3Wide m) //TODO: without in decoration, this had some really peculiar codegen in .net 6 preview 5.
{
Vector3Wide result;
result.X = v.X * m.XX + v.Y * m.YX + v.Z * m.ZX;
result.Y = v.X * m.YX + v.Y * m.YY + v.Z * m.ZY;
result.Z = v.X * m.ZX + v.Y * m.ZY + v.Z * m.ZZ;
return result;
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static Matrix3x3Wide operator +(in Symmetric3x3Wide a, in Matrix3x3Wide b)
{
Matrix3x3Wide result;
result.X.X = a.XX + b.X.X;
result.X.Y = a.YX + b.X.Y;
result.X.Z = a.ZX + b.X.Z;
result.Y.X = a.YX + b.Y.X;
result.Y.Y = a.YY + b.Y.Y;
result.Y.Z = a.ZY + b.Y.Z;
result.Z.X = a.ZX + b.Z.X;
result.Z.Y = a.ZY + b.Z.Y;
result.Z.Z = a.ZZ + b.Z.Z;
return result;
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static Matrix3x3Wide operator +(in Matrix3x3Wide a, in Symmetric3x3Wide b)
{
Matrix3x3Wide result;
result.X.X = a.X.X + b.XX;
result.X.Y = a.X.Y + b.YX;
result.X.Z = a.X.Z + b.ZX;
result.Y.X = a.Y.X + b.YX;
result.Y.Y = a.Y.Y + b.YY;
result.Y.Z = a.Y.Z + b.ZY;
result.Z.X = a.Z.X + b.ZX;
result.Z.Y = a.Z.Y + b.ZY;
result.Z.Z = a.Z.Z + b.ZZ;
return result;
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static void WriteFirst(in Symmetric3x3 scalar, ref Symmetric3x3Wide wide)
{
GatherScatter.GetFirst(ref wide.XX) = scalar.XX;
GatherScatter.GetFirst(ref wide.YX) = scalar.YX;
GatherScatter.GetFirst(ref wide.YY) = scalar.YY;
GatherScatter.GetFirst(ref wide.ZX) = scalar.ZX;
GatherScatter.GetFirst(ref wide.ZY) = scalar.ZY;
GatherScatter.GetFirst(ref wide.ZZ) = scalar.ZZ;
}
}
}