public static void EigenDecomposition(Matrix2x2f m, out float e1, out float e2)
{
// solve the characteristic polynomial
float a = 1.0f;
float b = -(m.m00 + m.m11);
float c = m.m00 * m.m11 - m.m01 * m.m10;
SolveQuadratic(a, b, c, out e1, out e2);
}
/// <summary>
/// Subtract two matrices.
/// </summary>
public static Matrix2x2f operator -(Matrix2x2f m1, Matrix2x2f m2)
{
Matrix2x2f kSum = new Matrix2x2f();
kSum.m00 = m1.m00 - m2.m00;
kSum.m10 = m1.m10 - m2.m10;
kSum.m01 = m1.m01 - m2.m01;
kSum.m11 = m1.m11 - m2.m11;
return(kSum);
}
public static Matrix2x2f QRDecomposition(Matrix2x2f m)
{
Vector2f a = m.GetColumn(0).Normalized;
Matrix2x2f q = new Matrix2x2f();
q.SetColumn(0, a);
q.SetColumn(1, a.PerpendicularCCW);
return(q);
}
/// <summary>
/// Are these matrices equal.
/// </summary>
public override bool Equals(object obj)
{
if (!(obj is Matrix2x2f))
{
return(false);
}
Matrix2x2f mat = (Matrix2x2f)obj;
return(this == mat);
}
/// <summary>
/// Multiply a matrix by a scalar.
/// </summary>
public static Matrix2x2f operator *(Matrix2x2f m, float s)
{
Matrix2x2f kProd = new Matrix2x2f();
kProd.m00 = m.m00 * s;
kProd.m10 = m.m10 * s;
kProd.m01 = m.m01 * s;
kProd.m11 = m.m11 * s;
return(kProd);
}
/// <summary>
/// Multiply two matrices.
/// </summary>
public static Matrix2x2f operator *(Matrix2x2f m1, Matrix2x2f m2)
{
Matrix2x2f kProd = new Matrix2x2f();
kProd.m00 = m1.m00 * m2.m00 + m1.m01 * m2.m10;
kProd.m10 = m1.m10 * m2.m00 + m1.m11 * m2.m10;
kProd.m01 = m1.m00 * m2.m01 + m1.m01 * m2.m11;
kProd.m11 = m1.m10 * m2.m01 + m1.m11 * m2.m11;
return(kProd);
}
public static Matrix2x2f PolarDecomposition(Matrix2x2f m)
{
Matrix2x2f q = m + new Matrix2x2f(m.m11, -m.m10, -m.m01, m.m00);
Vector2f c0 = q.GetColumn(0);
Vector2f c1 = q.GetColumn(1);
float s = c0.Magnitude;
q.SetColumn(0, c0 / s);
q.SetColumn(1, c1 / s);
return(q);
}
/// <summary>
/// The Inverse of the matrix copied into mInv.
/// Returns false if the matrix has no inverse.
/// A matrix multipled by its inverse is the idenity.
/// </summary>
public bool TryInverse(ref Matrix2x2f mInv)
{
float det = Determinant;
if (Math.Abs(det) <= 1e-06f)
{
return(false);
}
float invDet = 1.0f / det;
mInv.m00 = m11 * invDet;
mInv.m01 = -m01 * invDet;
mInv.m10 = -m10 * invDet;
mInv.m11 = m00 * invDet;
return(true);
}
/// <summary>
/// Are these matrices equal.
/// </summary>
public bool EqualsWithError(Matrix2x2f m, float eps)
{
if (Math.Abs(m00 - m.m00) > eps)
{
return(false);
}
if (Math.Abs(m10 - m.m10) > eps)
{
return(false);
}
if (Math.Abs(m01 - m.m01) > eps)
{
return(false);
}
if (Math.Abs(m11 - m.m11) > eps)
{
return(false);
}
return(true);
}
/// <summary>
/// A matrix copied from the matrix m.
/// </summary>
public Matrix2x2f(Matrix2x2f m)
{
m00 = m.m00; m01 = m.m01;
m10 = m.m10; m11 = m.m11;
}
/// <summary>
/// Are these matrices equal.
/// </summary>
public bool Equals(Matrix2x2f mat)
{
return(this == mat);
}
