/// <summary>
/// Constructs translation matrix for a vector in R x R
/// </summary>
/// <param name="x"> X coordinate. </param>
/// <param name="y"> Y coordinate.</param>
/// <returns> Returns translation matrix. </returns>
public static Matrix Translation(double x, double y)
{
Matrix translatioMatrix = new Matrix(Matrix.IdentityMatrix(3));
translatioMatrix[0, 2] = x;
translatioMatrix[1, 2] = y;
return(translatioMatrix);
}
/// <summary>
/// Constructs inverse matrix for instance if the latter is invertible.
/// </summary>
/// <returns> Returns inverse matrix. </returns>
public Matrix Inverse()
{
if (!this.IsSquare())
{
throw new Exception("Matrix must be square to have inverse matrix.");
}
Matrix res = new Matrix(this);
//this is identity matrix
//which will be transformed to inverse matrix
//if the given matrix is invertible
Matrix idM = new Matrix(Matrix.IdentityMatrix(res.Rows));
double temp;
int i, j;
//performing matrix inverse using Gauss-Jordan method
for (j = 0; j < this.Rows; j++)
{
for (i = j; i < this.Rows; i++)
{
if (res[i, j] != 0)
{
for (int k = 0; k < this.Rows; k++)
{
temp = res[j, k]; res[j, k] = res[i, k]; res[i, k] = temp;
temp = idM[j, k]; idM[j, k] = idM[i, k]; idM[i, k] = temp;
}
temp = 1 / res[j, j];
for (int k = 0; k < this.Rows; k++)
{
res[j, k] *= temp;
idM[j, k] *= temp;
}
for (int l = 0; l < this.Rows; l++)
{
if (l != j)
{
temp = (-res[l, j]);
for (int k = 0; k < this.Rows; k++)
{
res[l, k] = res[l, k] + temp * res[j, k];
idM[l, k] = idM[l, k] + temp * idM[j, k];
}
}
}
break;
}
//if detected a row with 0s throw exception
//because in that case matrix is non-invertible
if (res[i, j] == 0)
{
throw new Exception("Non-invertible matrix.");
}
}
}
return(idM);
}
/// <summary>
/// Constructs translation matrix for a vector in R x R x R
/// </summary>
/// <param name="x"> X coordinate. </param>
/// <param name="y"> Y coordinate. </param>
/// <param name="z"> Z coordinate.</param>
/// <returns> Returns translation matrix. </returns>
public static Matrix Translation(double x, double y, double z)
{
Matrix translationMatrix = new Matrix(Matrix.IdentityMatrix(4));
translationMatrix[0, 3] = x;
translationMatrix[1, 3] = y;
translationMatrix[2, 3] = z;
return(translationMatrix);
}
/// <summary>
/// Constructs translation matrix for a vector in R x R x ... x R
/// </summary>
/// <param name="VecCoord"> Coordinates for translation. </param>
/// <returns> Returns translation matrix. </returns>
public static Matrix Translation(params double[] VecCoord)
{
Matrix translationMatrix = Matrix.IdentityMatrix(VecCoord.Length + 1);
for (int i = 0; i < VecCoord.Length; i++)
{
translationMatrix[i, VecCoord.Length] = VecCoord[i];
}
return(translationMatrix);
}
/// <summary>
/// Checks if matrix is orthogonal.
/// </summary>
/// <returns> Returns true if matrix is orthogonal;otherwis:false. </returns>
public bool IsOrthogonal()
{
if (this.IsSquare())
{
Matrix res = new Matrix(this);
//Matrix is orthogonal if and only if it is square matrix
//and the multiplication of matrix and its transpose matrix is identity matrix
//calculating the multiplication
res = res.Mul(res.Transpose());
return(res.Equals(Matrix.IdentityMatrix(res.Rows)));
}
else
{
//if matrix is not square matrix return false
return(false);
}
}
