/// <summary>
/// Multiplies the two matrices. Remember that Matrix multiplication is not commutative.
/// </summary>
/// <param name="matA">The first matrix.</param>
/// <param name="matB">The second matrix.</param>
/// <param name="resultantDimension">The number of rows and columns in <paramref name="matA"/> and
/// <paramref name="matB"/> that should be used in the multiplication calculation. The resultant matrix will
/// also have this many rows and columns filled in.</param>
/// <returns><paramref name="matA"/> x <paramref name="matB"/></returns>
public static Matrix Multiply(Matrix matA, Matrix matB, int resultantDimension = 4)
{
Assure.BetweenOrEqualTo(resultantDimension, 1, 4, "Resultant dimension must be between 1 and 4.");
switch (resultantDimension)
{
case 1:
return(new Matrix(r0C0: Vector4.Dot(matA.RowA, matB.ColumnA)));
case 2:
return(new Matrix(
r0C0: Vector4.Dot(matA.RowA, matB.ColumnA),
r0C1: Vector4.Dot(matA.RowA, matB.ColumnB),
r1C0: Vector4.Dot(matA.RowB, matB.ColumnA),
r1C1: Vector4.Dot(matA.RowB, matB.ColumnB)
));
case 3:
Vector4 matBColA = matB.ColumnA;
Vector4 matBColB = matB.ColumnB;
Vector4 matBColC = matB.ColumnC;
return(new Matrix(
r0C0: Vector4.Dot(matA.RowA, matBColA),
r0C1: Vector4.Dot(matA.RowA, matBColB),
r0C2: Vector4.Dot(matA.RowA, matBColC),
r1C0: Vector4.Dot(matA.RowB, matBColA),
r1C1: Vector4.Dot(matA.RowB, matBColB),
r1C2: Vector4.Dot(matA.RowB, matBColC),
r2C0: Vector4.Dot(matA.RowC, matBColA),
r2C1: Vector4.Dot(matA.RowC, matBColB),
r2C2: Vector4.Dot(matA.RowC, matBColC)
));
case 4:
return(matA * matB);
default:
Logger.Warn("Matrix.Multiply called with resultantDimension of: " + resultantDimension + "!");
return(ZERO);
}
}
public void TestBetweenOrEqualTo()
{
// Define variables and constants
const int FIVE = 5;
const int FOUR = 4;
const int THREE = 3;
// Set up context
// Execute
Assure.BetweenOrEqualTo(FOUR, THREE, FIVE);
Assure.BetweenOrEqualTo(FOUR, FOUR, FIVE);
try {
Assure.BetweenOrEqualTo(THREE, FOUR, FIVE);
Assert.Fail();
}
catch (AssuranceFailedException) {
}
// Assert outcome
}
/// <summary>
/// Returns the determinant of this Matrix, used to calculate the <see cref="Cofactor"/> and <see cref="Inverse"/>.
/// </summary>
/// <param name="dimension">The number of rows and columns in this matrix to use in the determinant calculation.</param>
/// <returns>The determinant of this matrix.</returns>
public float GetDeterminant(int dimension = 4)
{
Assure.BetweenOrEqualTo(dimension, 1, 4, "Input dimension must be between 1 and 4.");
switch (dimension)
{
case 1: return(RowA.X);
case 2:
return(RowA.X * RowB.Y - RowA.Y * RowB.X);
case 3:
return(RowA.X * (RowB.Y * RowC.Z - RowB.Z * RowC.Y)
- RowA.Y * (RowB.X * RowC.Z - RowB.Z * RowC.X)
+ RowA.Z * (RowB.X * RowC.Y - RowB.Y * RowC.X));
default:
return
(RowA.X * GetMinor(0, 0).GetDeterminant(3)
- RowA.Y * GetMinor(0, 1).GetDeterminant(3)
+ RowA.Z * GetMinor(0, 2).GetDeterminant(3)
- RowA.W * GetMinor(0, 3).GetDeterminant(3));
}
}
/// <summary>
/// Returns a new <see cref="Matrix"/> that is the same as this Matrix, except with the row indexed by
/// <paramref name="row"/> and the column indexed by <paramref name="column"/> removed.
/// </summary>
/// <remarks>
/// The three remaining rows and columns will be 'squeezed up' in to a 3x3 matrix, and the fourth row and fourth
/// column will be filled with zeroes. An example follows:
/// <code>
/// Matrix matrix = new Matrix(
/// 00f, 01f, 02f, 03f,
/// 10f, 11f, 12f, 13f,
/// 20f, 21f, 22f, 23f,
/// 30f, 31f, 32f, 33f
/// );
///
/// Matrix minor22 = matrix.GetMinor(2, 2);
///
/// // minor22:
/// // [00f, 01f, 03f, 00f]
/// // [10f, 11f, 13f, 00f]
/// // [30f, 31f, 33f, 00f]
/// // [00f, 00f, 00f, 00f]
/// </code>
/// </remarks>
/// <param name="row">The row index to remove, from 0 to 3.</param>
/// <param name="column">The column index to remove, from 0 to 3.</param>
/// <exception cref="ArgumentException">Thrown if <paramref name="row"/> or <paramref name="column"/>
/// are < 0 or > 3.</exception>
/// <returns>The requested matrix minor.</returns>
public Matrix GetMinor(int row, int column)
{
Assure.BetweenOrEqualTo(row, 0, 3, "Row index must be between 0 and 3.");
Assure.BetweenOrEqualTo(column, 0, 3, "Column index must be between 0 and 3.");
switch (row)
{
case 0:
switch (column)
{
case 0: // Row 0 Column 0
return(new Matrix(RowB[1, 2, 3], RowC[1, 2, 3], RowD[1, 2, 3], Vector4.ZERO));
case 1: // Row 0 Column 1
return(new Matrix(RowB[0, 2, 3], RowC[0, 2, 3], RowD[0, 2, 3], Vector4.ZERO));
case 2: // Row 0 Column 2
return(new Matrix(RowB[0, 1, 3], RowC[0, 1, 3], RowD[0, 1, 3], Vector4.ZERO));
case 3: // Row 0 Column 3
return(new Matrix(RowB[0, 1, 2], RowC[0, 1, 2], RowD[0, 1, 2], Vector4.ZERO));
}
break;
case 1:
switch (column)
{
case 0: // Row 1 Column 0
return(new Matrix(RowA[1, 2, 3], RowC[1, 2, 3], RowD[1, 2, 3], Vector4.ZERO));
case 1: // Row 1 Column 1
return(new Matrix(RowA[0, 2, 3], RowC[0, 2, 3], RowD[0, 2, 3], Vector4.ZERO));
case 2: // Row 1 Column 2
return(new Matrix(RowA[0, 1, 3], RowC[0, 1, 3], RowD[0, 1, 3], Vector4.ZERO));
case 3: // Row 1 Column 3
return(new Matrix(RowA[0, 1, 2], RowC[0, 1, 2], RowD[0, 1, 2], Vector4.ZERO));
}
break;
case 2:
switch (column)
{
case 0: // Row 2 Column 0
return(new Matrix(RowA[1, 2, 3], RowB[1, 2, 3], RowD[1, 2, 3], Vector4.ZERO));
case 1: // Row 2 Column 1
return(new Matrix(RowA[0, 2, 3], RowB[0, 2, 3], RowD[0, 2, 3], Vector4.ZERO));
case 2: // Row 2 Column 2
return(new Matrix(RowA[0, 1, 3], RowB[0, 1, 3], RowD[0, 1, 3], Vector4.ZERO));
case 3: // Row 2 Column 3
return(new Matrix(RowA[0, 1, 2], RowB[0, 1, 2], RowD[0, 1, 2], Vector4.ZERO));
}
break;
case 3:
switch (column)
{
case 0: // Row 3 Column 0
return(new Matrix(RowA[1, 2, 3], RowB[1, 2, 3], RowC[1, 2, 3], Vector4.ZERO));
case 1: // Row 3 Column 1
return(new Matrix(RowA[0, 2, 3], RowB[0, 2, 3], RowC[0, 2, 3], Vector4.ZERO));
case 2: // Row 3 Column 2
return(new Matrix(RowA[0, 1, 3], RowB[0, 1, 3], RowC[0, 1, 3], Vector4.ZERO));
case 3: // Row 3 Column 3
return(new Matrix(RowA[0, 1, 2], RowB[0, 1, 2], RowC[0, 1, 2], Vector4.ZERO));
}
break;
}
throw new ArgumentException("Matrix minor requested with row: " + row + ", column: " + column + "!");
}