public void CanAddSparseMatricesBothWays()
{
var m1 = new SparseMatrix(1, 3);
var m2 = Matrix<double>.Build.SparseOfArray(new double[,] { { 0, 1, 1 } });
var sum1 = m1 + m2;
var sum2 = m2 + m1;
Assert.IsTrue(sum1.Equals(m2));
Assert.IsTrue(sum1.Equals(sum2));
Matrix<double> sparseResult = new SparseMatrix(1, 3);
sparseResult.Add(m2, sparseResult);
Assert.IsTrue(sparseResult.Equals(sum1));
sparseResult = Matrix<double>.Build.SparseOfArray(new double[,] { { 0, 1, 1 } });
sparseResult.Add(m1, sparseResult);
Assert.IsTrue(sparseResult.Equals(sum1));
sparseResult = Matrix<double>.Build.SparseOfArray(new double[,] { { 0, 1, 1 } });
m1.Add(sparseResult, sparseResult);
Assert.IsTrue(sparseResult.Equals(sum1));
sparseResult = Matrix<double>.Build.SparseOfArray(new double[,] { { 0, 1, 1 } });
sparseResult.Add(sparseResult, sparseResult);
Assert.IsTrue(sparseResult.Equals(2*sum1));
Matrix<double> denseResult = new DenseMatrix(1, 3);
denseResult.Add(m2, denseResult);
Assert.IsTrue(denseResult.Equals(sum1));
denseResult = Matrix<double>.Build.DenseOfArray(new double[,] { { 0, 1, 1 } });
denseResult.Add(m1, denseResult);
Assert.IsTrue(denseResult.Equals(sum1));
var m3 = Matrix<double>.Build.DenseOfArray(new double[,] { { 0, 1, 1 } });
var sum3 = m1 + m3;
var sum4 = m3 + m1;
Assert.IsTrue(sum3.Equals(m3));
Assert.IsTrue(sum3.Equals(sum4));
}
/// <summary>
/// Run example
/// </summary>
/// <seealso cref="http://en.wikipedia.org/wiki/Matrix_multiplication#Scalar_multiplication">Multiply matrix by scalar</seealso>
/// <seealso cref="http://reference.wolfram.com/mathematica/tutorial/MultiplyingVectorsAndMatrices.html">Multiply matrix by vector</seealso>
/// <seealso cref="http://en.wikipedia.org/wiki/Matrix_multiplication#Matrix_product">Multiply matrix by matrix</seealso>
/// <seealso cref="http://en.wikipedia.org/wiki/Matrix_multiplication#Hadamard_product">Pointwise multiplies matrix with another matrix</seealso>
/// <seealso cref="http://en.wikipedia.org/wiki/Matrix_%28mathematics%29#Basic_operations">Addition and subtraction</seealso>
public void Run()
{
// Initialize IFormatProvider to print matrix/vector data
var formatProvider = (CultureInfo)CultureInfo.InvariantCulture.Clone();
formatProvider.TextInfo.ListSeparator = " ";
// Create matrix "A"
var matrixA = new DenseMatrix(new[,] { { 1.0, 2.0, 3.0 }, { 4.0, 5.0, 6.0 }, { 7.0, 8.0, 9.0 } });
Console.WriteLine(@"Matrix A");
Console.WriteLine(matrixA.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// Create matrix "B"
var matrixB = new DenseMatrix(new[,] { { 1.0, 3.0, 5.0 }, { 2.0, 4.0, 6.0 }, { 3.0, 5.0, 7.0 } });
Console.WriteLine(@"Matrix B");
Console.WriteLine(matrixB.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// Multiply matrix by scalar
// 1. Using operator "*"
var resultM = 3.0 * matrixA;
Console.WriteLine(@"Multiply matrix by scalar using operator *. (result = 3.0 * A)");
Console.WriteLine(resultM.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// 2. Using Multiply method and getting result into different matrix instance
resultM = (DenseMatrix)matrixA.Multiply(3.0);
Console.WriteLine(@"Multiply matrix by scalar using method Multiply. (result = A.Multiply(3.0))");
Console.WriteLine(resultM.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// 3. Using Multiply method and updating matrix itself
matrixA.Multiply(3.0, matrixA);
Console.WriteLine(@"Multiply matrix by scalar using method Multiply. (A.Multiply(3.0, A))");
Console.WriteLine(matrixA.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// Multiply matrix by vector (right-multiply)
var vector = new DenseVector(new[] { 1.0, 2.0, 3.0 });
Console.WriteLine(@"Vector");
Console.WriteLine(vector.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// 1. Using operator "*"
var resultV = matrixA * vector;
Console.WriteLine(@"Multiply matrix by vector using operator *. (result = A * vec)");
Console.WriteLine(resultV.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// 2. Using Multiply method and getting result into different vector instance
resultV = (DenseVector)matrixA.Multiply(vector);
Console.WriteLine(@"Multiply matrix by vector using method Multiply. (result = A.Multiply(vec))");
Console.WriteLine(resultV.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// 3. Using Multiply method and updating vector itself
matrixA.Multiply(vector, vector);
Console.WriteLine(@"Multiply matrix by vector using method Multiply. (A.Multiply(vec, vec))");
Console.WriteLine(vector.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// Multiply vector by matrix (left-multiply)
// 1. Using operator "*"
resultV = vector * matrixA;
Console.WriteLine(@"Multiply vector by matrix using operator *. (result = vec * A)");
Console.WriteLine(resultV.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// 2. Using LeftMultiply method and getting result into different vector instance
resultV = (DenseVector)matrixA.LeftMultiply(vector);
Console.WriteLine(@"Multiply vector by matrix using method LeftMultiply. (result = A.LeftMultiply(vec))");
Console.WriteLine(resultV.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// 3. Using LeftMultiply method and updating vector itself
matrixA.LeftMultiply(vector, vector);
Console.WriteLine(@"Multiply vector by matrix using method LeftMultiply. (A.LeftMultiply(vec, vec))");
Console.WriteLine(vector.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// Multiply matrix by matrix
// 1. Using operator "*"
resultM = matrixA * matrixB;
Console.WriteLine(@"Multiply matrix by matrix using operator *. (result = A * B)");
Console.WriteLine(resultM.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// 2. Using Multiply method and getting result into different matrix instance
resultM = (DenseMatrix)matrixA.Multiply(matrixB);
Console.WriteLine(@"Multiply matrix by matrix using method Multiply. (result = A.Multiply(B))");
Console.WriteLine(resultM.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// 3. Using Multiply method and updating matrix itself
matrixA.Multiply(matrixB, matrixA);
Console.WriteLine(@"Multiply matrix by matrix using method Multiply. (A.Multiply(B, A))");
Console.WriteLine(matrixA.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// Pointwise multiplies matrix with another matrix
// 1. Using PointwiseMultiply method and getting result into different matrix instance
resultM = (DenseMatrix)matrixA.PointwiseMultiply(matrixB);
Console.WriteLine(@"Pointwise multiplies matrix with another matrix using method PointwiseMultiply. (result = A.PointwiseMultiply(B))");
Console.WriteLine(resultM.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// 2. Using PointwiseMultiply method and updating matrix itself
matrixA.PointwiseMultiply(matrixB, matrixA);
Console.WriteLine(@"Pointwise multiplies matrix with another matrix using method PointwiseMultiply. (A.PointwiseMultiply(B, A))");
Console.WriteLine(matrixA.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// Pointwise divide matrix with another matrix
// 1. Using PointwiseDivide method and getting result into different matrix instance
resultM = (DenseMatrix)matrixA.PointwiseDivide(matrixB);
Console.WriteLine(@"Pointwise divide matrix with another matrix using method PointwiseDivide. (result = A.PointwiseDivide(B))");
Console.WriteLine(resultM.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// 2. Using PointwiseDivide method and updating matrix itself
matrixA.PointwiseDivide(matrixB, matrixA);
Console.WriteLine(@"Pointwise divide matrix with another matrix using method PointwiseDivide. (A.PointwiseDivide(B, A))");
Console.WriteLine(matrixA.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// Addition
// 1. Using operator "+"
resultM = matrixA + matrixB;
Console.WriteLine(@"Add matrices using operator +. (result = A + B)");
Console.WriteLine(resultM.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// 2. Using Add method and getting result into different matrix instance
resultM = (DenseMatrix)matrixA.Add(matrixB);
Console.WriteLine(@"Add matrices using method Add. (result = A.Add(B))");
Console.WriteLine(resultM.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// 3. Using Add method and updating matrix itself
matrixA.Add(matrixB, matrixA);
Console.WriteLine(@"Add matrices using method Add. (A.Add(B, A))");
Console.WriteLine(matrixA.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// Subtraction
// 1. Using operator "-"
resultM = matrixA - matrixB;
Console.WriteLine(@"Subtract matrices using operator -. (result = A - B)");
Console.WriteLine(resultM.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// 2. Using Subtract method and getting result into different matrix instance
resultM = (DenseMatrix)matrixA.Subtract(matrixB);
Console.WriteLine(@"Subtract matrices using method Subtract. (result = A.Subtract(B))");
Console.WriteLine(resultM.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// 3. Using Subtract method and updating matrix itself
matrixA.Subtract(matrixB, matrixA);
Console.WriteLine(@"Subtract matrices using method Subtract. (A.Subtract(B, A))");
Console.WriteLine(matrixA.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// Divide by scalar
// 1. Using Divide method and getting result into different matrix instance
resultM = (DenseMatrix)matrixA.Divide(3.0);
Console.WriteLine(@"Divide matrix by scalar using method Divide. (result = A.Divide(3.0))");
Console.WriteLine(resultM.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// 2. Using Divide method and updating matrix itself
matrixA.Divide(3.0, matrixA);
Console.WriteLine(@"Divide matrix by scalar using method Divide. (A.Divide(3.0, A))");
Console.WriteLine(matrixA.ToString("#0.00\t", formatProvider));
Console.WriteLine();
}
public void StructureRecurse(DenseMatrix X, DenseMatrix Psi, DenseVector d, int n, ref DenseMatrix Q,
ref DenseMatrix O, ref DenseMatrix pT_n)
{
//O = O(t-1) O_enxt = O(t)
//o should be a column vector ( in matrix form)
var x = new DenseVector(X.RowCount);
var psi = new DenseVector(Psi.ColumnCount);
X.Column(n, x);
Psi.Row(n, psi);
DenseMatrix p_n = CalculateGreatPsi((DenseMatrix) x.ToColumnMatrix(), (DenseMatrix) psi.ToRowMatrix());
pT_n = (DenseMatrix) p_n.Transpose();
double ee = Math.Abs(d[n] - (pT_n.Multiply(O))[0, 0]);
double temp = 1 + (pT_n.Multiply(Q)).Multiply(p_n)[0, 0];
double ae = Math.Abs(ee/temp);
if (ee >= ae)
{
var L = (DenseMatrix) Q.Multiply(p_n).Multiply(1/temp);
Q = (DenseMatrix) ((DenseMatrix.Identity(Q.RowCount).Subtract(L.Multiply(pT_n))).Multiply(Q));
O = (DenseMatrix) O.Add(L*ee);
}
else
{
Q = (DenseMatrix) DenseMatrix.Identity(Q.RowCount).Multiply(Q);
}
}