public void CanCheckRankOfSquareSingular(int order)
{
var matrixA = new DenseMatrix(order, order);
matrixA[0, 0] = 1;
matrixA[order - 1, order - 1] = 1;
for (var i = 1; i < order - 1; i++)
{
matrixA[i, i - 1] = 1;
matrixA[i, i + 1] = 1;
matrixA[i - 1, i] = 1;
matrixA[i + 1, i] = 1;
}
var factorSvd = matrixA.Svd();
Assert.AreEqual(factorSvd.Determinant, Complex32.Zero);
Assert.AreEqual(factorSvd.Rank, order - 1);
}
public void CanCheckRankOfSquareSingular([Values(10, 50, 100)] int order)
{
var A = new DenseMatrix(order, order);
A[0, 0] = 1;
A[order - 1, order - 1] = 1;
for (var i = 1; i < order - 1; i++)
{
A[i, i - 1] = 1;
A[i, i + 1] = 1;
A[i - 1, i] = 1;
A[i + 1, i] = 1;
}
var factorEvd = A.Evd();
Assert.AreEqual(factorEvd.Determinant, Complex32.Zero);
Assert.AreEqual(factorEvd.Rank, order - 1);
}
public void CanAddSparseMatricesBothWays()
{
var m1 = new SparseMatrix(1, 3);
var m2 = SparseMatrix.OfArray(new Complex32[,] { { 0, 1, 1 } });
var sum1 = m1 + m2;
var sum2 = m2 + m1;
Assert.IsTrue(sum1.Equals(m2));
Assert.IsTrue(sum1.Equals(sum2));
var sparseResult = new SparseMatrix(1, 3);
sparseResult.Add(m2, sparseResult);
Assert.IsTrue(sparseResult.Equals(sum1));
sparseResult = SparseMatrix.OfArray(new Complex32[,] { { 0, 1, 1 } });
sparseResult.Add(m1, sparseResult);
Assert.IsTrue(sparseResult.Equals(sum1));
sparseResult = SparseMatrix.OfArray(new Complex32[,] { { 0, 1, 1 } });
m1.Add(sparseResult, sparseResult);
Assert.IsTrue(sparseResult.Equals(sum1));
sparseResult = SparseMatrix.OfArray(new Complex32[,] { { 0, 1, 1 } });
sparseResult.Add(sparseResult, sparseResult);
Assert.IsTrue(sparseResult.Equals(2*sum1));
var denseResult = new DenseMatrix(1, 3);
denseResult.Add(m2, denseResult);
Assert.IsTrue(denseResult.Equals(sum1));
denseResult = DenseMatrix.OfArray(new Complex32[,] {{0, 1, 1}});
denseResult.Add(m1, denseResult);
Assert.IsTrue(denseResult.Equals(sum1));
var m3 = DenseMatrix.OfArray(new Complex32[,] {{0, 1, 1}});
var sum3 = m1 + m3;
var sum4 = m3 + m1;
Assert.IsTrue(sum3.Equals(m3));
Assert.IsTrue(sum3.Equals(sum4));
}
/// <summary>
/// Initializes a square <see cref="DenseMatrix"/> with all zero's except for ones on the diagonal.
/// </summary>
/// <param name="order">the size of the square matrix.</param>
/// <returns>A dense identity matrix.</returns>
/// <exception cref="ArgumentException">
/// If <paramref name="order"/> is less than one.
/// </exception>
public static DenseMatrix Identity(int order)
{
var m = new DenseMatrix(order);
for (var i = 0; i < order; i++)
{
m.Data[(i * order) + i] = 1.0f;
}
return m;
}
/// <summary>
/// Create a new dense matrix with the diagonal as a copy of the given vector.
/// This new matrix will be independent from the vector.
/// A new memory block will be allocated for storing the matrix.
/// </summary>
public static DenseMatrix OfDiagonalVector(int rows, int columns, Vector<Complex32> diagonal)
{
var m = new DenseMatrix(rows, columns);
m.SetDiagonal(diagonal);
return m;
}
/// <summary>
/// Create a new dense matrix with the diagonal as a copy of the given array.
/// This new matrix will be independent from the array.
/// A new memory block will be allocated for storing the matrix.
/// </summary>
public static DenseMatrix OfDiagonalArray(int rows, int columns, Complex32[] diagonal)
{
var m = new DenseMatrix(rows, columns);
m.SetDiagonal(diagonal);
return m;
}
public void LUFailsWithNonSquareMatrix()
{
var matrix = new DenseMatrix(3, 1);
Assert.That(() => matrix.LU(), Throws.ArgumentException);
}
/// <summary>
/// Adds another matrix to this matrix.
/// </summary>
/// <param name="other">The matrix to add to this matrix.</param>
/// <returns>The result of the addition.</returns>
/// <exception cref="ArgumentNullException">If the other matrix is <see langword="null"/>.</exception>
/// <exception cref="ArgumentOutOfRangeException">If the two matrices don't have the same dimensions.</exception>
public override Matrix<Complex32> Add(Matrix<Complex32> other)
{
if (other == null)
{
throw new ArgumentNullException("other");
}
if (other.RowCount != RowCount || other.ColumnCount != ColumnCount)
{
throw new ArgumentOutOfRangeException("other", Resources.ArgumentMatrixDimensions);
}
Matrix<Complex32> result;
if (other is DiagonalMatrix)
{
result = new DiagonalMatrix(RowCount, ColumnCount);
}
else
{
result = new DenseMatrix(RowCount, ColumnCount);
}
Add(other, result);
return result;
}
/// <summary>
/// Subtracts another matrix from this matrix.
/// </summary>
/// <param name="other">The matrix to subtract.</param>
/// <returns>The result of the subtraction.</returns>
/// <exception cref="ArgumentNullException">If the other matrix is <see langword="null"/>.</exception>
/// <exception cref="ArgumentOutOfRangeException">If the two matrices don't have the same dimensions.</exception>
public override Matrix<Complex32> Subtract(Matrix<Complex32> other)
{
if (other == null)
{
throw new ArgumentNullException("other");
}
if (other.RowCount != RowCount || other.ColumnCount != ColumnCount)
{
throw DimensionsDontMatch<ArgumentOutOfRangeException>(this, other, "other");
}
Matrix<Complex32> result;
if (other is DiagonalMatrix)
{
result = new DiagonalMatrix(RowCount, ColumnCount);
}
else
{
result = new DenseMatrix(RowCount, ColumnCount);
}
Subtract(other, result);
return result;
}
public void CanComputeThinQRFactorTallMatrixWithWorkArray()
{
var matrix = _matrices["Tall3x2"];
var r = new Complex32[matrix.ColumnCount*matrix.ColumnCount];
var tau = new Complex32[3];
var q = new Complex32[matrix.RowCount*matrix.ColumnCount];
Array.Copy(matrix.Values, q, q.Length);
var work = new Complex32[matrix.ColumnCount*Control.BlockSize];
Control.LinearAlgebraProvider.ThinQRFactor(q, matrix.RowCount, matrix.ColumnCount, r, tau, work);
var mq = new DenseMatrix(matrix.RowCount, matrix.ColumnCount, q);
var mr = new DenseMatrix(matrix.ColumnCount, matrix.ColumnCount, r);
var a = mq*mr;
for (var row = 0; row < matrix.RowCount; row++)
{
for (var col = 0; col < matrix.ColumnCount; col++)
{
AssertHelpers.AlmostEqualRelative(matrix[row, col], a[row, col], 5);
}
}
}
public void CanComputeQRFactorWideMatrix()
{
var matrix = _matrices["Wide2x3"];
var r = new Complex32[matrix.RowCount*matrix.ColumnCount];
Array.Copy(matrix.Values, r, r.Length);
var tau = new Complex32[3];
var q = new Complex32[matrix.RowCount*matrix.RowCount];
Control.LinearAlgebraProvider.QRFactor(r, matrix.RowCount, matrix.ColumnCount, q, tau);
var mr = new DenseMatrix(matrix.RowCount, matrix.ColumnCount, r).UpperTriangle();
var mq = new DenseMatrix(matrix.RowCount, matrix.RowCount, q);
var a = mq*mr;
for (var row = 0; row < matrix.RowCount; row++)
{
for (var col = 0; col < matrix.ColumnCount; col++)
{
AssertHelpers.AlmostEqualRelative(matrix[row, col], a[row, col], 5);
}
}
}
public void CanSolveUsingCholesky()
{
var matrix = new DenseMatrix(3, 3, new Complex32[] {1, 1, 1, 1, 2, 3, 1, 3, 6});
var a = new Complex32[] {1, 1, 1, 1, 2, 3, 1, 3, 6};
var b = new[] {new Complex32(1.0f, 0.0f), 2.0f, 3.0f, 4.0f, 5.0f, 6.0f};
Control.LinearAlgebraProvider.CholeskySolve(a, 3, b, 2);
AssertHelpers.AlmostEqualRelative(b[0], 0, 5);
AssertHelpers.AlmostEqualRelative(b[1], 1, 5);
AssertHelpers.AlmostEqualRelative(b[2], 0, 5);
AssertHelpers.AlmostEqualRelative(b[3], 3, 5);
AssertHelpers.AlmostEqualRelative(b[4], 1, 5);
AssertHelpers.AlmostEqualRelative(b[5], 0, 5);
NotModified(3, 3, a, matrix);
}
public void CanMultiplyTallAndWideMatricesWithUpdate()
{
var x = _matrices["Tall3x2"];
var y = _matrices["Wide2x3"];
var c = new DenseMatrix(x.RowCount, y.ColumnCount);
Control.LinearAlgebraProvider.MatrixMultiplyWithUpdate(Transpose.DontTranspose, Transpose.DontTranspose, 2.2f, x.Values, x.RowCount, x.ColumnCount, y.Values, y.RowCount, y.ColumnCount, 1.0f, c.Values);
for (var i = 0; i < c.RowCount; i++)
{
for (var j = 0; j < c.ColumnCount; j++)
{
var test = 2.2f*x.Row(i)*y.Column(j);
// if they are both close to zero, skip
if (Math.Abs(test.Real) < 1e-7 && Math.Abs(c[i, j].Real) < 1e-7)
{
continue;
}
AssertHelpers.AlmostEqualRelative(2.2f*x.Row(i)*y.Column(j), c[i, j], 5);
}
}
}
public void CanMultiplyWideAndTallMatricesWithUpdate()
{
var x = _matrices["Wide2x3"];
var y = _matrices["Tall3x2"];
var c = new DenseMatrix(x.RowCount, y.ColumnCount);
Control.LinearAlgebraProvider.MatrixMultiplyWithUpdate(Transpose.DontTranspose, Transpose.DontTranspose, 2.2f, x.Values, x.RowCount, x.ColumnCount, y.Values, y.RowCount, y.ColumnCount, 1.0f, c.Values);
for (var i = 0; i < c.RowCount; i++)
{
for (var j = 0; j < c.ColumnCount; j++)
{
AssertHelpers.AlmostEqualRelative(2.2f*x.Row(i)*y.Column(j), c[i, j], 5);
}
}
}
public void CanMultiplyTallAndWideMatrices()
{
var x = _matrices["Tall3x2"];
var y = _matrices["Wide2x3"];
var c = new DenseMatrix(x.RowCount, y.ColumnCount);
Control.LinearAlgebraProvider.MatrixMultiply(x.Values, x.RowCount, x.ColumnCount, y.Values, y.RowCount, y.ColumnCount, c.Values);
for (var i = 0; i < c.RowCount; i++)
{
for (var j = 0; j < c.ColumnCount; j++)
{
AssertHelpers.AlmostEqualRelative(x.Row(i)*y.Column(j), c[i, j], 5);
}
}
}
public void CanSolveUsingSvdTallMatrixOnFactoredMatrix()
{
var matrix = _matrices["Tall3x2"];
var a = new Complex32[matrix.RowCount*matrix.ColumnCount];
Array.Copy(matrix.Values, a, a.Length);
var s = new Complex32[matrix.ColumnCount];
var u = new Complex32[matrix.RowCount*matrix.RowCount];
var vt = new Complex32[matrix.ColumnCount*matrix.ColumnCount];
Control.LinearAlgebraProvider.SingularValueDecomposition(true, a, matrix.RowCount, matrix.ColumnCount, s, u, vt);
var b = new[] {new Complex32(1.0f, 0.0f), 2.0f, 3.0f, 4.0f, 5.0f, 6.0f};
var x = new Complex32[matrix.ColumnCount*2];
Control.LinearAlgebraProvider.SvdSolveFactored(matrix.RowCount, matrix.ColumnCount, s, u, vt, b, 2, x);
var mb = new DenseMatrix(matrix.RowCount, 2, b);
var test = (matrix.Transpose()*matrix).Inverse()*matrix.Transpose()*mb;
AssertHelpers.AlmostEqual(test[0, 0], x[0], 5);
AssertHelpers.AlmostEqual(test[1, 0], x[1], 5);
AssertHelpers.AlmostEqual(test[0, 1], x[2], 5);
AssertHelpers.AlmostEqual(test[1, 1], x[3], 5);
}
/// <summary>
/// Returns the conjugate transpose of this matrix.
/// </summary>
/// <returns>The conjugate transpose of this matrix.</returns>
public override Matrix<Complex32> ConjugateTranspose()
{
var ret = new DenseMatrix(_columnCount, _rowCount);
for (var j = 0; j < _columnCount; j++)
{
var index = j * _rowCount;
for (var i = 0; i < _rowCount; i++)
{
ret._data[(i * _columnCount) + j] = _data[index + i].Conjugate();
}
}
return ret;
}
public void CanSolveUsingQRTallMatrixUsingWorkArray()
{
var matrix = _matrices["Tall3x2"];
var a = new Complex32[matrix.RowCount*matrix.ColumnCount];
Array.Copy(matrix.Values, a, a.Length);
var b = new[] {new Complex32(1.0f, 0.0f), 2.0f, 3.0f, 4.0f, 5.0f, 6.0f};
var x = new Complex32[matrix.ColumnCount*2];
var work = new Complex32[matrix.RowCount*matrix.RowCount];
Control.LinearAlgebraProvider.QRSolve(a, matrix.RowCount, matrix.ColumnCount, b, 2, x, work);
NotModified(3, 2, a, matrix);
var mb = new DenseMatrix(matrix.RowCount, 2, b);
var test = (matrix.Transpose()*matrix).Inverse()*matrix.Transpose()*mb;
AssertHelpers.AlmostEqualRelative(test[0, 0], x[0], 5);
AssertHelpers.AlmostEqualRelative(test[1, 0], x[1], 5);
AssertHelpers.AlmostEqualRelative(test[0, 1], x[2], 5);
AssertHelpers.AlmostEqualRelative(test[1, 1], x[3], 5);
}
/// <summary>
/// Outer product of two vectors
/// </summary>
/// <param name="u">First vector</param>
/// <param name="v">Second vector</param>
/// <returns>Matrix M[i,j] = u[i]*v[j] </returns>
/// <exception cref="ArgumentNullException">If the u vector is <see langword="null" />.</exception>
/// <exception cref="ArgumentNullException">If the v vector is <see langword="null" />.</exception>
public static DenseMatrix OuterProduct(DenseVector u, DenseVector v)
{
if (u == null)
{
throw new ArgumentNullException("u");
}
if (v == null)
{
throw new ArgumentNullException("v");
}
var matrix = new DenseMatrix(u.Count, v.Count);
CommonParallel.For(
0,
u.Count,
i =>
{
for (var j = 0; j < v.Count; j++)
{
matrix.At(i, j, u._values[i] * v._values[j]);
}
});
return matrix;
}
public void CanSolveUsingQRSquareMatrixOnFactoredMatrix()
{
var matrix = _matrices["Square3x3"];
var a = new Complex32[matrix.RowCount*matrix.RowCount];
Array.Copy(matrix.Values, a, a.Length);
var tau = new Complex32[matrix.ColumnCount];
var q = new Complex32[matrix.ColumnCount*matrix.ColumnCount];
Control.LinearAlgebraProvider.QRFactor(a, matrix.RowCount, matrix.ColumnCount, q, tau);
var b = new[] {new Complex32(1.0f, 0.0f), 2.0f, 3.0f, 4.0f, 5.0f, 6.0f};
var x = new Complex32[matrix.ColumnCount*2];
Control.LinearAlgebraProvider.QRSolveFactored(q, a, matrix.RowCount, matrix.ColumnCount, tau, b, 2, x);
var mx = new DenseMatrix(matrix.ColumnCount, 2, x);
var mb = matrix*mx;
AssertHelpers.AlmostEqualRelative(mb[0, 0], b[0], 5);
AssertHelpers.AlmostEqualRelative(mb[1, 0], b[1], 5);
AssertHelpers.AlmostEqualRelative(mb[2, 0], b[2], 5);
AssertHelpers.AlmostEqualRelative(mb[0, 1], b[3], 5);
AssertHelpers.AlmostEqualRelative(mb[1, 1], b[4], 4);
AssertHelpers.AlmostEqualRelative(mb[2, 1], b[5], 4);
}
public void CanSolveForRandomMatrixWhenResultMatrixGiven(int order)
{
var matrixA = Matrix<Complex32>.Build.Random(order, order, 1);
var matrixACopy = matrixA.Clone();
var factorLU = matrixA.LU();
var matrixB = Matrix<Complex32>.Build.Random(order, order, 1);
var matrixBCopy = matrixB.Clone();
var matrixX = new DenseMatrix(order, order);
factorLU.Solve(matrixB, matrixX);
// The solution X row dimension is equal to the column dimension of A
Assert.AreEqual(matrixA.ColumnCount, matrixX.RowCount);
// The solution X has the same number of columns as B
Assert.AreEqual(matrixB.ColumnCount, matrixX.ColumnCount);
var matrixBReconstruct = matrixA * matrixX;
// Check the reconstruction.
for (var i = 0; i < matrixB.RowCount; i++)
{
for (var j = 0; j < matrixB.ColumnCount; j++)
{
Assert.AreEqual(matrixB[i, j].Real, matrixBReconstruct[i, j].Real, 1e-3f);
Assert.AreEqual(matrixB[i, j].Imaginary, matrixBReconstruct[i, j].Imaginary, 1e-3f);
}
}
// Make sure A didn't change.
for (var i = 0; i < matrixA.RowCount; i++)
{
for (var j = 0; j < matrixA.ColumnCount; j++)
{
Assert.AreEqual(matrixACopy[i, j], matrixA[i, j]);
}
}
// Make sure B didn't change.
for (var i = 0; i < matrixB.RowCount; i++)
{
for (var j = 0; j < matrixB.ColumnCount; j++)
{
Assert.AreEqual(matrixBCopy[i, j], matrixB[i, j]);
}
}
}
public void CanSubtractSparseMatricesBothWays()
{
var m1 = new SparseMatrix(1, 3);
var m2 = SparseMatrix.OfArray(new Complex32[,] { { 0, 1, 1 } });
var diff1 = m1 - m2;
var diff2 = m2 - m1;
Assert.IsTrue(diff1.Equals(m2.Negate()));
Assert.IsTrue(diff1.Equals(diff2.Negate()));
var sparseResult = new SparseMatrix(1, 3);
sparseResult.Subtract(m2, sparseResult);
Assert.IsTrue(sparseResult.Equals(diff1));
sparseResult = SparseMatrix.OfArray(new Complex32[,] { { 0, 1, 1 } });
sparseResult.Subtract(m1, sparseResult);
Assert.IsTrue(sparseResult.Equals(diff2));
sparseResult = SparseMatrix.OfArray(new Complex32[,] { { 0, 1, 1 } });
m1.Subtract(sparseResult, sparseResult);
Assert.IsTrue(sparseResult.Equals(diff1));
sparseResult = SparseMatrix.OfArray(new Complex32[,] { { 0, 1, 1 } });
sparseResult.Subtract(sparseResult, sparseResult);
Assert.IsTrue(sparseResult.Equals(0*diff1));
var denseResult = new DenseMatrix(1, 3);
denseResult.Subtract(m2, denseResult);
Assert.IsTrue(denseResult.Equals(diff1));
denseResult = DenseMatrix.OfArray(new Complex32[,] {{0, 1, 1}});
denseResult.Subtract(m1, denseResult);
Assert.IsTrue(denseResult.Equals(diff2));
var m3 = DenseMatrix.OfArray(new Complex32[,] {{0, 1, 1}});
var diff3 = m1 - m3;
var diff4 = m3 - m1;
Assert.IsTrue(diff3.Equals(m3.Negate()));
Assert.IsTrue(diff3.Equals(diff4.Negate()));
}
/// <summary>
/// Create a new dense matrix with the diagonal as a copy of the given array.
/// This new matrix will be independent from the array.
/// A new memory block will be allocated for storing the matrix.
/// </summary>
public static DenseMatrix OfDiagonalArray(Complex32[] diagonal)
{
var m = new DenseMatrix(diagonal.Length, diagonal.Length);
m.SetDiagonal(diagonal);
return m;
}
public void CanSolveForRandomMatrixWhenResultMatrixGivenUsingThinQR(int order)
{
var matrixA = MatrixLoader.GenerateRandomDenseMatrix(order, order);
var matrixACopy = matrixA.Clone();
var factorQR = matrixA.QR(QRMethod.Thin);
var matrixB = MatrixLoader.GenerateRandomDenseMatrix(order, order);
var matrixBCopy = matrixB.Clone();
var matrixX = new DenseMatrix(order, order);
factorQR.Solve(matrixB, matrixX);
// The solution X row dimension is equal to the column dimension of A
Assert.AreEqual(matrixA.ColumnCount, matrixX.RowCount);
// The solution X has the same number of columns as B
Assert.AreEqual(matrixB.ColumnCount, matrixX.ColumnCount);
var matrixBReconstruct = matrixA * matrixX;
// Check the reconstruction.
for (var i = 0; i < matrixB.RowCount; i++)
{
for (var j = 0; j < matrixB.ColumnCount; j++)
{
Assert.AreEqual(matrixB[i, j].Real, matrixBReconstruct[i, j].Real, 1e-3);
Assert.AreEqual(matrixB[i, j].Imaginary, matrixBReconstruct[i, j].Imaginary, 1e-3);
}
}
// Make sure A didn't change.
for (var i = 0; i < matrixA.RowCount; i++)
{
for (var j = 0; j < matrixA.ColumnCount; j++)
{
Assert.AreEqual(matrixACopy[i, j], matrixA[i, j]);
}
}
// Make sure B didn't change.
for (var i = 0; i < matrixB.RowCount; i++)
{
for (var j = 0; j < matrixB.ColumnCount; j++)
{
Assert.AreEqual(matrixBCopy[i, j], matrixB[i, j]);
}
}
}
/// <summary>
/// Create a new dense matrix with the diagonal as a copy of the given vector.
/// This new matrix will be independent from the vector.
/// A new memory block will be allocated for storing the matrix.
/// </summary>
public static DenseMatrix OfDiagonalVector(Vector<Complex32> diagonal)
{
var m = new DenseMatrix(diagonal.Count, diagonal.Count);
m.SetDiagonal(diagonal);
return m;
}
public void CanSolveForRandomMatrixAndSymmetricMatrixWhenResultMatrixGiven(int order)
{
var matrixA = MatrixLoader.GenerateRandomPositiveDefiniteHermitianDenseMatrix(order);
MatrixHelpers.ForceConjugateSymmetric(matrixA);
var matrixACopy = matrixA.Clone();
var factorEvd = matrixA.Evd();
var matrixB = MatrixLoader.GenerateRandomDenseMatrix(order, order);
var matrixBCopy = matrixB.Clone();
var matrixX = new DenseMatrix(order, order);
factorEvd.Solve(matrixB, matrixX);
// The solution X row dimension is equal to the column dimension of A
Assert.AreEqual(matrixA.ColumnCount, matrixX.RowCount);
// The solution X has the same number of columns as B
Assert.AreEqual(matrixB.ColumnCount, matrixX.ColumnCount);
var matrixBReconstruct = matrixA * matrixX;
// Check the reconstruction.
for (var i = 0; i < matrixB.RowCount; i++)
{
for (var j = 0; j < matrixB.ColumnCount; j++)
{
Assert.AreEqual(matrixB[i, j].Real, matrixBReconstruct[i, j].Real, 1e-2f);
Assert.AreEqual(matrixB[i, j].Imaginary, matrixBReconstruct[i, j].Imaginary, 1e-2f);
}
}
// Make sure A didn't change.
for (var i = 0; i < matrixA.RowCount; i++)
{
for (var j = 0; j < matrixA.ColumnCount; j++)
{
Assert.AreEqual(matrixACopy[i, j], matrixA[i, j]);
}
}
// Make sure B didn't change.
for (var i = 0; i < matrixB.RowCount; i++)
{
for (var j = 0; j < matrixB.ColumnCount; j++)
{
Assert.AreEqual(matrixBCopy[i, j], matrixB[i, j]);
}
}
}
/// <summary>
/// Returns the transpose of this matrix.
/// </summary>
/// <returns>The transpose of this matrix.</returns>
public override Matrix<Complex32> Transpose()
{
var ret = new DenseMatrix(_columnCount, _rowCount);
for (var j = 0; j < _columnCount; j++)
{
var index = j * _rowCount;
for (var i = 0; i < _rowCount; i++)
{
ret._values[(i * _columnCount) + j] = _values[index + i];
}
}
return ret;
}
public void CanSolveForRandomMatrixWhenResultMatrixGiven(int row, int col)
{
var matrixA = Matrix<Complex32>.Build.RandomPositiveDefinite(row, 1);
var matrixACopy = matrixA.Clone();
var chol = matrixA.Cholesky();
var matrixB = Matrix<Complex32>.Build.Random(row, col, 1);
var matrixBCopy = matrixB.Clone();
var matrixX = new DenseMatrix(row, col);
chol.Solve(matrixB, matrixX);
Assert.AreEqual(matrixB.RowCount, matrixX.RowCount);
Assert.AreEqual(matrixB.ColumnCount, matrixX.ColumnCount);
var matrixBReconstruct = matrixA * matrixX;
// Check the reconstruction.
for (var i = 0; i < matrixB.RowCount; i++)
{
for (var j = 0; j < matrixB.ColumnCount; j++)
{
Assert.AreEqual(matrixB[i, j].Real, matrixBReconstruct[i, j].Real, 0.03f);
Assert.AreEqual(matrixB[i, j].Imaginary, matrixBReconstruct[i, j].Imaginary, 0.03f);
}
}
// Make sure A didn't change.
for (var i = 0; i < matrixA.RowCount; i++)
{
for (var j = 0; j < matrixA.ColumnCount; j++)
{
Assert.AreEqual(matrixACopy[i, j], matrixA[i, j]);
}
}
// Make sure B didn't change.
for (var i = 0; i < matrixB.RowCount; i++)
{
for (var j = 0; j < matrixB.ColumnCount; j++)
{
Assert.AreEqual(matrixBCopy[i, j], matrixB[i, j]);
}
}
}
/// <summary>
/// Returns the conjugate transpose of this matrix.
/// </summary>
/// <returns>The conjugate transpose of this matrix.</returns>
public override Matrix<Complex32> ConjugateTranspose()
{
var ret = new DenseMatrix(ColumnCount, RowCount);
for (var j = 0; j < ColumnCount; j++)
{
var index = j * RowCount;
for (var i = 0; i < RowCount; i++)
{
ret.Data[(i * ColumnCount) + j] = Data[index + i].Conjugate();
}
}
return ret;
}
public void CanSolveForRandomMatrixAndSymmetricMatrixWhenResultMatrixGiven([Values(1, 2, 5, 10, 50, 100)] int order)
{
var A = Matrix<Complex32>.Build.RandomPositiveDefinite(order, 1);
MatrixHelpers.ForceHermitian(A);
var ACopy = A.Clone();
var evd = A.Evd();
var B = Matrix<Complex32>.Build.Random(order, order, 2);
var BCopy = B.Clone();
var X = new DenseMatrix(order, order);
evd.Solve(B, X);
// The solution X row dimension is equal to the column dimension of A
Assert.AreEqual(A.ColumnCount, X.RowCount);
// The solution X has the same number of columns as B
Assert.AreEqual(B.ColumnCount, X.ColumnCount);
var BReconstruct = A * X;
// Check the reconstruction.
AssertHelpers.AlmostEqual(B, BReconstruct, 1);
// Make sure A/B didn't change.
AssertHelpers.AlmostEqual(ACopy, A, 14);
AssertHelpers.AlmostEqual(BCopy, B, 14);
}