public void CanSolveForRandomVector(int row, int column)
{
var matrixA = new UserDefinedMatrix(Matrix <Complex> .Build.Random(row, column, 1).ToArray());
var matrixACopy = matrixA.Clone();
var factorSvd = matrixA.Svd();
var vectorb = new UserDefinedVector(Vector <Complex> .Build.Random(row, 1).ToArray());
var resultx = factorSvd.Solve(vectorb);
Assert.AreEqual(matrixA.ColumnCount, resultx.Count);
var matrixBReconstruct = matrixA * resultx;
// Check the reconstruction.
for (var i = 0; i < vectorb.Count; i++)
{
AssertHelpers.AlmostEqual(vectorb[i], matrixBReconstruct[i], 10);
}
// 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]);
}
}
}
public void CanSolveForRandomMatrix(int row, int column)
{
var matrixA = new UserDefinedMatrix(Matrix <double> .Build.Random(row, column, 1).ToArray());
var matrixACopy = matrixA.Clone();
var factorSvd = matrixA.Svd();
var matrixB = new UserDefinedMatrix(Matrix <double> .Build.Random(row, column, 1).ToArray());
var matrixX = factorSvd.Solve(matrixB);
// 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], matrixBReconstruct[i, j], 1.0e-11);
}
}
// 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]);
}
}
}
public void CanSolveForRandomVectorWhenResultVectorGiven(int row, int column)
{
var matrixA = new UserDefinedMatrix(Matrix <double> .Build.Random(row, column, 1).ToArray());
var matrixACopy = matrixA.Clone();
var factorSvd = matrixA.Svd();
var vectorb = new UserDefinedVector(Vector <double> .Build.Random(row, 1).ToArray());
var vectorbCopy = vectorb.Clone();
var resultx = new UserDefinedVector(column);
factorSvd.Solve(vectorb, resultx);
var matrixBReconstruct = matrixA * resultx;
// Check the reconstruction.
for (var i = 0; i < vectorb.Count; i++)
{
Assert.AreEqual(vectorb[i], matrixBReconstruct[i], 1.0e-11);
}
// 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 < vectorb.Count; i++)
{
Assert.AreEqual(vectorbCopy[i], vectorb[i]);
}
}
public void CanFactorizeRandomMatrix(int row, int column)
{
var matrixA = new UserDefinedMatrix(Matrix <double> .Build.Random(row, column, 1).ToArray());
var factorSvd = matrixA.Svd();
var u = factorSvd.U;
var vt = factorSvd.VT;
var w = factorSvd.W;
// Make sure the U has the right dimensions.
Assert.AreEqual(row, u.RowCount);
Assert.AreEqual(row, u.ColumnCount);
// Make sure the VT has the right dimensions.
Assert.AreEqual(column, vt.RowCount);
Assert.AreEqual(column, vt.ColumnCount);
// Make sure the W has the right dimensions.
Assert.AreEqual(row, w.RowCount);
Assert.AreEqual(column, w.ColumnCount);
// Make sure the U*W*VT is the original matrix.
var matrix = u * w * vt;
for (var i = 0; i < matrix.RowCount; i++)
{
for (var j = 0; j < matrix.ColumnCount; j++)
{
Assert.AreEqual(matrixA[i, j], matrix[i, j], 1.0e-11);
}
}
}
public void CanFactorizeRandomMatrix(int row, int column)
{
var matrixA = new UserDefinedMatrix(Matrix<double>.Build.Random(row, column, 1).ToArray());
var factorSvd = matrixA.Svd();
var u = factorSvd.U;
var vt = factorSvd.VT;
var w = factorSvd.W;
// Make sure the U has the right dimensions.
Assert.AreEqual(row, u.RowCount);
Assert.AreEqual(row, u.ColumnCount);
// Make sure the VT has the right dimensions.
Assert.AreEqual(column, vt.RowCount);
Assert.AreEqual(column, vt.ColumnCount);
// Make sure the W has the right dimensions.
Assert.AreEqual(row, w.RowCount);
Assert.AreEqual(column, w.ColumnCount);
// Make sure the U*W*VT is the original matrix.
var matrix = u*w*vt;
for (var i = 0; i < matrix.RowCount; i++)
{
for (var j = 0; j < matrix.ColumnCount; j++)
{
Assert.AreEqual(matrixA[i, j], matrix[i, j], 1.0e-11);
}
}
}
public void CanCheckRankOfNonSquare(int row, int column)
{
var matrixA = new UserDefinedMatrix(Matrix<float>.Build.Random(row, column, 1).ToArray());
var factorSvd = matrixA.Svd();
var mn = Math.Min(row, column);
Assert.AreEqual(factorSvd.Rank, mn);
}
public void SolveMatrixIfVectorsNotComputedThrowsInvalidOperationException()
{
var matrixA = new UserDefinedMatrix(Matrix <Complex> .Build.Random(10, 9, 1).ToArray());
var factorSvd = matrixA.Svd(false);
var matrixB = new UserDefinedMatrix(Matrix <Complex> .Build.Random(10, 9, 1).ToArray());
Assert.That(() => factorSvd.Solve(matrixB), Throws.InvalidOperationException);
}
public void CanCheckRankOfNonSquare(int row, int column)
{
var matrixA = new UserDefinedMatrix(Matrix <double> .Build.Random(row, column, 1).ToArray());
var factorSvd = matrixA.Svd();
var mn = Math.Min(row, column);
Assert.AreEqual(factorSvd.Rank, mn);
}
public void SolveVectorIfVectorsNotComputedThrowsInvalidOperationException()
{
var matrixA = new UserDefinedMatrix(Matrix <double> .Build.Random(10, 10, 1).ToArray());
var factorSvd = matrixA.Svd(false);
var vectorb = new UserDefinedVector(Vector <double> .Build.Random(10, 1).ToArray());
Assert.That(() => factorSvd.Solve(vectorb), Throws.InvalidOperationException);
}
public void CanCheckRankSquare(int order)
{
var matrixA = new UserDefinedMatrix(Matrix <double> .Build.Random(order, order, 1).ToArray());
var factorSvd = matrixA.Svd();
if (factorSvd.Determinant != 0)
{
Assert.AreEqual(factorSvd.Rank, order);
}
else
{
Assert.AreEqual(factorSvd.Rank, order - 1);
}
}
public void CanSolveForRandomMatrixWhenResultMatrixGiven(int row, int column)
{
var matrixA = new UserDefinedMatrix(Matrix <Complex32> .Build.Random(row, column, 1).ToArray());
var matrixACopy = matrixA.Clone();
var factorSvd = matrixA.Svd();
var matrixB = new UserDefinedMatrix(Matrix <Complex32> .Build.Random(row, column, 1).ToArray());
var matrixBCopy = matrixB.Clone();
var matrixX = new UserDefinedMatrix(column, column);
factorSvd.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 CanCheckRankOfSquareSingular(int order)
{
var matrixA = new UserDefinedMatrix(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, 0);
Assert.AreEqual(factorSvd.Rank, order - 1);
}
public void CheckRankOfSquareSingular(int order)
{
var matrixA = new UserDefinedMatrix(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(true);
Assert.AreEqual(factorSvd.Determinant, 0);
Assert.AreEqual(factorSvd.Rank, order - 1);
}
public void CanCheckRankOfSquareSingular([Values(10, 50, 100)] int order)
{
var matrixA = new UserDefinedMatrix(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(true);
Assert.AreEqual(factorSvd.Determinant, Complex32.Zero);
Assert.AreEqual(factorSvd.Rank, order - 1);
}
public void SolveVectorIfVectorsNotComputedThrowsInvalidOperationException()
{
var matrixA = new UserDefinedMatrix(Matrix<float>.Build.Random(10, 10, 1).ToArray());
var factorSvd = matrixA.Svd(false);
var vectorb = new UserDefinedVector(Vector<float>.Build.Random(10, 1).ToArray());
Assert.That(() => factorSvd.Solve(vectorb), Throws.InvalidOperationException);
}
public void CanSolveForRandomVectorWhenResultVectorGiven(int row, int column)
{
var matrixA = new UserDefinedMatrix(Matrix<float>.Build.Random(row, column, 1).ToArray());
var matrixACopy = matrixA.Clone();
var factorSvd = matrixA.Svd();
var vectorb = new UserDefinedVector(Vector<float>.Build.Random(row, 1).ToArray());
var vectorbCopy = vectorb.Clone();
var resultx = new UserDefinedVector(column);
factorSvd.Solve(vectorb, resultx);
var matrixBReconstruct = matrixA*resultx;
// Check the reconstruction.
for (var i = 0; i < vectorb.Count; i++)
{
Assert.AreEqual(vectorb[i], matrixBReconstruct[i], 1e-4);
}
// 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 < vectorb.Count; i++)
{
Assert.AreEqual(vectorbCopy[i], vectorb[i]);
}
}
public void CanSolveForRandomMatrixWhenResultMatrixGiven(int row, int column)
{
var matrixA = new UserDefinedMatrix(Matrix<float>.Build.Random(row, column, 1).ToArray());
var matrixACopy = matrixA.Clone();
var factorSvd = matrixA.Svd();
var matrixB = new UserDefinedMatrix(Matrix<float>.Build.Random(row, column, 1).ToArray());
var matrixBCopy = matrixB.Clone();
var matrixX = new UserDefinedMatrix(column, column);
factorSvd.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], matrixBReconstruct[i, j], 1e-4);
}
}
// 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 CanCheckRankSquare(int order)
{
var matrixA = new UserDefinedMatrix(Matrix<float>.Build.Random(order, order, 1).ToArray());
var factorSvd = matrixA.Svd();
if (factorSvd.Determinant != 0)
{
Assert.AreEqual(factorSvd.Rank, order);
}
else
{
Assert.AreEqual(factorSvd.Rank, order - 1);
}
}
public void SolveMatrixIfVectorsNotComputedThrowsInvalidOperationException()
{
var matrixA = new UserDefinedMatrix(Matrix<Complex>.Build.Random(10, 9, 1).ToArray());
var factorSvd = matrixA.Svd(false);
var matrixB = new UserDefinedMatrix(Matrix<Complex>.Build.Random(10, 9, 1).ToArray());
Assert.That(() => factorSvd.Solve(matrixB), Throws.InvalidOperationException);
}
public void CanSolveForRandomVector(int row, int column)
{
var matrixA = new UserDefinedMatrix(Matrix<Complex>.Build.Random(row, column, 1).ToArray());
var matrixACopy = matrixA.Clone();
var factorSvd = matrixA.Svd();
var vectorb = new UserDefinedVector(Vector<Complex>.Build.Random(row, 1).ToArray());
var resultx = factorSvd.Solve(vectorb);
Assert.AreEqual(matrixA.ColumnCount, resultx.Count);
var matrixBReconstruct = matrixA*resultx;
// Check the reconstruction.
for (var i = 0; i < vectorb.Count; i++)
{
AssertHelpers.AlmostEqual(vectorb[i], matrixBReconstruct[i], 10);
}
// 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]);
}
}
}
