public void CanSolveForRandomMatrix(int row, int col)
{
var matrixA = new UserDefinedMatrix(Matrix <Complex> .Build.RandomPositiveDefinite(row, 1).ToArray());
var matrixACopy = matrixA.Clone();
var chol = matrixA.Cholesky();
var matrixB = new UserDefinedMatrix(Matrix <Complex> .Build.Random(row, col, 1).ToArray());
var matrixX = chol.Solve(matrixB);
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++)
{
AssertHelpers.AlmostEqual(matrixB[i, j], matrixBReconstruct[i, j], 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 CanSolveForRandomVector(int order)
{
var matrixA = new UserDefinedMatrix(Matrix <double> .Build.Random(order, order, 1).ToArray());
var matrixACopy = matrixA.Clone();
var factorQR = matrixA.QR();
var vectorb = new UserDefinedVector(Vector <double> .Build.Random(order, 1).ToArray());
var resultx = factorQR.Solve(vectorb);
Assert.AreEqual(matrixA.ColumnCount, resultx.Count);
var matrixBReconstruct = matrixA * resultx;
// Check the reconstruction.
for (var i = 0; i < order; 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]);
}
}
}
public void CanSolveForRandomMatrixUsingThinQR(int order)
{
var matrixA = new UserDefinedMatrix(Matrix <float> .Build.Random(order, order, 1).ToArray());
var matrixACopy = matrixA.Clone();
var factorQR = matrixA.QR(QRMethod.Thin);
var matrixB = new UserDefinedMatrix(Matrix <float> .Build.Random(order, order, 1).ToArray());
var matrixX = factorQR.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], 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]);
}
}
}
public void CanSolveForRandomVector(int order)
{
var matrixA = new UserDefinedMatrix(Matrix <Complex> .Build.RandomPositiveDefinite(order, 1).ToArray());
var matrixACopy = matrixA.Clone();
var chol = matrixA.Cholesky();
var b = new UserDefinedVector(Vector <Complex> .Build.Random(order, 1).ToArray());
var x = chol.Solve(b);
Assert.AreEqual(b.Count, x.Count);
var matrixBReconstruct = matrixA * x;
// Check the reconstruction.
for (var i = 0; i < order; i++)
{
AssertHelpers.AlmostEqual(b[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 CanSolveForRandomVectorUsingThinQR(int order)
{
var matrixA = new UserDefinedMatrix(Matrix <Complex32> .Build.Random(order, order, 1).ToArray());
var matrixACopy = matrixA.Clone();
var factorQR = matrixA.QR(QRMethod.Thin);
var vectorb = new UserDefinedVector(Vector <Complex32> .Build.Random(order, 1).ToArray());
var resultx = factorQR.Solve(vectorb);
Assert.AreEqual(matrixA.ColumnCount, resultx.Count);
var matrixBReconstruct = matrixA * resultx;
// Check the reconstruction.
for (var i = 0; i < order; i++)
{
Assert.AreEqual(vectorb[i].Real, matrixBReconstruct[i].Real, 1e-3f);
Assert.AreEqual(vectorb[i].Imaginary, matrixBReconstruct[i].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]);
}
}
}
public void CanSolveForRandomVectorWhenResultVectorGiven(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 vectorb = new UserDefinedVector(Vector <Complex32> .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].Real, matrixBReconstruct[i].Real, 1e-3f);
Assert.AreEqual(vectorb[i].Imaginary, matrixBReconstruct[i].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 < vectorb.Count; i++)
{
Assert.AreEqual(vectorbCopy[i], vectorb[i]);
}
}
public void CanInverse(int order)
{
var matrixA = new UserDefinedMatrix(Matrix <double> .Build.Random(order, order, 1).ToArray());
var matrixACopy = matrixA.Clone();
var factorLU = matrixA.LU();
var matrixAInverse = factorLU.Inverse();
// The inverse dimension is equal A
Assert.AreEqual(matrixAInverse.RowCount, matrixAInverse.RowCount);
Assert.AreEqual(matrixAInverse.ColumnCount, matrixAInverse.ColumnCount);
var matrixIdentity = matrixA * matrixAInverse;
// 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]);
}
}
// Check if multiplication of A and AI produced identity matrix.
for (var i = 0; i < matrixIdentity.RowCount; i++)
{
Assert.AreEqual(matrixIdentity[i, i], 1.0, 1.0e-11);
}
}
public void CanSolveForRandomMatrixAndSymmetricMatrixWhenResultMatrixGiven([Values(1, 2, 5, 10, 50, 100)] int order)
{
var A = new UserDefinedMatrix(Matrix <Complex32> .Build.RandomPositiveDefinite(order, 1).ToArray());
MatrixHelpers.ForceConjugateSymmetric(A);
var ACopy = A.Clone();
var evd = A.Evd();
var B = new UserDefinedMatrix(Matrix <Complex32> .Build.Random(order, order, 1).ToArray());
var BCopy = B.Clone();
var X = new UserDefinedMatrix(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);
}
public void CanSolveForRandomMatrix(int order)
{
var matrixA = new UserDefinedMatrix(Matrix <Complex> .Build.Random(order, order, 1).ToArray());
var matrixACopy = matrixA.Clone();
var factorGramSchmidt = matrixA.GramSchmidt();
var matrixB = new UserDefinedMatrix(Matrix <Complex> .Build.Random(order, order, 1).ToArray());
var matrixX = factorGramSchmidt.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++)
{
AssertHelpers.AlmostEqual(matrixB[i, j], matrixBReconstruct[i, j], 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 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 CanSolveForRandomMatrixWhenResultMatrixGiven(int order)
{
var matrixA = new UserDefinedMatrix(Matrix <Complex32> .Build.Random(order, order, 1).ToArray());
var matrixACopy = matrixA.Clone();
var factorQR = matrixA.QR();
var matrixB = new UserDefinedMatrix(Matrix <Complex32> .Build.Random(order, order, 1).ToArray());
var matrixBCopy = matrixB.Clone();
var matrixX = new UserDefinedMatrix(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-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 CanSolveForRandomMatrixAndSymmetricMatrixWhenResultMatrixGiven(int order)
{
var matrixA = new UserDefinedMatrix(Matrix <double> .Build.RandomPositiveDefinite(order, 1).ToArray());
var matrixACopy = matrixA.Clone();
var factorEvd = matrixA.Evd();
var matrixB = new UserDefinedMatrix(Matrix <double> .Build.Random(order, order, 1).ToArray());
var matrixBCopy = matrixB.Clone();
var matrixX = new UserDefinedMatrix(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], matrixBReconstruct[i, j], 1.0e-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]);
}
}
// 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 CanSolveForRandomMatrixWhenResultMatrixGiven(int row, int col)
{
var matrixA = new UserDefinedMatrix(Matrix <Complex32> .Build.RandomPositiveDefinite(row, 1).ToArray());
var matrixACopy = matrixA.Clone();
var chol = matrixA.Cholesky();
var matrixB = new UserDefinedMatrix(Matrix <Complex32> .Build.Random(row, col, 1).ToArray());
var matrixBCopy = matrixB.Clone();
var matrixX = new UserDefinedMatrix(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, 0.02f);
Assert.AreEqual(matrixB[i, j].Imaginary, matrixBReconstruct[i, j].Imaginary, 0.02f);
}
}
// 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 CanSolveForRandomVectorAndSymmetricMatrix([Values(1, 2, 5, 10, 50, 100)] int order)
{
var A = new UserDefinedMatrix(Matrix <double> .Build.RandomPositiveDefinite(order, 1).ToArray());
MatrixHelpers.ForceSymmetric(A);
var ACopy = A.Clone();
var evd = A.Evd();
var b = new UserDefinedVector(Vector <double> .Build.Random(order, 1).ToArray());
var bCopy = b.Clone();
var x = evd.Solve(b);
var bReconstruct = A * x;
// Check the reconstruction.
AssertHelpers.AlmostEqual(b, bReconstruct, 8);
// Make sure A/B didn't change.
AssertHelpers.AlmostEqual(ACopy, A, 14);
AssertHelpers.AlmostEqual(bCopy, b, 14);
}
public void CanSolveForRandomVectorWhenResultVectorGiven(int order)
{
var matrixA = new UserDefinedMatrix(Matrix <Complex32> .Build.RandomPositiveDefinite(order, 1).ToArray());
var matrixACopy = matrixA.Clone();
var chol = matrixA.Cholesky();
var b = new UserDefinedVector(Vector <Complex32> .Build.Random(order, 1).ToArray());
var matrixBCopy = b.Clone();
var x = new UserDefinedVector(order);
chol.Solve(b, x);
Assert.AreEqual(b.Count, x.Count);
var matrixBReconstruct = matrixA * x;
// Check the reconstruction.
for (var i = 0; i < order; i++)
{
Assert.AreEqual(b[i].Real, matrixBReconstruct[i].Real, 0.02f);
Assert.AreEqual(b[i].Imaginary, matrixBReconstruct[i].Imaginary, 0.02f);
}
// 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 < order; i++)
{
Assert.AreEqual(matrixBCopy[i], b[i]);
}
}
public void CanSolveForRandomVectorWhenResultVectorGivenUsingThinQR(int order)
{
var matrixA = new UserDefinedMatrix(Matrix <float> .Build.Random(order, order, 1).ToArray());
var matrixACopy = matrixA.Clone();
var factorQR = matrixA.QR(QRMethod.Thin);
var vectorb = new UserDefinedVector(Vector <float> .Build.Random(order, 1).ToArray());
var vectorbCopy = vectorb.Clone();
var resultx = new UserDefinedVector(order);
factorQR.Solve(vectorb, resultx);
Assert.AreEqual(vectorb.Count, resultx.Count);
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 CanSolveForRandomVectorWhenResultVectorGiven(int order)
{
var matrixA = new UserDefinedMatrix(Matrix <Complex> .Build.Random(order, order, 1).ToArray());
var matrixACopy = matrixA.Clone();
var factorGramSchmidt = matrixA.GramSchmidt();
var vectorb = new UserDefinedVector(Vector <Complex> .Build.Random(order, 1).ToArray());
var vectorbCopy = vectorb.Clone();
var resultx = new UserDefinedVector(order);
factorGramSchmidt.Solve(vectorb, resultx);
Assert.AreEqual(vectorb.Count, 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]);
}
}
// Make sure b didn't change.
for (var i = 0; i < vectorb.Count; i++)
{
Assert.AreEqual(vectorbCopy[i], vectorb[i]);
}
}
public void CanSolveForRandomVectorAndSymmetricMatrixWhenResultVectorGiven([Values(1, 2, 5, 10, 50, 100)] int order)
{
var A = new UserDefinedMatrix(Matrix <Complex32> .Build.RandomPositiveDefinite(order, 1).ToArray());
MatrixHelpers.ForceHermitian(A);
var ACopy = A.Clone();
var evd = A.Evd(Symmetricity.Hermitian);
var b = new UserDefinedVector(Vector <Complex32> .Build.Random(order, 1).ToArray());
var bCopy = b.Clone();
var x = new UserDefinedVector(order);
evd.Solve(b, x);
var bReconstruct = A * x;
// Check the reconstruction.
AssertHelpers.AlmostEqual(b, bReconstruct, 2);
// Make sure A/B didn't change.
AssertHelpers.AlmostEqual(ACopy, A, 14);
AssertHelpers.AlmostEqual(bCopy, b, 14);
}
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 CanSolveForRandomMatrixAndSymmetricMatrixWhenResultMatrixGiven([Values(1, 2, 5, 10, 50, 100)] int order)
{
var A = new UserDefinedMatrix(Matrix<Complex>.Build.RandomPositiveDefinite(order, 1).ToArray());
MatrixHelpers.ForceHermitian(A);
var ACopy = A.Clone();
var evd = A.Evd(Symmetricity.Hermitian);
var B = new UserDefinedMatrix(Matrix<Complex>.Build.Random(order, order, 1).ToArray());
var BCopy = B.Clone();
var X = new UserDefinedMatrix(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, 9);
// Make sure A/B didn't change.
AssertHelpers.AlmostEqual(ACopy, A, 14);
AssertHelpers.AlmostEqual(BCopy, B, 14);
}
public void CanSolveForRandomVectorAndSymmetricMatrixWhenResultVectorGiven([Values(1, 2, 5, 10, 50, 100)] int order)
{
var A = new UserDefinedMatrix(Matrix<Complex>.Build.RandomPositiveDefinite(order, 1).ToArray());
MatrixHelpers.ForceHermitian(A);
var ACopy = A.Clone();
var evd = A.Evd(Symmetricity.Hermitian);
var b = new UserDefinedVector(Vector<Complex>.Build.Random(order, 1).ToArray());
var bCopy = b.Clone();
var x = new UserDefinedVector(order);
evd.Solve(b, x);
var bReconstruct = A * x;
// Check the reconstruction.
AssertHelpers.AlmostEqual(b, bReconstruct, 9);
// Make sure A/B didn't change.
AssertHelpers.AlmostEqual(ACopy, A, 14);
AssertHelpers.AlmostEqual(bCopy, b, 14);
}
public void CanSolveForRandomVectorWhenResultVectorGiven(int order)
{
var matrixA = new UserDefinedMatrix(Matrix<Complex>.Build.Random(order, order, 1).ToArray());
var matrixACopy = matrixA.Clone();
var factorGramSchmidt = matrixA.GramSchmidt();
var vectorb = new UserDefinedVector(Vector<Complex>.Build.Random(order, 1).ToArray());
var vectorbCopy = vectorb.Clone();
var resultx = new UserDefinedVector(order);
factorGramSchmidt.Solve(vectorb, resultx);
Assert.AreEqual(vectorb.Count, 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]);
}
}
// Make sure b didn't change.
for (var i = 0; i < vectorb.Count; i++)
{
Assert.AreEqual(vectorbCopy[i], vectorb[i]);
}
}
public void CanSolveForRandomMatrixWhenResultMatrixGiven(int order)
{
var matrixA = new UserDefinedMatrix(Matrix<Complex>.Build.Random(order, order, 1).ToArray());
var matrixACopy = matrixA.Clone();
var factorGramSchmidt = matrixA.GramSchmidt();
var matrixB = new UserDefinedMatrix(Matrix<Complex>.Build.Random(order, order, 1).ToArray());
var matrixBCopy = matrixB.Clone();
var matrixX = new UserDefinedMatrix(order, order);
factorGramSchmidt.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++)
{
AssertHelpers.AlmostEqual(matrixB[i, j], matrixBReconstruct[i, j], 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]);
}
}
// 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 CanSolveForRandomVectorWhenResultVectorGivenUsingThinQR(int order)
{
var matrixA = new UserDefinedMatrix(Matrix<double>.Build.Random(order, order, 1).ToArray());
var matrixACopy = matrixA.Clone();
var factorQR = matrixA.QR(QRMethod.Thin);
var vectorb = new UserDefinedVector(Vector<double>.Build.Random(order, 1).ToArray());
var vectorbCopy = vectorb.Clone();
var resultx = new UserDefinedVector(order);
factorQR.Solve(vectorb, resultx);
Assert.AreEqual(vectorb.Count, resultx.Count);
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 CanSolveForRandomMatrixWhenResultMatrixGiven(int row, int col)
{
var matrixA = new UserDefinedMatrix(Matrix<float>.Build.RandomPositiveDefinite(row, 1).ToArray());
var matrixACopy = matrixA.Clone();
var chol = matrixA.Cholesky();
var matrixB = new UserDefinedMatrix(Matrix<float>.Build.Random(row, col, 1).ToArray());
var matrixBCopy = matrixB.Clone();
var matrixX = new UserDefinedMatrix(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], matrixBReconstruct[i, j], 1.0);
}
}
// 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 CanSolveForRandomVector(int order)
{
var matrixA = new UserDefinedMatrix(Matrix<Complex32>.Build.RandomPositiveDefinite(order, 1).ToArray());
var matrixACopy = matrixA.Clone();
var chol = matrixA.Cholesky();
var b = new UserDefinedVector(Vector<Complex32>.Build.Random(order, 1).ToArray());
var x = chol.Solve(b);
Assert.AreEqual(b.Count, x.Count);
var matrixBReconstruct = matrixA * x;
// Check the reconstruction.
for (var i = 0; i < order; i++)
{
Assert.AreEqual(b[i].Real, matrixBReconstruct[i].Real, 1e-3f);
Assert.AreEqual(b[i].Imaginary, matrixBReconstruct[i].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]);
}
}
}
public void CanSolveForRandomMatrix(int row, int col)
{
var matrixA = new UserDefinedMatrix(Matrix<Complex32>.Build.RandomPositiveDefinite(row, 1).ToArray());
var matrixACopy = matrixA.Clone();
var chol = matrixA.Cholesky();
var matrixB = new UserDefinedMatrix(Matrix<Complex32>.Build.Random(row, col, 1).ToArray());
var matrixX = chol.Solve(matrixB);
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, 0.01f);
Assert.AreEqual(matrixB[i, j].Imaginary, matrixBReconstruct[i, j].Imaginary, 0.01f);
}
}
// 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 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 CanSolveForRandomVectorUsingThinQR(int order)
{
var matrixA = new UserDefinedMatrix(Matrix<Complex>.Build.Random(order, order, 1).ToArray());
var matrixACopy = matrixA.Clone();
var factorQR = matrixA.QR(QRMethod.Thin);
var vectorb = new UserDefinedVector(Vector<Complex>.Build.Random(order, 1).ToArray());
var resultx = factorQR.Solve(vectorb);
Assert.AreEqual(matrixA.ColumnCount, resultx.Count);
var matrixBReconstruct = matrixA * resultx;
// Check the reconstruction.
for (var i = 0; i < order; 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 CanSolveForRandomMatrixAndSymmetricMatrix(int order)
{
var matrixA = new UserDefinedMatrix(Matrix<double>.Build.RandomPositiveDefinite(order, 1).ToArray());
var matrixACopy = matrixA.Clone();
var factorEvd = matrixA.Evd();
var matrixB = new UserDefinedMatrix(Matrix<double>.Build.Random(order, order, 1).ToArray());
var matrixX = factorEvd.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-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 CanInverse(int order)
{
var matrixA = new UserDefinedMatrix(Matrix<Complex>.Build.Random(order, order, 1).ToArray());
var matrixACopy = matrixA.Clone();
var factorLU = matrixA.LU();
var matrixAInverse = factorLU.Inverse();
// The inverse dimension is equal A
Assert.AreEqual(matrixAInverse.RowCount, matrixAInverse.RowCount);
Assert.AreEqual(matrixAInverse.ColumnCount, matrixAInverse.ColumnCount);
var matrixIdentity = matrixA * matrixAInverse;
// 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]);
}
}
// Check if multiplication of A and AI produced identity matrix.
for (var i = 0; i < matrixIdentity.RowCount; i++)
{
AssertHelpers.AlmostEqualRelative(matrixIdentity[i, i], Complex.One, 9);
}
}
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 CanSolveForRandomVectorAndSymmetricMatrix([Values(1, 2, 5, 10, 50, 100)] int order)
{
var A = new UserDefinedMatrix(Matrix<float>.Build.RandomPositiveDefinite(order, 1).ToArray());
MatrixHelpers.ForceSymmetric(A);
var ACopy = A.Clone();
var evd = A.Evd();
var b = new UserDefinedVector(Vector<float>.Build.Random(order, 1).ToArray());
var bCopy = b.Clone();
var x = evd.Solve(b);
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);
}
public void CanSolveForRandomVector(int order)
{
var matrixA = new UserDefinedMatrix(Matrix<float>.Build.Random(order, order, 1).ToArray());
var matrixACopy = matrixA.Clone();
var factorLU = matrixA.LU();
var vectorb = new UserDefinedVector(Vector<float>.Build.Random(order, 1).ToArray());
var resultx = factorLU.Solve(vectorb);
Assert.AreEqual(matrixA.ColumnCount, resultx.Count);
var matrixBReconstruct = matrixA * resultx;
// Check the reconstruction.
for (var i = 0; i < order; 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]);
}
}
}
public void CanSolveForRandomMatrixWhenResultMatrixGivenUsingThinQR(int order)
{
var matrixA = new UserDefinedMatrix(Matrix<double>.Build.Random(order, order, 1).ToArray());
var matrixACopy = matrixA.Clone();
var factorQR = matrixA.QR(QRMethod.Thin);
var matrixB = new UserDefinedMatrix(Matrix<double>.Build.Random(order, order, 1).ToArray());
var matrixBCopy = matrixB.Clone();
var matrixX = new UserDefinedMatrix(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], 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]);
}
}
// 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 CanSolveForRandomMatrix(int order)
{
var matrixA = new UserDefinedMatrix(Matrix<Complex32>.Build.Random(order, order, 1).ToArray());
var matrixACopy = matrixA.Clone();
var factorLU = matrixA.LU();
var matrixB = new UserDefinedMatrix(Matrix<Complex32>.Build.Random(order, order, 1).ToArray());
var matrixX = factorLU.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].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]);
}
}
}
public void CanSolveForRandomVectorWhenResultVectorGiven(int order)
{
var matrixA = new UserDefinedMatrix(Matrix<float>.Build.RandomPositiveDefinite(order, 1).ToArray());
var matrixACopy = matrixA.Clone();
var chol = matrixA.Cholesky();
var b = new UserDefinedVector(Vector<float>.Build.Random(order, 1).ToArray());
var matrixBCopy = b.Clone();
var x = new UserDefinedVector(order);
chol.Solve(b, x);
Assert.AreEqual(b.Count, x.Count);
var matrixBReconstruct = matrixA * x;
// Check the reconstruction.
for (var i = 0; i < order; i++)
{
Assert.AreEqual(b[i], matrixBReconstruct[i], 0.5);
}
// 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 < order; i++)
{
Assert.AreEqual(matrixBCopy[i], b[i]);
}
}
public void CanSolveForRandomVectorAndSymmetricMatrix([Values(1, 2, 5, 10, 50, 100)] int order)
{
var matrixA = new UserDefinedMatrix(Matrix<Complex32>.Build.RandomPositiveDefinite(order, 1).ToArray());
var matrixACopy = matrixA.Clone();
var factorEvd = matrixA.Evd();
var vectorb = new UserDefinedVector(Vector<Complex32>.Build.Random(order, 1).ToArray());
var resultx = factorEvd.Solve(vectorb);
Assert.AreEqual(matrixA.ColumnCount, resultx.Count);
var matrixBReconstruct = matrixA * resultx;
// Check the reconstruction.
for (var i = 0; i < vectorb.Count; i++)
{
Assert.AreEqual(vectorb[i].Real, matrixBReconstruct[i].Real, 1e-3f);
Assert.AreEqual(vectorb[i].Imaginary, matrixBReconstruct[i].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]);
}
}
}
public void CanSolveForRandomVector(int order)
{
var matrixA = new UserDefinedMatrix(Matrix<Complex32>.Build.Random(order, order, 1).ToArray());
var matrixACopy = matrixA.Clone();
var factorGramSchmidt = matrixA.GramSchmidt();
var vectorb = new UserDefinedVector(Vector<Complex32>.Build.Random(order, 1).ToArray());
var resultx = factorGramSchmidt.Solve(vectorb);
Assert.AreEqual(matrixA.ColumnCount, resultx.Count);
var matrixBReconstruct = matrixA * resultx;
// Check the reconstruction.
for (var i = 0; i < order; i++)
{
Assert.AreEqual(vectorb[i].Real, matrixBReconstruct[i].Real, 1e-3f);
Assert.AreEqual(vectorb[i].Imaginary, matrixBReconstruct[i].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]);
}
}
}
public void CanSolveForRandomVectorAndSymmetricMatrixWhenResultVectorGiven(int order)
{
var matrixA = new UserDefinedMatrix(Matrix<double>.Build.RandomPositiveDefinite(order, 1).ToArray());
var matrixACopy = matrixA.Clone();
var factorEvd = matrixA.Evd();
var vectorb = new UserDefinedVector(Vector<double>.Build.Random(order, 1).ToArray());
var vectorbCopy = vectorb.Clone();
var resultx = new UserDefinedVector(order);
factorEvd.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-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]);
}
}
// Make sure b didn't change.
for (var i = 0; i < vectorb.Count; i++)
{
Assert.AreEqual(vectorbCopy[i], vectorb[i]);
}
}
