/// <summary> /// Initializes a new instance of the <see cref="UserQR"/> class. This object will compute the /// QR factorization when the constructor is called and cache it's factorization. /// </summary> /// <param name="matrix">The matrix to factor.</param> /// <exception cref="ArgumentNullException">If <paramref name="matrix"/> is <c>null</c>.</exception> public UserQR(Matrix <double> matrix) { if (matrix == null) { throw new ArgumentNullException("matrix"); } if (matrix.RowCount < matrix.ColumnCount) { throw Matrix.DimensionsDontMatch <ArgumentException>(matrix); } MatrixR = matrix.Clone(); MatrixQ = matrix.CreateMatrix(matrix.RowCount, matrix.RowCount); for (var i = 0; i < matrix.RowCount; i++) { MatrixQ.At(i, i, 1.0); } var minmn = Math.Min(matrix.RowCount, matrix.ColumnCount); var u = new double[minmn][]; for (var i = 0; i < minmn; i++) { u[i] = GenerateColumn(MatrixR, i, i); ComputeQR(u[i], MatrixR, i, matrix.RowCount, i + 1, matrix.ColumnCount, Control.NumberOfParallelWorkerThreads); } for (var i = minmn - 1; i >= 0; i--) { ComputeQR(u[i], MatrixQ, i, matrix.RowCount, i, matrix.RowCount, Control.NumberOfParallelWorkerThreads); } }
/// <summary> /// Initializes a new instance of the <see cref="UserGramSchmidt"/> class. This object creates an unitary matrix /// using the modified Gram-Schmidt method. /// </summary> /// <param name="matrix">The matrix to factor.</param> /// <exception cref="ArgumentNullException">If <paramref name="matrix"/> is <c>null</c>.</exception> /// <exception cref="ArgumentException">If <paramref name="matrix"/> row count is less then column count</exception> /// <exception cref="ArgumentException">If <paramref name="matrix"/> is rank deficient</exception> public UserGramSchmidt(Matrix <Complex32> matrix) { if (matrix == null) { throw new ArgumentNullException("matrix"); } if (matrix.RowCount < matrix.ColumnCount) { throw new ArgumentException(Resources.ArgumentMatrixDimensions); } MatrixQ = matrix.Clone(); MatrixR = matrix.CreateMatrix(matrix.ColumnCount, matrix.ColumnCount); for (var k = 0; k < MatrixQ.ColumnCount; k++) { var norm = MatrixQ.Column(k).Norm(2).Real; if (norm == 0.0f) { throw new ArgumentException(Resources.ArgumentMatrixNotRankDeficient); } MatrixR.At(k, k, norm); for (var i = 0; i < MatrixQ.RowCount; i++) { MatrixQ.At(i, k, MatrixQ.At(i, k) / norm); } for (var j = k + 1; j < MatrixQ.ColumnCount; j++) { var dot = Complex32.Zero; for (int i = 0; i < MatrixQ.RowCount; i++) { dot += MatrixQ.Column(k)[i].Conjugate() * MatrixQ.Column(j)[i]; } MatrixR.At(k, j, dot); for (var i = 0; i < MatrixQ.RowCount; i++) { var value = MatrixQ.At(i, j) - (MatrixQ.At(i, k) * dot); MatrixQ.At(i, j, value); } } } }
/// <summary> /// Initializes a new instance of the <see cref="UserGramSchmidt"/> class. This object creates an orthogonal matrix /// using the modified Gram-Schmidt method. /// </summary> /// <param name="matrix">The matrix to factor.</param> /// <exception cref="ArgumentNullException">If <paramref name="matrix"/> is <c>null</c>.</exception> /// <exception cref="ArgumentException">If <paramref name="matrix"/> row count is less then column count</exception> /// <exception cref="ArgumentException">If <paramref name="matrix"/> is rank deficient</exception> public UserGramSchmidt(Matrix <float> matrix) { if (matrix == null) { throw new ArgumentNullException("matrix"); } if (matrix.RowCount < matrix.ColumnCount) { throw new ArgumentException(Resources.ArgumentMatrixDimensions); } MatrixQ = matrix.Clone(); MatrixR = matrix.CreateMatrix(matrix.ColumnCount, matrix.ColumnCount); for (var k = 0; k < MatrixQ.ColumnCount; k++) { var norm = MatrixQ.Column(k).Norm(2); if (norm == 0.0) { throw new ArgumentException(Resources.ArgumentMatrixNotRankDeficient); } MatrixR.At(k, k, norm); for (var i = 0; i < MatrixQ.RowCount; i++) { MatrixQ.At(i, k, MatrixQ.At(i, k) / norm); } for (var j = k + 1; j < MatrixQ.ColumnCount; j++) { var dot = MatrixQ.Column(k).DotProduct(MatrixQ.Column(j)); MatrixR.At(k, j, dot); for (var i = 0; i < MatrixQ.RowCount; i++) { var value = MatrixQ.At(i, j) - (MatrixQ.At(i, k) * dot); MatrixQ.At(i, j, value); } } } }
/// <summary> /// Solves a system of linear equations, <b>Ax = b</b>, with A QR factorized. /// </summary> /// <param name="input">The right hand side vector, <b>b</b>.</param> /// <param name="result">The left hand side <see cref="Matrix{T}"/>, <b>x</b>.</param> public override void Solve(Vector <double> input, Vector <double> result) { if (input == null) { throw new ArgumentNullException("input"); } if (result == null) { throw new ArgumentNullException("result"); } // Ax=b where A is an m x n matrix // Check that b is a column vector with m entries if (MatrixR.RowCount != input.Count) { throw new ArgumentException(Resources.ArgumentVectorsSameLength); } // Check that x is a column vector with n entries if (MatrixR.ColumnCount != result.Count) { throw Matrix.DimensionsDontMatch <ArgumentException>(MatrixR, result); } var inputCopy = input.Clone(); // Compute Y = transpose(Q)*B var column = new double[MatrixR.RowCount]; for (var k = 0; k < MatrixR.RowCount; k++) { column[k] = inputCopy[k]; } for (var i = 0; i < MatrixR.RowCount; i++) { double s = 0; for (var k = 0; k < MatrixR.RowCount; k++) { s += MatrixQ.At(k, i) * column[k]; } inputCopy[i] = s; } // Solve R*X = Y; for (var k = MatrixR.ColumnCount - 1; k >= 0; k--) { inputCopy[k] /= MatrixR.At(k, k); for (var i = 0; i < k; i++) { inputCopy[i] -= inputCopy[k] * MatrixR.At(i, k); } } for (var i = 0; i < MatrixR.ColumnCount; i++) { result[i] = inputCopy[i]; } }
/// <summary> /// Solves a system of linear equations, <b>AX = B</b>, with A QR factorized. /// </summary> /// <param name="input">The right hand side <see cref="Matrix{T}"/>, <b>B</b>.</param> /// <param name="result">The left hand side <see cref="Matrix{T}"/>, <b>X</b>.</param> public override void Solve(Matrix <double> input, Matrix <double> result) { // Check for proper arguments. if (input == null) { throw new ArgumentNullException("input"); } if (result == null) { throw new ArgumentNullException("result"); } // The solution X should have the same number of columns as B if (input.ColumnCount != result.ColumnCount) { throw new ArgumentException(Resources.ArgumentMatrixSameColumnDimension); } // The dimension compatibility conditions for X = A\B require the two matrices A and B to have the same number of rows if (MatrixR.RowCount != input.RowCount) { throw new ArgumentException(Resources.ArgumentMatrixSameRowDimension); } // The solution X row dimension is equal to the column dimension of A if (MatrixR.ColumnCount != result.RowCount) { throw new ArgumentException(Resources.ArgumentMatrixSameColumnDimension); } var inputCopy = input.Clone(); // Compute Y = transpose(Q)*B var column = new double[MatrixR.RowCount]; for (var j = 0; j < input.ColumnCount; j++) { for (var k = 0; k < MatrixR.RowCount; k++) { column[k] = inputCopy.At(k, j); } for (var i = 0; i < MatrixR.RowCount; i++) { double s = 0; for (var k = 0; k < MatrixR.RowCount; k++) { s += MatrixQ.At(k, i) * column[k]; } inputCopy.At(i, j, s); } } // Solve R*X = Y; for (var k = MatrixR.ColumnCount - 1; k >= 0; k--) { for (var j = 0; j < input.ColumnCount; j++) { inputCopy.At(k, j, inputCopy.At(k, j) / MatrixR.At(k, k)); } for (var i = 0; i < k; i++) { for (var j = 0; j < input.ColumnCount; j++) { inputCopy.At(i, j, inputCopy.At(i, j) - (inputCopy.At(k, j) * MatrixR.At(i, k))); } } } for (var i = 0; i < MatrixR.ColumnCount; i++) { for (var j = 0; j < inputCopy.ColumnCount; j++) { result.At(i, j, inputCopy.At(i, j)); } } }
/// <summary> /// Initializes a new instance of the <see cref="UserQR"/> class. This object will compute the /// QR factorization when the constructor is called and cache it's factorization. /// </summary> /// <param name="matrix">The matrix to factor.</param> /// <param name="method">The QR factorization method to use.</param> /// <exception cref="ArgumentNullException">If <paramref name="matrix"/> is <c>null</c>.</exception> public UserQR(Matrix <Complex32> matrix, QRMethod method = QRMethod.Full) { if (matrix == null) { throw new ArgumentNullException("matrix"); } if (matrix.RowCount < matrix.ColumnCount) { throw Matrix.DimensionsDontMatch <ArgumentException>(matrix); } QrMethod = method; var minmn = Math.Min(matrix.RowCount, matrix.ColumnCount); var u = new Complex32[minmn][]; if (method == QRMethod.Full) { MatrixR = matrix.Clone(); MatrixQ = matrix.CreateMatrix(matrix.RowCount, matrix.RowCount); for (var i = 0; i < matrix.RowCount; i++) { MatrixQ.At(i, i, 1.0f); } for (var i = 0; i < minmn; i++) { u[i] = GenerateColumn(MatrixR, i, i); ComputeQR(u[i], MatrixR, i, matrix.RowCount, i + 1, matrix.ColumnCount, Control.NumberOfParallelWorkerThreads); } for (var i = minmn - 1; i >= 0; i--) { ComputeQR(u[i], MatrixQ, i, matrix.RowCount, i, matrix.RowCount, Control.NumberOfParallelWorkerThreads); } } else { MatrixR = matrix.CreateMatrix(matrix.ColumnCount, matrix.ColumnCount); MatrixQ = matrix.Clone(); for (var i = 0; i < minmn; i++) { u[i] = GenerateColumn(MatrixQ, i, i); ComputeQR(u[i], MatrixQ, i, matrix.RowCount, i + 1, matrix.ColumnCount, Control.NumberOfParallelWorkerThreads); } MatrixR = MatrixQ.SubMatrix(0, matrix.ColumnCount, 0, matrix.ColumnCount); MatrixQ.Clear(); for (var i = 0; i < matrix.ColumnCount; i++) { MatrixQ.At(i, i, 1.0f); } for (var i = minmn - 1; i >= 0; i--) { ComputeQR(u[i], MatrixQ, i, matrix.RowCount, i, matrix.ColumnCount, Control.NumberOfParallelWorkerThreads); } } }