public void MultiplyTranspose() { double[][] square = { new double[] { 166.0, 188.0, 210.0 }, new double[] { 188.0, 214.0, 240.0 }, new double[] { 210.0, 240.0, 270.0 } }; GeneralMatrix sq = new GeneralMatrix(square); Assert.IsTrue(GeneralTests.Check(A.Multiply(A.Transpose()), sq)); }
public Point GetActualDisplayPosition(Point p) { GeneralMatrix mat = new GeneralMatrix(3, 1); mat.SetElement(0, 0, (double)p.X); mat.SetElement(1, 0, (double)p.Y); mat.SetElement(2, 0, 1.0); GeneralMatrix ret = m_transform.Multiply(mat); return(new Point((int)ret.GetElement(0, 0), (int)ret.GetElement(1, 0))); }
private double[] CalculateNextPoint(double[] pX, double[] pGrad, GeneralMatrix hessian) { int i = 0; double xmin = 0; double step = _step; GeneralMatrix alfaX = new GeneralMatrix(_nDim, 1); GeneralMatrix prevX = new GeneralMatrix(pX, _nDim); GeneralMatrix prevGrad = new GeneralMatrix(pGrad, _nDim); double[] intermediate = new double[_nDim];; alfaX = hessian.Multiply(prevGrad); //doing a line search to minimize alpha OneDWrapper wrapper = new OneDWrapper(_f, prevX, alfaX); LineSearch search = new LineSearch(); double[] interval = new double[Constants.BRACKET_POINTS]; int it1 = search.FindMinInterval(wrapper, _alpha, step, 50, ref interval); int it2 = search.FindMinimumViaBrent(wrapper, interval[0], interval[1], interval[2], 50, _epsilon, ref xmin); for (i = 0; i < _nDim; i++) { intermediate[i] = prevX.GetElement(i, 0) - xmin * alfaX.GetElement(i, 0); } _alpha = xmin; return(intermediate); }
public void Inverse() { GeneralMatrix r = GeneralMatrix.Random(4, 4); GeneralMatrix iR = r.Inverse(); Assert.IsTrue(GeneralTests.Check(r.Multiply(iR), GeneralMatrix.Identity(4, 4))); }
protected override GeneralMatrix CalculateNextHessianApproximation(GeneralMatrix previousH, double[] prevX, double[] curX, double[] prevGrad, double[] curGrad) { GeneralMatrix currentH = new GeneralMatrix(_nDim, _nDim); GeneralMatrix cX = new GeneralMatrix(curX, _nDim); GeneralMatrix pX = new GeneralMatrix(prevX, _nDim); GeneralMatrix cG = new GeneralMatrix(curGrad, _nDim); GeneralMatrix pG = new GeneralMatrix(prevGrad, _nDim); GeneralMatrix dX = cX.Subtract(pX); GeneralMatrix dG = cG.Subtract(pG); double aK1 = 1 / (dX.Transpose().Multiply(dG).GetElement(0, 0)); GeneralMatrix aK2 = dX.Multiply(dX.Transpose()); GeneralMatrix aK = aK2.Multiply(aK1); double bK1 = -1 / (dG.Transpose().Multiply(previousH).Multiply(dG).GetElement(0, 0)); GeneralMatrix bK2 = previousH.Multiply(dG).Multiply(dG.Transpose()).Multiply(previousH.Transpose()); GeneralMatrix bK = bK2.Multiply(bK1); currentH = previousH.Add(aK).Add(bK); return(currentH); }
public void CholeskyDecomposition2() { double[][] pvals = { new double[] { 1.0, 1.0, 1.0 }, new double[] { 1.0, 2.0, 3.0 }, new double[] { 1.0, 3.0, 6.0 } }; GeneralMatrix A = new GeneralMatrix(pvals); CholeskyDecomposition chol = A.chol(); GeneralMatrix X = chol.Solve(GeneralMatrix.Identity(3, 3)); Assert.IsTrue(GeneralTests.Check(A.Multiply(X), GeneralMatrix.Identity(3, 3))); }
public void CholeskyDecomposition1() { double[][] pvals = { new double[] { 1.0, 1.0, 1.0 }, new double[] { 1.0, 2.0, 3.0 }, new double[] { 1.0, 3.0, 6.0 } }; GeneralMatrix A = new GeneralMatrix(pvals); CholeskyDecomposition chol = A.chol(); GeneralMatrix L = chol.GetL(); Assert.IsTrue(GeneralTests.Check(A, L.Multiply(L.Transpose()))); }
public void EigenValueDecomposition2() { double[][] evals = { new double[] { 0.0, 1.0, 0.0, 0.0 }, new double[] { 1.0, 0.0, 2e-7, 0.0 }, new double[] { 0.0, -2e-7, 0.0, 1.0 }, new double[] { 0.0, 0.0, 1.0, 0.0 } }; GeneralMatrix A = new GeneralMatrix(evals); EigenvalueDecomposition Eig = A.Eigen(); GeneralMatrix D = Eig.D; GeneralMatrix V = Eig.GetV(); Assert.IsTrue(GeneralTests.Check(A.Multiply(V), V.Multiply(D))); }
private static void CalculatePCA(List <Point3D> _points, out Point3D pivotO, out Vector3D vecX, out Vector3D vecY, out Vector3D vecZ) { pivotO = new Point3D(0, 0, 0); vecX = new Vector3D(0, 0, 0); vecY = new Vector3D(0, 0, 0); vecZ = new Vector3D(0, 0, 0); if (_points == null || _points.Count < 1) { return; } Point3D pivot = GeometricTransforms.GetPivot(_points); pivotO = new Point3D(pivot.X, pivot.Y, pivot.Z); List <Vector3D> point_deviations = _points.Select(x => x - pivot).ToList(); int nrP = _points.Count; #region COVARIANCE:Old //// compute the covariance matrix //double[] m = new double[3*nrP]; //for(int i = 0; i < nrP; i++) //{ // m[i*3] = point_deviations[i].X; // m[i*3 + 1] = point_deviations[i].Y; // m[i*3 + 2] = point_deviations[i].Z; //} //MatrixNxN M = new MatrixNxN(nrP, 3, m); //MatrixNxN MtxM = MatrixNxN.Squared(M); //MtxM.Scale(1.0 / nrP); #endregion // compute the covariance matrix ... // using 3rd party library DotNetMatrix double[][] pd_as_array = new double[nrP][]; for (int i = 0; i < nrP; i++) { pd_as_array[i] = new double[] { point_deviations[i].X, point_deviations[i].Y, point_deviations[i].Z }; } GeneralMatrix gm_M = new GeneralMatrix(pd_as_array); GeneralMatrix gm_Mt = gm_M.Transpose(); GeneralMatrix gm_Msq = gm_Mt.Multiply(gm_M); GeneralMatrix gm_Msqn = gm_Msq.Multiply(1.0 / nrP); // extract the sorted Eigenvalues of the matrix... // using 3rd party library DotNetMatrix EigenvalueDecomposition decomp = gm_Msqn.Eigen(); GeneralMatrix gm_EVec = decomp.GetV(); double[] gm_EVal = decomp.RealEigenvalues; // from smallest to largest eigenvalue vecX = new Vector3D(gm_EVec.GetElement(0, 0), gm_EVec.GetElement(1, 0), gm_EVec.GetElement(2, 0)); vecY = new Vector3D(gm_EVec.GetElement(0, 1), gm_EVec.GetElement(1, 1), gm_EVec.GetElement(2, 1)); vecZ = new Vector3D(gm_EVec.GetElement(0, 2), gm_EVec.GetElement(1, 2), gm_EVec.GetElement(2, 2)); }
protected override GeneralMatrix CalculateNextHessianApproximation(GeneralMatrix pH, double[] prevX, double[] curX, double[] prevGrad, double[] curGrad) { GeneralMatrix cH = new GeneralMatrix(_nDim, _nDim); GeneralMatrix cX = new GeneralMatrix(curX, _nDim); GeneralMatrix pX = new GeneralMatrix(prevX, _nDim); GeneralMatrix cG = new GeneralMatrix(curGrad, _nDim); GeneralMatrix pG = new GeneralMatrix(prevGrad, _nDim); GeneralMatrix sigma = cX.Subtract(pX); GeneralMatrix gamma = cG.Subtract(pG); double sigmaTGamma = sigma.Transpose().Multiply(gamma).GetElement(0, 0); GeneralMatrix hGammaSigmaT = pH.Multiply(gamma.Multiply(sigma.Transpose())); GeneralMatrix sigmaGammaTH = sigma.Multiply(gamma.Transpose().Multiply(pH)); double gammaTHGamma = (gamma.Transpose().Multiply(pH.Multiply(gamma))).GetElement(0, 0); GeneralMatrix sigmaSigmaT = sigma.Multiply(sigma.Transpose()); GeneralMatrix term1 = (hGammaSigmaT.Add(sigmaGammaTH)).Multiply(1 / sigmaTGamma); GeneralMatrix term2 = (sigmaSigmaT.Multiply(1 / sigmaTGamma)).Multiply(1 + gammaTHGamma / sigmaTGamma); return(pH.Subtract(term1).Add(term2)); }
public static void Main(System.String[] argv) { /* | Tests LU, QR, SVD and symmetric Eig decompositions. | | n = order of magic square. | trace = diagonal sum, should be the magic sum, (n^3 + n)/2. | max_eig = maximum eigenvalue of (A + A')/2, should equal trace. | rank = linear algebraic rank, | should equal n if n is odd, be less than n if n is even. | cond = L_2 condition number, ratio of singular values. | lu_res = test of LU factorization, norm1(L*U-A(p,:))/(n*eps). | qr_res = test of QR factorization, norm1(Q*R-A)/(n*eps). */ print("\n Test of GeneralMatrix Class, using magic squares.\n"); print(" See MagicSquareExample.main() for an explanation.\n"); print("\n n trace max_eig rank cond lu_res qr_res\n\n"); System.DateTime start_time = System.DateTime.Now; double eps = System.Math.Pow(2.0, -52.0); for (int n = 3; n <= 32; n++) { print(fixedWidthIntegertoString(n, 7)); GeneralMatrix M = magic(n); //UPGRADE_WARNING: Narrowing conversions may produce unexpected results in C#. 'ms-help://MS.VSCC.2003/commoner/redir/redirect.htm?keyword="jlca1042"' int t = (int)M.Trace(); print(fixedWidthIntegertoString(t, 10)); EigenvalueDecomposition E = new EigenvalueDecomposition(M.Add(M.Transpose()).Multiply(0.5)); double[] d = E.RealEigenvalues; print(fixedWidthDoubletoString(d[n - 1], 14, 3)); int r = M.Rank(); print(fixedWidthIntegertoString(r, 7)); double c = M.Condition(); print(c < 1 / eps ? fixedWidthDoubletoString(c, 12, 3):" Inf"); LUDecomposition LU = new LUDecomposition(M); GeneralMatrix L = LU.L; GeneralMatrix U = LU.U; int[] p = LU.Pivot; GeneralMatrix R = L.Multiply(U).Subtract(M.GetMatrix(p, 0, n - 1)); double res = R.Norm1() / (n * eps); print(fixedWidthDoubletoString(res, 12, 3)); QRDecomposition QR = new QRDecomposition(M); GeneralMatrix Q = QR.Q; R = QR.R; R = Q.Multiply(R).Subtract(M); res = R.Norm1() / (n * eps); print(fixedWidthDoubletoString(res, 12, 3)); print("\n"); } System.DateTime stop_time = System.DateTime.Now; double etime = (stop_time.Ticks - start_time.Ticks) / 1000.0; print("\nElapsed Time = " + fixedWidthDoubletoString(etime, 12, 3) + " seconds\n"); print("Adios\n"); }
public void CalculateEigenvalueDecomposition() { double[] i = new double[3]; double[] j = new double[3]; double[] k = new double[3]; double[] u = new double[3]; double[] t_vol = new double[3]; double[] vol = new double[3]; vol[0] = 0; vol[1] = 0; vol[2] = 0; double[] func_sum = new double[3]; func_sum[0] = 0; func_sum[1] = 0; func_sum[2] = 0; double[] func_sum_inertia = new double[3]; func_sum_inertia[0] = 0; func_sum_inertia[1] = 0; func_sum_inertia[2] = 0; double func_sum_xy = 0; double func_sum_xz = 0; double func_sum_yz = 0; double surfaceArea = 0; //loop through all the triangles for (int count = 0; count < _connections.Length; count++) { //get the 3 points of the triangle double[] p1 = new double[3]; double[] p2 = new double[3]; double[] p3 = new double[3]; //Fix so its relative to the centroid center of mass p1[0] = (double)_pts[_connections[count][0]][0] - _centroid[0]; //fix x's first p2[0] = (double)_pts[_connections[count][1]][0] - _centroid[0]; p3[0] = (double)_pts[_connections[count][2]][0] - _centroid[0]; p1[1] = (double)_pts[_connections[count][0]][1] - _centroid[1]; //fix y's p2[1] = (double)_pts[_connections[count][1]][1] - _centroid[1]; p3[1] = (double)_pts[_connections[count][2]][1] - _centroid[1]; p1[2] = (double)_pts[_connections[count][0]][2] - _centroid[2]; //fix z's p2[2] = (double)_pts[_connections[count][1]][2] - _centroid[2]; p3[2] = (double)_pts[_connections[count][2]][2] - _centroid[2]; //calculate the i, j, k vectors i[0] = p2[0] - p1[0]; j[0] = p2[1] - p1[1]; k[0] = p2[2] - p1[2]; i[1] = p3[0] - p1[0]; j[1] = p3[1] - p1[1]; k[1] = p3[2] - p1[2]; i[2] = p3[0] - p2[0]; j[2] = p3[1] - p2[1]; k[2] = p3[2] - p2[2]; //cross product between two vectors, to determine normal vector u[0] = j[0] * k[1] - k[0] * j[1]; u[1] = k[0] * i[1] - i[0] * k[1]; u[2] = i[0] * j[1] - j[0] * i[1]; //Normalize vector to 1 double norm = Math.Sqrt(u[0] * u[0] + u[1] * u[1] + u[2] * u[2]); if (norm != 0.0) { u[0] = u[0] / norm; u[1] = u[1] / norm; u[2] = u[2] / norm; } else { u[0] = 0.0; u[1] = 0.0; u[2] = 0.0; } //This is reduced to ... //area of a triangle... double a = Math.Sqrt(i[1] * i[1] + j[1] * j[1] + k[1] * k[1]); double b = Math.Sqrt(i[0] * i[0] + j[0] * j[0] + k[0] * k[0]); double c = Math.Sqrt(i[2] * i[2] + j[2] * j[2] + k[2] * k[2]); double s = 0.5 * (a + b + c); double area = Math.Sqrt(Math.Abs(s * (s - a) * (s - b) * (s - c))); //patches(count,1) = area // surfaceArea += area; //volume elements ... double zavg = (p1[2] + p2[2] + p3[2]) / 3.0; double yavg = (p1[1] + p2[1] + p3[1]) / 3.0; double xavg = (p1[0] + p2[0] + p3[0]) / 3.0; //sum of function for centroid calculation func_sum[0] += t_vol[0] * xavg; func_sum[1] += t_vol[1] * yavg; func_sum[2] += t_vol[2] * zavg; //sum of function for inertia calculation func_sum_inertia[0] += area * u[0] * xavg * xavg * xavg; func_sum_inertia[1] += area * u[1] * yavg * yavg * yavg; func_sum_inertia[2] += area * u[2] * zavg * zavg * zavg; //sum of function for products of inertia calculation func_sum_xz += area * u[0] * xavg * xavg * zavg; func_sum_xy += area * u[1] * yavg * yavg * xavg; func_sum_yz += area * u[2] * zavg * zavg * yavg; } func_sum_inertia[0] /= 3; func_sum_inertia[1] /= 3; func_sum_inertia[2] /= 3; double Ixy = -1 * func_sum_xy / 2; double Ixz = -1 * func_sum_xz / 2; double Iyz = -1 * func_sum_yz / 2; double Iyx = Ixy; double Izx = Ixz; double Izy = Iyz; double Ixx = func_sum_inertia[1] + func_sum_inertia[2]; double Iyy = func_sum_inertia[0] + func_sum_inertia[2]; double Izz = func_sum_inertia[0] + func_sum_inertia[1]; GeneralMatrix i_CoM = new GeneralMatrix(3, 3); i_CoM.Array[0][0] = Ixx; i_CoM.Array[0][1] = Ixy; i_CoM.Array[0][2] = Ixz; i_CoM.Array[1][0] = Iyx; i_CoM.Array[1][1] = Iyy; i_CoM.Array[1][2] = Iyz; i_CoM.Array[2][0] = Izx; i_CoM.Array[2][1] = Izy; i_CoM.Array[2][2] = Izz; EigenvalueDecomposition eig = i_CoM.Eigen(); _eigenvalues = eig.D; _eigenvectors = eig.GetV(); //make sure this is a right handed matrix if (_eigenvectors.Determinant() < 0) { _eigenvectors = _eigenvectors.Multiply(-1); } }
/// <summary> /// multiply normalized priority matrix by sum of average rows /// </summary> /// <param name="argMatrix"></param> /// <param name="selection"></param> /// <returns></returns> private GeneralMatrix FCalc(GeneralMatrix argMatrix, GeneralMatrix selection) { GeneralMatrix matrix = argMatrix.Multiply(selection); return(matrix.ArrayRightDivide(selection)); }
private void computeaccCalButton_Click(object sender, EventArgs e) { int i, j; calStatusText.Text = "Computing Calibration..."; // Construct D matrix // D = [x.^2, y.^2, z.^2, x.*y, x.*z, y.*z, x, y, z, ones(N,1)]; for (i = 0; i < SAMPLES; i++) { // x^2 term D.SetElement(i, 0, loggedData[i, 0] * loggedData[i, 0]); // y^2 term D.SetElement(i, 1, loggedData[i, 1] * loggedData[i, 1]); // z^2 term D.SetElement(i, 2, loggedData[i, 2] * loggedData[i, 2]); // x*y term D.SetElement(i, 3, loggedData[i, 0] * loggedData[i, 1]); // x*z term D.SetElement(i, 4, loggedData[i, 0] * loggedData[i, 2]); // y*z term D.SetElement(i, 5, loggedData[i, 1] * loggedData[i, 2]); // x term D.SetElement(i, 6, loggedData[i, 0]); // y term D.SetElement(i, 7, loggedData[i, 1]); // z term D.SetElement(i, 8, loggedData[i, 2]); // Constant term D.SetElement(i, 9, 1); } // QR=triu(qr(D)) QRDecomposition QR = new QRDecomposition(D); // [U,S,V] = svd(D) SingularValueDecomposition SVD = new SingularValueDecomposition(QR.R); GeneralMatrix V = SVD.GetV(); GeneralMatrix A = new GeneralMatrix(3, 3); double[] p = new double[V.RowDimension]; for (i = 0; i < V.RowDimension; i++) { p[i] = V.GetElement(i, V.ColumnDimension - 1); } /* * A = [p(1) p(4)/2 p(5)/2; * p(4)/2 p(2) p(6)/2; * p(5)/2 p(6)/2 p(3)]; */ if (p[0] < 0) { for (i = 0; i < V.RowDimension; i++) { p[i] = -p[i]; } } A.SetElement(0, 0, p[0]); A.SetElement(0, 1, p[3] / 2); A.SetElement(1, 2, p[4] / 2); A.SetElement(1, 0, p[3] / 2); A.SetElement(1, 1, p[1]); A.SetElement(1, 2, p[5] / 2); A.SetElement(2, 0, p[4] / 2); A.SetElement(2, 1, p[5] / 2); A.SetElement(2, 2, p[2]); CholeskyDecomposition Chol = new CholeskyDecomposition(A); GeneralMatrix Ut = Chol.GetL(); GeneralMatrix U = Ut.Transpose(); double[] bvect = { p[6] / 2, p[7] / 2, p[8] / 2 }; double d = p[9]; GeneralMatrix b = new GeneralMatrix(bvect, 3); GeneralMatrix v = Ut.Solve(b); double vnorm_sqrd = v.GetElement(0, 0) * v.GetElement(0, 0) + v.GetElement(1, 0) * v.GetElement(1, 0) + v.GetElement(2, 0) * v.GetElement(2, 0); double s = 1 / Math.Sqrt(vnorm_sqrd - d); GeneralMatrix c = U.Solve(v); for (i = 0; i < 3; i++) { c.SetElement(i, 0, -c.GetElement(i, 0)); } U = U.Multiply(s); for (i = 0; i < 3; i++) { for (j = 0; j < 3; j++) { calMat[i, j] = U.GetElement(i, j); } } for (i = 0; i < 3; i++) { bias[i] = c.GetElement(i, 0); } accAlignment00.Text = calMat[0, 0].ToString(); accAlignment01.Text = calMat[0, 1].ToString(); accAlignment02.Text = calMat[0, 2].ToString(); accAlignment10.Text = calMat[1, 0].ToString(); accAlignment11.Text = calMat[1, 1].ToString(); accAlignment12.Text = calMat[1, 2].ToString(); accAlignment20.Text = calMat[2, 0].ToString(); accAlignment21.Text = calMat[2, 1].ToString(); accAlignment22.Text = calMat[2, 2].ToString(); biasX.Text = bias[0].ToString(); biasY.Text = bias[1].ToString(); biasZ.Text = bias[2].ToString(); calStatusText.Text = "Done"; flashCommitButton.Enabled = true; accAlignmentCommitButton.Enabled = true; }
public double[] GenerateCorrelatedShocks() { return(_L.Multiply(new GeneralMatrix(new double[][] { _randomNumberGenerators.Select(x => x.GetNormal()).ToArray() }).Transpose()).Array.Select(x => x.First()).ToArray()); }