349 lines
14 KiB
C#
349 lines
14 KiB
C#
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using System;
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using System.Collections.Generic;
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using System.Linq;
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using Microsoft.Msagl.Core.Geometry;
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using Microsoft.Msagl.Core.Layout;
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using Microsoft.Msagl.Layout.MDS;
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using Microsoft.Msagl.Core;
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namespace Microsoft.Msagl.Layout.Incremental {
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/// <summary>
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///
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/// </summary>
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public class ProcrustesCircleConstraint : IConstraint {
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Node[] V;
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int n;
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Point[] X;
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Point[] Y;
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/// <summary>
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/// Create a circle constraint with variable radius
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/// </summary>
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/// <param name="nodes"></param>
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public ProcrustesCircleConstraint(IEnumerable<Node> nodes) {
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V = nodes.ToArray();
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n = V.Length;
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X = new Point[n];
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Y = new Point[n];
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double angle = 2.0 * Math.PI / (double)n;
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double r = 10*(double)n; // we make our circle a reasonable size to aid numerical precision
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for (int i = 0; i < n; ++i) {
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double theta = angle * (double)i;
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Y[i] = new Point(r * Math.Cos(theta), r * Math.Sin(theta));
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}
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}
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/// <summary>
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/// A procrustes constraint with arbitrary target shape
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/// </summary>
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/// <param name="nodes"></param>
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/// <param name="targetConfiguration"></param>
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public ProcrustesCircleConstraint(IEnumerable<Node> nodes, IEnumerable<Point> targetConfiguration)
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{
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ValidateArg.IsNotNull(nodes, "nodes");
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ValidateArg.IsNotNull(targetConfiguration, "targetConfiguration");
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V = nodes.ToArray();
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n = V.Length;
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X = new Point[n];
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Y = new Point[n];
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int i = 0;
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Point yc = new Point();
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foreach (var p in targetConfiguration) {
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Y[i++] = p;
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yc += p;
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}
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yc /= n;
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for (i = 0; i < n; ++i) {
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Y[i] -= yc;
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}
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}
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#region IConstraint Members
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/// <summary>
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/// matrix product: A'B
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/// </summary>
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/// <param name="A"></param>
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/// <param name="B"></param>
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/// <returns>2X2 matrix</returns>
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private static Point[] matrixProduct(Point[] A, Point[] B) {
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Point[] R = new Point[2];
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double x0 = 0, y0 = 0, x1 = 0, y1 = 0;
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for (int i = 0; i < A.Length; ++i)
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{
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x0 += A[i].X * B[i].X;
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y0 += A[i].X * B[i].Y;
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x1 += A[i].Y * B[i].X;
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y1 += A[i].Y * B[i].Y;
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}
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R[0] = new Point(x0, y0);
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R[1] = new Point(x1, y1);
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return R;
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}
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/// <summary>
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/// matrix product of two 2x2 matrices with no transpose, i.e.: AB
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/// </summary>
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/// <param name="A"></param>
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/// <param name="B"></param>
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/// <returns>2X2 matrix</returns>
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private static Point[] matrixProductNoTranspose(Point[] A, Point[] B) {
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Point[] R = new Point[2];
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R[0] = new Point(A[0].X*B[0].X+A[0].Y*B[1].X, A[0].X*B[0].Y + A[0].Y*B[1].Y);
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R[1] = new Point(A[1].X*B[0].X+A[1].Y*B[1].X, A[1].X*B[0].Y + A[1].Y*B[1].Y);
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return R;
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}
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private static Point MatrixTimesVector(Point[] A, Point v) {
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double a = A[0].X, b = A[0].Y, c = A[1].X, d = A[1].Y;
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return new Point(a * v.X + b * v.Y, c * v.X + d * v.Y);
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}
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private static Point eigenSystem2(Point[] B, out Point[] Q) {
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double[][] b = new double[B.Length][];
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for (int i = 0; i < B.Length; i++) {
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b[i] = new double[2];
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b[i][0] = B[i].X;
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b[i][1] = B[i].Y;
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}
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double lambda1;
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double[] q1;
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double lambda2;
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double[] q2;
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MultidimensionalScaling.SpectralDecomposition(b, out q1, out lambda1, out q2, out lambda2,300,1e-8);
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Q = new Point[] { new Point(q1[0], q1[1]), new Point(q2[0], q2[1]) };
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return new Point(lambda1, lambda2);
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}
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/// <summary>
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/// Compute singular value decomposition of a 2X2 matrix X=PSQ'
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/// </summary>
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/// <param name="X">input 2x2 matrix</param>
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/// <param name="P">left singular vectors</param>
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/// <param name="Q">right singular vectors (eigenvectors of X'X)</param>
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/// <returns>Singular values (Sqrt of eigenvalues of X'X)</returns>
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private static Point SingularValueDecomposition(Point[] X, out Point[] P, out Point[] Q) {
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Point[] XX = matrixProduct(X, X);
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Point l = eigenSystem2(XX, out Q);
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/*
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Point[] Q0;
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Point l0 = eigenSystem3(XX, out Q0);
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Q0 = new Point[] { Q0[1], Q0[0] };
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Q0 = Transpose(Q0);
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Q0 = new Point[] { -Q0[0], -Q0[1] };
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double tmp = l0.X;
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l0.X = l0.Y;
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l0.Y = tmp;
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if (!cmpEigenSystem(Q0, Q, l0, l)) {
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System.Console.Write("XX=");
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printMatrix(XX);
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System.Console.Write("Q0=");
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printMatrix(Q0);
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System.Console.WriteLine("l0=" + l0 + ";");
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System.Console.Write("Q=");
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printMatrix(Q);
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System.Console.WriteLine("l=" + l + ";");
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}
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l = l0;
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Q = Q0;
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System.Console.Write("Q=");
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printMatrix(Q);
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System.Console.WriteLine("l=" + l + ";");
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*/
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Point s = new Point(Math.Sqrt(l.X), Math.Sqrt(l.Y));
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P = matrixProductNoTranspose(X, Q);
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P = matrixProductNoTranspose(P,new Point[]{new Point(1.0/s.X,0), new Point(0,1.0/s.Y)});
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return s;
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}
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#if OLDPROJECT
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/// <summary>
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///
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/// </summary>
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/// <returns></returns>
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public double Project() {
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Point barycenter = Barycenter();
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Point[] X = new Point[ni];
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Point[] Y = new Point[ni];
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double angle = 2.0 * Math.PI / nd;
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double r = 0;
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int i = 0;
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foreach(var v in nodes) {
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X[i] = v.Center - barycenter;
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r += X[i].LengthSquared;
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++i;
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}
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r = Math.Sqrt(r / nd);
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i = 0;
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foreach (var v in nodes) {
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double theta = angle * (double)i;
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Y[i] = new Point(r * Math.Cos(theta), r * Math.Sin(theta));
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++i;
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}
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Point[] C = matrixProduct(Y, X);
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Point[] P, Q;
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SingularValueDecomposition(C, out P, out Q);
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Point[] T = matrixProductNoTranspose(Q, Transpose(P));
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/*
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Point[] XY = matrixProduct(X, Y);
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Point[] XYT = matrixProductNoTranspose(XY, T);
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Point[] YY = matrixProduct(Y, Y);
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double s = XYT[0].X + XYT[1].Y;
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s /= YY[0].X + YY[1].Y;
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for (int i = 0; i < nodes.Count; ++i) {
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Y[i] = Y[i] * s;
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}
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*/
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i = 0;
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foreach (var v in nodes) {
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v.Center = barycenter + MatrixTimesVector(T, Y[i++]);
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}
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return 0;
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}
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#endif
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/// <summary>
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///
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/// </summary>
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/// <returns></returns>
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public double Project() {
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for (int i = 0; i < n; ++i)
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{
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X[i] = V[i].Center;
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}
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Point[] T;
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double s;
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Point t;
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FindTransform(X, Y, out T, out s, out t);
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//System.Console.WriteLine("X=");
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//printMatrix(X);
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//System.Console.WriteLine("Y=");
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//printMatrix(Y);
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//System.Console.WriteLine("T=");
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//printMatrix(T);
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//System.Console.WriteLine("s="+s);
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//System.Console.WriteLine("t="+t);
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Point[] TT = Transpose(T);
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double displacement = 0;
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for (int i = 0; i < n; ++i)
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{
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var v = V[i];
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v.Center = double.IsNaN(s) ? Y[i] : s * MatrixTimesVector(TT, Y[i]) + t;
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displacement += (v.Center - X[i]).Length;
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}
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return displacement;
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}
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/// <summary>
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/// output an n*2 point matrix in Mathematica format
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/// </summary>
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[System.Diagnostics.CodeAnalysis.SuppressMessage("Microsoft.Globalization", "CA1303:Do not pass literals as localized parameters", MessageId = "System.Console.Write(System.String,System.Object,System.Object)"), System.Diagnostics.CodeAnalysis.SuppressMessage("Microsoft.Globalization", "CA1303:Do not pass literals as localized parameters", MessageId = "System.Console.Write(System.String)"), System.Diagnostics.CodeAnalysis.SuppressMessage("Microsoft.Globalization", "CA1303:Do not pass literals as localized parameters", MessageId = "System.Console.WriteLine(System.String)")]
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public static void PrintMatrix(Point[] points) {
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ValidateArg.IsNotNull(points, "points");
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System.Console.Write("{");
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for (int i = 0; i < points.Length;) {
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System.Console.Write("{{{0},{1}}}", points[i].X, points[i].Y);
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if (++i != points.Length) {
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System.Console.Write(",");
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}
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}
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System.Console.WriteLine("};");
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}
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private static Point[] Transpose(Point[] X) {
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return new Point[] { new Point(X[0].X, X[1].X), new Point(X[0].Y, X[1].Y) };
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}
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//// <summary>
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////
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//// </summary>
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//public static void Test1() {
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// Random rand = new Random();
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// Point[] X = new Point[] { new Point(rand.NextDouble(), rand.NextDouble()), new Point(rand.NextDouble(), rand.NextDouble()) };
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// System.Console.Write("X="); printMatrix(X);
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// Point[] P, Q;
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// Point s = SingularValueDecomposition(X, out P, out Q);
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// Point[] S = new Point[] { new Point(s.X, 0), new Point(0, s.Y) };
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// System.Console.Write("S="); printMatrix(S);
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// System.Console.Write("Q="); printMatrix(Q);
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// System.Console.Write("P="); printMatrix(P);
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// Point[] R = matrixProductNoTranspose(P, S);
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// System.Console.Write("PS="); printMatrix(R);
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// R = matrixProductNoTranspose(R, Transpose(Q));
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// System.Console.Write("R="); printMatrix(R);
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// Debug.Assert(Math.Abs(R[0].X - X[0].X) < 0.01);
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// Debug.Assert(Math.Abs(R[0].Y - X[0].Y) < 0.01);
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// Debug.Assert(Math.Abs(R[1].X - X[1].X) < 0.01);
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// Debug.Assert(Math.Abs(R[1].Y - X[1].Y) < 0.01);
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//}
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//// <summary>
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////
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//// </summary>
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// public static void Test() {
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// double[,] XX = {{-0.342439, -0.815696}, {-0.772753, -0.807363}, {-0.264356,
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//0.847908}, {-0.524064, 0.826169}, {0.615021, -0.762655}};
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// List<Microsoft.Msagl.Node> vs = new List<Microsoft.Msagl.Node>();
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// for (int i = 0; i < XX.Length/2; ++i) {
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// var v = new Microsoft.Msagl.Node();
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// v.Center = new Point(XX[i,0], XX[i,1]);
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// vs.Add(v);
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// }
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// ProcrustesCircleConstraint c = new ProcrustesCircleConstraint(vs);
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// c.Project();
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// }
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///<summary>
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///</summary>
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[System.Diagnostics.CodeAnalysis.SuppressMessage("Microsoft.Performance", "CA1814:PreferJaggedArraysOverMultidimensional", MessageId = "Body"), System.Diagnostics.CodeAnalysis.SuppressMessage("Microsoft.Globalization", "CA1303:Do not pass literals as localized parameters", MessageId = "System.Console.WriteLine(System.String,System.Object)"), System.Diagnostics.CodeAnalysis.SuppressMessage("Microsoft.Globalization", "CA1303:Do not pass literals as localized parameters", MessageId = "System.Console.WriteLine(System.String,System.Object,System.Object)"), System.Diagnostics.CodeAnalysis.SuppressMessage("Microsoft.Globalization", "CA1303:Do not pass literals as localized parameters", MessageId = "System.Console.Write(System.String)")]
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public static void Test() {
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#if SHARPKIT //https://code.google.com/p/sharpkit/issues/detail?id=340
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double[,] XX = null;
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throw new InvalidOperationException();
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#else
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double[,] XX = { { 1, 2 }, { -1, 2 }, { -1, -2 }, { 1, -2 } },
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YY = { { 0.07, 2.62 }, { 0.93, 3.12 }, { 1.93, 1.38 }, { 1.07, 0.88 } };
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int ni = 4;
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Point[] X = new Point[ni];
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Point[] Y = new Point[ni];
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for (int i = 0; i < ni; ++i) {
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X[i] = new Point(XX[i, 0], XX[i, 1]);
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Y[i] = new Point(YY[i, 0], YY[i, 1]);
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}
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Point[] XY = matrixProduct(X, Y);
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System.Console.Write("XY=");
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PrintMatrix(XY);
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Point[] P, Q;
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SingularValueDecomposition(XY, out P, out Q);
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PrintMatrix(P);
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PrintMatrix(Q);
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Point[] T;
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double s;
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Point t;
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FindTransform(X, Y, out T, out s, out t);
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PrintMatrix(T);
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System.Console.WriteLine("s={0}", s);
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System.Console.WriteLine("t=({0},{1})", t.X,t.Y);
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#endif
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}
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private static void FindTransform(Point[] X, Point[] Y,
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out Point[] T, out double s, out Point t) {
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int ni = X.Length;
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Point[] C = matrixProduct(X, Y);
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Point[] P, Q;
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SingularValueDecomposition(C, out P, out Q);
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T = matrixProductNoTranspose(Q, Transpose(P));
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Point[] XYT = matrixProductNoTranspose(C, T);
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Point[] Y2 = matrixProduct(Y, Y);
|
||
|
|
s = XYT[0].X + XYT[1].Y;
|
||
|
|
s /= Y2[0].X + Y2[1].Y;
|
||
|
|
t = new Point();
|
||
|
|
for (int i = 0; i < ni; ++i) {
|
||
|
|
t += X[i] - s * MatrixTimesVector(T, Y[i]);
|
||
|
|
}
|
||
|
|
t /= ni;
|
||
|
|
}
|
||
|
|
/// <summary>
|
||
|
|
///
|
||
|
|
/// </summary>
|
||
|
|
public int Level {
|
||
|
|
get {
|
||
|
|
return 1;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
/// <summary>
|
||
|
|
/// Get the list of nodes involved in the constraint
|
||
|
|
/// </summary>
|
||
|
|
public IEnumerable<Node> Nodes { get { return V.AsEnumerable(); } }
|
||
|
|
#endregion
|
||
|
|
}
|
||
|
|
}
|