Previously graph layout was done using the Kamada-Kawai layout algorithm

implemented in Boost.  I am replacing this with a custom implementation of
a constrained stress-majorization algorithm.

The stress-majorization algorithm is more robust and has better convergence
characteristics than Kamada-Kawai, and also simple constraints can be placed
on node position (for example, to enforce downward-pointing edges, non-overlap constraints, or cluster constraints).

Another big advantage is that we no longer need Boost.

I've tested the basic functionality, but I have yet to properly handle
disconnected graphs or to properly scale the resulting layout.

This commit also includes significant refactoring... the quadratic program solver - libvpsc (Variable Placement with Separation Constraints) has been moved to src/libvpsc and the actual graph layout algorithm is in libcola.

(bzr r1394)

1 files changed, 113 insertions, 0 deletions

diff --git a/src/libcola/conjugate_gradient.cpp b/src/libcola/conjugate_gradient.cpp
new file mode 100644
index 000000000..5dfb4363d
--- /dev/null
+++ b/src/libcola/conjugate_gradient.cpp
@@ -0,0 +1,113 @@
+#include <math.h>
+#include <stdlib.h>
+#include <valarray>
+#include <cassert>
+#include "conjugate_gradient.h"
+
+/*
+* Authors:
+*   Nathan Hurst <njh@njhurst.com>
+*   Tim Dwyer <tgdwyer@gmail.com>
+*
+* Copyright (C) 2006 Authors
+*
+* Released under GNU LGPL.
+*/
+
+/* lifted wholely from wikipedia.  Well, apart from the bug in the wikipedia version. */
+
+using std::valarray;
+
+static void 
+matrix_times_vector(valarray<double> const &matrix, /* m * n */
+		    valarray<double> const &vec,  /* n */
+		    valarray<double> &result) /* m */
+{
+    unsigned n = vec.size();
+    unsigned m = result.size();
+    assert(m*n == matrix.size());
+    const double* mp = &matrix[0];
+    for (unsigned i = 0; i < m; i++) {
+        double res = 0;
+        for (unsigned j = 0; j < n; j++)
+            res += *mp++ * vec[j];
+        result[i] = res;
+    }
+}
+
+static double Linfty(valarray<double> const &vec) {
+    return std::max(vec.max(), -vec.min());
+}
+
+double
+inner(valarray<double> const &x, 
+      valarray<double> const &y) {
+    double total = 0;
+    for(unsigned i = 0; i < x.size(); i++)
+        total += x[i]*y[i];
+    return total;// (x*y).sum(); <- this is more concise, but ineff
+}
+
+void 
+conjugate_gradient(double **A, 
+                   double *x, 
+                   double *b, 
+                   unsigned n, 
+                   double tol,
+                   unsigned max_iterations) {
+    valarray<double> vA(n*n);
+    valarray<double> vx(n);
+    valarray<double> vb(n);
+    for(unsigned i=0;i<n;i++) {
+        vx[i]=x[i];
+        vb[i]=b[i];
+        for(unsigned j=0;j<n;j++) {
+            vA[i*n+j]=A[i][j];
+        }
+    }
+    conjugate_gradient(vA,vx,vb,n,tol,max_iterations);
+    for(unsigned i=0;i<n;i++) {
+        x[i]=vx[i];
+    }
+}
+void 
+conjugate_gradient(valarray<double> const &A, 
+		   valarray<double> &x, 
+		   valarray<double> const &b, 
+		   unsigned n, double tol,
+		   unsigned max_iterations) {
+    valarray<double> Ap(n), p(n), r(n);
+    matrix_times_vector(A,x,Ap);
+    r=b-Ap; 
+    double r_r = inner(r,r);
+    unsigned k = 0;
+    tol *= tol;
+    while(k < max_iterations && r_r > tol) {
+        k++;
+        double r_r_new = r_r;
+        if(k == 1)
+            p = r;
+        else {
+            r_r_new = inner(r,r);
+            p = r + (r_r_new/r_r)*p;
+        }
+        matrix_times_vector(A, p, Ap);
+        double alpha_k = r_r_new / inner(p, Ap);
+        x += alpha_k*p;
+        r -= alpha_k*Ap;
+        r_r = r_r_new;
+    }
+    printf("njh: %d iters, Linfty = %g L2 = %g\n", k, 
+    std::max(-r.min(), r.max()), sqrt(r_r));
+    // x is solution
+}
+/*
+  Local Variables:
+  mode:c++
+  c-file-style:"stroustrup"
+  c-file-offsets:((innamespace . 0)(inline-open . 0)(case-label . +))
+  indent-tabs-mode:nil
+  fill-column:99
+  End:
+*/
+// vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=4:softtabstop=4