add benchmarks

benchmarks/spectral-norm.ce

@@ -0,0 +1,50 @@
+function A(i,j) {
+  return 1/((i+j)*(i+j+1)/2+i+1);
+}
+
+function Au(u,v) {
+  for (var i=0; i<u.length; ++i) {
+    var t = 0;
+    for (var j=0; j<u.length; ++j)
+      t += A(i,j) * u[j];
+      
+    v[i] = t;
+  }
+}
+
+function Atu(u,v) {
+  for (var i=0; i<u.length; ++i) {
+    var t = 0;
+    for (var j=0; j<u.length; ++j)
+      t += A(j,i) * u[j];
+      
+    v[i] = t;
+  }
+}
+
+function AtAu(u,v,w) {
+  Au(u,w);
+  Atu(w,v);
+}
+
+function spectralnorm(n) {
+  var i, u=[], v=[], w=[], vv=0, vBv=0;
+  for (i=0; i<n; ++i)
+    u[i] = 1; v[i] = w[i] = 0; 
+
+  for (i=0; i<10; ++i) {
+    AtAu(u,v,w);
+    AtAu(v,u,w);
+  }
+  
+  for (i=0; i<n; ++i) {
+    vBv += u[i]*v[i];
+    vv  += v[i]*v[i];
+  }
+  
+  return Math.sqrt(vBv/vv);
+}
+
+log.console(spectralnorm(arg[0]).toFixed(9));
+
+$_.stop()