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added reciprocal averaging which seems to work. More tests are needed
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@jdfekete
jdfekete committed Aug 10, 2015
1 parent 8b4112e commit ac40b54
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325 changes: 325 additions & 0 deletions reorder.v1.js
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Expand Up @@ -2746,6 +2746,331 @@ reorder.ca_no_svd = ca_no_svd;

reorder.ca = ca_no_svd;

// Implementation of the decorana fortran code

function decorana(dat) {
var ZEROEIG = 1e-7, // consider as zero eigenvalue
x, y, aidot, adotj, mi, n, s1,
nr = dat.length,
nc = dat[0].length;

adotj = sumcols(dat);
aidot = sumrows(dat);
//console.log('adotj='); reorder.printvec(adotj);
//console.log('aidot='); reorder.printvec(aidot);

s1 = eigy(reorder.array1d(nr, 1.0),
reorder.array1d(nc, 1.0),
nr, nc, dat, aidot, adotj);
if (s1.eig < ZEROEIG) {
s1.rows = s1.cols = [];
s1.eig = 0;
}
else {
x = s1.rows;
y = s1.cols;
yxmult(y, x, nr, nc, dat);
for (var i = 0; i < nr; i++)
x[i] /= aidot[i];
}
return s1;
}

reorder.ca_decorana = decorana;

function trans(y, yy, x, aidot, mi, n, dat,prt) {
var i, j, a1;
if (prt) console.log('TRANS '+prt);
yxmult(y,x,mi,n,dat,prt);
for (i = 0; i < mi; i++) {
x[i] = x[i]/aidot[i]; // 10
}
// 100
// a1 = 0.0;
// for (i = 0; i < mi; i++)
// a1 += aidot[i]*x[i]; // 110
// for (i = 0; i < mi; i++)
// x[i] -= a1; // 120
// 200
xymult(x,yy,mi,n, dat,prt);
}

function printvec(y) {
console.log('');
for (var i = 0; i < y.length; i++) {
console.log('i:'+(i+1)+' v: '+y[i].toFixed(5));
}
}

function xymult(x, y, mi, n, dat, prt) {
var i, j, ax, row;

if (prt) {
console.log('xymult');
printvec(y,5, null, 'y=');
}
for (j = 0; j < n; j++)
y[j] = 0.0; // 10
for (i = 0; i < mi; i++) {
ax = x[i];
row = dat[i];
for (j = 0; j < n; j++)
y[j] += ax*row[j]; // 20
}
if (prt) {
//console.log('xymult[1]=');
printvec(y,5, null, 'y=');
}
}

function yxmult(y,x,mi,n,dat,prt) {
var i, j, ax, row;
if (prt) {
console.log('yxmult');
printvec(x,5, null, 'x=');
}
for (i = 0; i < mi; i++) {
ax = 0.0;
row = dat[i];
for (j = 0; j < n; j++) {
ax += y[j]*row[j]; // 10
}
x[i] = ax; // 20
}
if (prt) {
//console.log('yxmult[1]=');
printvec(x,5, null, 'x=');
}
}

function eigy(x, y, mi, n, dat, aidot, adotj) {
var i, j, tot, icount, a, ay, ex,
a11, a12, a22, a23, a33, a34, a44,
res, ax1, ax2, ax3, ax4,
b13, b14, b24, row,
y2 = reorder.zeroes(n),
y3 = reorder.zeroes(n),
y4 = reorder.zeroes(n),
y5 = reorder.zeroes(n),
tol;

tot = 0.0;
for (j = 0; j < n; j++) {
tot += adotj[j];
y[j] = j+1.0; // 10
}
y[0] = 1.1;
tol=0.000005;
trans(y,y,x,aidot,mi,n,dat);//,1);
icount = 0;
while(true) {
// 20
a = 0.0;
for (j = 0; j < n; j++)
a += y[j]*adotj[j]; // 30
a /= tot;
ex = 0.0;
for (j = 0; j < n; j++) {
ay = y[j]-a;
ex += ay*ay*adotj[j];
y[j] = ay; // 40
}
ex = Math.sqrt(ex);
for (j = 0; j < n; j++)
y[j] /= ex; // 50
trans(y,y2,x,aidot,mi,n,dat);//,2);
a=0.0;
a11=0.0;
a12=0.0;
a22=0.0;
a23=0.0;
a33=0.0;
a34=0.0;
a44=0.0;
for (j = 0; j < n; j++) {
ay = y2[j];
y2[j] = ay/adotj[j];
a += ay;
a11 += ay*y[j]; // 60
}
a /= tot;
for (j = 0; j < n; j++) {
ay = y2[j]-(a+a11*y[j]);
a12 += ay*ay*adotj[j];
y2[j] = ay; // 70
}
a12 = Math.sqrt(a12);
for (j = 0; j < n; j++)
y2[j] /= a12; // 80
if (a12 < tol || icount > 999)
break;
icount++;
trans(y2,y3,x,aidot,mi,n,dat);//,3);
a = 0.0;
b13 = 0.0;
for (j = 0; j < n; j++) {
ay = y3[j];
y3[j] = ay/adotj[j];
a += ay;
a22 +=ay*y2[j];
b13 += ay*y[j]; // 90
}
a /= tot;
for (j = 0; j < n; j++) {
ay = y3[j]-(a+a22*y2[j]+b13*y[j]);
a23 += ay*ay*adotj[j];
y3[j]=ay; // 100
}
a23=Math.sqrt(a23);
if (a23 > tol) {
// 105
for (j = 0; j < n; j++) {
y3[j] /= a23; // 110
}
trans(y3,y4,x,aidot,mi,n,dat);//,4);
a = 0.0;
b14 = 0.0,
b24 = 0.0;
for (j = 0; j < n; j++) {
ay = y4[j];
y4[j] /= adotj[j];
a += ay;
a33 += ay*y3[j];
b14 += ay*y[j];
b24 += ay*y2[j]; // 120
}
a /= tot;
for (j = 0; j < n; j++) {
ay = y4[j]-(a+a33*y3[j]+b14*y[j]+b24*y2[j]);
a34 += ay*ay*adotj[j];
y4[j] = ay; // 130
}
a34=Math.sqrt(a34);
if(a34 > tol) {
// 135
for (j = 0; j < n; j++)
y4[j] /= a34; // 140
trans(y4,y5,x,aidot,mi,n,dat);//,5);
for (j = 0; j < n; j++)
a44 += y4[j]*y5[j]; // 150
}
else {
a34=0.0;
}
}
else {
a23 = 0.0;
}
// 160
res = solve_tridiag(tol, a11, a12, a22, a23, a33, a34, a44);
ax1 = res[0]; ax2 = res[1]; ax3 = res[2]; ax4 =res[3];
// console.log('i '+icount+
// ' ax1 '+ax1.toFixed(6)+
// ' ax2 '+ax2.toFixed(6)+
// ' ax3 '+ax3.toFixed(6)+
// ' ax4 '+ax4.toFixed(6));

// 180
if(a12 < tol) break;
for (j = 0; j < n; j++)
y[j]= ax1*y[j]+ax2*y2[j]+ax3*y3[j]+ax4*y4[j]; // 190
// goto 20
}
// 200
//console.log('eigenvalue',a11.toFixed(6));
if (a12 > tol && reorder.debug > 0) {
console.log("residual bigger than tolerance on axis 1");
}
var aymax = y[0],
aymin = y[0],
sign = 1;
for (j = 1; j < n; j++) {
a = y[j];
if (a < aymin)
aymin = a;
else if (a > aymax)
aymax = a;
}
if (-aymin > aymax) {
for (j = 0; j < n; j++) // 210
y[j] = -y[j];
}
yxmult(y,x,mi,n,dat);//,true);
for (i = 0; i < mi; i++)
x[i] /= aidot[i]; // 220
// 225
var axlong = 0.0;
for (i = 0; i < mi; i++)
axlong += aidot[i]*sqr(x[i]); // 230
axlong = Math.sqrt(axlong);
for (i = 0; i < mi; i++)
x[i] /= axlong; // 240
for (j = 0; j < n; j++)
y[j] /= axlong; // 250
var sumsq=0.0,
ax;
for (i = 0; i < mi; i++) {
ax = x[i];
row = dat[i];
for (j = 0; j < n; j++) {
sumsq += row[j]*sqr(ax-y[j]); // 255
}
// 260
}
var sd = Math.sqrt(sumsq/tot);
if (a11 >= 0.999) {
sd = aymax/axlong;
var sd1 = -aymin/axlong;
if (sd1 > sd)
sd = sd1;
}
// 265
for (j = 0; j < n; j++)
y[j] /= sd; // 270

//printvec(x);
//printvec(y);
return {rows: x, cols: y, eig: a11};
}

function sqr(x) { return x*x; }

function solve_tridiag(tol, a11, a12, a22, a23, a33, a34, a44) {
var ax1=1.0, // 160
ax2=0.1,
ax3=0.01,
ax4=0.001,
itimes,
axx1, axx2, axx3, axx4, ex, exx, resi;
//console.log('a11:'+a11+' a12:'+a12+' a22:'+a22);
//console.log('a23:'+a23+' a33:'+a33+' a34:'+a34+' a44:'+a44);
for (itimes = 0; itimes < 100; itimes++) {
axx1=a11*ax1+a12*ax2;
axx2=a12*ax1+a22*ax2+a23*ax3;
axx3=a23*ax2+a33*ax3+a34*ax4;
axx4=a34*ax3+a44*ax4;
ax1=a11*axx1+a12*axx2;
ax2=a12*axx1+a22*axx2+a23*axx3;
ax3=a23*axx2+a33*axx3+a34*axx4;
ax4=a34*axx3+a44*axx4;
ex=Math.sqrt(sqr(ax1)+sqr(ax2)+sqr(ax3)+sqr(ax4));
ax1=ax1/ex;
ax2=ax2/ex;
ax3=ax3/ex;
ax4=ax4/ex;
if((itimes+1)%5 == 0) {
exx=Math.sqrt(ex);
resi=Math.sqrt(sqr(ax1-axx1/exx)+sqr(ax2-axx2/exx)+
sqr(ax3-axx3/exx)+sqr(ax4-axx4/exx));
}
if (resi < tol*0.05)
break;
// 170
}
// 180
return [ax1, ax2, ax3, ax4];
}


/*jshint loopfunc:true */
reorder.cuthill_mckee = function(graph, comp) {
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2 changes: 1 addition & 1 deletion reorder.v1.min.js
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