function portfolioOptim(x, pm, lows, highs) {
var i, j, k, Dmat, dvec, a1, a2, a3, a3neg, b3, Amat, bvec,
res, pw, px, ps;
x = stats.transpose(x);
k = x[0].length;
Dmat = stats.cov(x);
dvec = stats.repInt(0, k);
a1 = stats.repInt(1, k);
a2 = stats.colMeans(x);
a3 = stats.identity(k, 1);
a3neg = stats.identity(k, -1);
b3 = stats.repInt(0, k);
Amat = stats.rbind(a1, a2, a3, a3, a3neg);
Amat = stats.transpose(Amat);
if (pm === 0 || pm === undefined) {
pm = stats.mean(x);
}
bvec = [1].concat(pm).concat(b3).concat(lows).concat(highs);
for (i = 0; i < Dmat.length; i = i + 1) {
Dmat[i] = [undefined].concat(Dmat[i]);
}
Dmat = [undefined].concat(Dmat);
dvec = [undefined].concat(dvec);
for (i = 0; i < Amat.length; i = i + 1) {
Amat[i] = [undefined].concat(Amat[i]);
}
Amat = [undefined].concat(Amat);
bvec = [undefined].concat(bvec);
res = qp.solveQP(Dmat, dvec, Amat, bvec, 2);
res.solution.shift();
px = [];
pw = res.solution;
//~ ps = 0;
//~ pm = 0;
for (i = 0; i < x.length; i += 1) {
px[i] = 0;
for (j = 0; j < pw.length; j += 1) {
px[i] += (pw[j] * x[i][j]);
}
//~ ps += (px[i] - pm) * (px[i] - pm);
//~ pm += px[i];
}
//~ ps = Math.sqrt(ps / (x.length - 1));
//~ pm = pm / x.length;
ps = 0;
for (i = 0; i < x.length; i += 1) {
ps += (px[i] - pm) * (px[i] - pm);
}
ps = Math.sqrt(ps / (x.length - 1));
res.pm = pm;
res.ps = ps;
return res;
}
function portfolioOptim(x, pm, lows, highs) {
var i, j, k, Dmat, dvec, a1, a2, a3, a3neg, b3, Amat, bvec,
res, pw, px, ps;
function colMeans(x) {
var i, j, sum, means, nrows, ncols;
means = [];
nrows = x.length;
ncols = x[0].length;
for (j = 0; j < ncols; j = j + 1) {
sum = 0;
for (i = 0; i < nrows; i = i + 1) {
sum = sum + x[i][j];
}
means[j] = sum / nrows;
}
return means;
}
function mean(x) {
var i, sum = 0, means;
means = colMeans(x);
for (i = 0; i < means.length; i = i + 1) {
sum = sum + means[i];
}
return sum / means.length;
}
function cov(x) {
var i, j, j2, nrows, ncols,
sumX, sumX2, sumY, sumY2, sumXY,
covmat = [];
nrows = x.length;
ncols = x[0].length;
for (i = 0; i < ncols; i = i + 1) {
covmat[i] = [];
}
for (j = 0; j < ncols - 1; j = j + 1) {
for (j2 = j + 1; j2 < ncols; j2 = j2 + 1) {
sumX = 0;
sumY = 0;
sumX2 = 0;
sumY2 = 0;
sumXY = 0;
for (i = 0; i < nrows; i = i + 1) {
sumX = sumX + x[i][j];
sumY = sumY + x[i][j2];
sumX2 = sumX2 + (x[i][j] * x[i][j]);
sumY2 = sumY2 + (x[i][j2] * x[i][j2]);
sumXY = sumXY + (x[i][j] * x[i][j2]);
}
covmat[j][j] = (sumX2 - (sumX * sumX) / nrows) / (nrows - 1);
covmat[j2][j2] = (sumY2 - (sumY * sumY) / nrows) / (nrows - 1);
covmat[j][j2] = (sumXY - (sumX * sumY) / nrows) / (nrows - 1);
covmat[j2][j] = covmat[j][j2];
}
}
return covmat;
}
function repInt(n, k) {
var i, ans = [];
for (i = 0; i < k; i = i + 1) {
ans[i] = n;
}
return ans;
}
function identity(k, n) {
var i, j, m = [];
n = n || 1;
for (i = 0; i < k; i = i + 1) {
m[i] = [];
for (j = 0; j < k; j = j + 1) {
if (i === j) {
m[i][j] = n;
} else {
m[i][j] = 0;
}
}
}
return m;
}
function rbind() {
var i, j, k, n, rows, cols, arg, m = [];
for (n = 0, k = 0; n < arguments.length; n = n + 1) {
arg = arguments[n];
rows = arg.length;
cols = arg[0].length;
if (cols === undefined) {
m[k] = [];
for (i = 0; i < rows; i = i + 1) {
m[k][i] = arg[i];
}
k = k + 1;
} else {
for (i = 0; i < rows; i = i + 1) {
m[k] = [];
for (j = 0; j < cols; j = j + 1) {
m[k][j] = arg[i][j];
}
k = k + 1;
}
}
}
return m;
}
function transpose(m) {
var i, j, rows, cols, res = [];
rows = m.length;
cols = m[0].length;
for (i = 0; i < cols; i = i + 1) {
res[i] = [];
for (j = 0; j < rows; j = j + 1) {
res[i][j] = m[j][i];
}
}
return res;
}
x = transpose(x);
k = x[0].length;
Dmat = cov(x);
dvec = repInt(0, k);
a1 = repInt(1, k);
a2 = colMeans(x);
a3 = identity(k, 1);
a3neg = identity(k, -1);
b3 = repInt(0, k);
Amat = rbind(a1, a2, a3, a3, a3neg);
Amat = transpose(Amat);
if (pm === 0 || pm === undefined) {
pm = mean(x);
}
bvec = [1].concat(pm).concat(b3).concat(lows).concat(highs);
for (i = 0; i < Dmat.length; i = i + 1) {
Dmat[i] = [undefined].concat(Dmat[i]);
}
Dmat = [undefined].concat(Dmat);
dvec = [undefined].concat(dvec);
for (i = 0; i < Amat.length; i = i + 1) {
Amat[i] = [undefined].concat(Amat[i]);
}
Amat = [undefined].concat(Amat);
bvec = [undefined].concat(bvec);
res = qp.solveQP(Dmat, dvec, Amat, bvec, 2);
res.solution.shift();
px = [];
pw = res.solution;
//~ ps = 0;
//~ pm = 0;
for (i = 0; i < x.length; i += 1) {
px[i] = 0;
for (j = 0; j < pw.length; j += 1) {
px[i] += (pw[j] * x[i][j]);
}
//~ ps += (px[i] - pm) * (px[i] - pm);
//~ pm += px[i];
}
//~ ps = Math.sqrt(ps / (x.length - 1));
//~ pm = pm / x.length;
ps = 0;
for (i = 0; i < x.length; i += 1) {
ps += (px[i] - pm) * (px[i] - pm);
}
ps = Math.sqrt(ps / (x.length - 1));
res.pm = pm;
res.ps = ps;
return res;
}