func TestAcent(t *testing.T) {
// matrix string in row order presentation
Adata := [][]float64{
[]float64{-7.44e-01, 1.11e-01, 1.29e+00, 2.62e+00, -1.82e+00},
[]float64{4.59e-01, 7.06e-01, 3.16e-01, -1.06e-01, 7.80e-01},
[]float64{-2.95e-02, -2.22e-01, -2.07e-01, -9.11e-01, -3.92e-01},
[]float64{-7.75e-01, 1.03e-01, -1.22e+00, -5.74e-01, -3.32e-01},
[]float64{-1.80e+00, 1.24e+00, -2.61e+00, -9.31e-01, -6.38e-01}}
bdata := []float64{
8.38e-01, 9.92e-01, 9.56e-01, 6.14e-01, 6.56e-01,
3.57e-01, 6.36e-01, 5.08e-01, 8.81e-03, 7.08e-02}
// these are solution obtained from running cvxopt acent.py with above data
solData := []float64{-11.59728373909344512, -1.35196389161339936,
7.21894899350256303, -3.29159917142051528, 4.90454147385329176}
ntData := []float64{
1.5163484265903457, 1.2433928210771914, 1.0562922103520955, 0.8816246051011607,
0.7271128861543598, 0.42725003346248974, 0.0816777301914883, 0.0005458037072843131,
1.6259980735305693e-10}
b := matrix.FloatVector(bdata)
Al := matrix.FloatMatrixFromTable(Adata, matrix.RowOrder)
Au := matrix.Scale(Al, -1.0)
A := matrix.FloatZeros(2*Al.Rows(), Al.Cols())
A.SetSubMatrix(0, 0, Al)
A.SetSubMatrix(Al.Rows(), 0, Au)
x, nt, err := acent(A, b, 10)
if err != nil {
t.Logf("Acent error: %s", err)
t.Fail()
}
solref := matrix.FloatVector(solData)
ntref := matrix.FloatVector(ntData)
soldf := matrix.Minus(x, solref)
ntdf := matrix.Minus(matrix.FloatVector(nt), ntref)
solNrm := blas.Nrm2Float(soldf)
ntNrm := blas.Nrm2Float(ntdf)
t.Logf("x [diff=%.2e]:\n%v\n", solNrm, x)
t.Logf("nt [diff=%.2e]:\n%v\n", ntNrm, nt)
if solNrm > TOL {
t.Log("solution deviates too much from expected\n")
t.Fail()
}
}
func (p *acenterProg) F1(x *matrix.FloatMatrix) (f, Df *matrix.FloatMatrix, err error) {
f = nil
Df = nil
err = nil
max := matrix.Abs(x).Max()
if max >= 1.0 {
err = errors.New("max(abs(x)) >= 1.0")
return
}
// u = 1 - x**2
u := matrix.Pow(x, 2.0).Scale(-1.0).Add(1.0)
val := -matrix.Log(u).Sum()
f = matrix.FloatValue(val)
Df = matrix.Div(matrix.Scale(x, 2.0), u).Transpose()
return
}
// Computes analytic center of A*x <= b with A m by n of rank n.
// We assume that b > 0 and the feasible set is bounded.
func acent(A, b *matrix.FloatMatrix, niters int) (x *matrix.FloatMatrix, ntdecrs []float64, err error) {
err = nil
if niters <= 0 {
niters = MAXITERS
}
ntdecrs = make([]float64, 0, niters)
if A.Rows() != b.Rows() {
return nil, nil, errors.New("A.Rows() != b.Rows()")
}
m, n := A.Size()
x = matrix.FloatZeros(n, 1)
H := matrix.FloatZeros(n, n)
// Helper m*n matrix
Dmn := matrix.FloatZeros(m, n)
for i := 0; i < niters; i++ {
// Gradient is g = A^T * (1.0/(b - A*x)). d = 1.0/(b - A*x)
// d is m*1 matrix, g is n*1 matrix
d := matrix.Minus(b, matrix.Times(A, x)).Inv()
g := matrix.Times(A.Transpose(), d)
// Hessian is H = A^T * diag(1./(b-A*x))^2 * A.
// in the original python code expression d[:,n*[0]] creates
// a m*n matrix where each column is copy of column 0.
// We do it here manually.
for i := 0; i < n; i++ {
Dmn.SetColumn(i, d)
}
// Function mul creates element wise product of matrices.
Asc := matrix.Mul(Dmn, A)
blas.SyrkFloat(Asc, H, 1.0, 0.0, linalg.OptTrans)
// Newton step is v = H^-1 * g.
v := matrix.Scale(g, -1.0)
PosvFloat(H, v)
// Directional derivative and Newton decrement.
lam := blas.DotFloat(g, v)
ntdecrs = append(ntdecrs, math.Sqrt(-lam))
if ntdecrs[len(ntdecrs)-1] < TOL {
return x, ntdecrs, err
}
// Backtracking line search.
// y = d .* A*v
y := matrix.Mul(d, matrix.Times(A, v))
step := 1.0
for 1-step*y.Max() < 0 {
step *= BETA
}
search:
for {
// t = -step*y + 1 [e.g. t = 1 - step*y]
t := matrix.Scale(y, -step).Add(1.0)
// ts = sum(log(1-step*y))
ts := t.Log().Sum()
if -ts < ALPHA*step*lam {
break search
}
step *= BETA
}
v.Scale(step)
x.Plus(v)
}
// no solution !!
err = errors.New(fmt.Sprintf("Iteration %d exhausted\n", niters))
return x, ntdecrs, err
}
