func (gp *gpConvexProg) F1(x *matrix.FloatMatrix) (f, Df *matrix.FloatMatrix, err error) {
f = nil
Df = nil
err = nil
f = matrix.FloatZeros(gp.mnl+1, 1)
Df = matrix.FloatZeros(gp.mnl+1, gp.n)
y := gp.g.Copy()
blas.GemvFloat(gp.F, x, y, 1.0, 1.0)
for i, s := range gp.ind {
start := s[0]
stop := s[1]
// yi := exp(yi) = exp(Fi*x+gi)
ymax := maxvec(y.FloatArray()[start:stop])
// ynew = exp(y[start:stop] - ymax)
ynew := matrix.Exp(matrix.FloatVector(y.FloatArray()[start:stop]).Add(-ymax))
y.SetIndexesFromArray(ynew.FloatArray(), matrix.Indexes(start, stop)...)
// fi = log sum yi = log sum exp(Fi*x+gi)
ysum := blas.AsumFloat(y, &la.IOpt{"n", stop - start}, &la.IOpt{"offset", start})
f.SetIndex(i, ymax+math.Log(ysum))
blas.ScalFloat(y, 1.0/ysum, &la.IOpt{"n", stop - start}, &la.IOpt{"offset", start})
blas.GemvFloat(gp.F, y, Df, 1.0, 0.0, la.OptTrans, &la.IOpt{"m", stop - start},
&la.IOpt{"incy", gp.mnl + 1}, &la.IOpt{"offseta", start},
&la.IOpt{"offsetx", start}, &la.IOpt{"offsety", i})
}
return
}
// The small GP of section 9.3 (Geometric programming).
func TestGp(t *testing.T) {
xref := []float64{1.06032641296944741, 1.75347359157296845, 2.44603683900611868}
aflr := 1000.0
awall := 100.0
alpha := 0.5
beta := 2.0
gamma := 0.5
delta := 2.0
fdata := [][]float64{
[]float64{-1.0, 1.0, 1.0, 0.0, -1.0, 1.0, 0.0, 0.0},
[]float64{-1.0, 1.0, 0.0, 1.0, 1.0, -1.0, 1.0, -1.0},
[]float64{-1.0, 0.0, 1.0, 1.0, 0.0, 0.0, -1.0, 1.0}}
gdata := []float64{1.0, 2.0 / awall, 2.0 / awall, 1.0 / aflr, alpha, 1.0 / beta, gamma, 1.0 / delta}
g := matrix.FloatNew(8, 1, gdata).Log()
F := matrix.FloatMatrixFromTable(fdata)
K := []int{1, 2, 1, 1, 1, 1, 1}
var solopts SolverOptions
solopts.MaxIter = 40
solopts.ShowProgress = false
solopts.KKTSolverName = "ldl"
sol, err := Gp(K, F, g, nil, nil, nil, nil, &solopts)
if sol != nil && sol.Status == Optimal {
x := sol.Result.At("x")[0]
r := matrix.Exp(x)
h := r.GetIndex(0)
w := r.GetIndex(1)
d := r.GetIndex(2)
t.Logf("x=\n%v\n", x.ToString("%.9f"))
t.Logf("h = %f, w = %f, d = %f.\n", h, w, d)
xe, _ := nrmError(matrix.FloatVector(xref), x)
if xe > TOL {
t.Logf("x differs [%.3e] from exepted too much.", xe)
t.Fail()
}
} else {
t.Logf("status: %v\n", err)
t.Fail()
}
}
func (gp *gpConvexProg) F2(x, z *matrix.FloatMatrix) (f, Df, H *matrix.FloatMatrix, err error) {
err = nil
f = matrix.FloatZeros(gp.mnl+1, 1)
Df = matrix.FloatZeros(gp.mnl+1, gp.n)
H = matrix.FloatZeros(gp.n, gp.n)
y := gp.g.Copy()
Fsc := matrix.FloatZeros(gp.maxK, gp.n)
blas.GemvFloat(gp.F, x, y, 1.0, 1.0)
//fmt.Printf("y=\n%v\n", y.ToString("%.3f"))
for i, s := range gp.ind {
start := s[0]
stop := s[1]
// yi := exp(yi) = exp(Fi*x+gi)
ymax := maxvec(y.FloatArray()[start:stop])
ynew := matrix.Exp(matrix.FloatVector(y.FloatArray()[start:stop]).Add(-ymax))
y.SetIndexesFromArray(ynew.FloatArray(), matrix.Indexes(start, stop)...)
// fi = log sum yi = log sum exp(Fi*x+gi)
ysum := blas.AsumFloat(y, &la.IOpt{"n", stop - start}, &la.IOpt{"offset", start})
f.SetIndex(i, ymax+math.Log(ysum))
blas.ScalFloat(y, 1.0/ysum, &la.IOpt{"n", stop - start}, &la.IOpt{"offset", start})
blas.GemvFloat(gp.F, y, Df, 1.0, 0.0, la.OptTrans, &la.IOpt{"m", stop - start},
&la.IOpt{"incy", gp.mnl + 1}, &la.IOpt{"offseta", start},
&la.IOpt{"offsetx", start}, &la.IOpt{"offsety", i})
Fsc.SetSubMatrix(0, 0, gp.F.GetSubMatrix(start, 0, stop-start))
for k := start; k < stop; k++ {
blas.AxpyFloat(Df, Fsc, -1.0, &la.IOpt{"n", gp.n},
&la.IOpt{"incx", gp.mnl + 1}, &la.IOpt{"incy", Fsc.Rows()},
&la.IOpt{"offsetx", i}, &la.IOpt{"offsety", k - start})
blas.ScalFloat(Fsc, math.Sqrt(y.GetIndex(k)),
&la.IOpt{"inc", Fsc.Rows()}, &la.IOpt{"offset", k - start})
}
// H += z[i]*Hi = z[i] *Fisc' * Fisc
blas.SyrkFloat(Fsc, H, z.GetIndex(i), 1.0, la.OptTrans,
&la.IOpt{"k", stop - start})
}
return
}
