func main() {
flag.Parse()
if len(spPath) > 0 {
checkpnt.Reset(spPath)
checkpnt.Activate()
checkpnt.Verbose(spVerbose)
checkpnt.Format("%.17f")
}
adata := [][]float64{
[]float64{0.3, -0.4, -0.2, -0.4, 1.3},
[]float64{0.6, 1.2, -1.7, 0.3, -0.3},
[]float64{-0.3, 0.0, 0.6, -1.2, -2.0}}
A := matrix.FloatMatrixFromTable(adata, matrix.ColumnOrder)
b := matrix.FloatVector([]float64{1.5, 0.0, -1.2, -0.7, 0.0})
_, n := A.Size()
N := n + 1 + n
h := matrix.FloatZeros(N, 1)
h.SetIndex(n, 1.0)
I0 := matrix.FloatDiagonal(n, -1.0)
I1 := matrix.FloatIdentity(n)
G, _ := matrix.FloatMatrixStacked(matrix.StackDown, I0, matrix.FloatZeros(1, n), I1)
At := A.Transpose()
P := At.Times(A)
q := At.Times(b).Scale(-1.0)
dims := sets.NewDimensionSet("l", "q", "s")
dims.Set("l", []int{n})
dims.Set("q", []int{n + 1})
var solopts cvx.SolverOptions
solopts.MaxIter = 20
solopts.ShowProgress = true
if maxIter > 0 {
solopts.MaxIter = maxIter
}
if len(solver) > 0 {
solopts.KKTSolverName = solver
}
sol, err := cvx.ConeQp(P, q, G, h, nil, nil, dims, &solopts, nil)
if err == nil {
x := sol.Result.At("x")[0]
s := sol.Result.At("s")[0]
z := sol.Result.At("z")[0]
fmt.Printf("Optimal\n")
fmt.Printf("x=\n%v\n", x.ToString("%.9f"))
fmt.Printf("s=\n%v\n", s.ToString("%.9f"))
fmt.Printf("z=\n%v\n", z.ToString("%.9f"))
check(x, s, z)
}
}
func main() {
flag.Parse()
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 cvx.SolverOptions
solopts.MaxIter = 40
if maxIter > 0 {
solopts.MaxIter = maxIter
}
if len(spPath) > 0 {
checkpnt.Reset(spPath)
checkpnt.Activate()
checkpnt.Verbose(spVerbose)
checkpnt.Format("%.7f")
}
solopts.ShowProgress = true
if maxIter > 0 {
solopts.MaxIter = maxIter
}
if len(solver) > 0 {
solopts.KKTSolverName = solver
}
sol, err := cvx.Gp(K, F, g, nil, nil, nil, nil, &solopts)
if sol != nil && sol.Status == cvx.Optimal {
x := sol.Result.At("x")[0]
r := matrix.Exp(x)
h := r.GetIndex(0)
w := r.GetIndex(1)
d := r.GetIndex(2)
fmt.Printf("x=\n%v\n", x.ToString("%.9f"))
fmt.Printf("\n h = %f, w = %f, d = %f.\n", h, w, d)
check(x)
} else {
fmt.Printf("status: %v\n", err)
}
}
func main() {
flag.Parse()
if len(spPath) > 0 {
checkpnt.Reset(spPath)
checkpnt.Activate()
checkpnt.Verbose(spVerbose)
checkpnt.Format("%.17f")
}
gdata := [][]float64{
[]float64{16., 7., 24., -8., 8., -1., 0., -1., 0., 0., 7.,
-5., 1., -5., 1., -7., 1., -7., -4.},
[]float64{-14., 2., 7., -13., -18., 3., 0., 0., -1., 0., 3.,
13., -6., 13., 12., -10., -6., -10., -28.},
[]float64{5., 0., -15., 12., -6., 17., 0., 0., 0., -1., 9.,
6., -6., 6., -7., -7., -6., -7., -11.}}
hdata := []float64{-3., 5., 12., -2., -14., -13., 10., 0., 0., 0., 68.,
-30., -19., -30., 99., 23., -19., 23., 10.}
c := matrix.FloatVector([]float64{-6., -4., -5.})
G := matrix.FloatMatrixFromTable(gdata)
h := matrix.FloatVector(hdata)
dims := sets.NewDimensionSet("l", "q", "s")
dims.Set("l", []int{2})
dims.Set("q", []int{4, 4})
dims.Set("s", []int{3})
var solopts cvx.SolverOptions
solopts.MaxIter = 30
solopts.ShowProgress = true
if maxIter > 0 {
solopts.MaxIter = maxIter
}
if len(solver) > 0 {
solopts.KKTSolverName = solver
}
sol, err := cvx.ConeLp(c, G, h, nil, nil, dims, &solopts, nil, nil)
if err == nil {
x := sol.Result.At("x")[0]
s := sol.Result.At("s")[0]
z := sol.Result.At("z")[0]
fmt.Printf("Optimal\n")
fmt.Printf("x=\n%v\n", x.ToString("%.9f"))
fmt.Printf("s=\n%v\n", s.ToString("%.9f"))
fmt.Printf("z=\n%v\n", z.ToString("%.9f"))
check(x, s, z)
} else {
fmt.Printf("status: %s\n", err)
}
}
func main() {
flag.Parse()
gdata0 := [][]float64{
[]float64{12., 13., 12.},
[]float64{6., -3., -12.},
[]float64{-5., -5., 6.}}
gdata1 := [][]float64{
[]float64{3., 3., -1., 1.},
[]float64{-6., -6., -9., 19.},
[]float64{10., -2., -2., -3.}}
c := matrix.FloatVector([]float64{-2.0, 1.0, 5.0})
g0 := matrix.FloatMatrixFromTable(gdata0, matrix.ColumnOrder)
g1 := matrix.FloatMatrixFromTable(gdata1, matrix.ColumnOrder)
Ghq := sets.FloatSetNew("Gq", "hq")
Ghq.Append("Gq", g0, g1)
h0 := matrix.FloatVector([]float64{-12.0, -3.0, -2.0})
h1 := matrix.FloatVector([]float64{27.0, 0.0, 3.0, -42.0})
Ghq.Append("hq", h0, h1)
var Gl, hl, A, b *matrix.FloatMatrix = nil, nil, nil, nil
var solopts cvx.SolverOptions
solopts.MaxIter = 30
solopts.ShowProgress = true
if maxIter > -1 {
solopts.MaxIter = maxIter
}
if len(solver) > 0 {
solopts.KKTSolverName = solver
}
sol, err := cvx.Socp(c, Gl, hl, A, b, Ghq, &solopts, nil, nil)
fmt.Printf("status: %v\n", err)
if sol != nil && sol.Status == cvx.Optimal {
x := sol.Result.At("x")[0]
fmt.Printf("x=\n%v\n", x.ToString("%.9f"))
for i, m := range sol.Result.At("sq") {
fmt.Printf("sq[%d]=\n%v\n", i, m.ToString("%.9f"))
}
for i, m := range sol.Result.At("zq") {
fmt.Printf("zq[%d]=\n%v\n", i, m.ToString("%.9f"))
}
sq0 := sol.Result.At("sq")[0]
sq1 := sol.Result.At("sq")[1]
zq0 := sol.Result.At("zq")[0]
zq1 := sol.Result.At("zq")[1]
check(x, sq0, sq1, zq0, zq1)
}
}
func main() {
flag.Parse()
if len(spPath) > 0 {
checkpnt.Reset(spPath)
checkpnt.Activate()
checkpnt.Verbose(spVerbose)
checkpnt.Format("%.17f")
}
A := matrix.FloatNew(2, 3, []float64{1.0, -1.0, 0.0, 1.0, 0.0, 1.0})
b := matrix.FloatNew(2, 1, []float64{1.0, 0.0})
c := matrix.FloatNew(3, 1, []float64{0.0, 1.0, 0.0})
G := matrix.FloatNew(1, 3, []float64{0.0, -1.0, 1.0})
h := matrix.FloatNew(1, 1, []float64{0.0})
//dims := sets.NewDimensionSet("l", "q", "s")
//dims.Set("l", []int{1})
fmt.Printf("A=\n%v\n", A)
fmt.Printf("b=\n%v\n", b)
fmt.Printf("G=\n%v\n", G)
fmt.Printf("h=\n%v\n", h)
fmt.Printf("c=\n%v\n", c)
var solopts cvx.SolverOptions
solopts.MaxIter = 30
solopts.ShowProgress = true
if maxIter > -1 {
solopts.MaxIter = maxIter
}
if len(solver) > 0 {
solopts.KKTSolverName = solver
}
sol, err := cvx.Lp(c, G, h, A, b, &solopts, nil, nil)
if sol != nil && sol.Status == cvx.Optimal {
x := sol.Result.At("x")[0]
s := sol.Result.At("s")[0]
z := sol.Result.At("z")[0]
fmt.Printf("x=\n%v\n", x.ToString("%.9f"))
fmt.Printf("s=\n%v\n", s.ToString("%.9f"))
fmt.Printf("z=\n%v\n", z.ToString("%.9f"))
check(x, s, z)
} else {
fmt.Printf("status: %v\n", err)
}
}
func main() {
flag.Parse()
if len(spPath) > 0 {
checkpnt.Reset(spPath)
checkpnt.Activate()
checkpnt.Verbose(spVerbose)
checkpnt.Format("%.17f")
}
gdata := [][]float64{
[]float64{2.0, 1.0, -1.0, 0.0},
[]float64{1.0, 2.0, 0.0, -1.0}}
c := matrix.FloatVector([]float64{-4.0, -5.0})
G := matrix.FloatMatrixFromTable(gdata, matrix.ColumnOrder)
h := matrix.FloatVector([]float64{3.0, 3.0, 0.0, 0.0})
var solopts cvx.SolverOptions
solopts.MaxIter = 30
solopts.ShowProgress = true
if maxIter > -1 {
solopts.MaxIter = maxIter
}
if len(solver) > 0 {
solopts.KKTSolverName = solver
}
sol, err := cvx.Lp(c, G, h, nil, nil, &solopts, nil, nil)
if sol != nil && sol.Status == cvx.Optimal {
x := sol.Result.At("x")[0]
s := sol.Result.At("s")[0]
z := sol.Result.At("z")[0]
fmt.Printf("x=\n%v\n", x.ToString("%.9f"))
fmt.Printf("s=\n%v\n", s.ToString("%.9f"))
fmt.Printf("z=\n%v\n", z.ToString("%.9f"))
check(x, s, z)
} else {
fmt.Printf("status: %v\n", err)
}
}
func acenter() *matrix.FloatMatrix {
F := &acenterProg{3, 1}
gdata := [][]float64{
[]float64{0., -1., 0., 0., -21., -11., 0., -11., 10., 8., 0., 8., 5.},
[]float64{0., 0., -1., 0., 0., 10., 16., 10., -10., -10., 16., -10., 3.},
[]float64{0., 0., 0., -1., -5., 2., -17., 2., -6., 8., -17., -7., 6.}}
G := matrix.FloatMatrixFromTable(gdata)
h := matrix.FloatVector(
[]float64{1.0, 0.0, 0.0, 0.0, 20., 10., 40., 10., 80., 10., 40., 10., 15.})
var solopts cvx.SolverOptions
solopts.MaxIter = 40
solopts.ShowProgress = true
if maxIter > -1 {
solopts.MaxIter = maxIter
}
if len(solver) > 0 {
solopts.KKTSolverName = solver
}
dims := sets.NewDimensionSet("l", "q", "s")
dims.Set("l", []int{0})
dims.Set("q", []int{4})
dims.Set("s", []int{3})
var err error
var sol *cvx.Solution
sol, err = cvx.Cp(F, G, h, nil, nil, dims, &solopts)
if err == nil && sol.Status == cvx.Optimal {
return sol.Result.At("x")[0]
} else {
fmt.Printf("result: %v\n", err)
}
return nil
}
func main() {
Sdata := [][]float64{
[]float64{4e-2, 6e-3, -4e-3, 0.0},
[]float64{6e-3, 1e-2, 0.0, 0.0},
[]float64{-4e-3, 0.0, 2.5e-3, 0.0},
[]float64{0.0, 0.0, 0.0, 0.0}}
pbar := matrix.FloatVector([]float64{.12, .10, .07, .03})
S := matrix.FloatMatrixFromTable(Sdata)
n := pbar.Rows()
G := matrix.FloatDiagonal(n, -1.0)
h := matrix.FloatZeros(n, 1)
A := matrix.FloatWithValue(1, n, 1.0)
b := matrix.FloatNew(1, 1, []float64{1.0})
var solopts cvx.SolverOptions
solopts.MaxIter = 30
solopts.ShowProgress = true
mu := 1.0
Smu := matrix.Scale(S, mu)
pbarNeg := matrix.Scale(pbar, -1.0)
fmt.Printf("Smu=\n%v\n", Smu.String())
fmt.Printf("-pbar=\n%v\n", pbarNeg.String())
sol, err := cvx.Qp(Smu, pbarNeg, G, h, A, b, &solopts, nil)
fmt.Printf("status: %v\n", err)
if sol != nil && sol.Status == cvx.Optimal {
x := sol.Result.At("x")[0]
ret := blas.DotFloat(x, pbar)
risk := math.Sqrt(blas.DotFloat(x, S.Times(x)))
fmt.Printf("ret=%.3f, risk=%.3f\n", ret, risk)
fmt.Printf("x=\n%v\n", x)
}
}
func main() {
flag.Parse()
if len(spPath) > 0 {
checkpnt.Reset(spPath)
checkpnt.Activate()
checkpnt.Verbose(spVerbose)
checkpnt.Format("%.17f")
}
gdata0 := [][]float64{
[]float64{-7., -11., -11., 3.},
[]float64{7., -18., -18., 8.},
[]float64{-2., -8., -8., 1.}}
gdata1 := [][]float64{
[]float64{-21., -11., 0., -11., 10., 8., 0., 8., 5.},
[]float64{0., 10., 16., 10., -10., -10., 16., -10., 3.},
[]float64{-5., 2., -17., 2., -6., 8., -17., -7., 6.}}
hdata0 := [][]float64{
[]float64{33., -9.},
[]float64{-9., 26.}}
hdata1 := [][]float64{
[]float64{14., 9., 40.},
[]float64{9., 91., 10.},
[]float64{40., 10., 15.}}
g0 := matrix.FloatMatrixFromTable(gdata0, matrix.ColumnOrder)
g1 := matrix.FloatMatrixFromTable(gdata1, matrix.ColumnOrder)
Ghs := sets.FloatSetNew("Gs", "hs")
Ghs.Append("Gs", g0, g1)
h0 := matrix.FloatMatrixFromTable(hdata0, matrix.ColumnOrder)
h1 := matrix.FloatMatrixFromTable(hdata1, matrix.ColumnOrder)
Ghs.Append("hs", h0, h1)
c := matrix.FloatVector([]float64{1.0, -1.0, 1.0})
var Gs, hs, A, b *matrix.FloatMatrix = nil, nil, nil, nil
var solopts cvx.SolverOptions
solopts.MaxIter = 30
solopts.ShowProgress = true
if maxIter > -1 {
solopts.MaxIter = maxIter
}
if len(solver) > 0 {
solopts.KKTSolverName = solver
}
sol, err := cvx.Sdp(c, Gs, hs, A, b, Ghs, &solopts, nil, nil)
if sol != nil && sol.Status == cvx.Optimal {
x := sol.Result.At("x")[0]
fmt.Printf("x=\n%v\n", x.ToString("%.9f"))
for i, m := range sol.Result.At("zs") {
fmt.Printf("zs[%d]=\n%v\n", i, m.ToString("%.9f"))
}
ss0 := sol.Result.At("ss")[0]
ss1 := sol.Result.At("ss")[1]
zs0 := sol.Result.At("zs")[0]
zs1 := sol.Result.At("zs")[1]
check(x, ss0, ss1, zs0, zs1)
} else {
fmt.Printf("status: %v\n", err)
}
checkpnt.Report()
}
func floorplan(Amin *matrix.FloatMatrix) *matrix.FloatMatrix {
rho := 1.0
gamma := 5.0
c := matrix.FloatZeros(22, 1)
c.SetAtColumnArray(0, []int{0, 1}, []float64{1.0, 1.0})
G := matrix.FloatZeros(26, 22)
h := matrix.FloatZeros(26, 1)
// -x1 <= 0
G.SetAt(0, 2, -1.0)
// -x2 <= 0
G.SetAt(1, 3, -1.0)
// -x4 <= 0
G.SetAt(2, 5, -1.0)
// x1 - x3 + w1 <= -rho
G.SetAtRowArray(3, []int{2, 4, 12}, []float64{1.0, -1.0, 1.0})
h.SetAt(3, 0, -rho)
// x2 - x3 + w2 <= -rho
G.SetAtRowArray(4, []int{3, 4, 13}, []float64{1.0, -1.0, 1.0})
h.SetAt(4, 0, -rho)
// x3 - x5 + w3 <= -rho
G.SetAtRowArray(5, []int{4, 6, 14}, []float64{1.0, -1.0, 1.0})
h.SetAt(5, 0, -rho)
// x4 - x5 + w4 <= -rho
G.SetAtRowArray(6, []int{5, 6, 15}, []float64{1.0, -1.0, 1.0})
h.SetAt(6, 0, -rho)
// -W + x5 + w5 <= 0
G.SetAtRowArray(7, []int{0, 6, 16}, []float64{-1.0, 1.0, 1.0})
// -y2 <= 0
G.SetAt(8, 8, -1.0)
// -y3 <= 0
G.SetAt(9, 9, -1.0)
// -y5 <= 0
G.SetAt(10, 11, -1.0)
// -y1 + y2 + h2 <= -rho
G.SetAtRowArray(11, []int{7, 8, 18}, []float64{-1.0, 1.0, 1.0})
h.SetAt(11, 0, -rho)
// y1 - y4 + h1 <= -rho
G.SetAtRowArray(12, []int{7, 10, 17}, []float64{1.0, -1.0, 1.0})
h.SetAt(12, 0, -rho)
// y3 - y4 + h3 <= -rho
G.SetAtRowArray(13, []int{9, 10, 19}, []float64{1.0, -1.0, 1.0})
h.SetAt(13, 0, -rho)
// -H + y4 + h4 <= 0
G.SetAtRowArray(14, []int{1, 10, 20}, []float64{-1.0, 1.0, 1.0})
// -H + y5 + h5 <= 0
G.SetAtRowArray(15, []int{1, 11, 21}, []float64{-1.0, 1.0, 1.0})
// -w1 + h1/gamma <= 0
G.SetAtRowArray(16, []int{12, 17}, []float64{-1.0, 1.0 / gamma})
// w1 - gamma * h1 <= 0
G.SetAtRowArray(17, []int{12, 17}, []float64{1.0, -gamma})
// -w2 + h2/gamma <= 0
G.SetAtRowArray(18, []int{13, 18}, []float64{-1.0, 1.0 / gamma})
// w2 - gamma * h2 <= 0
G.SetAtRowArray(19, []int{13, 18}, []float64{1.0, -gamma})
// -w3 + h3/gamma <= 0
G.SetAtRowArray(20, []int{14, 18}, []float64{-1.0, 1.0 / gamma})
// w3 - gamma * h3 <= 0
G.SetAtRowArray(21, []int{14, 19}, []float64{1.0, -gamma})
// -w4 + h4/gamma <= 0
G.SetAtRowArray(22, []int{15, 19}, []float64{-1.0, 1.0 / gamma})
// w4 - gamma * h4 <= 0
G.SetAtRowArray(23, []int{15, 20}, []float64{1.0, -gamma})
// -w5 + h5/gamma <= 0
G.SetAtRowArray(24, []int{16, 21}, []float64{-1.0, 1.0 / gamma})
// w5 - gamma * h5 <= 0.0
G.SetAtRowArray(25, []int{16, 21}, []float64{1.0, -gamma})
F := newFloorPlan(Amin)
var dims *sets.DimensionSet = nil
var solopts cvx.SolverOptions
solopts.MaxIter = 50
solopts.ShowProgress = true
if maxIter > 0 {
solopts.MaxIter = maxIter
}
if len(solver) > 0 {
solopts.KKTSolverName = solver
}
sol, err := cvx.Cpl(F, c, G, h, nil, nil, dims, &solopts)
if err == nil && sol.Status == cvx.Optimal {
return sol.Result.At("x")[0]
} else {
fmt.Printf("result: %v\n", err)
}
return nil
}
func main() {
flag.Parse()
m := len(udata)
nvars := 2 * m
u := matrix.FloatVector(udata[:m])
y := matrix.FloatVector(ydata[:m])
// minimize (1/2) * || yhat - y ||_2^2
// subject to yhat[j] >= yhat[i] + g[i]' * (u[j] - u[i]), j, i = 0,...,m-1
//
// Variables yhat (m), g (m).
P := matrix.FloatZeros(nvars, nvars)
// set m first diagonal indexes to 1.0
//P.SetIndexes(1.0, matrix.DiagonalIndexes(P)[:m]...)
P.Diag().SubMatrix(0, 0, 1, m).SetIndexes(1.0)
q := matrix.FloatZeros(nvars, 1)
q.SubMatrix(0, 0, y.NumElements(), 1).Plus(matrix.Scale(y, -1.0))
// m blocks (i = 0,...,m-1) of linear inequalities
//
// yhat[i] + g[i]' * (u[j] - u[i]) <= yhat[j], j = 0,...,m-1.
G := matrix.FloatZeros(m*m, nvars)
I := matrix.FloatDiagonal(m, 1.0)
for i := 0; i < m; i++ {
// coefficients of yhat[i] (column i)
//G.Set(1.0, matrix.ColumnIndexes(G, i)[i*m:(i+1)*m]...)
column(G, i).SetIndexes(1.0)
// coefficients of gi[i] (column i, rows i*m ... (i+1)*m)
//rows := matrix.Indexes(i*m, (i+1)*m)
//G.SetAtColumnArray(m+i, rows, matrix.Add(u, -u.GetIndex(i)).FloatArray())
// coefficients of gi[i] (column i, rows i*m ... (i+1)*m)
// from column m+i staring at row i*m select m rows and one column
G.SubMatrix(i*m, m+i, m, 1).Plus(matrix.Add(u, -u.GetIndex(i)))
// coeffients of yhat[i]) from rows i*m ... (i+1)*m, cols 0 ... m
//G.SetSubMatrix(i*m, 0, matrix.Minus(G.GetSubMatrix(i*m, 0, m, m), I))
G.SubMatrix(i*m, 0, m, m).Minus(I)
}
h := matrix.FloatZeros(m*m, 1)
var A, b *matrix.FloatMatrix = nil, nil
var solopts cvx.SolverOptions
solopts.ShowProgress = true
solopts.KKTSolverName = solver
sol, err := cvx.Qp(P, q, G, h, A, b, &solopts, nil)
if err != nil {
fmt.Printf("error: %v\n", err)
return
}
if sol != nil && sol.Status != cvx.Optimal {
fmt.Printf("status not optimal\n")
return
}
x := sol.Result.At("x")[0]
//yhat := matrix.FloatVector(x.FloatArray()[:m])
//g := matrix.FloatVector(x.FloatArray()[m:])
yhat := x.SubMatrix(0, 0, m, 1).Copy()
g := x.SubMatrix(m, 0).Copy()
rangeFunc := func(n int) []float64 {
r := make([]float64, 0)
for i := 0; i < n; i++ {
r = append(r, float64(i)*2.2/float64(n))
}
return r
}
ts := rangeFunc(1000)
fitFunc := func(points []float64) []float64 {
res := make([]float64, len(points))
for k, t := range points {
res[k] = matrix.Plus(yhat, matrix.Mul(g, matrix.Scale(u, -1.0).Add(t))).Max()
}
return res
}
fs := fitFunc(ts)
plotData("cvxfit.png", u.FloatArray(), y.FloatArray(), ts, fs)
}
func qcl1(A, b *matrix.FloatMatrix) (*cvx.Solution, error) {
// Returns the solution u, z of
//
// (primal) minimize || u ||_1
// subject to || A * u - b ||_2 <= 1
//
// (dual) maximize b^T z - ||z||_2
// subject to || A'*z ||_inf <= 1.
//
// Exploits structure, assuming A is m by n with m >= n.
m, n := A.Size()
Fkkt := func(W *sets.FloatMatrixSet) (f cvx.KKTFunc, err error) {
minor := 0
if !checkpnt.MinorEmpty() {
minor = checkpnt.MinorTop()
}
err = nil
f = nil
beta := W.At("beta")[0].GetIndex(0)
v := W.At("v")[0]
// As = 2 * v *(v[1:].T * A)
//v_1 := matrix.FloatNew(1, v.NumElements()-1, v.FloatArray()[1:])
v_1 := v.SubMatrix(1, 0).Transpose()
As := matrix.Times(v, matrix.Times(v_1, A)).Scale(2.0)
//As_1 := As.GetSubMatrix(1, 0, m, n)
//As_1.Scale(-1.0)
//As.SetSubMatrix(1, 0, matrix.Minus(As_1, A))
As_1 := As.SubMatrix(1, 0, m, n)
As_1.Scale(-1.0)
As_1.Minus(A)
As.Scale(1.0 / beta)
S := matrix.Times(As.Transpose(), As)
checkpnt.AddMatrixVar("S", S)
d1 := W.At("d")[0].SubMatrix(0, 0, n, 1).Copy()
d2 := W.At("d")[0].SubMatrix(n, 0).Copy()
// D = 4.0 * (d1**2 + d2**2)**-1
d := matrix.Plus(matrix.Mul(d1, d1), matrix.Mul(d2, d2)).Inv().Scale(4.0)
// S[::n+1] += d
S.Diag().Plus(d.Transpose())
err = lapack.Potrf(S)
checkpnt.Check("00-Fkkt", minor)
if err != nil {
return
}
f = func(x, y, z *matrix.FloatMatrix) (err error) {
minor := 0
if !checkpnt.MinorEmpty() {
minor = checkpnt.MinorTop()
} else {
loopf += 1
minor = loopf
}
checkpnt.Check("00-f", minor)
// -- z := - W**-T * z
// z[:n] = -div( z[:n], d1 )
z_val := z.SubMatrix(0, 0, n, 1)
z_res := matrix.Div(z_val, d1).Scale(-1.0)
z.SubMatrix(0, 0, n, 1).Set(z_res)
// z[n:2*n] = -div( z[n:2*n], d2 )
z_val = z.SubMatrix(n, 0, n, 1)
z_res = matrix.Div(z_val, d2).Scale(-1.0)
z.SubMatrix(n, 0, n, 1).Set(z_res)
// z[2*n:] -= 2.0*v*( v[0]*z[2*n] - blas.dot(v[1:], z[2*n+1:]) )
v0_z2n := v.GetIndex(0) * z.GetIndex(2*n)
v1_z2n := blas.DotFloat(v, z, &linalg.IOpt{"offsetx", 1}, &linalg.IOpt{"offsety", 2*n + 1})
z_res = matrix.Scale(v, -2.0*(v0_z2n-v1_z2n))
z.SubMatrix(2*n, 0, z_res.NumElements(), 1).Plus(z_res)
// z[2*n+1:] *= -1.0
z.SubMatrix(2*n+1, 0).Scale(-1.0)
// z[2*n:] /= beta
z.SubMatrix(2*n, 0).Scale(1.0 / beta)
// -- x := x - G' * W**-1 * z
// z_n = z[:n], z_2n = z[n:2*n], z_m = z[-(m+1):],
z_n := z.SubMatrix(0, 0, n, 1)
z_2n := z.SubMatrix(n, 0, n, 1)
z_m := z.SubMatrix(z.NumElements()-(m+1), 0)
// x[:n] -= div(z[:n], d1) - div(z[n:2*n], d2) + As.T * z[-(m+1):]
z_res = matrix.Minus(matrix.Div(z_n, d1), matrix.Div(z_2n, d2))
a_res := matrix.Times(As.Transpose(), z_m)
z_res.Plus(a_res).Scale(-1.0)
x.SubMatrix(0, 0, n, 1).Plus(z_res)
// x[n:] += div(z[:n], d1) + div(z[n:2*n], d2)
z_res = matrix.Plus(matrix.Div(z_n, d1), matrix.Div(z_2n, d2))
x.SubMatrix(n, 0, z_res.NumElements(), 1).Plus(z_res)
checkpnt.Check("15-f", minor)
// Solve for x[:n]:
//
// S*x[:n] = x[:n] - (W1**2 - W2**2)(W1**2 + W2**2)^-1 * x[n:]
// w1 = (d1**2 - d2**2), w2 = (d1**2 + d2**2)
w1 := matrix.Minus(matrix.Mul(d1, d1), matrix.Mul(d2, d2))
w2 := matrix.Plus(matrix.Mul(d1, d1), matrix.Mul(d2, d2))
// x[:n] += -mul( div(w1, w2), x[n:])
x_n := x.SubMatrix(n, 0)
x_val := matrix.Mul(matrix.Div(w1, w2), x_n).Scale(-1.0)
x.SubMatrix(0, 0, n, 1).Plus(x_val)
checkpnt.Check("25-f", minor)
// Solve for x[n:]:
//
// (d1**-2 + d2**-2) * x[n:] = x[n:] + (d1**-2 - d2**-2)*x[:n]
err = lapack.Potrs(S, x)
if err != nil {
fmt.Printf("Potrs error: %s\n", err)
}
checkpnt.Check("30-f", minor)
// Solve for x[n:]:
//
// (d1**-2 + d2**-2) * x[n:] = x[n:] + (d1**-2 - d2**-2)*x[:n]
// w1 = (d1**-2 - d2**-2), w2 = (d1**-2 + d2**-2)
w1 = matrix.Minus(matrix.Mul(d1, d1).Inv(), matrix.Mul(d2, d2).Inv())
w2 = matrix.Plus(matrix.Mul(d1, d1).Inv(), matrix.Mul(d2, d2).Inv())
x_n = x.SubMatrix(0, 0, n, 1)
// x[n:] += mul( d1**-2 - d2**-2, x[:n])
x_val = matrix.Mul(w1, x_n)
x.SubMatrix(n, 0, x_val.NumElements(), 1).Plus(x_val)
checkpnt.Check("35-f", minor)
// x[n:] = div( x[n:], d1**-2 + d2**-2)
x_n = x.SubMatrix(n, 0)
x_val = matrix.Div(x_n, w2)
x.SubMatrix(n, 0, x_val.NumElements(), 1).Set(x_val)
checkpnt.Check("40-f", minor)
// x_n = x[:n], x-2n = x[n:2*n]
x_n = x.SubMatrix(0, 0, n, 1)
x_2n := x.SubMatrix(n, 0, n, 1)
// z := z + W^-T * G*x
// z[:n] += div( x[:n] - x[n:2*n], d1)
x_val = matrix.Div(matrix.Minus(x_n, x_2n), d1)
z.SubMatrix(0, 0, n, 1).Plus(x_val)
checkpnt.Check("44-f", minor)
// z[n:2*n] += div( -x[:n] - x[n:2*n], d2)
x_val = matrix.Div(matrix.Plus(x_n, x_2n).Scale(-1.0), d2)
z.SubMatrix(n, 0, n, 1).Plus(x_val)
checkpnt.Check("48-f", minor)
// z[2*n:] += As*x[:n]
x_val = matrix.Times(As, x_n)
z.SubMatrix(2*n, 0, x_val.NumElements(), 1).Plus(x_val)
checkpnt.Check("50-f", minor)
return nil
}
return
}
// matrix(n*[0.0] + n*[1.0])
c := matrix.FloatZeros(2*n, 1)
c.SubMatrix(n, 0).SetIndexes(1.0)
h := matrix.FloatZeros(2*n+m+1, 1)
h.SetIndexes(1.0, 2*n)
// h[2*n+1:] = -b
h.SubMatrix(2*n+1, 0).Plus(b).Scale(-1.0)
G := &matrixFs{A}
dims := sets.DSetNew("l", "q", "s")
dims.Set("l", []int{2 * n})
dims.Set("q", []int{m + 1})
var solopts cvx.SolverOptions
solopts.ShowProgress = true
if maxIter > 0 {
solopts.MaxIter = maxIter
}
if len(solver) > 0 {
solopts.KKTSolverName = solver
}
return cvx.ConeLpCustomMatrix(c, G, h, nil, nil, dims, Fkkt, &solopts, nil, nil)
}
func mcsdp(w *matrix.FloatMatrix) (*cvx.Solution, error) {
//
// Returns solution x, z to
//
// (primal) minimize sum(x)
// subject to w + diag(x) >= 0
//
// (dual) maximize -tr(w*z)
// subject to diag(z) = 1
// z >= 0.
//
n := w.Rows()
G := &matrixFs{n}
cngrnc := func(r, x *matrix.FloatMatrix, alpha float64) (err error) {
// Congruence transformation
//
// x := alpha * r'*x*r.
//
// r and x are square matrices.
//
err = nil
// tx = matrix(x, (n,n)) is copying and reshaping
// scale diagonal of x by 1/2, (x is (n,n))
tx := x.Copy()
matrix.Reshape(tx, n, n)
tx.Diag().Scale(0.5)
// a := tril(x)*r
// (python: a = +r is really making a copy of r)
a := r.Copy()
err = blas.TrmmFloat(tx, a, 1.0, linalg.OptLeft)
// x := alpha*(a*r' + r*a')
err = blas.Syr2kFloat(r, a, tx, alpha, 0.0, linalg.OptTrans)
// x[:] = tx[:]
tx.CopyTo(x)
return
}
Fkkt := func(W *sets.FloatMatrixSet) (cvx.KKTFunc, error) {
// Solve
// -diag(z) = bx
// -diag(x) - inv(rti*rti') * z * inv(rti*rti') = bs
//
// On entry, x and z contain bx and bs.
// On exit, they contain the solution, with z scaled
// (inv(rti)'*z*inv(rti) is returned instead of z).
//
// We first solve
//
// ((rti*rti') .* (rti*rti')) * x = bx - diag(t*bs*t)
//
// and take z = -rti' * (diag(x) + bs) * rti.
var err error = nil
rti := W.At("rti")[0]
// t = rti*rti' as a nonsymmetric matrix.
t := matrix.FloatZeros(n, n)
err = blas.GemmFloat(rti, rti, t, 1.0, 0.0, linalg.OptTransB)
if err != nil {
return nil, err
}
// Cholesky factorization of tsq = t.*t.
tsq := matrix.Mul(t, t)
err = lapack.Potrf(tsq)
if err != nil {
return nil, err
}
f := func(x, y, z *matrix.FloatMatrix) (err error) {
// tbst := t * zs * t = t * bs * t
tbst := z.Copy()
matrix.Reshape(tbst, n, n)
cngrnc(t, tbst, 1.0)
// x := x - diag(tbst) = bx - diag(rti*rti' * bs * rti*rti')
diag := tbst.Diag().Transpose()
x.Minus(diag)
// x := (t.*t)^{-1} * x = (t.*t)^{-1} * (bx - diag(t*bs*t))
err = lapack.Potrs(tsq, x)
if err != nil {
fmt.Printf("Fkkt.f.Potrs: %v\n", err)
}
// z := z + diag(x) = bs + diag(x)
// z, x are really column vectors here
z.AddIndexes(matrix.MakeIndexSet(0, n*n, n+1), x.FloatArray())
// z := -rti' * z * rti = -rti' * (diag(x) + bs) * rti
cngrnc(rti, z, -1.0)
return nil
}
return f, nil
}
c := matrix.FloatWithValue(n, 1, 1.0)
// initial feasible x: x = 1.0 - min(lmbda(w))
lmbda := matrix.FloatZeros(n, 1)
wp := w.Copy()
lapack.Syevx(wp, lmbda, nil, 0.0, nil, []int{1, 1}, linalg.OptRangeInt)
x0 := matrix.FloatZeros(n, 1).Add(-lmbda.GetAt(0, 0) + 1.0)
s0 := w.Copy()
// Diag() return a row vector, x0 is column vector
s0.Diag().Plus(x0.Transpose())
matrix.Reshape(s0, n*n, 1)
// initial feasible z is identity
z0 := matrix.FloatIdentity(n)
matrix.Reshape(z0, n*n, 1)
dims := sets.DSetNew("l", "q", "s")
dims.Set("s", []int{n})
primalstart := sets.FloatSetNew("x", "s")
dualstart := sets.FloatSetNew("z")
primalstart.Set("x", x0)
primalstart.Set("s", s0)
dualstart.Set("z", z0)
var solopts cvx.SolverOptions
solopts.ShowProgress = true
if maxIter > 0 {
solopts.MaxIter = maxIter
}
if len(solver) > 0 {
solopts.KKTSolverName = solver
}
h := w.Copy()
matrix.Reshape(h, h.NumElements(), 1)
return cvx.ConeLpCustomMatrix(c, G, h, nil, nil, dims, Fkkt, &solopts, primalstart, dualstart)
}