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 (m *mVariable) ShowError(dataline string) {
refdata, err := matrix.FloatParse(dataline)
if err != nil {
fmt.Printf("parse error: %s", err)
return
}
df := matrix.Minus(m.mtx, refdata)
emtx, _ := matrix.FloatMatrixStacked(matrix.StackRight, m.mtx, refdata, df)
fmt.Printf("my data | ref.data | diff \n%v\n", emtx.ToString(spformat))
}
func (p *floorPlan) F1(x *matrix.FloatMatrix) (f, Df *matrix.FloatMatrix, err error) {
err = nil
mn := x.Min(-1, -2, -3, -4, -5)
if mn <= 0.0 {
f, Df = nil, nil
return
}
zeros := matrix.FloatZeros(5, 12)
dk1 := matrix.FloatDiagonal(5, -1.0)
dk2 := matrix.FloatZeros(5, 5)
x17 := matrix.FloatVector(x.FloatArray()[17:])
// -( Amin ./ (x17 .* x17) )
diag := matrix.Div(p.Amin, matrix.Mul(x17, x17)).Scale(-1.0)
dk2.SetIndexesFromArray(diag.FloatArray(), matrix.MakeDiagonalSet(5)...)
Df, _ = matrix.FloatMatrixStacked(matrix.StackRight, zeros, dk1, dk2)
x12 := matrix.FloatVector(x.FloatArray()[12:17])
// f = -x[12:17] + div(Amin, x[17:]) == div(Amin, x[17:]) - x[12:17]
f = matrix.Minus(matrix.Div(p.Amin, x17), x12)
return
}
func main() {
m := 6
Vdata := [][]float64{
[]float64{1.0, -1.0, -2.0, -2.0, 0.0, 1.5, 1.0},
[]float64{1.0, 2.0, 1.0, -1.0, -2.0, -1.0, 1.0}}
V := matrix.FloatMatrixFromTable(Vdata, matrix.RowOrder)
// V[1, :m] - V[1,1:]
a0 := matrix.Minus(V.GetSubMatrix(1, 0, 1, m), V.GetSubMatrix(1, 1, 1))
// V[0, :m] - V[0,1:]
a1 := matrix.Minus(V.GetSubMatrix(0, 0, 1, m), V.GetSubMatrix(0, 1, 1))
A0, _ := matrix.FloatMatrixStacked(matrix.StackDown, a0.Scale(-1.0), a1)
A0 = A0.Transpose()
b0 := matrix.Mul(A0, V.GetSubMatrix(0, 0, 2, m).Transpose())
b0 = matrix.Times(b0, matrix.FloatWithValue(2, 1, 1.0))
A := make([]*matrix.FloatMatrix, 0)
b := make([]*matrix.FloatMatrix, 0)
A = append(A, A0)
b = append(b, b0)
// List of symbols
C := make([]*matrix.FloatMatrix, 0)
C = append(C, matrix.FloatZeros(2, 1))
var row *matrix.FloatMatrix = nil
for k := 0; k < m; k++ {
row = A0.GetRow(k, row)
nrm := blas.Nrm2Float(row)
row.Scale(2.0 * b0.GetIndex(k) / (nrm * nrm))
C = append(C, row.Transpose())
}
// Voronoi set around C[1]
A1 := matrix.FloatZeros(3, 2)
A1.SetSubMatrix(0, 0, A0.GetSubMatrix(0, 0, 1).Scale(-1.0))
A1.SetSubMatrix(1, 0, matrix.Minus(C[m], C[1]).Transpose())
A1.SetSubMatrix(2, 0, matrix.Minus(C[2], C[1]).Transpose())
b1 := matrix.FloatZeros(3, 1)
b1.SetIndex(0, -b0.GetIndex(0))
v := matrix.Times(A1.GetRow(1, nil), matrix.Plus(C[m], C[1])).Float() * 0.5
b1.SetIndex(1, v)
v = matrix.Times(A1.GetRow(2, nil), matrix.Plus(C[2], C[1])).Float() * 0.5
b1.SetIndex(2, v)
A = append(A, A1)
b = append(b, b1)
// Voronoi set around C[2] ... C[5]
for k := 2; k < 6; k++ {
A1 = matrix.FloatZeros(3, 2)
A1.SetSubMatrix(0, 0, A0.GetSubMatrix(k-1, 0, 1).Scale(-1.0))
A1.SetSubMatrix(1, 0, matrix.Minus(C[k-1], C[k]).Transpose())
A1.SetSubMatrix(2, 0, matrix.Minus(C[k+1], C[k]).Transpose())
b1 = matrix.FloatZeros(3, 1)
b1.SetIndex(0, -b0.GetIndex(k-1))
v := matrix.Times(A1.GetRow(1, nil), matrix.Plus(C[k-1], C[k])).Float() * 0.5
b1.SetIndex(1, v)
v = matrix.Times(A1.GetRow(2, nil), matrix.Plus(C[k+1], C[k])).Float() * 0.5
b1.SetIndex(2, v)
A = append(A, A1)
b = append(b, b1)
}
// Voronoi set around C[6]
A1 = matrix.FloatZeros(3, 2)
A1.SetSubMatrix(0, 0, A0.GetSubMatrix(5, 0, 1).Scale(-1.0))
A1.SetSubMatrix(1, 0, matrix.Minus(C[1], C[6]).Transpose())
A1.SetSubMatrix(2, 0, matrix.Minus(C[5], C[6]).Transpose())
b1 = matrix.FloatZeros(3, 1)
b1.SetIndex(0, -b0.GetIndex(5))
v = matrix.Times(A1.GetRow(1, nil), matrix.Plus(C[1], C[6])).Float() * 0.5
b1.SetIndex(1, v)
v = matrix.Times(A1.GetRow(2, nil), matrix.Plus(C[5], C[6])).Float() * 0.5
b1.SetIndex(2, v)
A = append(A, A1)
b = append(b, b1)
P := matrix.FloatIdentity(2)
q := matrix.FloatZeros(2, 1)
solopts := &cvx.SolverOptions{ShowProgress: false, MaxIter: 30}
ovals := make([]float64, 0)
for k := 1; k < 7; k++ {
sol, err := cvx.Qp(P, q, A[k], b[k], nil, nil, solopts, nil)
_ = err
x := sol.Result.At("x")[0]
ovals = append(ovals, math.Pow(blas.Nrm2Float(x), 2.0))
}
optvals := matrix.FloatVector(ovals)
//fmt.Printf("optvals=\n%v\n", optvals)
rangeFunc := func(n int) []float64 {
r := make([]float64, 0)
for i := 0; i < n; i++ {
r = append(r, float64(i))
}
return r
}
nopts := 200
sigmas := matrix.FloatVector(rangeFunc(nopts))
sigmas.Scale((0.5 - 0.2) / float64(nopts)).Add(0.2)
bndsVal := func(sigma float64) float64 {
// 1.0 - sum(exp( -optvals/(2*sigma**2)))
return 1.0 - matrix.Exp(matrix.Scale(optvals, -1.0/(2*sigma*sigma))).Sum()
}
bnds := matrix.FloatZeros(sigmas.NumElements(), 1)
for j, v := range sigmas.FloatArray() {
bnds.SetIndex(j, bndsVal(v))
}
plotData("plot.png", sigmas.FloatArray(), bnds.FloatArray())
}
// Solves a pair of primal and dual SDPs
//
// minimize c'*x
// subject to Gl*x + sl = hl
// mat(Gs[k]*x) + ss[k] = hs[k], k = 0, ..., N-1
// A*x = b
// sl >= 0, ss[k] >= 0, k = 0, ..., N-1
//
// maximize -hl'*z - sum_k trace(hs[k]*zs[k]) - b'*y
// subject to Gl'*zl + sum_k Gs[k]'*vec(zs[k]) + A'*y + c = 0
// zl >= 0, zs[k] >= 0, k = 0, ..., N-1.
//
// The inequalities sl >= 0 and zl >= 0 are elementwise vector
// inequalities. The inequalities ss[k] >= 0, zs[k] >= 0 are matrix
// inequalities, i.e., the symmetric matrices ss[k] and zs[k] must be
// positive semidefinite. mat(Gs[k]*x) is the symmetric matrix X with
// X[:] = Gs[k]*x. For a symmetric matrix, zs[k], vec(zs[k]) is the
// vector zs[k][:].
//
func Sdp(c, Gl, hl, A, b *matrix.FloatMatrix, Ghs *sets.FloatMatrixSet, solopts *SolverOptions,
primalstart, dualstart *sets.FloatMatrixSet) (sol *Solution, err error) {
if c == nil {
err = errors.New("'c' must a column matrix")
return
}
n := c.Rows()
if n < 1 {
err = errors.New("Number of variables must be at least 1")
return
}
if Gl == nil {
Gl = matrix.FloatZeros(0, n)
}
if Gl.Cols() != n {
err = errors.New(fmt.Sprintf("'G' must be matrix with %d columns", n))
return
}
ml := Gl.Rows()
if hl == nil {
hl = matrix.FloatZeros(0, 1)
}
if !hl.SizeMatch(ml, 1) {
err = errors.New(fmt.Sprintf("'hl' must be matrix of size (%d,1)", ml))
return
}
Gsset := Ghs.At("Gs")
ms := make([]int, 0)
for i, Gs := range Gsset {
if Gs.Cols() != n {
err = errors.New(fmt.Sprintf("'Gs' must be list of matrices with %d columns", n))
return
}
sz := int(math.Sqrt(float64(Gs.Rows())))
if Gs.Rows() != sz*sz {
err = errors.New(fmt.Sprintf("the squareroot of the number of rows of 'Gq[%d]' is not an integer", i))
return
}
ms = append(ms, sz)
}
hsset := Ghs.At("hs")
if len(Gsset) != len(hsset) {
err = errors.New(fmt.Sprintf("'hs' must be a list of %d matrices", len(Gsset)))
return
}
for i, hs := range hsset {
if !hs.SizeMatch(ms[i], ms[i]) {
s := fmt.Sprintf("hq[%d] has size (%d,%d). Expected size is (%d,%d)",
i, hs.Rows(), hs.Cols(), ms[i], ms[i])
err = errors.New(s)
return
}
}
if A == nil {
A = matrix.FloatZeros(0, n)
}
if A.Cols() != n {
err = errors.New(fmt.Sprintf("'A' must be matrix with %d columns", n))
return
}
p := A.Rows()
if b == nil {
b = matrix.FloatZeros(0, 1)
}
if !b.SizeMatch(p, 1) {
err = errors.New(fmt.Sprintf("'b' must be matrix of size (%d,1)", p))
return
}
dims := sets.NewDimensionSet("l", "q", "s")
dims.Set("l", []int{ml})
dims.Set("s", ms)
N := dims.Sum("l") + dims.SumSquared("s")
// Map hs matrices to h vector
h := matrix.FloatZeros(N, 1)
h.SetIndexesFromArray(hl.FloatArray()[:ml], matrix.MakeIndexSet(0, ml, 1)...)
ind := ml
for k, hs := range hsset {
h.SetIndexesFromArray(hs.FloatArray(), matrix.MakeIndexSet(ind, ind+ms[k]*ms[k], 1)...)
ind += ms[k] * ms[k]
}
Gargs := make([]*matrix.FloatMatrix, 0)
Gargs = append(Gargs, Gl)
Gargs = append(Gargs, Gsset...)
G, sizeg := matrix.FloatMatrixStacked(matrix.StackDown, Gargs...)
var pstart, dstart *sets.FloatMatrixSet = nil, nil
if primalstart != nil {
pstart = sets.NewFloatSet("x", "s")
pstart.Set("x", primalstart.At("x")[0])
slset := primalstart.At("sl")
margs := make([]*matrix.FloatMatrix, 0, len(slset)+1)
margs = append(margs, primalstart.At("s")[0])
margs = append(margs, slset...)
sl, _ := matrix.FloatMatrixStacked(matrix.StackDown, margs...)
pstart.Set("s", sl)
}
if dualstart != nil {
dstart = sets.NewFloatSet("y", "z")
dstart.Set("y", dualstart.At("y")[0])
zlset := primalstart.At("zl")
margs := make([]*matrix.FloatMatrix, 0, len(zlset)+1)
margs = append(margs, dualstart.At("z")[0])
margs = append(margs, zlset...)
zl, _ := matrix.FloatMatrixStacked(matrix.StackDown, margs...)
dstart.Set("z", zl)
}
//fmt.Printf("h=\n%v\n", h.ToString("%.3f"))
//fmt.Printf("G=\n%v\n", G.ToString("%.3f"))
sol, err = ConeLp(c, G, h, A, b, dims, solopts, pstart, dstart)
// unpack sol.Result
if err == nil {
s := sol.Result.At("s")[0]
sl := matrix.FloatVector(s.FloatArray()[:ml])
sol.Result.Append("sl", sl)
ind := ml
for _, m := range ms {
sk := matrix.FloatNew(m, m, s.FloatArray()[ind:ind+m*m])
sol.Result.Append("ss", sk)
ind += m * m
}
z := sol.Result.At("z")[0]
zl := matrix.FloatVector(s.FloatArray()[:ml])
sol.Result.Append("zl", zl)
ind = ml
for i, k := range sizeg[1:] {
zk := matrix.FloatNew(ms[i], ms[i], z.FloatArray()[ind:ind+k])
sol.Result.Append("zs", zk)
ind += k
}
}
sol.Result.Remove("s")
sol.Result.Remove("z")
return
}
// Solves a pair of primal and dual SOCPs
//
// minimize c'*x
// subject to Gl*x + sl = hl
// Gq[k]*x + sq[k] = hq[k], k = 0, ..., N-1
// A*x = b
// sl >= 0,
// sq[k] >= 0, k = 0, ..., N-1
//
// maximize -hl'*z - sum_k hq[k]'*zq[k] - b'*y
// subject to Gl'*zl + sum_k Gq[k]'*zq[k] + A'*y + c = 0
// zl >= 0, zq[k] >= 0, k = 0, ..., N-1.
//
// The inequalities sl >= 0 and zl >= 0 are elementwise vector
// inequalities. The inequalities sq[k] >= 0, zq[k] >= 0 are second
// order cone inequalities, i.e., equivalent to
//
// sq[k][0] >= || sq[k][1:] ||_2, zq[k][0] >= || zq[k][1:] ||_2.
//
func Socp(c, Gl, hl, A, b *matrix.FloatMatrix, Ghq *sets.FloatMatrixSet, solopts *SolverOptions,
primalstart, dualstart *sets.FloatMatrixSet) (sol *Solution, err error) {
if c == nil {
err = errors.New("'c' must a column matrix")
return
}
n := c.Rows()
if n < 1 {
err = errors.New("Number of variables must be at least 1")
return
}
if Gl == nil {
Gl = matrix.FloatZeros(0, n)
}
if Gl.Cols() != n {
err = errors.New(fmt.Sprintf("'G' must be matrix with %d columns", n))
return
}
ml := Gl.Rows()
if hl == nil {
hl = matrix.FloatZeros(0, 1)
}
if !hl.SizeMatch(ml, 1) {
err = errors.New(fmt.Sprintf("'hl' must be matrix of size (%d,1)", ml))
return
}
Gqset := Ghq.At("Gq")
mq := make([]int, 0)
for i, Gq := range Gqset {
if Gq.Cols() != n {
err = errors.New(fmt.Sprintf("'Gq' must be list of matrices with %d columns", n))
return
}
if Gq.Rows() == 0 {
err = errors.New(fmt.Sprintf("the number of rows of 'Gq[%d]' is zero", i))
return
}
mq = append(mq, Gq.Rows())
}
hqset := Ghq.At("hq")
if len(Gqset) != len(hqset) {
err = errors.New(fmt.Sprintf("'hq' must be a list of %d matrices", len(Gqset)))
return
}
for i, hq := range hqset {
if !hq.SizeMatch(Gqset[i].Rows(), 1) {
s := fmt.Sprintf("hq[%d] has size (%d,%d). Expected size is (%d,1)",
i, hq.Rows(), hq.Cols(), Gqset[i].Rows())
err = errors.New(s)
return
}
}
if A == nil {
A = matrix.FloatZeros(0, n)
}
if A.Cols() != n {
err = errors.New(fmt.Sprintf("'A' must be matrix with %d columns", n))
return
}
p := A.Rows()
if b == nil {
b = matrix.FloatZeros(0, 1)
}
if !b.SizeMatch(p, 1) {
err = errors.New(fmt.Sprintf("'b' must be matrix of size (%d,1)", p))
return
}
dims := sets.NewDimensionSet("l", "q", "s")
dims.Set("l", []int{ml})
dims.Set("q", mq)
//N := dims.Sum("l", "q")
hargs := make([]*matrix.FloatMatrix, 0, len(hqset)+1)
hargs = append(hargs, hl)
hargs = append(hargs, hqset...)
h, indh := matrix.FloatMatrixStacked(matrix.StackDown, hargs...)
Gargs := make([]*matrix.FloatMatrix, 0, len(Gqset)+1)
Gargs = append(Gargs, Gl)
Gargs = append(Gargs, Gqset...)
G, indg := matrix.FloatMatrixStacked(matrix.StackDown, Gargs...)
var pstart, dstart *sets.FloatMatrixSet = nil, nil
if primalstart != nil {
pstart = sets.NewFloatSet("x", "s")
pstart.Set("x", primalstart.At("x")[0])
slset := primalstart.At("sl")
margs := make([]*matrix.FloatMatrix, 0, len(slset)+1)
margs = append(margs, primalstart.At("s")[0])
margs = append(margs, slset...)
sl, _ := matrix.FloatMatrixStacked(matrix.StackDown, margs...)
pstart.Set("s", sl)
}
if dualstart != nil {
dstart = sets.NewFloatSet("y", "z")
dstart.Set("y", dualstart.At("y")[0])
zlset := primalstart.At("zl")
margs := make([]*matrix.FloatMatrix, 0, len(zlset)+1)
margs = append(margs, dualstart.At("z")[0])
margs = append(margs, zlset...)
zl, _ := matrix.FloatMatrixStacked(matrix.StackDown, margs...)
dstart.Set("z", zl)
}
sol, err = ConeLp(c, G, h, A, b, dims, solopts, pstart, dstart)
// unpack sol.Result
if err == nil {
s := sol.Result.At("s")[0]
sl := matrix.FloatVector(s.FloatArray()[:ml])
sol.Result.Append("sl", sl)
ind := ml
for _, k := range indh[1:] {
sk := matrix.FloatVector(s.FloatArray()[ind : ind+k])
sol.Result.Append("sq", sk)
ind += k
}
z := sol.Result.At("z")[0]
zl := matrix.FloatVector(z.FloatArray()[:ml])
sol.Result.Append("zl", zl)
ind = ml
for _, k := range indg[1:] {
zk := matrix.FloatVector(z.FloatArray()[ind : ind+k])
sol.Result.Append("zq", zk)
ind += k
}
}
sol.Result.Remove("s")
sol.Result.Remove("z")
return
}
func TestConeQp(t *testing.T) {
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}}
// reference values from cvxopt coneqp.py
xref := []float64{0.72558318685981904, 0.61806264311119252, 0.30253527966423444}
sref := []float64{
0.72558318685981904, 0.61806264311119263,
0.30253527966423449, 1.00000000000041678,
-0.72558318686012169, -0.61806264311145032,
-0.30253527966436067}
zref := []float64{
0.00000003332583626, 0.00000005116586239,
0.00000009993673262, 0.56869648433154019,
0.41264857754144563, 0.35149286573190930,
0.17201618570052318}
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 := matrix.Times(At, A)
q := matrix.Times(At, b).Scale(-1.0)
dims := sets.DSetNew("l", "q", "s")
dims.Set("l", []int{n})
dims.Set("q", []int{n + 1})
var solopts SolverOptions
solopts.MaxIter = 10
solopts.ShowProgress = false
sol, err := ConeQp(P, q, G, h, nil, nil, dims, &solopts, nil)
if err == nil {
fail := false
x := sol.Result.At("x")[0]
s := sol.Result.At("s")[0]
z := sol.Result.At("z")[0]
t.Logf("Optimal\n")
t.Logf("x=\n%v\n", x.ToString("%.9f"))
t.Logf("s=\n%v\n", s.ToString("%.9f"))
t.Logf("z=\n%v\n", z.ToString("%.9f"))
xe, _ := nrmError(matrix.FloatVector(xref), x)
if xe > TOL {
t.Logf("x differs [%.3e] from exepted too much.", xe)
fail = true
}
se, _ := nrmError(matrix.FloatVector(sref), s)
if se > TOL {
t.Logf("s differs [%.3e] from exepted too much.", se)
fail = true
}
ze, _ := nrmError(matrix.FloatVector(zref), z)
if ze > TOL {
t.Logf("z differs [%.3e] from exepted too much.", ze)
fail = true
}
if fail {
t.Fail()
}
}
}