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 (u *epigraph) ShowError(line string) { lpar := strings.Index(line, "[") rpar := strings.LastIndex(line, "]") mstart := strings.Index(line, "{") refval, _ := matrix.FloatParse(line[mstart:rpar]) fval, _ := strconv.ParseFloat(strings.Trim(line[lpar+1:mstart], " "), 64) df := matrix.Minus(u.m(), refval) em, _ := matrix.FloatMatrixStacked(matrix.StackRight, u.m(), refval, df) fmt.Printf("my data | ref.data | diff \n%v\n", em.ToString("%.4e")) d := u.t() - fval fmt.Printf("/%.4e/ | /%.4e/ | /%4e/\n", u.t(), fval, d) }
// 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 (u *matrixVar) ShowError(dataline string) { refval, _ := matrix.FloatParse(dataline) em := matrix.Minus(u.val, refval) r, _ := matrix.FloatMatrixStacked(matrix.StackRight, u.val, refval, em) fmt.Printf("my data | ref.data | diff \n%v\n", r.ToString("%.4e")) }
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() } } }