// Solves a pair of primal and dual LPs
//
// minimize c'*x
// subject to G*x + s = h
// A*x = b
// s >= 0
//
// maximize -h'*z - b'*y
// subject to G'*z + A'*y + c = 0
// z >= 0.
//
func Lp(c, G, h, A, b *matrix.FloatMatrix, 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 G == nil || G.Cols() != n {
err = errors.New(fmt.Sprintf("'G' must be matrix with %d columns", n))
return
}
m := G.Rows()
if h == nil || !h.SizeMatch(m, 1) {
err = errors.New(fmt.Sprintf("'h' must be matrix of size (%d,1)", m))
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{m})
return ConeLp(c, G, h, A, b, dims, solopts, primalstart, dualstart)
}
//
// Solves a geometric program
//
// minimize log sum exp (F0*x+g0)
// subject to log sum exp (Fi*x+gi) <= 0, i=1,...,m
// G*x <= h
// A*x = b
//
func Gp(K []int, F, g, G, h, A, b *matrix.FloatMatrix, solopts *SolverOptions) (sol *Solution, err error) {
if err = checkArgK(K); err != nil {
return
}
l := sumdim(K)
if F == nil || F.Rows() != l {
err = errors.New(fmt.Sprintf("'F' must matrix with %d rows", l))
return
}
if g == nil || !g.SizeMatch(l, 1) {
err = errors.New(fmt.Sprintf("'g' must matrix with size (%d,1)", l))
return
}
n := F.Cols()
if G == nil {
G = matrix.FloatZeros(0, n)
}
if h == nil {
h = matrix.FloatZeros(0, 1)
}
if G.Cols() != n {
err = errors.New(fmt.Sprintf("'G' must matrix with size %d columns", n))
return
}
ml := G.Rows()
if h == nil || !h.SizeMatch(ml, 1) {
err = errors.New(fmt.Sprintf("'h' must matrix with size (%d,1)", ml))
return
}
if A == nil {
A = matrix.FloatZeros(0, n)
}
if b == nil {
b = matrix.FloatZeros(0, 1)
}
if A.Cols() != n {
err = errors.New(fmt.Sprintf("'A' must matrix with size %d columns", n))
return
}
p := A.Rows()
if b == nil || !b.SizeMatch(p, 1) {
err = errors.New(fmt.Sprintf("'b' must matrix with size (%d,1)", p))
return
}
dims := sets.NewDimensionSet("l", "q", "s")
dims.Set("l", []int{ml})
gpProg := createGpProg(K, F, g)
return Cp(gpProg, G, h, A, b, dims, solopts)
}
// 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
}
// Solves a convex optimization problem with a linear objective
//
// minimize c'*x
// subject to f(x) <= 0
// G*x <= h
// A*x = b.
//
// f is vector valued, convex and twice differentiable. The linear
// inequalities are with respect to a cone C defined as the Cartesian
// product of N + M + 1 cones:
//
// C = C_0 x C_1 x .... x C_N x C_{N+1} x ... x C_{N+M}.
//
// The first cone C_0 is the nonnegative orthant of dimension ml. The
// next N cones are second order cones of dimension r[0], ..., r[N-1].
// The second order cone of dimension m is defined as
//
// { (u0, u1) in R x R^{m-1} | u0 >= ||u1||_2 }.
//
// The next M cones are positive semidefinite cones of order t[0], ..., t[M-1] >= 0.
//
// The structure of C is specified by DimensionSet dims which holds following sets
//
// dims.At("l") l, the dimension of the nonnegative orthant (array of length 1)
// dims.At("q") r[0], ... r[N-1], list with the dimesions of the second-order cones
// dims.At("s") t[0], ... t[M-1], array with the dimensions of the positive
// semidefinite cones
//
// The default value for dims is l: []int{h.Rows()}, q: []int{}, s: []int{}.
//
// On exit Solution contains the result and information about the accurancy of the
// solution. if SolutionStatus is Optimal then Solution.Result contains solutions
// for the problems.
//
// Result.At("x")[0] primal solution
// Result.At("snl")[0] non-linear constraint slacks
// Result.At("sl")[0] linear constraint slacks
// Result.At("y")[0] values for linear equality constraints y
// Result.At("znl")[0] values of dual variables for nonlinear inequalities
// Result.At("zl")[0] values of dual variables for linear inequalities
//
// If err is non-nil then sol is nil and err contains information about the argument or
// computation error.
//
func Cpl(F ConvexProg, c, G, h, A, b *matrix.FloatMatrix, dims *sets.DimensionSet, solopts *SolverOptions) (sol *Solution, err error) {
var mnl int
var x0 *matrix.FloatMatrix
mnl, x0, err = F.F0()
if err != nil {
return
}
if x0.Cols() != 1 {
err = errors.New("'x0' must be matrix with one column")
return
}
if c == nil {
err = errors.New("'c' must be non nil matrix")
return
}
if !c.SizeMatch(x0.Size()) {
err = errors.New(fmt.Sprintf("'c' must be matrix of size (%d,1)", x0.Rows()))
return
}
if h == nil {
h = matrix.FloatZeros(0, 1)
}
if h.Cols() > 1 {
err = errors.New("'h' must be matrix with 1 column")
return
}
if dims == nil {
dims = sets.NewDimensionSet("l", "q", "s")
dims.Set("l", []int{h.Rows()})
}
cdim := dims.Sum("l", "q") + dims.SumSquared("s")
//cdim_pckd := dims.Sum("l", "q") + dims.SumPacked("s")
//cdim_diag := dims.Sum("l", "q", "s")
if h.Rows() != cdim {
err = errors.New(fmt.Sprintf("'h' must be float matrix of size (%d,1)", cdim))
return
}
if G == nil {
G = matrix.FloatZeros(0, c.Rows())
}
if !G.SizeMatch(cdim, c.Rows()) {
estr := fmt.Sprintf("'G' must be of size (%d,%d)", cdim, c.Rows())
err = errors.New(estr)
return
}
// Check A and set defaults if it is nil
if A == nil {
// zeros rows reduces Gemv to vector products
A = matrix.FloatZeros(0, c.Rows())
}
if A.Cols() != c.Rows() {
estr := fmt.Sprintf("'A' must have %d columns", c.Rows())
err = errors.New(estr)
return
}
// Check b and set defaults if it is nil
if b == nil {
b = matrix.FloatZeros(0, 1)
}
if b.Cols() != 1 {
estr := fmt.Sprintf("'b' must be a matrix with 1 column")
err = errors.New(estr)
return
}
if b.Rows() != A.Rows() {
estr := fmt.Sprintf("'b' must have length %d", A.Rows())
err = errors.New(estr)
return
}
var mc = matrixVar{c}
var mb = matrixVar{b}
var mA = matrixVarA{A}
var mG = matrixVarG{G, dims}
solvername := solopts.KKTSolverName
if len(solvername) == 0 {
if len(dims.At("q")) > 0 || len(dims.At("s")) > 0 {
solvername = "chol"
} else {
solvername = "chol2"
}
}
var factor kktFactor
var kktsolver KKTCpSolver = nil
if kktfunc, ok := solvers[solvername]; ok {
// kkt function returns us problem spesific factor function.
factor, err = kktfunc(G, dims, A, mnl)
// solver is
kktsolver = func(W *sets.FloatMatrixSet, x, z *matrix.FloatMatrix) (KKTFunc, error) {
_, Df, H, err := F.F2(x, z)
if err != nil {
return nil, err
}
return factor(W, H, Df)
}
} else {
err = errors.New(fmt.Sprintf("solver '%s' not known", solvername))
return
}
//return CplCustom(F, c, &mG, h, &mA, b, dims, kktsolver, solopts)
return cpl_problem(F, &mc, &mG, h, &mA, &mb, dims, kktsolver, solopts, x0, mnl)
}
// Solves a convex optimization problem with a linear objective
//
// minimize c'*x
// subject to f(x) <= 0
// G*x <= h
// A*x = b.
//
// using custom KTT equation solver and custom constraints G and A.
//
func CplCustomMatrix(F ConvexProg, c *matrix.FloatMatrix, G MatrixG, h *matrix.FloatMatrix,
A MatrixA, b *matrix.FloatMatrix, dims *sets.DimensionSet, kktsolver KKTCpSolver,
solopts *SolverOptions) (sol *Solution, err error) {
var mnl int
var x0 *matrix.FloatMatrix
mnl, x0, err = F.F0()
if err != nil {
return
}
if x0.Cols() != 1 {
err = errors.New("'x0' must be matrix with one column")
return
}
if c == nil {
err = errors.New("'c' must be non nil matrix")
return
}
if !c.SizeMatch(x0.Size()) {
err = errors.New(fmt.Sprintf("'c' must be matrix of size (%d,1)", x0.Rows()))
return
}
if h == nil {
h = matrix.FloatZeros(0, 1)
}
if h.Cols() > 1 {
err = errors.New("'h' must be matrix with 1 column")
return
}
if dims == nil {
dims = sets.NewDimensionSet("l", "q", "s")
dims.Set("l", []int{h.Rows()})
}
cdim := dims.Sum("l", "q") + dims.SumSquared("s")
if h.Rows() != cdim {
err = errors.New(fmt.Sprintf("'h' must be float matrix of size (%d,1)", cdim))
return
}
// Check b and set defaults if it is nil
if b == nil {
b = matrix.FloatZeros(0, 1)
}
if b.Cols() != 1 {
estr := fmt.Sprintf("'b' must be a matrix with 1 column")
err = errors.New(estr)
return
}
mc := matrixVar{c}
mb := matrixVar{b}
var mG MatrixVarG
var mA MatrixVarA
if G == nil {
mG = &matrixVarG{matrix.FloatZeros(0, c.Rows()), dims}
} else {
mG = &matrixIfG{G}
}
if A == nil {
mA = &matrixVarA{matrix.FloatZeros(0, c.Rows())}
} else {
mA = &matrixIfA{A}
}
return cpl_problem(F, &mc, mG, h, mA, &mb, dims, kktsolver, solopts, x0, mnl)
}
// Solves a convex optimization problem with a linear objective
//
// minimize c'*x
// subject to f(x) <= 0
// G*x <= h
// A*x = b.
//
// using custom KTT equation solver.
//
func CplCustomKKT(F ConvexProg, c *matrix.FloatMatrix, G, h, A, b *matrix.FloatMatrix,
dims *sets.DimensionSet, kktsolver KKTCpSolver,
solopts *SolverOptions) (sol *Solution, err error) {
var mnl int
var x0 *matrix.FloatMatrix
mnl, x0, err = F.F0()
if err != nil {
return
}
if x0.Cols() != 1 {
err = errors.New("'x0' must be matrix with one column")
return
}
if c == nil {
err = errors.New("'c' must be non nil matrix")
return
}
if !c.SizeMatch(x0.Size()) {
err = errors.New(fmt.Sprintf("'c' must be matrix of size (%d,1)", x0.Rows()))
return
}
if h == nil {
h = matrix.FloatZeros(0, 1)
}
if h.Cols() > 1 {
err = errors.New("'h' must be matrix with 1 column")
return
}
if dims == nil {
dims = sets.NewDimensionSet("l", "q", "s")
dims.Set("l", []int{h.Rows()})
}
cdim := dims.Sum("l", "q") + dims.SumSquared("s")
if h.Rows() != cdim {
err = errors.New(fmt.Sprintf("'h' must be float matrix of size (%d,1)", cdim))
return
}
if G == nil {
G = matrix.FloatZeros(0, c.Rows())
}
if !G.SizeMatch(cdim, c.Rows()) {
estr := fmt.Sprintf("'G' must be of size (%d,%d)", cdim, c.Rows())
err = errors.New(estr)
return
}
// Check A and set defaults if it is nil
if A == nil {
// zeros rows reduces Gemv to vector products
A = matrix.FloatZeros(0, c.Rows())
}
if A.Cols() != c.Rows() {
estr := fmt.Sprintf("'A' must have %d columns", c.Rows())
err = errors.New(estr)
return
}
// Check b and set defaults if it is nil
if b == nil {
b = matrix.FloatZeros(0, 1)
}
if b.Cols() != 1 {
estr := fmt.Sprintf("'b' must be a matrix with 1 column")
err = errors.New(estr)
return
}
if b.Rows() != A.Rows() {
estr := fmt.Sprintf("'b' must have length %d", A.Rows())
err = errors.New(estr)
return
}
var mc = matrixVar{c}
var mb = matrixVar{b}
var mA = matrixVarA{A}
var mG = matrixVarG{G, dims}
return cpl_problem(F, &mc, &mG, h, &mA, &mb, dims, kktsolver, solopts, x0, mnl)
}
// Solves a pair of primal and dual convex quadratic cone programs
//
// minimize (1/2)*x'*P*x + q'*x
// subject to G*x + s = h
// A*x = b
// s >= 0
//
// maximize -(1/2)*(q + G'*z + A'*y)' * pinv(P) * (q + G'*z + A'*y)
// - h'*z - b'*y
// subject to q + G'*z + A'*y in range(P)
// z >= 0.
//
// The inequalities are with respect to a cone C defined as the Cartesian
// product of N + M + 1 cones:
//
// C = C_0 x C_1 x .... x C_N x C_{N+1} x ... x C_{N+M}.
//
// The first cone C_0 is the nonnegative orthant of dimension ml.
// The next N cones are 2nd order cones of dimension r[0], ..., r[N-1].
// The second order cone of dimension m is defined as
//
// { (u0, u1) in R x R^{m-1} | u0 >= ||u1||_2 }.
//
// The next M cones are positive semidefinite cones of order t[0], ..., t[M-1] >= 0.
//
// The structure of C is specified by DimensionSet dims which holds following sets
//
// dims.At("l") l, the dimension of the nonnegative orthant (array of length 1)
// dims.At("q") r[0], ... r[N-1], list with the dimesions of the second-order cones
// dims.At("s") t[0], ... t[M-1], array with the dimensions of the positive
// semidefinite cones
//
// The default value for dims is l: []int{G.Rows()}, q: []int{}, s: []int{}.
//
// Argument initval contains optional starting points for primal and
// dual problems. If non-nil then initval is a FloatMatrixSet having following entries.
//
// initvals.At("x")[0] starting point for x
// initvals.At("s")[0] starting point for s
// initvals.At("y")[0] starting point for y
// initvals.At("z")[0] starting point for z
//
// On exit Solution contains the result and information about the accurancy of the
// solution. if SolutionStatus is Optimal then Solution.Result contains solutions
// for the problems.
//
// Result.At("x")[0] solution for x
// Result.At("y")[0] solution for y
// Result.At("s")[0] solution for s
// Result.At("z")[0] solution for z
//
func ConeQp(P, q, G, h, A, b *matrix.FloatMatrix, dims *sets.DimensionSet, solopts *SolverOptions,
initvals *sets.FloatMatrixSet) (sol *Solution, err error) {
if q == nil || q.Cols() != 1 {
err = errors.New("'q' must be non-nil matrix with one column")
return
}
if P == nil || P.Rows() != q.Rows() || P.Cols() != q.Rows() {
err = errors.New(fmt.Sprintf("'P' must be non-nil matrix of size (%d, %d)",
q.Rows(), q.Rows()))
return
}
if h == nil {
h = matrix.FloatZeros(0, 1)
}
if h.Cols() != 1 {
err = errors.New("'h' must be non-nil matrix with one column")
return
}
if dims == nil {
dims = sets.NewDimensionSet("l", "q", "s")
dims.Set("l", []int{h.Rows()})
}
err = checkConeQpDimensions(dims)
if err != nil {
return
}
cdim := dims.Sum("l", "q") + dims.SumSquared("s")
if h.Rows() != cdim {
err = errors.New(fmt.Sprintf("'h' must be float matrix of size (%d,1)", cdim))
return
}
if G == nil {
G = matrix.FloatZeros(0, q.Rows())
}
if !G.SizeMatch(cdim, q.Rows()) {
estr := fmt.Sprintf("'G' must be of size (%d,%d)", cdim, q.Rows())
err = errors.New(estr)
return
}
// Check A and set defaults if it is nil
if A == nil {
// zeros rows reduces Gemv to vector products
A = matrix.FloatZeros(0, q.Rows())
}
if A.Cols() != q.Rows() {
estr := fmt.Sprintf("'A' must have %d columns", q.Rows())
err = errors.New(estr)
return
}
// Check b and set defaults if it is nil
if b == nil {
b = matrix.FloatZeros(0, 1)
}
if b.Cols() != 1 {
estr := fmt.Sprintf("'b' must be a matrix with 1 column")
err = errors.New(estr)
return
}
if b.Rows() != A.Rows() {
estr := fmt.Sprintf("'b' must have length %d", A.Rows())
err = errors.New(estr)
return
}
solvername := solopts.KKTSolverName
if len(solvername) == 0 {
if len(dims.At("q")) > 0 || len(dims.At("s")) > 0 {
solvername = "ldl"
} else {
solvername = "chol2"
}
}
var factor kktFactor
var kktsolver KKTConeSolver = nil
if kktfunc, ok := solvers[solvername]; ok {
// kkt function returns us problem spesific factor function.
factor, err = kktfunc(G, dims, A, 0)
if err != nil {
return nil, err
}
kktsolver = func(W *sets.FloatMatrixSet) (KKTFunc, error) {
return factor(W, P, nil)
}
} else {
err = errors.New(fmt.Sprintf("solver '%s' not known", solvername))
return
}
mA := &matrixVarA{A}
mG := &matrixVarG{G, dims}
mP := &matrixVarP{P}
mq := &matrixVar{q}
mb := &matrixVar{b}
return coneqp_problem(mP, mq, mG, h, mA, mb, dims, kktsolver, solopts, initvals)
}
// Solves a pair of primal and dual convex quadratic cone programs using custom KKT solver.
//
func ConeQpCustomKKT(P, q, G, h, A, b *matrix.FloatMatrix, dims *sets.DimensionSet, kktsolver KKTConeSolver,
solopts *SolverOptions, initvals *sets.FloatMatrixSet) (sol *Solution, err error) {
if q == nil || q.Cols() != 1 {
err = errors.New("'q' must be non-nil matrix with one column")
return
}
if P == nil || P.Rows() != q.Rows() || P.Cols() != q.Rows() {
err = errors.New(fmt.Sprintf("'P' must be non-nil matrix of size (%d, %d)",
q.Rows(), q.Rows()))
return
}
if h == nil {
h = matrix.FloatZeros(0, 1)
}
if h.Cols() != 1 {
err = errors.New("'h' must be non-nil matrix with one column")
return
}
if dims == nil {
dims = sets.NewDimensionSet("l", "q", "s")
dims.Set("l", []int{h.Rows()})
}
err = checkConeQpDimensions(dims)
if err != nil {
return
}
cdim := dims.Sum("l", "q") + dims.SumSquared("s")
if h.Rows() != cdim {
err = errors.New(fmt.Sprintf("'h' must be float matrix of size (%d,1)", cdim))
return
}
if G == nil {
G = matrix.FloatZeros(0, q.Rows())
}
if !G.SizeMatch(cdim, q.Rows()) {
estr := fmt.Sprintf("'G' must be of size (%d,%d)", cdim, q.Rows())
err = errors.New(estr)
return
}
// Check A and set defaults if it is nil
if A == nil {
// zeros rows reduces Gemv to vector products
A = matrix.FloatZeros(0, q.Rows())
}
if A.Cols() != q.Rows() {
estr := fmt.Sprintf("'A' must have %d columns", q.Rows())
err = errors.New(estr)
return
}
// Check b and set defaults if it is nil
if b == nil {
b = matrix.FloatZeros(0, 1)
}
if b.Cols() != 1 {
estr := fmt.Sprintf("'b' must be a matrix with 1 column")
err = errors.New(estr)
return
}
if b.Rows() != A.Rows() {
estr := fmt.Sprintf("'b' must have length %d", A.Rows())
err = errors.New(estr)
return
}
if kktsolver == nil {
err = errors.New("nil kktsolver not allowed")
return
}
mA := &matrixVarA{A}
mG := &matrixVarG{G, dims}
mP := &matrixVarP{P}
mq := &matrixVar{q}
mb := &matrixVar{b}
return coneqp_problem(mP, mq, mG, h, mA, mb, dims, kktsolver, solopts, initvals)
}
// Solves a pair of primal and dual cone programs using custom KKT solver.
//
func ConeLpCustomKKT(c, G, h, A, b *matrix.FloatMatrix, dims *sets.DimensionSet,
kktsolver KKTConeSolver, solopts *SolverOptions, primalstart,
dualstart *sets.FloatMatrixSet) (sol *Solution, err error) {
if c == nil || c.Cols() > 1 {
err = errors.New("'c' must be matrix with 1 column")
return
}
if h == nil {
h = matrix.FloatZeros(0, 1)
}
if h.Cols() > 1 {
err = errors.New("'h' must be matrix with 1 column")
return
}
if dims == nil {
dims = sets.NewDimensionSet("l", "q", "s")
dims.Set("l", []int{h.Rows()})
}
cdim := dims.Sum("l", "q") + dims.SumSquared("s")
cdim_pckd := dims.Sum("l", "q") + dims.SumPacked("s")
//cdim_diag := dims.Sum("l", "q", "s")
if G == nil {
G = matrix.FloatZeros(0, c.Rows())
}
if !G.SizeMatch(cdim, c.Rows()) {
estr := fmt.Sprintf("'G' must be of size (%d,%d)", cdim, c.Rows())
err = errors.New(estr)
return
}
// Check A and set defaults if it is nil
if A == nil {
// zeros rows reduces Gemv to vector products
A = matrix.FloatZeros(0, c.Rows())
}
if A.Cols() != c.Rows() {
estr := fmt.Sprintf("'A' must have %d columns", c.Rows())
err = errors.New(estr)
return
}
// Check b and set defaults if it is nil
if b == nil {
b = matrix.FloatZeros(0, 1)
}
if b.Cols() != 1 {
estr := fmt.Sprintf("'b' must be a matrix with 1 column")
err = errors.New(estr)
return
}
if b.Rows() != A.Rows() {
estr := fmt.Sprintf("'b' must have length %d", A.Rows())
err = errors.New(estr)
return
}
if b.Rows() > c.Rows() || b.Rows()+cdim_pckd < c.Rows() {
err = errors.New("Rank(A) < p or Rank([G; A]) < n")
return
}
mA := &matrixVarA{A}
mG := &matrixVarG{G, dims}
mc := &matrixVar{c}
mb := &matrixVar{b}
return conelp_problem(mc, mG, h, mA, mb, dims, kktsolver, solopts, primalstart, dualstart)
}
// Solves a pair of primal and dual cone programs
//
// minimize c'*x
// subject to G*x + s = h
// A*x = b
// s >= 0
//
// maximize -h'*z - b'*y
// subject to G'*z + A'*y + c = 0
// z >= 0.
//
// The inequalities are with respect to a cone C defined as the Cartesian
// product of N + M + 1 cones:
//
// C = C_0 x C_1 x .... x C_N x C_{N+1} x ... x C_{N+M}.
//
// The first cone C_0 is the nonnegative orthant of dimension ml.
// The next N cones are second order cones of dimension r[0], ..., r[N-1].
// The second order cone of dimension m is defined as
//
// { (u0, u1) in R x R^{m-1} | u0 >= ||u1||_2 }.
//
// The next M cones are positive semidefinite cones of order t[0], ..., t[M-1] >= 0.
//
// The structure of C is specified by DimensionSet dims which holds following sets
//
// dims.At("l") l, the dimension of the nonnegative orthant (array of length 1)
// dims.At("q") r[0], ... r[N-1], list with the dimesions of the second-order cones
// dims.At("s") t[0], ... t[M-1], array with the dimensions of the positive
// semidefinite cones
//
// The default value for dims is l: []int{G.Rows()}, q: []int{}, s: []int{}.
//
// Arguments primalstart, dualstart are optional starting points for primal and
// dual problems. If non-nil then primalstart is a FloatMatrixSet having two entries.
//
// primalstart.At("x")[0] starting point for x
// primalstart.At("s")[0] starting point for s
// dualstart.At("y")[0] starting point for y
// dualstart.At("z")[0] starting point for z
//
// On exit Solution contains the result and information about the accurancy of the
// solution. if SolutionStatus is Optimal then Solution.Result contains solutions
// for the problems.
//
// Result.At("x")[0] solution for x
// Result.At("y")[0] solution for y
// Result.At("s")[0] solution for s
// Result.At("z")[0] solution for z
//
func ConeLp(c, G, h, A, b *matrix.FloatMatrix, dims *sets.DimensionSet, solopts *SolverOptions,
primalstart, dualstart *sets.FloatMatrixSet) (sol *Solution, err error) {
if c == nil || c.Cols() > 1 {
err = errors.New("'c' must be matrix with 1 column")
return
}
if c.Rows() < 1 {
err = errors.New("No variables, 'c' must have at least one row")
return
}
if h == nil || h.Cols() > 1 {
err = errors.New("'h' must be matrix with 1 column")
return
}
if dims == nil {
dims = sets.NewDimensionSet("l", "q", "s")
dims.Set("l", []int{h.Rows()})
}
cdim := dims.Sum("l", "q") + dims.SumSquared("s")
cdim_pckd := dims.Sum("l", "q") + dims.SumPacked("s")
if h.Rows() != cdim {
err = errors.New(fmt.Sprintf("'h' must be float matrix of size (%d,1)", cdim))
return
}
if G == nil {
G = matrix.FloatZeros(0, c.Rows())
}
if !G.SizeMatch(cdim, c.Rows()) {
estr := fmt.Sprintf("'G' must be of size (%d,%d)", cdim, c.Rows())
err = errors.New(estr)
return
}
// Check A and set defaults if it is nil
if A == nil {
// zeros rows reduces Gemv to vector products
A = matrix.FloatZeros(0, c.Rows())
}
if A.Cols() != c.Rows() {
estr := fmt.Sprintf("'A' must have %d columns", c.Rows())
err = errors.New(estr)
return
}
// Check b and set defaults if it is nil
if b == nil {
b = matrix.FloatZeros(0, 1)
}
if b.Cols() != 1 {
estr := fmt.Sprintf("'b' must be a matrix with 1 column")
err = errors.New(estr)
return
}
if b.Rows() != A.Rows() {
estr := fmt.Sprintf("'b' must have length %d", A.Rows())
err = errors.New(estr)
return
}
if b.Rows() > c.Rows() || b.Rows()+cdim_pckd < c.Rows() {
err = errors.New("Rank(A) < p or Rank([G; A]) < n")
return
}
solvername := solopts.KKTSolverName
if len(solvername) == 0 {
if len(dims.At("q")) > 0 || len(dims.At("s")) > 0 {
solvername = "qr"
} else {
solvername = "chol2"
}
}
var factor kktFactor
var kktsolver KKTConeSolver = nil
if kktfunc, ok := lpsolvers[solvername]; ok {
// kkt function returns us problem spesific factor function.
factor, err = kktfunc(G, dims, A, 0)
if err != nil {
return nil, err
}
kktsolver = func(W *sets.FloatMatrixSet) (KKTFunc, error) {
return factor(W, nil, nil)
}
} else {
err = errors.New(fmt.Sprintf("solver '%s' not known", solvername))
return
}
//return ConeLpCustom(c, &mG, h, &mA, b, dims, kktsolver, solopts, primalstart, dualstart)
c_e := &matrixVar{c}
G_e := &matrixVarG{G, dims}
A_e := &matrixVarA{A}
b_e := &matrixVar{b}
return conelp_problem(c_e, G_e, h, A_e, b_e, dims, kktsolver, solopts, primalstart, dualstart)
}
// Solves a convex optimization problem with a linear objective
//
// minimize f0(x)
// subject to fk(x) <= 0, k = 1, ..., mnl
// G*x <= h
// A*x = b.
//
// using custom solver for KKT equations.
//
func CpCustomKKT(F ConvexProg, G, h, A, b *matrix.FloatMatrix, dims *sets.DimensionSet,
kktsolver KKTCpSolver, solopts *SolverOptions) (sol *Solution, err error) {
var mnl int
var x0 *matrix.FloatMatrix
mnl, x0, err = F.F0()
if err != nil {
return
}
if x0.Cols() != 1 {
err = errors.New("'x0' must be matrix with one column")
return
}
if h == nil {
h = matrix.FloatZeros(0, 1)
}
if h.Cols() > 1 {
err = errors.New("'h' must be matrix with 1 column")
return
}
if dims == nil {
dims = sets.NewDimensionSet("l", "q", "s")
dims.Set("l", []int{h.Rows()})
}
if err = checkConeLpDimensions(dims); err != nil {
return
}
cdim := dims.Sum("l", "q") + dims.SumSquared("s")
if h.Rows() != cdim {
err = errors.New(fmt.Sprintf("'h' must be float matrix of size (%d,1)", cdim))
return
}
if G == nil {
G = matrix.FloatZeros(0, x0.Rows())
}
if !G.SizeMatch(cdim, x0.Rows()) {
estr := fmt.Sprintf("'G' must be of size (%d,%d)", cdim, x0.Rows())
err = errors.New(estr)
return
}
// Check A and set defaults if it is nil
if A == nil {
// zeros rows reduces Gemv to vector products
A = matrix.FloatZeros(0, x0.Rows())
}
if A.Cols() != x0.Rows() {
estr := fmt.Sprintf("'A' must have %d columns", x0.Rows())
err = errors.New(estr)
return
}
// Check b and set defaults if it is nil
if b == nil {
b = matrix.FloatZeros(0, 1)
}
if b.Cols() != 1 {
estr := fmt.Sprintf("'b' must be a matrix with 1 column")
err = errors.New(estr)
return
}
if b.Rows() != A.Rows() {
estr := fmt.Sprintf("'b' must have length %d", A.Rows())
err = errors.New(estr)
return
}
if kktsolver == nil {
err = errors.New("'kktsolver' must be non-nil function.")
return
}
c_e := newEpigraph(x0, 1.0)
blas.ScalFloat(x0, 0.0)
G_e := epMatrixG{G, dims}
A_e := epMatrixA{A}
b_e := matrixVar{b}
return cp_problem(F, c_e, &G_e, h, &A_e, &b_e, dims, kktsolver, solopts, x0, mnl)
}
// Solves a convex optimization problem with a linear objective
//
// minimize f0(x)
// subject to fk(x) <= 0, k = 1, ..., mnl
// G*x <= h
// A*x = b.
//
// f is vector valued, convex and twice differentiable. The linear
// inequalities are with respect to a cone C defined as the Cartesian
// product of N + M + 1 cones:
//
// C = C_0 x C_1 x .... x C_N x C_{N+1} x ... x C_{N+M}.
//
// The first cone C_0 is the nonnegative orthant of dimension ml. The
// next N cones are second order cones of dimension r[0], ..., r[N-1].
// The second order cone of dimension m is defined as
//
// { (u0, u1) in R x R^{m-1} | u0 >= ||u1||_2 }.
//
// The next M cones are positive semidefinite cones of order t[0], ..., t[M-1] >= 0.
//
// The structure of C is specified by DimensionSet dims which holds following sets
//
// dims.At("l") l, the dimension of the nonnegative orthant (array of length 1)
// dims.At("q") r[0], ... r[N-1], list with the dimesions of the second-order cones
// dims.At("s") t[0], ... t[M-1], array with the dimensions of the positive
// semidefinite cones
//
// The default value for dims is l: []int{h.Rows()}, q: []int{}, s: []int{}.
//
// On exit Solution contains the result and information about the accurancy of the
// solution. if SolutionStatus is Optimal then Solution.Result contains solutions
// for the problems.
//
// Result.At("x")[0] primal solution
// Result.At("snl")[0] non-linear constraint slacks
// Result.At("sl")[0] linear constraint slacks
// Result.At("y")[0] values for linear equality constraints y
// Result.At("znl")[0] values of dual variables for nonlinear inequalities
// Result.At("zl")[0] values of dual variables for linear inequalities
//
// If err is non-nil then sol is nil and err contains information about the argument or
// computation error.
//
func Cp(F ConvexProg, G, h, A, b *matrix.FloatMatrix, dims *sets.DimensionSet, solopts *SolverOptions) (sol *Solution, err error) {
var mnl int
var x0 *matrix.FloatMatrix
mnl, x0, err = F.F0()
if err != nil {
return
}
if x0.Cols() != 1 {
err = errors.New("'x0' must be matrix with one column")
return
}
if h == nil {
h = matrix.FloatZeros(0, 1)
}
if h.Cols() > 1 {
err = errors.New("'h' must be matrix with 1 column")
return
}
if dims == nil {
dims = sets.NewDimensionSet("l", "q", "s")
dims.Set("l", []int{h.Rows()})
}
if err = checkConeLpDimensions(dims); err != nil {
return
}
cdim := dims.Sum("l", "q") + dims.SumSquared("s")
if h.Rows() != cdim {
err = errors.New(fmt.Sprintf("'h' must be float matrix of size (%d,1)", cdim))
return
}
if G == nil {
G = matrix.FloatZeros(0, x0.Rows())
}
if !G.SizeMatch(cdim, x0.Rows()) {
estr := fmt.Sprintf("'G' must be of size (%d,%d)", cdim, x0.Rows())
err = errors.New(estr)
return
}
// Check A and set defaults if it is nil
if A == nil {
// zeros rows reduces Gemv to vector products
A = matrix.FloatZeros(0, x0.Rows())
}
if A.Cols() != x0.Rows() {
estr := fmt.Sprintf("'A' must have %d columns", x0.Rows())
err = errors.New(estr)
return
}
// Check b and set defaults if it is nil
if b == nil {
b = matrix.FloatZeros(0, 1)
}
if b.Cols() != 1 {
estr := fmt.Sprintf("'b' must be a matrix with 1 column")
err = errors.New(estr)
return
}
if b.Rows() != A.Rows() {
estr := fmt.Sprintf("'b' must have length %d", A.Rows())
err = errors.New(estr)
return
}
solvername := solopts.KKTSolverName
if len(solvername) == 0 {
if len(dims.At("q")) > 0 || len(dims.At("s")) > 0 {
solvername = "chol"
} else {
solvername = "chol2"
}
}
c_e := newEpigraph(x0, 1.0)
blas.ScalFloat(c_e.m(), 0.0)
//F_e := &cpProg{F}
G_e := epMatrixG{G, dims}
A_e := epMatrixA{A}
b_e := matrixVar{b}
var factor kktFactor
var kktsolver KKTCpSolver = nil
if kktfunc, ok := solvers[solvername]; ok {
// kkt function returns us problem spesific factor function.
factor, err = kktfunc(G, dims, A, mnl)
if err != nil {
return nil, err
}
// solver is
kktsolver = func(W *sets.FloatMatrixSet, x, z *matrix.FloatMatrix) (KKTFunc, error) {
_, Df, H, err := F.F2(x, z)
if err != nil {
return nil, err
}
return factor(W, H, Df.GetSubMatrix(1, 0))
}
} else {
err = errors.New(fmt.Sprintf("solver '%s' not known", solvername))
return
}
return cp_problem(F, c_e, &G_e, h, &A_e, &b_e, dims, kktsolver, solopts, x0, mnl)
}