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conelp.go
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// Copyright (c) Harri Rautila, 2012
// This file is part of github.com/hrautila/cvx package.
// It is free software, distributed under the terms of GNU Lesser General Public
// License Version 3, or any later version. See the COPYING tile included in this archive.
package cvx
import (
"errors"
"fmt"
"github.com/hrautila/cvx/checkpnt"
"github.com/hrautila/cvx/sets"
la "github.com/hrautila/linalg"
"github.com/hrautila/linalg/blas"
"github.com/hrautila/matrix"
"math"
)
// Implements MatrixA interface for standard matrix valued A.
type matrixA struct {
mA *matrix.FloatMatrix
}
func (a *matrixA) Af(x, y *matrix.FloatMatrix, alpha, beta float64, trans la.Option) error {
return blas.GemvFloat(a.mA, x, y, alpha, beta, trans)
}
// Implements MatrixG interface for standard matrix valued G.
type matrixG struct {
mG *matrix.FloatMatrix
dims *sets.DimensionSet
}
func (g *matrixG) Gf(x, y *matrix.FloatMatrix, alpha, beta float64, trans la.Option) error {
return sgemv(g.mG, x, y, alpha, beta, g.dims, trans)
}
type fClosure struct {
wx, wy, ws, wz *matrix.FloatMatrix
wx2, wy2, ws2, wz2 *matrix.FloatMatrix
// these are singleton matrices
wtau, wkappa, wtau2, wkappa2 *matrix.FloatMatrix
}
type fVarClosure struct {
wx, wy MatrixVariable
ws, wz *matrix.FloatMatrix
wx2, wy2 MatrixVariable
ws2, wz2 *matrix.FloatMatrix
// these are singleton matrices
wtau, wkappa, wtau2, wkappa2 *matrix.FloatMatrix
}
func checkConeLpDimensions(dims *sets.DimensionSet) error {
if len(dims.At("l")) == 0 {
dims.Set("l", []int{0})
} else if dims.At("l")[0] < 0 {
return errors.New("dimension 'l' must be nonnegative integer")
}
for _, m := range dims.At("q") {
if m < 1 {
return errors.New("dimension 'q' must be list of positive integers")
}
}
for _, m := range dims.At("s") {
if m < 1 {
return errors.New("dimension 's' must be list of positive integers")
}
}
return nil
}
// 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 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 using custom KKT solver and constraint
// interfaces MatrixG and MatrixA
//
func ConeLpCustomMatrix(c *matrix.FloatMatrix, G MatrixG, h *matrix.FloatMatrix,
A MatrixA, b *matrix.FloatMatrix, dims *sets.DimensionSet, kktsolver KKTConeSolver,
solopts *SolverOptions, primalstart, dualstart *sets.FloatMatrixSet) (sol *Solution, err error) {
err = nil
if c == nil || c.Cols() > 1 {
err = errors.New("'c' must be matrix with 1 column")
return
}
if h == nil || h.Cols() > 1 {
err = errors.New("'h' must be matrix with 1 column")
return
}
if err = checkConeLpDimensions(dims); err != nil {
return
}
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
}
// Data for kth 'q' constraint are found in rows indq[k]:indq[k+1] of G.
indq := make([]int, 0)
indq = append(indq, dims.At("l")[0])
for _, k := range dims.At("q") {
indq = append(indq, indq[len(indq)-1]+k)
}
// Data for kth 's' constraint are found in rows inds[k]:inds[k+1] of G.
inds := make([]int, 0)
inds = append(inds, indq[len(indq)-1])
for _, k := range dims.At("s") {
inds = append(inds, inds[len(inds)-1]+k*k)
}
// 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() > c.Rows() || b.Rows()+cdim_pckd < c.Rows() {
err = errors.New("Rank(A) < p or Rank([G; A]) < n")
return
}
if kktsolver == nil {
err = errors.New("nil kktsolver not allowed.")
return
}
var mA MatrixVarA
var mG MatrixVarG
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}
}
var mc = &matrixVar{c}
var mb = &matrixVar{b}
return conelp_problem(mc, mG, h, mA, mb, dims, kktsolver, solopts, primalstart, dualstart)
}
func conelp_problem(c MatrixVariable, G MatrixVarG, h *matrix.FloatMatrix,
A MatrixVarA, b MatrixVariable, dims *sets.DimensionSet, kktsolver KKTConeSolver,
solopts *SolverOptions, primalstart, dualstart *sets.FloatMatrixSet) (sol *Solution, err error) {
kktsolver_u := func(W *sets.FloatMatrixSet) (KKTFuncVar, error) {
g, err := kktsolver(W)
solver := func(x, y MatrixVariable, z *matrix.FloatMatrix) error {
return g(x.Matrix(), y.Matrix(), z)
}
return solver, err
}
return conelp_solver(c, G, h, A, b, dims, kktsolver_u, solopts, primalstart, dualstart)
}
func conelp_solver(c MatrixVariable, G MatrixVarG, h *matrix.FloatMatrix,
A MatrixVarA, b MatrixVariable, dims *sets.DimensionSet, kktsolver KKTConeSolverVar,
solopts *SolverOptions, primalstart, dualstart *sets.FloatMatrixSet) (sol *Solution, err error) {
err = nil
const EXPON = 3
const STEP = 0.99
sol = &Solution{Unknown,
nil,
0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0}
var refinement int
if solopts.Refinement > 0 {
refinement = solopts.Refinement
} else {
refinement = 0
if len(dims.At("q")) > 0 || len(dims.At("s")) > 0 {
refinement = 1
}
}
feasTolerance := FEASTOL
absTolerance := ABSTOL
relTolerance := RELTOL
maxIter := MAXITERS
if solopts.FeasTol > 0.0 {
feasTolerance = solopts.FeasTol
}
if solopts.AbsTol > 0.0 {
absTolerance = solopts.AbsTol
}
if solopts.RelTol > 0.0 {
relTolerance = solopts.RelTol
}
if solopts.MaxIter > 0 {
maxIter = solopts.MaxIter
}
if err = checkConeLpDimensions(dims); err != nil {
return
}
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
}
// Data for kth 'q' constraint are found in rows indq[k]:indq[k+1] of G.
indq := make([]int, 0)
indq = append(indq, dims.At("l")[0])
for _, k := range dims.At("q") {
indq = append(indq, indq[len(indq)-1]+k)
}
// Data for kth 's' constraint are found in rows inds[k]:inds[k+1] of G.
inds := make([]int, 0)
inds = append(inds, indq[len(indq)-1])
for _, k := range dims.At("s") {
inds = append(inds, inds[len(inds)-1]+k*k)
}
Gf := func(x, y MatrixVariable, alpha, beta float64, trans la.Option) error {
return G.Gf(x, y, alpha, beta, trans)
}
Af := func(x, y MatrixVariable, alpha, beta float64, trans la.Option) error {
return A.Af(x, y, alpha, beta, trans)
}
// kktsolver(W) returns a routine for solving 3x3 block KKT system
//
// [ 0 A' G'*W^{-1} ] [ ux ] [ bx ]
// [ A 0 0 ] [ uy ] = [ by ].
// [ G 0 -W' ] [ uz ] [ bz ]
if kktsolver == nil {
err = errors.New("nil kktsolver not allowed.")
return
}
// res() evaluates residual in 5x5 block KKT system
//
// [ vx ] [ 0 ] [ 0 A' G' c ] [ ux ]
// [ vy ] [ 0 ] [-A 0 0 b ] [ uy ]
// [ vz ] += [ W'*us ] - [-G 0 0 h ] [ W^{-1}*uz ]
// [ vtau ] [ dg*ukappa ] [-c' -b' -h' 0 ] [ utau/dg ]
//
// vs += lmbda o (dz + ds)
// vkappa += lmbdg * (dtau + dkappa).
ws3 := matrix.FloatZeros(cdim, 1)
wz3 := matrix.FloatZeros(cdim, 1)
checkpnt.AddMatrixVar("ws3", ws3)
checkpnt.AddMatrixVar("wz3", wz3)
//
res := func(ux, uy MatrixVariable, uz, utau, us, ukappa *matrix.FloatMatrix,
vx, vy MatrixVariable, vz, vtau, vs, vkappa *matrix.FloatMatrix,
W *sets.FloatMatrixSet, dg float64, lmbda *matrix.FloatMatrix) (err error) {
err = nil
// vx := vx - A'*uy - G'*W^{-1}*uz - c*utau/dg
Af(uy, vx, -1.0, 1.0, la.OptTrans)
//fmt.Printf("post-Af vx=\n%v\n", vx)
blas.Copy(uz, wz3)
scale(wz3, W, false, true)
Gf(&matrixVar{wz3}, vx, -1.0, 1.0, la.OptTrans)
//blas.AxpyFloat(c, vx, -utau.Float()/dg)
c.Axpy(vx, -utau.Float()/dg)
// vy := vy + A*ux - b*utau/dg
Af(ux, vy, 1.0, 1.0, la.OptNoTrans)
//blas.AxpyFloat(b, vy, -utau.Float()/dg)
b.Axpy(vy, -utau.Float()/dg)
// vz := vz + G*ux - h*utau/dg + W'*us
Gf(ux, &matrixVar{vz}, 1.0, 1.0, la.OptNoTrans)
blas.AxpyFloat(h, vz, -utau.Float()/dg)
blas.Copy(us, ws3)
scale(ws3, W, true, false)
blas.AxpyFloat(ws3, vz, 1.0)
// vtau := vtau + c'*ux + b'*uy + h'*W^{-1}*uz + dg*ukappa
var vtauplus float64 = dg*ukappa.Float() + c.Dot(ux) +
b.Dot(uy) + sdot(h, wz3, dims, 0)
vtau.SetValue(vtau.Float() + vtauplus)
// vs := vs + lmbda o (uz + us)
blas.Copy(us, ws3)
blas.AxpyFloat(uz, ws3, 1.0)
sprod(ws3, lmbda, dims, 0, &la.SOpt{"diag", "D"})
blas.AxpyFloat(ws3, vs, 1.0)
// vkappa += vkappa + lmbdag * (utau + ukappa)
lscale := lmbda.GetIndex(-1)
var vkplus float64 = lscale * (utau.Float() + ukappa.Float())
vkappa.SetValue(vkappa.Float() + vkplus)
return
}
resx0 := math.Max(1.0, math.Sqrt(c.Dot(c)))
resy0 := math.Max(1.0, math.Sqrt(b.Dot(b)))
resz0 := math.Max(1.0, snrm2(h, dims, 0))
// select initial points
//fmt.Printf("** initial resx0=%.4f, resy0=%.4f, resz0=%.4f \n", resx0, resy0, resz0)
x := c.Copy()
//blas.ScalFloat(x, 0.0)
x.Scal(0.0)
y := b.Copy()
//blas.ScalFloat(y, 0.0)
y.Scal(0.0)
s := matrix.FloatZeros(cdim, 1)
z := matrix.FloatZeros(cdim, 1)
dx := c.Copy()
dy := b.Copy()
ds := matrix.FloatZeros(cdim, 1)
dz := matrix.FloatZeros(cdim, 1)
// these are singleton matrix
dkappa := matrix.FloatValue(0.0)
dtau := matrix.FloatValue(0.0)
checkpnt.AddVerifiable("x", x)
checkpnt.AddMatrixVar("s", s)
checkpnt.AddMatrixVar("z", z)
checkpnt.AddVerifiable("dx", dx)
checkpnt.AddMatrixVar("ds", ds)
checkpnt.AddMatrixVar("dz", dz)
checkpnt.Check("00init", 1)
var W *sets.FloatMatrixSet
var f KKTFuncVar
if primalstart == nil || dualstart == nil {
// Factor
//
// [ 0 A' G' ]
// [ A 0 0 ].
// [ G 0 -I ]
//
W = sets.NewFloatSet("d", "di", "v", "beta", "r", "rti")
dd := dims.At("l")[0]
mat := matrix.FloatOnes(dd, 1)
W.Set("d", mat)
mat = matrix.FloatOnes(dd, 1)
W.Set("di", mat)
dq := len(dims.At("q"))
W.Set("beta", matrix.FloatOnes(dq, 1))
for _, n := range dims.At("q") {
vm := matrix.FloatZeros(n, 1)
vm.SetIndex(0, 1.0)
W.Append("v", vm)
}
for _, n := range dims.At("s") {
W.Append("r", matrix.FloatIdentity(n))
W.Append("rti", matrix.FloatIdentity(n))
}
f, err = kktsolver(W)
if err != nil {
fmt.Printf("kktsolver error: %s\n", err)
return
}
checkpnt.AddScaleVar(W)
}
checkpnt.Check("05init", 5)
if primalstart == nil {
// minimize || G * x - h ||^2
// subject to A * x = b
//
// by solving
//
// [ 0 A' G' ] [ x ] [ 0 ]
// [ A 0 0 ] * [ dy ] = [ b ].
// [ G 0 -I ] [ -s ] [ h ]
//blas.ScalFloat(x, 0.0)
//blas.CopyFloat(b, dy)
checkpnt.MinorPush(5)
x.Scal(0.0)
mCopy(b, dy)
blas.CopyFloat(h, s)
err = f(x, dy, s)
if err != nil {
fmt.Printf("f(x,dy,s): %s\n", err)
return
}
blas.ScalFloat(s, -1.0)
//fmt.Printf("initial s=\n%v\n", s.ToString("%.5f"))
checkpnt.MinorPop()
} else {
mCopy(&matrixVar{primalstart.At("x")[0]}, x)
blas.Copy(primalstart.At("s")[0], s)
}
// ts = min{ t | s + t*e >= 0 }
ts, _ := maxStep(s, dims, 0, nil)
if ts >= 0 && primalstart != nil {
err = errors.New("initial s is not positive")
return
}
//fmt.Printf("initial ts=%.5f\n", ts)
checkpnt.Check("10init", 10)
if dualstart == nil {
// minimize || z ||^2
// subject to G'*z + A'*y + c = 0
//
// by solving
//
// [ 0 A' G' ] [ dx ] [ -c ]
// [ A 0 0 ] [ y ] = [ 0 ].
// [ G 0 -I ] [ z ] [ 0 ]
//blas.Copy(c, dx)
//blas.ScalFloat(dx, -1.0)
//blas.ScalFloat(y, 0.0)
checkpnt.MinorPush(10)
mCopy(c, dx)
dx.Scal(-1.0)
y.Scal(0.0)
blas.ScalFloat(z, 0.0)
err = f(dx, y, z)
if err != nil {
fmt.Printf("f(dx,y,z): %s\n", err)
return
}
//fmt.Printf("initial z=\n%v\n", z.ToString("%.5f"))
checkpnt.MinorPop()
} else {
if len(dualstart.At("y")) > 0 {
mCopy(&matrixVar{dualstart.At("y")[0]}, y)
}
blas.Copy(dualstart.At("z")[0], z)
}
// ts = min{ t | z + t*e >= 0 }
tz, _ := maxStep(z, dims, 0, nil)
if tz >= 0 && dualstart != nil {
err = errors.New("initial z is not positive")
return
}
//fmt.Printf("initial tz=%.5f\n", tz)
nrms := snrm2(s, dims, 0)
nrmz := snrm2(z, dims, 0)
gap := 0.0
pcost := 0.0
dcost := 0.0
relgap := 0.0
checkpnt.Check("20init", 0)
if primalstart == nil && dualstart == nil {
gap = sdot(s, z, dims, 0)
pcost = c.Dot(x)
dcost = -b.Dot(y) - sdot(h, z, dims, 0)
if pcost < 0.0 {
relgap = gap / -pcost
} else if dcost > 0.0 {
relgap = gap / dcost
} else {
relgap = math.NaN()
}
if ts <= 0 && tz < 0 &&
(gap <= absTolerance || (!math.IsNaN(relgap) && relgap <= relTolerance)) {
// Constructed initial points happen to be feasible and optimal
ind := dims.At("l")[0] + dims.Sum("q")
for _, m := range dims.At("s") {
symm(s, m, ind)
symm(z, m, ind)
ind += m * m
}
// rx = A'*y + G'*z + c
rx := c.Copy()
Af(y, rx, 1.0, 1.0, la.OptTrans)
Gf(&matrixVar{z}, rx, 1.0, 1.0, la.OptTrans)
resx := math.Sqrt(rx.Dot(rx))
// ry = b - A*x
ry := b.Copy()
Af(x, ry, -1.0, -1.0, la.OptNoTrans)
resy := math.Sqrt(ry.Dot(ry))
// rz = s + G*x - h
rz := matrix.FloatZeros(cdim, 1)
Gf(x, &matrixVar{rz}, 1.0, 0.0, la.OptNoTrans)
blas.AxpyFloat(s, rz, 1.0)
blas.AxpyFloat(h, rz, -1.0)
resz := snrm2(rz, dims, 0)
pres := math.Max(resy/resy0, resz/resz0)
dres := resx / resx0
cx := c.Dot(x)
by := b.Dot(y)
hz := sdot(h, z, dims, 0)
//sol.X = x; sol.Y = y; sol.S = s; sol.Z = z
sol.Result = sets.NewFloatSet("x", "y", "s", "x")
sol.Result.Append("x", x.Matrix())
sol.Result.Append("y", y.Matrix())
sol.Result.Append("s", s)
sol.Result.Append("z", z)
sol.Status = Optimal
sol.Gap = gap
sol.RelativeGap = relgap
sol.PrimalObjective = cx
sol.DualObjective = -(by + hz)
sol.PrimalInfeasibility = pres
sol.DualInfeasibility = dres
sol.PrimalSlack = -ts
sol.DualSlack = -tz
return
}
if ts >= -1e-8*math.Max(nrms, 1.0) {
a := 1.0 + ts
is := make([]int, 0)
// indexes s[:dims['l']]
if dims.At("l")[0] > 0 {
is = append(is, matrix.MakeIndexSet(0, dims.At("l")[0], 1)...)
}
// indexes s[indq[:-1]]
if len(indq) > 1 {
is = append(is, indq[:len(indq)-1]...)
}
// indexes s[ind:ind+m*m:m+1] (diagonal)
ind := dims.Sum("l", "q")
for _, m := range dims.At("s") {
is = append(is, matrix.MakeIndexSet(ind, ind+m*m, m+1)...)
ind += m * m
}
for _, k := range is {
s.SetIndex(k, a+s.GetIndex(k))
}
}
if tz >= -1e-8*math.Max(nrmz, 1.0) {
a := 1.0 + tz
is := make([]int, 0)
// indexes z[:dims['l']]
if dims.At("l")[0] > 0 {
is = append(is, matrix.MakeIndexSet(0, dims.At("l")[0], 1)...)
}
// indexes z[indq[:-1]]
if len(indq) > 1 {
is = append(is, indq[:len(indq)-1]...)
}
// indexes z[ind:ind+m*m:m+1] (diagonal)
ind := dims.Sum("l", "q")
for _, m := range dims.At("s") {
is = append(is, matrix.MakeIndexSet(ind, ind+m*m, m+1)...)
ind += m * m
}
for _, k := range is {
z.SetIndex(k, a+z.GetIndex(k))
}
}
} else if primalstart == nil && dualstart != nil {
if ts >= -1e-8*math.Max(nrms, 1.0) {
a := 1.0 + ts
is := make([]int, 0)
if dims.At("l")[0] > 0 {
is = append(is, matrix.MakeIndexSet(0, dims.At("l")[0], 1)...)
}
if len(indq) > 1 {
is = append(is, indq[:len(indq)-1]...)
}
ind := dims.Sum("l", "q")
for _, m := range dims.At("s") {
is = append(is, matrix.MakeIndexSet(ind, ind+m*m, m+1)...)
ind += m * m
}
for _, k := range is {
s.SetIndex(k, a+s.GetIndex(k))
}
}
} else if primalstart != nil && dualstart == nil {
if tz >= -1e-8*math.Max(nrmz, 1.0) {
a := 1.0 + tz
is := make([]int, 0)
if dims.At("l")[0] > 0 {
is = append(is, matrix.MakeIndexSet(0, dims.At("l")[0], 1)...)
}
if len(indq) > 1 {
is = append(is, indq[:len(indq)-1]...)
}
ind := dims.Sum("l", "q")
for _, m := range dims.At("s") {
is = append(is, matrix.MakeIndexSet(ind, ind+m*m, m+1)...)
ind += m * m
}
for _, k := range is {
z.SetIndex(k, a+z.GetIndex(k))
}
}
}
tau := matrix.FloatValue(1.0)
kappa := matrix.FloatValue(1.0)
wkappa3 := matrix.FloatValue(0.0)
rx := c.Copy()
hrx := c.Copy()
ry := b.Copy()
hry := b.Copy()
rz := matrix.FloatZeros(cdim, 1)
hrz := matrix.FloatZeros(cdim, 1)
sigs := matrix.FloatZeros(dims.Sum("s"), 1)
sigz := matrix.FloatZeros(dims.Sum("s"), 1)
lmbda := matrix.FloatZeros(cdim_diag+1, 1)
lmbdasq := matrix.FloatZeros(cdim_diag+1, 1)
gap = sdot(s, z, dims, 0)
var x1, y1 MatrixVariable
var z1 *matrix.FloatMatrix
var dg, dgi float64
var th *matrix.FloatMatrix
var WS fVarClosure
var f3 KKTFuncVar
var cx, by, hz, rt float64
var hresx, resx, hresy, resy, hresz, resz float64
var dres, pres, dinfres, pinfres float64
// check point variables
checkpnt.AddMatrixVar("lmbda", lmbda)
checkpnt.AddMatrixVar("lmbdasq", lmbdasq)
checkpnt.AddVerifiable("rx", rx)
checkpnt.AddVerifiable("ry", ry)
checkpnt.AddMatrixVar("rz", rz)
checkpnt.AddFloatVar("resx", &resx)
checkpnt.AddFloatVar("resy", &resy)
checkpnt.AddFloatVar("resz", &resz)
checkpnt.AddFloatVar("hresx", &hresx)
checkpnt.AddFloatVar("hresy", &hresy)
checkpnt.AddFloatVar("hresz", &hresz)
checkpnt.AddFloatVar("cx", &cx)
checkpnt.AddFloatVar("by", &by)
checkpnt.AddFloatVar("hz", &hz)
checkpnt.AddFloatVar("gap", &gap)
checkpnt.AddFloatVar("pres", &pres)
checkpnt.AddFloatVar("dres", &dres)
for iter := 0; iter < maxIter+1; iter++ {
checkpnt.MajorNext()
checkpnt.Check("loop-start", 100)
// hrx = -A'*y - G'*z
Af(y, hrx, -1.0, 0.0, la.OptTrans)
Gf(&matrixVar{z}, hrx, -1.0, 1.0, la.OptTrans)
hresx = math.Sqrt(hrx.Dot(hrx))
// rx = hrx - c*tau
// = -A'*y - G'*z - c*tau
mCopy(hrx, rx)
c.Axpy(rx, -tau.Float())
resx = math.Sqrt(rx.Dot(rx)) / tau.Float()
// hry = A*x
Af(x, hry, 1.0, 0.0, la.OptNoTrans)
hresy = math.Sqrt(hry.Dot(hry))
// ry = hry - b*tau
// = A*x - b*tau
mCopy(hry, ry)
b.Axpy(ry, -tau.Float())
resy = math.Sqrt(ry.Dot(ry)) / tau.Float()
// hrz = s + G*x
Gf(x, &matrixVar{hrz}, 1.0, 0.0, la.OptNoTrans)
blas.AxpyFloat(s, hrz, 1.0)
hresz = snrm2(hrz, dims, 0)
// rz = hrz - h*tau
// = s + G*x - h*tau
blas.ScalFloat(rz, 0.0)
blas.AxpyFloat(hrz, rz, 1.0)
blas.AxpyFloat(h, rz, -tau.Float())
resz = snrm2(rz, dims, 0) / tau.Float()
// rt = kappa + c'*x + b'*y + h'*z '
cx = c.Dot(x)
by = b.Dot(y)
hz = sdot(h, z, dims, 0)
rt = kappa.Float() + cx + by + hz
// Statistics for stopping criteria
pcost = cx / tau.Float()
dcost = -(by + hz) / tau.Float()
if pcost < 0.0 {
relgap = gap / -pcost
} else if dcost > 0.0 {
relgap = gap / dcost
} else {
relgap = math.NaN()
}
pres = math.Max(resy/resy0, resz/resz0)
dres = resx / resx0
pinfres = math.NaN()
if hz+by < 0.0 {
pinfres = hresx / resx0 / (-hz - by)
}
dinfres = math.NaN()
if cx < 0.0 {
dinfres = math.Max(hresy/resy0, hresz/resz0) / (-cx)
}
if solopts.ShowProgress {
if iter == 0 {
// show headers of something
fmt.Printf("% 10s% 12s% 10s% 8s% 7s % 5s\n",
"pcost", "dcost", "gap", "pres", "dres", "k/t")
}
// show something
fmt.Printf("%2d: % 8.4e % 8.4e % 4.0e% 7.0e% 7.0e% 7.0e\n",
iter, pcost, dcost, gap, pres, dres, kappa.GetIndex(0)/tau.GetIndex(0))
}
checkpnt.Check("isready", 200)
if (pres <= feasTolerance && dres <= feasTolerance &&
(gap <= absTolerance || (!math.IsNaN(relgap) && relgap <= relTolerance))) ||
iter == maxIter {
// done
x.Scal(1.0 / tau.Float())
y.Scal(1.0 / tau.Float())
blas.ScalFloat(s, 1.0/tau.Float())
blas.ScalFloat(z, 1.0/tau.Float())
ind := dims.Sum("l", "q")
for _, m := range dims.At("s") {
symm(s, m, ind)
symm(z, m, ind)
ind += m * m
}
ts, _ = maxStep(s, dims, 0, nil)
tz, _ = maxStep(z, dims, 0, nil)
if iter == maxIter {
// MaxIterations exceeded
if solopts.ShowProgress {
fmt.Printf("No solution. Max iterations exceeded\n")
}
err = errors.New("No solution. Max iterations exceeded")
//sol.X = x; sol.Y = y; sol.S = s; sol.Z = z
sol.Result = sets.NewFloatSet("x", "y", "s", "x")
sol.Result.Append("x", x.Matrix())
sol.Result.Append("y", y.Matrix())
sol.Result.Append("s", s)
sol.Result.Append("z", z)
sol.Status = Unknown
sol.Gap = gap
sol.RelativeGap = relgap
sol.PrimalObjective = pcost
sol.DualObjective = dcost