/
gp.go
205 lines (177 loc) · 6.04 KB
/
gp.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/sets"
la "github.com/hrautila/linalg"
"github.com/hrautila/linalg/blas"
"github.com/hrautila/matrix"
"math"
)
func checkArgK(K []int) (err error) {
err = nil
if len(K) == 0 {
err = errors.New("'K' must be a non-empty list of positive integers")
return
}
for _, k := range K {
if k <= 0 {
err = errors.New("'K' must be a non-empty list of positive integers")
return
}
}
return
}
type gpConvexProg struct {
mnl int
l int
n int
ind [][2]int
F *matrix.FloatMatrix
g *matrix.FloatMatrix
maxK int
}
func createGpProg(K []int, F, g *matrix.FloatMatrix) *gpConvexProg {
gp := &gpConvexProg{mnl: len(K) - 1, l: F.Rows(), n: F.Cols()}
gp.ind = make([][2]int, len(K))
s := 0
for i := 0; i < len(K); i++ {
gp.ind[i][0] = s
gp.ind[i][1] = s + K[i]
s += K[i]
}
gp.F = F
gp.g = g
gp.maxK = maxdim(K)
return gp
}
func (gp *gpConvexProg) F0() (mnl int, x *matrix.FloatMatrix, err error) {
return gp.mnl, matrix.FloatZeros(gp.n, 1), nil
}
func (gp *gpConvexProg) F1(x *matrix.FloatMatrix) (f, Df *matrix.FloatMatrix, err error) {
f = nil
Df = nil
err = nil
f = matrix.FloatZeros(gp.mnl+1, 1)
Df = matrix.FloatZeros(gp.mnl+1, gp.n)
y := gp.g.Copy()
blas.GemvFloat(gp.F, x, y, 1.0, 1.0)
for i, s := range gp.ind {
start := s[0]
stop := s[1]
// yi := exp(yi) = exp(Fi*x+gi)
ymax := maxvec(y.FloatArray()[start:stop])
// ynew = exp(y[start:stop] - ymax)
ynew := matrix.Exp(matrix.FloatVector(y.FloatArray()[start:stop]).Add(-ymax))
y.SetIndexesFromArray(ynew.FloatArray(), matrix.Indexes(start, stop)...)
// fi = log sum yi = log sum exp(Fi*x+gi)
ysum := blas.AsumFloat(y, &la.IOpt{"n", stop - start}, &la.IOpt{"offset", start})
f.SetIndex(i, ymax+math.Log(ysum))
blas.ScalFloat(y, 1.0/ysum, &la.IOpt{"n", stop - start}, &la.IOpt{"offset", start})
blas.GemvFloat(gp.F, y, Df, 1.0, 0.0, la.OptTrans, &la.IOpt{"m", stop - start},
&la.IOpt{"incy", gp.mnl + 1}, &la.IOpt{"offseta", start},
&la.IOpt{"offsetx", start}, &la.IOpt{"offsety", i})
}
return
}
func (gp *gpConvexProg) F2(x, z *matrix.FloatMatrix) (f, Df, H *matrix.FloatMatrix, err error) {
err = nil
f = matrix.FloatZeros(gp.mnl+1, 1)
Df = matrix.FloatZeros(gp.mnl+1, gp.n)
H = matrix.FloatZeros(gp.n, gp.n)
y := gp.g.Copy()
Fsc := matrix.FloatZeros(gp.maxK, gp.n)
blas.GemvFloat(gp.F, x, y, 1.0, 1.0)
//fmt.Printf("y=\n%v\n", y.ToString("%.3f"))
for i, s := range gp.ind {
start := s[0]
stop := s[1]
// yi := exp(yi) = exp(Fi*x+gi)
ymax := maxvec(y.FloatArray()[start:stop])
ynew := matrix.Exp(matrix.FloatVector(y.FloatArray()[start:stop]).Add(-ymax))
y.SetIndexesFromArray(ynew.FloatArray(), matrix.Indexes(start, stop)...)
// fi = log sum yi = log sum exp(Fi*x+gi)
ysum := blas.AsumFloat(y, &la.IOpt{"n", stop - start}, &la.IOpt{"offset", start})
f.SetIndex(i, ymax+math.Log(ysum))
blas.ScalFloat(y, 1.0/ysum, &la.IOpt{"n", stop - start}, &la.IOpt{"offset", start})
blas.GemvFloat(gp.F, y, Df, 1.0, 0.0, la.OptTrans, &la.IOpt{"m", stop - start},
&la.IOpt{"incy", gp.mnl + 1}, &la.IOpt{"offseta", start},
&la.IOpt{"offsetx", start}, &la.IOpt{"offsety", i})
Fsc.SetSubMatrix(0, 0, gp.F.GetSubMatrix(start, 0, stop-start))
for k := start; k < stop; k++ {
blas.AxpyFloat(Df, Fsc, -1.0, &la.IOpt{"n", gp.n},
&la.IOpt{"incx", gp.mnl + 1}, &la.IOpt{"incy", Fsc.Rows()},
&la.IOpt{"offsetx", i}, &la.IOpt{"offsety", k - start})
blas.ScalFloat(Fsc, math.Sqrt(y.GetIndex(k)),
&la.IOpt{"inc", Fsc.Rows()}, &la.IOpt{"offset", k - start})
}
// H += z[i]*Hi = z[i] *Fisc' * Fisc
blas.SyrkFloat(Fsc, H, z.GetIndex(i), 1.0, la.OptTrans,
&la.IOpt{"k", stop - start})
}
return
}
//
// 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)
}
// Local Variables:
// tab-width: 4
// End: