func (g *matrixFs) Gf(x, y *matrix.FloatMatrix, alpha, beta float64, trans linalg.Option) error {
//
minor := 0
if !checkpnt.MinorEmpty() {
minor = checkpnt.MinorTop()
} else {
loopg += 1
minor = loopg
}
checkpnt.Check("00-Gfunc", minor)
m, n := g.A.Size()
y.Scale(beta)
// x_n = x[:n]
//x_n := matrix.FloatVector(x.FloatArray()[:n])
x_n := x.SubMatrix(0, 0, n, 1).Copy()
// x_n_2n = x[n:2*n]
//x_n_2n := matrix.FloatVector(x.FloatArray()[n : 2*n])
x_n_2n := x.SubMatrix(n, 0, n, 1).Copy()
if linalg.Equal(trans, linalg.OptNoTrans) {
// y += alpha * G * x
// y[:n] += alpha * (x[:n] - x[n:2*n])
y_n := matrix.Minus(x_n, x_n_2n).Scale(alpha)
y.SubMatrix(0, 0, n, 1).Plus(y_n)
//y.AddIndexes(matrix.Indexes(n), y_n.FloatArray())
// y[n:2*n] += alpha * (-x[:n] - x[n:2*n]) = -alpha * (x[:n]+x[n:2*n])
y_n = matrix.Plus(x_n, x_n_2n).Scale(-alpha)
y.SubMatrix(n, 0, n, 1).Plus(y_n)
//y.AddIndexes(matrix.Indexes(n, 2*n), y_n.FloatArray())
// y[2*n+1:] += -alpha * A * x[:n]
y_2n := matrix.Times(g.A, x_n).Scale(-alpha)
//y.AddIndexes(matrix.Indexes(2*n+1, y.NumElements()), y_2n.FloatArray())
y.SubMatrix(2*n+1, 0, y_2n.NumElements(), 1).Plus(y_2n)
} else {
// x_m = x[-m:]
//x_m := matrix.FloatVector(x.FloatArray()[x.NumElements()-m:])
x_m := x.SubMatrix(x.NumElements()-m, 0)
// x_tmp = (x[:n] - x[n:2*n] - A.T * x[-m:])
x_tmp := matrix.Minus(x_n, x_n_2n, matrix.Times(g.A.Transpose(), x_m))
// y[:n] += alpha * (x[:n] - x[n:2*n] - A.T * x[-m:])
//y.AddIndexes(matrix.Indexes(n), x_tmp.Scale(alpha).FloatArray())
y.SubMatrix(0, 0, n, 1).Plus(x_tmp.Scale(alpha))
x_tmp = matrix.Plus(x_n, x_n_2n).Scale(-alpha)
//y.AddIndexes(matrix.Indexes(n, y.NumElements()), x_tmp.FloatArray())
y.SubMatrix(n, 0).Plus(x_tmp)
}
checkpnt.Check("10-Gfunc", minor)
return nil
}
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())
}
func main() {
flag.Parse()
m := len(udata)
nvars := 2 * m
u := matrix.FloatVector(udata[:m])
y := matrix.FloatVector(ydata[:m])
// minimize (1/2) * || yhat - y ||_2^2
// subject to yhat[j] >= yhat[i] + g[i]' * (u[j] - u[i]), j, i = 0,...,m-1
//
// Variables yhat (m), g (m).
P := matrix.FloatZeros(nvars, nvars)
// set m first diagonal indexes to 1.0
//P.SetIndexes(1.0, matrix.DiagonalIndexes(P)[:m]...)
P.Diag().SubMatrix(0, 0, 1, m).SetIndexes(1.0)
q := matrix.FloatZeros(nvars, 1)
q.SubMatrix(0, 0, y.NumElements(), 1).Plus(matrix.Scale(y, -1.0))
// m blocks (i = 0,...,m-1) of linear inequalities
//
// yhat[i] + g[i]' * (u[j] - u[i]) <= yhat[j], j = 0,...,m-1.
G := matrix.FloatZeros(m*m, nvars)
I := matrix.FloatDiagonal(m, 1.0)
for i := 0; i < m; i++ {
// coefficients of yhat[i] (column i)
//G.Set(1.0, matrix.ColumnIndexes(G, i)[i*m:(i+1)*m]...)
column(G, i).SetIndexes(1.0)
// coefficients of gi[i] (column i, rows i*m ... (i+1)*m)
//rows := matrix.Indexes(i*m, (i+1)*m)
//G.SetAtColumnArray(m+i, rows, matrix.Add(u, -u.GetIndex(i)).FloatArray())
// coefficients of gi[i] (column i, rows i*m ... (i+1)*m)
// from column m+i staring at row i*m select m rows and one column
G.SubMatrix(i*m, m+i, m, 1).Plus(matrix.Add(u, -u.GetIndex(i)))
// coeffients of yhat[i]) from rows i*m ... (i+1)*m, cols 0 ... m
//G.SetSubMatrix(i*m, 0, matrix.Minus(G.GetSubMatrix(i*m, 0, m, m), I))
G.SubMatrix(i*m, 0, m, m).Minus(I)
}
h := matrix.FloatZeros(m*m, 1)
var A, b *matrix.FloatMatrix = nil, nil
var solopts cvx.SolverOptions
solopts.ShowProgress = true
solopts.KKTSolverName = solver
sol, err := cvx.Qp(P, q, G, h, A, b, &solopts, nil)
if err != nil {
fmt.Printf("error: %v\n", err)
return
}
if sol != nil && sol.Status != cvx.Optimal {
fmt.Printf("status not optimal\n")
return
}
x := sol.Result.At("x")[0]
//yhat := matrix.FloatVector(x.FloatArray()[:m])
//g := matrix.FloatVector(x.FloatArray()[m:])
yhat := x.SubMatrix(0, 0, m, 1).Copy()
g := x.SubMatrix(m, 0).Copy()
rangeFunc := func(n int) []float64 {
r := make([]float64, 0)
for i := 0; i < n; i++ {
r = append(r, float64(i)*2.2/float64(n))
}
return r
}
ts := rangeFunc(1000)
fitFunc := func(points []float64) []float64 {
res := make([]float64, len(points))
for k, t := range points {
res[k] = matrix.Plus(yhat, matrix.Mul(g, matrix.Scale(u, -1.0).Add(t))).Max()
}
return res
}
fs := fitFunc(ts)
plotData("cvxfit.png", u.FloatArray(), y.FloatArray(), ts, fs)
}
func qcl1(A, b *matrix.FloatMatrix) (*cvx.Solution, error) {
// Returns the solution u, z of
//
// (primal) minimize || u ||_1
// subject to || A * u - b ||_2 <= 1
//
// (dual) maximize b^T z - ||z||_2
// subject to || A'*z ||_inf <= 1.
//
// Exploits structure, assuming A is m by n with m >= n.
m, n := A.Size()
Fkkt := func(W *sets.FloatMatrixSet) (f cvx.KKTFunc, err error) {
minor := 0
if !checkpnt.MinorEmpty() {
minor = checkpnt.MinorTop()
}
err = nil
f = nil
beta := W.At("beta")[0].GetIndex(0)
v := W.At("v")[0]
// As = 2 * v *(v[1:].T * A)
//v_1 := matrix.FloatNew(1, v.NumElements()-1, v.FloatArray()[1:])
v_1 := v.SubMatrix(1, 0).Transpose()
As := matrix.Times(v, matrix.Times(v_1, A)).Scale(2.0)
//As_1 := As.GetSubMatrix(1, 0, m, n)
//As_1.Scale(-1.0)
//As.SetSubMatrix(1, 0, matrix.Minus(As_1, A))
As_1 := As.SubMatrix(1, 0, m, n)
As_1.Scale(-1.0)
As_1.Minus(A)
As.Scale(1.0 / beta)
S := matrix.Times(As.Transpose(), As)
checkpnt.AddMatrixVar("S", S)
d1 := W.At("d")[0].SubMatrix(0, 0, n, 1).Copy()
d2 := W.At("d")[0].SubMatrix(n, 0).Copy()
// D = 4.0 * (d1**2 + d2**2)**-1
d := matrix.Plus(matrix.Mul(d1, d1), matrix.Mul(d2, d2)).Inv().Scale(4.0)
// S[::n+1] += d
S.Diag().Plus(d.Transpose())
err = lapack.Potrf(S)
checkpnt.Check("00-Fkkt", minor)
if err != nil {
return
}
f = func(x, y, z *matrix.FloatMatrix) (err error) {
minor := 0
if !checkpnt.MinorEmpty() {
minor = checkpnt.MinorTop()
} else {
loopf += 1
minor = loopf
}
checkpnt.Check("00-f", minor)
// -- z := - W**-T * z
// z[:n] = -div( z[:n], d1 )
z_val := z.SubMatrix(0, 0, n, 1)
z_res := matrix.Div(z_val, d1).Scale(-1.0)
z.SubMatrix(0, 0, n, 1).Set(z_res)
// z[n:2*n] = -div( z[n:2*n], d2 )
z_val = z.SubMatrix(n, 0, n, 1)
z_res = matrix.Div(z_val, d2).Scale(-1.0)
z.SubMatrix(n, 0, n, 1).Set(z_res)
// z[2*n:] -= 2.0*v*( v[0]*z[2*n] - blas.dot(v[1:], z[2*n+1:]) )
v0_z2n := v.GetIndex(0) * z.GetIndex(2*n)
v1_z2n := blas.DotFloat(v, z, &linalg.IOpt{"offsetx", 1}, &linalg.IOpt{"offsety", 2*n + 1})
z_res = matrix.Scale(v, -2.0*(v0_z2n-v1_z2n))
z.SubMatrix(2*n, 0, z_res.NumElements(), 1).Plus(z_res)
// z[2*n+1:] *= -1.0
z.SubMatrix(2*n+1, 0).Scale(-1.0)
// z[2*n:] /= beta
z.SubMatrix(2*n, 0).Scale(1.0 / beta)
// -- x := x - G' * W**-1 * z
// z_n = z[:n], z_2n = z[n:2*n], z_m = z[-(m+1):],
z_n := z.SubMatrix(0, 0, n, 1)
z_2n := z.SubMatrix(n, 0, n, 1)
z_m := z.SubMatrix(z.NumElements()-(m+1), 0)
// x[:n] -= div(z[:n], d1) - div(z[n:2*n], d2) + As.T * z[-(m+1):]
z_res = matrix.Minus(matrix.Div(z_n, d1), matrix.Div(z_2n, d2))
a_res := matrix.Times(As.Transpose(), z_m)
z_res.Plus(a_res).Scale(-1.0)
x.SubMatrix(0, 0, n, 1).Plus(z_res)
// x[n:] += div(z[:n], d1) + div(z[n:2*n], d2)
z_res = matrix.Plus(matrix.Div(z_n, d1), matrix.Div(z_2n, d2))
x.SubMatrix(n, 0, z_res.NumElements(), 1).Plus(z_res)
checkpnt.Check("15-f", minor)
// Solve for x[:n]:
//
// S*x[:n] = x[:n] - (W1**2 - W2**2)(W1**2 + W2**2)^-1 * x[n:]
// w1 = (d1**2 - d2**2), w2 = (d1**2 + d2**2)
w1 := matrix.Minus(matrix.Mul(d1, d1), matrix.Mul(d2, d2))
w2 := matrix.Plus(matrix.Mul(d1, d1), matrix.Mul(d2, d2))
// x[:n] += -mul( div(w1, w2), x[n:])
x_n := x.SubMatrix(n, 0)
x_val := matrix.Mul(matrix.Div(w1, w2), x_n).Scale(-1.0)
x.SubMatrix(0, 0, n, 1).Plus(x_val)
checkpnt.Check("25-f", minor)
// Solve for x[n:]:
//
// (d1**-2 + d2**-2) * x[n:] = x[n:] + (d1**-2 - d2**-2)*x[:n]
err = lapack.Potrs(S, x)
if err != nil {
fmt.Printf("Potrs error: %s\n", err)
}
checkpnt.Check("30-f", minor)
// Solve for x[n:]:
//
// (d1**-2 + d2**-2) * x[n:] = x[n:] + (d1**-2 - d2**-2)*x[:n]
// w1 = (d1**-2 - d2**-2), w2 = (d1**-2 + d2**-2)
w1 = matrix.Minus(matrix.Mul(d1, d1).Inv(), matrix.Mul(d2, d2).Inv())
w2 = matrix.Plus(matrix.Mul(d1, d1).Inv(), matrix.Mul(d2, d2).Inv())
x_n = x.SubMatrix(0, 0, n, 1)
// x[n:] += mul( d1**-2 - d2**-2, x[:n])
x_val = matrix.Mul(w1, x_n)
x.SubMatrix(n, 0, x_val.NumElements(), 1).Plus(x_val)
checkpnt.Check("35-f", minor)
// x[n:] = div( x[n:], d1**-2 + d2**-2)
x_n = x.SubMatrix(n, 0)
x_val = matrix.Div(x_n, w2)
x.SubMatrix(n, 0, x_val.NumElements(), 1).Set(x_val)
checkpnt.Check("40-f", minor)
// x_n = x[:n], x-2n = x[n:2*n]
x_n = x.SubMatrix(0, 0, n, 1)
x_2n := x.SubMatrix(n, 0, n, 1)
// z := z + W^-T * G*x
// z[:n] += div( x[:n] - x[n:2*n], d1)
x_val = matrix.Div(matrix.Minus(x_n, x_2n), d1)
z.SubMatrix(0, 0, n, 1).Plus(x_val)
checkpnt.Check("44-f", minor)
// z[n:2*n] += div( -x[:n] - x[n:2*n], d2)
x_val = matrix.Div(matrix.Plus(x_n, x_2n).Scale(-1.0), d2)
z.SubMatrix(n, 0, n, 1).Plus(x_val)
checkpnt.Check("48-f", minor)
// z[2*n:] += As*x[:n]
x_val = matrix.Times(As, x_n)
z.SubMatrix(2*n, 0, x_val.NumElements(), 1).Plus(x_val)
checkpnt.Check("50-f", minor)
return nil
}
return
}
// matrix(n*[0.0] + n*[1.0])
c := matrix.FloatZeros(2*n, 1)
c.SubMatrix(n, 0).SetIndexes(1.0)
h := matrix.FloatZeros(2*n+m+1, 1)
h.SetIndexes(1.0, 2*n)
// h[2*n+1:] = -b
h.SubMatrix(2*n+1, 0).Plus(b).Scale(-1.0)
G := &matrixFs{A}
dims := sets.DSetNew("l", "q", "s")
dims.Set("l", []int{2 * n})
dims.Set("q", []int{m + 1})
var solopts cvx.SolverOptions
solopts.ShowProgress = true
if maxIter > 0 {
solopts.MaxIter = maxIter
}
if len(solver) > 0 {
solopts.KKTSolverName = solver
}
return cvx.ConeLpCustomMatrix(c, G, h, nil, nil, dims, Fkkt, &solopts, nil, nil)
}