// Solution of KKT equations by a dense LDL factorization of the
// 3 x 3 system.
//
// Returns a function that (1) computes the LDL factorization of
//
// [ H A' GG'*W^{-1} ]
// [ A 0 0 ],
// [ W^{-T}*GG 0 -I ]
//
// given H, Df, W, where GG = [Df; G], and (2) returns a function for
// solving
//
// [ H A' GG' ] [ ux ] [ bx ]
// [ A 0 0 ] * [ uy ] = [ by ].
// [ GG 0 -W'*W ] [ uz ] [ bz ]
//
// H is n x n, A is p x n, Df is mnl x n, G is N x n where
// N = dims['l'] + sum(dims['q']) + sum( k**2 for k in dims['s'] ).
//
func kktLdl(G *matrix.FloatMatrix, dims *sets.DimensionSet, A *matrix.FloatMatrix, mnl int) (kktFactor, error) {
p, n := A.Size()
ldK := n + p + mnl + dims.At("l")[0] + dims.Sum("q") + dims.SumPacked("s")
K := matrix.FloatZeros(ldK, ldK)
ipiv := make([]int32, ldK)
u := matrix.FloatZeros(ldK, 1)
g := matrix.FloatZeros(mnl+G.Rows(), 1)
//checkpnt.AddMatrixVar("u", u)
//checkpnt.AddMatrixVar("K", K)
factor := func(W *sets.FloatMatrixSet, H, Df *matrix.FloatMatrix) (KKTFunc, error) {
var err error = nil
// Zero K for each call.
blas.ScalFloat(K, 0.0)
if H != nil {
K.SetSubMatrix(0, 0, H)
}
K.SetSubMatrix(n, 0, A)
for k := 0; k < n; k++ {
// g is (mnl + G.Rows(), 1) matrix, Df is (mnl, n), G is (N, n)
if mnl > 0 {
// set values g[0:mnl] = Df[,k]
g.SetIndexesFromArray(Df.GetColumnArray(k, nil), matrix.MakeIndexSet(0, mnl, 1)...)
}
// set values g[mnl:] = G[,k]
g.SetIndexesFromArray(G.GetColumnArray(k, nil), matrix.MakeIndexSet(mnl, mnl+g.Rows(), 1)...)
scale(g, W, true, true)
if err != nil {
//fmt.Printf("scale error: %s\n", err)
}
pack(g, K, dims, &la.IOpt{"mnl", mnl}, &la.IOpt{"offsety", k*ldK + n + p})
}
setDiagonal(K, n+p, n+n, ldK, ldK, -1.0)
err = lapack.Sytrf(K, ipiv)
if err != nil {
return nil, err
}
solve := func(x, y, z *matrix.FloatMatrix) (err error) {
// Solve
//
// [ H A' GG'*W^{-1} ] [ ux ] [ bx ]
// [ A 0 0 ] * [ uy [ = [ by ]
// [ W^{-T}*GG 0 -I ] [ W*uz ] [ W^{-T}*bz ]
//
// and return ux, uy, W*uz.
//
// On entry, x, y, z contain bx, by, bz. On exit, they contain
// the solution ux, uy, W*uz.
err = nil
blas.Copy(x, u)
blas.Copy(y, u, &la.IOpt{"offsety", n})
err = scale(z, W, true, true)
if err != nil {
return
}
err = pack(z, u, dims, &la.IOpt{"mnl", mnl}, &la.IOpt{"offsety", n + p})
if err != nil {
return
}
err = lapack.Sytrs(K, u, ipiv)
if err != nil {
return
}
blas.Copy(u, x, &la.IOpt{"n", n})
blas.Copy(u, y, &la.IOpt{"n", p}, &la.IOpt{"offsetx", n})
err = unpack(u, z, dims, &la.IOpt{"mnl", mnl}, &la.IOpt{"offsetx", n + p})
return
}
return solve, err
}
return factor, nil
}