func syrk2Test(t *testing.T, C, A, B *matrix.FloatMatrix, flags Flags, vlen, nb int) bool {
//var B0 *matrix.FloatMatrix
P := A.Cols()
S := 0
E := C.Rows()
C0 := C.Copy()
trans := linalg.OptNoTrans
if flags&TRANSA != 0 {
trans = linalg.OptTrans
P = A.Rows()
}
uplo := linalg.OptUpper
if flags&LOWER != 0 {
uplo = linalg.OptLower
}
blas.Syr2kFloat(A, B, C0, 1.0, 1.0, uplo, trans)
if A.Rows() < 8 {
//t.Logf("..A\n%v\n", A)
t.Logf(" BLAS C0:\n%v\n", C0)
}
Ar := A.FloatArray()
Br := B.FloatArray()
Cr := C.FloatArray()
DSymmRank2Blk(Cr, Ar, Br, 1.0, 1.0, flags, C.LeadingIndex(), A.LeadingIndex(),
B.LeadingIndex(), P, S, E, vlen, nb)
result := C0.AllClose(C)
t.Logf(" C0 == C: %v\n", result)
if A.Rows() < 8 {
t.Logf(" DMRank2 C:\n%v\n", C)
}
return result
}
func mcsdp(w *matrix.FloatMatrix) (*Solution, error) {
//
// Returns solution x, z to
//
// (primal) minimize sum(x)
// subject to w + diag(x) >= 0
//
// (dual) maximize -tr(w*z)
// subject to diag(z) = 1
// z >= 0.
//
n := w.Rows()
G := &matrixFs{n}
cngrnc := func(r, x *matrix.FloatMatrix, alpha float64) (err error) {
// Congruence transformation
//
// x := alpha * r'*x*r.
//
// r and x are square matrices.
//
err = nil
// tx = matrix(x, (n,n)) is copying and reshaping
// scale diagonal of x by 1/2, (x is (n,n))
tx := x.Copy()
matrix.Reshape(tx, n, n)
tx.Diag().Scale(0.5)
// a := tril(x)*r
// (python: a = +r is really making a copy of r)
a := r.Copy()
err = blas.TrmmFloat(tx, a, 1.0, linalg.OptLeft)
// x := alpha*(a*r' + r*a')
err = blas.Syr2kFloat(r, a, tx, alpha, 0.0, linalg.OptTrans)
// x[:] = tx[:]
tx.CopyTo(x)
return
}
Fkkt := func(W *sets.FloatMatrixSet) (KKTFunc, error) {
// Solve
// -diag(z) = bx
// -diag(x) - inv(rti*rti') * z * inv(rti*rti') = bs
//
// On entry, x and z contain bx and bs.
// On exit, they contain the solution, with z scaled
// (inv(rti)'*z*inv(rti) is returned instead of z).
//
// We first solve
//
// ((rti*rti') .* (rti*rti')) * x = bx - diag(t*bs*t)
//
// and take z = -rti' * (diag(x) + bs) * rti.
var err error = nil
rti := W.At("rti")[0]
// t = rti*rti' as a nonsymmetric matrix.
t := matrix.FloatZeros(n, n)
err = blas.GemmFloat(rti, rti, t, 1.0, 0.0, linalg.OptTransB)
if err != nil {
return nil, err
}
// Cholesky factorization of tsq = t.*t.
tsq := matrix.Mul(t, t)
err = lapack.Potrf(tsq)
if err != nil {
return nil, err
}
f := func(x, y, z *matrix.FloatMatrix) (err error) {
// tbst := t * zs * t = t * bs * t
tbst := z.Copy()
matrix.Reshape(tbst, n, n)
cngrnc(t, tbst, 1.0)
// x := x - diag(tbst) = bx - diag(rti*rti' * bs * rti*rti')
diag := tbst.Diag().Transpose()
x.Minus(diag)
// x := (t.*t)^{-1} * x = (t.*t)^{-1} * (bx - diag(t*bs*t))
err = lapack.Potrs(tsq, x)
// z := z + diag(x) = bs + diag(x)
// z, x are really column vectors here
z.AddIndexes(matrix.MakeIndexSet(0, n*n, n+1), x.FloatArray())
// z := -rti' * z * rti = -rti' * (diag(x) + bs) * rti
cngrnc(rti, z, -1.0)
return nil
}
return f, nil
}
c := matrix.FloatWithValue(n, 1, 1.0)
// initial feasible x: x = 1.0 - min(lmbda(w))
lmbda := matrix.FloatZeros(n, 1)
wp := w.Copy()
lapack.Syevx(wp, lmbda, nil, 0.0, nil, []int{1, 1}, linalg.OptRangeInt)
x0 := matrix.FloatZeros(n, 1).Add(-lmbda.GetAt(0, 0) + 1.0)
s0 := w.Copy()
s0.Diag().Plus(x0.Transpose())
matrix.Reshape(s0, n*n, 1)
// initial feasible z is identity
z0 := matrix.FloatIdentity(n)
matrix.Reshape(z0, n*n, 1)
dims := sets.DSetNew("l", "q", "s")
dims.Set("s", []int{n})
primalstart := sets.FloatSetNew("x", "s")
dualstart := sets.FloatSetNew("z")
primalstart.Set("x", x0)
primalstart.Set("s", s0)
dualstart.Set("z", z0)
var solopts SolverOptions
solopts.MaxIter = 30
solopts.ShowProgress = false
h := w.Copy()
matrix.Reshape(h, h.NumElements(), 1)
return ConeLpCustomMatrix(c, G, h, nil, nil, dims, Fkkt, &solopts, primalstart, dualstart)
}
/*
Applies Nesterov-Todd scaling or its inverse.
Computes
x := W*x (trans is false 'N', inverse = false 'N')
x := W^T*x (trans is true 'T', inverse = false 'N')
x := W^{-1}*x (trans is false 'N', inverse = true 'T')
x := W^{-T}*x (trans is true 'T', inverse = true 'T').
x is a dense float matrix.
W is a MatrixSet with entries:
- W['dnl']: positive vector
- W['dnli']: componentwise inverse of W['dnl']
- W['d']: positive vector
- W['di']: componentwise inverse of W['d']
- W['v']: lists of 2nd order cone vectors with unit hyperbolic norms
- W['beta']: list of positive numbers
- W['r']: list of square matrices
- W['rti']: list of square matrices. rti[k] is the inverse transpose
of r[k].
The 'dnl' and 'dnli' entries are optional, and only present when the
function is called from the nonlinear solver.
*/
func scale(x *matrix.FloatMatrix, W *sets.FloatMatrixSet, trans, inverse bool) (err error) {
/*DEBUGGED*/
var wl []*matrix.FloatMatrix
var w *matrix.FloatMatrix
ind := 0
err = nil
// var minor int = 0
//if ! checkpnt.MinorEmpty() {
// minor = checkpnt.MinorTop()
//}
//fmt.Printf("\n%d.%04d scaling x=\n%v\n", checkpnt.Major(), minor, x.ToString("%.17f"))
// Scaling for nonlinear component xk is xk := dnl .* xk; inverse
// scaling is xk ./ dnl = dnli .* xk, where dnl = W['dnl'],
// dnli = W['dnli'].
if wl = W.At("dnl"); wl != nil {
if inverse {
w = W.At("dnli")[0]
} else {
w = W.At("dnl")[0]
}
for k := 0; k < x.Cols(); k++ {
err = blas.TbmvFloat(w, x, &la_.IOpt{"n", w.Rows()}, &la_.IOpt{"k", 0},
&la_.IOpt{"lda", 1}, &la_.IOpt{"offsetx", k * x.Rows()})
if err != nil {
//fmt.Printf("1. TbmvFloat: %v\n", err)
return
}
}
ind += w.Rows()
}
//if ! checkpnt.MinorEmpty() {
// checkpnt.Check("000scale", minor)
//}
// Scaling for linear 'l' component xk is xk := d .* xk; inverse
// scaling is xk ./ d = di .* xk, where d = W['d'], di = W['di'].
if inverse {
w = W.At("di")[0]
} else {
w = W.At("d")[0]
}
for k := 0; k < x.Cols(); k++ {
err = blas.TbmvFloat(w, x, &la_.IOpt{"n", w.Rows()}, &la_.IOpt{"k", 0},
&la_.IOpt{"lda", 1}, &la_.IOpt{"offsetx", k*x.Rows() + ind})
if err != nil {
//fmt.Printf("2. TbmvFloat: %v\n", err)
return
}
}
ind += w.Rows()
//if ! checkpnt.MinorEmpty() {
// checkpnt.Check("010scale", minor)
//}
// Scaling for 'q' component is
//
// xk := beta * (2*v*v' - J) * xk
// = beta * (2*v*(xk'*v)' - J*xk)
//
// where beta = W['beta'][k], v = W['v'][k], J = [1, 0; 0, -I].
//
//Inverse scaling is
//
// xk := 1/beta * (2*J*v*v'*J - J) * xk
// = 1/beta * (-J) * (2*v*((-J*xk)'*v)' + xk).
//wf := matrix.FloatZeros(x.Cols(), 1)
w = matrix.FloatZeros(x.Cols(), 1)
for k, v := range W.At("v") {
m := v.Rows()
if inverse {
blas.ScalFloat(x, -1.0, &la_.IOpt{"offset", ind}, &la_.IOpt{"inc", x.Rows()})
}
err = blas.GemvFloat(x, v, w, 1.0, 0.0, la_.OptTrans, &la_.IOpt{"m", m},
&la_.IOpt{"n", x.Cols()}, &la_.IOpt{"offsetA", ind},
&la_.IOpt{"lda", x.Rows()})
if err != nil {
//fmt.Printf("3. GemvFloat: %v\n", err)
return
}
err = blas.ScalFloat(x, -1.0, &la_.IOpt{"offset", ind}, &la_.IOpt{"inc", x.Rows()})
if err != nil {
return
}
err = blas.GerFloat(v, w, x, 2.0, &la_.IOpt{"m", m},
&la_.IOpt{"n", x.Cols()}, &la_.IOpt{"lda", x.Rows()},
&la_.IOpt{"offsetA", ind})
if err != nil {
//fmt.Printf("4. GerFloat: %v\n", err)
return
}
var a float64
if inverse {
blas.ScalFloat(x, -1.0,
&la_.IOpt{"offset", ind}, &la_.IOpt{"inc", x.Rows()})
// a[i,j] := 1.0/W[i,j]
a = 1.0 / W.At("beta")[0].GetIndex(k)
} else {
a = W.At("beta")[0].GetIndex(k)
}
for i := 0; i < x.Cols(); i++ {
blas.ScalFloat(x, a, &la_.IOpt{"n", m}, &la_.IOpt{"offset", ind + i*x.Rows()})
}
ind += m
}
//if ! checkpnt.MinorEmpty() {
// checkpnt.Check("020scale", minor)
//}
// Scaling for 's' component xk is
//
// xk := vec( r' * mat(xk) * r ) if trans = 'N'
// xk := vec( r * mat(xk) * r' ) if trans = 'T'.
//
// r is kth element of W['r'].
//
// Inverse scaling is
//
// xk := vec( rti * mat(xk) * rti' ) if trans = 'N'
// xk := vec( rti' * mat(xk) * rti ) if trans = 'T'.
//
// rti is kth element of W['rti'].
maxn := 0
for _, r := range W.At("r") {
if r.Rows() > maxn {
maxn = r.Rows()
}
}
a := matrix.FloatZeros(maxn, maxn)
for k, v := range W.At("r") {
t := trans
var r *matrix.FloatMatrix
if !inverse {
r = v
t = !trans
} else {
r = W.At("rti")[k]
}
n := r.Rows()
for i := 0; i < x.Cols(); i++ {
// scale diagonal of xk by 0.5
blas.ScalFloat(x, 0.5, &la_.IOpt{"offset", ind + i*x.Rows()},
&la_.IOpt{"inc", n + 1}, &la_.IOpt{"n", n})
// a = r*tril(x) (t is 'N') or a = tril(x)*r (t is 'T')
blas.Copy(r, a)
if !t {
err = blas.TrmmFloat(x, a, 1.0, la_.OptRight, &la_.IOpt{"m", n},
&la_.IOpt{"n", n}, &la_.IOpt{"lda", n}, &la_.IOpt{"ldb", n},
&la_.IOpt{"offsetA", ind + i*x.Rows()})
if err != nil {
//fmt.Printf("5. TrmmFloat: %v\n", err)
return
}
// x := (r*a' + a*r') if t is 'N'
err = blas.Syr2kFloat(r, a, x, 1.0, 0.0, la_.OptNoTrans, &la_.IOpt{"n", n},
&la_.IOpt{"k", n}, &la_.IOpt{"ldb", n}, &la_.IOpt{"ldc", n},
&la_.IOpt{"offsetC", ind + i*x.Rows()})
if err != nil {
//fmt.Printf("6. Syr2kFloat: %v\n", err)
return
}
} else {
err = blas.TrmmFloat(x, a, 1.0, la_.OptLeft, &la_.IOpt{"m", n},
&la_.IOpt{"n", n}, &la_.IOpt{"lda", n}, &la_.IOpt{"ldb", n},
&la_.IOpt{"offsetA", ind + i*x.Rows()})
if err != nil {
//fmt.Printf("7. TrmmFloat: %v\n", err)
return
}
// x := (r'*a + a'*r) if t is 'T'
err = blas.Syr2kFloat(r, a, x, 1.0, 0.0, la_.OptTrans, &la_.IOpt{"n", n},
&la_.IOpt{"k", n}, &la_.IOpt{"ldb", n}, &la_.IOpt{"ldc", n},
&la_.IOpt{"offsetC", ind + i*x.Rows()})
if err != nil {
//fmt.Printf("8. Syr2kFloat: %v\n", err)
return
}
}
}
ind += n * n
}
//if ! checkpnt.MinorEmpty() {
// checkpnt.Check("030scale", minor)
//}
return
}
// The product x := (y o x). If diag is 'D', the 's' part of y is
// diagonal and only the diagonal is stored.
func sprod(x, y *matrix.FloatMatrix, dims *sets.DimensionSet, mnl int, opts ...la_.Option) (err error) {
err = nil
diag := la_.GetStringOpt("diag", "N", opts...)
// For the nonlinear and 'l' blocks:
//
// yk o xk = yk .* xk.
ind := mnl + dims.At("l")[0]
err = blas.Tbmv(y, x, &la_.IOpt{"n", ind}, &la_.IOpt{"k", 0}, &la_.IOpt{"lda", 1})
if err != nil {
return
}
//fmt.Printf("Sprod l:x=\n%v\n", x)
// For 'q' blocks:
//
// [ l0 l1' ]
// yk o xk = [ ] * xk
// [ l1 l0*I ]
//
// where yk = (l0, l1).
for _, m := range dims.At("q") {
dd := blas.DotFloat(x, y, &la_.IOpt{"offsetx", ind}, &la_.IOpt{"offsety", ind},
&la_.IOpt{"n", m})
//fmt.Printf("dd=%v\n", dd)
alpha := y.GetIndex(ind)
//fmt.Printf("scal=%v\n", alpha)
blas.ScalFloat(x, alpha, &la_.IOpt{"offset", ind + 1}, &la_.IOpt{"n", m - 1})
alpha = x.GetIndex(ind)
//fmt.Printf("axpy=%v\n", alpha)
blas.AxpyFloat(y, x, alpha, &la_.IOpt{"offsetx", ind + 1}, &la_.IOpt{"offsety", ind + 1},
&la_.IOpt{"n", m - 1})
x.SetIndex(ind, dd)
ind += m
}
//fmt.Printf("Sprod q :x=\n%v\n", x)
// For the 's' blocks:
//
// yk o sk = .5 * ( Yk * mat(xk) + mat(xk) * Yk )
//
// where Yk = mat(yk) if diag is 'N' and Yk = diag(yk) if diag is 'D'.
if diag[0] == 'N' {
// DEBUGGED
maxm := maxdim(dims.At("s"))
A := matrix.FloatZeros(maxm, maxm)
for _, m := range dims.At("s") {
blas.Copy(x, A, &la_.IOpt{"offsetx", ind}, &la_.IOpt{"n", m * m})
for i := 0; i < m-1; i++ { // i < m-1 --> i < m
symm(A, m, 0)
symm(y, m, ind)
}
err = blas.Syr2kFloat(A, y, x, 0.5, 0.0, &la_.IOpt{"n", m}, &la_.IOpt{"k", m},
&la_.IOpt{"lda", m}, &la_.IOpt{"ldb", m}, &la_.IOpt{"ldc", m},
&la_.IOpt{"offsetb", ind}, &la_.IOpt{"offsetc", ind})
if err != nil {
return
}
ind += m * m
}
//fmt.Printf("Sprod diag=N s:x=\n%v\n", x)
} else {
ind2 := ind
for _, m := range dims.At("s") {
for i := 0; i < m; i++ {
// original: u = 0.5 * ( y[ind2+i:ind2+m] + y[ind2+i] )
// creates matrix of elements: [ind2+i ... ind2+m] then
// element wisely adds y[ind2+i] and scales by 0.5
iset := matrix.MakeIndexSet(ind2+i, ind2+m, 1)
u := matrix.FloatVector(y.GetIndexes(iset...))
u.Add(y.GetIndex(ind2 + i))
u.Scale(0.5)
err = blas.Tbmv(u, x, &la_.IOpt{"n", m - i}, &la_.IOpt{"k", 0}, &la_.IOpt{"lda", 1},
&la_.IOpt{"offsetx", ind + i*(m+1)})
if err != nil {
return
}
}
ind += m * m
ind2 += m
}
//fmt.Printf("Sprod diag=T s:x=\n%v\n", x)
}
return
}