Example #1
0
func syrkTest(t *testing.T, C, A *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.SyrkFloat(A, 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()
	Cr := C.FloatArray()
	DSymmRankBlk(Cr, Ar, 1.0, 1.0, flags, C.LeadingIndex(), A.LeadingIndex(),
		P, S, E, vlen, nb)
	result := C0.AllClose(C)
	t.Logf("   C0 == C: %v\n", result)
	if A.Rows() < 8 {
		t.Logf("  DMRank C:\n%v\n", C)
	}
	return result
}
Example #2
0
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
}
Example #3
0
func kktChol2(G *matrix.FloatMatrix, dims *sets.DimensionSet, A *matrix.FloatMatrix, mnl int) (kktFactor, error) {

	if len(dims.At("q")) > 0 || len(dims.At("s")) > 0 {
		return nil, errors.New("'chol2' solver only for problems with no second-order or " +
			"semidefinite cone constraints")
	}

	p, n := A.Size()
	ml := dims.At("l")[0]
	F := &chol2Data{firstcall: true, singular: false, A: A, G: G, dims: dims}

	factor := func(W *sets.FloatMatrixSet, H, Df *matrix.FloatMatrix) (KKTFunc, error) {
		var err error = nil
		minor := 0
		if !checkpnt.MinorEmpty() {
			minor = checkpnt.MinorTop()
		}
		if F.firstcall {
			F.Gs = matrix.FloatZeros(F.G.Size())
			if mnl > 0 {
				F.Dfs = matrix.FloatZeros(Df.Size())
			}
			F.S = matrix.FloatZeros(n, n)
			F.K = matrix.FloatZeros(p, p)
			checkpnt.AddMatrixVar("Gs", F.Gs)
			checkpnt.AddMatrixVar("Dfs", F.Dfs)
			checkpnt.AddMatrixVar("S", F.S)
			checkpnt.AddMatrixVar("K", F.K)
		}

		if mnl > 0 {
			dnli := matrix.FloatZeros(mnl, mnl)
			dnli.SetIndexesFromArray(W.At("dnli")[0].FloatArray(), matrix.DiagonalIndexes(dnli)...)
			blas.GemmFloat(dnli, Df, F.Dfs, 1.0, 0.0)
		}
		checkpnt.Check("02factor_chol2", minor)
		di := matrix.FloatZeros(ml, ml)
		di.SetIndexesFromArray(W.At("di")[0].FloatArray(), matrix.DiagonalIndexes(di)...)
		err = blas.GemmFloat(di, G, F.Gs, 1.0, 0.0)
		checkpnt.Check("06factor_chol2", minor)

		if F.firstcall {
			blas.SyrkFloat(F.Gs, F.S, 1.0, 0.0, la.OptTrans)
			if mnl > 0 {
				blas.SyrkFloat(F.Dfs, F.S, 1.0, 1.0, la.OptTrans)
			}
			if H != nil {
				F.S.Plus(H)
			}
			checkpnt.Check("10factor_chol2", minor)
			err = lapack.Potrf(F.S)
			if err != nil {
				err = nil // reset error
				F.singular = true
				// original code recreates F.S as dense if it is sparse and
				// A is dense, we don't do it as currently no sparse matrices
				//F.S = matrix.FloatZeros(n, n)
				//checkpnt.AddMatrixVar("S", F.S)
				blas.SyrkFloat(F.Gs, F.S, 1.0, 0.0, la.OptTrans)
				if mnl > 0 {
					blas.SyrkFloat(F.Dfs, F.S, 1.0, 1.0, la.OptTrans)
				}
				checkpnt.Check("14factor_chol2", minor)
				blas.SyrkFloat(F.A, F.S, 1.0, 1.0, la.OptTrans)
				if H != nil {
					F.S.Plus(H)
				}
				lapack.Potrf(F.S)
			}
			F.firstcall = false
			checkpnt.Check("20factor_chol2", minor)
		} else {
			blas.SyrkFloat(F.Gs, F.S, 1.0, 0.0, la.OptTrans)
			if mnl > 0 {
				blas.SyrkFloat(F.Dfs, F.S, 1.0, 1.0, la.OptTrans)
			}
			if H != nil {
				F.S.Plus(H)
			}
			checkpnt.Check("40factor_chol2", minor)
			if F.singular {
				blas.SyrkFloat(F.A, F.S, 1.0, 1.0, la.OptTrans)
			}
			lapack.Potrf(F.S)
			checkpnt.Check("50factor_chol2", minor)
		}

		// Asct := L^{-1}*A'.  Factor K = Asct'*Asct.
		Asct := F.A.Transpose()
		blas.TrsmFloat(F.S, Asct, 1.0)
		blas.SyrkFloat(Asct, F.K, 1.0, 0.0, la.OptTrans)
		lapack.Potrf(F.K)
		checkpnt.Check("90factor_chol2", minor)

		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.
			//
			// If not F['singular']:
			//
			//     K*uy = A * S^{-1} * ( bx + GG'*W^{-1}*W^{-T}*bz ) - by
			//     S*ux = bx + GG'*W^{-1}*W^{-T}*bz - A'*uy
			//     W*uz = W^{-T} * ( GG*ux - bz ).
			//
			// If F['singular']:
			//
			//     K*uy = A * S^{-1} * ( bx + GG'*W^{-1}*W^{-T}*bz + A'*by )
			//            - by
			//     S*ux = bx + GG'*W^{-1}*W^{-T}*bz + A'*by - A'*y.
			//     W*uz = W^{-T} * ( GG*ux - bz ).

			minor := 0
			if !checkpnt.MinorEmpty() {
				minor = checkpnt.MinorTop()
			}

			// z := W^{-1} * z = W^{-1} * bz
			scale(z, W, true, true)
			checkpnt.Check("10solve_chol2", minor)

			// If not F['singular']:
			//     x := L^{-1} * P * (x + GGs'*z)
			//        = L^{-1} * P * (x + GG'*W^{-1}*W^{-T}*bz)
			//
			// If F['singular']:
			//     x := L^{-1} * P * (x + GGs'*z + A'*y))
			//        = L^{-1} * P * (x + GG'*W^{-1}*W^{-T}*bz + A'*y)
			if mnl > 0 {
				blas.GemvFloat(F.Dfs, z, x, 1.0, 1.0, la.OptTrans)
			}
			blas.GemvFloat(F.Gs, z, x, 1.0, 1.0, la.OptTrans, &la.IOpt{"offsetx", mnl})
			//checkpnt.Check("20solve_chol2", minor)
			if F.singular {
				blas.GemvFloat(F.A, y, x, 1.0, 1.0, la.OptTrans)
			}
			checkpnt.Check("30solve_chol2", minor)
			blas.TrsvFloat(F.S, x)
			//checkpnt.Check("50solve_chol2", minor)

			// y := K^{-1} * (Asc*x - y)
			//    = K^{-1} * (A * S^{-1} * (bx + GG'*W^{-1}*W^{-T}*bz) - by)
			//      (if not F['singular'])
			//    = K^{-1} * (A * S^{-1} * (bx + GG'*W^{-1}*W^{-T}*bz +
			//      A'*by) - by)
			//      (if F['singular']).
			blas.GemvFloat(Asct, x, y, 1.0, -1.0, la.OptTrans)
			//checkpnt.Check("55solve_chol2", minor)
			lapack.Potrs(F.K, y)
			//checkpnt.Check("60solve_chol2", minor)

			// x := P' * L^{-T} * (x - Asc'*y)
			//    = S^{-1} * (bx + GG'*W^{-1}*W^{-T}*bz - A'*y)
			//      (if not F['singular'])
			//    = S^{-1} * (bx + GG'*W^{-1}*W^{-T}*bz + A'*by - A'*y)
			//      (if F['singular'])
			blas.GemvFloat(Asct, y, x, -1.0, 1.0)
			blas.TrsvFloat(F.S, x, la.OptTrans)
			checkpnt.Check("70solve_chol2", minor)

			// W*z := GGs*x - z = W^{-T} * (GG*x - bz)
			if mnl > 0 {
				blas.GemvFloat(F.Dfs, x, z, 1.0, -1.0)
			}
			blas.GemvFloat(F.Gs, x, z, 1.0, -1.0, &la.IOpt{"offsety", mnl})

			checkpnt.Check("90solve_chol2", minor)
			return nil
		}
		return solve, err
	}
	return factor, nil
}
Example #4
0
// Computes analytic center of A*x <= b with A m by n of rank n.
// We assume that b > 0 and the feasible set is bounded.
func acent(A, b *matrix.FloatMatrix, niters int) (x *matrix.FloatMatrix, ntdecrs []float64, err error) {

	err = nil
	if niters <= 0 {
		niters = MAXITERS
	}
	ntdecrs = make([]float64, 0, niters)

	if A.Rows() != b.Rows() {
		return nil, nil, errors.New("A.Rows() != b.Rows()")
	}

	m, n := A.Size()
	x = matrix.FloatZeros(n, 1)
	H := matrix.FloatZeros(n, n)
	// Helper m*n matrix
	Dmn := matrix.FloatZeros(m, n)

	for i := 0; i < niters; i++ {

		// Gradient is g = A^T * (1.0/(b - A*x)). d = 1.0/(b - A*x)
		// d is m*1 matrix, g is n*1 matrix
		d := matrix.Minus(b, matrix.Times(A, x)).Inv()
		g := matrix.Times(A.Transpose(), d)

		// Hessian is H = A^T * diag(1./(b-A*x))^2 * A.
		// in the original python code expression d[:,n*[0]] creates
		// a m*n matrix where each column is copy of column 0.
		// We do it here manually.
		for i := 0; i < n; i++ {
			Dmn.SetColumn(i, d)
		}

		// Function mul creates element wise product of matrices.
		Asc := matrix.Mul(Dmn, A)
		blas.SyrkFloat(Asc, H, 1.0, 0.0, linalg.OptTrans)

		// Newton step is v = H^-1 * g.
		v := matrix.Scale(g, -1.0)
		PosvFloat(H, v)

		// Directional derivative and Newton decrement.
		lam := blas.DotFloat(g, v)
		ntdecrs = append(ntdecrs, math.Sqrt(-lam))
		if ntdecrs[len(ntdecrs)-1] < TOL {
			return x, ntdecrs, err
		}

		// Backtracking line search.
		// y = d .* A*v
		y := matrix.Mul(d, matrix.Times(A, v))
		step := 1.0
		for 1-step*y.Max() < 0 {
			step *= BETA
		}

	search:
		for {
			// t = -step*y + 1 [e.g. t = 1 - step*y]
			t := matrix.Scale(y, -step).Add(1.0)

			// ts = sum(log(1-step*y))
			ts := t.Log().Sum()
			if -ts < ALPHA*step*lam {
				break search
			}
			step *= BETA
		}
		v.Scale(step)
		x.Plus(v)
	}
	// no solution !!
	err = errors.New(fmt.Sprintf("Iteration %d exhausted\n", niters))
	return x, ntdecrs, err
}
Example #5
0
//    Solution of KKT equations by reduction to a 2 x 2 system, a QR
//    factorization to eliminate the equality constraints, and a dense
//    Cholesky factorization of order n-p.
//
//    Computes the QR factorization
//
//        A' = [Q1, Q2] * [R; 0]
//
//    and returns a function that (1) computes the Cholesky factorization
//
//        Q_2^T * (H + GG^T * W^{-1} * W^{-T} * GG) * Q2 = L * L^T,
//
//    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 kktChol(G *matrix.FloatMatrix, dims *sets.DimensionSet, A *matrix.FloatMatrix, mnl int) (kktFactor, error) {

	p, n := A.Size()
	cdim := mnl + dims.Sum("l", "q") + dims.SumSquared("s")
	cdim_pckd := mnl + dims.Sum("l", "q") + dims.SumPacked("s")

	QA := A.Transpose()
	tauA := matrix.FloatZeros(p, 1)
	lapack.Geqrf(QA, tauA)

	Gs := matrix.FloatZeros(cdim, n)
	K := matrix.FloatZeros(n, n)
	bzp := matrix.FloatZeros(cdim_pckd, 1)
	yy := matrix.FloatZeros(p, 1)
	checkpnt.AddMatrixVar("tauA", tauA)
	checkpnt.AddMatrixVar("Gs", Gs)
	checkpnt.AddMatrixVar("K", K)

	factor := func(W *sets.FloatMatrixSet, H, Df *matrix.FloatMatrix) (KKTFunc, error) {
		// Compute
		//
		//     K = [Q1, Q2]' * (H + GG' * W^{-1} * W^{-T} * GG) * [Q1, Q2]
		//
		// and take the Cholesky factorization of the 2,2 block
		//
		//     Q_2' * (H + GG^T * W^{-1} * W^{-T} * GG) * Q2.

		var err error = nil
		minor := 0
		if !checkpnt.MinorEmpty() {
			minor = checkpnt.MinorTop()
		}
		// Gs = W^{-T} * GG in packed storage.
		if mnl > 0 {
			Gs.SetSubMatrix(0, 0, Df)
		}
		Gs.SetSubMatrix(mnl, 0, G)
		checkpnt.Check("00factor_chol", minor)
		scale(Gs, W, true, true)
		pack2(Gs, dims, mnl)
		//checkpnt.Check("10factor_chol", minor)

		// K = [Q1, Q2]' * (H + Gs' * Gs) * [Q1, Q2].
		blas.SyrkFloat(Gs, K, 1.0, 0.0, la.OptTrans, &la.IOpt{"k", cdim_pckd})
		if H != nil {
			K.SetSubMatrix(0, 0, matrix.Plus(H, K.GetSubMatrix(0, 0, H.Rows(), H.Cols())))
		}
		//checkpnt.Check("20factor_chol", minor)
		symm(K, n, 0)
		lapack.Ormqr(QA, tauA, K, la.OptLeft, la.OptTrans)
		lapack.Ormqr(QA, tauA, K, la.OptRight)
		//checkpnt.Check("30factor_chol", minor)

		// Cholesky factorization of 2,2 block of K.
		lapack.Potrf(K, &la.IOpt{"n", n - p}, &la.IOpt{"offseta", p * (n + 1)})
		checkpnt.Check("40factor_chol", minor)

		solve := func(x, y, z *matrix.FloatMatrix) (err error) {
			// Solve
			//
			//     [ 0          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.
			//
			// If we change variables ux = Q1*v + Q2*w, the system becomes
			//
			//     [ K11 K12 R ]   [ v  ]   [Q1'*(bx+GG'*W^{-1}*W^{-T}*bz)]
			//     [ K21 K22 0 ] * [ w  ] = [Q2'*(bx+GG'*W^{-1}*W^{-T}*bz)]
			//     [ R^T 0   0 ]   [ uy ]   [by                           ]
			//
			//     W*uz = W^{-T} * ( GG*ux - bz ).
			minor := 0
			if !checkpnt.MinorEmpty() {
				minor = checkpnt.MinorTop()
			}

			// bzp := W^{-T} * bz in packed storage
			scale(z, W, true, true)
			pack(z, bzp, dims, &la.IOpt{"mnl", mnl})

			// x := [Q1, Q2]' * (x + Gs' * bzp)
			//    = [Q1, Q2]' * (bx + Gs' * W^{-T} * bz)
			blas.GemvFloat(Gs, bzp, x, 1.0, 1.0, la.OptTrans, &la.IOpt{"m", cdim_pckd})
			lapack.Ormqr(QA, tauA, x, la.OptLeft, la.OptTrans)

			// y := x[:p]
			//    = Q1' * (bx + Gs' * W^{-T} * bz)
			blas.Copy(y, yy)
			blas.Copy(x, y, &la.IOpt{"n", p})

			// x[:p] := v = R^{-T} * by
			blas.Copy(yy, x)
			lapack.Trtrs(QA, x, la.OptUpper, la.OptTrans, &la.IOpt{"n", p})

			// x[p:] := K22^{-1} * (x[p:] - K21*x[:p])
			//        = K22^{-1} * (Q2' * (bx + Gs' * W^{-T} * bz) - K21*v)
			blas.GemvFloat(K, x, x, -1.0, 1.0, &la.IOpt{"m", n - p}, &la.IOpt{"n", p},
				&la.IOpt{"offseta", p}, &la.IOpt{"offsety", p})
			lapack.Potrs(K, x, &la.IOpt{"n", n - p}, &la.IOpt{"offseta", p * (n + 1)},
				&la.IOpt{"offsetb", p})

			// y := y - [K11, K12] * x
			//    = Q1' * (bx + Gs' * W^{-T} * bz) - K11*v - K12*w
			blas.GemvFloat(K, x, y, -1.0, 1.0, &la.IOpt{"m", p}, &la.IOpt{"n", n})

			// y := R^{-1}*y
			//    = R^{-1} * (Q1' * (bx + Gs' * W^{-T} * bz) - K11*v
			//      - K12*w)
			lapack.Trtrs(QA, y, la.OptUpper, &la.IOpt{"n", p})

			// x := [Q1, Q2] * x
			lapack.Ormqr(QA, tauA, x, la.OptLeft)

			// bzp := Gs * x - bzp.
			//      = W^{-T} * ( GG*ux - bz ) in packed storage.
			// Unpack and copy to z.
			blas.GemvFloat(Gs, x, bzp, 1.0, -1.0, &la.IOpt{"m", cdim_pckd})
			unpack(bzp, z, dims, &la.IOpt{"mnl", mnl})

			checkpnt.Check("90solve_chol", minor)
			return nil
		}
		return solve, err
	}
	return factor, nil
}