Esempio n. 1
0
func GbtrsFloat(A, B *matrix.FloatMatrix, ipiv []int32, KL int, opts ...linalg.Option) error {
	pars, err := linalg.GetParameters(opts...)
	if err != nil {
		return err
	}
	ind := linalg.GetIndexOpts(opts...)

	ind.Kl = KL
	err = checkGbtrs(ind, A, B, ipiv)
	if err != nil {
		return err
	}
	if ind.N == 0 || ind.Nrhs == 0 {
		return nil
	}
	Aa := A.FloatArray()
	Ba := B.FloatArray()
	trans := linalg.ParamString(pars.Trans)
	info := dgbtrs(trans, ind.N, ind.Kl, ind.Ku, ind.Nrhs,
		Aa[ind.OffsetA:], ind.LDa, ipiv, Ba[ind.OffsetB:], ind.LDb)
	if info != 0 {
		return errors.New(fmt.Sprintf("Gbtrs: call error: %d", info))
	}
	return nil
}
Esempio n. 2
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// See function Trsm.
func TrsmFloat(A, B *matrix.FloatMatrix, alpha float64, opts ...linalg.Option) (err error) {

	params, e := linalg.GetParameters(opts...)
	if e != nil {
		err = e
		return
	}
	ind := linalg.GetIndexOpts(opts...)
	err = check_level3_func(ind, ftrsm, A, B, nil, params)
	if err != nil {
		return
	}
	if ind.N == 0 || ind.M == 0 {
		return
	}
	Aa := A.FloatArray()
	Ba := B.FloatArray()
	uplo := linalg.ParamString(params.Uplo)
	transA := linalg.ParamString(params.TransA)
	side := linalg.ParamString(params.Side)
	diag := linalg.ParamString(params.Diag)
	dtrsm(side, uplo, transA, diag, ind.M, ind.N, alpha,
		Aa[ind.OffsetA:], ind.LDa, Ba[ind.OffsetB:], ind.LDb)
	return
}
Esempio n. 3
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// See function Syrk.
func SyrkFloat(A, C *matrix.FloatMatrix, alpha, beta float64, opts ...linalg.Option) (err error) {

	params, e := linalg.GetParameters(opts...)
	if e != nil {
		err = e
		return
	}
	ind := linalg.GetIndexOpts(opts...)
	err = check_level3_func(ind, fsyrk, A, nil, C, params)
	if e != nil || err != nil {
		return
	}
	if ind.N == 0 {
		return
	}
	Aa := A.FloatArray()
	Ca := C.FloatArray()
	uplo := linalg.ParamString(params.Uplo)
	trans := linalg.ParamString(params.Trans)
	//diag := linalg.ParamString(params.Diag)
	dsyrk(uplo, trans, ind.N, ind.K, alpha, Aa[ind.OffsetA:], ind.LDa, beta,
		Ca[ind.OffsetC:], ind.LDc)

	return
}
Esempio n. 4
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func (p *FloorPlan) F2(x, z *matrix.FloatMatrix) (f, Df, H *matrix.FloatMatrix, err error) {
	f, Df, err = p.F1(x)
	x17 := matrix.FloatVector(x.FloatArray()[17:])
	tmp := p.Amin.Div(x17.Pow(3.0))
	tmp = z.Mul(tmp).Scale(2.0)
	diag := matrix.FloatDiagonal(5, tmp.FloatArray()...)
	H = matrix.FloatZeros(22, 22)
	H.SetSubMatrix(17, 17, diag)
	return
}
Esempio n. 5
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func sinv(x, y *matrix.FloatMatrix, dims *DimensionSet, mnl int) (err error) {
	/*DEBUGGED*/

	err = nil

	// For the nonlinear and 'l' blocks:
	//
	//     yk o\ xk = yk .\ xk.

	ind := mnl + dims.At("l")[0]
	blas.Tbsv(y, x, &la_.IOpt{"n", ind}, &la_.IOpt{"k", 0}, &la_.IOpt{"ldA", 1})

	// For the 'q' blocks:
	//
	//                        [ l0   -l1'              ]
	//     yk o\ xk = 1/a^2 * [                        ] * xk
	//                        [ -l1  (a*I + l1*l1')/l0 ]
	//
	// where yk = (l0, l1) and a = l0^2 - l1'*l1.

	for _, m := range dims.At("q") {
		aa := blas.Nrm2Float(y, &la_.IOpt{"n", m - 1}, &la_.IOpt{"offset", ind + 1})
		ee := y.GetIndex(ind)
		aa = (ee + aa) * (ee - aa)
		cc := x.GetIndex(ind)
		dd := blas.DotFloat(x, y, &la_.IOpt{"n", m - 1}, &la_.IOpt{"offsetx", ind + 1},
			&la_.IOpt{"offsety", ind + 1})
		x.SetIndex(ind, cc*ee-dd)
		blas.ScalFloat(x, aa/ee, &la_.IOpt{"n", m - 1}, &la_.IOpt{"offset", ind + 1})
		blas.AxpyFloat(y, x, dd/ee-cc, &la_.IOpt{"n", m - 1},
			&la_.IOpt{"offsetx", ind + 1}, &la_.IOpt{"offsety", ind + 1})
		blas.ScalFloat(x, 1.0/aa, &la_.IOpt{"n", m}, &la_.IOpt{"offset", ind})
		ind += m
	}

	// For the 's' blocks:
	//
	//     yk o\ xk =  xk ./ gamma
	//
	// where gammaij = .5 * (yk_i + yk_j).

	ind2 := ind
	for _, m := range dims.At("s") {
		for j := 0; j < m; j++ {
			u := matrix.FloatVector(y.FloatArray()[ind2+j : ind2+m])
			u.Add(y.GetIndex(ind2 + j))
			u.Scale(0.5)
			blas.Tbsv(u, x, &la_.IOpt{"n", m - j}, &la_.IOpt{"k", 0}, &la_.IOpt{"lda", 1},
				&la_.IOpt{"offsetx", ind + j*(m+1)})
		}
		ind += m * m
		ind2 += m
	}
	return
}
Esempio n. 6
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// See function Scal.
func ScalFloat(X *matrix.FloatMatrix, alpha float64, opts ...linalg.Option) (err error) {
	ind := linalg.GetIndexOpts(opts...)
	err = check_level1_func(ind, fscal, X, nil)
	if err != nil {
		return
	}
	if ind.Nx == 0 {
		return
	}
	Xa := X.FloatArray()
	dscal(ind.Nx, alpha, Xa[ind.OffsetX:], ind.IncX)
	return
}
Esempio n. 7
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// Returns min {t | x + t*e >= 0}, where e is defined as follows
//
//  - For the nonlinear and 'l' blocks: e is the vector of ones.
//  - For the 'q' blocks: e is the first unit vector.
//  - For the 's' blocks: e is the identity matrix.
//
// When called with the argument sigma, also returns the eigenvalues
// (in sigma) and the eigenvectors (in x) of the 's' components of x.
func maxStep(x *matrix.FloatMatrix, dims *DimensionSet, mnl int, sigma *matrix.FloatMatrix) (rval float64, err error) {
	/*DEBUGGED*/

	rval = 0.0
	err = nil
	t := make([]float64, 0, 10)
	ind := mnl + dims.Sum("l")
	if ind > 0 {
		t = append(t, -minvec(x.FloatArray()[:ind]))
	}
	for _, m := range dims.At("q") {
		if m > 0 {
			v := blas.Nrm2Float(x, &la_.IOpt{"offset", ind + 1}, &la_.IOpt{"n", m - 1})
			v -= x.GetIndex(ind)
			t = append(t, v)
		}
		ind += m
	}

	var Q *matrix.FloatMatrix
	var w *matrix.FloatMatrix
	ind2 := 0
	if sigma == nil && len(dims.At("s")) > 0 {
		mx := dims.Max("s")
		Q = matrix.FloatZeros(mx, mx)
		w = matrix.FloatZeros(mx, 1)
	}
	for _, m := range dims.At("s") {
		if sigma == nil {
			blas.Copy(x, Q, &la_.IOpt{"offsetx", ind}, &la_.IOpt{"n", m * m})
			err = lapack.SyevrFloat(Q, w, nil, 0.0, nil, []int{1, 1}, la_.OptRangeInt,
				&la_.IOpt{"n", m}, &la_.IOpt{"lda", m})
			if m > 0 {
				t = append(t, -w.GetIndex(0))
			}
		} else {
			err = lapack.SyevdFloat(x, sigma, la_.OptJobZValue, &la_.IOpt{"n", m},
				&la_.IOpt{"lda", m}, &la_.IOpt{"offseta", ind}, &la_.IOpt{"offsetw", ind2})
			if m > 0 {
				t = append(t, -sigma.GetIndex(ind2))
			}
		}
		ind += m * m
		ind2 += m
	}

	if len(t) > 0 {
		rval = maxvec(t)
	}
	return
}
Esempio n. 8
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func GesvdFloat(A, S, U, Vt *matrix.FloatMatrix, opts ...linalg.Option) error {
	pars, err := linalg.GetParameters(opts...)
	if err != nil {
		return err
	}
	ind := linalg.GetIndexOpts(opts...)
	err = checkGesvd(ind, pars, A, S, U, Vt)
	if err != nil {
		return err
	}
	if ind.M == 0 || ind.N == 0 {
		return nil
	}
	Aa := A.FloatArray()
	Sa := S.FloatArray()
	var Ua, Va []float64
	Ua = nil
	Va = nil
	if U != nil {
		Ua = U.FloatArray()[ind.OffsetU:]
	}
	if Vt != nil {
		Va = Vt.FloatArray()[ind.OffsetVt:]
	}
	info := dgesvd(linalg.ParamString(pars.Jobu), linalg.ParamString(pars.Jobvt),
		ind.M, ind.N, Aa[ind.OffsetA:], ind.LDa, Sa[ind.OffsetS:], Ua, ind.LDu, Va, ind.LDvt)
	if info != 0 {
		return errors.New("GesvdFloat not implemented yet")
	}
	return nil
}
Esempio n. 9
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// See function Copy.
func CopyFloat(X, Y *matrix.FloatMatrix, opts ...linalg.Option) (err error) {
	ind := linalg.GetIndexOpts(opts...)
	err = check_level1_func(ind, fcopy, X, Y)
	if err != nil {
		return
	}
	if ind.Nx == 0 {
		return
	}
	Xa := X.FloatArray()
	Ya := Y.FloatArray()
	dcopy(ind.Nx, Xa[ind.OffsetX:], ind.IncX, Ya[ind.OffsetY:], ind.IncY)
	return
}
Esempio n. 10
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// See function Asum.
func AsumFloat(X *matrix.FloatMatrix, opts ...linalg.Option) (v float64) {
	v = math.NaN()
	ind := linalg.GetIndexOpts(opts...)
	err := check_level1_func(ind, fasum, X, nil)
	if err != nil {
		return
	}
	if ind.Nx == 0 {
		v = 0.0
		return
	}
	Xa := X.FloatArray()
	v = dasum(ind.Nx, Xa[ind.OffsetX:], ind.IncX)
	return
}
Esempio n. 11
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// See functin Dot.
func DotFloat(X, Y *matrix.FloatMatrix, opts ...linalg.Option) (v float64) {
	v = math.NaN()
	ind := linalg.GetIndexOpts(opts...)
	err := check_level1_func(ind, fdot, X, Y)
	if err != nil {
		return
	}
	if ind.Nx == 0 {
		v = 0.0
		return
	}
	Xa := X.FloatArray()
	Ya := Y.FloatArray()
	v = ddot(ind.Nx, Xa[ind.OffsetX:], ind.IncX, Ya[ind.OffsetY:], ind.IncY)
	return
}
Esempio n. 12
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func GbtrfFloat(A *matrix.FloatMatrix, ipiv []int32, M, KL int, opts ...linalg.Option) error {
	ind := linalg.GetIndexOpts(opts...)
	ind.M = M
	ind.Kl = KL
	err := checkGbtrf(ind, A, ipiv)
	if err != nil {
		return err
	}
	if ind.M == 0 || ind.N == 0 {
		return nil
	}
	Aa := A.FloatArray()
	info := dgbtrf(ind.M, ind.N, ind.Kl, ind.Ku, Aa[ind.OffsetA:], ind.LDa, ipiv)
	if info != 0 {
		return errors.New(fmt.Sprintf("Gbtrf call error: %d", info))
	}
	return nil
}
Esempio n. 13
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func PotrfFloat(A *matrix.FloatMatrix, opts ...linalg.Option) error {
	pars, err := linalg.GetParameters(opts...)
	if err != nil {
		return err
	}
	ind := linalg.GetIndexOpts(opts...)
	err = checkPotrf(ind, A)
	if ind.N == 0 {
		return nil
	}
	Aa := A.FloatArray()
	uplo := linalg.ParamString(pars.Uplo)
	info := dpotrf(uplo, ind.N, Aa[ind.OffsetA:], ind.LDa)
	if info != 0 {
		return errors.New(fmt.Sprintf("Potrf: call error %d", info))
	}
	return nil
}
Esempio n. 14
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func GbsvFloat(A, B *matrix.FloatMatrix, ipiv []int32, kl int, opts ...linalg.Option) error {

	ind := linalg.GetIndexOpts(opts...)
	ind.Kl = kl
	err := checkGbsv(ind, A, B, ipiv)
	if err != nil {
		return err
	}
	if ind.N == 0 || ind.Nrhs == 0 {
		return nil
	}

	Aa := A.FloatArray()
	Ba := B.FloatArray()
	info := dgbsv(ind.N, ind.Kl, ind.Ku, ind.Nrhs, Aa[ind.OffsetA:], ind.LDa,
		ipiv, Ba[ind.OffsetB:], ind.LDb)
	if info != 0 {
		return errors.New(fmt.Sprintf("Gbsv call error: %d", info))
	}
	return nil
}
Esempio n. 15
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// See function Syr.
func SyrFloat(X, A *matrix.FloatMatrix, alpha float64, opts ...linalg.Option) (err error) {

	var params *linalg.Parameters
	params, err = linalg.GetParameters(opts...)
	if err != nil {
		return
	}
	ind := linalg.GetIndexOpts(opts...)
	err = check_level2_func(ind, fsyr, X, nil, A, params)
	if err != nil {
		return
	}
	if ind.N == 0 {
		return
	}
	Xa := X.FloatArray()
	Aa := A.FloatArray()
	uplo := linalg.ParamString(params.Uplo)
	dsyr(uplo, ind.N, alpha, Xa[ind.OffsetX:], ind.IncX, Aa[ind.OffsetA:], ind.LDa)
	return
}
Esempio n. 16
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func (p *FloorPlan) F1(x *matrix.FloatMatrix) (f, Df *matrix.FloatMatrix, err error) {
	err = nil
	mn := x.Min(-1, -2, -3, -4, -5)
	if mn <= 0.0 {
		f, Df = nil, nil
		return
	}
	zeros := matrix.FloatZeros(5, 12)
	dk1 := matrix.FloatDiagonal(5, -1.0)
	dk2 := matrix.FloatZeros(5, 5)
	x17 := matrix.FloatVector(x.FloatArray()[17:])
	// -( Amin ./ (x17 .* x17) )
	diag := p.Amin.Div(x17.Mul(x17)).Scale(-1.0)
	dk2.SetIndexes(matrix.MakeDiagonalSet(5, 5), diag.FloatArray())
	Df, _ = matrix.FloatMatrixCombined(matrix.StackRight, zeros, dk1, dk2)

	x12 := matrix.FloatVector(x.FloatArray()[12:17])
	// f = -x[12:17] + div(Amin, x[17:])
	f = p.Amin.Div(x17).Minus(x12)
	return
}
Esempio n. 17
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// See function Symm.
func SymmFloat(A, B, C *matrix.FloatMatrix, alpha, beta float64, opts ...linalg.Option) (err error) {

	params, e := linalg.GetParameters(opts...)
	if e != nil {
		err = e
		return
	}
	ind := linalg.GetIndexOpts(opts...)
	err = check_level3_func(ind, fsymm, A, B, C, params)
	if err != nil {
		return
	}
	if ind.M == 0 || ind.N == 0 {
		return
	}
	Aa := A.FloatArray()
	Ba := B.FloatArray()
	Ca := C.FloatArray()
	uplo := linalg.ParamString(params.Uplo)
	side := linalg.ParamString(params.Side)
	dsymm(side, uplo, ind.M, ind.N, alpha, Aa[ind.OffsetA:], ind.LDa,
		Ba[ind.OffsetB:], ind.LDb, beta, Ca[ind.OffsetC:], ind.LDc)

	return
}
Esempio n. 18
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// See function Gemm.
func GemmFloat(A, B, C *matrix.FloatMatrix, alpha, beta float64, opts ...linalg.Option) (err error) {

	params, e := linalg.GetParameters(opts...)
	if e != nil {
		err = e
		return
	}
	ind := linalg.GetIndexOpts(opts...)
	err = check_level3_func(ind, fgemm, A, B, C, params)
	if err != nil {
		return
	}
	if ind.M == 0 || ind.N == 0 {
		return
	}
	Aa := A.FloatArray()
	Ba := B.FloatArray()
	Ca := C.FloatArray()
	transB := linalg.ParamString(params.TransB)
	transA := linalg.ParamString(params.TransA)
	//diag := linalg.ParamString(params.Diag)
	dgemm(transA, transB, ind.M, ind.N, ind.K, alpha,
		Aa[ind.OffsetA:], ind.LDa, Ba[ind.OffsetB:], ind.LDb, beta,
		Ca[ind.OffsetC:], ind.LDc)
	return
}
Esempio n. 19
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// See function Gbmv.
func GbmvFloat(A, X, Y *matrix.FloatMatrix, alpha, beta float64, opts ...linalg.Option) (err error) {

	var params *linalg.Parameters
	params, err = linalg.GetParameters(opts...)
	if err != nil {
		return
	}
	ind := linalg.GetIndexOpts(opts...)
	err = check_level2_func(ind, fgbmv, X, Y, A, params)
	if err != nil {
		return
	}
	if ind.M == 0 && ind.N == 0 {
		return
	}

	Xa := X.FloatArray()
	Ya := Y.FloatArray()
	Aa := A.FloatArray()
	if params.Trans == linalg.PNoTrans && ind.N == 0 {
		dscal(ind.M, beta, Ya[ind.OffsetY:], ind.IncY)
	} else if params.Trans == linalg.PTrans && ind.M == 0 {
		dscal(ind.N, beta, Ya[ind.OffsetY:], ind.IncY)
	} else {
		trans := linalg.ParamString(params.Trans)
		dgbmv(trans, ind.M, ind.N, ind.Kl, ind.Ku,
			alpha, Aa[ind.OffsetA:], ind.LDa, Xa[ind.OffsetX:], ind.IncX,
			beta, Ya[ind.OffsetY:], ind.IncY)
	}
	return
}
Esempio n. 20
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func SyevdFloat(A, W *matrix.FloatMatrix, opts ...linalg.Option) error {
	pars, err := linalg.GetParameters(opts...)
	if err != nil {
		return err
	}
	ind := linalg.GetIndexOpts(opts...)
	err = checkSyevd(ind, A, W)
	if err != nil {
		return err
	}
	if ind.N == 0 {
		return nil
	}
	jobz := linalg.ParamString(pars.Jobz)
	uplo := linalg.ParamString(pars.Uplo)
	Aa := A.FloatArray()
	Wa := W.FloatArray()
	info := dsyevd(jobz, uplo, ind.N, Aa[ind.OffsetA:], ind.LDa, Wa[ind.OffsetW:])
	if info != 0 {
		return errors.New(fmt.Sprintf("Syevd: call error %d", info))
	}
	return nil
}
Esempio n. 21
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// See function Tbsv.
func TbsvFloat(A, X *matrix.FloatMatrix, opts ...linalg.Option) (err error) {

	var params *linalg.Parameters
	params, err = linalg.GetParameters(opts...)
	if err != nil {
		return
	}
	ind := linalg.GetIndexOpts(opts...)
	err = check_level2_func(ind, ftbsv, X, nil, A, params)
	if err != nil {
		return
	}
	if ind.N == 0 {
		return
	}
	Xa := X.FloatArray()
	Aa := A.FloatArray()
	uplo := linalg.ParamString(params.Uplo)
	trans := linalg.ParamString(params.Trans)
	diag := linalg.ParamString(params.Diag)
	dtbsv(uplo, trans, diag, ind.N, ind.K,
		Aa[ind.OffsetA:], ind.LDa, Xa[ind.OffsetX:], ind.IncX)
	return
}
Esempio n. 22
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// See function Ger.
func GerFloat(X, Y, A *matrix.FloatMatrix, alpha float64, opts ...linalg.Option) (err error) {

	var params *linalg.Parameters
	params, err = linalg.GetParameters(opts...)
	if err != nil {
		return
	}
	ind := linalg.GetIndexOpts(opts...)
	err = check_level2_func(ind, fger, X, Y, A, params)
	if err != nil {
		return
	}
	if ind.N == 0 || ind.M == 0 {
		return
	}
	Xa := X.FloatArray()
	Ya := Y.FloatArray()
	Aa := A.FloatArray()
	dger(ind.M, ind.N, alpha, Xa[ind.OffsetX:], ind.IncX,
		Ya[ind.OffsetY:], ind.IncY, Aa[ind.OffsetA:], ind.LDa)

	return
}
Esempio n. 23
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// See function Sbmv.
func SbmvFloat(A, X, Y *matrix.FloatMatrix, alpha, beta float64, opts ...linalg.Option) (err error) {

	var params *linalg.Parameters
	params, err = linalg.GetParameters(opts...)
	if err != nil {
		return
	}
	ind := linalg.GetIndexOpts(opts...)
	err = check_level2_func(ind, fsbmv, X, Y, A, params)
	if err != nil {
		return
	}
	if ind.N == 0 {
		return
	}
	Xa := X.FloatArray()
	Ya := Y.FloatArray()
	Aa := A.FloatArray()
	uplo := linalg.ParamString(params.Uplo)
	dsbmv(uplo, ind.N, ind.K, alpha, Aa[ind.OffsetA:], ind.LDa, Xa[ind.OffsetX:],
		ind.IncX, beta, Ya[ind.OffsetY:], ind.IncY)
	return
}
Esempio n. 24
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//    Solves a pair of primal and dual SDPs
//
//        minimize    c'*x
//        subject to  Gl*x + sl = hl
//                    mat(Gs[k]*x) + ss[k] = hs[k], k = 0, ..., N-1
//                    A*x = b
//                    sl >= 0,  ss[k] >= 0, k = 0, ..., N-1
//
//        maximize    -hl'*z - sum_k trace(hs[k]*zs[k]) - b'*y
//        subject to  Gl'*zl + sum_k Gs[k]'*vec(zs[k]) + A'*y + c = 0
//                    zl >= 0,  zs[k] >= 0, k = 0, ..., N-1.
//
//    The inequalities sl >= 0 and zl >= 0 are elementwise vector
//    inequalities.  The inequalities ss[k] >= 0, zs[k] >= 0 are matrix
//    inequalities, i.e., the symmetric matrices ss[k] and zs[k] must be
//    positive semidefinite.  mat(Gs[k]*x) is the symmetric matrix X with
//    X[:] = Gs[k]*x.  For a symmetric matrix, zs[k], vec(zs[k]) is the
//    vector zs[k][:].
//
func Sdp(c, Gl, hl, A, b *matrix.FloatMatrix, Ghs *FloatMatrixSet, solopts *SolverOptions, primalstart, dualstart *FloatMatrixSet) (sol *Solution, err error) {
	if c == nil {
		err = errors.New("'c' must a column matrix")
		return
	}
	n := c.Rows()
	if n < 1 {
		err = errors.New("Number of variables must be at least 1")
		return
	}
	if Gl == nil {
		Gl = matrix.FloatZeros(0, n)
	}
	if Gl.Cols() != n {
		err = errors.New(fmt.Sprintf("'G' must be matrix with %d columns", n))
		return
	}
	ml := Gl.Rows()
	if hl == nil {
		hl = matrix.FloatZeros(0, 1)
	}
	if !hl.SizeMatch(ml, 1) {
		err = errors.New(fmt.Sprintf("'hl' must be matrix of size (%d,1)", ml))
		return
	}
	Gsset := Ghs.At("Gs")
	ms := make([]int, 0)
	for i, Gs := range Gsset {
		if Gs.Cols() != n {
			err = errors.New(fmt.Sprintf("'Gs' must be list of matrices with %d columns", n))
			return
		}
		sz := int(math.Sqrt(float64(Gs.Rows())))
		if Gs.Rows() != sz*sz {
			err = errors.New(fmt.Sprintf("the squareroot of the number of rows of 'Gq[%d]' is not an integer", i))
			return
		}
		ms = append(ms, sz)
	}

	hsset := Ghs.At("hs")
	if len(Gsset) != len(hsset) {
		err = errors.New(fmt.Sprintf("'hs' must be a list of %d matrices", len(Gsset)))
		return
	}
	for i, hs := range hsset {
		if !hs.SizeMatch(ms[i], ms[i]) {
			s := fmt.Sprintf("hq[%d] has size (%d,%d). Expected size is (%d,%d)",
				i, hs.Rows(), hs.Cols(), ms[i], ms[i])
			err = errors.New(s)
			return
		}
	}
	if A == nil {
		A = matrix.FloatZeros(0, n)
	}
	if A.Cols() != n {
		err = errors.New(fmt.Sprintf("'A' must be matrix with %d columns", n))
		return
	}
	p := A.Rows()
	if b == nil {
		b = matrix.FloatZeros(0, 1)
	}
	if !b.SizeMatch(p, 1) {
		err = errors.New(fmt.Sprintf("'b' must be matrix of size (%d,1)", p))
		return
	}
	dims := DSetNew("l", "q", "s")
	dims.Set("l", []int{ml})
	dims.Set("s", ms)
	N := dims.Sum("l") + dims.SumSquared("s")

	// Map hs matrices to h vector
	h := matrix.FloatZeros(N, 1)
	h.SetIndexes(matrix.MakeIndexSet(0, ml, 1), hl.FloatArray()[:ml])
	ind := ml
	for k, hs := range hsset {
		h.SetIndexes(matrix.MakeIndexSet(ind, ind+ms[k]*ms[k], 1), hs.FloatArray())
		ind += ms[k] * ms[k]
	}

	Gargs := make([]*matrix.FloatMatrix, 0)
	Gargs = append(Gargs, Gl)
	Gargs = append(Gargs, Gsset...)
	G, sizeg := matrix.FloatMatrixCombined(matrix.StackDown, Gargs...)

	var pstart, dstart *FloatMatrixSet = nil, nil
	if primalstart != nil {
		pstart = FloatSetNew("x", "s")
		pstart.Set("x", primalstart.At("x")[0])
		slset := primalstart.At("sl")
		margs := make([]*matrix.FloatMatrix, 0, len(slset)+1)
		margs = append(margs, primalstart.At("s")[0])
		margs = append(margs, slset...)
		sl, _ := matrix.FloatMatrixCombined(matrix.StackDown, margs...)
		pstart.Set("s", sl)
	}

	if dualstart != nil {
		dstart = FloatSetNew("y", "z")
		dstart.Set("y", dualstart.At("y")[0])
		zlset := primalstart.At("zl")
		margs := make([]*matrix.FloatMatrix, 0, len(zlset)+1)
		margs = append(margs, dualstart.At("z")[0])
		margs = append(margs, zlset...)
		zl, _ := matrix.FloatMatrixCombined(matrix.StackDown, margs...)
		dstart.Set("z", zl)
	}

	sol, err = ConeLp(c, G, h, A, b, dims, solopts, pstart, dstart)
	// unpack sol.Result
	if err == nil {
		s := sol.Result.At("s")[0]
		sl := matrix.FloatVector(s.FloatArray()[:ml])
		sol.Result.Append("sl", sl)
		ind := ml
		for _, m := range ms {
			sk := matrix.FloatNew(m, m, s.FloatArray()[ind:ind+m*m])
			sol.Result.Append("ss", sk)
			ind += m * m
		}

		z := sol.Result.At("z")[0]
		zl := matrix.FloatVector(s.FloatArray()[:ml])
		sol.Result.Append("zl", zl)
		ind = ml
		for i, k := range sizeg[1:] {
			zk := matrix.FloatNew(ms[i], ms[i], z.FloatArray()[ind:ind+k])
			sol.Result.Append("zs", zk)
			ind += k
		}
	}
	sol.Result.Remove("s")
	sol.Result.Remove("z")

	return

}
Esempio n. 25
0
func updateScaling(W *FloatMatrixSet, lmbda, s, z *matrix.FloatMatrix) (err error) {
	err = nil
	var stmp, ztmp *matrix.FloatMatrix
	/*
	   Nonlinear and 'l' blocks

	      d :=  d .* sqrt( s ./ z )
	      lmbda := lmbda .* sqrt(s) .* sqrt(z)
	*/
	mnl := 0
	dnlset := W.At("dnl")
	dnliset := W.At("dnli")
	dset := W.At("d")
	diset := W.At("di")
	beta := W.At("beta")[0]
	if dnlset != nil && dnlset[0].NumElements() > 0 {
		mnl = dnlset[0].NumElements()
	}
	ml := dset[0].NumElements()
	m := mnl + ml
	//fmt.Printf("ml=%d, mnl=%d, m=%d'n", ml, mnl, m)

	stmp = matrix.FloatVector(s.FloatArray()[:m])
	stmp.Apply(stmp, math.Sqrt)
	s.SetIndexes(matrix.MakeIndexSet(0, m, 1), stmp.FloatArray())

	ztmp = matrix.FloatVector(z.FloatArray()[:m])
	ztmp.Apply(ztmp, math.Sqrt)
	z.SetIndexes(matrix.MakeIndexSet(0, m, 1), ztmp.FloatArray())

	// d := d .* s .* z
	if len(dnlset) > 0 {
		blas.TbmvFloat(s, dnlset[0], &la_.IOpt{"n", mnl}, &la_.IOpt{"k", 0}, &la_.IOpt{"lda", 1})
		blas.TbsvFloat(z, dnlset[0], &la_.IOpt{"n", mnl}, &la_.IOpt{"k", 0}, &la_.IOpt{"lda", 1})
		dnliset[0].Apply(dnlset[0], func(a float64) float64 { return 1.0 / a })
	}
	blas.TbmvFloat(s, dset[0], &la_.IOpt{"n", ml},
		&la_.IOpt{"k", 0}, &la_.IOpt{"lda", 1}, &la_.IOpt{"offseta", mnl})
	blas.TbsvFloat(z, dset[0], &la_.IOpt{"n", ml},
		&la_.IOpt{"k", 0}, &la_.IOpt{"lda", 1}, &la_.IOpt{"offseta", mnl})
	diset[0].Apply(dset[0], func(a float64) float64 { return 1.0 / a })

	// lmbda := s .* z
	blas.CopyFloat(s, lmbda, &la_.IOpt{"n", m})
	blas.TbmvFloat(z, lmbda, &la_.IOpt{"n", m}, &la_.IOpt{"k", 0}, &la_.IOpt{"lda", 1})

	//fmt.Printf("-- end of l:\nz=\n%v\nlmbda=\n%v\n", z.ConvertToString(), lmbda.ConvertToString())
	//fmt.Printf("W[d]=\n%v\n", dset[0].ConvertToString())
	//fmt.Printf("W[di]=\n%v\n", diset[0].ConvertToString())

	// 'q' blocks.
	// Let st and zt be the new variables in the old scaling:
	//
	//     st = s_k,   zt = z_k
	//
	// and a = sqrt(st' * J * st),  b = sqrt(zt' * J * zt).
	//
	// 1. Compute the hyperbolic Householder transformation 2*q*q' - J
	//    that maps st/a to zt/b.
	//
	//        c = sqrt( (1 + st'*zt/(a*b)) / 2 )
	//        q = (st/a + J*zt/b) / (2*c).
	//
	//    The new scaling point is
	//
	//        wk := betak * sqrt(a/b) * (2*v[k]*v[k]' - J) * q
	//
	//    with betak = W['beta'][k].
	//
	// 3. The scaled variable:
	//
	//        lambda_k0 = sqrt(a*b) * c
	//        lambda_k1 = sqrt(a*b) * ( (2vk*vk' - J) * (-d*q + u/2) )_1
	//
	//    where
	//
	//        u = st/a - J*zt/b
	//        d = ( vk0 * (vk'*u) + u0/2 ) / (2*vk0 *(vk'*q) - q0 + 1).
	//
	// 4. Update scaling
	//
	//        v[k] := wk^1/2
	//              = 1 / sqrt(2*(wk0 + 1)) * (wk + e).
	//        beta[k] *=  sqrt(a/b)

	ind := m
	for k, v := range W.At("v") {
		m = v.NumElements()

		// ln = sqrt( lambda_k' * J * lambda_k ) !! NOT USED!!
		jnrm2(lmbda, m, ind) // ?? NOT USED ??

		// a = sqrt( sk' * J * sk ) = sqrt( st' * J * st )
		// s := s / a = st / a
		aa := jnrm2(s, m, ind)
		blas.ScalFloat(s, 1.0/aa, &la_.IOpt{"n", m}, &la_.IOpt{"offset", ind})

		// b = sqrt( zk' * J * zk ) = sqrt( zt' * J * zt )
		// z := z / a = zt / b
		bb := jnrm2(z, m, ind)
		blas.ScalFloat(z, 1.0/bb, &la_.IOpt{"n", m}, &la_.IOpt{"offset", ind})

		// c = sqrt( ( 1 + (st'*zt) / (a*b) ) / 2 )
		cc := blas.DotFloat(s, z, &la_.IOpt{"offsetx", ind}, &la_.IOpt{"offsety", ind},
			&la_.IOpt{"n", m})
		cc = math.Sqrt((1.0 + cc) / 2.0)

		// vs = v' * st / a
		vs := blas.DotFloat(v, s, &la_.IOpt{"offsety", ind}, &la_.IOpt{"n", m})

		// vz = v' * J *zt / b
		vz := jdot(v, z, m, 0, ind)

		// vq = v' * q where q = (st/a + J * zt/b) / (2 * c)
		vq := (vs + vz) / 2.0 / cc

		// vq = v' * q where q = (st/a + J * zt/b) / (2 * c)
		vu := vs - vz
		// lambda_k0 = c
		lmbda.SetIndex(ind, cc)

		// wk0 = 2 * vk0 * (vk' * q) - q0
		wk0 := 2.0*v.GetIndex(0)*vq - (s.GetIndex(ind)+z.GetIndex(ind))/2.0/cc

		// d = (v[0] * (vk' * u) - u0/2) / (wk0 + 1)
		dd := (v.GetIndex(0)*vu - s.GetIndex(ind)/2.0 + z.GetIndex(ind)/2.0) / (wk0 + 1.0)

		// lambda_k1 = 2 * v_k1 * vk' * (-d*q + u/2) - d*q1 + u1/2
		blas.CopyFloat(v, lmbda, &la_.IOpt{"offsetx", 1}, &la_.IOpt{"offsety", ind + 1},
			&la_.IOpt{"n", m - 1})
		blas.ScalFloat(lmbda, (2.0 * (-dd*vq + 0.5*vu)),
			&la_.IOpt{"offsetx", ind + 1}, &la_.IOpt{"offsety", ind + 1}, &la_.IOpt{"n", m - 1})
		blas.AxpyFloat(s, lmbda, 0.5*(1.0-dd/cc),
			&la_.IOpt{"offsetx", ind + 1}, &la_.IOpt{"offsety", ind + 1}, &la_.IOpt{"n", m - 1})
		blas.AxpyFloat(z, lmbda, 0.5*(1.0+dd/cc),
			&la_.IOpt{"offsetx", ind + 1}, &la_.IOpt{"offsety", ind + 1}, &la_.IOpt{"n", m - 1})

		// Scale so that sqrt(lambda_k' * J * lambda_k) = sqrt(aa*bb).
		blas.ScalFloat(lmbda, math.Sqrt(aa*bb), &la_.IOpt{"offset", ind}, &la_.IOpt{"n", m})

		// v := (2*v*v' - J) * q
		//    = 2 * (v'*q) * v' - (J* st/a + zt/b) / (2*c)
		blas.ScalFloat(v, 2.0*vq)
		v.SetIndex(0, v.GetIndex(0)-(s.GetIndex(ind)/2.0/cc))
		blas.AxpyFloat(s, v, 0.5/cc, &la_.IOpt{"offsetx", ind + 1}, &la_.IOpt{"offsety", 1},
			&la_.IOpt{"n", m - 1})
		blas.AxpyFloat(z, v, -0.5/cc, &la_.IOpt{"offsetx", ind}, &la_.IOpt{"n", m})

		// v := v^{1/2} = 1/sqrt(2 * (v0 + 1)) * (v + e)
		v0 := v.GetIndex(0) + 1.0
		v.SetIndex(0, v0)
		blas.ScalFloat(v, 1.0/math.Sqrt(2.0*v0))

		// beta[k] *= ( aa / bb )**1/2
		bk := beta.GetIndex(k)
		beta.SetIndex(k, bk*math.Sqrt(aa/bb))

		ind += m
	}
	//fmt.Printf("-- end of q:\nz=\n%v\nlmbda=\n%v\n", z.ConvertToString(), lmbda.ConvertToString())
	//fmt.Printf("beta=\n%v\n", beta.ConvertToString())

	// 's' blocks
	//
	// Let st, zt be the updated variables in the old scaling:
	//
	//     st = Ls * Ls', zt = Lz * Lz'.
	//
	// where Ls and Lz are the 's' components of s, z.
	//
	// 1.  SVD Lz'*Ls = Uk * lambda_k^+ * Vk'.
	//
	// 2.  New scaling is
	//
	//         r[k] := r[k] * Ls * Vk * diag(lambda_k^+)^{-1/2}
	//         rti[k] := r[k] * Lz * Uk * diag(lambda_k^+)^{-1/2}.
	//

	maxr := 0
	for _, m := range W.At("r") {
		if m.Rows() > maxr {
			maxr = m.Rows()
		}
	}
	work := matrix.FloatZeros(maxr*maxr, 1)
	vlensum := 0
	for _, m := range W.At("v") {
		vlensum += m.NumElements()
	}
	ind = mnl + ml + vlensum
	ind2 := ind
	ind3 := 0
	rset := W.At("r")
	rtiset := W.At("rti")

	for k, _ := range rset {
		r := rset[k]
		rti := rtiset[k]
		m = r.Rows()
		//fmt.Printf("m=%d, r=\n%v\nrti=\n%v\n", m, r.ConvertToString(), rti.ConvertToString())

		// r := r*sk = r*Ls
		blas.GemmFloat(r, s, work, 1.0, 0.0, &la_.IOpt{"m", m}, &la_.IOpt{"n", m},
			&la_.IOpt{"k", m}, &la_.IOpt{"ldb", m}, &la_.IOpt{"ldc", m},
			&la_.IOpt{"offsetb", ind2})
		//fmt.Printf("1 work=\n%v\n", work.ConvertToString())
		blas.CopyFloat(work, r, &la_.IOpt{"n", m * m})

		// rti := rti*zk = rti*Lz
		blas.GemmFloat(rti, z, work, 1.0, 0.0, &la_.IOpt{"m", m}, &la_.IOpt{"n", m},
			&la_.IOpt{"k", m}, &la_.IOpt{"ldb", m}, &la_.IOpt{"ldc", m},
			&la_.IOpt{"offsetb", ind2})
		//fmt.Printf("2 work=\n%v\n", work.ConvertToString())
		blas.CopyFloat(work, rti, &la_.IOpt{"n", m * m})

		// SVD Lz'*Ls = U * lmbds^+ * V'; store U in sk and V' in zk. '
		blas.GemmFloat(z, s, work, 1.0, 0.0, la_.OptTransA, &la_.IOpt{"m", m},
			&la_.IOpt{"n", m}, &la_.IOpt{"k", m}, &la_.IOpt{"lda", m}, &la_.IOpt{"ldb", m},
			&la_.IOpt{"ldc", m}, &la_.IOpt{"offseta", ind2}, &la_.IOpt{"offsetb", ind2})
		//fmt.Printf("3 work=\n%v\n", work.ConvertToString())

		// U = s, Vt = z
		lapack.GesvdFloat(work, lmbda, s, z, la_.OptJobuAll, la_.OptJobvtAll,
			&la_.IOpt{"m", m}, &la_.IOpt{"n", m}, &la_.IOpt{"lda", m}, &la_.IOpt{"ldu", m},
			&la_.IOpt{"ldvt", m}, &la_.IOpt{"offsets", ind}, &la_.IOpt{"offsetu", ind2},
			&la_.IOpt{"offsetvt", ind2})

		// r := r*V
		blas.GemmFloat(r, z, work, 1.0, 0.0, la_.OptTransB, &la_.IOpt{"m", m},
			&la_.IOpt{"n", m}, &la_.IOpt{"k", m}, &la_.IOpt{"ldb", m}, &la_.IOpt{"ldc", m},
			&la_.IOpt{"offsetb", ind2})
		//fmt.Printf("4 work=\n%v\n", work.ConvertToString())
		blas.CopyFloat(work, r, &la_.IOpt{"n", m * m})

		// rti := rti*U
		blas.GemmFloat(rti, s, work, 1.0, 0.0, &la_.IOpt{"m", m}, &la_.IOpt{"n", m},
			&la_.IOpt{"k", m}, &la_.IOpt{"ldb", m}, &la_.IOpt{"ldc", m},
			&la_.IOpt{"offsetb", ind2})
		//fmt.Printf("5 work=\n%v\n", work.ConvertToString())
		blas.CopyFloat(work, rti, &la_.IOpt{"n", m * m})

		for i := 0; i < m; i++ {
			a := 1.0 / math.Sqrt(lmbda.GetIndex(ind+i))
			blas.ScalFloat(r, a, &la_.IOpt{"n", m}, &la_.IOpt{"offset", m * i})
			blas.ScalFloat(rti, a, &la_.IOpt{"n", m}, &la_.IOpt{"offset", m * i})
		}
		ind += m
		ind2 += m * m
		ind3 += m // !!NOT USED: ind3!!
	}

	//fmt.Printf("-- end of s:\nz=\n%v\nlmbda=\n%v\n", z.ConvertToString(), lmbda.ConvertToString())

	return

}
Esempio n. 26
0
/*
   Returns the Nesterov-Todd scaling W at points s and z, and stores the
   scaled variable in lmbda.

       W * z = W^{-T} * s = lmbda.

   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].

*/
func computeScaling(s, z, lmbda *matrix.FloatMatrix, dims *DimensionSet, mnl int) (W *FloatMatrixSet, err error) {
	/*DEBUGGED*/
	err = nil
	W = FloatSetNew("dnl", "dnli", "d", "di", "v", "beta", "r", "rti")

	// For the nonlinear block:
	//
	//     W['dnl'] = sqrt( s[:mnl] ./ z[:mnl] )
	//     W['dnli'] = sqrt( z[:mnl] ./ s[:mnl] )
	//     lambda[:mnl] = sqrt( s[:mnl] .* z[:mnl] )

	var stmp, ztmp, lmd *matrix.FloatMatrix
	if mnl > 0 {
		stmp = matrix.FloatVector(s.FloatArray()[:mnl])
		ztmp = matrix.FloatVector(z.FloatArray()[:mnl])
		dnl := stmp.Div(ztmp)
		dnl.Apply(dnl, math.Sqrt)
		dnli := dnl.Copy()
		dnli.Apply(dnli, func(a float64) float64 { return 1.0 / a })
		W.Set("dnl", dnl)
		W.Set("dnli", dnli)
		lmd = stmp.Mul(ztmp)
		lmd.Apply(lmd, math.Sqrt)
		lmbda.SetIndexes(matrix.MakeIndexSet(0, mnl, 1), lmd.FloatArray())
	} else {
		mnl = 0
	}

	// For the 'l' block:
	//
	//     W['d'] = sqrt( sk ./ zk )
	//     W['di'] = sqrt( zk ./ sk )
	//     lambdak = sqrt( sk .* zk )
	//
	// where sk and zk are the first dims['l'] entries of s and z.
	// lambda_k is stored in the first dims['l'] positions of lmbda.

	m := dims.At("l")[0]
	td := s.FloatArray()
	stmp = matrix.FloatVector(td[mnl : mnl+m])
	zd := z.FloatArray()
	//fmt.Printf("zdata=%v\n", zd[mnl:mnl+m])
	ztmp = matrix.FloatVector(zd[mnl : mnl+m])
	d := stmp.Div(ztmp)
	d.Apply(d, math.Sqrt)
	di := d.Copy()
	di.Apply(di, func(a float64) float64 { return 1.0 / a })
	//fmt.Printf("d:\n%v\n", d)
	//fmt.Printf("di:\n%v\n", di)
	W.Set("d", d)
	W.Set("di", di)
	lmd = stmp.Mul(ztmp)
	lmd.Apply(lmd, math.Sqrt)
	// lmd has indexes mnl:mnl+m and length of m
	lmbda.SetIndexes(matrix.MakeIndexSet(mnl, mnl+m, 1), lmd.FloatArray())
	//fmt.Printf("after l:\n%v\n", lmbda)

	/*
	   For the 'q' blocks, compute lists 'v', 'beta'.

	   The vector v[k] has unit hyperbolic norm:

	       (sqrt( v[k]' * J * v[k] ) = 1 with J = [1, 0; 0, -I]).

	   beta[k] is a positive scalar.

	   The hyperbolic Householder matrix H = 2*v[k]*v[k]' - J
	   defined by v[k] satisfies

	       (beta[k] * H) * zk  = (beta[k] * H) \ sk = lambda_k

	   where sk = s[indq[k]:indq[k+1]], zk = z[indq[k]:indq[k+1]].

	   lambda_k is stored in lmbda[indq[k]:indq[k+1]].
	*/
	ind := mnl + dims.At("l")[0]
	var beta *matrix.FloatMatrix

	for _, k := range dims.At("q") {
		W.Append("v", matrix.FloatZeros(k, 1))
	}
	beta = matrix.FloatZeros(len(dims.At("q")), 1)
	W.Set("beta", beta)
	vset := W.At("v")
	for k, m := range dims.At("q") {
		v := vset[k]
		// a = sqrt( sk' * J * sk )  where J = [1, 0; 0, -I]
		aa := jnrm2(s, m, ind)
		// b = sqrt( zk' * J * zk )
		bb := jnrm2(z, m, ind)
		// beta[k] = ( a / b )**1/2
		beta.SetIndex(k, math.Sqrt(aa/bb))
		// c = sqrt( (sk/a)' * (zk/b) + 1 ) / sqrt(2)
		c0 := blas.DotFloat(s, z, &la_.IOpt{"n", m},
			&la_.IOpt{"offsetx", ind}, &la_.IOpt{"offsety", ind})
		cc := math.Sqrt((c0/aa/bb + 1.0) / 2.0)

		// vk = 1/(2*c) * ( (sk/a) + J * (zk/b) )
		blas.CopyFloat(z, v, &la_.IOpt{"offsetx", ind}, &la_.IOpt{"n", m})
		blas.ScalFloat(v, -1.0/bb)
		v.SetIndex(0, -1.0*v.GetIndex(0))
		blas.AxpyFloat(s, v, 1.0/aa, &la_.IOpt{"offsetx", ind}, &la_.IOpt{"n", m})
		blas.ScalFloat(v, 1.0/2.0/cc)

		// v[k] = 1/sqrt(2*(vk0 + 1)) * ( vk + e ),  e = [1; 0]
		v.SetIndex(0, v.GetIndex(0)+1.0)
		blas.ScalFloat(v, (1.0 / math.Sqrt(2.0*v.GetIndex(0))))
		/*
		   To get the scaled variable lambda_k

		       d =  sk0/a + zk0/b + 2*c
		       lambda_k = [ c;
		                    (c + zk0/b)/d * sk1/a + (c + sk0/a)/d * zk1/b ]
		       lambda_k *= sqrt(a * b)
		*/
		lmbda.SetIndex(ind, cc)
		dd := 2*cc + s.GetIndex(ind)/aa + z.GetIndex(ind)/bb
		blas.CopyFloat(s, lmbda, &la_.IOpt{"offsetx", ind + 1}, &la_.IOpt{"offsety", ind + 1},
			&la_.IOpt{"n", m - 1})
		zz := (cc + z.GetIndex(ind)/bb) / dd / aa
		ss := (cc + s.GetIndex(ind)/aa) / dd / bb
		blas.ScalFloat(lmbda, zz, &la_.IOpt{"offset", ind + 1}, &la_.IOpt{"n", m - 1})
		blas.AxpyFloat(z, lmbda, ss, &la_.IOpt{"offsetx", ind + 1},
			&la_.IOpt{"offsety", ind + 1}, &la_.IOpt{"n", m - 1})
		blas.ScalFloat(lmbda, math.Sqrt(aa*bb), &la_.IOpt{"offset", ind}, &la_.IOpt{"n", m})

		ind += m
		//fmt.Printf("after q[%d]:\n%v\n", k, lmbda)
	}
	/*
	   For the 's' blocks: compute two lists 'r' and 'rti'.

	       r[k]' * sk^{-1} * r[k] = diag(lambda_k)^{-1}
	       r[k]' * zk * r[k] = diag(lambda_k)

	   where sk and zk are the entries inds[k] : inds[k+1] of
	   s and z, reshaped into symmetric matrices.

	   rti[k] is the inverse of r[k]', so

	       rti[k]' * sk * rti[k] = diag(lambda_k)^{-1}
	       rti[k]' * zk^{-1} * rti[k] = diag(lambda_k).

	   The vectors lambda_k are stored in

	       lmbda[ dims['l'] + sum(dims['q']) : -1 ]
	*/
	for _, k := range dims.At("s") {
		W.Append("r", matrix.FloatZeros(k, k))
		W.Append("rti", matrix.FloatZeros(k, k))
	}
	maxs := maxdim(dims.At("s"))
	work := matrix.FloatZeros(maxs*maxs, 1)
	Ls := matrix.FloatZeros(maxs*maxs, 1)
	Lz := matrix.FloatZeros(maxs*maxs, 1)
	ind2 := ind
	for k, m := range dims.At("s") {
		r := W.At("r")[k]
		rti := W.At("rti")[k]

		// Factor sk = Ls*Ls'; store Ls in ds[inds[k]:inds[k+1]].
		blas.CopyFloat(s, Ls, &la_.IOpt{"offsetx", ind2}, &la_.IOpt{"n", m * m})
		lapack.PotrfFloat(Ls, &la_.IOpt{"n", m}, &la_.IOpt{"lda", m})

		// Factor zs[k] = Lz*Lz'; store Lz in dz[inds[k]:inds[k+1]].
		blas.CopyFloat(z, Lz, &la_.IOpt{"offsetx", ind2}, &la_.IOpt{"n", m * m})
		lapack.PotrfFloat(Lz, &la_.IOpt{"n", m}, &la_.IOpt{"lda", m})

		// SVD Lz'*Ls = U*diag(lambda_k)*V'.  Keep U in work.
		for i := 0; i < m; i++ {
			blas.ScalFloat(Ls, 0.0, &la_.IOpt{"offset", i * m}, &la_.IOpt{"n", i})
		}
		blas.CopyFloat(Ls, work, &la_.IOpt{"n", m * m})
		blas.TrmmFloat(Lz, work, 1.0, la_.OptTransA, &la_.IOpt{"lda", m}, &la_.IOpt{"ldb", m},
			&la_.IOpt{"n", m}, &la_.IOpt{"m", m})
		lapack.GesvdFloat(work, lmbda, nil, nil,
			la_.OptJobuO, &la_.IOpt{"lda", m}, &la_.IOpt{"offsetS", ind},
			&la_.IOpt{"n", m}, &la_.IOpt{"m", m})

		// r = Lz^{-T} * U
		blas.CopyFloat(work, r, &la_.IOpt{"n", m * m})
		blas.TrsmFloat(Lz, r, 1.0, la_.OptTransA,
			&la_.IOpt{"lda", m}, &la_.IOpt{"n", m}, &la_.IOpt{"m", m})

		// rti = Lz * U
		blas.CopyFloat(work, rti, &la_.IOpt{"n", m * m})
		blas.TrmmFloat(Lz, rti, 1.0,
			&la_.IOpt{"lda", m}, &la_.IOpt{"n", m}, &la_.IOpt{"m", m})

		// r := r * diag(sqrt(lambda_k))
		// rti := rti * diag(1 ./ sqrt(lambda_k))
		for i := 0; i < m; i++ {
			a := math.Sqrt(lmbda.GetIndex(ind + i))
			blas.ScalFloat(r, a, &la_.IOpt{"offset", m * i}, &la_.IOpt{"n", m})
			blas.ScalFloat(rti, 1.0/a, &la_.IOpt{"offset", m * i}, &la_.IOpt{"n", m})
		}
		ind += m
		ind2 += m * m
	}
	return
}
Esempio n. 27
0
/*
   Evaluates

       x := H(lambda^{1/2}) * x   (inverse is 'N')
       x := H(lambda^{-1/2}) * x  (inverse is 'I').

   H is the Hessian of the logarithmic barrier.

*/
func scale2(lmbda, x *matrix.FloatMatrix, dims *DimensionSet, mnl int, inverse bool) (err error) {
	err = nil

	// For the nonlinear and 'l' blocks,
	//
	//     xk := xk ./ l   (inverse is 'N')
	//     xk := xk .* l   (inverse is 'I')
	//
	// where l is lmbda[:mnl+dims['l']].
	ind := mnl + dims.Sum("l")
	if !inverse {
		blas.TbsvFloat(lmbda, x, &la_.IOpt{"n", ind}, &la_.IOpt{"k", 0}, &la_.IOpt{"lda", 1})
	} else {
		blas.TbmvFloat(lmbda, x, &la_.IOpt{"n", ind}, &la_.IOpt{"k", 0}, &la_.IOpt{"lda", 1})
	}

	// For 'q' blocks, if inverse is 'N',
	//
	//     xk := 1/a * [ l'*J*xk;
	//         xk[1:] - (xk[0] + l'*J*xk) / (l[0] + 1) * l[1:] ].
	//
	// If inverse is 'I',
	//
	//     xk := a * [ l'*xk;
	//         xk[1:] + (xk[0] + l'*xk) / (l[0] + 1) * l[1:] ].
	//
	// a = sqrt(lambda_k' * J * lambda_k), l = lambda_k / a.
	for _, m := range dims.At("q") {
		var lx, a, c, x0 float64
		a = jnrm2(lmbda, m, ind) //&la_.IOpt{"n", m}, &la_.IOpt{"offset", ind})
		if !inverse {
			lx = jdot(lmbda, x, m, ind, ind) //&la_.IOpt{"n", m}, &la_.IOpt{"offsetx", ind},
			//&la_.IOpt{"offsety", ind})
			lx /= a
		} else {
			lx = blas.DotFloat(lmbda, x, &la_.IOpt{"n", m}, &la_.IOpt{"offsetx", ind},
				&la_.IOpt{"offsety", ind})
			lx /= a
		}
		x0 = x.GetIndex(ind)
		x.SetIndex(ind, lx)
		c = (lx + x0) / (lmbda.GetIndex(ind)/a + 1.0) / a
		if !inverse {
			c *= -1.0
		}
		blas.AxpyFloat(lmbda, x, c, &la_.IOpt{"n", m - 1}, &la_.IOpt{"offsetx", ind + 1},
			&la_.IOpt{"offsety", ind + 1})
		if !inverse {
			a = 1.0 / a
		}
		blas.ScalFloat(x, a, &la_.IOpt{"offset", ind}, &la_.IOpt{"n", m})
		ind += m
	}
	// For the 's' blocks, if inverse is 'N',
	//
	//     xk := vec( diag(l)^{-1/2} * mat(xk) * diag(k)^{-1/2}).
	//
	// If inverse is true,
	//
	//     xk := vec( diag(l)^{1/2} * mat(xk) * diag(k)^{1/2}).
	//
	// where l is kth block of lambda.
	//
	// We scale upper and lower triangular part of mat(xk) because the
	// inverse operation will be applied to nonsymmetric matrices.
	ind2 := ind
	sdims := dims.At("s")
	for k := 0; k < len(sdims); k++ {
		m := sdims[k]
		scaleF := func(v, x float64) float64 {
			return math.Sqrt(v) * math.Sqrt(x)
		}
		for j := 0; j < m; j++ {
			c := matrix.FloatVector(lmbda.FloatArray()[ind2 : ind2+m])
			c.ApplyConst(c, scaleF, lmbda.GetIndex(ind2+j))
			if !inverse {
				blas.Tbsv(c, x, &la_.IOpt{"n", m}, &la_.IOpt{"k", 0}, &la_.IOpt{"lda", 1},
					&la_.IOpt{"offsetx", ind + j*m})
			} else {
				blas.Tbmv(c, x, &la_.IOpt{"n", m}, &la_.IOpt{"k", 0}, &la_.IOpt{"lda", 1},
					&la_.IOpt{"offsetx", ind + j*m})
			}
		}
		ind += m * m
		ind2 += m
	}
	return
}