Golang DimensionSet.Sum方法代码示例

// In-place version of pack(), which also accepts matrix arguments x.
// The columns of x are elements of S, with the 's' components stored
// in unpacked storage.  On return, the 's' components are stored in
// packed storage and the off-diagonal entries are scaled by sqrt(2).
//
func pack2(x *matrix.FloatMatrix, dims *sets.DimensionSet, mnl int) (err error) {
	if len(dims.At("s")) == 0 {
		return nil
	}

	const sqrt2 = 1.41421356237309504880

	iu := mnl + dims.Sum("l", "q")
	ip := iu
	row := matrix.FloatZeros(1, x.Cols())
	//fmt.Printf("x.size = %d %d\n", x.Rows(), x.Cols())
	for _, n := range dims.At("s") {
		for k := 0; k < n; k++ {
			cnt := n - k
			row = x.GetRow(iu+(n+1)*k, row)
			//fmt.Printf("%02d: %v\n", iu+(n+1)*k, x.FloatArray())
			x.SetRow(ip, row)
			for i := 1; i < n-k; i++ {
				row = x.GetRow(iu+(n+1)*k+i, row)
				//fmt.Printf("%02d: %v\n", iu+(n+1)*k+i, x.FloatArray())
				x.SetRow(ip+i, row.Scale(sqrt2))
			}
			ip += cnt
		}
		iu += n * n
	}
	return nil
}

/*
   Matrix-vector multiplication.

   A is a matrix or spmatrix of size (m, n) where

       N = dims['l'] + sum(dims['q']) + sum( k**2 for k in dims['s'] )

   representing a mapping from R^n to S.

   If trans is 'N':

       y := alpha*A*x + beta * y   (trans = 'N').

   x is a vector of length n.  y is a vector of length N.

   If trans is 'T':

       y := alpha*A'*x + beta * y  (trans = 'T').

   x is a vector of length N.  y is a vector of length n.

   The 's' components in S are stored in unpacked 'L' storage.
*/
func sgemv(A, x, y *matrix.FloatMatrix, alpha, beta float64, dims *sets.DimensionSet, opts ...la_.Option) error {

	m := dims.Sum("l", "q") + dims.SumSquared("s")
	n := la_.GetIntOpt("n", -1, opts...)
	if n == -1 {
		n = A.Cols()
	}
	trans := la_.GetIntOpt("trans", int(la_.PNoTrans), opts...)
	offsetX := la_.GetIntOpt("offsetx", 0, opts...)
	offsetY := la_.GetIntOpt("offsety", 0, opts...)
	offsetA := la_.GetIntOpt("offseta", 0, opts...)

	if trans == int(la_.PTrans) && alpha != 0.0 {
		trisc(x, dims, offsetX)
		//fmt.Printf("trisc x=\n%v\n", x.ConvertToString())
	}
	//fmt.Printf("alpha=%.4f beta=%.4f m=%d n=%d\n", alpha, beta, m, n)
	//fmt.Printf("A=\n%v\nx=\n%v\ny=\n%v\n", A, x.ConvertToString(), y.ConvertToString())
	err := blas.GemvFloat(A, x, y, alpha, beta, &la_.IOpt{"trans", trans},
		&la_.IOpt{"n", n}, &la_.IOpt{"m", m}, &la_.IOpt{"offseta", offsetA},
		&la_.IOpt{"offsetx", offsetX}, &la_.IOpt{"offsety", offsetY})
	//fmt.Printf("gemv y=\n%v\n", y.ConvertToString())

	if trans == int(la_.PTrans) && alpha != 0.0 {
		triusc(x, dims, offsetX)
	}
	return err
}

/*
   Copy x to y using packed storage.

   The vector x is an element of S, with the 's' components stored in
   unpacked storage.  On return, x is copied to y with the 's' components
   stored in packed storage and the off-diagonal entries scaled by
   sqrt(2).
*/
func pack(x, y *matrix.FloatMatrix, dims *sets.DimensionSet, opts ...la_.Option) (err error) {
	/*DEBUGGED*/
	err = nil
	mnl := la_.GetIntOpt("mnl", 0, opts...)
	offsetx := la_.GetIntOpt("offsetx", 0, opts...)
	offsety := la_.GetIntOpt("offsety", 0, opts...)

	nlq := mnl + dims.At("l")[0] + dims.Sum("q")
	blas.Copy(x, y, &la_.IOpt{"n", nlq}, &la_.IOpt{"offsetx", offsetx},
		&la_.IOpt{"offsety", offsety})

	iu, ip := offsetx+nlq, offsety+nlq
	for _, n := range dims.At("s") {
		for k := 0; k < n; k++ {
			blas.Copy(x, y, &la_.IOpt{"n", n - k}, &la_.IOpt{"offsetx", iu + k*(n+1)},
				&la_.IOpt{"offsety", ip})
			y.SetIndex(ip, (y.GetIndex(ip) / math.Sqrt(2.0)))
			ip += n - k
		}
		iu += n * n
	}
	np := dims.SumPacked("s")
	blas.ScalFloat(y, math.Sqrt(2.0), &la_.IOpt{"n", np}, &la_.IOpt{"offset", offsety + nlq})
	return
}

// 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 *sets.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 {
			Q := matrix.FloatZeros(m, m)
			w := matrix.FloatZeros(m, 1)
			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 && err == nil {
				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
}

/*
   Scales the strictly lower triangular part of the 's' components of x
   by 0.5.

*/
func triusc(x *matrix.FloatMatrix, dims *sets.DimensionSet, offset int) error {

	//m := dims.Sum("l", "q") + dims.SumSquared("s")
	ind := offset + dims.Sum("l", "q")

	for _, mk := range dims.At("s") {
		for j := 1; j < mk; j++ {
			blas.ScalFloat(x, 0.5, &la_.IOpt{"n", mk - j}, &la_.IOpt{"offset", ind + mk*(j-1) + j})
		}
		ind += mk * mk
	}
	return nil
}

// Inner product of two vectors in S.
func sdot(x, y *matrix.FloatMatrix, dims *sets.DimensionSet, mnl int) float64 {
	/*DEBUGGED*/
	ind := mnl + dims.At("l")[0] + dims.Sum("q")
	a := blas.DotFloat(x, y, &la_.IOpt{"n", ind})
	for _, m := range dims.At("s") {
		a += blas.DotFloat(x, y, &la_.IOpt{"offsetx", ind}, &la_.IOpt{"offsety", ind},
			&la_.IOpt{"incx", m + 1}, &la_.IOpt{"incy", m + 1}, &la_.IOpt{"n", m})
		for j := 1; j < m; j++ {
			a += 2.0 * blas.DotFloat(x, y, &la_.IOpt{"offsetx", ind + j}, &la_.IOpt{"offsety", ind + j},
				&la_.IOpt{"incx", m + 1}, &la_.IOpt{"incy", m + 1}, &la_.IOpt{"n", m - j})
		}
		ind += m * m
	}
	return a
}

/*
   Sets upper triangular part of the 's' components of x equal to zero
   and scales the strictly lower triangular part by 2.0.
*/
func trisc(x *matrix.FloatMatrix, dims *sets.DimensionSet, offset int) error {

	//m := dims.Sum("l", "q") + dims.SumSquared("s")
	ind := offset + dims.Sum("l", "q")

	for _, mk := range dims.At("s") {
		for j := 1; j < mk; j++ {
			blas.ScalFloat(x, 0.0, la_.IntOpt("n", mk-j), la_.IntOpt("inc", mk),
				la_.IntOpt("offset", ind+j*(mk+1)-1))
			blas.ScalFloat(x, 2.0, la_.IntOpt("n", mk-j), la_.IntOpt("offset", ind+mk*(j-1)+j))
		}
		ind += mk * mk
	}
	return nil
}

// Here problem is already translated to epigraph format except original convex problem.
// We wrap it and create special CP epigraph kktsolver.
func cp_problem(F ConvexProg, c MatrixVariable, G MatrixVarG, h *matrix.FloatMatrix, A MatrixVarA,
	b MatrixVariable, dims *sets.DimensionSet, kktsolver KKTCpSolver,
	solopts *SolverOptions, x0 *matrix.FloatMatrix, mnl int) (sol *Solution, err error) {

	err = nil

	F_e := &cpProg{F}

	//mx0 := newEpigraph(x0, 0.0)
	cdim := dims.Sum("l", "q") + dims.SumSquared("s")
	ux := x0.Copy()
	uz := matrix.FloatZeros(mnl+cdim, 1)

	kktsolver_e := func(W *sets.FloatMatrixSet, xa MatrixVariable, znl *matrix.FloatMatrix) (KKTFuncVar, error) {
		x, x_ok := xa.(*epigraph)
		_ = x_ok
		We := W.Copy()
		// dnl is matrix
		dnl := W.At("dnl")[0]
		dnli := W.At("dnli")[0]
		We.Set("dnl", matrix.FloatVector(dnl.FloatArray()[1:]))
		We.Set("dnli", matrix.FloatVector(dnli.FloatArray()[1:]))
		g, err := kktsolver(We, x.m(), znl)
		_, Df, _ := F.F1(x.m())
		gradf0 := Df.GetRow(0, nil).Transpose()

		solve := func(xa, ya MatrixVariable, z *matrix.FloatMatrix) (err error) {
			x, x_ok := xa.(*epigraph)
			_ = x_ok // TODO: remove or use x_ok
			y := ya.Matrix()
			err = nil
			a := z.GetIndex(0)
			blas.Copy(x.m(), ux)
			blas.AxpyFloat(gradf0, ux, x.t())
			blas.Copy(z, uz, &la.IOpt{"offsetx", 1})
			err = g(ux, y, uz)
			z.SetIndex(0, -x.t()*dnl.GetIndex(0))
			blas.Copy(uz, z, &la.IOpt{"offsety", 1})
			blas.Copy(ux, x.m())
			val := blas.DotFloat(gradf0, x.m()) + dnl.GetIndex(0)*dnl.GetIndex(0)*x.t() - a
			x.set(val)
			return
		}
		return solve, err
	}
	return cpl_solver(F_e, c, G, h, A, b, dims, kktsolver_e, solopts, nil, mnl)
}

// The product x := y o y.   The 's' components of y are diagonal and
// only the diagonals of x and y are stored.
func ssqr(x, y *matrix.FloatMatrix, dims *sets.DimensionSet, mnl int) (err error) {
	/*DEBUGGED*/
	blas.Copy(y, x)
	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
	}

	for _, m := range dims.At("q") {
		v := blas.Nrm2Float(y, &la_.IOpt{"n", m}, &la_.IOpt{"offset", ind})
		x.SetIndex(ind, v*v)
		blas.ScalFloat(x, 2.0*y.GetIndex(ind), &la_.IOpt{"n", m - 1}, &la_.IOpt{"offset", ind + 1})
		ind += m
	}
	err = blas.Tbmv(y, x, &la_.IOpt{"n", dims.Sum("s")}, &la_.IOpt{"k", 0},
		&la_.IOpt{"lda", 1}, &la_.IOpt{"offseta", ind}, &la_.IOpt{"offsetx", ind})
	return
}

/*
   The vector x is an element of S, with the 's' components stored
   in unpacked storage and off-diagonal entries scaled by sqrt(2).
   On return, x is copied to y with the 's' components stored in
   unpacked storage.

*/
func unpack(x, y *matrix.FloatMatrix, dims *sets.DimensionSet, opts ...la_.Option) (err error) {
	/*DEBUGGED*/
	err = nil
	mnl := la_.GetIntOpt("mnl", 0, opts...)
	offsetx := la_.GetIntOpt("offsetx", 0, opts...)
	offsety := la_.GetIntOpt("offsety", 0, opts...)

	nlq := mnl + dims.At("l")[0] + dims.Sum("q")
	err = blas.Copy(x, y, &la_.IOpt{"n", nlq}, &la_.IOpt{"offsetx", offsetx},
		&la_.IOpt{"offsety", offsety})
	if err != nil {
		return
	}

	ip, iu := offsetx+nlq, offsety+nlq
	for _, n := range dims.At("s") {
		for k := 0; k < n; k++ {
			err = blas.Copy(x, y, &la_.IOpt{"n", n - k}, &la_.IOpt{"offsetx", ip},
				&la_.IOpt{"offsety", iu + k*(n+1)})
			if err != nil {
				return
			}

			ip += n - k
			blas.ScalFloat(y, 1.0/math.Sqrt(2.0),
				&la_.IOpt{"n", n - k - 1}, &la_.IOpt{"offset", iu + k*(n+1) + 1})
		}
		iu += n * n
	}
	/*
		nu := dims.SumSquared("s")
		fmt.Printf("-- UnPack: nu=%d, offset=%d\n", nu, offsety+nlq)
		err = blas.ScalFloat(y,
			&la_.IOpt{"n", nu}, &la_.IOpt{"offset", offsety+nlq})
	*/
	return
}

// Solves a convex optimization problem with a linear objective
//
//       minimize    f0(x)
//       subject to  fk(x) <= 0, k = 1, ..., mnl
//                   G*x   <= h
//                   A*x    = b.
//
// using custom solver for KKT equations.
//
func CpCustomKKT(F ConvexProg, G, h, A, b *matrix.FloatMatrix, dims *sets.DimensionSet,
	kktsolver KKTCpSolver, solopts *SolverOptions) (sol *Solution, err error) {

	var mnl int
	var x0 *matrix.FloatMatrix

	mnl, x0, err = F.F0()
	if err != nil {
		return
	}

	if x0.Cols() != 1 {
		err = errors.New("'x0' must be matrix with one column")
		return
	}
	if h == nil {
		h = matrix.FloatZeros(0, 1)
	}
	if h.Cols() > 1 {
		err = errors.New("'h' must be matrix with 1 column")
		return
	}

	if dims == nil {
		dims = sets.NewDimensionSet("l", "q", "s")
		dims.Set("l", []int{h.Rows()})
	}
	if err = checkConeLpDimensions(dims); err != nil {
		return
	}
	cdim := dims.Sum("l", "q") + dims.SumSquared("s")

	if h.Rows() != cdim {
		err = errors.New(fmt.Sprintf("'h' must be float matrix of size (%d,1)", cdim))
		return
	}

	if G == nil {
		G = matrix.FloatZeros(0, x0.Rows())
	}
	if !G.SizeMatch(cdim, x0.Rows()) {
		estr := fmt.Sprintf("'G' must be of size (%d,%d)", cdim, x0.Rows())
		err = errors.New(estr)
		return
	}

	// Check A and set defaults if it is nil
	if A == nil {
		// zeros rows reduces Gemv to vector products
		A = matrix.FloatZeros(0, x0.Rows())
	}
	if A.Cols() != x0.Rows() {
		estr := fmt.Sprintf("'A' must have %d columns", x0.Rows())
		err = errors.New(estr)
		return
	}

	// Check b and set defaults if it is nil
	if b == nil {
		b = matrix.FloatZeros(0, 1)
	}
	if b.Cols() != 1 {
		estr := fmt.Sprintf("'b' must be a matrix with 1 column")
		err = errors.New(estr)
		return
	}
	if b.Rows() != A.Rows() {
		estr := fmt.Sprintf("'b' must have length %d", A.Rows())
		err = errors.New(estr)
		return
	}

	if kktsolver == nil {
		err = errors.New("'kktsolver' must be non-nil function.")
		return
	}

	c_e := newEpigraph(x0, 1.0)
	blas.ScalFloat(x0, 0.0)
	G_e := epMatrixG{G, dims}
	A_e := epMatrixA{A}
	b_e := matrixVar{b}

	return cp_problem(F, c_e, &G_e, h, &A_e, &b_e, dims, kktsolver, solopts, x0, mnl)
}

//    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() {
//.........这里部分代码省略.........

// Internal CPL solver for CP and CLP problems. Everything is wrapped to proper interfaces
func cpl_solver(F ConvexVarProg, c MatrixVariable, G MatrixVarG, h *matrix.FloatMatrix,
	A MatrixVarA, b MatrixVariable, dims *sets.DimensionSet, kktsolver KKTCpSolverVar,
	solopts *SolverOptions, x0 MatrixVariable, mnl int) (sol *Solution, err error) {

	const (
		STEP              = 0.99
		BETA              = 0.5
		ALPHA             = 0.01
		EXPON             = 3
		MAX_RELAXED_ITERS = 8
	)

	var refinement int

	sol = &Solution{Unknown,
		nil,
		0.0, 0.0, 0.0, 0.0, 0.0,
		0.0, 0.0, 0.0, 0.0, 0.0, 0}

	feasTolerance := FEASTOL
	absTolerance := ABSTOL
	relTolerance := RELTOL
	maxIter := MAXITERS
	if solopts.FeasTol > 0.0 {
		feasTolerance = solopts.FeasTol
	}
	if solopts.AbsTol > 0.0 {
		absTolerance = solopts.AbsTol
	}
	if solopts.RelTol > 0.0 {
		relTolerance = solopts.RelTol
	}
	if solopts.Refinement > 0 {
		refinement = solopts.Refinement
	} else {
		refinement = 1
	}
	if solopts.MaxIter > 0 {
		maxIter = solopts.MaxIter
	}

	if x0 == nil {
		mnl, x0, err = F.F0()
		if err != nil {
			return
		}
	}

	if c == nil {
		err = errors.New("Must define objective.")
		return
	}

	if h == nil {
		h = matrix.FloatZeros(0, 1)
	}
	if dims == nil {
		err = errors.New("Problem dimensions not defined.")
		return
	}
	if err = checkConeLpDimensions(dims); err != nil {
		return
	}

	cdim := dims.Sum("l", "q") + dims.SumSquared("s")
	cdim_diag := dims.Sum("l", "q", "s")

	if h.Rows() != cdim {
		err = errors.New(fmt.Sprintf("'h' must be float matrix of size (%d,1)", cdim))
		return
	}

	if G == nil {
		err = errors.New("'G' must be non-nil MatrixG interface.")
		return
	}
	fG := func(x, y MatrixVariable, alpha, beta float64, trans la.Option) error {
		return G.Gf(x, y, alpha, beta, trans)
	}

	// Check A and set defaults if it is nil
	if A == nil {
		err = errors.New("'A' must be non-nil MatrixA interface.")
		return
	}
	fA := func(x, y MatrixVariable, alpha, beta float64, trans la.Option) error {
		return A.Af(x, y, alpha, beta, trans)
	}

	if b == nil {
		err = errors.New("'b' must be non-nil MatrixVariable interface.")
		return
	}

	if kktsolver == nil {
		err = errors.New("nil kktsolver not allowed.")
		return
	}

//.........这里部分代码省略.........

// Solves a convex optimization problem with a linear objective
//
//        minimize    c'*x
//        subject to  f(x) <= 0
//                    G*x <= h
//                    A*x = b.
//
// using custom KTT equation solver.
//
func CplCustomKKT(F ConvexProg, c *matrix.FloatMatrix, G, h, A, b *matrix.FloatMatrix,
	dims *sets.DimensionSet, kktsolver KKTCpSolver,
	solopts *SolverOptions) (sol *Solution, err error) {

	var mnl int
	var x0 *matrix.FloatMatrix

	mnl, x0, err = F.F0()
	if err != nil {
		return
	}

	if x0.Cols() != 1 {
		err = errors.New("'x0' must be matrix with one column")
		return
	}
	if c == nil {
		err = errors.New("'c' must be non nil matrix")
		return
	}
	if !c.SizeMatch(x0.Size()) {
		err = errors.New(fmt.Sprintf("'c' must be matrix of size (%d,1)", x0.Rows()))
		return
	}

	if h == nil {
		h = matrix.FloatZeros(0, 1)
	}
	if h.Cols() > 1 {
		err = errors.New("'h' must be matrix with 1 column")
		return
	}

	if dims == nil {
		dims = sets.NewDimensionSet("l", "q", "s")
		dims.Set("l", []int{h.Rows()})
	}

	cdim := dims.Sum("l", "q") + dims.SumSquared("s")

	if h.Rows() != cdim {
		err = errors.New(fmt.Sprintf("'h' must be float matrix of size (%d,1)", cdim))
		return
	}

	if G == nil {
		G = matrix.FloatZeros(0, c.Rows())
	}
	if !G.SizeMatch(cdim, c.Rows()) {
		estr := fmt.Sprintf("'G' must be of size (%d,%d)", cdim, c.Rows())
		err = errors.New(estr)
		return
	}

	// Check A and set defaults if it is nil
	if A == nil {
		// zeros rows reduces Gemv to vector products
		A = matrix.FloatZeros(0, c.Rows())
	}
	if A.Cols() != c.Rows() {
		estr := fmt.Sprintf("'A' must have %d columns", c.Rows())
		err = errors.New(estr)
		return
	}

	// Check b and set defaults if it is nil
	if b == nil {
		b = matrix.FloatZeros(0, 1)
	}
	if b.Cols() != 1 {
		estr := fmt.Sprintf("'b' must be a matrix with 1 column")
		err = errors.New(estr)
		return
	}
	if b.Rows() != A.Rows() {
		estr := fmt.Sprintf("'b' must have length %d", A.Rows())
		err = errors.New(estr)
		return
	}

	var mc = matrixVar{c}
	var mb = matrixVar{b}
	var mA = matrixVarA{A}
	var mG = matrixVarG{G, dims}

	return cpl_problem(F, &mc, &mG, h, &mA, &mb, dims, kktsolver, solopts, x0, mnl)
}

// Solves a convex optimization problem with a linear objective
//
//       minimize    f0(x)
//       subject to  fk(x) <= 0, k = 1, ..., mnl
//                   G*x   <= h
//                   A*x    = b.
//
// f is vector valued, convex and twice differentiable.  The linear
// inequalities are with respect to a cone C defined as the Cartesian
// product of N + M + 1 cones:
//
//        C = C_0 x C_1 x .... x C_N x C_{N+1} x ... x C_{N+M}.
//
// The first cone C_0 is the nonnegative orthant of dimension ml.  The
// next N cones are second order cones of dimension r[0], ..., r[N-1].
// The second order cone of dimension m is defined as
//
//        { (u0, u1) in R x R^{m-1} | u0 >= ||u1||_2 }.
//
// The next M cones are positive semidefinite cones of order t[0], ..., t[M-1] >= 0.
//
// The structure of C is specified by DimensionSet dims which holds following sets
//
//   dims.At("l")  l, the dimension of the nonnegative orthant (array of length 1)
//   dims.At("q")  r[0], ... r[N-1], list with the dimesions of the second-order cones
//   dims.At("s")  t[0], ... t[M-1], array with the dimensions of the positive
//                 semidefinite cones
//
// The default value for dims is l: []int{h.Rows()}, q: []int{}, s: []int{}.
//
// On exit Solution contains the result and information about the accurancy of the
// solution. if SolutionStatus is Optimal then Solution.Result contains solutions
// for the problems.
//
//   Result.At("x")[0]    primal solution
//   Result.At("snl")[0]  non-linear constraint slacks
//   Result.At("sl")[0]   linear constraint slacks
//   Result.At("y")[0]    values for linear equality constraints y
//   Result.At("znl")[0]  values of dual variables for nonlinear inequalities
//   Result.At("zl")[0]   values of dual variables for linear inequalities
//
// If err is non-nil then sol is nil and err contains information about the argument or
// computation error.
//
func Cp(F ConvexProg, G, h, A, b *matrix.FloatMatrix, dims *sets.DimensionSet, solopts *SolverOptions) (sol *Solution, err error) {

	var mnl int
	var x0 *matrix.FloatMatrix

	mnl, x0, err = F.F0()
	if err != nil {
		return
	}

	if x0.Cols() != 1 {
		err = errors.New("'x0' must be matrix with one column")
		return
	}
	if h == nil {
		h = matrix.FloatZeros(0, 1)
	}
	if h.Cols() > 1 {
		err = errors.New("'h' must be matrix with 1 column")
		return
	}

	if dims == nil {
		dims = sets.NewDimensionSet("l", "q", "s")
		dims.Set("l", []int{h.Rows()})
	}
	if err = checkConeLpDimensions(dims); err != nil {
		return
	}
	cdim := dims.Sum("l", "q") + dims.SumSquared("s")

	if h.Rows() != cdim {
		err = errors.New(fmt.Sprintf("'h' must be float matrix of size (%d,1)", cdim))
		return
	}

	if G == nil {
		G = matrix.FloatZeros(0, x0.Rows())
	}
	if !G.SizeMatch(cdim, x0.Rows()) {
		estr := fmt.Sprintf("'G' must be of size (%d,%d)", cdim, x0.Rows())
		err = errors.New(estr)
		return
	}

	// Check A and set defaults if it is nil
	if A == nil {
		// zeros rows reduces Gemv to vector products
		A = matrix.FloatZeros(0, x0.Rows())
	}
	if A.Cols() != x0.Rows() {
		estr := fmt.Sprintf("'A' must have %d columns", x0.Rows())
		err = errors.New(estr)
		return
	}

//.........这里部分代码省略.........