Golang Dense.SetCol方法代码示例

//.........这里部分代码省略.........
	r := make([]float64, n-m)
	move := make([]float64, m)

	// Solve the linear program starting from the initial feasible set. This is
	// the "Phase 2" problem.
	//
	// Algorithm:
	// 1) Compute the "reduced costs" for the non-basic variables. The reduced
	// costs are the lagrange multipliers of the constraints.
	// 	 r = cn - an^T * ab^-T * cb
	// 2) If all of the reduced costs are positive, no improvement is possible,
	// and the solution is optimal (xn can only increase because of
	// non-negativity constraints). Otherwise, the solution can be improved and
	// one element will be exchanged in the basic set.
	// 3) Choose the x_n with the most negative value of r. Call this value xe.
	// This variable will be swapped into the basic set.
	// 4) Increase xe until the next constraint boundary is met. This will happen
	// when the first element in xb becomes 0. The distance xe can increase before
	// a given element in xb becomes negative can be found from
	//	xb = Ab^-1 b - Ab^-1 An xn
	//     = Ab^-1 b - Ab^-1 Ae xe
	//     = bhat + d x_e
	//  xe = bhat_i / - d_i
	// where Ae is the column of A corresponding to xe.
	// The constraining basic index is the first index for which this is true,
	// so remove the element which is min_i (bhat_i / -d_i), assuming d_i is negative.
	// If no d_i is less than 0, then the problem is unbounded.
	// 5) If the new xe is 0 (that is, bhat_i == 0), then this location is at
	// the intersection of several constraints. Use the Bland rule instead
	// of the rule in step 4 to avoid cycling.
	for {
		// Compute reduced costs -- r = cn - an^T ab^-T cb
		var tmp mat64.Vector
		err = tmp.SolveVec(ab.T(), cbVec)
		if err != nil {
			break
		}
		data := make([]float64, n-m)
		tmp2 := mat64.NewVector(n-m, data)
		tmp2.MulVec(an.T(), &tmp)
		floats.SubTo(r, cn, data)

		// Replace the most negative element in the simplex. If there are no
		// negative entries then the optimal solution has been found.
		minIdx := floats.MinIdx(r)
		if r[minIdx] >= -tol {
			break
		}

		for i, v := range r {
			if math.Abs(v) < rRoundTol {
				r[i] = 0
			}
		}

		// Compute the moving distance.
		err = computeMove(move, minIdx, A, ab, xb, nonBasicIdx)
		if err != nil {
			if err == ErrUnbounded {
				return math.Inf(-1), nil, nil, ErrUnbounded
			}
			break
		}

		// Replace the basic index along the tightest constraint.
		replace := floats.MinIdx(move)
		if move[replace] <= 0 {
			replace, minIdx, err = replaceBland(A, ab, xb, basicIdxs, nonBasicIdx, r, move)
			if err != nil {
				if err == ErrUnbounded {
					return math.Inf(-1), nil, nil, ErrUnbounded
				}
				break
			}
		}

		// Replace the constrained basicIdx with the newIdx.
		basicIdxs[replace], nonBasicIdx[minIdx] = nonBasicIdx[minIdx], basicIdxs[replace]
		cb[replace], cn[minIdx] = cn[minIdx], cb[replace]
		tmpCol1 := mat64.Col(nil, replace, ab)
		tmpCol2 := mat64.Col(nil, minIdx, an)
		ab.SetCol(replace, tmpCol2)
		an.SetCol(minIdx, tmpCol1)

		// Compute the new xb.
		xbVec := mat64.NewVector(len(xb), xb)
		err = xbVec.SolveVec(ab, bVec)
		if err != nil {
			break
		}
	}
	// Found the optimum successfully or died trying. The basic variables get
	// their values, and the non-basic variables are all zero.
	opt := floats.Dot(cb, xb)
	xopt := make([]float64, n)
	for i, v := range basicIdxs {
		xopt[v] = xb[i]
	}
	return opt, xopt, basicIdxs, err
}