示例#1
0
func main() {

	// input matrix in Triplet format
	// including repeated positions. e.g. (0,0)
	var A la.Triplet
	A.Init(5, 5, 13)
	A.Put(0, 0, 1.0) // << repeated
	A.Put(0, 0, 1.0) // << repeated
	A.Put(1, 0, 3.0)
	A.Put(0, 1, 3.0)
	A.Put(2, 1, -1.0)
	A.Put(4, 1, 4.0)
	A.Put(1, 2, 4.0)
	A.Put(2, 2, -3.0)
	A.Put(3, 2, 1.0)
	A.Put(4, 2, 2.0)
	A.Put(2, 3, 2.0)
	A.Put(1, 4, 6.0)
	A.Put(4, 4, 1.0)

	// right-hand-side
	b := []float64{8.0, 45.0, -3.0, 3.0, 19.0}

	// solve
	x, err := la.SolveRealLinSys(&A, b)
	if err != nil {
		io.Pfred("solver failed:\n%v", err)
		return
	}

	// output
	la.PrintMat("a", A.ToMatrix(nil).ToDense(), "%5g", false)
	la.PrintVec("b", b, "%v ", false)
	la.PrintVec("x", x, "%v ", false)
}
示例#2
0
func main() {

	// input matrix in Triplet format
	// including repeated positions. e.g. (0,0)
	var A la.Triplet
	A.Init(5, 5, 13)
	A.Put(0, 0, 1.0) // << repeated
	A.Put(0, 0, 1.0) // << repeated
	A.Put(1, 0, 3.0)
	A.Put(0, 1, 3.0)
	A.Put(2, 1, -1.0)
	A.Put(4, 1, 4.0)
	A.Put(1, 2, 4.0)
	A.Put(2, 2, -3.0)
	A.Put(3, 2, 1.0)
	A.Put(4, 2, 2.0)
	A.Put(2, 3, 2.0)
	A.Put(1, 4, 6.0)
	A.Put(4, 4, 1.0)

	// right-hand-side
	b := []float64{8.0, 45.0, -3.0, 3.0, 19.0}

	// allocate solver
	lis := la.GetSolver("umfpack")
	defer lis.Clean()

	// info
	symmetric := false
	verbose := false
	timing := false

	// initialise solver (R)eal
	err := lis.InitR(&A, symmetric, verbose, timing)
	if err != nil {
		io.Pfred("solver failed:\n%v", err)
		return
	}

	// factorise
	err = lis.Fact()
	if err != nil {
		io.Pfred("solver failed:\n%v", err)
		return
	}

	// solve (R)eal
	var dummy bool
	x := make([]float64, len(b))
	err = lis.SolveR(x, b, dummy) // x := inv(a) * b
	if err != nil {
		io.Pfred("solver failed:\n%v", err)
		return
	}

	// output
	la.PrintMat("a", A.ToMatrix(nil).ToDense(), "%5g", false)
	la.PrintVec("b", b, "%v ", false)
	la.PrintVec("x", x, "%v ", false)
}
示例#3
0
func (o *Rjoint) debug_update(idx int, Δwb0, Δwb1, Δwb2, σc float64) {
	τ := o.States[idx].Sig
	qn1 := o.States[idx].Phi[0]
	qn2 := o.States[idx].Phi[1]
	la.PrintVec("Δw", o.Δw, "%13.10f", false)
	io.Pf("Δwb0=%13.10f Δwb1=%13.10f Δwb2=%13.10f\n", Δwb0, Δwb1, Δwb2)
	la.PrintVec("σIp", o.σIp, "%13.10f", false)
	io.Pf("σc=%13.10f t1=%13.10f t2=%13.10f\n", σc, o.t1, o.t2)
	io.Pf("τ=%13.10f qn1=%13.10f qn2=%13.10f\n", τ, qn1, qn2)
}
示例#4
0
func Test_linipm02(tst *testing.T) {

	//verbose()
	chk.PrintTitle("linipm02")

	// linear program
	//   min   2*x0 +   x1
	//   s.t.   -x0 +   x1 ≤ 1
	//           x0 +   x1 ≥ 2   →  -x0 - x1 ≤ -2
	//           x0 - 2*x1 ≤ 4
	//         x1 ≥ 0
	// standard (step 1) add slack
	//   s.t.   -x0 +   x1 + x2           = 1
	//          -x0 -   x1      + x3      = -2
	//           x0 - 2*x1           + x4 = 4
	// standard (step 2)
	//    replace x0 := x0_ - x5
	//    because it's unbounded
	//    min  2*x0_ +   x1                - 2*x5
	//    s.t.  -x0_ +   x1 + x2           +   x5 = 1
	//          -x0_ -   x1      + x3      +   x5 = -2
	//           x0_ - 2*x1           + x4 -   x5 = 4
	//         x0_,x1,x2,x3,x4,x5 ≥ 0
	var T la.Triplet
	T.Init(3, 6, 12)
	T.Put(0, 0, -1)
	T.Put(0, 1, 1)
	T.Put(0, 2, 1)
	T.Put(0, 5, 1)
	T.Put(1, 0, -1)
	T.Put(1, 1, -1)
	T.Put(1, 3, 1)
	T.Put(1, 5, 1)
	T.Put(2, 0, 1)
	T.Put(2, 1, -2)
	T.Put(2, 4, 1)
	T.Put(2, 5, -1)
	Am := T.ToMatrix(nil)
	A := Am.ToDense()
	c := []float64{2, 1, 0, 0, 0, -2}
	b := []float64{1, -2, 4}

	// print LP
	la.PrintMat("A", A, "%6g", false)
	la.PrintVec("b", b, "%6g", false)
	la.PrintVec("c", c, "%6g", false)
	io.Pf("\n")

	// solve LP
	var ipm LinIpm
	defer ipm.Clean()
	ipm.Init(Am, b, c, nil)
	err := ipm.Solve(chk.Verbose)
	if err != nil {
		tst.Errorf("ipm failed:\n%v", err)
		return
	}

	// check
	io.Pf("\n")
	bres := make([]float64, len(b))
	la.MatVecMul(bres, 1, A, ipm.X)
	io.Pforan("bres = %v\n", bres)
	chk.Vector(tst, "A*x=b", 1e-8, bres, b)

	// fix and check x
	x := ipm.X[:2]
	x[0] -= ipm.X[5]
	io.Pforan("x = %v\n", x)
	chk.Vector(tst, "x", 1e-8, x, []float64{0.5, 1.5})

	// plot
	if true && chk.Verbose {
		f := func(x []float64) float64 {
			return c[0]*x[0] + c[1]*x[1]
		}
		g := func(x []float64, i int) float64 {
			return A[i][0]*x[0] + A[i][1]*x[1] - b[i]
		}
		np := 41
		vmin, vmax := []float64{-2.0, -2.0}, []float64{2.0, 2.0}
		PlotTwoVarsContour("/tmp/gosl", "test_linipm02", x, np, nil, true, vmin, vmax, f,
			func(x []float64) float64 { return g(x, 0) },
			func(x []float64) float64 { return g(x, 1) },
		)
	}
}
示例#5
0
func Test_linipm01(tst *testing.T) {

	//verbose()
	chk.PrintTitle("linipm01")

	// linear programming problem
	//   min  -4*x0 - 5*x1
	//   s.t.  2*x0 +   x1 ≤ 3
	//           x0 + 2*x1 ≤ 3
	//         x0,x1 ≥ 0
	// standard:
	//         2*x0 +   x1 + x2     = 3
	//           x0 + 2*x1     + x3 = 3
	//         x0,x1,x2,x3 ≥ 0
	var T la.Triplet
	T.Init(2, 4, 6)
	T.Put(0, 0, 2.0)
	T.Put(0, 1, 1.0)
	T.Put(0, 2, 1.0)
	T.Put(1, 0, 1.0)
	T.Put(1, 1, 2.0)
	T.Put(1, 3, 1.0)
	Am := T.ToMatrix(nil)
	A := Am.ToDense()
	c := []float64{-4, -5, 0, 0}
	b := []float64{3, 3}

	// print LP
	la.PrintMat("A", A, "%6g", false)
	la.PrintVec("b", b, "%6g", false)
	la.PrintVec("c", c, "%6g", false)
	io.Pf("\n")

	// solve LP
	var ipm LinIpm
	defer ipm.Clean()
	ipm.Init(Am, b, c, nil)
	err := ipm.Solve(chk.Verbose)
	if err != nil {
		tst.Errorf("ipm failed:\n%v", err)
		return
	}

	// check
	io.Pf("\n")
	io.Pforan("x = %v\n", ipm.X)
	io.Pfcyan("λ = %v\n", ipm.L)
	io.Pforan("s = %v\n", ipm.S)
	x := ipm.X[:2]
	bres := make([]float64, 2)
	la.MatVecMul(bres, 1, A, x)
	io.Pforan("bres = %v\n", bres)
	chk.Vector(tst, "x", 1e-9, x, []float64{1, 1})
	chk.Vector(tst, "A*x=b", 1e-8, bres, b)

	// plot
	if true && chk.Verbose {
		f := func(x []float64) float64 {
			return c[0]*x[0] + c[1]*x[1]
		}
		g := func(x []float64, i int) float64 {
			return A[i][0]*x[0] + A[i][1]*x[1] - b[i]
		}
		np := 41
		vmin, vmax := []float64{-2.0, -2.0}, []float64{2.0, 2.0}
		PlotTwoVarsContour("/tmp/gosl", "test_linipm01", x, np, nil, true, vmin, vmax, f,
			func(x []float64) float64 { return g(x, 0) },
			func(x []float64) float64 { return g(x, 1) },
		)
	}
}
示例#6
0
// CheckEigenprojs checks eigen projectors
func CheckEigenprojs(a []float64, tolP, tolS float64, ver bool) (λsorted []float64) {

	// compute eigenvalues and eigenprojectors
	ncp := len(a)
	λ := make([]float64, 3)
	P := la.MatAlloc(3, ncp)
	err := M_EigenValsProjsNum(P, λ, a)
	if err != nil {
		chk.Panic("eigenprojs.go: CheckEigenprojs failed:\n %v", err.Error())
	}

	// print projectors
	if ver {
		la.PrintVec("P0", P[0], "%14.6e", false)
		la.PrintVec("P1", P[1], "%14.6e", false)
		la.PrintVec("P2", P[2], "%14.6e", false)
	}

	// check P dot P
	PdotP := make([]float64, ncp)
	Z := make([]float64, ncp)
	for i := 0; i < 3; i++ {
		for j := 0; j < 3; j++ {
			err := M_Dot(PdotP, P[i], P[j], 1e-14)
			if err != nil {
				chk.Panic("%v", err)
			}
			if i == j {
				diff := la.VecMaxDiff(PdotP, P[i])
				if diff > tolP {
					chk.Panic("eigenprojs.go: CheckEigenprojs failed: P%d dot P%d != P%d (diff=%g)", i, j, i, diff)
				} else if ver {
					io.Pf("P%d dot P%d == P%d OK (diff=%g)\n", i, j, i, diff)
				}
			} else {
				diff := la.VecMaxDiff(PdotP, Z)
				if diff > tolP {
					chk.Panic("eigenprojs.go: CheckEigenprojs failed: P%d dot P%d !=  0 (diff=%g)", i, j, diff)
				} else if ver {
					io.Pf("P%d dot P%d ==  0 OK (diff=%g)\n", i, j, diff)
				}
			}
		}
	}

	// check sum of eigenprojectors
	sumP := make([]float64, ncp)
	for k := 0; k < 3; k++ {
		for i := 0; i < ncp; i++ {
			sumP[i] += P[k][i]
		}
	}
	diff := la.VecMaxDiff(sumP, Im[:ncp])
	if diff > tolP {
		chk.Panic("eigenprojs.go: CheckEigenprojs failed: sumP != I (diff=%g)", diff)
	} else if ver {
		io.Pf("sum(P) OK (diff=%g)\n", diff)
	}

	// check spectral decomposition
	as := make([]float64, len(a))
	for k := 0; k < 3; k++ {
		for i := 0; i < len(a); i++ {
			as[i] += λ[k] * P[k][i]
		}
	}
	diff = la.VecMaxDiff(as, a)
	if diff > tolS {
		chk.Panic("eigenprojs.go: CheckEigenprojs failed: a(spectral) != a (diff=%g)", diff)
	} else if ver {
		io.Pf("a(spectral) == a OK (diff=%g)\n", diff)
	}

	// sort eigenvalues
	λsorted = make([]float64, 3)
	I := []int{0, 1, 2}
	I, λsorted, _, _, err = utl.SortQuadruples(I, λ, nil, nil, "x")
	if err != nil {
		chk.Panic("%v", err)
	}
	return
}