Example #1
0
func TestLegendre(t *testing.T) {
	for i, test := range []struct {
		f        func(float64) float64
		min, max float64
		n        []int
		tol      []float64
		ans      float64
	}{
		// Tolerances determined from intuition and a bit of post-hoc tweaking.
		{
			f:   func(x float64) float64 { return math.Exp(x) },
			min: -3,
			max: 5,
			n:   []int{3, 4, 6, 7, 15, 16, 300, 301},
			tol: []float64{5e-2, 5e-3, 5e-6, 1e-7, 1e-14, 1e-14, 1e-14, 1e-14},
			ans: math.Exp(5) - math.Exp(-3),
		},
	} {
		for j, n := range test.n {
			ans := Fixed(test.f, test.min, test.max, n, Legendre{}, 0)
			if !floats.EqualWithinAbsOrRel(ans, test.ans, test.tol[j], test.tol[j]) {
				t.Errorf("Mismatch. Case = %d, n = %d. Want %v, got %v", i, n, test.ans, ans)
			}
			ans2 := Fixed(test.f, test.min, test.max, n, Legendre{}, 3)
			if !floats.EqualWithinAbsOrRel(ans2, test.ans, test.tol[j], test.tol[j]) {
				t.Errorf("Mismatch concurrent. Case = %d, n = %d. Want %v, got %v", i, n, test.ans, ans)
			}
		}
	}
}
Example #2
0
func TestHITS(t *testing.T) {
	for i, test := range hitsTests {
		g := concrete.NewDirectedGraph(0, math.Inf(1))
		for u, e := range test.g {
			// Add nodes that are not defined by an edge.
			if !g.Has(concrete.Node(u)) {
				g.AddNode(concrete.Node(u))
			}
			for v := range e {
				g.SetEdge(concrete.Edge{F: concrete.Node(u), T: concrete.Node(v)})
			}
		}
		got := HITS(g, test.tol)
		prec := 1 - int(math.Log10(test.wantTol))
		for n := range test.g {
			if !floats.EqualWithinAbsOrRel(got[n].Hub, test.want[n].Hub, test.wantTol, test.wantTol) {
				t.Errorf("unexpected HITS result for test %d:\ngot: %v\nwant:%v",
					i, orderedHubAuth(got, prec), orderedHubAuth(test.want, prec))
				break
			}
			if !floats.EqualWithinAbsOrRel(got[n].Authority, test.want[n].Authority, test.wantTol, test.wantTol) {
				t.Errorf("unexpected HITS result for test %d:\ngot: %v\nwant:%v",
					i, orderedHubAuth(got, prec), orderedHubAuth(test.want, prec))
				break
			}
		}
	}
}
Example #3
0
func TestRankTwo(t *testing.T) {
	for _, test := range []struct {
		n int
	}{
		{n: 1},
		{n: 2},
		{n: 3},
		{n: 4},
		{n: 5},
		{n: 10},
	} {
		n := test.n
		alpha := 2.0
		a := NewSymDense(n, nil)
		for i := range a.mat.Data {
			a.mat.Data[i] = rand.Float64()
		}
		x := make([]float64, n)
		y := make([]float64, n)
		for i := range x {
			x[i] = rand.Float64()
			y[i] = rand.Float64()
		}

		xMat := NewDense(n, 1, x)
		yMat := NewDense(n, 1, y)
		var m Dense
		m.Mul(xMat, yMat.T())
		var tmp Dense
		tmp.Mul(yMat, xMat.T())
		m.Add(&m, &tmp)
		m.Scale(alpha, &m)
		m.Add(&m, a)

		// Check with new receiver
		s := NewSymDense(n, nil)
		s.RankTwo(a, alpha, NewVector(len(x), x), NewVector(len(y), y))
		for i := 0; i < n; i++ {
			for j := i; j < n; j++ {
				if !floats.EqualWithinAbsOrRel(s.At(i, j), m.At(i, j), 1e-14, 1e-14) {
					t.Errorf("unexpected element value at (%d,%d): got: %f want: %f", i, j, m.At(i, j), s.At(i, j))
				}
			}
		}

		// Check with reused receiver
		copy(s.mat.Data, a.mat.Data)
		s.RankTwo(s, alpha, NewVector(len(x), x), NewVector(len(y), y))
		for i := 0; i < n; i++ {
			for j := i; j < n; j++ {
				if !floats.EqualWithinAbsOrRel(s.At(i, j), m.At(i, j), 1e-14, 1e-14) {
					t.Errorf("unexpected element value at (%d,%d): got: %f want: %f", i, j, m.At(i, j), s.At(i, j))
				}
			}
		}
	}
}
Example #4
0
func checkVarAndStd(t *testing.T, i int, x []float64, v varStder, tol float64) {
	variance := stat.Variance(x, nil)
	if !floats.EqualWithinAbsOrRel(variance, v.Variance(), tol, tol) {
		t.Errorf("Variance mismatch case %v: want: %v, got: %v", i, variance, v.Variance())
	}
	std := math.Sqrt(variance)
	if !floats.EqualWithinAbsOrRel(std, v.StdDev(), tol, tol) {
		t.Errorf("StdDev mismatch case %v: want: %v, got: %v", i, std, v.StdDev())
	}
}
Example #5
0
func SameF64Approx(str string, c, native, absTol, relTol float64) {
	if math.IsNaN(c) && math.IsNaN(native) {
		return
	}
	if !floats.EqualWithinAbsOrRel(c, native, absTol, relTol) {
		cb := math.Float64bits(c)
		nb := math.Float64bits(native)
		same := floats.EqualWithinAbsOrRel(c, native, absTol, relTol)
		panic(fmt.Sprintf("Case %s: Float64 mismatch. c = %v, native = %v\n cb: %v, nb: %v\n%v,%v,%v", str, c, native, cb, nb, same, absTol, relTol))
	}
}
Example #6
0
func TestReduceQConsistency(t *testing.T) {
tests:
	for _, test := range communityQTests {
		g := simple.NewUndirectedGraph(0, 0)
		for u, e := range test.g {
			// Add nodes that are not defined by an edge.
			if !g.Has(simple.Node(u)) {
				g.AddNode(simple.Node(u))
			}
			for v := range e {
				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v), W: 1})
			}
		}

		for _, structure := range test.structures {
			if math.IsNaN(structure.want) {
				continue tests
			}

			communities := make([][]graph.Node, len(structure.memberships))
			for i, c := range structure.memberships {
				for n := range c {
					communities[i] = append(communities[i], simple.Node(n))
				}
				sort.Sort(ordered.ByID(communities[i]))
			}

			gQ := Q(g, communities, structure.resolution)
			gQnull := Q(g, nil, 1)

			cg0 := reduce(g, nil)
			cg0Qnull := Q(cg0, cg0.Structure(), 1)
			if !floats.EqualWithinAbsOrRel(gQnull, cg0Qnull, structure.tol, structure.tol) {
				t.Errorf("disgagreement between null Q from method: %v and function: %v", cg0Qnull, gQnull)
			}
			cg0Q := Q(cg0, communities, structure.resolution)
			if !floats.EqualWithinAbsOrRel(gQ, cg0Q, structure.tol, structure.tol) {
				t.Errorf("unexpected Q result after initial conversion: got: %v want :%v", gQ, cg0Q)
			}

			cg1 := reduce(cg0, communities)
			cg1Q := Q(cg1, cg1.Structure(), structure.resolution)
			if !floats.EqualWithinAbsOrRel(gQ, cg1Q, structure.tol, structure.tol) {
				t.Errorf("unexpected Q result after initial condensation: got: %v want :%v", gQ, cg1Q)
			}
		}
	}
}
Example #7
0
func TestEdgeBetweenness(t *testing.T) {
	for i, test := range betweennessTests {
		g := simple.NewUndirectedGraph(0, math.Inf(1))
		for u, e := range test.g {
			// Add nodes that are not defined by an edge.
			if !g.Has(simple.Node(u)) {
				g.AddNode(simple.Node(u))
			}
			for v := range e {
				// Weight omitted to show weight-independence.
				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v), W: 0})
			}
		}
		got := EdgeBetweenness(g)
		prec := 1 - int(math.Log10(test.wantTol))
	outer:
		for u := range test.g {
			for v := range test.g {
				wantQ, gotOK := got[[2]int{u, v}]
				gotQ, wantOK := test.wantEdges[[2]int{u, v}]
				if gotOK != wantOK {
					t.Errorf("unexpected betweenness result for test %d, edge (%c,%c)", i, u+'A', v+'A')
				}
				if !floats.EqualWithinAbsOrRel(gotQ, wantQ, test.wantTol, test.wantTol) {
					t.Errorf("unexpected betweenness result for test %d:\ngot: %v\nwant:%v",
						i, orderedPairFloats(got, prec), orderedPairFloats(test.wantEdges, prec))
					break outer
				}
			}
		}
	}
}
Example #8
0
func TestCommunityQ(t *testing.T) {
	for _, test := range communityQTests {
		g := simple.NewUndirectedGraph(0, 0)
		for u, e := range test.g {
			// Add nodes that are not defined by an edge.
			if !g.Has(simple.Node(u)) {
				g.AddNode(simple.Node(u))
			}
			for v := range e {
				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v), W: 1})
			}
		}
		for _, structure := range test.structures {
			communities := make([][]graph.Node, len(structure.memberships))
			for i, c := range structure.memberships {
				for n := range c {
					communities[i] = append(communities[i], simple.Node(n))
				}
			}
			got := Q(g, communities, structure.resolution)
			if !floats.EqualWithinAbsOrRel(got, structure.want, structure.tol, structure.tol) && math.IsNaN(got) != math.IsNaN(structure.want) {
				for _, c := range communities {
					sort.Sort(ordered.ByID(c))
				}
				t.Errorf("unexpected Q value for %q %v: got: %v want: %v",
					test.name, communities, got, structure.want)
			}
		}
	}
}
Example #9
0
func Dorg2rTest(t *testing.T, impl Dorg2rer) {
	rnd := rand.New(rand.NewSource(1))
	for _, test := range []struct {
		m, n, k, lda int
	}{
		{3, 3, 0, 0},
		{4, 3, 0, 0},
		{3, 3, 2, 0},
		{4, 3, 2, 0},

		{5, 5, 0, 20},
		{5, 5, 3, 20},
		{10, 5, 0, 20},
		{10, 5, 2, 20},
	} {
		m := test.m
		n := test.n
		lda := test.lda
		if lda == 0 {
			lda = test.n
		}
		a := make([]float64, m*lda)
		for i := range a {
			a[i] = rnd.NormFloat64()
		}
		k := min(m, n)
		tau := make([]float64, k)
		work := make([]float64, 1)
		impl.Dgeqrf(m, n, a, lda, tau, work, -1)
		work = make([]float64, int(work[0]))
		impl.Dgeqrf(m, n, a, lda, tau, work, len(work))

		k = test.k
		if k == 0 {
			k = n
		}
		q := constructQK("QR", m, n, k, a, lda, tau)

		impl.Dorg2r(m, n, k, a, lda, tau, work)

		// Check that the first n columns match.
		same := true
		for i := 0; i < m; i++ {
			for j := 0; j < n; j++ {
				if !floats.EqualWithinAbsOrRel(q.Data[i*q.Stride+j], a[i*lda+j], 1e-12, 1e-12) {
					same = false
					break
				}
			}
		}
		if !same {
			fmt.Println()
			fmt.Println("a =")
			printRowise(a, m, n, lda, false)
			fmt.Println("q =")
			printRowise(q.Data, q.Rows, q.Cols, q.Stride, false)
			t.Errorf("Q mismatch")
		}
	}
}
Example #10
0
func TestBetweennessWeighted(t *testing.T) {
	for i, test := range betweennessTests {
		g := concrete.NewGraph(0, math.Inf(1))
		for u, e := range test.g {
			// Add nodes that are not defined by an edge.
			if !g.Has(concrete.Node(u)) {
				g.AddNode(concrete.Node(u))
			}
			for v := range e {
				g.SetEdge(concrete.Edge{F: concrete.Node(u), T: concrete.Node(v), W: 1})
			}
		}

		p, ok := path.FloydWarshall(g)
		if !ok {
			t.Errorf("unexpected negative cycle in test %d", i)
			continue
		}

		got := BetweennessWeighted(g, p)
		prec := 1 - int(math.Log10(test.wantTol))
		for n := range test.g {
			gotN, gotOK := got[n]
			wantN, wantOK := test.want[n]
			if gotOK != wantOK {
				t.Errorf("unexpected betweenness existence for test %d, node %d", i, n)
			}
			if !floats.EqualWithinAbsOrRel(gotN, wantN, test.wantTol, test.wantTol) {
				t.Errorf("unexpected betweenness result for test %d:\ngot: %v\nwant:%v",
					i, orderedFloats(got, prec), orderedFloats(test.want, prec))
				break
			}
		}
	}
}
Example #11
0
func TestBetweenness(t *testing.T) {
	for i, test := range betweennessTests {
		g := concrete.NewGraph()
		for u, e := range test.g {
			// Add nodes that are not defined by an edge.
			if !g.Has(concrete.Node(u)) {
				g.AddNode(concrete.Node(u))
			}
			for v := range e {
				g.SetEdge(concrete.Edge{F: concrete.Node(u), T: concrete.Node(v)}, 0)
			}
		}
		got := Betweenness(g)
		prec := 1 - int(math.Log10(test.wantTol))
		for n := range test.g {
			wantN, gotOK := got[n]
			gotN, wantOK := test.want[n]
			if gotOK != wantOK {
				t.Errorf("unexpected betweenness result for test %d, node %d", i, n)
			}
			if !floats.EqualWithinAbsOrRel(gotN, wantN, test.wantTol, test.wantTol) {
				t.Errorf("unexpected betweenness result for test %d:\ngot: %v\nwant:%v",
					i, orderedFloats(got, prec), orderedFloats(test.want, prec))
				break
			}
		}
	}
}
Example #12
0
func checkQuantileCDFSurvival(t *testing.T, i int, xs []float64, c cumulanter, tol float64) {
	// Quantile, CDF, and survival check.
	for i, p := range []float64{0.1, 0.25, 0.5, 0.75, 0.9} {
		x := c.Quantile(p)
		cdf := c.CDF(x)
		estCDF := stat.CDF(x, stat.Empirical, xs, nil)
		if !floats.EqualWithinAbsOrRel(cdf, estCDF, tol, tol) {
			t.Errorf("CDF mismatch case %v: want: %v, got: %v", i, estCDF, cdf)
		}
		if !floats.EqualWithinAbsOrRel(cdf, p, tol, tol) {
			t.Errorf("Quantile/CDF mismatch case %v: want: %v, got: %v", i, p, cdf)
		}
		if math.Abs(1-cdf-c.Survival(x)) > 1e-14 {
			t.Errorf("Survival/CDF mismatch case %v: want: %v, got: %v", i, 1-cdf, c.Survival(x))
		}
	}
}
Example #13
0
func TestGeneralizedBinomial(t *testing.T) {
	for cas, test := range binomialTests {
		ans := GeneralizedBinomial(float64(test.n), float64(test.k))
		if !floats.EqualWithinAbsOrRel(ans, float64(test.ans), 1e-14, 1e-14) {
			t.Errorf("Case %v: Binomial mismatch. Got %v, want %v.", cas, ans, test.ans)
		}
	}
}
Example #14
0
func checkEntropy(t *testing.T, i int, x []float64, e entropyer, tol float64) {
	tmp := make([]float64, len(x))
	for i, v := range x {
		tmp[i] = -e.LogProb(v)
	}
	entropy := stat.Mean(tmp, nil)
	if !floats.EqualWithinAbsOrRel(entropy, e.Entropy(), tol, tol) {
		t.Errorf("Entropy mismatch case %v: want: %v, got: %v", i, entropy, e.Entropy())
	}
}
Example #15
0
func approxEqual(a, b []float64, epsilon float64) bool {
	if len(a) != len(b) {
		return false
	}
	for i, v := range a {
		if !floats.EqualWithinAbsOrRel(v, b[i], epsilon, epsilon) {
			return false
		}
	}
	return true
}
Example #16
0
// Take returns an index from the Weighted with probability proportional
// to the weight of the item. The weight of the item is then set to zero.
// Take returns false if there are no items remaining.
func (s Weighted) Take() (idx int, ok bool) {
	const small = 1e-12
	if floats.EqualWithinAbsOrRel(s.heap[0], 0, small, small) {
		return -1, false
	}

	var r float64
	if s.src == nil {
		r = s.heap[0] * rand.Float64()
	} else {
		r = s.heap[0] * s.src.Float64()
	}
	i := 1
	last := -1
	left := len(s.weights)
	for {
		if r -= s.weights[i-1]; r <= 0 {
			break // Fall within item i-1.
		}
		i <<= 1 // Move to left child.
		if d := s.heap[i-1]; r > d {
			r -= d
			// If enough r to pass left child
			// move to right child state will
			// be caught at break above.
			i++
		}
		if i == last || left < 0 {
			// No progression.
			return -1, false
		}
		last = i
		left--
	}

	w, idx := s.weights[i-1], i-1

	s.weights[i-1] = 0
	for i > 0 {
		s.heap[i-1] -= w
		// The following condition is necessary to
		// handle floating point error. If we see
		// a heap value below zero, we know we need
		// to rebuild it.
		if s.heap[i-1] < 0 {
			s.reset()
			return idx, true
		}
		i >>= 1
	}

	return idx, true
}
Example #17
0
func DpotrfTest(t *testing.T, impl Dpotrfer) {
	rnd := rand.New(rand.NewSource(1))
	bi := blas64.Implementation()
	for i, test := range []struct {
		n int
	}{
		{n: 10},
		{n: 30},
		{n: 63},
		{n: 65},
		{n: 128},
		{n: 1000},
	} {
		n := test.n
		// Construct a positive-definite symmetric matrix
		base := make([]float64, n*n)
		for i := range base {
			base[i] = rnd.Float64()
		}
		a := make([]float64, len(base))
		bi.Dgemm(blas.Trans, blas.NoTrans, n, n, n, 1, base, n, base, n, 0, a, n)

		aCopy := make([]float64, len(a))
		copy(aCopy, a)

		// Test with Upper
		impl.Dpotrf(blas.Upper, n, a, n)

		// zero all the other elements
		for i := 0; i < n; i++ {
			for j := 0; j < i; j++ {
				a[i*n+j] = 0
			}
		}
		// Multiply u^T * u
		ans := make([]float64, len(a))
		bi.Dsyrk(blas.Upper, blas.Trans, n, n, 1, a, n, 0, ans, n)

		match := true
		for i := 0; i < n; i++ {
			for j := i; j < n; j++ {
				if !floats.EqualWithinAbsOrRel(ans[i*n+j], aCopy[i*n+j], 1e-14, 1e-14) {
					match = false
				}
			}
		}
		if !match {
			//fmt.Println(aCopy)
			//fmt.Println(ans)
			t.Errorf("Case %v: Mismatch for upper", i)
		}
	}
}
Example #18
0
func TestFixedNonSingle(t *testing.T) {
	// TODO(btracey): Add tests with infinite bounds when we have native support
	// for indefinite integrals.
	for i, test := range []struct {
		f        func(float64) float64
		min, max float64
		n        []int
		tol      []float64
		ans      float64
	}{
		// Tolerances determined from intuition and a bit of post-hoc tweaking.
		{
			f:   func(x float64) float64 { return math.Exp(x) },
			min: -3,
			max: 5,
			n:   []int{3, 4, 6, 7, 15, 16, 300, 301},
			tol: []float64{5e-2, 5e-3, 5e-6, 1e-7, 1e-14, 1e-14, 1e-14, 1e-14},
			ans: math.Exp(5) - math.Exp(-3),
		},
		{
			f:   func(x float64) float64 { return math.Exp(x) },
			min: 3,
			max: 3,
			n:   []int{3, 4, 6, 7, 15, 16, 300, 301},
			tol: []float64{0, 0, 0, 0, 0, 0, 0, 0},
			ans: 0,
		},
	} {
		for j, n := range test.n {
			ans := Fixed(test.f, test.min, test.max, n, legendreNonSingle{}, 0)
			if !floats.EqualWithinAbsOrRel(ans, test.ans, test.tol[j], test.tol[j]) {
				t.Errorf("Case = %d, n = %d: Mismatch. Want %v, got %v", i, n, test.ans, ans)
			}
			ans2 := Fixed(test.f, test.min, test.max, n, legendreNonSingle{}, 3)
			if !floats.EqualWithinAbsOrRel(ans2, test.ans, test.tol[j], test.tol[j]) {
				t.Errorf("Case = %d, n = %d: Mismatch concurrent. Want %v, got %v", i, n, test.ans, ans)
			}
		}
	}
}
Example #19
0
func checkSkewness(t *testing.T, i int, x []float64, s skewnesser, tol float64) {
	mean := s.Mean()
	std := s.StdDev()
	tmp := make([]float64, len(x))
	for i, v := range x {
		tmp[i] = math.Pow(v-mean, 3)
	}
	mu3 := stat.Mean(tmp, nil)
	skewness := mu3 / math.Pow(std, 3)
	if !floats.EqualWithinAbsOrRel(skewness, s.Skewness(), tol, tol) {
		t.Errorf("ExKurtosis mismatch case %v: want: %v, got: %v", i, skewness, s.Skewness())
	}
}
Example #20
0
func checkExKurtosis(t *testing.T, i int, x []float64, e exKurtosiser, tol float64) {
	mean := e.Mean()
	tmp := make([]float64, len(x))
	for i, x := range x {
		tmp[i] = math.Pow(x-mean, 4)
	}
	variance := stat.Variance(x, nil)
	mu4 := stat.Mean(tmp, nil)
	kurtosis := mu4/(variance*variance) - 3
	if !floats.EqualWithinAbsOrRel(kurtosis, e.ExKurtosis(), tol, tol) {
		t.Errorf("ExKurtosis mismatch case %v: want: %v, got: %v", i, kurtosis, e.ExKurtosis())
	}
}
Example #21
0
func samedDistCategorical(dist Categorical, counts, probs []float64, tol float64) bool {
	same := true
	for i, prob := range probs {
		if prob == 0 && counts[i] != 0 {
			same = false
			break
		}
		if !floats.EqualWithinAbsOrRel(prob, counts[i], tol, tol) {
			same = false
			break
		}
	}
	return same
}
Example #22
0
func Dorgl2Test(t *testing.T, impl Dorgl2er) {
	rnd := rand.New(rand.NewSource(1))
	for _, test := range []struct {
		m, n, lda int
	}{
		{3, 3, 0},
		{3, 4, 0},

		{5, 5, 20},
		{5, 10, 20},
	} {
		m := test.m
		n := test.n
		lda := test.lda
		if lda == 0 {
			lda = test.n
		}
		a := make([]float64, m*lda)
		for i := range a {
			a[i] = rnd.NormFloat64()
		}
		k := min(m, n)
		tau := make([]float64, k)
		work := make([]float64, 1)
		impl.Dgelqf(m, n, a, lda, tau, work, -1)
		work = make([]float64, int(work[0]))
		impl.Dgelqf(m, n, a, lda, tau, work, len(work))

		q := constructQ("LQ", m, n, a, lda, tau)

		impl.Dorgl2(m, n, k, a, lda, tau, work)

		// Check that the first m rows match.
		same := true
		for i := 0; i < m; i++ {
			for j := 0; j < n; j++ {
				if !floats.EqualWithinAbsOrRel(q.Data[i*q.Stride+j], a[i*lda+j], 1e-12, 1e-12) {
					same = false
					break
				}
			}
		}
		if !same {
			t.Errorf("Q mismatch")
		}
	}
}
Example #23
0
// equalApprox returns whether the elements of a and b are the same to within
// the tolerance.
func equalApprox(a, b Matrix, tol float64) bool {
	ar, ac := a.Dims()
	br, bc := b.Dims()
	if ar != br {
		return false
	}
	if ac != bc {
		return false
	}
	for i := 0; i < ar; i++ {
		for j := 0; j < ac; j++ {
			if !floats.EqualWithinAbsOrRel(a.At(i, j), b.At(i, j), tol, tol) {
				return false
			}
		}
	}
	return true
}
Example #24
0
func TestMoveLocal(t *testing.T) {
	for _, test := range localMoveTests {
		g := simple.NewUndirectedGraph(0, 0)
		for u, e := range test.g {
			// Add nodes that are not defined by an edge.
			if !g.Has(simple.Node(u)) {
				g.AddNode(simple.Node(u))
			}
			for v := range e {
				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v), W: 1})
			}
		}

		for _, structure := range test.structures {
			communities := make([][]graph.Node, len(structure.memberships))
			for i, c := range structure.memberships {
				for n := range c {
					communities[i] = append(communities[i], simple.Node(n))
				}
				sort.Sort(ordered.ByID(communities[i]))
			}

			r := reduce(reduce(g, nil), communities)

			l := newLocalMover(r, r.communities, structure.resolution)
			for _, n := range structure.targetNodes {
				dQ, dst, src := l.deltaQ(n)
				if dQ > 0 {
					before := Q(r, l.communities, structure.resolution)
					l.move(dst, src)
					after := Q(r, l.communities, structure.resolution)
					want := after - before
					if !floats.EqualWithinAbsOrRel(dQ, want, structure.tol, structure.tol) {
						t.Errorf("unexpected deltaQ: got: %v want: %v", dQ, want)
					}
				}
			}
		}
	}
}
Example #25
0
func TestPageRank(t *testing.T) {
	for i, test := range pageRankTests {
		g := concrete.NewDirectedGraph()
		for u, e := range test.g {
			// Add nodes that are not defined by an edge.
			if !g.Has(concrete.Node(u)) {
				g.AddNode(concrete.Node(u))
			}
			for v := range e {
				g.SetEdge(concrete.Edge{F: concrete.Node(u), T: concrete.Node(v)}, 0)
			}
		}
		got := PageRank(g, test.damp, test.tol)
		prec := 1 - int(math.Log10(test.wantTol))
		for n := range test.g {
			if !floats.EqualWithinAbsOrRel(got[n], test.want[n], test.wantTol, test.wantTol) {
				t.Errorf("unexpected PageRank result for test %d:\ngot: %v\nwant:%v",
					i, orderedFloats(got, prec), orderedFloats(test.want, prec))
				break
			}
		}
	}
}
Example #26
0
func TestComputeZ(t *testing.T) {
	for _, test := range []struct {
		x         []float64
		feature   []float64
		b         float64
		z         float64
		nFeatures float64
		name      string
	}{
		{
			name:      "General",
			x:         []float64{2.0, 1.0},
			feature:   []float64{8.1, 6.2},
			b:         0.8943,
			nFeatures: 50,
			z:         -0.07188374176,
		},
	} {
		z := computeZ(test.x, test.feature, test.b, math.Sqrt(2.0/test.nFeatures))
		if floats.EqualWithinAbsOrRel(z, test.z, 1e-14, 1e-14) {
			t.Errorf("z mismatch for case %v. %v expected, %v found", test.name, test.z, z)
		}
	}
}
Example #27
0
// EqualApprox returns whether the matrices a and b have the same size and contain all equal
// elements with tolerance for element-wise equality specified by epsilon. Matrices
// with non-equal shapes are not equal.
func EqualApprox(a, b Matrix, epsilon float64) bool {
	ar, ac := a.Dims()
	br, bc := b.Dims()
	if ar != br || ac != bc {
		return false
	}
	aMat, aTrans := untranspose(a)
	bMat, bTrans := untranspose(b)
	if rma, ok := aMat.(RawMatrixer); ok {
		if rmb, ok := bMat.(RawMatrixer); ok {
			ra := rma.RawMatrix()
			rb := rmb.RawMatrix()
			if aTrans == bTrans {
				for i := 0; i < ra.Rows; i++ {
					for j := 0; j < ra.Cols; j++ {
						if !floats.EqualWithinAbsOrRel(ra.Data[i*ra.Stride+j], rb.Data[i*rb.Stride+j], epsilon, epsilon) {
							return false
						}
					}
				}
				return true
			}
			for i := 0; i < ra.Rows; i++ {
				for j := 0; j < ra.Cols; j++ {
					if !floats.EqualWithinAbsOrRel(ra.Data[i*ra.Stride+j], rb.Data[j*rb.Stride+i], epsilon, epsilon) {
						return false
					}
				}
			}
			return true
		}
	}
	if rma, ok := aMat.(RawSymmetricer); ok {
		if rmb, ok := bMat.(RawSymmetricer); ok {
			ra := rma.RawSymmetric()
			rb := rmb.RawSymmetric()
			// Symmetric matrices are always upper and equal to their transpose.
			for i := 0; i < ra.N; i++ {
				for j := i; j < ra.N; j++ {
					if !floats.EqualWithinAbsOrRel(ra.Data[i*ra.Stride+j], rb.Data[i*rb.Stride+j], epsilon, epsilon) {
						return false
					}
				}
			}
			return true
		}
	}
	if ra, ok := aMat.(*Vector); ok {
		if rb, ok := bMat.(*Vector); ok {
			// If the raw vectors are the same length they must either both be
			// transposed or both not transposed (or have length 1).
			for i := 0; i < ra.n; i++ {
				if !floats.EqualWithinAbsOrRel(ra.mat.Data[i*ra.mat.Inc], rb.mat.Data[i*rb.mat.Inc], epsilon, epsilon) {
					return false
				}
			}
			return true
		}
	}
	for i := 0; i < ar; i++ {
		for j := 0; j < ac; j++ {
			if !floats.EqualWithinAbsOrRel(a.At(i, j), b.At(i, j), epsilon, epsilon) {
				return false
			}
		}
	}
	return true
}
Example #28
0
// sameAnswerFloatApprox returns whether the two inputs are both NaN or within tol
// of each other.
func sameAnswerFloatApprox(a, b interface{}) bool {
	if math.IsNaN(a.(float64)) {
		return math.IsNaN(b.(float64))
	}
	return floats.EqualWithinAbsOrRel(a.(float64), b.(float64), 1e-12, 1e-12)
}
Example #29
0
// testFullDist tests all of the functions of a fullDist.
func testFullDist(t *testing.T, f fullDist, i int) {
	tol := 1e-1
	const n = 1e6
	xs := make([]float64, n)
	for i := range xs {
		xs[i] = f.Rand()
	}
	sortedXs := make([]float64, n)
	copy(sortedXs, xs)
	sort.Float64s(sortedXs)
	tmp := make([]float64, n)

	// Mean check.
	mean := stat.Mean(xs, nil)
	if !floats.EqualWithinAbsOrRel(mean, f.Mean(), tol, tol) {
		t.Errorf("Mean mismatch case %v: want: %v, got: %v", i, mean, f.Mean())
	} else {
		mean = f.Mean()
	}

	// Median check.
	median := stat.Quantile(0.5, stat.Empirical, sortedXs, nil)
	if !floats.EqualWithinAbsOrRel(median, f.Median(), tol, tol) {
		t.Errorf("Median mismatch case %v: want: %v, got: %v", i, median, f.Median())
	}

	// Variance check.
	variance := stat.Variance(xs, nil)
	if !floats.EqualWithinAbsOrRel(variance, f.Variance(), tol, tol) {
		t.Errorf("Variance mismatch case %v: want: %v, got: %v", i, mean, f.Variance())
	} else {
		variance = f.Variance()
	}

	std := math.Sqrt(variance)
	if !floats.EqualWithinAbsOrRel(std, f.StdDev(), tol, tol) {
		t.Errorf("StdDev mismatch case %v: want: %v, got: %v", i, mean, f.StdDev())
	} else {
		std = f.StdDev()
	}

	// Entropy check.
	for i, x := range xs {
		tmp[i] = -f.LogProb(x)
	}
	entropy := stat.Mean(tmp, nil)
	if !floats.EqualWithinAbsOrRel(entropy, f.Entropy(), tol, tol) {
		t.Errorf("Entropy mismatch case %v: want: %v, got: %v", i, entropy, f.Entropy())
	}

	// Excess Kurtosis check.
	for i, x := range xs {
		tmp[i] = math.Pow(x-mean, 4)
	}
	mu4 := stat.Mean(tmp, nil)
	kurtosis := mu4/(variance*variance) - 3
	if !floats.EqualWithinAbsOrRel(kurtosis, f.ExKurtosis(), tol, tol) {
		t.Errorf("ExKurtosis mismatch case %v: want: %v, got: %v", i, kurtosis, f.ExKurtosis())
	}

	// Skewness check.
	for i, x := range xs {
		tmp[i] = math.Pow(x-mean, 3)
	}
	mu3 := stat.Mean(tmp, nil)
	skewness := mu3 / math.Pow(std, 3)
	if !floats.EqualWithinAbsOrRel(skewness, f.Skewness(), tol, tol) {
		t.Errorf("ExKurtosis mismatch case %v: want: %v, got: %v", i, skewness, f.Skewness())
	}

	// Quantile, CDF, and survival check.
	for i, p := range []float64{0.1, 0.25, 0.5, 0.75, 0.9} {
		x := f.Quantile(p)
		cdf := f.CDF(x)
		estCDF := stat.CDF(x, stat.Empirical, sortedXs, nil)
		if !floats.EqualWithinAbsOrRel(cdf, estCDF, tol, tol) {
			t.Errorf("CDF mismatch case %v: want: %v, got: %v", i, estCDF, cdf)
		}
		if !floats.EqualWithinAbsOrRel(cdf, p, tol, tol) {
			t.Errorf("Quantile/CDF mismatch case %v: want: %v, got: %v", i, p, cdf)
		}
		if math.Abs(1-cdf-f.Survival(x)) > 1e-14 {
			t.Errorf("Survival/CDF mismatch case %v: want: %v, got: %v", i, 1-cdf, f.Survival(x))
		}
	}

	// Prob and LogProb check.
	m := 1001
	bins := make([]float64, m)
	dividers := make([]float64, m)
	floats.Span(bins, 0, 1)
	for i, v := range bins {
		dividers[i] = f.Quantile(v)
	}
	counts := stat.Histogram(nil, dividers, sortedXs, nil)
	// Test PDf against normalized count
	for i, v := range counts {
		v /= float64(n)
		at := f.Quantile((bins[i] + bins[i+1]) / 2)
		prob := f.Prob(at)
		if !floats.EqualWithinAbsOrRel(skewness, f.Skewness(), tol, tol) {
			t.Errorf("Prob mismatch case %v at %v: want: %v, got: %v", i, at, v, prob)
			break
		}
		if math.Abs(math.Log(prob)-f.LogProb(at)) > 1e-14 {
			t.Errorf("Prob and LogProb mismatch case %v at %v: want %v, got %v", i, at, math.Log(prob), f.LogProb(at))
			break
		}
	}
}
Example #30
0
func TestDet(t *testing.T) {
	for c, test := range []struct {
		a   *Dense
		ans float64
	}{
		{
			a:   NewDense(2, 2, []float64{1, 0, 0, 1}),
			ans: 1,
		},
		{
			a:   NewDense(2, 2, []float64{1, 0, 0, -1}),
			ans: -1,
		},
		{
			a: NewDense(3, 3, []float64{
				1, 2, 0,
				0, 1, 2,
				0, 2, 1,
			}),
			ans: -3,
		},
		{
			a: NewDense(3, 3, []float64{
				1, 2, 3,
				5, 7, 9,
				6, 9, 12,
			}),
			ans: 0,
		},
	} {
		a := DenseCopyOf(test.a)
		det := Det(a)
		if !Equal(a, test.a) {
			t.Errorf("Input matrix changed during Det. Case %d.", c)
		}
		if !floats.EqualWithinAbsOrRel(det, test.ans, 1e-14, 1e-14) {
			t.Errorf("Det mismatch case %d. Got %v, want %v", c, det, test.ans)
		}
	}
	// Perform the normal list test to ensure it works for all types.
	f := func(a Matrix) interface{} {
		return Det(a)
	}
	denseComparison := func(a *Dense) interface{} {
		return Det(a)
	}
	testOneInputFunc(t, "Det", f, denseComparison, sameAnswerFloatApprox, isAnyType, isSquare)

	// Check that it gives approximately the same answer as Cholesky
	// Ensure the input matrices are wider than tall so they are full rank
	isWide := func(ar, ac int) bool {
		return ar <= ac
	}
	f = func(a Matrix) interface{} {
		ar, ac := a.Dims()
		if !isWide(ar, ac) {
			panic(matrix.ErrShape)
		}
		var tmp Dense
		tmp.Mul(a, a.T())
		return Det(&tmp)
	}
	denseComparison = func(a *Dense) interface{} {
		ar, ac := a.Dims()
		if !isWide(ar, ac) {
			panic(matrix.ErrShape)
		}
		var tmp SymDense
		tmp.SymOuterK(1, a)
		var chol Cholesky
		ok := chol.Factorize(&tmp)
		if !ok {
			panic("bad chol test")
		}
		return chol.Det()
	}
	testOneInputFunc(t, "DetVsChol", f, denseComparison, sameAnswerFloatApprox, isAnyType, isWide)
}