Golang mat64.Col函数代码示例

// GcvInitCameraMatrix2D takes one 3-by-N matrix and one 2-by-N Matrix as input.
// Each column in the input matrix represents a point in real world (objPts) or
// in image (imgPts).
// Return: the camera matrix.
func GcvInitCameraMatrix2D(objPts, imgPts *mat64.Dense, dims [2]int,
	aspectRatio float64) (camMat *mat64.Dense) {

	objDim, nObjPts := objPts.Dims()
	imgDim, nImgPts := imgPts.Dims()

	if objDim != 3 || imgDim != 2 || nObjPts != nImgPts {
		panic("Invalid dimensions for objPts and imgPts")
	}

	objPtsVec := NewGcvPoint3f32Vector(int64(nObjPts))
	imgPtsVec := NewGcvPoint2f32Vector(int64(nObjPts))

	for j := 0; j < nObjPts; j++ {
		objPtsVec.Set(j, NewGcvPoint3f32(mat64.Col(nil, j, objPts)...))
	}

	for j := 0; j < nObjPts; j++ {
		imgPtsVec.Set(j, NewGcvPoint2f32(mat64.Col(nil, j, imgPts)...))
	}

	_imgSize := NewGcvSize2i(dims[0], dims[1])

	camMat = GcvMatToMat64(GcvInitCameraMatrix2D_(
		objPtsVec, imgPtsVec, _imgSize, aspectRatio))
	return camMat
}

func TestMarginal(t *testing.T) {
	for _, test := range []struct {
		mu       []float64
		sigma    *mat64.SymDense
		marginal []int
	}{
		{
			mu:       []float64{2, 3, 4},
			sigma:    mat64.NewSymDense(3, []float64{2, 0.5, 3, 0.5, 1, 0.6, 3, 0.6, 10}),
			marginal: []int{0},
		},
		{
			mu:       []float64{2, 3, 4},
			sigma:    mat64.NewSymDense(3, []float64{2, 0.5, 3, 0.5, 1, 0.6, 3, 0.6, 10}),
			marginal: []int{0, 2},
		},
		{
			mu:    []float64{2, 3, 4, 5},
			sigma: mat64.NewSymDense(4, []float64{2, 0.5, 3, 0.1, 0.5, 1, 0.6, 0.2, 3, 0.6, 10, 0.3, 0.1, 0.2, 0.3, 3}),

			marginal: []int{0, 3},
		},
	} {
		normal, ok := NewNormal(test.mu, test.sigma, nil)
		if !ok {
			t.Fatalf("Bad test, covariance matrix not positive definite")
		}
		marginal, ok := normal.MarginalNormal(test.marginal, nil)
		if !ok {
			t.Fatalf("Bad test, marginal matrix not positive definite")
		}
		dim := normal.Dim()
		nSamples := 1000000
		samps := mat64.NewDense(nSamples, dim, nil)
		for i := 0; i < nSamples; i++ {
			normal.Rand(samps.RawRowView(i))
		}
		estMean := make([]float64, dim)
		for i := range estMean {
			estMean[i] = stat.Mean(mat64.Col(nil, i, samps), nil)
		}
		for i, v := range test.marginal {
			if math.Abs(marginal.mu[i]-estMean[v]) > 1e-2 {
				t.Errorf("Mean mismatch: want: %v, got %v", estMean[v], marginal.mu[i])
			}
		}

		marginalCov := marginal.CovarianceMatrix(nil)
		estCov := stat.CovarianceMatrix(nil, samps, nil)
		for i, v1 := range test.marginal {
			for j, v2 := range test.marginal {
				c := marginalCov.At(i, j)
				ec := estCov.At(v1, v2)
				if math.Abs(c-ec) > 5e-2 {
					t.Errorf("Cov mismatch element i = %d, j = %d: want: %v, got %v", i, j, c, ec)
				}
			}
		}
	}
}

// findLinearlyIndependnt finds a set of linearly independent columns of A, and
// returns the column indexes of the linearly independent columns.
func findLinearlyIndependent(A mat64.Matrix) []int {
	m, n := A.Dims()
	idxs := make([]int, 0, m)
	columns := mat64.NewDense(m, m, nil)
	newCol := make([]float64, m)
	// Walk in reverse order because slack variables are typically the last columns
	// of A.
	for i := n - 1; i >= 0; i-- {
		if len(idxs) == m {
			break
		}
		mat64.Col(newCol, i, A)
		if len(idxs) == 0 {
			// A column is linearly independent from the null set.
			// This is what needs to be changed if zero columns are allowed, as
			// a column of all zeros is not linearly independent from itself.
			columns.SetCol(len(idxs), newCol)
			idxs = append(idxs, i)
			continue
		}
		if linearlyDependent(mat64.NewVector(m, newCol), columns.View(0, 0, m, len(idxs))) {
			continue
		}
		columns.SetCol(len(idxs), newCol)
		idxs = append(idxs, i)
	}
	return idxs
}

// linearlyDependent returns whether the vector is linearly dependent
// with the columns of A. It assumes that A is a full-rank matrix.
func linearlyDependent(vec *mat64.Vector, A mat64.Matrix) bool {
	// Add vec to the columns of A, and see if the condition number is reasonable.
	m, n := A.Dims()
	aNew := mat64.NewDense(m, n+1, nil)
	aNew.Copy(A)
	col := mat64.Col(nil, 0, vec)
	aNew.SetCol(n, col)
	cond := mat64.Cond(aNew, 1)
	return cond > 1e12
}

// extractColumns creates a new matrix out of the columns of A specified by cols.
// TODO(btracey): Allow this to take a receiver.
func extractColumns(A mat64.Matrix, cols []int) *mat64.Dense {
	r, _ := A.Dims()
	sub := mat64.NewDense(r, len(cols), nil)
	col := make([]float64, r)
	for j, idx := range cols {
		mat64.Col(col, idx, A)
		sub.SetCol(j, col)
	}
	return sub
}

func TestGcvCalibrateCamera(t *testing.T) {
	objPts := mat64.NewDense(10, 3, []float64{
		-1.482676, -1.419348, 1.166475,
		-0.043819, -0.729445, 1.212821,
		0.960825, 1.147328, 0.485541,
		1.738245, 0.597865, 1.026016,
		-0.430206, -1.281281, 0.870726,
		-1.627323, -2.203264, -0.381758,
		0.166347, -0.571246, 0.428893,
		0.376266, 0.213996, -0.299131,
		-0.226950, 0.942377, -0.899869,
		-1.148912, 0.093725, 0.634745,
	})
	objPts.Clone(objPts.T())

	imgPts := mat64.NewDense(10, 2, []float64{
		-0.384281, -0.299055,
		0.361833, 0.087737,
		1.370253, 1.753933,
		1.421390, 0.853312,
		0.107177, -0.443076,
		3.773328, 5.437829,
		0.624914, -0.280949,
		-0.825577, -0.245594,
		0.631444, -0.340257,
		-0.647580, 0.502113,
	})
	imgPts.Clone(imgPts.T())

	camMat := GcvInitCameraMatrix2D(objPts, imgPts, [2]int{1920, 1080}, 1)

	distCoeffs := mat64.NewDense(5, 1, []float64{0, 0, 0, 0, 0})

	camMat, rvec, tvec := GcvCalibrateCamera(
		objPts, imgPts, camMat, distCoeffs, [2]int{1920, 1080}, 14575)

	assert.InDeltaSlice(t, []float64{-46.15296606, 0., 959.5}, mat64.Row(nil, 0, camMat), DELTA)
	assert.InDeltaSlice(t, []float64{0., -46.15296606, 539.5}, mat64.Row(nil, 1, camMat), DELTA)
	assert.InDeltaSlice(t, []float64{0., 0., 1.}, mat64.Row(nil, 2, camMat), DELTA)

	assert.InDeltaSlice(t, []float64{-0.98405029, -0.93443411, -0.26304667}, mat64.Col(nil, 0, rvec), DELTA)
	assert.InDeltaSlice(t, []float64{0.6804739, 0.47530207, -0.04833094}, mat64.Col(nil, 0, tvec), DELTA)
}

func getColumnVector(index int, M mat.Matrix) *mat.Vector {
	rows, _ := M.Dims()
	var colData []float64

	if rows == 0 {
		colData = []float64{}
	} else {
		colData = mat.Col(nil, index, M)
	}

	return mat.NewVector(rows, colData)
}

func TestNormRand(t *testing.T) {
	for _, test := range []struct {
		mean []float64
		cov  []float64
	}{
		{
			mean: []float64{0, 0},
			cov: []float64{
				1, 0,
				0, 1,
			},
		},
		{
			mean: []float64{0, 0},
			cov: []float64{
				1, 0.9,
				0.9, 1,
			},
		},
		{
			mean: []float64{6, 7},
			cov: []float64{
				5, 0.9,
				0.9, 2,
			},
		},
	} {
		dim := len(test.mean)
		cov := mat64.NewSymDense(dim, test.cov)
		n, ok := NewNormal(test.mean, cov, nil)
		if !ok {
			t.Errorf("bad covariance matrix")
		}

		nSamples := 1000000
		samps := mat64.NewDense(nSamples, dim, nil)
		for i := 0; i < nSamples; i++ {
			n.Rand(samps.RawRowView(i))
		}
		estMean := make([]float64, dim)
		for i := range estMean {
			estMean[i] = stat.Mean(mat64.Col(nil, i, samps), nil)
		}
		if !floats.EqualApprox(estMean, test.mean, 1e-2) {
			t.Errorf("Mean mismatch: want: %v, got %v", test.mean, estMean)
		}
		estCov := stat.CovarianceMatrix(nil, samps, nil)
		if !mat64.EqualApprox(estCov, cov, 1e-2) {
			t.Errorf("Cov mismatch: want: %v, got %v", cov, estCov)
		}
	}
}

func GcvCalibrateCamera(objPts, imgPts, camMat, distCoeffs *mat64.Dense,
	dims [2]int, flags int) (calCamMat, rvec, tvec *mat64.Dense) {

	objDim, nObjPts := objPts.Dims()
	imgDim, nImgPts := imgPts.Dims()

	if objDim != 3 || imgDim != 2 || nObjPts != nImgPts {
		panic("Invalid dimensions for objPts and imgPts")
	}

	objPtsVec := NewGcvPoint3f32Vector(int64(nObjPts))
	imgPtsVec := NewGcvPoint2f32Vector(int64(nObjPts))

	for j := 0; j < nObjPts; j++ {
		objPtsVec.Set(j, NewGcvPoint3f32(mat64.Col(nil, j, objPts)...))
	}

	for j := 0; j < nObjPts; j++ {
		imgPtsVec.Set(j, NewGcvPoint2f32(mat64.Col(nil, j, imgPts)...))
	}

	_camMat := Mat64ToGcvMat(camMat)
	_distCoeffs := Mat64ToGcvMat(distCoeffs)
	_rvec := NewGcvMat()
	_tvec := NewGcvMat()
	_imgSize := NewGcvSize2i(dims[0], dims[1])

	GcvCalibrateCamera_(
		objPtsVec, imgPtsVec,
		_imgSize, _camMat, _distCoeffs,
		_rvec, _tvec, flags)

	calCamMat = GcvMatToMat64(_camMat)
	rvec = GcvMatToMat64(_rvec)
	tvec = GcvMatToMat64(_tvec)

	return calCamMat, rvec, tvec
}

func TestMat64(t *testing.T) {
	fm := readFm()
	dense := fm.Mat64(false, false)

	compareCol := func(i int, exp []float64) {
		col := mat64.Col(nil, i, dense)
		assert.Equal(t, len(col), len(exp))
		for i := range exp {
			assert.Equal(t, col[i], exp[i])
		}
	}

	compareCol(1, []float64{0, 0, 0, 0, 0, 1, 1, 1})
	compareCol(2, []float64{0, 0, 0, 0, 0, 0, 0, 1})
}

// PrincipalComponents returns the principal component direction vectors and
// the column variances of the principal component scores, vecs * a, computed
// using the singular value decomposition of the input. The input a is an n×d
// matrix where each row is an observation and each column represents a variable.
//
// PrincipalComponents centers the variables but does not scale the variance.
//
// The slice weights is used to weight the observations. If weights is nil,
// each weight is considered to have a value of one, otherwise the length of
// weights must match the number of observations or PrincipalComponents will
// panic.
//
// On successful completion, the principal component direction vectors are
// returned in vecs as a d×min(n, d) matrix, and the variances are returned in
// vars as a min(n, d)-long slice in descending sort order.
//
// If no singular value decomposition is possible, vecs and vars are returned
// nil and ok is returned false.
func PrincipalComponents(a mat64.Matrix, weights []float64) (vecs *mat64.Dense, vars []float64, ok bool) {
	n, d := a.Dims()
	if weights != nil && len(weights) != n {
		panic("stat: len(weights) != observations")
	}

	centered := mat64.NewDense(n, d, nil)
	col := make([]float64, n)
	for j := 0; j < d; j++ {
		mat64.Col(col, j, a)
		floats.AddConst(-Mean(col, weights), col)
		centered.SetCol(j, col)
	}
	for i, w := range weights {
		floats.Scale(math.Sqrt(w), centered.RawRowView(i))
	}

	kind := matrix.SVDFull
	if n > d {
		kind = matrix.SVDThin
	}
	var svd mat64.SVD
	ok = svd.Factorize(centered, kind)
	if !ok {
		return nil, nil, false
	}

	vecs = &mat64.Dense{}
	vecs.VFromSVD(&svd)
	if n < d {
		// Don't retain columns that are not valid direction vectors.
		vecs.Clone(vecs.View(0, 0, d, n))
	}
	vars = svd.Values(nil)
	var f float64
	if weights == nil {
		f = 1 / float64(n-1)
	} else {
		f = 1 / (floats.Sum(weights) - 1)
	}
	for i, v := range vars {
		vars[i] = f * v * v
	}
	return vecs, vars, true
}

func TestRejection(t *testing.T) {
	// Test by finding the expected value of a uniform.
	dim := 3
	bounds := make([]distmv.Bound, dim)
	for i := 0; i < dim; i++ {
		min := rand.NormFloat64()
		max := rand.NormFloat64()
		if min > max {
			min, max = max, min
		}
		bounds[i].Min = min
		bounds[i].Max = max
	}
	target := distmv.NewUniform(bounds, nil)
	mu := target.Mean(nil)

	muImp := make([]float64, dim)
	sigmaImp := mat64.NewSymDense(dim, nil)
	for i := 0; i < dim; i++ {
		sigmaImp.SetSym(i, i, 6)
	}
	proposal, ok := distmv.NewNormal(muImp, sigmaImp, nil)
	if !ok {
		t.Fatal("bad test, sigma not pos def")
	}

	nSamples := 1000
	batch := mat64.NewDense(nSamples, dim, nil)
	weights := make([]float64, nSamples)
	_, ok = Rejection(batch, target, proposal, 1000, nil)
	if !ok {
		t.Error("Bad test, nan samples")
	}

	for i := 0; i < dim; i++ {
		col := mat64.Col(nil, i, batch)
		ev := stat.Mean(col, weights)
		if math.Abs(ev-mu[i]) > 1e-2 {
			t.Errorf("Mean mismatch: Want %v, got %v", mu[i], ev)
		}
	}
}

// computeMove computes how far can be moved replacing each index. The results
// are stored into move.
func computeMove(move []float64, minIdx int, A mat64.Matrix, ab *mat64.Dense, xb []float64, nonBasicIdx []int) error {
	// Find ae.
	col := mat64.Col(nil, nonBasicIdx[minIdx], A)
	aCol := mat64.NewVector(len(col), col)

	// d = - Ab^-1 Ae
	nb, _ := ab.Dims()
	d := make([]float64, nb)
	dVec := mat64.NewVector(nb, d)
	err := dVec.SolveVec(ab, aCol)
	if err != nil {
		return ErrLinSolve
	}
	floats.Scale(-1, d)

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

	// If no di < 0, then problem is unbounded.
	if floats.Min(d) >= 0 {
		return ErrUnbounded
	}

	// move = bhat_i / - d_i, assuming d is negative.
	bHat := xb // ab^-1 b
	for i, v := range d {
		if v >= 0 {
			move[i] = math.Inf(1)
		} else {
			move[i] = bHat[i] / math.Abs(v)
		}
	}
	return nil
}

func compareNormal(t *testing.T, want *distmv.Normal, batch *mat64.Dense, weights []float64) {
	dim := want.Dim()
	mu := want.Mean(nil)
	sigma := want.CovarianceMatrix(nil)
	n, _ := batch.Dims()
	if weights == nil {
		weights = make([]float64, n)
		for i := range weights {
			weights[i] = 1
		}
	}
	for i := 0; i < dim; i++ {
		col := mat64.Col(nil, i, batch)
		ev := stat.Mean(col, weights)
		if math.Abs(ev-mu[i]) > 1e-2 {
			t.Errorf("Mean mismatch: Want %v, got %v", mu[i], ev)
		}
	}

	cov := stat.CovarianceMatrix(nil, batch, weights)
	if !mat64.EqualApprox(cov, sigma, 1.5e-1) {
		t.Errorf("Covariance matrix mismatch")
	}
}

func TestCorrelationMatrix(t *testing.T) {
	for i, test := range []struct {
		data    *mat64.Dense
		weights []float64
		ans     *mat64.Dense
	}{
		{
			data: mat64.NewDense(3, 3, []float64{
				1, 2, 3,
				3, 4, 5,
				5, 6, 7,
			}),
			weights: nil,
			ans: mat64.NewDense(3, 3, []float64{
				1, 1, 1,
				1, 1, 1,
				1, 1, 1,
			}),
		},
		{
			data: mat64.NewDense(5, 2, []float64{
				-2, -4,
				-1, 2,
				0, 0,
				1, -2,
				2, 4,
			}),
			weights: nil,
			ans: mat64.NewDense(2, 2, []float64{
				1, 0.6,
				0.6, 1,
			}),
		}, {
			data: mat64.NewDense(3, 2, []float64{
				1, 1,
				2, 4,
				3, 9,
			}),
			weights: []float64{
				1,
				1.5,
				1,
			},
			ans: mat64.NewDense(2, 2, []float64{
				1, 0.9868703275903379,
				0.9868703275903379, 1,
			}),
		},
	} {
		// Make a copy of the data to check that it isn't changing.
		r := test.data.RawMatrix()
		d := make([]float64, len(r.Data))
		copy(d, r.Data)

		w := make([]float64, len(test.weights))
		if test.weights != nil {
			copy(w, test.weights)
		}
		c := CorrelationMatrix(nil, test.data, test.weights)
		if !mat64.Equal(c, test.ans) {
			t.Errorf("%d: expected corr %v, found %v", i, test.ans, c)
		}
		if !floats.Equal(d, r.Data) {
			t.Errorf("%d: data was modified during execution", i)
		}
		if !floats.Equal(w, test.weights) {
			t.Errorf("%d: weights was modified during execution", i)
		}

		// compare with call to Covariance
		_, cols := c.Dims()
		for ci := 0; ci < cols; ci++ {
			for cj := 0; cj < cols; cj++ {
				x := mat64.Col(nil, ci, test.data)
				y := mat64.Col(nil, cj, test.data)
				corr := Correlation(x, y, test.weights)
				if math.Abs(corr-c.At(ci, cj)) > 1e-14 {
					t.Errorf("CorrMat does not match at (%v, %v). Want %v, got %v.", ci, cj, corr, c.At(ci, cj))
				}
			}
		}

	}
	if !Panics(func() { CorrelationMatrix(nil, mat64.NewDense(5, 2, nil), []float64{}) }) {
		t.Errorf("CorrelationMatrix did not panic with weight size mismatch")
	}
	if !Panics(func() { CorrelationMatrix(mat64.NewDense(1, 1, nil), mat64.NewDense(5, 2, nil), nil) }) {
		t.Errorf("CorrelationMatrix did not panic with preallocation size mismatch")
	}
	if !Panics(func() { CorrelationMatrix(nil, mat64.NewDense(2, 2, []float64{1, 2, 3, 4}), []float64{1, -1}) }) {
		t.Errorf("CorrelationMatrix did not panic with negative weights")
	}
}