Пример #1
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//This is a temporal function. It returns the determinant of a 3x3 matrix. Panics if the matrix is not 3x3.
//It is also defined in the chem package which is not-so-clean.
func det(A mat64.Matrix) float64 {
	r, c := A.Dims()
	if r != 3 || c != 3 {
		panic(ErrDeterminant)
	}
	return (A.At(0, 0)*(A.At(1, 1)*A.At(2, 2)-A.At(2, 1)*A.At(1, 2)) - A.At(1, 0)*(A.At(0, 1)*A.At(2, 2)-A.At(2, 1)*A.At(0, 2)) + A.At(2, 0)*(A.At(0, 1)*A.At(1, 2)-A.At(1, 1)*A.At(0, 2)))
}
Пример #2
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// MeanBatch predicts the mean at the set of locations specified by x. Stores in-place into yPred
// If yPred is nil new memory is allocated.
func (g *GP) MeanBatch(yPred []float64, x mat64.Matrix) []float64 {
	rx, cx := x.Dims()
	if cx != g.inputDim {
		panic(badInputLength)
	}
	if yPred == nil {
		yPred = make([]float64, rx)
	}
	ry := len(yPred)
	if rx != ry {
		panic(badOutputLength)
	}
	nSamples, _ := g.inputs.Dims()

	covariance := mat64.NewDense(nSamples, rx, nil)
	row := make([]float64, g.inputDim)
	for j := 0; j < rx; j++ {
		for k := 0; k < g.inputDim; k++ {
			row[k] = x.At(j, k)
		}
		for i := 0; i < nSamples; i++ {
			v := g.kernel.Distance(g.inputs.RawRowView(i), row)
			covariance.Set(i, j, v)
		}
	}
	yPredVec := mat64.NewVector(len(yPred), yPred)
	yPredVec.MulVec(covariance.T(), g.sigInvY)
	// Rescale the outputs
	for i, v := range yPred {
		yPred[i] = v*g.std + g.mean
	}
	return yPred
}
Пример #3
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func columnMean(M mat.Matrix) mat.Matrix {
	r, c := M.Dims()

	SumMatrix := columnSum(M)

	switch t := SumMatrix.(type) {
	case *mat.Dense:
		M := mat.NewDense(1, c, nil)
		M.Scale(1/float64(r), SumMatrix)
		return M
	case mat.Mutable:
		_ = t
		V := SumMatrix.(mat.Mutable)
		_, cols := V.Dims()

		for i := 0; i < cols; i++ {
			V.Set(0, i, SumMatrix.At(0, i)/float64(r))
		}

		return V
	default:
		panic("M is of an unknown type")
	}

}
Пример #4
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// 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
}
Пример #5
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// Cov returns the covariance between a set of data points based on the current
// GP fit.
func (g *GP) Cov(m *mat64.SymDense, x mat64.Matrix) *mat64.SymDense {
	if m != nil {
		// TODO(btracey): Make this k**
		panic("resuing m not coded")
	}
	// The joint covariance matrix is
	// K(x_*, k_*) - k(x_*, x) k(x,x)^-1 k(x, x*)
	nSamp, nDim := x.Dims()
	if nDim != g.inputDim {
		panic(badInputLength)
	}

	// Compute K(x_*, x) K(x, x)^-1 K(x, x_*)
	kstar := g.formKStar(x)
	var tmp mat64.Dense
	tmp.SolveCholesky(g.cholK, kstar)
	var tmp2 mat64.Dense
	tmp2.Mul(kstar.T(), &tmp)

	// Compute k(x_*, x_*) and perform the subtraction.
	kstarstar := mat64.NewSymDense(nSamp, nil)
	for i := 0; i < nSamp; i++ {
		for j := i; j < nSamp; j++ {
			v := g.kernel.Distance(mat64.Row(nil, i, x), mat64.Row(nil, j, x))
			if i == j {
				v += g.noise
			}
			kstarstar.SetSym(i, j, v-tmp2.At(i, j))
		}
	}
	return kstarstar
}
Пример #6
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func benchmarkCovarianceMatrixInPlace(b *testing.B, m mat64.Matrix) {
	_, c := m.Dims()
	res := mat64.NewDense(c, c, nil)
	b.ResetTimer()
	for i := 0; i < b.N; i++ {
		CovarianceMatrix(res, m, nil)
	}
}
Пример #7
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func MatrixToImage(src mat64.Matrix) image.Image {
	width, height := src.Dims()
	img := image.NewRGBA(image.Rect(0, 0, width, height))
	for x := 0; x < width; x++ {
		for y := 0; y < height; y++ {
			img.Set(x, y, Float64ToColor(src.At(x, y)))
		}
	}
	return img
}
Пример #8
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// 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
}
Пример #9
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func rowSum(M mat.Matrix) mat.Matrix {
	rows, _ := M.Dims()

	floatRes := make([]float64, rows)
	for i := 0; i < rows; i++ {
		floatRes[i] = mat.Sum(getRowVector(i, M))
	}

	return mat.NewDense(rows, 1, floatRes)
}
Пример #10
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func columnSum(M mat.Matrix) mat.Matrix {
	_, cols := M.Dims()

	floatRes := make([]float64, cols)
	for i := 0; i < cols; i++ {
		floatRes[i] = mat.Sum(getColumnVector(i, M))
	}

	return mat.NewDense(1, cols, floatRes)
}
Пример #11
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// 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
}
Пример #12
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func verifyInputs(initialBasic []int, c []float64, A mat64.Matrix, b []float64) error {
	m, n := A.Dims()
	if len(c) != n {
		panic("lp: c vector incorrect length")
	}
	if len(b) != m {
		panic("lp: b vector incorrect length")
	}
	if len(c) != n {
		panic("lp: c vector incorrect length")
	}
	if len(initialBasic) != 0 && len(initialBasic) != m {
		panic("lp: initialBasic incorrect length")
	}

	// Do some sanity checks so that ab does not become singular during the
	// simplex solution. If the ZeroRow checks are removed then the code for
	// finding a set of linearly indepent columns must be improved.

	// Check that if a row of A only has zero elements that corresponding
	// element in b is zero, otherwise the problem is infeasible.
	// Otherwise return ErrZeroRow.
	for i := 0; i < m; i++ {
		isZero := true
		for j := 0; j < n; j++ {
			if A.At(i, j) != 0 {
				isZero = false
				break
			}
		}
		if isZero && b[i] != 0 {
			// Infeasible
			return ErrInfeasible
		} else if isZero {
			return ErrZeroRow
		}
	}
	// Check that if a column only has zero elements that the respective C vector
	// is positive (otherwise unbounded). Otherwise return ErrZeroColumn.
	for j := 0; j < n; j++ {
		isZero := true
		for i := 0; i < m; i++ {
			if A.At(i, j) != 0 {
				isZero = false
				break
			}
		}
		if isZero && c[j] < 0 {
			return ErrUnbounded
		} else if isZero {
			return ErrZeroColumn
		}
	}
	return nil
}
Пример #13
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// AssignCentroid assigns all of the examples in X to one of the groups
// in Mu
// X -> (m*n), Mu -> (K*n)
// returns (m*1)
func AssignCentroid(X, Mu mat.Matrix) *mat.Vector {
	m, _ := X.Dims()
	idx := mat.NewVector(m, nil)

	for i := 0; i < m; i++ {
		x := getRowVector(i, X)
		idx.SetVec(i, float64(NearestCentroid(x, Mu)))
	}

	return idx
}
Пример #14
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func getRowVector(index int, M mat.Matrix) *mat.Vector {
	_, cols := M.Dims()
	var rowData []float64

	if cols == 0 {
		rowData = []float64{}
	} else {
		rowData = mat.Row(nil, index, M)
	}
	return mat.NewVector(cols, rowData)
}
Пример #15
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func J(idx *mat.Vector, X, Mu mat.Matrix) float64 {
	Mux := ConstructXCentroidMatrix(idx, Mu)
	xRows, xCols := X.Dims()

	Diff := mat.NewDense(xRows, xCols, nil)
	Diff.Sub(X, Mux)
	Diff.MulElem(Diff, Diff)
	Diff = rowSum(Diff).(*mat.Dense)

	return columnSum(Diff).At(0, 0) / float64(xRows)
}
Пример #16
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func benchmarkCovarianceMatrixWeighted(b *testing.B, m mat64.Matrix) {
	r, _ := m.Dims()
	wts := make([]float64, r)
	for i := range wts {
		wts[i] = 0.5
	}
	b.ResetTimer()
	for i := 0; i < b.N; i++ {
		CovarianceMatrix(nil, m, wts)
	}
}
Пример #17
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// MoveCentroid computes the averages for all the points inside each of the cluster
// centroid groups, then move the cluster centroid points to those averages.
// It then returns the new Centroids
func MoveCentroids(idx *mat.Vector, X, Mu mat.Matrix) mat.Matrix {
	muRows, muCols := Mu.Dims()
	NewMu := mat.NewDense(muRows, muCols, nil)

	for k := 0; k < muRows; k++ {
		CentroidKMean := columnMean(rowIndexIn(findIn(float64(k), idx), X))
		NewMu.SetRow(k,
			mat.Row(nil, 0, CentroidKMean))
	}

	return NewMu
}
Пример #18
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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)
}
Пример #19
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// NewComplex returns a complex matrix constructed from r and i. At least one of
// r or i must be non-nil otherwise NewComplex will panic. If one of the inputs
// is nil, that part of the complex number will be zero when returned by At.
// If both are non-nil but differ in their sizes, NewComplex will panic.
func NewComplex(r, i mat64.Matrix) Complex {
	if r == nil && i == nil {
		panic("conv: no matrix")
	} else if r != nil && i != nil {
		rr, rc := r.Dims()
		ir, ic := i.Dims()
		if rr != ir || rc != ic {
			panic(matrix.ErrShape)
		}
	}
	return Complex{r: r, i: i, imagSign: 1}
}
Пример #20
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// rowIndexIn returns a matrix contains the rows in indexes vector
func rowIndexIn(indexes *mat.Vector, M mat.Matrix) mat.Matrix {
	m := indexes.Len()
	_, n := M.Dims()
	Res := mat.NewDense(m, n, nil)

	for i := 0; i < m; i++ {
		Res.SetRow(i, mat.Row(
			nil,
			int(indexes.At(i, 0)),
			M))
	}

	return Res
}
Пример #21
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// CovarianceMatrix calculates a covariance matrix (also known as a
// variance-covariance matrix) from a matrix of data, using a two-pass
// algorithm.
//
// The weights must have length equal to the number of rows in
// input data matrix x. If cov is nil, then a new matrix with appropriate size will
// be constructed. If cov is not nil, it should have the same number of columns as the
// input data matrix x, and it will be used as the destination for the covariance
// data. Weights must not be negative.
func CovarianceMatrix(cov *mat64.SymDense, x mat64.Matrix, weights []float64) *mat64.SymDense {
	// This is the matrix version of the two-pass algorithm. It doesn't use the
	// additional floating point error correction that the Covariance function uses
	// to reduce the impact of rounding during centering.

	r, c := x.Dims()

	if cov == nil {
		cov = mat64.NewSymDense(c, nil)
	} else if n := cov.Symmetric(); n != c {
		panic(matrix.ErrShape)
	}

	var xt mat64.Dense
	xt.Clone(x.T())
	// Subtract the mean of each of the columns.
	for i := 0; i < c; i++ {
		v := xt.RawRowView(i)
		// This will panic with ErrShape if len(weights) != len(v), so
		// we don't have to check the size later.
		mean := Mean(v, weights)
		floats.AddConst(-mean, v)
	}

	if weights == nil {
		// Calculate the normalization factor
		// scaled by the sample size.
		cov.SymOuterK(1/(float64(r)-1), &xt)
		return cov
	}

	// Multiply by the sqrt of the weights, so that multiplication is symmetric.
	sqrtwts := make([]float64, r)
	for i, w := range weights {
		if w < 0 {
			panic("stat: negative covariance matrix weights")
		}
		sqrtwts[i] = math.Sqrt(w)
	}
	// Weight the rows.
	for i := 0; i < c; i++ {
		v := xt.RawRowView(i)
		floats.Mul(v, sqrtwts)
	}

	// Calculate the normalization factor
	// scaled by the weighted sample size.
	cov.SymOuterK(1/(floats.Sum(weights)-1), &xt)
	return cov
}
Пример #22
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func transpose(A mat64.Matrix) mat64.Matrix {
	r, s := A.Dims()
	var data []float64

	for j := 0; j < s; j++ {
		for i := 0; i < r; i++ {
			data = append(data, A.At(i, j))
		}
	}

	// Está medio chafa que regrese Dense, cómo hacemos para que regrese
	// el mismo tipo de A?
	return mat64.NewDense(s, r, data)
}
Пример #23
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// NearestCentroid returns the index of the row in Mu for which its
// vector magnitude with x is the least.
// x should be (n*1) space and M (K*n) space
func NearestCentroid(x *mat.Vector, Mu mat.Matrix) (rowIndex int) {
	k, _ := Mu.Dims()
	rowIndex = 0
	leastDistance := vectorDistance(x, getRowVector(rowIndex, Mu))

	for i := 1; i < k; i++ {
		distance := vectorDistance(x, getRowVector(i, Mu))
		if distance < leastDistance {
			leastDistance = distance
			rowIndex = i
		}
	}

	return
}
Пример #24
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// PrintMat imprime una matriz con un formato entendible
func PrintMat(A mat64.Matrix) {
	r, s := A.Dims()

	fmt.Printf("(")
	for i := 0; i < r; i++ {
		fmt.Printf("\t")
		for j := 0; j < s; j++ {
			fmt.Printf("%0.1f\t", A.At(i, j))
		}
		if i != r-1 {
			fmt.Printf("\n")
		}
	}
	fmt.Printf(")\n")
}
Пример #25
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//ScaleByCol scales each column of matrix A by Col, putting the result
//in the received.
func (F *Matrix) ScaleByCol(A, Col mat64.Matrix) {
	ar, ac := A.Dims()
	cr, cc := Col.Dims()
	fr, fc := F.Dims()
	if ar != cr || cc > 1 || ar != fr || ac != fc {
		panic(ErrShape)
	}
	if F != A {
		F.Copy(A)
	}
	for i := 0; i < ac; i++ {
		temp := F.ColView(i)
		temp.MulElem(temp, Col)
	}

}
Пример #26
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// VerifyInputs returns true if the number of rows in inputs is not the same
// as the number of rows in outputs and the length of weights. As a special case,
// the length of weights is allowed to be zero.
func VerifyInputs(inputs, outputs mat64.Matrix, weights []float64) error {
	if inputs == nil || outputs == nil {
		return NoData
	}
	nSamples, _ := inputs.Dims()
	nOutputSamples, _ := outputs.Dims()
	nWeights := len(weights)
	if nSamples != nOutputSamples || (nWeights != 0 && nSamples != nWeights) {
		return DataMismatch{
			Input:  nSamples,
			Output: nOutputSamples,
			Weight: nWeights,
		}
	}
	return nil
}
Пример #27
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// 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
}
Пример #28
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// formKStar forms the covariance matrix between the inputs and new points.
func (g *GP) formKStar(x mat64.Matrix) *mat64.Dense {
	// TODO(btracey): Parallelize
	r, c := x.Dims()
	n := len(g.outputs)
	kStar := mat64.NewDense(n, r, nil)
	data := make([]float64, c)
	for j := 0; j < r; j++ {
		for k := 0; k < c; k++ {
			data[k] = x.At(j, k)
		}
		for i := 0; i < n; i++ {
			row := g.inputs.RawRowView(i)
			v := g.kernel.Distance(row, data)
			kStar.Set(i, j, v)
		}
	}
	return kStar
}
Пример #29
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// Given number of clusters K and the training set X of dimension (m*n)
// InitializeCentroids returns matrix Mu of dimension (K*n)
// The steps to initialize the centroids are as follows
//     1. Randomly pick K training examples (Make sure the selected examples are unique)
//     2. Set Mu to the K examples
func InitializeCentroids(K int, X mat.Matrix) (Mu mat.Matrix) {
	m, n := X.Dims()

	// panic if K >= m
	if K >= m {
		panic("K should be less than the size of the training set")
	}

	randomIndexes := randArray(0, m, K, true) // 1. pick K training examples

	// 2. set Mu
	Mu = mat.NewDense(K, n, nil)
	for i := 0; i < K; i++ {
		Mu.(*mat.Dense).SetRow(i, mat.Row(nil, randomIndexes[i], X))
	}

	return
}
Пример #30
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// StdDevBatch predicts the standard deviation at a set of locations of x.
func (g *GP) StdDevBatch(std []float64, x mat64.Matrix) []float64 {
	r, c := x.Dims()
	if c != g.inputDim {
		panic(badInputLength)
	}
	if std == nil {
		std = make([]float64, r)
	}
	if len(std) != r {
		panic(badStorage)
	}
	// For a single point, the stddev is
	// 		sigma = k(x,x) - k_*^T * K^-1 * k_*
	// where k is the vector of kernels between the input points and the output points
	// For many points, the formula is:
	// 		nu_* = k(x_*, k_*) - k_*^T * K^-1 * k_*
	// This creates the full covariance matrix which is an rxr matrix. However,
	// the standard deviations are just the diagonal of this matrix. Instead, be
	// smart about it and compute the diagonal terms one at a time.
	kStar := g.formKStar(x)
	var tmp mat64.Dense
	tmp.SolveCholesky(g.cholK, kStar)

	// set k(x_*, x_*) into std then subtract k_*^T K^-1 k_* , computed one row at a time
	var tmp2 mat64.Vector
	row := make([]float64, c)
	for i := range std {
		for k := 0; k < c; k++ {
			row[k] = x.At(i, k)
		}
		std[i] = g.kernel.Distance(row, row)
		tmp2.MulVec(kStar.ColView(i).T(), tmp.ColView(i))
		rt, ct := tmp2.Dims()
		if rt != 1 && ct != 1 {
			panic("bad size")
		}
		std[i] -= tmp2.At(0, 0)
		std[i] = math.Sqrt(std[i])
	}
	// Need to scale the standard deviation to be in the same units as y.
	floats.Scale(g.std, std)
	return std
}