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d39f7d1528
MulTrans is much faster than Mul, and by taking the square root of the weights we can always use MulTrans. add test for negative weights add benchmarks for weighted covariance reorder code so simple path is first fix test error message to include fixture number re-add comment on making the returned type symmetric
83 lines
2.3 KiB
Go
83 lines
2.3 KiB
Go
// Copyright ©2014 The gonum Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package stat
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import (
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"github.com/gonum/floats"
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"github.com/gonum/matrix/mat64"
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"math"
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)
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// CovarianceMatrix calculates a covariance matrix (also known as a
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// variance-covariance matrix) from a matrix of data, using a two-pass
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// algorithm. The matrix returned will be symmetric, square, and
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// positive-semidefinite.
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//
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// The weights wts should have the length equal to the number of rows in
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// input data matrix x. cov should either be a square matrix with the same
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// number of columns as the input data matrix x, or nil in which case a new
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// Dense matrix will be constructed. Weights cannot be negative.
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func CovarianceMatrix(cov *mat64.Dense, x mat64.Matrix, wts []float64) *mat64.Dense {
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// This is the matrix version of the two-pass algorithm. It doesn't use the
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// additional floating point error correction that the Covariance function uses
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// to reduce the impact of rounding during centering.
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// TODO(jonlawlor): indicate that the resulting matrix is symmetric, and change
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// the returned type from a *mat.Dense to a *mat.Symmetric.
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r, c := x.Dims()
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if cov == nil {
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cov = mat64.NewDense(c, c, nil)
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} else if covr, covc := cov.Dims(); covr != covc || covc != c {
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panic(mat64.ErrShape)
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}
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var xt mat64.Dense
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xt.TCopy(x)
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// Subtract the mean of each of the columns.
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for i := 0; i < c; i++ {
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v := xt.RawRowView(i)
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// This will panic with ErrShape if len(wts) != len(v), so
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// we don't have to check the size later.
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mean := Mean(v, wts)
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floats.AddConst(-mean, v)
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}
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var n float64
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if wts == nil {
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n = float64(r)
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cov.MulTrans(&xt, false, &xt, true)
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// Scale by the sample size.
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cov.Scale(1/(n-1), cov)
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return cov
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}
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// Multiply by the sqrt of the weights, so that multiplication is symmetric.
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sqrtwts := make([]float64, r)
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for i, w := range wts {
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if w < 0 {
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panic("stat: negative covariance matrix weights")
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}
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sqrtwts[i] = math.Sqrt(w)
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}
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// Weight the rows.
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for i := 0; i < c; i++ {
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v := xt.RawRowView(i)
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floats.Mul(v, sqrtwts)
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}
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// Calculate the normalization factor.
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n = floats.Sum(wts)
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cov.MulTrans(&xt, false, &xt, true)
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// Scale by the sample size.
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cov.Scale(1/(n-1), cov)
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return cov
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}
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