// CovarianceMatrix calculates a covariance matrix (also known as a // variance-covariance matrix) from a matrix of data, using a two-pass // algorithm. The matrix returned will be symmetric and square. // // The weights wts should have the length equal to the number of rows in // input data matrix x. If c is nil, then a new matrix with appropriate size will // be constructed. If c is not nil, it should be a square matrix with the same // number of columns as the input data matrix x, and it will be used as the receiver // for the covariance data. Weights cannot be negative. func CovarianceMatrix(cov *mat64.Dense, x mat64.Matrix, wts []float64) *mat64.Dense { // 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. // TODO(jonlawlor): indicate that the resulting matrix is symmetric, and change // the returned type from a *mat.Dense to a *mat.Symmetric. r, c := x.Dims() if cov == nil { cov = mat64.NewDense(c, c, nil) } else if covr, covc := cov.Dims(); covr != covc || covc != c { panic(mat64.ErrShape) } var xt mat64.Dense xt.TCopy(x) // 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(wts) != len(v), so // we don't have to check the size later. mean := Mean(v, wts) floats.AddConst(-mean, v) } var n float64 if wts == nil { n = float64(r) cov.MulTrans(&xt, false, &xt, true) // Scale by the sample size. cov.Scale(1/(n-1), cov) return cov } // Multiply by the sqrt of the weights, so that multiplication is symmetric. sqrtwts := make([]float64, r) for i, w := range wts { 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. n = floats.Sum(wts) cov.MulTrans(&xt, false, &xt, true) // Scale by the sample size. cov.Scale(1/(n-1), cov) return cov }