gonum: mat: performance of calculating eigenvalues in gonum is slower than numpy

What are you trying to do?

I am comparing the performance of certain numpy operations against gonum for equivalency. In this specific benchmark I am assessing the performance of calculating the eigenvalues of a matrix to determine whether the matrix is positive definite.

What did you do?

I ran the following scripts in Python and Go respectively:

import numpy as np

def is_pos_def(x):
    return np.all(np.linalg.eigvals(x) > 0)

a = np.random.rand(1000, 1000)
print is_pos_def(a)

package main

import (
	"fmt"
	"math/rand"
	"gonum.org/v1/gonum/mat"
)

func randMat(d int) mat.Matrix {
	data := make([]float64, d*d)
	for i := range data {
		data[i] = rand.NormFloat64()
	}
	return mat.NewDense(d, d, data)
}

func isPosDef(x mat.Matrix) bool {
	var eig mat.Eigen
	eig.Factorize(x, false, false)
	allGreaterThanZero := true
	for _, v := range eig.Values(nil) {
		if real(v) <= 0.0 {
			allGreaterThanZero = false
			break
		}
	}
	return allGreaterThanZero
}

func main() {
	a := randMat(1000)
	fmt.Println(isPosDef(a))
}

What did you expect to happen?

I expected the Go script to run equally fast as the Python script

What actually happened?

The Go script runs about 5x slower than the Python script:

python demo.py  1.36s user 0.12s system 135% cpu 1.092 total

go run demo.go  6.04s user 0.26s system 129% cpu 4.855 total

The Go script runs about 16x slower when left and/or right are set to true when calculating the eigenvector factorization. Am I setting up the Go code incorrectly at all or is there something degrading performance in the library implementation?

What version of Go and Gonum are you using?

$ go version
go version go1.10 darwin/amd64

gonum$ git rev-parse HEAD
c75679ee1eff8582bca7583704825721ea1ff701