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I am trying to use the Go gonum/mat matrix library to find the Cholesky factorization of a matrix.

The goal is to get similar results to Matlab chol(). In Matlab chol(P_inno) outputs:

P_inno = [0.10062    -0.042635    -0.072741    -0.1434;
-0.042635    0.21293    -0.02717    -0.052181;
-0.072741    -0.02717    0.26536    0.27184;
-0.1434    -0.052181    0.27184    0.86335] 

chol(P_inno) = 
0.31721    -0.13441    -0.22932    -0.45207
0    0.44143    -0.13137    -0.25585
0    0    0.44217    0.30432
0    0    0    0.70775

So far in Go I have matrix:

arr := []float64{0.067503,0,0,0,0,0.063724,0,0,0,0,0.11575,0,0,0,0,0.05}
P_inno := mat.NewSymDense(4, arr)

// attempt at Cholesky matrix
    var chol mat.Cholesky
    if ok := chol.Factorize(P_inno); !ok {
        fmt.Println("a matrix is not positive semi-definite.")
    }
    var t mat.TriDense
    fmt.Println(chol.UTo(&t))

The code doesn't work because t TriDense is empty. I'm not sure how to call UTo().

The library documentation says

The decomposition can be constructed using the Factorize method. The factorization itself can be extracted using the UTo or LTo methods, and the original symmetric matrix can be recovered with ToSym.

I could use help to understand how to do this step. I don't understand how to extract the actual factorization.

I have tried the fololwing: chol.UTo(&t) and chol.UTo(t) (no value) used as value; chol.Factorize(P_inno) returns boolean, not factorization.

blackgreen
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Chrissy Heu
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    `chol.UTo(&t)` doesn't return anything, as you can see from the [docs](https://pkg.go.dev/gonum.org/v1/gonum/mat#Cholesky.UTo). The method simply populates the `mat.TriDense` argument with the relevant L or U result of the factorization. Instead of passing `chol.UTo(&t)` to `fmt.Println`, simply print `t` afterwards https://go.dev/play/p/pjJwUiAKrVS – blackgreen Nov 28 '22 at 21:19
  • @blackgreen You were correct. I added your change ` chol.UTo(&t)` ` fmt.Println(t) ` and found the 4x4 matrix which matches the expected matlab output! Thanks a bunch! – Chrissy Heu Nov 28 '22 at 21:27

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