Enable -log_view

[boriskaus]

In PETSc, the command-line option -log_view will show an overview with timings and memory allocations of the simulation, once the simulation is finalised. This is currently not working, but would be handy to have (good for benchmarking and running simulations).
I recall that -log_view is treated slightly different than other parameter options and should be set at the beginning of the simulation, but @psanan can probably explain this better.

[jkozdon]

We can run the logger directly:

using PETSc
using MPI

petsclib = PETSc.getlib()
PETSc.initialize(petsclib)

# Start the logger
PETSc.LibPETSc.PetscLogDefaultBegin(petsclib)

# Run some PETSc code
using SparseArrays: spdiagm
PetscScalar = petsclib.PetscScalar
Nq = 100
n = Nq - 2
x = range(PetscScalar(0), length = Nq, stop = 1)[2:(end - 1)]
Δx = PetscScalar(x.step)
A =
    spdiagm(
        -1 => -ones(PetscScalar, n - 1),
        0 => 2ones(PetscScalar, n),
        1 => -ones(PetscScalar, n - 1),
    ) / Δx^2
κ = 2PetscScalar(π)
u(x) = sin(κ * x)
f(x) = κ^2 * sin(κ * x)
ksp = PETSc.KSP(A; ksp_monitor = true);
v = ksp \ f.(x);
ϵ = sqrt(sum((v - u.(x)) .^ 2 * Δx))

# Dump the logger
viewer = PETSc.LibPETSc.PETSC_VIEWER_STDOUT_(petsclib, MPI.COMM_SELF)
PETSc.LibPETSc.PetscLogView(petsclib, viewer)

# Finalize PETSc
PETSc.finalize(petsclib)

(This obviously isn't clean yet, and the calls to LibPETSc should be hidden in some way).

I tried pushing log_view directly but got some errors from PETSc on finalize. My guess is they want the options set with PetscInitialize whereas we use PetscInitializeNoArguments