refactor: More type-stable and concrete implementation

[oameye]

Benchmark	PR #4	Now	Speedup
SLH Algebra — symbolic
3-cavity cascade	49.348 ms	120.281 μs	410x
concatenate + cascade	9.722 ms	40.050 μs	243x
feedback OPO loop	1.664 ms	32.680 μs	51x
SLH Algebra — numeric
2-QD waveguide composition	70.020 μs	63.105 μs	1.1x
SLH Algebra — closure eval
2-QD waveguide H(t)	64.030 μs	78.410 μs	~noise
2-QD waveguide L(t)	45.750 μs	9.140 μs	5.0x
Translation
static / atom-cavity	458.006 μs	453.731 μs	~same
time-dep / atom-cavity	810.541 μs	786.002 μs	~same
time-dep / 3-cavity H+L	3.239 ms	3.218 ms	~same
closure eval / 3-cavity H(t)	20.010 μs	18.080 μs	1.1x
closure eval / 3-cavity L(t)	14.970 μs	13.820 μs	1.1x
Pulse Couplings
single-pulse / input	1.329 ms	335.406 μs	4.0x
single-pulse / output	1.523 ms	366.541 μs	4.2x
multi-pulse / output 2 modes	2.709 ms	432.596 μs	6.3x
multi-pulse / input 2 modes	4.688 ms	383.831 μs	12.2x
Interaction Picture
coupling matrix / 2 modes	449.259 ns	326.082 ns	1.4x
coupling matrix / 4 modes	3.720 μs	2.140 μs	1.7x
coefficient matrix M / ODE	233.490 μs	181.781 μs	1.3x
coefficient matrix M / analytical	18.300 μs	28.020 μs	~noise
operator substitution / TLS	557.508 ms	550.204 ms	~same
Correlations
single photon cavity	405.307 ms	297.480 ms	1.4x

[oameye]

It's failing due to SciML/NonlinearSolve.jl#893

[ChristophHotter]

Looks already good.

Main points:

• contents of pulses.jl and utils.jl are swapped?
• fix _slh_matvec in SLH.jl (suggested fix added as comment; error of example 07-1)
• function description was sometimes deleted, and sometimes a strange description was added