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Update guide.md
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shinaoka committed Dec 15, 2023
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Expand Up @@ -18,8 +18,46 @@ We first import `SparseIR` and construct an appropriate basis (``\omega_\mathrm{
```julia-repl
julia> using SparseIR
julia> basis = FiniteTempBasis(fermion, 10, 8)
FiniteTempBasis{LogisticKernel, Float64}(fermion, 10.0, 8.0)
julia> basis = FiniteTempBasis(Fermionic(), 10, 8)
38-element FiniteTempBasis{Fermionic} with β = 10.0, ωmax = 8.0 and singular values:
1.4409730317545622
1.2153954454510796
0.7652662478347486
0.49740673945822544
0.28856209562310586
0.16398195527438167
0.08901271087151325
0.04683797435429747
0.0238576532335063
0.011793733096027617
0.0056624000214117775
0.0026427291749051077
0.0011996720525663928
0.0005299554043095772
0.00022790287514550184
9.544046906619731e-5
3.893189538316289e-5
1.547291956701861e-5
5.992753725069489e-6
2.262327623958672e-6
8.326134974145948e-7
2.987946971803453e-7
1.0457471180503993e-7
3.5701720120493045e-8
1.1891781849704674e-8
3.8653572177285625e-9
1.2263378230199123e-9
3.798435437588598e-10
1.1488765720437616e-10
3.394058119073853e-11
9.796004365155715e-12
2.7629432401376287e-12
7.617289242492584e-13
2.053283747601055e-13
5.4129508727263855e-14
1.3959632874817246e-14
3.5228017131146852e-15
8.701560285902632e-16
```
There's quite a lot happening behind the scenes in this first innocuous-looking statement, so let's break it down:
Because we did not specify otherwise, the constructor chose the analytic continuation kernel for fermions, `LogisticKernel(80.0)`, defined by
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