expand tests of symmetry analysis

Author: thchr

src/symmetry_analysis.jl

@@ -83,6 +83,10 @@ and are otherwise initialized by the function.
 
 The symmetry eigenvalues are returned as a matrix, with rows running over the elements of
 `ops` and columns running over the bands of `ptbm`.
+
+!!! note
+    The inputs `ops`, `k`, and `lg` must be provided in a primitive setting. See
+    Crystalline.jl's `primitivize`.
 """
 function symmetry_eigenvalues(
     ptbm::ParameterizedTightBindingModel{D},
@@ -112,7 +116,7 @@ function symmetry_eigenvalues(
         Θᴳ = reciprocal_translation_phase(orbital_positions(ptbm), G) # TODO: preallocate & fill
         ρ = sgrep(k)
         for (n, v) in enumerate(eachcol(vs))
-            v_kpG = Θᴳ * v # correct the phase factor
+            v_kpG = Θᴳ * v # incorporate phase factor
             symeigs[j, n] = dot(v_kpG, ρ, v)
             # TODO: preallocate and `mul!` the `Θᴳ * v` term to avoid allocations
         end
@@ -123,10 +127,9 @@ end
 function symmetry_eigenvalues(
     ptbm::ParameterizedTightBindingModel{D},
     lg::LittleGroup{D},
-    sgreps::AbstractVector{SiteInducedSGRepElement{D}} = sgrep_induced_by_siteir.(
-        Ref(ptbm.tbm.cbr),
-        lg,
-    ),
+    sgreps::AbstractVector{SiteInducedSGRepElement{D}} = begin
+        sgrep_induced_by_siteir.(Ref(ptbm.tbm.cbr), lg)
+    end,
 ) where D
     kv = position(lg)
     isspecial(kv) || error("input k-point has free parameters")

test/symmetry_analysis.jl

@@ -1,23 +1,92 @@
 using Test
-using SymmetricTightBinding, Crystalline
+using SymmetricTightBinding
+using Crystalline
+using Crystalline: free
 
-@testset "Symmetry analysis" begin
+@testset "Symmetry analysis (documentation example)" begin
+    # Example 1
+    sgnum = 17                         # plane group p6mm
+    brs = calc_bandreps(sgnum, Val(2)) # band representations
+    cbr = @composite brs[5]            # (2b|A₁) EBR
+    tbm = tb_hamiltonian(cbr)          # tight-binding model (nearest neigbors)
+    ptbm = tbm([0, 1])                 # zero self-energy, nonzero nearest-neighbor hopping
+    ns = collect_compatible(ptbm)
+    @test only(ns) == SymmetryVector(cbr) == SymmetryVector(CompositeBandRep(ptbm))
+
+    # Example 2
+    cbr′ = @composite brs[3] + brs[5] # (2a|A₁) + (3c|B₂)
+    tbm′ = tb_hamiltonian(cbr′)
+    ptbm′ = tbm′([2.5, 0, 0.2, 0, -1, 0])
+    ns′ = collect_compatible(ptbm′)
+    @test length(ns′) == 1 # bands are overlapping and not separable
+    @test only(ns′) == SymmetryVector(cbr′)
+
+    ptbm′′ = tbm′([2.5, 0, 0.2, 0, -1, .5]) # turn on hybridization and split bands
+    ns′′ = collect_compatible(ptbm′′)
+    @test length(ns′′) == 2 # bands are overlapping and not separable
+    @test ns′′[1] ∉ brs[[3, 5]]
+    @test ns′′[2] ∉ brs[[3, 5]]
+    @test sum(ns′′) == SymmetryVector(cbr′)
+end
+
+@testset "Symmetry analysis (full scan over EBRs)" begin
+    # construct a tb-model for every EBR and verify that `collect_compatible` returns a set
+    # of symmetry vectors whose sum is equal to the underlying EBR's: note that we cannot
+    # generally require that `collect_compatible` returns a _single_ symmetry vector
+    # equaling the EBR's symmetry vector, since the EBR might be decomposable (either into
+    # fragile or genuinely topological EBRs): i.e., we don't know if the model is a single
+    # connected band or not, only what the "sum" of symmetry vectors will be
     for D in 1:3
-        for sgnum in MAX_SGNUM[D]
-            @testset "Space group $sgnum in dimension $D" begin
+        αβγ = D == 1 ? [.1] : D == 2 ? [.1, .2] : [.1, .2, .3] # for `pin_free!`
+        println("--- D = $D ---")
+        for sgnum in 1:MAX_SGNUM[D]
+            showed_sgnum = false
+            #@testset "Space group $sgnum in dimension $D" begin
                 brs = calc_bandreps(sgnum, Val(D))
                 for i in eachindex(brs)
                     coefs = zeros(length(brs))
                     coefs[i] = 1
                     cbr = CompositeBandRep(coefs, brs)
-                    ptbm = tb_hamiltonian(cbr)(randn(length(cbr)))
 
-                    v = SymmetryVector(cbr)
-                    v_model = collect_compatible(ptbm)
+                    # if the EBR had any free parameters associated with its Wyckoff
+                    # position, we must pin them, using `pin_free!`
+                    iszero(free(position(brs[i]))) || pin_free!(brs, i=>αβγ)
+
+                    # build a random tight-binding model for the `i`th EBR
+                    tbm = try
+                        tb_hamiltonian(cbr)
+                    catch e
+                        showed_sgnum || (showed_sgnum = true; println("#$sgnum"))
+                        println("  brs[$i] = $cbr:\t`tb_hamiltonian` error")
+                        continue
+                    end
+                    ptbm = tbm(randn(length(tbm)))
 
-                    @test v == v_model[1] # check that the symmetry vector is compatible with the model
+                    # check that the symmetry vector returned by `collect_compatible` is
+                    # what we started with (i.e. equal to `cbr`)
+                    try
+                        ns = collect_compatible(ptbm)
+                        if length(ns) == 0
+                            showed_sgnum || (showed_sgnum = true; println("#$sgnum:"))
+                            println("  brs[$i] = $cbr:\tfailed to collect any compatible symmetry vectors")
+                        else
+                            cond = sum(ns) == SymmetryVector(cbr)
+                            if !cond
+                                showed_sgnum || (showed_sgnum = true; println("#$sgnum:"))
+                                println("  brs[$i] = $cbr:\tsymmetry vector discrepancy")
+                                println("    n   = $(sum(ns))\n    cbr = $(SymmetryVector(cbr))")
+                            end
+                        end
+                    catch e
+                        showed_sgnum || (showed_sgnum = true; println("#$sgnum:"))
+                        println("  brs[$i] = $cbr:\t`collect_compatible` error")
+                        println("    ", e)
+                        continue
+                    end
+                    #@test cbr == only(collect_compatible(ptbm)) 
                 end # for br in brs
-            end # @testset "Space group $sgnum in dimension $D"
+            #end # @testset "Space group $sgnum in dimension $D"
         end # for sgnum in MAX_SGNUM[D]
+        println()
     end # for D in 1:3
 end # @testset "Symmetry analysis"