Manual LGIrrep{3} additions for missing k-points in Φ-Ω

build/write_littlegroup_irreps.jl

@@ -118,9 +118,17 @@ foreach(jldfile -> close(jldfile), values(Crystalline.LGIRREPS_JLDFILES))
 foreach(jldfile -> close(jldfile), values(Crystalline.LGS_JLDFILES))
 
 # 3D (from ISOTROPY)
-include("build/ParseIsotropy.jl") # load the ParseIsotropy module which 
-using Main.ParseIsotropy              # exports `parselittlegroupirreps`
-__write_littlegroupirreps(parselittlegroupirreps())
+include(joinpath((@__DIR__), "ParseIsotropy.jl")) # load the ParseIsotropy module
+using Main.ParseIsotropy                                # (exports `parselittlegroupirreps`)
+LGIRS_3D = parselittlegroupirreps()
+# ... ISOTROPY is missing several irreps; we bring those in below, obtained from manual
+# transcription of irreps from Bilbao; script below defines `LGIRS_add` which stores these
+# manual additions (a Dict with `sgnum` keys)
+include(joinpath((@__DIR__), "..", "data/lgirreps/manual_lgirrep_additions.jl"))
+for (sgnum, lgirsd_add) in LGIRS_add # merge Bilbao additions with ISOTROPY irreps
+    merge!(LGIRS_3D[sgnum], lgirsd_add)
+end
+__write_littlegroupirreps(LGIRS_3D)
 
 # 2D (from point group matching)
 __write_littlegroupirreps(LGIRS_2D′)

src/special_representation_domain_kpoints.jl

@@ -1,35 +1,7 @@
-# The basic goal of this endeavor is only to find the irreps that 
-# are missing in ISOTROPY but feature in the bandreps from Bilbao. 
-# There are 145 such irreps, across 20 space groups, they are:                                (... I manually pieced this table together)
-# ┌───────┬─────────────────────────────────────────────────────────────────────────────┬───────────────┬────────────────────────────────┐
-# │       │  Missing                                                                    │  Missing      │  [NS≡nonsymmorph; S≡symmorph]  │
-# │  SGs  │  LGIrrep labels                                                             │  KVec labels  │  Match method                  │
-# │───────┼─────────────────────────────────────────────────────────────────────────────┼───────────────┼────────────────────────────────│
-# │  23   │  WA₁, WA₂, WA₃, WA₄                                                         │  WA           │  S:  MonoOrthTetraCubic ┐      │
-# │  24   │  WA₁                                                                        │  WA           │  NS: Inherits from      └ 23   │
-# │  82   │  PA₁, PA₂, PA₃, PA₄                                                         │  PA           │  S:  MonoOrthTetraCubic        │
-# │  121  │  PA₁, PA₂, PA₃, PA₄, PA₅                                                    │  PA           │  S:  MonoOrthTetraCubic ┐      │
-# │  122  │  PA₁, PA₂                                                                   │  PA           │  NS: Inherits from      └ 121  │
-# │  143  │  HA₁, HA₂, HA₃, KA₁, KA₂, KA₃, PA₁, PA₂, PA₃                                │  HA, KA, PA   │  S:  TriHex                    │
-# │  144  │  HA₁, HA₂, HA₃, KA₁, KA₂, KA₃, PA₁, PA₂, PA₃                                │  HA, KA, PA   │  NS: Orphan (type b) ┐         │
-# │  145  │  HA₁, HA₂, HA₃, KA₁, KA₂, KA₃, PA₁, PA₂, PA₃                                │  HA, KA, PA   │  NS: Orphan (type b) ┘         │
-# │  150  │  HA₁, HA₂, HA₃, KA₁, KA₂, KA₃, PA₁, PA₂, PA₃                                │  HA, KA, PA   │  S:  TriHex                    │
-# │  152  │  HA₁, HA₂, HA₃, KA₁, KA₂, KA₃, PA₁, PA₂, PA₃                                │  HA, KA, PA   │  NS: Orphan (type b) ┐         │
-# │  154  │  HA₁, HA₂, HA₃, KA₁, KA₂, KA₃, PA₁, PA₂, PA₃                                │  HA, KA, PA   │  NS: Orphan (type b) ┘         │
-# │  157  │  HA₁, HA₂, HA₃, KA₁, KA₂, KA₃, PA₁, PA₂, PA₃                                │  HA, KA, PA   │  S:  TriHex ───────┐           │
-# │  159  │  HA₁, HA₂, HA₃, KA₁, KA₂, KA₃, PA₁, PA₂, PA₃                                │  HA, KA, PA   │  NS: Inherits from └ 157       │
-# │  174  │  HA₁, HA₂, HA₃, HA₄, HA₅, HA₆, KA₁, KA₂, KA₃, KA₄, KA₅, KA₆, PA₁, PA₂, PA₃  │  HA, KA, PA   │  S:  TriHex                    │
-# │  189  │  HA₁, HA₂, HA₃, HA₄, HA₅, HA₆, KA₁, KA₂, KA₃, KA₄, KA₅, KA₆, PA₁, PA₂, PA₃  │  HA, KA, PA   │  S:  TriHex ───────┐           │
-# │  190  │  HA₁, HA₂, HA₃, KA₁, KA₂, KA₃, KA₄, KA₅, KA₆, PA₁, PA₂, PA₃                 │  HA, KA, PA   │  NS: Inherits from └ 189       │
-# │  197  │  PA₁, PA₂, PA₃, PA₄                                                         │  PA           │  S:  MonoOrthTetraCubic ┐      │
-# │  199  │  PA₁, PA₂, PA₃                                                              │  PA           │  NS: Inherits from      └ 197  │
-# │  217  │  PA₁, PA₂, PA₃, PA₄, PA₅                                                    │  PA           │  S:  MonoOrthTetraCubic ┐      │
-# │  220  │  PA₁, PA₂, PA₃                                                              │  PA           │  NS: Inherits from      └ 217  │
-# └───────┴─────────────────────────────────────────────────────────────────────────────┴───────────────┴────────────────────────────────┘
-# Of course, in principle, we might consider trying to create ALL the missing points from Φ-Ω,
-# but for what we need, this is sufficient.
-# Of these space groups, only sg 82 has a nontrivial symmetry indicator classification for 
-# bosons with TR.
+# The basic goal of this endeavor is only to find the k-points and irreps that 
+# are missing in ISOTROPY still belong to representation domain Φ (ISOTROPY all points from
+# the basic domain Ω and some - but not all - from Φ).
+# TODO: Unfortunately, it doesn't currently work.
 
 # --- STRUCTS ---
 

src/symops.jl

@@ -379,7 +379,8 @@ function check_multtable_vs_ir(lgir::LGIrrep{D}, αβγ=nothing) where D
     primitive_ops = primitivize.(ops, cntr) # must do multiplication table in primitive basis, cf. choices in `compose`
     check_multtable_vs_ir(MultTable(primitive_ops), lgir, αβγ)
 end
-function check_multtable_vs_ir(mt::MultTable, ir::AbstractIrrep, αβγ=nothing)
+function check_multtable_vs_ir(mt::MultTable, ir::AbstractIrrep, αβγ=nothing;
+            verbose::Bool=false)
     havewarned = false
     Ds = ir(αβγ)
     ops = operations(ir)
@@ -419,19 +420,17 @@ function check_multtable_vs_ir(mt::MultTable, ir::AbstractIrrep, αβγ=nothing)
             end
             if !match
                 checked[i,j] = false
-                if !havewarned
-                    if verbose
-                        println("""Provided irreps do not match group multiplication table for group $(num(ir)) in irrep $(label(ir)):
-                                 First failure at (row,col) = ($(i),$(j));
-                                 Expected idx $(mtidx), got idx $(findall(≈(Dⁱʲ), Ds))""")
-                        print("Expected irrep = ")
-                        if ir isa LGIrrep
-                            println(cis(ϕ)*Ds[mtidx])
-                        else
-                            println(Dⁱʲ)
-                        end
-                        println("Got irrep      = $(Dⁱʲ)")
+                if !havewarned && verbose
+                    println("""Provided irreps do not match group multiplication table for group $(num(ir)) in irrep $(label(ir)):
+                                First failure at (row,col) = ($(i),$(j));
+                                Expected idx $(mtidx), got idx $(findall(≈(Dⁱʲ), Ds))""")
+                    print("Expected irrep = ")
+                    if ir isa LGIrrep
+                        println(cis(ϕ)*Ds[mtidx])
+                    else
+                        println(Dⁱʲ)
                     end
+                    println("Got irrep      = $(Dⁱʲ)")
                     havewarned = true
                 end
             end

test/bandrep.jl

@@ -7,7 +7,7 @@ end
 @testset "k-vectors required by BandRepSet analysis" begin
 allpaths = false
 spinful  = false
-verbose = false
+debug = false
 
 @testset "Complex (no TR) irreps" begin
 # --- test complex-form irreps (not assuming time-reversal symmetry) ---
@@ -21,35 +21,20 @@ for (sgnum, lgirsd) in enumerate(LGIRS)
 
     for (iridx_BRS, irlab_BRS) in enumerate(irlabs_BRS)
         klab = klabel(irlab_BRS)
-        if irlab_BRS ∉ irlabs_ISO
-            if verbose
-                @info "Cannot find complex irrep $(irlab_BRS) in ISOTROPY dataset (sgnum = $sgnum)"
-            end
-            @test_broken false
-            kidx_BRS = findfirst(==(klab), klabs_BRS)
-
-            # test that for each of the (P,K,W,H)A k-label variants, that the associated k-vector is 
-            # just equal to minus the kvector in the (P,K,W,H) variant (i.e. without the 'A' postscript)
-            @test -BRS.kvs[kidx_BRS] == kvec(first(lgirsd[klab[1:1]]))
-
-            # TODO: to get the irreps of these variants, we need to follow the prescription 
-            # detailed in CDML p. 69-73 (though that won't work, presumably, for sgnum=205)
-            # This is the subject of Cracknell & Davies 1976b (On the completeness of tables
-            # of irreducible representations of the classical space groups)
-        else
-            kidx_BRS = findfirst(==(klab), klabs_BRS)
+        @test irlab_BRS ∈ irlabs_ISO
+        if debug && irlab_BRS ∉ irlabs_ISO
+            @info "Cannot find complex irrep $(irlab_BRS) in ISOTROPY dataset (sgnum = $sgnum)"
+        end
 
-            # test that ISOTROPY's labelling & representation of k-vectors agree with BCD
-            @test BRS.kvs[kidx_BRS] == kvec(first(lgirsd[klab]))
-            if verbose
-                if BRS.kvs[kidx_BRS] ≠ kvec(first(lgirsd[klab]))
-                    println("Different definitions of k-point labels in space group ", sgnum)
-                    println("   BRS, ", klab, ": ",string(BRS.kvs[kidx_BRS]))
-                    println("   ISO, ", klab, ": ",string(kvec(first(lgirsd[klab]))))
-                    println()
-                end
-            end
+        # test that ISOTROPY's labelling & representation of k-vectors agree with BCD
+        kidx_BRS = findfirst(==(klab), klabs_BRS)
+        @test BRS.kvs[kidx_BRS] == kvec(first(lgirsd[klab]))
+        if debug && BRS.kvs[kidx_BRS] ≠ kvec(first(lgirsd[klab]))
+            println("Different definitions of k-point labels in space group ", sgnum)
+            println("   BRS, ", klab, ": ",string(BRS.kvs[kidx_BRS]))
+            println("   ISO, ", klab, ": ",string(kvec(first(lgirsd[klab]))), "\n")
         end
+
     end
 end
 end
@@ -74,18 +59,14 @@ for (sgnum, lgirsd) in enumerate(LGIRS)
 
     for (iridx_BRS, irlab_BRS) in enumerate(irlabs_BRS)
         klab = klabel(irlab_BRS)
-        if irlab_BRS ∉ realirlabs_ISO
-            if verbose
-                @info "Cannot find real irrep $(irlab_BRS) in ISOTROPY dataset (sgnum = $sgnum)"
-            end
-            @test_broken false
-
-        else
-            kidx_BRS = findfirst(==(klab), klabs_BRS)
-
-            # test that ISOTROPY's labelling & representation of k-vectors agree with BCD
-            @test BRS.kvs[kidx_BRS] == kvec(first(lgirsd[klab]))
+        @test irlab_BRS ∈ realirlabs_ISO
+        if debug && irlab_BRS ∉ realirlabs_ISO
+            @info "Cannot find real irrep $(irlab_BRS) in ISOTROPY dataset (sgnum = $sgnum)"
         end
+
+        # test that ISOTROPY's labelling & representation of k-vectors agree with BCD
+        kidx_BRS = findfirst(==(klab), klabs_BRS)
+        @test BRS.kvs[kidx_BRS] == kvec(first(lgirsd[klab]))
     end
 end
 end

test/parsed_vs_loaded_littlegroup_irreps.jl

@@ -10,12 +10,31 @@ if !isdefined(Main, :LGIRS)
 end
 
 @testset "Test equivalence of parsed and loaded LGIrreps" begin
-    for sgnum in 1:230
+    addition_klabs = ("WA", "HA", "KA", "PA")
+    for sgnum in 1:MAX_SGNUM[3]
         lgirsd′ = LGIRS′[sgnum] # parsed variant
-        lgirsd  = LGIRS[sgnum]  # loaded variant
+        lgirsd  = LGIRS[sgnum]  # loaded variant; may contain more irreps than parsed ISOTROPY (cf. `manual_lgirrep_additions.jl`)
+
+        # test we have same k-points in `lgirsd` and `lgirsd′` (or, possibly more in
+        # k-points `lgirsd`, if it contains manual additions)
+        klabs  = sort!(collect(keys(lgirsd)))
+        klabs′ = sort!(collect(keys(lgirsd′)))
+        if klabs == klabs′
+            @test length(lgirsd) == length(lgirsd′)
+        else
+            # in case loaded irreps contain manually added 'xA'-type k-points (either "HA",
+            # "HA", "KA", or "PA", see `addition_klabs`) from Φ-Ω
+            extra_klabidxs = findall(klab -> klab ∉ klabs′, klabs)::Vector{Int}
+            extra_klabs = klabs[extra_klabidxs]
+            @test length(lgirsd) > length(lgirsd′) && all(∈(addition_klabs), extra_klabs)
+        end
 
-        @test length(lgirsd) == length(lgirsd′)
         for (kidx, (klab, lgirs)) in enumerate(lgirsd)
+            if !haskey(lgirsd′, klab) && klab ∈ addition_klabs
+                # `lgirs` is a manual addition that is not in ISOTROPY; nothing to compare
+                continue
+            end
+
             lgirs′ = lgirsd′[klab]
             @test length(lgirs) == length(lgirs′)
             for (iridx, lgir) in enumerate(lgirs)