Add a rudimentary precompile workload

Author: lkdvos

Project.toml

@@ -5,6 +5,7 @@ authors = ["Jutho Haegeman <jutho.haegeman@ugent.be>, Lukas Devos, Katharine Hya
 
 [deps]
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+PrecompileTools = "aea7be01-6a6a-4083-8856-8a6e6704d82a"
 
 [weakdeps]
 AMDGPU = "21141c5a-9bdb-4563-92ae-f87d6854732e"
@@ -35,6 +36,7 @@ EnzymeTestUtils = "0.2.5"
 GenericLinearAlgebra = "0.3.19, 0.4"
 GenericSchur = "0.5.6"
 LinearAlgebra = "1"
+PrecompileTools = "1"
 Mooncake = "0.5.27"
 ParallelTestRunner = "2"
 Random = "1"

src/MatrixAlgebraKit.jl

@@ -129,4 +129,6 @@ include("pullbacks/eigh.jl")
 include("pullbacks/svd.jl")
 include("pullbacks/polar.jl")
 
+include("precompile.jl")
+
 end

src/precompile.jl

@@ -0,0 +1,67 @@
+using PrecompileTools: @compile_workload
+
+@compile_workload begin
+    truncation_strategies = [
+        truncrank(2), trunctol(; atol = 1.0e-2), truncrank(2) & trunctol(; atol = 1.0e-2), truncerror(; atol = 1.0e-2) | truncfilter(x -> abs(x) < 1.0e-2),
+    ]
+    for T in (Float32, Float64, ComplexF32, ComplexF64)
+        A = diagm(ones(T, 4))      # 4×4 Matrix{T}, Hermitian, nonsingular
+        Atall = rand(T, 4, 2)
+        Awide = rand(T, 2, 4)
+
+        # decompositions
+        # --------------
+        qr_compact(A)
+        qr_full(Atall)
+        qr_null(Atall)
+
+        lq_compact(A)
+        lq_full(Awide)
+        lq_null(Awide)
+
+        svd_compact(A)
+        svd_full(A)
+        svd_vals(A)
+
+        schur_full(A)
+        schur_vals(A)
+
+        eigh_full(A)
+        eigh_vals(A)
+
+        eig_full(A)
+        eig_vals(A)
+
+        gen_eig_full(A, A)
+        gen_eig_vals(A, A)
+
+        left_polar(A)
+        right_polar(A)
+
+        # derived decompositions
+        left_orth(A)
+        left_null(A)
+        right_orth(A)
+        right_null(A)
+
+        # truncated decompositions
+        for trunc in truncation_strategies
+            svd_trunc(A; trunc)
+            eigh_trunc(A; trunc)
+            eig_trunc(A; trunc)
+        end
+        left_orth(A; trunc = truncrank(2))
+        right_orth(A; trunc = truncrank(2))
+
+        # projections
+        project_hermitian(A)
+        project_antihermitian(A)
+        project_isometric(A)
+
+        # properties
+        isisometric(A)
+        isunitary(A)
+        ishermitian(A)
+        isantihermitian(A)
+    end
+end