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| 1 | +using FillArrays: Ones |
| 2 | +using DiagonalArrays: δ, DeltaMatrix |
| 3 | +using KroneckerArrays: ⊗, arguments |
| 4 | +using LinearAlgebra: Hermitian, I, diag, hermitianpart, norm |
| 5 | +using MatrixAlgebraKit: |
| 6 | + eig_full, |
| 7 | + eig_trunc, |
| 8 | + eig_vals, |
| 9 | + eigh_full, |
| 10 | + eigh_trunc, |
| 11 | + eigh_vals, |
| 12 | + left_null, |
| 13 | + left_orth, |
| 14 | + left_polar, |
| 15 | + lq_compact, |
| 16 | + lq_full, |
| 17 | + qr_compact, |
| 18 | + qr_full, |
| 19 | + right_null, |
| 20 | + right_orth, |
| 21 | + right_polar, |
| 22 | + svd_compact, |
| 23 | + svd_full, |
| 24 | + svd_trunc, |
| 25 | + svd_vals |
| 26 | +using Test: @test, @test_broken, @test_throws, @testset |
| 27 | +using TestExtras: @constinferred |
| 28 | + |
| 29 | +herm(a) = parent(hermitianpart(a)) |
| 30 | + |
| 31 | +@testset "MatrixAlgebraKit + DeltaMatrix" begin |
| 32 | + for elt in (Float32, ComplexF32) |
| 33 | + a = δ(elt, 3, 3) ⊗ randn(elt, 3, 3) |
| 34 | + d, v = @constinferred eig_full(a) |
| 35 | + @test a * v ≈ v * d |
| 36 | + @test arguments(d, 1) isa DeltaMatrix{complex(elt)} |
| 37 | + @test arguments(v, 1) isa DeltaMatrix{complex(elt)} |
| 38 | + |
| 39 | + a = parent(hermitianpart(randn(elt, 3, 3))) ⊗ δ(elt, 3, 3) |
| 40 | + d, v = @constinferred eig_full(a) |
| 41 | + @test a * v ≈ v * d |
| 42 | + @test arguments(d, 2) isa DeltaMatrix{complex(elt)} |
| 43 | + @test arguments(v, 2) isa DeltaMatrix{complex(elt)} |
| 44 | + |
| 45 | + a = δ(elt, 3, 3) ⊗ δ(elt, 3, 3) |
| 46 | + d, v = @constinferred eig_full(a) |
| 47 | + @test a * v ≈ v * d |
| 48 | + @test arguments(d, 1) isa DeltaMatrix{complex(elt)} |
| 49 | + @test arguments(d, 2) isa DeltaMatrix{complex(elt)} |
| 50 | + @test arguments(v, 1) isa DeltaMatrix{complex(elt)} |
| 51 | + @test arguments(v, 2) isa DeltaMatrix{complex(elt)} |
| 52 | + end |
| 53 | + |
| 54 | + for elt in (Float32, ComplexF32) |
| 55 | + a = δ(elt, 3, 3) ⊗ parent(hermitianpart(randn(elt, 3, 3))) |
| 56 | + d, v = @constinferred eigh_full($a) |
| 57 | + @test a * v ≈ v * d |
| 58 | + @test arguments(d, 1) isa DeltaMatrix{real(elt)} |
| 59 | + @test arguments(v, 1) isa DeltaMatrix{elt} |
| 60 | + |
| 61 | + a = parent(hermitianpart(randn(elt, 3, 3))) ⊗ δ(elt, 3, 3) |
| 62 | + d, v = @constinferred eigh_full($a) |
| 63 | + @test a * v ≈ v * d |
| 64 | + @test arguments(d, 2) isa DeltaMatrix{real(elt)} |
| 65 | + @test arguments(v, 2) isa DeltaMatrix{elt} |
| 66 | + |
| 67 | + a = δ(elt, 3, 3) ⊗ δ(elt, 3, 3) |
| 68 | + d, v = @constinferred eigh_full($a) |
| 69 | + @test a * v ≈ v * d |
| 70 | + @test arguments(d, 1) isa DeltaMatrix{real(elt)} |
| 71 | + @test arguments(d, 2) isa DeltaMatrix{real(elt)} |
| 72 | + @test arguments(v, 1) isa DeltaMatrix{elt} |
| 73 | + @test arguments(v, 2) isa DeltaMatrix{elt} |
| 74 | + end |
| 75 | + |
| 76 | + ## TODO: Broken, need to fix truncation. |
| 77 | + ## for f in (eig_trunc, eigh_trunc) |
| 78 | + ## a = δ(3, 3) ⊗ parent(hermitianpart(randn(3, 3))) |
| 79 | + ## d, v = f(a; trunc=(; maxrank=7)) |
| 80 | + ## @test a * v ≈ v * d |
| 81 | + ## @test arguments(d, 1) isa DeltaMatrix |
| 82 | + ## @test arguments(v, 1) isa DeltaMatrix |
| 83 | + ## @test size(d) == (6, 6) |
| 84 | + ## @test size(v) == (9, 6) |
| 85 | + |
| 86 | + ## a = parent(hermitianpart(randn(3, 3))) ⊗ δ(3, 3) |
| 87 | + ## d, v = f(a; trunc=(; maxrank=7)) |
| 88 | + ## @test a * v ≈ v * d |
| 89 | + ## @test arguments(d, 2) isa DeltaMatrix |
| 90 | + ## @test arguments(v, 2) isa DeltaMatrix |
| 91 | + ## @test size(d) == (6, 6) |
| 92 | + ## @test size(v) == (9, 6) |
| 93 | + |
| 94 | + ## a = δ(3, 3) ⊗ δ(3, 3) |
| 95 | + ## @test_throws ArgumentError f(a) |
| 96 | + ## end |
| 97 | + |
| 98 | + for f in (eig_vals, eigh_vals) |
| 99 | + a = δ(3, 3) ⊗ parent(hermitianpart(randn(3, 3))) |
| 100 | + d = @constinferred f(a) |
| 101 | + d′ = f(Matrix(a)) |
| 102 | + @test sort(Vector(d); by=abs) ≈ sort(d′; by=abs) |
| 103 | + @test arguments(d, 1) isa Ones |
| 104 | + @test arguments(d, 2) ≈ f(arguments(a, 2)) |
| 105 | + |
| 106 | + a = parent(hermitianpart(randn(3, 3))) ⊗ δ(3, 3) |
| 107 | + d = @constinferred f(a) |
| 108 | + d′ = f(Matrix(a)) |
| 109 | + @test sort(Vector(d); by=abs) ≈ sort(d′; by=abs) |
| 110 | + @test arguments(d, 2) isa Ones |
| 111 | + @test arguments(d, 1) ≈ f(arguments(a, 1)) |
| 112 | + |
| 113 | + a = δ(3, 3) ⊗ δ(3, 3) |
| 114 | + d = @constinferred f(a) |
| 115 | + @test d == Ones(3) ⊗ Ones(3) |
| 116 | + @test arguments(d, 1) isa Ones |
| 117 | + @test arguments(d, 2) isa Ones |
| 118 | + end |
| 119 | + |
| 120 | + for f in ( |
| 121 | + left_orth, right_orth, left_polar, right_polar, qr_compact, lq_compact, qr_full, lq_full |
| 122 | + ) |
| 123 | + a = δ(3, 3) ⊗ randn(3, 3) |
| 124 | + x, y = @constinferred f($a) |
| 125 | + @test x * y ≈ a |
| 126 | + @test arguments(x, 1) isa DeltaMatrix |
| 127 | + @test arguments(y, 1) isa DeltaMatrix |
| 128 | + |
| 129 | + a = randn(3, 3) ⊗ δ(3, 3) |
| 130 | + x, y = @constinferred f($a) |
| 131 | + @test x * y ≈ a |
| 132 | + @test arguments(x, 2) isa DeltaMatrix |
| 133 | + @test arguments(y, 2) isa DeltaMatrix |
| 134 | + |
| 135 | + a = δ(3, 3) ⊗ δ(3, 3) |
| 136 | + x, y = @constinferred f($a) |
| 137 | + @test x * y ≈ a |
| 138 | + @test arguments(x, 1) isa DeltaMatrix |
| 139 | + @test arguments(y, 1) isa DeltaMatrix |
| 140 | + @test arguments(x, 2) isa DeltaMatrix |
| 141 | + @test arguments(y, 2) isa DeltaMatrix |
| 142 | + end |
| 143 | + |
| 144 | + for f in (svd_compact, svd_full) |
| 145 | + for elt in (Float32, ComplexF32) |
| 146 | + a = δ(elt, 3, 3) ⊗ randn(elt, 3, 3) |
| 147 | + u, s, v = @constinferred f($a) |
| 148 | + @test u * s * v ≈ a |
| 149 | + @test eltype(u) === elt |
| 150 | + @test eltype(s) === real(elt) |
| 151 | + @test eltype(v) === elt |
| 152 | + @test arguments(u, 1) isa DeltaMatrix{elt} |
| 153 | + @test arguments(s, 1) isa DeltaMatrix{real(elt)} |
| 154 | + @test arguments(v, 1) isa DeltaMatrix{elt} |
| 155 | + |
| 156 | + a = randn(elt, 3, 3) ⊗ δ(elt, 3, 3) |
| 157 | + u, s, v = @constinferred f($a) |
| 158 | + @test u * s * v ≈ a |
| 159 | + @test eltype(u) === elt |
| 160 | + @test eltype(s) === real(elt) |
| 161 | + @test eltype(v) === elt |
| 162 | + @test arguments(u, 2) isa DeltaMatrix{elt} |
| 163 | + @test arguments(s, 2) isa DeltaMatrix{real(elt)} |
| 164 | + @test arguments(v, 2) isa DeltaMatrix{elt} |
| 165 | + |
| 166 | + a = δ(elt, 3, 3) ⊗ δ(elt, 3, 3) |
| 167 | + u, s, v = @constinferred f($a) |
| 168 | + @test u * s * v ≈ a |
| 169 | + @test eltype(u) === elt |
| 170 | + @test eltype(s) === real(elt) |
| 171 | + @test eltype(v) === elt |
| 172 | + @test arguments(u, 1) isa DeltaMatrix{elt} |
| 173 | + @test arguments(s, 1) isa DeltaMatrix{real(elt)} |
| 174 | + @test arguments(v, 1) isa DeltaMatrix{elt} |
| 175 | + @test arguments(u, 2) isa DeltaMatrix{elt} |
| 176 | + @test arguments(s, 2) isa DeltaMatrix{real(elt)} |
| 177 | + @test arguments(v, 2) isa DeltaMatrix{elt} |
| 178 | + end |
| 179 | + end |
| 180 | + |
| 181 | + ## TODO: Need to implement truncation. |
| 182 | + ## # svd_trunc |
| 183 | + ## for elt in (Float32, ComplexF32) |
| 184 | + ## a = δ(elt, 3, 3) ⊗ randn(elt, 3, 3) |
| 185 | + ## # TODO: Type inference is broken for `svd_trunc`, |
| 186 | + ## # look into fixing it. |
| 187 | + ## # u, s, v = @constinferred svd_trunc(a; trunc=(; maxrank=7)) |
| 188 | + ## u, s, v = svd_trunc(a; trunc=(; maxrank=7)) |
| 189 | + ## @test eltype(u) === elt |
| 190 | + ## @test eltype(s) === real(elt) |
| 191 | + ## @test eltype(v) === elt |
| 192 | + ## u′, s′, v′ = svd_trunc(Matrix(a); trunc=(; maxrank=6)) |
| 193 | + ## @test Matrix(u * s * v) ≈ u′ * s′ * v′ |
| 194 | + ## @test arguments(u, 1) isa DeltaMatrix{elt} |
| 195 | + ## @test arguments(s, 1) isa DeltaMatrix{real(elt)} |
| 196 | + ## @test arguments(v, 1) isa DeltaMatrix{elt} |
| 197 | + ## @test size(u) == (9, 6) |
| 198 | + ## @test size(s) == (6, 6) |
| 199 | + ## @test size(v) == (6, 9) |
| 200 | + ## end |
| 201 | + |
| 202 | + ## TODO: Need to implement truncation. |
| 203 | + ## for elt in (Float32, ComplexF32) |
| 204 | + ## a = randn(elt, 3, 3) ⊗ δ(elt, 3, 3) |
| 205 | + ## # TODO: Type inference is broken for `svd_trunc`, |
| 206 | + ## # look into fixing it. |
| 207 | + ## # u, s, v = @constinferred svd_trunc(a; trunc=(; maxrank=7)) |
| 208 | + ## u, s, v = svd_trunc(a; trunc=(; maxrank=7)) |
| 209 | + ## @test eltype(u) === elt |
| 210 | + ## @test eltype(s) === real(elt) |
| 211 | + ## @test eltype(v) === elt |
| 212 | + ## u′, s′, v′ = svd_trunc(Matrix(a); trunc=(; maxrank=6)) |
| 213 | + ## @test Matrix(u * s * v) ≈ u′ * s′ * v′ |
| 214 | + ## @test arguments(u, 2) isa DeltaMatrix{elt} |
| 215 | + ## @test arguments(s, 2) isa DeltaMatrix{real(elt)} |
| 216 | + ## @test arguments(v, 2) isa DeltaMatrix{elt} |
| 217 | + ## @test size(u) == (9, 6) |
| 218 | + ## @test size(s) == (6, 6) |
| 219 | + ## @test size(v) == (6, 9) |
| 220 | + ## end |
| 221 | + |
| 222 | + a = δ(3, 3) ⊗ δ(3, 3) |
| 223 | + @test_broken svd_trunc(a) |
| 224 | + |
| 225 | + # svd_vals |
| 226 | + for elt in (Float32, ComplexF32) |
| 227 | + a = δ(elt, 3, 3) ⊗ randn(elt, 3, 3) |
| 228 | + d = @constinferred svd_vals(a) |
| 229 | + d′ = svd_vals(Matrix(a)) |
| 230 | + @test sort(Vector(d); by=abs) ≈ sort(d′; by=abs) |
| 231 | + @test arguments(d, 1) isa Ones{real(elt)} |
| 232 | + @test arguments(d, 2) ≈ svd_vals(arguments(a, 2)) |
| 233 | + end |
| 234 | + |
| 235 | + for elt in (Float32, ComplexF32) |
| 236 | + a = randn(elt, 3, 3) ⊗ δ(elt, 3, 3) |
| 237 | + d = @constinferred svd_vals(a) |
| 238 | + d′ = svd_vals(Matrix(a)) |
| 239 | + @test sort(Vector(d); by=abs) ≈ sort(d′; by=abs) |
| 240 | + @test arguments(d, 2) isa Ones{real(elt)} |
| 241 | + @test arguments(d, 1) ≈ svd_vals(arguments(a, 1)) |
| 242 | + end |
| 243 | + |
| 244 | + for elt in (Float32, ComplexF32) |
| 245 | + a = δ(elt, 3, 3) ⊗ δ(elt, 3, 3) |
| 246 | + d = @constinferred svd_vals(a) |
| 247 | + @test d ≡ Ones{real(elt)}(3) ⊗ Ones{real(elt)}(3) |
| 248 | + @test arguments(d, 1) isa Ones{real(elt)} |
| 249 | + @test arguments(d, 2) isa Ones{real(elt)} |
| 250 | + end |
| 251 | + |
| 252 | + # left_null |
| 253 | + a = δ(3, 3) ⊗ randn(3, 3) |
| 254 | + @test_broken left_null(a) |
| 255 | + ## n = @constinferred left_null(a) |
| 256 | + ## @test norm(n' * a) ≈ 0 |
| 257 | + ## @test arguments(n, 1) isa DeltaMatrix |
| 258 | + |
| 259 | + a = randn(3, 3) ⊗ δ(3, 3) |
| 260 | + @test_broken left_null(a) |
| 261 | + ## n = @constinferred left_null(a) |
| 262 | + ## @test norm(n' * a) ≈ 0 |
| 263 | + ## @test arguments(n, 2) isa DeltaMatrix |
| 264 | + |
| 265 | + a = δ(3, 3) ⊗ δ(3, 3) |
| 266 | + @test_broken left_null(a) |
| 267 | + |
| 268 | + # right_null |
| 269 | + a = δ(3, 3) ⊗ randn(3, 3) |
| 270 | + @test_broken right_null(a) |
| 271 | + ## n = @constinferred right_null(a) |
| 272 | + ## @test norm(a * n') ≈ 0 |
| 273 | + ## @test arguments(n, 1) isa DeltaMatrix |
| 274 | + |
| 275 | + a = randn(3, 3) ⊗ δ(3, 3) |
| 276 | + @test_broken right_null(a) |
| 277 | + ## n = @constinferred right_null(a) |
| 278 | + ## @test norm(a * n') ≈ 0 |
| 279 | + ## @test arguments(n, 2) isa DeltaMatrix |
| 280 | + |
| 281 | + a = δ(3, 3) ⊗ δ(3, 3) |
| 282 | + @test_broken right_null(a) |
| 283 | +end |
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