Add tests for TensorAlgebra.MatrixAlgebra

Author: mtfishman

src/MatrixAlgebra.jl

@@ -128,7 +128,7 @@ for (factorize, orth_f) in ((:factorize, :(MatrixAlgebra.orth)), (:factorize!, :
       else
         throw(ArgumentError("`orth=$orth` not supported."))
       end
-      return f(A; kwargs...)
+      return f(A; side=orth, kwargs...)
     end
   end
 end

test/test_matrixalgebra.jl

@@ -0,0 +1,148 @@
+using LinearAlgebra: I, diag
+using TensorAlgebra.MatrixAlgebra: MatrixAlgebra
+using Test: @test, @testset
+
+elts = (Float32, Float64, ComplexF32, ComplexF64)
+
+@testset "elt=$elt" for elt in elts
+  A = randn(elt, 3, 2)
+  for positive in (false, true)
+    for (Q, R) in (MatrixAlgebra.qr(A; positive), MatrixAlgebra.qr(A; full=false, positive))
+      @test A ≈ Q * R
+      @test size(Q) == size(A)
+      @test size(R) == (size(A, 2), size(A, 2))
+      @test Q' * Q ≈ I
+      @test Q * Q' ≉ I
+      if positive
+        @test all(≥(0), real(diag(R)))
+        @test all(≈(0), imag(diag(R)))
+      end
+    end
+  end
+
+  A = randn(elt, 3, 2)
+  for positive in (false, true)
+    Q, R = MatrixAlgebra.qr(A; full=true, positive)
+    @test A ≈ Q * R
+    @test size(Q) == (size(A, 1), size(A, 1))
+    @test size(R) == size(A)
+    @test Q' * Q ≈ I
+    @test Q * Q' ≈ I
+    if positive
+      @test all(≥(0), real(diag(R)))
+      @test all(≈(0), imag(diag(R)))
+    end
+  end
+
+  A = randn(elt, 2, 3)
+  for positive in (false, true)
+    for (L, Q) in (MatrixAlgebra.lq(A; positive), MatrixAlgebra.lq(A; full=false, positive))
+      @test A ≈ L * Q
+      @test size(L) == (size(A, 1), size(A, 1))
+      @test size(Q) == size(A)
+      @test Q * Q' ≈ I
+      @test Q' * Q ≉ I
+      if positive
+        @test all(≥(0), real(diag(L)))
+        @test all(≈(0), imag(diag(L)))
+      end
+    end
+  end
+
+  A = randn(elt, 3, 2)
+  for positive in (false, true)
+    L, Q = MatrixAlgebra.lq(A; full=true, positive)
+    @test A ≈ L * Q
+    @test size(L) == size(A)
+    @test size(Q) == (size(A, 2), size(A, 2))
+    @test Q * Q' ≈ I
+    @test Q' * Q ≈ I
+    if positive
+      @test all(≥(0), real(diag(L)))
+      @test all(≈(0), imag(diag(L)))
+    end
+  end
+
+  A = randn(elt, 3, 2)
+  for (W, C) in (MatrixAlgebra.orth(A), MatrixAlgebra.orth(A; side=:left))
+    @test A ≈ W * C
+    @test size(W) == size(A)
+    @test size(C) == (size(A, 2), size(A, 2))
+    @test W' * W ≈ I
+    @test W * W' ≉ I
+  end
+
+  A = randn(elt, 2, 3)
+  C, W = MatrixAlgebra.orth(A; side=:right)
+  @test A ≈ C * W
+  @test size(C) == (size(A, 1), size(A, 1))
+  @test size(W) == size(A)
+  @test W * W' ≈ I
+  @test W' * W ≉ I
+
+  A = randn(elt, 3, 2)
+  for (W, P) in (MatrixAlgebra.polar(A), MatrixAlgebra.polar(A; side=:left))
+    @test A ≈ W * P
+    @test size(W) == size(A)
+    @test size(P) == (size(A, 2), size(A, 2))
+    @test W' * W ≈ I
+    @test W * W' ≉ I
+    @test isposdef(P)
+  end
+
+  A = randn(elt, 2, 3)
+  P, W = MatrixAlgebra.polar(A; side=:right)
+  @test A ≈ P * W
+  @test size(P) == (size(A, 1), size(A, 1))
+  @test size(W) == size(A)
+  @test W * W' ≈ I
+  @test W' * W ≉ I
+  @test isposdef(P)
+
+  A = randn(elt, 3, 2)
+  for (W, C) in (MatrixAlgebra.factorize(A), MatrixAlgebra.factorize(A; orth=:left))
+    @test A ≈ W * C
+    @test size(W) == size(A)
+    @test size(C) == (size(A, 2), size(A, 2))
+    @test W' * W ≈ I
+    @test W * W' ≉ I
+  end
+
+  A = randn(elt, 2, 3)
+  C, W = MatrixAlgebra.factorize(A; orth=:right)
+  @test A ≈ C * W
+  @test size(C) == (size(A, 1), size(A, 1))
+  @test size(W) == size(A)
+  @test W * W' ≈ I
+  @test W' * W ≉ I
+
+  A = randn(elt, 3, 3)
+  D, V = MatrixAlgebra.eigen(A)
+  @test A * V ≈ V * D
+  @test MatrixAlgebra.eigvals(A) ≈ diag(D)
+
+  A = randn(elt, 3, 2)
+  for (U, S, V) in (MatrixAlgebra.svd(A), MatrixAlgebra.svd(A; full=false))
+    @test A ≈ U * S * V
+    @test size(U) == size(A)
+    @test size(S) == (size(A, 2), size(A, 2))
+    @test size(V) == (size(A, 2), size(A, 2))
+    @test U' * U ≈ I
+    @test U * U' ≉ I
+    @test V * V' ≈ I
+    @test V' * V ≈ I
+    @test MatrixAlgebra.svdvals(A) ≈ diag(S)
+  end
+
+  A = randn(elt, 3, 2)
+  U, S, V = MatrixAlgebra.svd(A; full=true)
+  @test A ≈ U * S * V
+  @test size(U) == (size(A, 1), size(A, 1))
+  @test size(S) == size(A)
+  @test size(V) == (size(A, 2), size(A, 2))
+  @test U' * U ≈ I
+  @test U * U' ≈ I
+  @test V * V' ≈ I
+  @test V' * V ≈ I
+  @test MatrixAlgebra.svdvals(A) ≈ diag(S)
+end