LAPACK: Aggressive constprop to concretely infer syev!/syevd! (#55295)

Currently, these are inferred as a 2-Tuple of possible return types
depending on `jobz`, but since `jobz` is usually a constant, we may
propagate it aggressively and have the return types inferred concretely.

(cherry picked from commit 686804d)

Author: jishnub

stdlib/LinearAlgebra/src/lapack.jl

@@ -5183,7 +5183,7 @@ for (syev, syevr, syevd, sygvd, elty) in
         #       INTEGER            INFO, LDA, LWORK, N
         # *     .. Array Arguments ..
         #       DOUBLE PRECISION   A( LDA, * ), W( * ), WORK( * )
-        function syev!(jobz::AbstractChar, uplo::AbstractChar, A::AbstractMatrix{$elty})
+        Base.@constprop :aggressive function syev!(jobz::AbstractChar, uplo::AbstractChar, A::AbstractMatrix{$elty})
             chkstride1(A)
             n = checksquare(A)
             W     = similar(A, $elty, n)
@@ -5277,7 +5277,7 @@ for (syev, syevr, syevd, sygvd, elty) in
         # *     .. Array Arguments ..
         #       INTEGER            IWORK( * )
         #       DOUBLE PRECISION   A( LDA, * ), W( * ), WORK( * )
-        function syevd!(jobz::AbstractChar, uplo::AbstractChar, A::AbstractMatrix{$elty})
+        Base.@constprop :aggressive function syevd!(jobz::AbstractChar, uplo::AbstractChar, A::AbstractMatrix{$elty})
             chkstride1(A)
             n = checksquare(A)
             chkuplofinite(A, uplo)
@@ -5368,7 +5368,7 @@ for (syev, syevr, syevd, sygvd, elty, relty) in
         # *     .. Array Arguments ..
         #       DOUBLE PRECISION   RWORK( * ), W( * )
         #       COMPLEX*16         A( LDA, * ), WORK( * )
-        function syev!(jobz::AbstractChar, uplo::AbstractChar, A::AbstractMatrix{$elty})
+        Base.@constprop :aggressive function syev!(jobz::AbstractChar, uplo::AbstractChar, A::AbstractMatrix{$elty})
             chkstride1(A)
             chkuplofinite(A, uplo)
             n = checksquare(A)
@@ -5476,7 +5476,7 @@ for (syev, syevr, syevd, sygvd, elty, relty) in
         #       INTEGER            IWORK( * )
         #       DOUBLE PRECISION   RWORK( * )
         #       COMPLEX*16         A( LDA, * ), WORK( * )
-        function syevd!(jobz::AbstractChar, uplo::AbstractChar, A::AbstractMatrix{$elty})
+        Base.@constprop :aggressive function syevd!(jobz::AbstractChar, uplo::AbstractChar, A::AbstractMatrix{$elty})
             chkstride1(A)
             chkuplofinite(A, uplo)
             n = checksquare(A)

stdlib/LinearAlgebra/test/lapack.jl

@@ -729,4 +729,14 @@ a = zeros(2,0), zeros(0)
     @test_throws DimensionMismatch LinearAlgebra.LAPACK.getrs!('N', A, ipiv, b)
 end
 
+@testset "inference in syev!/syevd!" begin
+    for T in (Float32, Float64), CT in (T, Complex{T})
+        A = rand(CT, 4,4)
+        @inferred (A -> LAPACK.syev!('N', 'U', A))(A)
+        @inferred (A -> LAPACK.syev!('V', 'U', A))(A)
+        @inferred (A -> LAPACK.syevd!('N', 'U', A))(A)
+        @inferred (A -> LAPACK.syevd!('V', 'U', A))(A)
+    end
+end
+
 end # module TestLAPACK