Minor updates to BLAS/hpmv! as in JuliaLang#34320. [JuliaLang#34439]

Follow the syntax, docstring and testing conventions
elaborated in JuliaLang#34320.

stdlib/LinearAlgebra/src/blas.jl

@@ -838,7 +838,7 @@ for (fname, elty) in ((:zhpmv_, :ComplexF64),
         # *     .. Array Arguments ..
         #       DOUBLE PRECISION A(N,N),X(N),Y(N)
         function hpmv!(uplo::AbstractChar,
-                       n::BlasInt,
+                       n::Integer,
                        α::$elty,
                        AP::Union{Ptr{$elty}, AbstractArray{$elty}},
                        x::Union{Ptr{$elty}, AbstractArray{$elty}},
@@ -881,21 +881,29 @@ function hpmv!(uplo::AbstractChar,
     if length(AP) < Int64(N*(N+1)/2)
         throw(DimensionMismatch("Packed Hermitian matrix A has size smaller than length(x) =  $(N)."))
     end
-    GC.@preserve x y AP hpmv!(uplo, BlasInt(N), convert(T, α), AP, pointer(x), BlasInt(stride(x, 1)), convert(T, β), pointer(y), BlasInt(stride(y, 1)))
+    GC.@preserve x y AP hpmv!(uplo, N, convert(T, α), AP, pointer(x), stride(x, 1), convert(T, β), pointer(y), stride(y, 1))
     y
 end
 
 """
     hpmv!(uplo, α, AP, x, β, y)
 
-Update vector `y` as `α*AP*x + β*y` where `AP` is a packed Hermitian matrix.
-The storage layout for `AP` is described in the reference BLAS module, level-2 BLAS at
-<http://www.netlib.org/lapack/explore-html/>.
+Update vector `y` as `α*A*x + β*y`, where `A` is a Hermitian matrix provided
+in packed format `AP`.
+
+With `uplo = 'U'`, the array AP must contain the upper triangular part of the
+Hermitian matrix packed sequentially, column by column, so that `AP[1]`
+contains `A[1, 1]`, `AP[2]` and `AP[3]` contain `A[1, 2]` and `A[2, 2]`
+respectively, and so on.
+
+With `uplo = 'L'`, the array AP must contain the lower triangular part of the
+Hermitian matrix packed sequentially, column by column, so that `AP[1]`
+contains `A[1, 1]`, `AP[2]` and `AP[3]` contain `A[2, 1]` and `A[3, 1]`
+respectively, and so on.
 
-The scalar inputs `α` and `β` shall be numbers.
+The scalar inputs `α` and `β` must be complex or real numbers.
 
-The array inputs `x`, `y` and `AP` must be complex one-dimensional julia arrays of the
-same type that is either `ComplexF32` or `ComplexF64`.
+The array inputs `x`, `y` and `AP` must all be of `ComplexF32` or `ComplexF64` type.
 
 Return the updated `y`.
 """

stdlib/LinearAlgebra/test/blas.jl

@@ -208,36 +208,39 @@ Random.seed!(100)
                 # Define the inputs and outputs of hpmv!, y = α*A*x+β*y
                 α = rand(elty)
                 M = rand(elty, n, n)
-                A = (M+M')/elty(2.0)
+                AL = Hermitian(M, :L)
+                AU = Hermitian(M, :U)
                 x = rand(elty, n)
                 β = rand(elty)
                 y = rand(elty, n)
 
-                y_result_julia = α*A*x+β*y
+                y_result_julia_lower = α*AL*x+β*y
 
-                # Create lower triangular packing of A
-                AP = typeof(A[1,1])[]
+                # Create lower triangular packing of AL
+                AP = typeof(AL[1,1])[]
                 for j in 1:n
                     for i in j:n
-                        push!(AP, A[i,j])
+                        push!(AP, AL[i,j])
                     end
                 end
 
                 y_result_blas_lower = copy(y)
                 BLAS.hpmv!('L', α, AP, x, β, y_result_blas_lower)
-                @test y_result_julia≈y_result_blas_lower
+                @test y_result_julia_lower≈y_result_blas_lower
 
-                # Create upper triangular packing of A
-                AP = typeof(A[1,1])[]
+                y_result_julia_upper = α*AU*x+β*y
+
+                # Create upper triangular packing of AU
+                AP = typeof(AU[1,1])[]
                 for j in 1:n
                     for i in 1:j
-                        push!(AP, A[i,j])
+                        push!(AP, AU[i,j])
                     end
                 end
 
                 y_result_blas_upper = copy(y)
                 BLAS.hpmv!('U', α, AP, x, β, y_result_blas_upper)
-                @test y_result_julia≈y_result_blas_upper
+                @test y_result_julia_upper≈y_result_blas_upper
             end
         end