[Statistics] fix type determination in corm (#32271)

* [Statistics] fix type determination in corm

* remove obsolete typeof

* use first element(s) for type initialization

* add test for inhomogeneous data and for overflow

* fix test with NaN

(cherry picked from commit a8a567e)

Author: dkarrasch

stdlib/Statistics/src/Statistics.jl

@@ -583,8 +583,8 @@ function corm(x::AbstractVector, mx, y::AbstractVector, my)
 
     @inbounds begin
         # Initialize the accumulators
-        xx = zero(sqrt(abs2(x[1])))
-        yy = zero(sqrt(abs2(y[1])))
+        xx = zero(sqrt(abs2(one(x[1]))))
+        yy = zero(sqrt(abs2(one(y[1]))))
         xy = zero(x[1] * y[1]')
 
         @simd for i in eachindex(x, y)

stdlib/Statistics/test/runtests.jl

@@ -420,6 +420,8 @@ end
     @test cor(repeat(1:17, 1, 17))[2] <= 1.0
     @test cor(1:17, 1:17) <= 1.0
     @test cor(1:17, 18:34) <= 1.0
+    @test cor(Any[1, 2], Any[1, 2]) == 1.0
+    @test isnan(cor([0], Int8[81]))
     let tmp = range(1, stop=85, length=100)
         tmp2 = Vector(tmp)
         @test cor(tmp, tmp) <= 1.0