Fix of null column error in geqrf! and gerqf! (#42844)

* Fix of null column error in geqrf! and gerqf!

* Added tests

* Trailing blanks removed

* Correct issue number

* Adjusted lwork to max(m, 1, Int(real(work[1])))

* Fine tuning

Author: andreasvarga

stdlib/LinearAlgebra/src/lapack.jl

@@ -523,7 +523,7 @@ for (gebrd, gelqf, geqlf, geqrf, geqp3, geqrt, geqrt3, gerqf, getrf, elty, relty
                       m, n, A, max(1,stride(A,2)), tau, work, lwork, info)
                 chklapackerror(info[])
                 if i == 1
-                    lwork = BlasInt(real(work[1]))
+                    lwork = max(BlasInt(1),BlasInt(real(work[1])))
                     resize!(work, lwork)
                 end
             end
@@ -552,7 +552,7 @@ for (gebrd, gelqf, geqlf, geqrf, geqp3, geqrt, geqrt3, gerqf, getrf, elty, relty
                       m, n, A, max(1,stride(A,2)), tau, work, lwork, info)
                 chklapackerror(info[])
                 if i == 1
-                    lwork = BlasInt(real(work[1]))
+                    lwork = max(BlasInt(m), BlasInt(real(work[1])))
                     resize!(work, lwork)
                 end
             end

stdlib/LinearAlgebra/test/lapack.jl

@@ -705,4 +705,10 @@ end
 # # https://github.com/JuliaLang/julia/pull/39845
 @test LinearAlgebra.LAPACK.liblapack == "libblastrampoline"
 
+# Issue #42762 https://github.com/JuliaLang/julia/issues/42762
+# Tests geqrf! and gerqf! with null column dimensions
+a = zeros(2,0), zeros(0)
+@test LinearAlgebra.LAPACK.geqrf!(a...) === a
+@test LinearAlgebra.LAPACK.gerqf!(a...) === a
+
 end # module TestLAPACK