Construct LazyString in error paths for tridiag (#54648)

Similar to #54631, this would
help reduce dynamic dispatches involved in concatenating a `String` and
a `LazyString`.

These show up in
```julia
julia> @report_opt Tridiagonal(rand(1), rand(2), rand(1)) \ rand(2)
[ Info: tracking Base
┌ Warning: skipping var"#sprint#594"(context, sizehint::Integer, ::typeof(sprint), f::Function, args...) @ Base strings/io.jl:107 to avoid parsing too much code
└ @ Revise ~/.julia/packages/Revise/bAgL0/src/packagedef.jl:1092
┌ Warning: skipping (::Base.var"#120#121")(io) @ Base strings/lazy.jl:84 to avoid parsing too much code
└ @ Revise ~/.julia/packages/Revise/bAgL0/src/packagedef.jl:1092
═════ 1 possible error found ═════
┌ \(A::Tridiagonal{Float64, Vector{Float64}}, B::Vector{Float64}) @ LinearAlgebra /cache/build/builder-amdci4-5/julialang/julia-release-1-dot-11/usr/share/julia/stdlib/v1.11/LinearAlgebra/src/generic.jl:1132
│┌ lu(::Tridiagonal{Float64, Vector{Float64}}) @ LinearAlgebra /cache/build/builder-amdci4-5/julialang/julia-release-1-dot-11/usr/share/julia/stdlib/v1.11/LinearAlgebra/src/lu.jl:341
││┌ lu(::Tridiagonal{Float64, Vector{Float64}}; kwargs::@kwargs{}) @ LinearAlgebra /cache/build/builder-amdci4-5/julialang/julia-release-1-dot-11/usr/share/julia/stdlib/v1.11/LinearAlgebra/src/lu.jl:341
│││┌ _lucopy(A::Tridiagonal{Float64, Vector{Float64}}, T::Type{Float64}) @ LinearAlgebra /cache/build/builder-amdci4-5/julialang/julia-release-1-dot-11/usr/share/julia/stdlib/v1.11/LinearAlgebra/src/lu.jl:351
││││┌ copymutable_oftype(A::Tridiagonal{Float64, Vector{Float64}}, ::Type{Float64}) @ LinearAlgebra /cache/build/builder-amdci4-5/julialang/julia-release-1-dot-11/usr/share/julia/stdlib/v1.11/LinearAlgebra/src/LinearAlgebra.jl:463
│││││┌ similar(M::Tridiagonal{Float64, Vector{Float64}}, ::Type{Float64}) @ LinearAlgebra /cache/build/builder-amdci4-5/julialang/julia-release-1-dot-11/usr/share/julia/stdlib/v1.11/LinearAlgebra/src/tridiag.jl:603
││││││┌ Tridiagonal(dl::Vector{Float64}, d::Vector{Float64}, du::Vector{Float64}) @ LinearAlgebra /cache/build/builder-amdci4-5/julialang/julia-release-1-dot-11/usr/share/julia/stdlib/v1.11/LinearAlgebra/src/tridiag.jl:520
│││││││┌ Tridiagonal{Float64, Vector{Float64}}(dl::Vector{Float64}, d::Vector{Float64}, du::Vector{Float64}) @ LinearAlgebra /cache/build/builder-amdci4-5/julialang/julia-release-1-dot-11/usr/share/julia/stdlib/v1.11/LinearAlgebra/src/tridiag.jl:477
││││││││┌ string(::String, ::String, ::LazyString) @ Base ./strings/io.jl:189
│││││││││┌ print_to_string(::String, ::String, ::LazyString) @ Base ./strings/io.jl:148
││││││││││┌ print(io::IOBuffer, s::LazyString) @ Base ./strings/io.jl:195
│││││││││││┌ iterate(s::LazyString) @ Base ./strings/lazy.jl:94
││││││││││││┌ String(l::LazyString) @ Base ./strings/lazy.jl:83
│││││││││││││┌ sprint(::Base.var"#120#121"{LazyString}) @ Base ./strings/io.jl:107
││││││││││││││┌ sprint(::Base.var"#120#121"{LazyString}; context::Nothing, sizehint::Int64) @ Base ./strings/io.jl:114
│││││││││││││││┌ (::Base.var"#120#121"{LazyString})(io::IOBuffer) @ Base ./strings/lazy.jl:85
││││││││││││││││ runtime dispatch detected: print(io::IOBuffer, %16::Any)::Any
│││││││││││││││└────────────────────
```

Co-authored-by: Shuhei Kadowaki <[email protected]>
Co-authored-by: Dilum Aluthge <[email protected]>

Author: 3 people

stdlib/LinearAlgebra/src/tridiag.jl

@@ -183,6 +183,12 @@ issymmetric(S::SymTridiagonal) = true
 
 tr(S::SymTridiagonal) = sum(S.dv)
 
+@noinline function throw_diag_outofboundserror(n, sz)
+    sz1, sz2 = sz
+    throw(ArgumentError(LazyString(lazy"requested diagonal, $n, must be at least $(-sz1) ",
+            lazy"and at most $sz2 for an $(sz1)-by-$(sz2) matrix")))
+end
+
 function diag(M::SymTridiagonal{T}, n::Integer=0) where T<:Number
     # every branch call similar(..., ::Int) to make sure the
     # same vector type is returned independent of n
@@ -194,8 +200,7 @@ function diag(M::SymTridiagonal{T}, n::Integer=0) where T<:Number
     elseif absn <= size(M,1)
         return fill!(similar(M.dv, size(M,1)-absn), zero(T))
     else
-        throw(ArgumentError(string(lazy"requested diagonal, $n, must be at least $(-size(M, 1)) ",
-            lazy"and at most $(size(M, 2)) for an $(size(M, 1))-by-$(size(M, 2)) matrix")))
+        throw_diag_outofboundserror(n, size(M))
     end
 end
 function diag(M::SymTridiagonal, n::Integer=0)
@@ -210,8 +215,7 @@ function diag(M::SymTridiagonal, n::Integer=0)
     elseif n <= size(M,1)
         throw(ArgumentError("requested diagonal contains undefined zeros of an array type"))
     else
-        throw(ArgumentError(string(lazy"requested diagonal, $n, must be at least $(-size(M, 1)) ",
-            lazy"and at most $(size(M, 2)) for an $(size(M, 1))-by-$(size(M, 2)) matrix")))
+        throw_diag_outofboundserror(n, size(M))
     end
 end
 
@@ -353,7 +357,7 @@ isdiag(M::SymTridiagonal) =  iszero(_evview(M))
 function tril!(M::SymTridiagonal{T}, k::Integer=0) where T
     n = length(M.dv)
     if !(-n - 1 <= k <= n - 1)
-        throw(ArgumentError(string(lazy"the requested diagonal, $k, must be at least ",
+        throw(ArgumentError(LazyString(lazy"the requested diagonal, $k, must be at least ",
             lazy"$(-n - 1) and at most $(n - 1) in an $n-by-$n matrix")))
     elseif k < -1
         fill!(M.ev, zero(T))
@@ -372,7 +376,7 @@ end
 function triu!(M::SymTridiagonal{T}, k::Integer=0) where T
     n = length(M.dv)
     if !(-n + 1 <= k <= n + 1)
-        throw(ArgumentError(string(lazy"the requested diagonal, $k, must be at least ",
+        throw(ArgumentError(LazyString(lazy"the requested diagonal, $k, must be at least ",
             lazy"$(-n + 1) and at most $(n + 1) in an $n-by-$n matrix")))
     elseif k > 1
         fill!(M.ev, zero(T))
@@ -485,7 +489,7 @@ struct Tridiagonal{T,V<:AbstractVector{T}} <: AbstractMatrix{T}
         require_one_based_indexing(dl, d, du)
         n = length(d)
         if (length(dl) != n-1 || length(du) != n-1) && !(length(d) == 0 && length(dl) == 0 && length(du) == 0)
-            throw(ArgumentError(string("cannot construct Tridiagonal from incompatible ",
+            throw(ArgumentError(LazyString("cannot construct Tridiagonal from incompatible ",
                 "lengths of subdiagonal, diagonal and superdiagonal: ",
                 lazy"($(length(dl)), $(length(d)), $(length(du)))")))
         end
@@ -658,7 +662,7 @@ function diag(M::Tridiagonal{T}, n::Integer=0) where T
     elseif abs(n) <= size(M,1)
         return fill!(similar(M.d, size(M,1)-abs(n)), zero(T))
     else
-        throw(ArgumentError(string(lazy"requested diagonal, $n, must be at least $(-size(M, 1)) ",
+        throw(ArgumentError(LazyString(lazy"requested diagonal, $n, must be at least $(-size(M, 1)) ",
             lazy"and at most $(size(M, 2)) for an $(size(M, 1))-by-$(size(M, 2)) matrix")))
     end
 end
@@ -724,7 +728,7 @@ end
     elseif j - i == 1
         @inbounds A.du[i] = x
     elseif !iszero(x)
-        throw(ArgumentError(string(lazy"cannot set entry ($i, $j) off ",
+        throw(ArgumentError(LazyString(lazy"cannot set entry ($i, $j) off ",
             lazy"the tridiagonal band to a nonzero value ($x)")))
     end
     return x
@@ -780,7 +784,7 @@ isdiag(M::Tridiagonal) = iszero(M.dl) && iszero(M.du)
 function tril!(M::Tridiagonal{T}, k::Integer=0) where T
     n = length(M.d)
     if !(-n - 1 <= k <= n - 1)
-        throw(ArgumentError(string(lazy"the requested diagonal, $k, must be at least ",
+        throw(ArgumentError(LazyString(lazy"the requested diagonal, $k, must be at least ",
             lazy"$(-n - 1) and at most $(n - 1) in an $n-by-$n matrix")))
     elseif k < -1
         fill!(M.dl, zero(T))
@@ -798,7 +802,7 @@ end
 function triu!(M::Tridiagonal{T}, k::Integer=0) where T
     n = length(M.d)
     if !(-n + 1 <= k <= n + 1)
-        throw(ArgumentError(string(lazy"the requested diagonal, $k, must be at least ",
+        throw(ArgumentError(LazyString(lazy"the requested diagonal, $k, must be at least ",
             lazy"$(-n + 1) and at most $(n + 1) in an $n-by-$n matrix")))
     elseif k > 1
         fill!(M.dl, zero(T))