@@ -14,7 +14,7 @@ Base.size(H::HessenbergMatrix, i::Integer) = size(H.data, i)
1414function LinearAlgebra. ldiv! (H:: HessenbergMatrix , B:: AbstractVecOrMat )
1515 n = size (H, 1 )
1616 Hd = H. data
17- for i = 1 : n- 1
17+ for i = 1 : ( n- 1 )
1818 G, _ = givens (Hd, i, i + 1 , i)
1919 lmul! (G, view (Hd, 1 : n, i: n))
2020 lmul! (G, B)
@@ -35,13 +35,13 @@ Base.copy(HF::HessenbergFactorization{T,S,U}) where {T,S,U} =
3535function _hessenberg! (A:: StridedMatrix{T} ) where {T}
3636 n = LinearAlgebra. checksquare (A)
3737 τ = Vector {Householder{T}} (undef, n - 1 )
38- for i = 1 : n- 1
39- xi = view (A, i+ 1 : n, i)
38+ for i = 1 : ( n- 1 )
39+ xi = view (A, ( i+ 1 ) : n, i)
4040 t = LinearAlgebra. reflector! (xi)
41- H = Householder {T,typeof(xi)} (view (xi, 2 : n- i), t)
41+ H = Householder {T,typeof(xi)} (view (xi, 2 : ( n- i) ), t)
4242 τ[i] = H
43- lmul! (H' , view (A, i+ 1 : n, i+ 1 : n))
44- rmul! (view (A, :, i+ 1 : n), H)
43+ lmul! (H' , view (A, ( i+ 1 ) : n, ( i+ 1 ) : n))
44+ rmul! (view (A, :, ( i+ 1 ) : n), H)
4545 end
4646 return HessenbergFactorization {T,typeof(A),eltype(τ)} (A, τ)
4747end
@@ -96,7 +96,7 @@ function _schur!(
9696 end
9797
9898 # Determine if the matrix splits. Find lowest positioned subdiagonal "zero"
99- for _istart = iend- 1 : - 1 : 1
99+ for _istart = ( iend- 1 ) : - 1 : 1
100100 if abs (HH[_istart+ 1 , _istart]) <=
101101 tol * (abs (HH[_istart, _istart]) + abs (HH[_istart+ 1 , _istart+ 1 ]))
102102 # Check if subdiagonal element H[i+1,i] is "zero" such that we can split the matrix
@@ -183,17 +183,17 @@ function singleShiftQR!(
183183 end
184184 G, _ = givens (H11 - shift, H21, istart, istart + 1 )
185185 lmul! (G, view (HH, :, istart: m))
186- rmul! (view (HH, 1 : min (istart + 2 , iend), :), G' )
186+ rmul! (view (HH, 1 : min (istart+ 2 , iend), :), G' )
187187 lmul! (G, τ)
188- for i = istart: iend- 2
188+ for i = istart: ( iend- 2 )
189189 G, _ = givens (HH[i+ 1 , i], HH[i+ 2 , i], i + 1 , i + 2 )
190190 lmul! (G, view (HH, :, i: m))
191191 HH[i+ 2 , i] = Htmp
192192 if i < iend - 2
193193 Htmp = HH[i+ 3 , i+ 1 ]
194194 HH[i+ 3 , i+ 1 ] = 0
195195 end
196- rmul! (view (HH, 1 : min (i + 3 , iend), :), G' )
196+ rmul! (view (HH, 1 : min (i+ 3 , iend), :), G' )
197197 # mul!(G, τ)
198198 end
199199 return HH
@@ -231,12 +231,12 @@ function doubleShiftQR!(
231231 vHH = view (HH, :, istart: m)
232232 lmul! (G1, vHH)
233233 lmul! (G2, vHH)
234- vHH = view (HH, 1 : min (istart + 3 , m), :)
234+ vHH = view (HH, 1 : min (istart+ 3 , m), :)
235235 rmul! (vHH, G1' )
236236 rmul! (vHH, G2' )
237237 lmul! (G1, τ)
238238 lmul! (G2, τ)
239- for i = istart: iend- 2
239+ for i = istart: ( iend- 2 )
240240 for j = 1 : 2
241241 if i + j + 1 > iend
242242 break
@@ -254,7 +254,7 @@ function doubleShiftQR!(
254254 Htmp22 = HH[i+ 4 , i+ j]
255255 HH[i+ 4 , i+ j] = 0
256256 end
257- rmul! (view (HH, 1 : min (i + j + 2 , iend), :), G' )
257+ rmul! (view (HH, 1 : min (i+ j + 2 , iend), :), G' )
258258 # mul!(G, τ)
259259 end
260260 end
@@ -333,5 +333,9 @@ function eigen!(
333333 return eigen! (Hermitian (A); sortby)
334334 end
335335
336- throw (ArgumentError (" eigen! for general matrices not yet supported. Consider using schur!" ))
337- end
336+ throw (
337+ ArgumentError (
338+ " eigen! for general matrices not yet supported. Consider using schur!" ,
339+ ),
340+ )
341+ end
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