@@ -14,7 +14,7 @@ Base.size(H::HessenbergMatrix, i::Integer) = size(H.data, i)
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function LinearAlgebra. ldiv! (H:: HessenbergMatrix , B:: AbstractVecOrMat )
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n = size (H, 1 )
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Hd = H. data
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- for i = 1 : n- 1
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+ for i = 1 : ( n- 1 )
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G, _ = givens (Hd, i, i + 1 , i)
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lmul! (G, view (Hd, 1 : n, i: n))
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lmul! (G, B)
@@ -35,13 +35,13 @@ Base.copy(HF::HessenbergFactorization{T,S,U}) where {T,S,U} =
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function _hessenberg! (A:: StridedMatrix{T} ) where {T}
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n = LinearAlgebra. checksquare (A)
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τ = Vector {Householder{T}} (undef, n - 1 )
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- for i = 1 : n- 1
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- xi = view (A, i+ 1 : n, i)
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+ for i = 1 : ( n- 1 )
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+ xi = view (A, ( i+ 1 ) : n, i)
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t = LinearAlgebra. reflector! (xi)
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- H = Householder {T,typeof(xi)} (view (xi, 2 : n- i), t)
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+ H = Householder {T,typeof(xi)} (view (xi, 2 : ( n- i) ), t)
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τ[i] = H
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- lmul! (H' , view (A, i+ 1 : n, i+ 1 : n))
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- rmul! (view (A, :, i+ 1 : n), H)
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+ lmul! (H' , view (A, ( i+ 1 ) : n, ( i+ 1 ) : n))
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+ rmul! (view (A, :, ( i+ 1 ) : n), H)
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end
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return HessenbergFactorization {T,typeof(A),eltype(τ)} (A, τ)
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end
@@ -96,7 +96,7 @@ function _schur!(
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end
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# Determine if the matrix splits. Find lowest positioned subdiagonal "zero"
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- for _istart = iend- 1 : - 1 : 1
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+ for _istart = ( iend- 1 ) : - 1 : 1
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if abs (HH[_istart+ 1 , _istart]) <=
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tol * (abs (HH[_istart, _istart]) + abs (HH[_istart+ 1 , _istart+ 1 ]))
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# Check if subdiagonal element H[i+1,i] is "zero" such that we can split the matrix
@@ -183,17 +183,17 @@ function singleShiftQR!(
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end
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G, _ = givens (H11 - shift, H21, istart, istart + 1 )
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lmul! (G, view (HH, :, istart: m))
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- rmul! (view (HH, 1 : min (istart + 2 , iend), :), G' )
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+ rmul! (view (HH, 1 : min (istart+ 2 , iend), :), G' )
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lmul! (G, τ)
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- for i = istart: iend- 2
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+ for i = istart: ( iend- 2 )
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G, _ = givens (HH[i+ 1 , i], HH[i+ 2 , i], i + 1 , i + 2 )
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lmul! (G, view (HH, :, i: m))
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HH[i+ 2 , i] = Htmp
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if i < iend - 2
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Htmp = HH[i+ 3 , i+ 1 ]
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HH[i+ 3 , i+ 1 ] = 0
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end
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- rmul! (view (HH, 1 : min (i + 3 , iend), :), G' )
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+ rmul! (view (HH, 1 : min (i+ 3 , iend), :), G' )
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# mul!(G, τ)
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end
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return HH
@@ -231,12 +231,12 @@ function doubleShiftQR!(
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vHH = view (HH, :, istart: m)
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lmul! (G1, vHH)
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lmul! (G2, vHH)
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- vHH = view (HH, 1 : min (istart + 3 , m), :)
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+ vHH = view (HH, 1 : min (istart+ 3 , m), :)
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rmul! (vHH, G1' )
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rmul! (vHH, G2' )
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lmul! (G1, τ)
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lmul! (G2, τ)
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- for i = istart: iend- 2
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+ for i = istart: ( iend- 2 )
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for j = 1 : 2
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if i + j + 1 > iend
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break
@@ -254,7 +254,7 @@ function doubleShiftQR!(
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Htmp22 = HH[i+ 4 , i+ j]
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HH[i+ 4 , i+ j] = 0
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end
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- rmul! (view (HH, 1 : min (i + j + 2 , iend), :), G' )
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+ rmul! (view (HH, 1 : min (i+ j + 2 , iend), :), G' )
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# mul!(G, τ)
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end
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end
@@ -333,5 +333,9 @@ function eigen!(
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return eigen! (Hermitian (A); sortby)
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end
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- throw (ArgumentError (" eigen! for general matrices not yet supported. Consider using schur!" ))
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- end
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+ throw (
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+ ArgumentError (
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+ " eigen! for general matrices not yet supported. Consider using schur!" ,
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+ ),
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+ )
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+ end
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