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Adds mineig and maxeig methods #2725

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Apr 2, 2013
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Adds mineig and maxeig methods #2725

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481b661
Adds mineig and maxeig methods
jiahao Apr 1, 2013
76ad001
Renames to eigmax and eigmin
jiahao Apr 2, 2013
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2 changes: 2 additions & 0 deletions base/exports.jl
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Expand Up @@ -590,6 +590,8 @@ export
lu,
lufact,
lufact!,
maxeig,
mineig,
norm,
normfro,
null,
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2 changes: 2 additions & 0 deletions base/linalg.jl
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Expand Up @@ -73,6 +73,8 @@ export
lu,
lufact,
lufact!,
maxeig,
mineig,
norm,
normfro,
null,
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10 changes: 10 additions & 0 deletions base/linalg/factorization.jl
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Expand Up @@ -443,6 +443,16 @@ end

eigvals(x::Number) = [one(x)]

#Computes maximum and minimum eigenvalue
function maxeig(A::Union(Number, StridedMatrix))
v = eigvals(A)
iscomplex(v) ? error("Complex eigenvalues cannot be ordered") : max(v)
end
function mineig(A::Union(Number, StridedMatrix))
v = eigvals(A)
iscomplex(v) ? error("Complex eigenvalues cannot be ordered") : min(v)
end

inv(A::EigenDense) = diagmm(A.vectors, 1.0/A.values)*A.vectors'
det(A::EigenDense) = prod(A.values)

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5 changes: 5 additions & 0 deletions base/linalg/tridiag.jl
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Expand Up @@ -67,6 +67,11 @@ eig(m::SymTridiagonal) = LAPACK.stegr!('V', copy(m.dv), copy(m.ev))
eigvals(m::SymTridiagonal, il::Int, iu::Int) = LAPACK.stebz!('I', 'E', 0.0, 0.0, il, iu, -1.0, copy(m.dv), copy(m.ev))[1]
eigvals(m::SymTridiagonal, vl::Float64, vu::Float64) = LAPACK.stebz!('V', 'E', vl, vu, 0, 0, -1.0, copy(m.dv), copy(m.ev))[1]
eigvals(m::SymTridiagonal) = LAPACK.stebz!('A', 'E', 0.0, 0.0, 0, 0, -1.0, copy(m.dv), copy(m.ev))[1]

#Computes largest and smallest eigenvalue
maxeig(m::SymTridiagonal) = eigvals(m, size(m)[1], size(m)[1])[1]
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size(m, 1) avoids the creation of an array.

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I think size returns a tuple, but we should still do size(m,1) to avoid the tuple creation.

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so this should be eigvals(m, size(m,1), size(m,1))[1]? I'm assuming the last one can't be helped.

mineig(m::SymTridiagonal) = eigvals(m, 1, 1)[1]

#Compute selected eigenvectors only corresponding to particular eigenvalues
eigvecs(m::SymTridiagonal) = eig(m)[2]
eigvecs{Eigenvalue<:Real}(m::SymTridiagonal, eigvals::Vector{Eigenvalue}) = LAPACK.stein!(m.dv, m.ev, eigvals)
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10 changes: 9 additions & 1 deletion doc/stdlib/linalg.rst
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Expand Up @@ -95,11 +95,19 @@ Linear algebra functions in Julia are largely implemented by calling functions f

Returns the eigenvalues of ``A``.

.. function:: maxeig(A)

Returns the largest eigenvalue of ``A``.

.. function:: minvals(A)

Returns the smallest eigenvalue of ``A``.

.. function:: eigvecs(A, [eigvals])

Returns the eigenvectors of ``A``.

If the optional vector of eigenvalues ``eigvals`` is specified, returns the specific corresponding eigenvectors. (Currently this optional syntax only works for SymTridiagonal matrices.)
For SymTridiagonal matrices, if the optional vector of eigenvalues ``eigvals`` is specified, returns the specific corresponding eigenvectors.

.. function:: eigfact(A)

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