Merge pull request #2725 from jiahao/maxeig

Adds mineig and maxeig methods

Author: ViralBShah

base/exports.jl

@@ -566,6 +566,8 @@ export
     eig,
     eigfact,
     eigfact!,
+    eigmax,
+    eigmin,
     eigs,
     eigvals,
     eigvecs,

base/linalg.jl

@@ -49,6 +49,8 @@ export
     eig,
     eigfact,
     eigfact!,
+    eigmax,
+    eigmin,
     eigs,
     eigvals,
     eigvecs,

base/linalg/factorization.jl

@@ -443,6 +443,16 @@ end
 
 eigvals(x::Number) = [one(x)]
 
+#Computes maximum and minimum eigenvalue
+function eigmax(A::Union(Number, StridedMatrix))
+    v = eigvals(A)
+    iscomplex(v) ? error("Complex eigenvalues cannot be ordered") : max(v)
+end
+function eigmin(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)
 

base/linalg/hermitian.jl

@@ -37,6 +37,7 @@ eigvals(A::Hermitian, il::Int, ih::Int) = LAPACK.syevr!('N', 'I', A.uplo, copy(A
 eigvals(A::Hermitian, vl::Real, vh::Real) = LAPACK.syevr!('N', 'V', A.uplo, copy(A.S), vl, vh, 0, 0, -1.0)[1]
 eigvals(A::Hermitian) = eigvals(A, 1, size(A, 1))
 eigmax(A::Hermitian) = eigvals(A, size(A, 1), size(A, 1))[1]
+eigmin(A::Hermitian) = eigvals(A, 1, 1)[1]
 
 function expm(A::Hermitian)
     F = eigfact(A)

base/linalg/tridiag.jl

@@ -68,6 +68,11 @@ 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
+eigmax(m::SymTridiagonal) = eigvals(m, size(m, 1), size(m, 1))[1]
+eigmin(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)

doc/stdlib/linalg.rst

@@ -95,11 +95,19 @@ Linear algebra functions in Julia are largely implemented by calling functions f
 
    Returns the eigenvalues of ``A``.
 
+.. function:: eigmax(A)
+
+   Returns the largest eigenvalue of ``A``.
+
+.. function:: eigmin(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)