Adds eig, eigfact, eigvals and eigvecs for Bidiagonal

Addresses #3688

base/linalg/bidiag.jl

@@ -102,6 +102,44 @@ function \{T<:BlasFloat}(M::Bidiagonal{T}, rhs::StridedVecOrMat{T})
     apply(LAPACK.gtsv!, M.isupper ? (z, copy(M.dv), copy(M.ev), copy(rhs)) : (copy(M.ev), copy(M.dv), z, copy(rhs)))
 end
 
+
+#######################
+# Eigenvalues/vectors #
+#######################
+
+eigvals{T<:Number}(M::Bidiagonal{T}) = M.isupper ? M.dv : reverse(M.dv)
+function eigvecs{T<:Number}(M::Bidiagonal{T})
+  n = length(M.dv)
+  Q=zeros(T, n, n)
+  v=zeros(T, n)
+  if M.isupper
+    for i=1:n #index of eigenvector
+      v[1] = convert(T, 1.0)
+      for j=1:i-1 #Starting from j=i, eigenvector elements will be 0
+        v[j+1] = (M.dv[i]-M.dv[j])/M.ev[j] * v[j]
+      end
+      v /= norm(v)
+      Q[:,i] = v
+    end
+  else
+    for i=n:-1:1 #index of eigenvector
+      v[n] = convert(T, 1.0)
+      for j=(n-1):-1:max(1,(i-1)) #Starting from j=i-1, eigenvector elements will be 0
+        v[j] = (M.dv[i]-M.dv[j+1])/M.ev[j] * v[j+1]
+      end
+      v /= norm(v)
+      Q[:,n+1-i] = v
+    end
+  end
+  Q
+end
+
+eig{T<:Number}(M::Bidiagonal{T}) = eigvals(M), eigvecs(M)
+eigfact{T<:Number}(M::Bidiagonal{T}) = Eigen{T,T}(eigvals(M), eigvecs(M))
+
+###################
+# Singular values #
+###################
 #Wrap bdsdc to compute singular values and vectors
 svdvals{T<:Real}(M::Bidiagonal{T})=LAPACK.bdsdc!(M.isupper?'U':'L', 'N', copy(M.dv), copy(M.ev))
 svd    {T<:Real}(M::Bidiagonal{T})=LAPACK.bdsdc!(M.isupper?'U':'L', 'I', copy(M.dv), copy(M.ev))