Add getindex method to LU{Tridiagonal} for extracting factors and full

method to reconstruct the Tridiagonal matrix.

base/linalg/lu.jl

@@ -113,23 +113,18 @@ function ipiv2perm{T}(v::AbstractVector{T}, maxi::Integer)
     return p
 end
 
-function getindex{T,S<:StridedMatrix}(A::LU{T,S}, d::Symbol)
-    m, n = size(A)
+function getindex{T,S<:StridedMatrix}(F::LU{T,S}, d::Symbol)
+    m, n = size(F)
     if d == :L
-        L = tril!(A.factors[1:m, 1:min(m,n)])
+        L = tril!(F.factors[1:m, 1:min(m,n)])
         for i = 1:min(m,n); L[i,i] = one(T); end
         return L
     elseif d == :U
-        return triu!(A.factors[1:min(m,n), 1:n])
+        return triu!(F.factors[1:min(m,n), 1:n])
     elseif d == :p
-        return ipiv2perm(A.ipiv, m)
+        return ipiv2perm(F.ipiv, m)
     elseif d == :P
-        p = A[:p]
-        P = zeros(T, m, m)
-        for i in 1:m
-            P[i,p[i]] = one(T)
-        end
-        return P
+        return eye(T, m)[:,invperm(F[:p])]
     else
         throw(KeyError(d))
     end
@@ -263,6 +258,65 @@ end
 
 factorize(A::Tridiagonal) = lufact(A)
 
+function getindex{T}(F::Base.LinAlg.LU{T,Tridiagonal{T}}, d::Symbol)
+    m, n = size(F)
+    if d == :L
+        L = full(Bidiagonal(ones(T, n), F.factors.dl, false))
+        for i = 2:n
+            tmp = L[F.ipiv[i], 1:i - 1]
+            L[F.ipiv[i], 1:i - 1] = L[i, 1:i - 1]
+            L[i, 1:i - 1] = tmp
+        end
+        return L
+    elseif d == :U
+        U = full(Bidiagonal(F.factors.d, F.factors.du, true))
+        for i = 1:n - 2
+            U[i,i + 2] = F.factors.du2[i]
+        end
+        return U
+    elseif d == :p
+        return ipiv2perm(F.ipiv, m)
+    elseif d == :P
+        return eye(T, m)[:,invperm(F[:p])]
+    end
+    throw(KeyError(d))
+end
+
+function full{T}(F::Base.LinAlg.LU{T,Tridiagonal{T}})
+    n = size(F, 1)
+
+    dl     = copy(F.factors.dl)
+    d      = copy(F.factors.d)
+    du     = copy(F.factors.du)
+    du2    = copy(F.factors.du2)
+
+    for i = n - 1:-1:1
+        li         = dl[i]
+        dl[i]      = li*d[i]
+        d[i + 1]  += li*du[i]
+        if i < n - 1
+            du[i + 1] += li*du2[i]
+        end
+
+        if F.ipiv[i] != i
+            tmp   = dl[i]
+            dl[i] = d[i]
+            d[i]  = tmp
+
+            tmp      = d[i + 1]
+            d[i + 1] = du[i]
+            du[i]    = tmp
+
+            if i < n - 1
+                tmp       = du[i + 1]
+                du[i + 1] = du2[i]
+                du2[i]    = tmp
+            end
+        end
+    end
+    return Tridiagonal(dl, d, du)
+end
+
 # See dgtts2.f
 function A_ldiv_B!{T}(A::LU{T,Tridiagonal{T}}, B::AbstractVecOrMat)
     n = size(A,1)

test/linalg/lu.jl

@@ -2,6 +2,8 @@
 
 debug = false
 
+using Base.Test
+
 n = 10
 
 # Split n into 2 parts for tests needing two matrices
@@ -57,6 +59,9 @@ debug && println("(Automatic) Square LU decomposition")
 debug && println("Tridiagonal LU")
         κd    = cond(full(d),1)
         lud   = lufact(d)
+        @test_approx_eq lud[:L]*lud[:U] lud[:P]*full(d)
+        @test_approx_eq lud[:L]*lud[:U] full(d)[lud[:p],:]
+        @test_approx_eq full(lud) d
         @test norm(d*(lud\b) - b, 1) < ε*κd*n*2 # Two because the right hand side has two columns
         if eltya <: Real
             @test norm((lud.'\b) - full(d.')\b, 1) < ε*κd*n*2 # Two because the right hand side has two columns
@@ -112,6 +117,5 @@ for elty in (Float32, Float64, Complex64, Complex128)
     # @test norm(F[:vectors]*Diagonal(F[:values])/F[:vectors] - A) > 0.01
 end
 
-
 @test @inferred(logdet(Complex64[1.0f0 0.5f0; 0.5f0 -1.0f0])) === 0.22314355f0 + 3.1415927f0im
 @test_throws DomainError logdet([1 1; 1 -1])