Upgrade to Julia 0.7/1.0

.travis.yml

@@ -3,7 +3,6 @@ os:
     - linux
     - osx
 julia:
-    - 0.6
     - 0.7
     - nightly
 matrix:

README.md

@@ -22,7 +22,7 @@ Pkg.add("Expokit")
 w = expmv!{T}( w::Vector{T}, t::Number, A, v::Vector{T}; kwargs...)
 ```
 The function `expmv!` calculates `w = exp(t*A)*v`, where `A` is a
-matrix or any type that supports `size` and `A_mul_B!` and `v` a dense vector by using Krylov subspace projections. The result is
+matrix or any type that supports `size`, `eltype` and `mul!` and `v` is a dense vector by using Krylov subspace projections. The result is
 stored in `w`.
 
 The following keywords are supported
@@ -43,7 +43,7 @@ w = expmv{T}( t::Number, A, v::Vector{T}; kwargs...)
 w = phimv!{T}( w::Vector{T}, t::Number, A, u::Vector{T}, v::Vector{T}; kwargs...)
 ```
 The function `phimv!` calculates `w = e^{tA}v + t φ(t A) u` with `φ(z) = (exp(z)-1)/z`, where `A` is a
-matrix or any type that supports `size` and `A_mul_B!`, `u` and `v` are dense vectors by using Krylov subspace projections. The result is stored in `w`. The supported keywords are the same as for `expmv!`.
+matrix or any type that supports `size`, `eltype` and `mul!`, `u` and `v` are dense vectors by using Krylov subspace projections. The result is stored in `w`. The supported keywords are the same as for `expmv!`.
 
 ## chbv
 

REQUIRE

@@ -1,2 +1 @@
-julia 0.6
-Compat
+julia 0.7

src/Expokit.jl

@@ -11,18 +11,10 @@ R.B. Sidje, ACM Trans. Math. Softw., 24(1):130-156, 1998 (or its
 """
 module Expokit
 
-using Compat, Compat.LinearAlgebra
-import Compat:view, String
-const LinearAlgebra = Compat.LinearAlgebra
-
-if VERSION < v"0.7-"
-    nothing
-else
-    using LinearAlgebra, SparseArrays
-end
+using LinearAlgebra
 
 const axpy! = LinearAlgebra.axpy!
-const expm! = LinearAlgebra.expm!
+const exp! = LinearAlgebra.exp!
 
 include("expmv.jl")
 include("padm.jl")

src/chbv.jl

@@ -77,7 +77,7 @@ chbv!(A, vec::Vector{T}) where {T} = chbv!(vec, A, copy(vec))
 
 function chbv!(w::Vector{T}, A, vec::Vector{T}) where {T<:Real}
     p = min(length(θ), length(α))
-    scale!(copy!(w, vec), α0)
+    rmul!(copyto!(w, vec), α0)
     @inbounds for i = 1:p
         w .+= real((A - θ[i]*I) \ (α[i] * vec))
     end
@@ -86,7 +86,7 @@ end
 
 function chbv!(w::Vector{T}, A, vec::Vector{T}) where {T<:Complex}
     p = min(length(θ), length(α))
-    scale!(copy!(w, vec), α0)
+    rmul!(copyto!(w, vec), α0)
     t = [θ; θconj]
     a = 0.5 * [α; αconj]
     @inbounds for i = 1:2*p

src/expmv.jl

@@ -2,11 +2,11 @@ export expmv, expmv!
 
 function default_anorm(A)
     try
-        Compat.opnorm(A, Inf)
+        opnorm(A, Inf)
     catch err
         if err isa MethodError
-            warn("opnorm($(typeof(A)), Inf) is not defined, fall back to using `anorm = 1.0`.
-To suppress this warning, please specify the anorm parameter manually.")
+            @warn "opnorm($(typeof(A)), Inf) is not defined, fall back to using `anorm = 1.0`.
+To suppress this warning, please specify the `anorm` keyword manually."
             1.0
         else
             throw(err)
@@ -28,7 +28,7 @@ function expmv( t::Number,
                    A, vec::Vector{T};
                    tol::Real=1e-7,
                    m::Int=min(30, size(A, 1)),
-                   norm=Base.norm, anorm=default_anorm(A)) where {T}
+                   norm=LinearAlgebra.norm, anorm=default_anorm(A)) where {T}
 
     result = convert(Vector{promote_type(eltype(A), T, typeof(t))}, copy(vec))
     expmv!(t, A, result; tol=tol, m=m, norm=norm, anorm=anorm)
@@ -39,10 +39,10 @@ expmv!( t::Number,
            A, vec::Vector{T};
            tol::Real=1e-7,
            m::Int=min(30,size(A,1)),
-           norm=Base.norm, anorm=default_anorm(A)) where {T} = expmv!(vec, t, A, vec; tol=tol, m=m, norm=norm, anorm=anorm)
+           norm=LinearAlgebra.norm, anorm=default_anorm(A)) where {T} = expmv!(vec, t, A, vec; tol=tol, m=m, norm=norm, anorm=anorm)
 
 function expmv!(w::Vector{T}, t::Number, A, vec::Vector{T};
-                   tol::Real=1e-7, m::Int=min(30,size(A,1)), norm=Base.norm, anorm=default_anorm(A)) where {T}
+                   tol::Real=1e-7, m::Int=min(30,size(A,1)), norm=LinearAlgebra.norm, anorm=default_anorm(A)) where {T}
 
     if size(vec,1) != size(A,2)
         error("dimension mismatch")
@@ -62,10 +62,10 @@ function expmv!(w::Vector{T}, t::Number, A, vec::Vector{T};
     r = 1/m
     fact = (((m+1)/exp(1.0))^(m+1))*sqrt(2.0*pi*(m+1))
     tau = (1.0/anorm)*((fact*tol)/(4.0*beta*anorm))^r
-    tau = signif(tau, 2)
+    tau = round(tau, sigdigits=2)
 
     # storage for Krylov subspace vectors
-    vm = Array{typeof(w)}(m+1)
+    vm = Array{typeof(w)}(undef,m+1)
     for i=1:m+1
         vm[i]=similar(w)
     end
@@ -75,19 +75,19 @@ function expmv!(w::Vector{T}, t::Number, A, vec::Vector{T};
     tsgn = sign(t)
     tk = zero(tf)
 
-    copy!(w, vec)
+    copyto!(w, vec)
     p = similar(w)
     mx = m
     while tk < tf
         tau = min(tf-tk, tau)
 
         # Arnoldi procedure
         # vm[1] = v/beta
-        scale!(copy!(vm[1],w),1/beta)
+        rmul!(copyto!(vm[1],w),1/beta)
         mx = m
         for j=1:m
             # p[:] = A*vm[j]
-            Base.A_mul_B!(p, A, vm[j])
+            mul!(p, A, vm[j])
 
             for i=1:j
                 hm[i,j] = dot(vm[i], p)
@@ -102,7 +102,7 @@ function expmv!(w::Vector{T}, t::Number, A, vec::Vector{T};
 
                 # F = expm(tsgn*tau*hm[1:j,1:j])
                 # F = expm!(scale(tsgn*tau,view(hm,1:j,1:j)))
-                F = expm!(tsgn*tau*view(hm,1:j,1:j))
+                F = exp!(tsgn*tau*view(hm,1:j,1:j))
 
                 fill!(w, zero(T))
                 for k=1:j
@@ -115,18 +115,18 @@ function expmv!(w::Vector{T}, t::Number, A, vec::Vector{T};
             hm[j+1,j] = s
 
             # vm[j+1] = p/hm[j+1,j]
-            scale!(copy!(vm[j+1],p),1/hm[j+1,j])
+            rmul!(copyto!(vm[j+1],p),1/hm[j+1,j])
         end
         hm[m+2,m+1] = one(T)
-        (mx != m) || (avnorm = norm(Base.A_mul_B!(p,A,vm[m+1])))
+        (mx != m) || (avnorm = norm(mul!(p,A,vm[m+1])))
 
         # propagate using adaptive step size
         iter = 1
         while (iter < maxiter) && (mx == m)
 
             # F = expm(tsgn*tau*hm)
             # F = expm!(scale(tsgn*tau,hm))
-            F = expm!(tsgn*tau*hm)
+            F = exp!(tsgn*tau*hm)
 
             # local error estimation
             err1 = abs( beta*F[m+1,1] )
@@ -154,7 +154,7 @@ function expmv!(w::Vector{T}, t::Number, A, vec::Vector{T};
                 break
             end
             tau = gamma * tau * (tau*tol/err_loc)^r # estimate new time-step
-            tau = signif(tau, 2) # round to 2 significant digits
+            tau = round(tau, sigdigits=2) # round to 2 significant digits
                                  # to prevent numerical noise
             iter = iter + 1
         end
@@ -167,7 +167,7 @@ function expmv!(w::Vector{T}, t::Number, A, vec::Vector{T};
         tk = tk + tau
 
         tau = gamma * tau * (tau*tol/err_loc)^r # estimate new time-step
-        tau = signif(tau, 2) # round to 2 significant digits
+        tau = round(tau, sigdigits=2) # round to 2 significant digits
                              # to prevent numerical noise
         err_loc = max(err_loc,rndoff)
 

src/padm.jl

@@ -56,7 +56,7 @@ function padm(A; p::Int64=6)
     end
 
     # scaling
-    normA = norm(A, Inf)
+    normA = opnorm(A, Inf)
     s = 0
     if normA > 0.5
         s = max(0, round(Int64, log(normA)/log(2), RoundToZero) + 2)
@@ -65,8 +65,8 @@ function padm(A; p::Int64=6)
 
     # Horner evaluation of the irreducible fraction
     A2 = A * A
-    Q = c[p+1]*eye(A)
-    P = c[p]*eye(A)
+    Q = c[p+1]*Matrix{eltype(A)}(I, size(A))
+    P = c[p]*Matrix{eltype(A)}(I, size(A))
     odd = 1
     @inbounds begin 
         for k = p-1:-1:1
@@ -82,11 +82,11 @@ function padm(A; p::Int64=6)
     if odd == 1
         Q = Q * A
         Q = Q - P
-        E = -(I + 2 * \(Q, full(P)))
+        E = -(I + 2 * \(Q, Matrix(P)))
     else
         P = P * A
         Q = Q - P
-        E = I + 2 * \(Q, full(P))
+        E = I + 2 * \(Q, Matrix(P))
     end
 
     # squaring

src/phimv.jl

@@ -31,12 +31,11 @@ Calculate the solution of a nonhomogeneous linear ODE problem with constant inpu
     EXPOKIT: Software Package for Computing Matrix Exponentials.
     ACM - Transactions On Mathematical Software, 24(1):130-156, 1998
 """
-
 function phimv( t::Number,
                    A, u::Vector{T}, vec::Vector{T};
                    tol::Real=1e-7,
                    m::Int=min(30, size(A, 1)),
-                   norm=Base.norm, anorm=default_anorm(A)) where {T}
+                   norm=LinearAlgebra.norm, anorm=default_anorm(A)) where {T}
 
     result = convert(Vector{promote_type(eltype(A), T, typeof(t))}, copy(vec))
     phimv!(t, A, u, result; tol=tol, m=m, norm=norm, anorm=anorm)
@@ -47,10 +46,10 @@ phimv!( t::Number,
            A, u::Vector{T}, vec::Vector{T};
            tol::Real=1e-7,
            m::Int=min(30, size(A, 1)),
-           norm=Base.norm, anorm=default_anorm(A)) where {T} = phimv!(vec, t, A, u, vec; tol=tol, m=m, norm=norm, anorm=anorm)
+           norm=LinearAlgebra.norm, anorm=default_anorm(A)) where {T} = phimv!(vec, t, A, u, vec; tol=tol, m=m, norm=norm, anorm=anorm)
 
 function phimv!( w::Vector{T}, t::Number, A, u::Vector{T}, vec::Vector{T};
-                   tol::Real=1e-7, m::Int=min(30, size(A, 1)), norm=Base.norm, anorm=default_anorm(A)) where {T}
+                   tol::Real=1e-7, m::Int=min(30, size(A, 1)), norm=LinearAlgebra.norm, anorm=default_anorm(A)) where {T}
 
     if size(vec, 1) != size(A, 2)
         error("dimension mismatch")
@@ -70,10 +69,10 @@ function phimv!( w::Vector{T}, t::Number, A, u::Vector{T}, vec::Vector{T};
     r = 1/m
     fact = (((m+1)/exp(1))^(m+1))*sqrt(2*pi*(m+1))
     tau = (1.0/anorm)*((fact*tol)/(4.0*beta*anorm))^r
-    tau = signif(tau, 2)
+    tau = round(tau, sigdigits=2)
 
     # storage for Krylov subspace vectors
-    vm = Array{typeof(w)}(m+1)
+    vm = Array{typeof(w)}(undef,m+1)
     for i = 1:m+1
         vm[i] = similar(w)
     end
@@ -83,7 +82,7 @@ function phimv!( w::Vector{T}, t::Number, A, u::Vector{T}, vec::Vector{T};
     tsgn = sign(t)
     tk = zero(tf)
 
-    copy!(w, vec)
+    copyto!(w, vec)
     p = similar(w)
     k1 = 3
     mb = m
@@ -92,10 +91,10 @@ function phimv!( w::Vector{T}, t::Number, A, u::Vector{T}, vec::Vector{T};
         tau = min(tf-tk, tau)
 
         # Arnoldi procedure
-        scale!(copy!(vm[1], A*w+u), 1/beta)
+        rmul!(copyto!(vm[1], A*w+u), 1/beta)
 
         for j = 1:m
-            Base.A_mul_B!(p, A, vm[j])
+            mul!(p, A, vm[j])
 
             for i = 1:j
                 hm[i, j] = dot(vm[i], p)
@@ -110,7 +109,7 @@ function phimv!( w::Vector{T}, t::Number, A, u::Vector{T}, vec::Vector{T};
                 break
             end
             hm[j+1,j] = s
-            scale!(copy!(vm[j+1], p), 1/hm[j+1,j])
+            rmul!(copyto!(vm[j+1], p), 1/hm[j+1,j])
         end
 
         hm[1, mb+1] = one(T)
@@ -125,7 +124,7 @@ function phimv!( w::Vector{T}, t::Number, A, u::Vector{T}, vec::Vector{T};
         iter = 0
         while iter <= maxiter
             mx = mb + max(1,k1)
-            F = expm!(tsgn*tau*view(hm, 1:mx, 1:mx))
+            F = exp!(tsgn*tau*view(hm, 1:mx, 1:mx))
             if k1 == 0
                 err_loc = btol
                 break
@@ -151,7 +150,7 @@ function phimv!( w::Vector{T}, t::Number, A, u::Vector{T}, vec::Vector{T};
                 break
             else
                 tau = gamma * tau * (tau*tol/err_loc)^r # estimate new time-step
-                tau = signif(tau, 2) # round to 2 significant digits
+                tau = round(tau, sigdigits=2) # round to 2 significant digits
                                      # to prevent numerical noise
                 if iter == maxiter
                     error("Number of iterations exceeded $(maxiter). Requested tolerance might be too high.")
@@ -169,7 +168,7 @@ function phimv!( w::Vector{T}, t::Number, A, u::Vector{T}, vec::Vector{T};
         tk = tk + tau
 
         tau = gamma * tau * (tau*tol/err_loc)^r # estimate new time-step
-        tau = signif(tau, 2) # round to 2 significant digits
+        tau = round(tau, sigdigits=2) # round to 2 significant digits
                              # to prevent numerical noise
 
         err_loc = max(err_loc, rndoff)