recursive vecnorm

base/linalg/generic.jl

@@ -280,10 +280,10 @@ diag(A::AbstractVector) = throw(ArgumentError("use diagm instead of diag to cons
 function generic_vecnormMinusInf(x)
     s = start(x)
     (v, s) = next(x, s)
-    minabs = norm(v)
+    minabs = vecnormMinusInf(v)
     while !done(x, s)
         (v, s) = next(x, s)
-        vnorm = norm(v)
+        vnorm = vecnormMinusInf(v)
         minabs = ifelse(isnan(minabs) | (minabs < vnorm), minabs, vnorm)
     end
     return float(minabs)
@@ -292,10 +292,10 @@ end
 function generic_vecnormInf(x)
     s = start(x)
     (v, s) = next(x, s)
-    maxabs = norm(v)
+    maxabs = vecnormInf(v)
     while !done(x, s)
         (v, s) = next(x, s)
-        vnorm = norm(v)
+        vnorm = vecnormInf(v)
         maxabs = ifelse(isnan(maxabs) | (maxabs > vnorm), maxabs, vnorm)
     end
     return float(maxabs)
@@ -304,20 +304,20 @@ end
 function generic_vecnorm1(x)
     s = start(x)
     (v, s) = next(x, s)
-    av = float(norm(v))
+    av = float(vecnorm1(v))
     T = typeof(av)
     sum::promote_type(Float64, T) = av
     while !done(x, s)
         (v, s) = next(x, s)
-        sum += norm(v)
+        sum += vecnorm1(v)
     end
     return convert(T, sum)
 end
 
 # faster computation of norm(x)^2, avoiding overflow for integers
-norm_sqr(x) = norm(x)^2
-norm_sqr(x::Number) = abs2(x)
-norm_sqr(x::Union{T,Complex{T},Rational{T}}) where {T<:Integer} = abs2(float(x))
+vecnorm_sqr(x) = vecnorm(x)^2
+vecnorm_sqr(x::Number) = abs2(x)
+vecnorm_sqr(x::Union{T,Complex{T},Rational{T}}) where {T<:Integer} = abs2(float(x))
 
 function generic_vecnorm2(x)
     maxabs = vecnormInf(x)
@@ -326,17 +326,17 @@ function generic_vecnorm2(x)
     (v, s) = next(x, s)
     T = typeof(maxabs)
     if isfinite(_length(x)*maxabs*maxabs) && maxabs*maxabs != 0 # Scaling not necessary
-        sum::promote_type(Float64, T) = norm_sqr(v)
+        sum::promote_type(Float64, T) = vecnorm_sqr(v)
         while !done(x, s)
             (v, s) = next(x, s)
-            sum += norm_sqr(v)
+            sum += vecnorm_sqr(v)
         end
         return convert(T, sqrt(sum))
     else
-        sum = abs2(norm(v)/maxabs)
+        sum = abs2(vecnorm(v)/maxabs)
         while !done(x, s)
             (v, s) = next(x, s)
-            sum += (norm(v)/maxabs)^2
+            sum += (vecnorm(v)/maxabs)^2
         end
         return convert(T, maxabs*sqrt(sum))
     end
@@ -352,21 +352,21 @@ function generic_vecnormp(x, p)
         (maxabs == 0 || isinf(maxabs)) && return maxabs
         T = typeof(maxabs)
     else
-        T = typeof(float(norm(v)))
+        T = typeof(float(vecnorm(v)))
     end
     spp::promote_type(Float64, T) = p
     if -1 <= p <= 1 || (isfinite(_length(x)*maxabs^spp) && maxabs^spp != 0) # scaling not necessary
-        sum::promote_type(Float64, T) = norm(v)^spp
+        sum::promote_type(Float64, T) = vecnormp(v, p)^spp
         while !done(x, s)
             (v, s) = next(x, s)
-            sum += norm(v)^spp
+            sum += vecnormp(v, p)^spp
         end
         return convert(T, sum^inv(spp))
     else # rescaling
-        sum = (norm(v)/maxabs)^spp
+        sum = (vecnormp(v, p)/maxabs)^spp
         while !done(x, s)
             (v, s) = next(x, s)
-            sum += (norm(v)/maxabs)^spp
+            sum += (vecnorm(v, p)/maxabs)^spp
         end
         return convert(T, maxabs*sum^inv(spp))
     end
@@ -449,6 +449,11 @@ julia> vecnorm(-2, Inf)
 ```
 """
 @inline vecnorm(x::Number, p::Real=2) = p == 0 ? (x==0 ? zero(abs(x)) : oneunit(abs(x))) : abs(x)
+@inline vecnormMinusInf(x::Number) = abs(x)
+@inline vecnormInf(x::Number) = abs(x)
+@inline vecnorm1(x::Number) = abs(x)
+@inline vecnorm2(x::Number) = abs(x)
+@inline vecnormp(x::Number, p) = p == 0 ? (x==0 ? zero(abs(x)) : oneunit(abs(x))) : abs(x)
 
 function norm1(A::AbstractMatrix{T}) where T
     m, n = size(A)
@@ -621,11 +626,11 @@ function vecdot(x::AbstractArray, y::AbstractArray)
         throw(DimensionMismatch("first array has length $(lx) which does not match the length of the second, $(_length(y))."))
     end
     if lx == 0
-        return dot(zero(eltype(x)), zero(eltype(y)))
+        return vecdot(zero(eltype(x)), zero(eltype(y)))
     end
-    s = zero(dot(first(x), first(y)))
+    s = zero(vecdot(first(x), first(y)))
     for (Ix, Iy) in zip(eachindex(x), eachindex(y))
-        @inbounds  s += dot(x[Ix], y[Iy])
+        @inbounds  s += vecdot(x[Ix], y[Iy])
     end
     s
 end
@@ -656,22 +661,22 @@ function vecdot(x, y) # arbitrary iterables
         if !isempty(y)
             throw(DimensionMismatch("x and y are of different lengths!"))
         end
-        return dot(zero(eltype(x)), zero(eltype(y)))
+        return vecdot(zero(eltype(x)), zero(eltype(y)))
     end
     iy = start(y)
     if done(y, iy)
         throw(DimensionMismatch("x and y are of different lengths!"))
     end
     (vx, ix) = next(x, ix)
     (vy, iy) = next(y, iy)
-    s = dot(vx, vy)
+    s = vecdot(vx, vy)
     while !done(x, ix)
         if done(y, iy)
             throw(DimensionMismatch("x and y are of different lengths!"))
         end
         (vx, ix) = next(x, ix)
         (vy, iy) = next(y, iy)
-        s += dot(vx, vy)
+        s += vecdot(vx, vy)
     end
     if !done(y, iy)
             throw(DimensionMismatch("x and y are of different lengths!"))