Add norm2 and norm1 shortcuts

Author: asterycs

README.md

@@ -48,9 +48,9 @@ to_std(derivative(tr(A), A)) # "I"
 The function `to_std` will throw an exception when given an expression that that cannot be converted to
 standard notation.
 
-### Supported operators
+### Supported functions and operators
 
-`tr`, `sum`, `sin`, `cos`, `+`, `-`, `'`, `*`, `.*`, `.^`, `^`, `abs`
+`tr`, `sum`, `sin`, `cos`, `+`, `-`, `'`, `*`, `.*`, `.^`, `^`, `abs`, `norm2`, `norm1`
 
 ### Installation
 

src/ricci.jl

@@ -6,6 +6,7 @@ import LinearAlgebra.tr
 
 export tr
 export sum
+export norm1, norm2
 
 abstract type Tensor end
 
@@ -257,6 +258,28 @@ function tr(arg::Tensor)
     return evaluate(BinaryOperation{Mult}(arg, KrD(flip(free_ids[2]), flip(free_ids[1]))))
 end
 
+function norm2(arg::Tensor)
+    free_ids = get_free_indices(arg)
+
+    if length(free_ids) != 1
+        throw(DomainError("Norms are currently implemented only for vectors."))
+    end
+
+    p = 2
+
+    return sum(arg .^ p)^(1//p)
+end
+
+function norm1(arg::Tensor)
+    free_ids = get_free_indices(arg)
+
+    if length(free_ids) != 1
+        throw(DomainError("Norms are currently implemented only for vectors."))
+    end
+
+    return sum(abs(arg))
+end
+
 function Base.sum(arg::Tensor)
     free_ids = get_free_indices(arg)
 

test/RicciTest.jl

@@ -110,6 +110,40 @@ end
     @test typeof(op.arg) == dc.BinaryOperation{dc.Mult}
 end
 
+@testset "norm2 throws for inputs other than vectors" begin
+    c = Variable("c")
+    A = Variable("A", Upper(1), Lower(2))
+
+    @test_throws DomainError norm2(c)
+    @test_throws DomainError norm2(A)
+end
+
+@testset "norm1 throws for inputs other than vectors" begin
+    c = Variable("c")
+    A = Variable("A", Upper(1), Lower(2))
+
+    @test_throws DomainError norm1(c)
+    @test_throws DomainError norm1(A)
+end
+
+@testset "norm2 output" begin
+    x = Variable("x", Upper(2))
+
+    op = norm2(x)
+
+    @test typeof(op) == dc.Power
+    @test op.base == sum(x .^ 2)
+    @test op.exponent == 1//2
+end
+
+@testset "norm1 output" begin
+    x = Variable("x", Upper(2))
+
+    op = norm1(x)
+
+    @test op == sum(abs(x))
+end
+
 @testset "UnaryOperation equality operator" begin
     a = KrD(Upper(1), Lower(2))
     b = Variable("b", Upper(2))