Merge branch 'main' into 20240906study

src/linear_algebra.jl → src/linear_algebra_basic.jl

@@ -81,11 +81,11 @@ end
 
 """
     function reflection(v::Vector, w::Vector) -> Vector
-The projection P from 'w' onto 'v' is the midpoint of the reflection of w around v
+The midpoint of the segment from `v` to the reflection of `v` is the projection P from 'v'  to the line along 'w' 
 """
-function reflection(v::Vector, w::Vector)
-    P = orthproj(v,w)
-    (2 * P ) - X
+function reflection(v::Vector,w::Vector)
+    P = orthproj(w,v)
+    (2 * P ) - w
 end
 
 """
@@ -280,12 +280,3 @@ function intersection_2_implicit_lines(a₁::Number, b₁::Number, c₁::Number,
     A\b
 end
 
-"""
-    function matrix_orthproj_basis(v::Vector) -> Matrix
-Compute matrix of orthogonal projection of basis vectors on line along vector v
-"""
-function matrix_orthproj_basis(v::Vector)
-    e₁ =[1,0]
-    e₂ = [0,1]
-    [permutedims(orthproj(v, e₁)); permutedims(orthproj(v, e₂))]
-end

src/linear_algebra_transform.jl

@@ -0,0 +1,22 @@
+using Symbolics
+include("./linear_algebra_basic.jl")
+
+@variables u v
+"""
+    function projection_matrix_symbolic() -> Matrix
+Create symbolic matrix for projection on [u, v] using E₁ = [1,0] and E₂ =[0,1] to get first and second row
+"""
+function projection_matrix_symbolic()
+    [orthproj([u, v], [1, 0])[1] orthproj([u, v], [0, 1])[1]; orthproj([u, v], [1, 0])[2] orthproj([u, v], [0, 1])[2]]
+end
+
+function projection_matrix_symbolic_polar()
+    simplify.(substitute.(projection_matrix_symbolic(),(Dict(u => cos(θ), v => sin(θ)),)))
+end
+"""
+    function projection_matrix(x::Vector) -> Matrix
+value of Matrix with an actual x  
+"""
+function projection_matrix(x::Vector)
+    Symbolics.value.(substitute.(projection_matrix_symbolic(), (Dict(u =>x[1], v=> x[2]), )))
+end