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minres.jl
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minres.jl
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### A Pluto.jl notebook ###
# v0.19.16
using Markdown
using InteractiveUtils
# ╔═╡ 000a42f0-6a6e-11ed-07c8-17d3667314e4
function multiplyVecs(a::Vector{Float32},b::Vector{Float32})
size = length(a);
if(length(a) != length(b))
error("Dimension must match!");
end
return [a[i]*b[i] for i in 1:size]
end
# ╔═╡ c240b882-90b2-43e0-90d6-266218c9a76e
function plotvector(a, name="")
plot!([0,a[1]],[0,a[2]],arrow=true, labels=name, legend = :outertopleft);
end
# ╔═╡ b2515529-b438-43f6-8f4d-1dbeb0cfa9f5
function basecircle()
xc = yc = range(-1, 1, 100);
contour!(xc, yc, (x, y) -> x^2 + y^2, levels=1);
end
# ╔═╡ 39150468-fed6-4b00-9fe3-63864fba61f0
begin
using Plots;
plot();
v = Vector{Float32}([0,1]);
w = Vector{Float32}([1,0]);
plotvector(v, "v");
plotvector(w, "w");
basecircle();
end
# ╔═╡ 16ba1e01-598b-4491-9954-32eaa60c2f00
function plotvector3d(a, name="")
plot!([0,a[1]],[0,a[2]],[0, a[3]],arrow=true, labels=name, legend = :outertopleft);
end
# ╔═╡ 9e2bb0c2-5f3a-4663-b306-85b9c8b550b7
begin
using LinearAlgebra
plot()
k = [3,2];
e1 = [1,0];
e2 = [0,1];
k = k/norm(k);
plotvector(k, "k");
plotvector(e1, "e1");
plotvector(e2, "e2");
basecircle();
end
# ╔═╡ 0cbdc6d0-1087-4b12-b95f-906d0d8c5460
function basesphere()
n_s = 100
u_s = range(-pi, pi; length = n_s)
v_s = range(0, pi; length = n_s)
x_s = cos.(u_s) * sin.(v_s)'
y_s = sin.(u_s) * sin.(v_s)'
z_s = ones(n_s) * cos.(v_s)'
const_color = cgrad( [ RGB{Float64}(0.5,0.5,0.5) for _ in 1:2 ] )
surface!(x_s, y_s, z_s, color = const_color, minogrid = :false, colorbar = false, alpha = 0.5)
end
# ╔═╡ 6f1cbff4-96bf-4970-9058-b49044dc6d75
begin
#Determine angle of k wrt e1
angle = acosd(transpose(k)*e1)/(norm(k)*norm(e1))
print(angle);
end
# ╔═╡ ef7fde60-db68-4b68-a2fd-07e9957e64a8
begin
#Since e1 and e2 are orthogonal, the product should be zero
transpose(e1)*e2 == transpose(e2)*e1 == 0
end
# ╔═╡ 31680638-5366-4511-90f0-fbf4160e673e
begin
#Projection of k wrt e1
k_par_e1 = transpose(e1)*k*e1;
k_perp_e1 = k - k_par_e1;
plot();
plotvector(k_par_e1, "k // e1");
plotvector(k_perp_e1, "k _|_ e1");
plotvector(k, "k");
#plotvector(e1, "e1");
print(k == k_par_e1 + k_perp_e1)
basecircle();
end
# ╔═╡ 2cf19c10-0f9d-41d2-8dc7-23cbbd492b2e
function graham_schmidt_naive(A )
r,c = size(A);
Q = zeros(r, c);
R = zeros(c, c);
for i in 1:r
z = A[:, i];
sub = zeros(r, 1)
for j in 1:(i-1)
#Calculate the j-th element as q'v(i)
R[j, i] = transpose(Q[:, j]) * A[:, i]
#Sum the component of the j-th vector
sub = sub + R[j, i] * Q[:, j];
end
#Subtract the accumulated sum
z = z - sub;
R[i, i] = norm(z);
Q[:, i] = z / R[i, i];
end
return (Q,R)
end
# ╔═╡ 971cee94-854d-443d-9708-dc5df9c210cc
graham_schmidt_naive(I(10))
# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[deps]
LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
[compat]
Plots = "~1.36.3"
PlutoUI = "~0.7.48"
"""
# ╔═╡ 00000000-0000-0000-0000-000000000002
PLUTO_MANIFEST_TOML_CONTENTS = """
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