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pluto_schmidt.jl
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pluto_schmidt.jl
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### A Pluto.jl notebook ###
# v0.19.32
using Markdown
using InteractiveUtils
# This Pluto notebook uses @bind for interactivity. When running this notebook outside of Pluto, the following 'mock version' of @bind gives bound variables a default value (instead of an error).
macro bind(def, element)
quote
local iv = try Base.loaded_modules[Base.PkgId(Base.UUID("6e696c72-6542-2067-7265-42206c756150"), "AbstractPlutoDingetjes")].Bonds.initial_value catch; b -> missing; end
local el = $(esc(element))
global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : iv(el)
el
end
end
# ╔═╡ 5ffc5ec0-f91f-11ec-0552-37ef5f25102d
begin
using PlutoUI
using Plots
using Symbolics
using ForwardDiff
using LaTeXStrings
using Images
using TestImages
using ImageView
using LinearAlgebra
# using FFTW
# using DSP
end
# ╔═╡ 2dc43448-3cf4-475f-8b61-d16c3594d9e3
md"""
## Schmidt Program
"""
# ╔═╡ d7b68e9f-8924-4434-95cc-7e70e5426830
begin
v1=[1;1;0];
v2=[1;3;1];
v3=[2;-1;1];
u1=v1/sqrt(v1'*v1);
w2=v2-v2'*u1*u1;
u2=w2/sqrt(w2'*w2);
w3=v3-v3'*u1*u1-v3'u2*u2;
u3=w3/sqrt(w3'*w3);
det([v1 v2 v3]);
end
# ╔═╡ 0fad2be9-9a9c-4409-94a0-d0a5b36b3f38
# ╔═╡ 7cd547e1-e3d8-4a0d-8197-217bcc04aea4
# ╔═╡ 9ee2d078-8769-422b-b5f1-80761ff77fb3
begin
f1=[1;3;3];
f2=[1;3;0];
f3=[0;0;3];
0;
end
# ╔═╡ bb9ef0b8-eeab-4a03-be05-9baf073f4409
# ╔═╡ 38ea56dd-c2f9-4a67-af20-c01234fbee5b
begin
nbsp = html" "
end
# ╔═╡ 0711e2bc-f6c0-4f62-9682-6789d46bc3ee
md"""
latitude = $(@bind l Slider(-90:1:90, show_value=true, default=30))
$nbsp $nbsp
longitude = $(@bind m Slider(-180:1:180, show_value=true, default=30))
"""
# ╔═╡ ed1435f3-9098-4b9c-9576-5f8edb95f5a5
begin
plot3d([0,v1[1]],[0,v1[2]],[0,v1[3]],grid=false,arrow=3,linewidth=2,label=:"\$v_1\$",legendfontsize=12,xticks=false,yticks=false,zticks=false,camera = (m, l))
plot3d!([0,v2[1]],[0,v2[2]],[0,v2[3]],arrow=3,linewidth=2,label="\$v_2\$")
plot3d!([0,v3[1]],[0,v3[2]],[0,v3[3]],arrow=3,linewidth=2,label="\$v_3\$")
plot3d!([0,w2[1]],[0,w2[2]],[0,w2[3]],arrow=3,linewidth=2,label="\$w_2\$")
plot3d!([0,w3[1]],[0,w3[2]],[0,w3[3]],arrow=3,linewidth=2,label="\$w_3\$")
end
# ╔═╡ 13781d50-c95e-4f90-8bfe-b49d741e568d
md"""
latitude = $(@bind l1 Slider(-90:1:90, show_value=true, default=30))
$nbsp $nbsp
longitude = $(@bind m1 Slider(-180:1:180, show_value=true, default=30))
"""
# ╔═╡ b8d01a05-a78d-40f4-a38d-e404d6a7add3
begin
plot3d([0,f1[1]],[0,f1[2]],[0,f1[3]],grid=false,arrow=3,linewidth=2,label=:"\$f\$",legendfontsize=12,xticks=false,yticks=false,zticks=false,camera = (m1, l1))
plot3d!([0,f2[1]],[0,f2[2]],[0,f2[3]],arrow=3,linewidth=2,label="\$S_N(f)\$")
plot3d!([f2[1],f2[1]],[f2[2],f2[2]],[f2[3],f3[3]],arrow=3,linewidth=2,label="\$f-S_N(f)\$")
end
# ╔═╡ d2cec051-e237-4c2a-baa2-56e5ce5d7f5f
# ╔═╡ 30a21f2a-cd27-43d1-9a37-794064f12172
# ╔═╡ d1db737a-73f4-458c-890b-63f9e6be58a8
# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
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[compat]
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ImageView = "~0.11.5"
Images = "~0.25.3"
LaTeXStrings = "~1.3.0"
Plots = "~1.38.15"
PlutoUI = "~0.7.51"
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"""
# ╔═╡ 00000000-0000-0000-0000-000000000002
PLUTO_MANIFEST_TOML_CONTENTS = """
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