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ch3.py
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rJNAL Jupyter notebooks for Linear Algebra
ch3.py
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#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Wed Mar 13 16:42:29 2019
@author: jecker, tenderini, ronssin
"""
from
__future__
import
division
import
numpy
as
np
from
IPython.display
import
display
,
Latex
import
plotly
import
plotly.graph_objs
as
go
plotly
.
offline
.
init_notebook_mode
(
connected
=
True
)
from
IPython.core.magic
import
register_cell_magic
from
IPython.display
import
HTML
import
ipywidgets
as
widgets
import
random
from
ipywidgets
import
interact_manual
from
plotly.subplots
import
make_subplots
def
concepts_cle
(
v
,
u
,
lam
):
#Initial settings, change to np.array
o
=
[[
0
],[
0
]]
u
=
np
.
array
(
u
)
v
=
np
.
array
(
v
)
data
=
[]
t
=
np
.
linspace
(
-
5
,
5
,
51
)
s
=
np
.
linspace
(
0
,
1
,
10
)
peak
=
go
.
Scatter
(
x
=
u
[
0
],
y
=
u
[
1
],
marker
=
dict
(
symbol
=
6
,
size
=
12
,
color
=
'teal'
),
showlegend
=
False
)
peak2
=
go
.
Scatter
(
x
=
v
[
0
],
y
=
v
[
1
],
marker
=
dict
(
symbol
=
6
,
size
=
12
,
color
=
'slateblue'
),
showlegend
=
False
)
vector
=
go
.
Scatter
(
x
=
o
[
0
]
+
s
*
u
[
0
],
y
=
o
[
1
]
+
s
*
u
[
1
],
mode
=
'lines'
,
line
=
dict
(
width
=
3
,
color
=
'teal'
),
name
=
'Vecteur u'
)
vector2
=
go
.
Scatter
(
x
=
o
[
0
]
+
s
*
v
[
0
],
y
=
o
[
1
]
+
s
*
v
[
1
],
mode
=
'lines'
,
line
=
dict
(
width
=
3
,
color
=
'slateblue'
),
name
=
'Vecteur v'
)
zero
=
go
.
Scatter
(
x
=
t
*
0
,
y
=
t
*
0
,
name
=
'Origine'
,
marker
=
dict
(
symbol
=
6
,
size
=
12
,
color
=
'black'
),
showlegend
=
False
)
data
.
append
(
vector
)
data
.
append
(
vector2
)
data
.
append
(
zero
)
data
.
append
(
peak
)
data
.
append
(
peak2
)
#règle du parallelogramme
trace1
=
go
.
Scatter
(
x
=
u
[
0
]
+
s
*
v
[
0
],
y
=
u
[
1
]
+
s
*
v
[
1
],
mode
=
'lines'
,
line
=
dict
(
width
=
1
,
color
=
'slateblue'
,
dash
=
'dash'
),
name
=
'"v"'
)
trace2
=
go
.
Scatter
(
x
=
v
[
0
]
+
s
*
u
[
0
],
y
=
v
[
1
]
+
s
*
u
[
1
],
mode
=
'lines'
,
line
=
dict
(
width
=
1
,
color
=
'teal'
,
dash
=
'dash'
),
name
=
'"u"'
)
w
=
u
+
v
sumUV
=
go
.
Scatter
(
x
=
o
[
0
]
+
s
*
w
[
0
],
y
=
o
[
1
]
+
s
*
w
[
1
],
mode
=
'lines'
,
line
=
dict
(
width
=
1
,
color
=
'orangered'
,
dash
=
'dash'
),
name
=
'u+v'
,
hoverinfo
=
'none'
)
peakUV
=
go
.
Scatter
(
x
=
w
[
0
],
y
=
w
[
1
],
marker
=
dict
(
symbol
=
6
,
size
=
12
,
color
=
'orangered'
),
showlegend
=
False
)
data
.
append
(
trace1
)
data
.
append
(
trace2
)
data
.
append
(
sumUV
)
data
.
append
(
peakUV
)
fig
=
go
.
FigureWidget
(
data
=
data
)
fig
.
update_layout
(
title
=
"Addition de deux vecteurs"
,
autosize
=
False
,
width
=
700
,
height
=
700
,
font
=
dict
(
size
=
10
,
color
=
"RebeccaPurple"
),
legend
=
dict
(
font
=
dict
(
size
=
12
)),
scene
=
dict
(
aspectmode
=
"data"
)
)
plotly
.
offline
.
iplot
(
fig
)
#multiplication par lambda
data
=
[]
peak
=
go
.
Scatter
(
x
=
u
[
0
],
y
=
u
[
1
],
marker
=
dict
(
symbol
=
6
,
size
=
12
,
color
=
'teal'
),
opacity
=
1
,
showlegend
=
False
)
data
.
append
(
peak
)
vector
=
go
.
Scatter
(
x
=
o
[
0
]
+
s
*
u
[
0
],
y
=
o
[
1
]
+
s
*
u
[
1
],
mode
=
'lines'
,
line
=
dict
(
width
=
3
,
color
=
'teal'
),
opacity
=
1
,
name
=
'Vecteur $u$'
)
data
.
append
(
vector
)
peak2
=
go
.
Scatter
(
x
=
lam
*
u
[
0
],
y
=
lam
*
u
[
1
],
marker
=
dict
(
symbol
=
6
,
size
=
12
,
color
=
'orangered'
),
opacity
=
0.5
,
showlegend
=
False
)
data
.
append
(
peak2
)
vector2
=
go
.
Scatter
(
x
=
o
[
0
]
+
lam
*
s
*
u
[
0
],
y
=
o
[
1
]
+
lam
*
s
*
u
[
1
],
mode
=
'lines'
,
line
=
dict
(
width
=
3
,
color
=
'orangered'
),
opacity
=
0.5
,
name
=
'Vecteur $\lambda u$'
)
data
.
append
(
vector2
)
fig
=
go
.
FigureWidget
(
data
=
data
)
fig
.
update_layout
(
title
=
"Multiplication par un scalaire"
,
autosize
=
False
,
width
=
700
,
height
=
700
,
font
=
dict
(
size
=
10
,
color
=
"RebeccaPurple"
),
legend
=
dict
(
font
=
dict
(
size
=
12
)),
scene
=
dict
(
aspectmode
=
"data"
)
)
plotly
.
offline
.
iplot
(
fig
)
return
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