%matplotlib inline
%config InlineBackend.figure_format='retina'
# import libraries
import numpy as np
import matplotlib as mp
import pandas as pd
import matplotlib.pyplot as plt
import laUtilities as ut
import slideUtilities as sl
import demoUtilities as dm
from IPython.display import Image
from IPython.display import display_html
from IPython.display import display
from IPython.display import Math
from IPython.display import Latex
reload(dm)
reload(ut)
print ''

%%html
<style>
 .container.slides .celltoolbar, .container.slides .hide-in-slideshow {
    display: None ! important;
}
</style>

# image credit: Scan from Lay, 4th edition
sl.hide_code_in_slideshow()
display(Image("images/Lay-fig-1-8-1.jpg", width=450))

# image credit: Scan from Lay, 4th edition
sl.hide_code_in_slideshow()
display(Image("images/Lay-fig-1-8-2.jpg", width=450))

square = np.array([[0.0,1,1,0],[1,1,0,0]])
ax = dm.plotSetup(-3,3,-3,3)
print square
dm.plotSquare(square)

ax = dm.plotSetup(-3,3,-3,3)
print "square = "; print square
dm.plotSquare(square)
#
# create the A matrix
A = np.array([[1.0, 1.5],[0.0,1.0]])
print "A matrix = "; print A
#
# apply the shear matrix to the square
ssquare = np.zeros(np.shape(square))
for i in range(4):
    ssquare[:,i] = dm.AxVS(A,square[:,i])
print "sheared square = "; print ssquare
dm.plotSquare(ssquare,'r')

sl.hide_code_in_slideshow()
ax = dm.plotSetup(-3,3,-3,3)
ax.plot([0],[1],'ro')
ax.text(0.25,1,'(0,1)')
ax.plot([1],[0],'ro')
ax.text(1.25,0.25,'(1,0)')
print ''

# image credit: Scan from Lay, 4th edition
sl.hide_code_in_slideshow()
display(Image("images/rotate-example.jpeg", width=450))

ax = dm.plotSetup(-4,4,-4,4)
note = dm.mnote()
angle = 180.0; phi = (angle/360.0) * 2.0 * np.pi
rotate = np.array([[np.cos(phi), -np.sin(phi)],[np.sin(phi), np.cos(phi)]])
rnote = rotate.dot(note)
dm.plotShape(rnote)

sl.hide_code_in_slideshow()
ax = dm.plotSetup(-3,3,-3,3)
ax.plot([0],[1],'ro')
ax.text(0.25,1,'(0,1)')
ax.plot([1],[0],'ro')
ax.text(1.25,0.25,'(1,0)')
print ''

A = np.array([[2.5,0],[0,2.5]])
print A
ax = dm.plotSetup(-3,3,-3,3)
dm.plotSquare(square)
dm.plotSquare(A.dot(square),'r')

sl.hide_code_in_slideshow()
ax = dm.plotSetup(-3,3,-3,3)
ax.plot([0],[1],'ro')
ax.text(0.25,1,'(0,1)')
ax.plot([1],[0],'ro')
ax.text(1.25,0.25,'(1,0)')
print ''

A = np.array([[1,0],[0,-1]])
print A
ax = dm.plotSetup(-3,3,-3,3)
dm.plotSquare(square)
dm.plotSquare(A.dot(square),'r')
Latex(r'Reflection through the $x_1$ axis')

A = np.array([[-1,0],[0,1]])
print A
ax = dm.plotSetup(-3,3,-3,3)
dm.plotSquare(square)
dm.plotSquare(A.dot(square),'r')
Latex(r'Reflection through the $x_2$ axis')

A = np.array([[0,1],[1,0]])
print A
ax = dm.plotSetup(-3,3,-3,3)
dm.plotSquare(square)
dm.plotSquare(A.dot(square),'r')
plt.plot([-2,2],[-2,2],'b--')
Latex(r'Reflection through the line $x_1 = x_2$')

A = np.array([[0,-1],[-1,0]])
print A
ax = dm.plotSetup(-3,3,-3,3)
dm.plotSquare(square)
dm.plotSquare(A.dot(square),'r')
plt.plot([-2,2],[2,-2],'b--')
Latex(r'Reflection through the line $x_1 = -x_2$')

A = np.array([[-1,0],[0,-1]])
print A
ax = dm.plotSetup(-3,3,-3,3)
dm.plotSquare(square)
dm.plotSquare(A.dot(square),'r')
Latex(r'Reflection through the origin')

A = np.array([[0.45,0],[0,1]])
print A
ax = dm.plotSetup(-3,3,-3,3)
dm.plotSquare(square)
dm.plotSquare(A.dot(square),'r')
ax.arrow(1.0,1.5,-1.0,0,head_width=0.15, head_length=0.1, length_includes_head=True)
Latex(r'Horizontal Contraction')

A = np.array([[2.5,0],[0,1]])
print A
ax = dm.plotSetup(-3,3,-3,3)
dm.plotSquare(square)
dm.plotSquare(A.dot(square),'r')
Latex(r'Horizontal Expansion')

A = np.array([[1,0],[-1.5,1]])
print A
ax = dm.plotSetup(-3,3,-3,3)
dm.plotSquare(square)
dm.plotSquare(A.dot(square),'r')
Latex(r'Vertical Shear')

A = np.array([[1,0],[0,0]])
print A
ax = dm.plotSetup(-3,3,-3,3)
# dm.plotSquare(square)
dm.plotSquare(A.dot(square),'r')
# ax.arrow(1.0,1.0,0,-0.9,head_width=0.15, head_length=0.1, length_includes_head=True)
# ax.arrow(0.0,1.0,0,-0.9,head_width=0.15, head_length=0.1, length_includes_head=True)
Latex(r'Projection onto the $x_1$ axis')

A = np.array([[0,0],[0,1]])
print A
ax = dm.plotSetup(-3,3,-3,3)
# dm.plotSquare(square)
dm.plotSquare(A.dot(square))
#ax.arrow(1.0,1.0,-0.9,0,head_width=0.15, head_length=0.1, length_includes_head=True)
#ax.arrow(1.0,0.0,-0.9,0,head_width=0.15, head_length=0.1, length_includes_head=True)
Latex(r'Projection onto the $x_2$ axis')

# image credit: Scan from Lay, 4th edition
sl.hide_code_in_slideshow()
display(Image("images/Lay-fig-1-9-3.jpeg", width=450))

# image credit: Scan from Lay, 4th edition
sl.hide_code_in_slideshow()
display(Image("images/Lay-fig-1-9-4.jpeg", width=450))