CS代写 L5 – cscodehelp代写
L5
APS1070 Week 5 Lecture Code¶
Part 1 – Linear Algebra¶
Inverting a Matrix¶
In [1]:
import numpy as np
from numpy.linalg import inv
In [2]:
mat = np.array([[1,0,2,0],[1,1,0,0], [1,2,0,1],[1,1,0,1]])
mat
Out[2]:
array([[1, 0, 2, 0],
[1, 1, 0, 0],
[1, 2, 0, 1],
[1, 1, 0, 1]])
In [3]:
mat_inv = inv(mat)
mat_inv
Out[3]:
array([[ 0. , 1. , -1. , 1. ],
[ 0. , 0. , 1. , -1. ],
[ 0.5, -0.5, 0.5, -0.5],
[ 0. , -1. , 0. , 1. ]])
In [4]:
Out[4]:
array([[1., 0., 0., 0.],
[0., 1., 0., 0.],
[0., 0., 1., 0.],
[0., 0., 0., 1.]])
In [5]:
Out[5]:
array([[1., 0., 0., 0.],
[0., 1., 0., 0.],
[0., 0., 1., 0.],
[0., 0., 0., 1.]])
Part 2 – Analytical Geometry¶
NORM
In [6]:
from numpy import linalg as LA
a = np.array([3,4])
a
Out[6]:
array([3, 4])
In [7]:
LA.norm(a)
Out[7]:
5.0
DOT PRODUCT
In [8]:
x = np.array([1,2,3])
y = np.array([4,5,6])
print(x,y)
[1 2 3] [4 5 6]
In [9]:
product = x.T * y
product.sum()
Out[9]:
32
In [10]:
np.dot(x,y)
Out[10]:
32
Lengths and distances
In [11]:
x = np.array([1,0,1])
y = np.array([0,1,1])
print(x,y)
[1 0 1] [0 1 1]
In [12]:
np.linalg.norm(x-y)
Out[12]:
1.4142135623730951
Angles and orthogonality
In [13]:
x = np.array([1,1])
y = np.array([1,2])
print(x,y)
[1 1] [1 2]
In [14]:
np.degrees(np.arccos(np.dot(x,y)/(np.dot(x,x)*np.dot(y,y))**0.5))
Out[14]:
18.434948822922017
Part 3 – Data Augmentation¶
Many of the transformation techniques covered in lecture can be implemented on on image data to improve the performance of our machine learning algorithms. Provided is a demonstration of some of the common transformations used for data augmentation.
Load Sample Image
In [15]:
import numpy as np
from skimage.io import imread, imsave
import matplotlib.pyplot as plt
from skimage import transform
from skimage.transform import rotate, AffineTransform, resize
from skimage.util import random_noise
from skimage.filters import gaussian
from scipy import ndimage
In [17]:
# load Image
img = imread(‘https://www.eecg.utoronto.ca/~hadizade/APS1070/hand.jpg’) / 255
# plot original Image
plt.imshow(img)
plt.show()
Rotations
In [18]:
# image rotation using skimage.transformation.rotate
image_rot = rotate(img, angle=30)
plt.title(‘Rotation’)
plt.imshow(image_rot)
plt.show()
[19]:
# image shearing using sklearn.transform.AffineTransform
tf = AffineTransform(shear=-0.5)
sheared = transform.warp(img, tf, order=1, preserve_range=True, mode=’wrap’)
plt.title(‘Sheared’)
plt.imshow(sheared)
plt.show()
Scaling
In [20]:
# Image rescaling with sklearn.transform.resize
rows = img.shape[0]
cols = img.shape[1]
scaled = resize(img[70:170,60:260,:], (rows, cols))
plt.title(‘Scaled’)
plt.imshow(scaled)
plt.show()
print(‘Original Shape: ‘,img.shape)
print(‘Rescaled Shape: ‘,scaled.shape)
Original Shape: (167, 218, 3)
Rescaled Shape: (167, 218, 3)
Flipping or Reflection
In [21]:
# flip up-down using np.flipud
up_down = np.flipud(img)
plt.imshow(up_down)
plt.show()
In [22]:
# flip left-right using np.fliplr
left_right = np.fliplr(img)
plt.imshow(left_right)
plt.show()
Add Noise
In [23]:
# Apply Random Noise to image using skimage.utils.random_noise
noised = random_noise(img, var=0.1**2)
plt.imshow(noised)
plt.show()
Increase Brightness
In [24]:
# Increasing the brighness of the Image
# Note: Here we add 100/255 since we scaled Intensity values of Image when loading (by dividing it 255)
highB = img + (100/255)
plt.imshow(highB)
plt.show()
Clipping input data to the valid range for imshow with RGB data ([0..1] for floats or [0..255] for integers).
Increase Contrast
In [25]:
# Increasing the contrast of the Image
highC = img * 1.5
plt.imshow(highC)
plt.show()
Clipping input data to the valid range for imshow with RGB data ([0..1] for floats or [0..255] for integers).
From a single image we were able to generate many different images which we could use to augment our training data.
