# 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.

In [15]:

import numpy as np
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]:

# 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()

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.