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cindygrcindygr
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Short and sweet video tweaks
1 parent 430e241 commit 59080ad

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‎Week_10_classes/matrix_routines.py‎

Lines changed: 36 additions & 15 deletions
Original file line numberDiff line numberDiff line change
@@ -7,7 +7,8 @@
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# --------------------------- Matrix routines -------------------------
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#
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# This will be our first example of making a .py file that is imported into the jupyter notebook/other .py file
10-
# This is so that the basic matrix functions - making matrices, checking them, plotting - can be in one place.
10+
# This is so that the basic matrix functions - making matrices, checking them, plotting - can be in one place,
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# the re-used in multiple places using "import".
1112
#
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# The code is organized as
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# Making scaling, rotation, translation matrices
@@ -29,11 +30,12 @@ def make_scale_matrix(scale_x=1.0, scale_y=1.0):
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@param scale_x - scale in x. Should NOT be 0.0
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@param scale_y - scale in y. Should NOT be 0.0
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@returns a 3x3 scaling matrix"""
33+
# Throw an error if a zero scale
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if np.isclose(scale_x, 0.0) or np.isclose(scale_y, 0.0):
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raise ValueError(f"Scale values should be non_zero {scale_x}, {scale_y}")
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# Set the diagonal elements to the scale values
36-
mat = np.identity(3)
38+
mat = np.identity(3) # Always use identity to make the initial 3x3 matrix
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mat[0, 0] = scale_x
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mat[1, 1] = scale_y
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@@ -46,7 +48,7 @@ def make_translation_matrix(d_x=0.0, d_y=0.0):
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@param d_y - translate in y
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@returns a 3x3 translation matrix"""
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49-
# Set the last column to the amount to move
51+
# Set the last column to be the amount to move
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mat = np.identity(3)
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mat[0, 2] = d_x
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mat[1, 2] = d_y
@@ -60,6 +62,7 @@ def make_rotation_matrix(theta=0.0):
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@param theta - rotate by theta (theta in radians)
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@returns a 3x3 rotation matrix"""
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65+
# If you multiply [x y 1]^t by the matrix, this is what you get
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# x rotated = cos(theta) * x - sin(theta) * y
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# y rotated = sin(theta) * x + cos(theta) * y
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mat = np.identity(3)
@@ -74,21 +77,22 @@ def make_rotation_matrix(theta=0.0):
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# ------------------------------- What kind of matrix is it? What does it do? -------------------------------------
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def get_dx_dy_from_matrix(mat):
77-
"""Where does the matrix translate 0,0 to?
80+
"""Where does the matrix translate 0, 0 to?
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@param mat - the matrix
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@returns dx, dy - the transformed point 0,0"""
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81-
# Don't forget to turn origin into a homogenous point...
84+
# Create a point for the origin (0,0) ... don't forget that the 3rd component should be 1
8285
# Multiply the origin by the matrix then return the x and y components
8386
# Reminder: @ is the matrix multiplication
8487
origin = np.zeros(shape=(3,))
8588
origin[2] = 1.0
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87-
xy_one = mat @ origin
88-
return xy_one[0], xy_one[1]
90+
xy_ret = mat @ origin
91+
# Ditch the 1 at the end and return a tuple (x,y)
92+
return xy_ret[0], xy_ret[1]
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9094

91-
# Doing this one in two pieces - first, get out how the axes (1,0) and (0,1) are transformed, then in the mext
95+
# Doing this one in two pieces - first, get out how the axes (1,0) and (0,1) are transformed, then in the next
9296
# method get theta out of how (1,0) is transformed
9397
def get_axes_from_matrix(mat):
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"""Where does the matrix rotate (1,0) (0,1) to?
@@ -99,14 +103,16 @@ def get_axes_from_matrix(mat):
99103
# 1) Set x_axis to be a unit vector pointing down the x axis
100104
# 2) Set y_axis to be a unit vector pointing down the y axis
101105
# Multiply by the matrix to get the new "x" and "y" axes
106+
# Reminder: zeros in the third row, not ones, because vectors can't translate
102107
x_axis = np.zeros(shape=(3,))
103108
y_axis = np.zeros(shape=(3,))
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105-
x_axis[0] = 1.0
106-
y_axis[1] = 1.0
110+
x_axis[0] = 1.0 # 1, 0, 0
111+
y_axis[1] = 1.0 # 0, 1, 0
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108113
x_axis_rotated = mat @ x_axis
109114
y_axis_rotated = mat @ y_axis
115+
# Get out the first two values. This is a tuple with a 2 dimensional array for each vector
110116
return x_axis_rotated[0:2], y_axis_rotated[0:2]
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112118

@@ -119,7 +125,9 @@ def get_theta_from_matrix(mat):
119125
# Step 2) use arctan2 to turn the rotated x axis vector into an angle
120126
# Use the x axis because theta for the x axis is 0 (makes the math easier)
121127
# Reminder: arctan2 takes (y, x)
122-
x_axis_rotated, _ = get_axes_from_matrix(mat)
128+
x_axis_rotated, _ = get_axes_from_matrix(mat) # The _ says ignore the second returned vector
129+
130+
# arctan2 takes y, x and returns the angle in the range -pi to pi
123131
theta = np.arctan2(x_axis_rotated[1], x_axis_rotated[0])
124132
return theta
125133

@@ -133,8 +141,11 @@ def plot_pts(axs, pts, fmt='-k'):
133141
@param fmt - optional format parameter"""
134142

135143
# This gets the x values (in row 0) and the y values and just does a regular plot
144+
#
136145
axs.plot(pts[0, :], pts[1, :], fmt)
137146

147+
# We have to do this get the line to go from the last point to the first
148+
# (Not necessary if you duplicate the first point as the last point in pts)
138149
pts_close = np.zeros((2, 2))
139150
pts_close[:, 0] = pts[0:2, 0]
140151
pts_close[:, 1] = pts[0:2, -1]
@@ -168,25 +179,32 @@ def plot_transformed_axes(axs, mat):
168179
axs.arrow(x=origin_moved[0], y=origin_moved[1], dx=y_axis_moved[0], dy=y_axis_moved[1], color='blue', linestyle="--")
169180

170181

171-
def plot_axes_and_big_box(axs):
182+
def plot_axes_and_big_box(axs, box_size=5):
172183
"""Plot the origin and x,y axes with a box at -5, -5 to 5, 5
173184
@param axs - figure axes"""
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175186
# Put a black + at the origin
176187
axs.plot(0, 0, '+k')
188+
189+
arrow_length = 1.0
190+
if box_size < 1.0:
191+
arrow_length = box_size * 0.9
177192
# Draw one red arrow for the x axis (x,y, dx, dy)
178-
axs.arrow(x=0, y=0, dx=1, dy=0, color='red')
193+
axs.arrow(x=0, y=0, dx=arrow_length, dy=0, color='red')
179194
# Draw a blue arrow for the y axis
180-
axs.arrow(x=0, y=0, dx=0, dy=1, color='blue')
195+
axs.arrow(x=0, y=0, dx=0, dy=arrow_length, color='blue')
181196

182197
# Draw a box around the world to make sure the plots stay the same size
183-
axs.plot([-5, 5, 5, -5, -5], [-5, -5, 5, 5, -5], '-k')
198+
axs.plot([-box_size, box_size, box_size, -box_size, -box_size], [-box_size, -box_size, box_size, box_size, -box_size], '-k')
184199

185200
# This makes sure the x and y axes are scaled the same
186201
axs.axis('equal')
187202

188203

189204

205+
""" Everything after __name__ is NOT imported when you import matrix_routines.py. However, if you run
206+
this file - by using the triangle in the upper right - this code will get executed. It's usually used
207+
to hold test code"""
190208
if __name__ == '__main__':
191209
# Create a matrix that has one of each type and call the plot code
192210
fig, axs = plt.subplots(1, 1, figsize=(6, 3))
@@ -210,6 +228,9 @@ def plot_axes_and_big_box(axs):
210228

211229
# Depending on if your mac, windows, linux, and if interactive is true, you may need to call this to get the plt
212230
# windows to show
231+
213232
plt.show()
233+
234+
# If it exits on you then put a break point at the line below and run in the debugger
214235
print("Done")
215236

‎Week_1_data_structures/Data/proxy_data_description.json‎

Lines changed: 0 additions & 112 deletions
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