我一直在尝试复制一些类似于下面这段代码的工作，但是当我尝试使用此链接中的数据时 https://raw.githubusercontent.com/plotly/datasets/master/api_docs/mt_bruno_elevation.csv它抛出一些错误。我认为这是因为形状，但不知道如何修改它。
如果你能帮我解决这个问题，那就太好了。
这是我的代码
from IPython.core.display import HTML
import plotly
import plotly.graph_objects as go
import noise
import numpy as np
import matplotlib
from mpl_toolkits.mplot3d import axes3d
%matplotlib inline
import pandas as pd
data = = pd.read_csv('https://raw.githubusercontent.com/plotly/datasets/master/api_docs/mt_bruno_elevation.csv')
z = data
import numpy as np
from numpy.lib.stride_tricks import as_strided
def sliding_window(arr, window_size):
""" Construct a sliding window view of the array"""
arr = np.asarray(arr)
window_size = int(window_size)
if arr.ndim != 2:
raise ValueError("need 2-D input")
if not (window_size > 0):
raise ValueError("need a positive window size")
shape = (arr.shape[0] - window_size + 1,
arr.shape[1] - window_size + 1,
window_size, window_size)
if shape[0] <= 0:
shape = (1, shape[1], arr.shape[0], shape[3])
if shape[1] <= 0:
shape = (shape[0], 1, shape[2], arr.shape[1])
strides = (arr.shape[1]*arr.itemsize, arr.itemsize,
arr.shape[1]*arr.itemsize, arr.itemsize)
return as_strided(arr, shape=shape, strides=strides)
def cell_neighbours(arr, i, j, d):
"""Return d-th neighbors of cell (i, j)"""
w = sliding_window(arr, 2*d+1)
ix = np.clip(i - d, 0, w.shape[0]-1)
jx = np.clip(j - d, 0, w.shape[1]-1)
i0 = max(0, i - d - ix)
j0 = max(0, j - d - jx)
i1 = w.shape[2] - max(0, d - i + ix)
j1 = w.shape[3] - max(0, d - j + jx)
return w[ix, jx][i0:i1,j0:j1].ravel()
from dataclasses import dataclass
@dataclass
class descent_step:
"""Class for storing each step taken in gradient descent"""
value: float
x_index: float
y_index: float
def gradient_descent_3d(array,x_start,y_start,steps=50,step_size=1,plot=False):
# Initial point to start gradient descent at
step = descent_step(array[y_start][x_start],x_start,y_start)
# Store each step taken in gradient descent in a list
step_history = []
step_history.append(step)
# Plot 2D representation of array with startng point as a red marker
if plot:
matplotlib.pyplot.imshow(array,origin='lower',cmap='terrain')
matplotlib.pyplot.plot(x_start,y_start,'ro')
current_x = x_start
current_y = y_start
# Loop through specified number of steps of gradient descent to take
for i in range(steps):
prev_x = current_x
prev_y = current_y
# Extract array of neighbouring cells around current step location with size nominated
neighbours=cell_neighbours(array,current_y,current_x,step_size)
# Locate minimum in array (steepest slope from current point)
next_step = neighbours.min()
indices = np.where(array == next_step)
# Update current point to now be the next point after stepping
current_x, current_y = (indices[1][0],indices[0][0])
step = descent_step(array[current_y][current_x],current_x,current_y)
step_history.append(step)
# Plot each step taken as a black line to the current point nominated by a red marker
if plot:
matplotlib.pyplot.plot([prev_x,current_x],[prev_y,current_y],'k-')
matplotlib.pyplot.plot(current_x,current_y,'ro')
# If step is to the same location as previously, this infers convergence and end loop
if prev_y == current_y and prev_x == current_x:
print(f"Converged in {i} steps")
break
return next_step,step_history
np.random.seed(42)
global_minimum = z.min()
indices = np.where(z == global_minimum)
print(f"Target: {global_minimum} @ {indices}")
step_size = 0
found_minimum = 99999
# Random starting point
start_x = np.random.randint(0,50)
start_y = np.random.randint(0,50)
# Increase step size until convergence on global minimum
while found_minimum != global_minimum:
step_size += 1
found_minimum,steps = gradient_descent_3d(z,start_x,start_y,step_size=step_size,plot=False)
print(f"Optimal step size {step_size}")
found_minimum,steps = gradient_descent_3d(z,start_x,start_y,step_size=step_size,plot=True)
print(f"Steps: {steps}")
def multiDimenDist(point1,point2):
#find the difference between the two points, its really the same as below
deltaVals = [point2[dimension]-point1[dimension] for dimension in range(len(point1))]
runningSquared = 0
#because the pythagarom theorm works for any dimension we can just use that
for coOrd in deltaVals:
runningSquared += coOrd**2
return runningSquared**(1/2)
def findVec(point1,point2,unitSphere = False):
#setting unitSphere to True will make the vector scaled down to a sphere with a radius one, instead of it's orginal length
finalVector = [0 for coOrd in point1]
for dimension, coOrd in enumerate(point1):
#finding total differnce for that co-ordinate(x,y,z...)
deltaCoOrd = point2[dimension]-coOrd
#adding total difference
finalVector[dimension] = deltaCoOrd
if unitSphere:
totalDist = multiDimenDist(point1,point2)
unitVector =[]
for dimen in finalVector:
unitVector.append( dimen/totalDist)
return unitVector
else:
return finalVector
def generate_3d_plot(step_history):
# Initialise empty lists for markers
step_markers_x = []
step_markers_y = []
step_markers_z = []
step_markers_u = []
step_markers_v = []
step_markers_w = []
for index, step in enumerate(step_history):
step_markers_x.append(step.x_index)
step_markers_y.append(step.y_index)
step_markers_z.append(step.value)
# If we haven't reached the final step, calculate the vector between the current step and the next step
if index < len(steps)-1:
vec1 = [step.x_index,step.y_index,step.value]
vec2 = [steps[index+1].x_index,steps[index+1].y_index,steps[index+1].value]
result_vector = findVec(vec1,vec2)
step_markers_u.append(result_vector[0])
step_markers_v.append(result_vector[1])
step_markers_w.append(result_vector[2])
else:
step_markers_u.append(0.1)
step_markers_v.append(0.1)
step_markers_w.append(0.1)
# Include cones at each marker to show direction of step, scatter3d is to show the red line between points and surface for the terrain
fig = go.Figure(data=[
go.Cone(
x=step_markers_x,
y=step_markers_y,
z=step_markers_z,
u=step_markers_u,
v=step_markers_v,
w=step_markers_w,
sizemode="absolute",
sizeref=2,
anchor='tail'),
go.Scatter3d(
x=step_markers_x,
y=step_markers_y,
z=step_markers_z,
mode='lines',
line=dict(
color='red',
width=2
)),
go.Surface(colorscale=terrain,z=world,opacity=0.5)])
# Z axis is limited to the extent of the terrain array
fig.update_layout(
title='Gradient Descent Steps',
scene = dict(zaxis = dict(range=[world.min(),world.max()],),),)
return fig
# Generate 3D plot from previous random starting location
fig = generate_3d_plot(steps)
HTML(plotly.offline.plot(fig, filename='random_starting_point_3d_gradient_descent.html',include_plotlyjs='cdn'))
最佳答案
发生错误是因为 found_minimum 是一个 int，但 global_minimum 是一个 Series。我认为您引用的教程假定数据作为 numpy array 加载，但从未明确说明。
因此，z = data.to_numpy() 解决了一个问题并揭示了另一个问题，即教程数据集是 50x50 而你的数据是 25x25。只是改变随机起点的限制很诱人，但这最终效果不佳。数据集太小，梯度下降的实现无法适当收敛。
为了解决这个问题，我刚刚更改了您的数据集以制作一个 50x50 的集合:
data_arr = data.to_numpy()
double_arr = np.append(data_arr, 1.5*data_arr + 50, axis=0)
quad_arr = np.append(double_arr, 1.5*double_arr + 50, axis=1)
根据需要在整个代码中传递此 quad_arr 并将 plotly colorscale 更新为 go.Surface(colorscale=Earth) 给出:
完整的、可复制粘贴的代码:
from IPython.core.display import HTML
import plotly
import plotly.graph_objects as go
import noise
import numpy as np
import matplotlib
from mpl_toolkits.mplot3d import axes3d
%matplotlib inline
import pandas as pd
data = pd.read_csv('https://raw.githubusercontent.com/plotly/datasets/master/api_docs/mt_bruno_elevation.csv')
data_arr = data.to_numpy()
double_arr = np.append(data_arr, 1.5*data_arr + 50, axis=0)
quad_arr = np.append(double_arr, 1.5*double_arr + 50, axis=1)
z = quad_arr
matplotlib.pyplot.imshow(z,origin='lower',cmap='terrain')
# Find maximum value index in numpy array
indices = np.where(z == z.max())
max_z_x_location, max_z_y_location = (indices[1][0],indices[0][0])
matplotlib.pyplot.plot(max_z_x_location,max_z_y_location,'ro',markersize=15)
# Find minimum value index in numpy array
indices = np.where(z == z.min())
min_z_x_location, min_z_y_location = (indices[1][0],indices[0][0])
matplotlib.pyplot.plot(min_z_x_location,min_z_y_location,'yo',markersize=15)
import numpy as np
from numpy.lib.stride_tricks import as_strided
def sliding_window(arr, window_size):
""" Construct a sliding window view of the array"""
arr = np.asarray(arr)
window_size = int(window_size)
if arr.ndim != 2:
raise ValueError("need 2-D input")
if not (window_size > 0):
raise ValueError("need a positive window size")
shape = (arr.shape[0] - window_size + 1,
arr.shape[1] - window_size + 1,
window_size, window_size)
if shape[0] <= 0:
shape = (1, shape[1], arr.shape[0], shape[3])
if shape[1] <= 0:
shape = (shape[0], 1, shape[2], arr.shape[1])
strides = (arr.shape[1]*arr.itemsize, arr.itemsize,
arr.shape[1]*arr.itemsize, arr.itemsize)
return as_strided(arr, shape=shape, strides=strides)
def cell_neighbours(arr, i, j, d):
"""Return d-th neighbors of cell (i, j)"""
w = sliding_window(arr, 2*d+1)
ix = np.clip(i - d, 0, w.shape[0]-1)
jx = np.clip(j - d, 0, w.shape[1]-1)
i0 = max(0, i - d - ix)
j0 = max(0, j - d - jx)
i1 = w.shape[2] - max(0, d - i + ix)
j1 = w.shape[3] - max(0, d - j + jx)
return w[ix, jx][i0:i1,j0:j1].ravel()
from dataclasses import dataclass
@dataclass
class descent_step:
"""Class for storing each step taken in gradient descent"""
value: float
x_index: float
y_index: float
def gradient_descent_3d(array,x_start,y_start,steps=50,step_size=1,plot=False):
# Initial point to start gradient descent at
step = descent_step(array[y_start][x_start],x_start,y_start)
# Store each step taken in gradient descent in a list
step_history = []
step_history.append(step)
# Plot 2D representation of array with startng point as a red marker
if plot:
matplotlib.pyplot.imshow(array,origin='lower',cmap='terrain')
matplotlib.pyplot.plot(x_start,y_start,'ro')
current_x = x_start
current_y = y_start
# Loop through specified number of steps of gradient descent to take
for i in range(steps):
prev_x = current_x
prev_y = current_y
# Extract array of neighbouring cells around current step location with size nominated
neighbours=cell_neighbours(array,current_y,current_x,step_size)
# Locate minimum in array (steepest slope from current point)
next_step = neighbours.min()
indices = np.where(array == next_step)
# Update current point to now be the next point after stepping
current_x, current_y = (indices[1][0],indices[0][0])
step = descent_step(array[current_y][current_x],current_x,current_y)
step_history.append(step)
# Plot each step taken as a black line to the current point nominated by a red marker
if plot:
matplotlib.pyplot.plot([prev_x,current_x],[prev_y,current_y],'k-')
matplotlib.pyplot.plot(current_x,current_y,'ro')
# If step is to the same location as previously, this infers convergence and end loop
if prev_y == current_y and prev_x == current_x:
print(f"Converged in {i} steps")
break
return next_step,step_history
np.random.seed(42)
global_minimum = z.min()
indices = np.where(z == global_minimum)
print(f"Target: {global_minimum} @ {indices}")
step_size = 0
found_minimum = 99999
# Random starting point
start_x = np.random.randint(0,50)
start_y = np.random.randint(0,50)
# Increase step size until convergence on global minimum
print('==========================')
print(found_minimum)
print(global_minimum)
print('==========================')
while found_minimum != global_minimum:
step_size += 1
try:
found_minimum,steps = gradient_descent_3d(z,start_x,start_y,step_size=step_size,plot=True)
except ValueError:
pass
print(f"Optimal step size {step_size}")
found_minimum,steps = gradient_descent_3d(z,start_x,start_y,step_size=step_size,plot=True)
print(f"Steps: {steps}")
def multiDimenDist(point1,point2):
#find the difference between the two points, its really the same as below
deltaVals = [point2[dimension]-point1[dimension] for dimension in range(len(point1))]
runningSquared = 0
#because the pythagarom theorm works for any dimension we can just use that
for coOrd in deltaVals:
runningSquared += coOrd**2
return runningSquared**(1/2)
def findVec(point1,point2,unitSphere = False):
#setting unitSphere to True will make the vector scaled down to a sphere with a radius one, instead of it's orginal length
finalVector = [0 for coOrd in point1]
for dimension, coOrd in enumerate(point1):
#finding total differnce for that co-ordinate(x,y,z...)
deltaCoOrd = point2[dimension]-coOrd
#adding total difference
finalVector[dimension] = deltaCoOrd
if unitSphere:
totalDist = multiDimenDist(point1,point2)
unitVector =[]
for dimen in finalVector:
unitVector.append( dimen/totalDist)
return unitVector
else:
return finalVector
def generate_3d_plot(step_history):
# Initialise empty lists for markers
step_markers_x = []
step_markers_y = []
step_markers_z = []
step_markers_u = []
step_markers_v = []
step_markers_w = []
for index, step in enumerate(step_history):
step_markers_x.append(step.x_index)
step_markers_y.append(step.y_index)
step_markers_z.append(step.value)
# If we haven't reached the final step, calculate the vector between the current step and the next step
if index < len(steps)-1:
vec1 = [step.x_index,step.y_index,step.value]
vec2 = [steps[index+1].x_index,steps[index+1].y_index,steps[index+1].value]
result_vector = findVec(vec1,vec2)
step_markers_u.append(result_vector[0])
step_markers_v.append(result_vector[1])
step_markers_w.append(result_vector[2])
else:
step_markers_u.append(0.1)
step_markers_v.append(0.1)
step_markers_w.append(0.1)
# Include cones at each marker to show direction of step, scatter3d is to show the red line between points and surface for the terrain
fig = go.Figure(data=[
go.Cone(
x=step_markers_x,
y=step_markers_y,
z=step_markers_z,
u=step_markers_u,
v=step_markers_v,
w=step_markers_w,
sizemode="absolute",
sizeref=2,
anchor='tail'),
go.Scatter3d(
x=step_markers_x,
y=step_markers_y,
z=step_markers_z,
mode='lines',
line=dict(
color='red',
width=2
)),
go.Surface(colorscale='Earth', z=quad_arr,opacity=0.5)])
# Z axis is limited to the extent of the terrain array
fig.update_layout(
title='Gradient Descent Steps',
scene = dict(zaxis = dict(range=[quad_arr.min(),quad_arr.max()],),),)
return fig
# Generate 3D plot from previous random starting location
fig = generate_3d_plot(steps)
HTML(plotly.offline.plot(fig, filename='random_starting_point_3d_gradient_descent.html',include_plotlyjs='cdn'))
关于python - 如何使用 plotly 绘制梯度下降，我们在Stack Overflow上找到一个类似的问题： https://stackoverflow.com/questions/67508362/