I have written two algorithms for creating unique mazes, one of them using depth-first-search (DFS) and the other using Kruskal's. The DFS algorithm performs as expected, however Kruskal's algorithm runs marginally slower than DFS and I do not know why.
I had written Kruskal's algorithm in Python.
I suspect the random.choice() function seems to be the underlying problem. The difference in runtime becomes noticeable when (r, c) > 30.
Here is the code for Kruskal's algorithm:
# Create a list of all possible edges
def create_edges(r, c):
edges = []
for y in range(r):
for x in range(c):
i = (y, x)
for d in ((0, 1), (0, -1), (1, 0), (-1, 0)):
p = tuple(map(sum, zip(d, i)))
py = p[0]
px = p[1]
if px in range(c) and py in range(r):
edges.append([i, p])
return edges
def kruskal(r, c, sz):
path = []
# Create a list of parent root nodes
roots = {(y, x) : [(y, x)] for y in range(r) for x in range(c)}
edges = create_edges(r, c)
while edges:
# Choose a random edge
edge = random.choice(edges)
parent = edge[0]
child = edge[1]
parent_set = get_set(roots, parent)
child_set = get_set(roots, child)
# Check if the parent / child are already in the same set
if parent_set == child_set:
rev_edge = edge.reverse()
if rev_edge in edges:
edges.remove(rev_edge)
edges.remove(edge)
continue
roots[parent_set] += roots[child_set]
roots.pop(child_set)
path.extend((parent, child))
rev_edge = edge.reverse()
if rev_edge in edges:
edges.remove(rev_edge)
edges.remove(edge)
return path
def get_set(roots, member):
s = None
for parent, children in roots.items():
if member in children:
s = parent
return s
def create_maze(t, r, c, sz):
maze = [['|_' for _ in range(c)] for _ in range(r)]
for cell in maze: cell.append('| ')
wd = {'DOWN' : ( 1, 0),
'UP' : (-1, 0),
'LEFT' : ( 0, -1),
'RIGHT': ( 0, 1)}
for n in range(len(t) - 1):
a = n
b = n + 1
p1 = t[a]
p2 = t[b]
ay, ax = p1[0], p1[1]
by, bx = p2[0], p2[1]
w = tuple(numpy.array(p2) - numpy.array(p1))
if w in wd.values():
k = list(wd.keys())[list(wd.values()).index(w)]
if k == 'DOWN': maze[ay][ax] = maze[ay][ax].replace('_', ' ')
if k == 'UP': maze[by][bx] = maze[by][bx].replace('_', ' ')
if k == 'LEFT': maze[ay][ax] = maze[ay][ax].replace('|', ' ')
if k == 'RIGHT': maze[by][bx] = maze[by][bx].replace('|', ' ')
return maze
def print_maze(maze, r, c, delay = 0):
s, l = min((r, c)), max((r, c))
a = 1 / (4 * r * c)
e = (1 / (s * l)) ** 2
delay = (a * 2.718 ** (-1 * e)) ** 0.5
time.sleep(delay)
print(' _' * c)
for iy in range(r):
for ix in range(c + 1):
print(maze[iy][ix], end = '')
print('')
print('')
def main():
r = 30
c = 30
sz = r * c
path = kruskal(r, c, sz)
maze = create_maze(path, r, c, sz)
print_maze(maze, r, c)
if __name__ == "__main__":
main()
Related
I read about the error and try to cast map into list, but the error still appeared, I will show you the main file that contain the error.
def power(L, C, Erange):
assert len(L) == len(C), "The L and C must be corresponded to each other"
E = copy.deepcopy(Erange)
E[0] -= 1
power_table = dict()
for c in set(C): # for each type of class
first = [index for index, eachc in enumerate(C) if eachc == c]
rest = [index for index, eachc in enumerate(C) if eachc != c]
p_first = len(first) / len(L)
p_rest = len(rest) / len(L)
powerc = []
for u, v in zip(E[0:-1], E[1:]): # checking the range (u,v]
like_first = sum([1 for i in first if u < L[i] <= v]) / len(first) * p_first
like_rest = sum([1 for i in rest if u < L[i] <= v]) / len(rest) * p_rest
try:
powerc.append((like_first ** 2 / (like_first + like_rest)))
except ZeroDivisionError:
powerc.append(0)
power_table[c] = powerc
power = []
for l, c in zip(L, C):
for e_cursor in range(len(E)):
if E[e_cursor] >= l: break
power.append(round(power_table[c][e_cursor - 1], 2))
return power
def cliff_core(data, percentage, obj_as_binary, handled_obj=False):
if len(data) < 50:
logging.debug("no enough data to cliff. return the whole dataset")
return range(len(data))
classes = map(toolkit.str2num, zip(*data)[-1])
if not handled_obj:
if obj_as_binary:
classes = [1 if i > 0 else 0 for i in classes]
else:
classes = toolkit.apply_bin_range(classes)
data_power = list()
for col in zip(*data):
col = map(toolkit.str2num, col)
E = toolkit.binrange(col)
data_power.append(power(col, classes, E))
data_power = map(list, zip(*data_power)) # transposing the data power
row_sum = [sum(row) for row in data_power]
index = range(len(data))
zips = zip(data, classes, row_sum, index)
output = list()
for cls in set(classes):
matched = filter(lambda z: z[1] == cls, zips)
random.shuffle(matched)
matched = sorted(matched, key=lambda z: z[2], reverse=True)
if len(matched) < 5:
output.extend([m[3] for m in matched]) # all saved
continue
for i in range(int(len(matched) * percentage)):
output.append(matched[i][3])
return sorted(output)
def cliff(attribute_names,data_matrix,independent_attrs,objective_attr,objective_as_binary=False,
cliff_percentage=0.4):
ori_attrs, alldata = attribute_names, data_matrix # load the database
alldata_t = map(list, zip(*alldata))
valued_data_t = list()
for attr, col in zip(ori_attrs, alldata_t):
if attr in independent_attrs:
valued_data_t.append(col)
valued_data_t.append(alldata_t[attribute_names.index(objective_attr)])
alldata = map(list, zip(*valued_data_t))
alldata = map(lambda row: map(toolkit.str2num, row), alldata) # numbering the 2d table
after_cliff = cliff_core(alldata, cliff_percentage, objective_as_binary)
res = [data_matrix[i] for i in after_cliff]
return res
there is a code written with tensorflow1 on this link.
https://github.com/carlthome/tensorflow-convlstm-cell/blob/master/cell.py
I want to use this class as a layer in TensorFlow.Keras. So it should be written with TensorFlow version 2.
How can do it?
this is this code:
import tensorflow as tf
class ConvLSTMCell(tf.nn.rnn_cell.RNNCell):
"""A LSTM cell with convolutions instead of multiplications.
Reference:
Xingjian, S. H. I., et al. "Convolutional LSTM network: A machine learning approach for precipitation nowcasting." Advances in Neural Information Processing Systems. 2015.
"""
def __init__(self, shape, filters, kernel, forget_bias=1.0, activation=tf.tanh, normalize=True, peephole=True, data_format='channels_last', reuse=None):
super(ConvLSTMCell, self).__init__(_reuse=reuse)
self._kernel = kernel
self._filters = filters
self._forget_bias = forget_bias
self._activation = activation
self._normalize = normalize
self._peephole = peephole
if data_format == 'channels_last':
self._size = tf.TensorShape(shape + [self._filters])
self._feature_axis = self._size.ndims
self._data_format = None
elif data_format == 'channels_first':
self._size = tf.TensorShape([self._filters] + shape)
self._feature_axis = 0
self._data_format = 'NC'
else:
raise ValueError('Unknown data_format')
#property
def state_size(self):
return tf.nn.rnn_cell.LSTMStateTuple(self._size, self._size)
#property
def output_size(self):
return self._size
def call(self, x, state):
c, h = state
x = tf.concat([x, h], axis=self._feature_axis)
n = x.shape[-1].value
m = 4 * self._filters if self._filters > 1 else 4
W = tf.get_variable('kernel', self._kernel + [n, m])
y = tf.nn.convolution(x, W, 'SAME', data_format=self._data_format)
if not self._normalize:
y += tf.get_variable('bias', [m], initializer=tf.zeros_initializer())
j, i, f, o = tf.split(y, 4, axis=self._feature_axis)
if self._peephole:
i += tf.get_variable('W_ci', c.shape[1:]) * c
f += tf.get_variable('W_cf', c.shape[1:]) * c
if self._normalize:
j = tf.contrib.layers.layer_norm(j)
i = tf.contrib.layers.layer_norm(i)
f = tf.contrib.layers.layer_norm(f)
f = tf.sigmoid(f + self._forget_bias)
i = tf.sigmoid(i)
c = c * f + i * self._activation(j)
if self._peephole:
o += tf.get_variable('W_co', c.shape[1:]) * c
if self._normalize:
o = tf.contrib.layers.layer_norm(o)
c = tf.contrib.layers.layer_norm(c)
o = tf.sigmoid(o)
h = o * self._activation(c)
state = tf.nn.rnn_cell.LSTMStateTuple(c, h)
return h, state
I have a list D containing 50 sub-lists. The number of elements in these sub-lists are decreasing. I visualize the list D by
for i, array in enumerate(D):
plt.scatter([i]*len(array), array)
I have 50 functions taking values from St_Sp, and Y is a list containing 50 elements, each of them is the output of each function. I visualize these functions
fig, ax = plt.subplots()
for i in range(len(Y)):
ax.plot(St_Sp, Y[i])
I found that too many colors are not easy to eyes. I would like to ask how to alternate color of the graphs between blue and white? I mean the color of the functions and dots in D are white > blue > white > blue ...
Could you please elaborate on how to do so?
##### Import packages
import numpy as np
import scipy.linalg as la
import time
import matplotlib
import matplotlib.pyplot as plt
##### Initial conditions
N = 100
lamda = 7
mu = 2
a = np.exp(-0.05)
r = - np.log(a).copy()
St_Sp = np.arange(- N, N + 1)
Card = St_Sp.shape[0]
##### Define infintesimal generator
def LL(x, y):
if x == N or x == - N: re = 0
elif x - y == - 1: re = lamda
elif x - y == 1: re = mu
elif x - y == 0: re = - (mu + lamda)
else: re = 0
return re
def L(x):
return - LL(x, x)
##### Define function Phi
def Phi(x):
return max(x, 0)
Phi = np.vectorize(Phi)
##### Define vector b
b = np.array(Phi(St_Sp))
##### Define function Psi
def Psi(x):
return L(x) / (L(x) + r)
Psi = np.vectorize(Psi)
##### Generate a Boolean vector whose all elements are False
d = np.array([0] * Card).astype(bool)
##### Define matrix A
A = np.zeros((Card, Card))
for i in range(Card):
for j in range(Card):
if (i != j) & (L(St_Sp[i]) != 0):
A[i, j] = LL(St_Sp[i], St_Sp[j]) / L(St_Sp[i])
elif (i != j) & (L(St_Sp[i]) == 0):
A[i, j] = 0
elif (i == j) & (Psi(St_Sp[i]) != 0):
A[i, j] = - 1 / Psi(St_Sp[i])
else: A[i, j] = 1
##### Row names of A
rows = np.arange(0, Card)
##### Define matrix B
B = np.zeros((Card, Card))
for i in range(Card):
for j in range(Card):
if i != j:
B[i, j] = LL(St_Sp[i], St_Sp[j])
else: B[i, j] = LL(St_Sp[i], St_Sp[j]) - r
start = time.time()
##### Generate I_0
I = [np.array([1] * Card).astype(bool), d.copy()]
Z = np.array(b.copy())
Z = Z.astype(float)
D = [St_Sp]
index0 = np.matmul(B, Z) <= 0
index1 = ~ index0
Y = [b.copy()]
##### Iterations
for i in range(1, Card):
I = [I[0] & index0, I[1] | index1]
Z = np.array(b.copy())
Z = Z.astype(float)
A1 = A[np.ix_(rows[I[1]], rows[I[1]])]
A2 = A[np.ix_(rows[I[1]], rows[I[0]])]
Z[I[1]] = la.solve(A1, - np.matmul(A2, Z[I[0]]))
Y = np.concatenate((Y, [Z]))
D.append(St_Sp[I[0]])
index = np.matmul(B[I[0]], Z) <= 0
index0, index1 = d.copy(), d.copy()
index0[I[0]], index1[I[0]] = index, ~ index
if (I[0] == index0).all() == True: break
for i, array in enumerate(D):
plt.scatter([i]*len(array), array)
fig, ax = plt.subplots()
for i in range(len(Y)):
ax.plot(St_Sp, Y[i])
The easiest approach is to set a custom color cycler. Instead of cycling between the 10 typical colors, the default colors for the plots will cycle through the given colors.
from cycler import cycler
custom_cycler = cycler(color=['white', 'blue'])
plt.gca().set_prop_cycle(custom_cycler)
for i, array in enumerate(D[:-1]):
plt.scatter([i] * len(array), array)
plt.scatter([len(D) - 1] * len(D[-1]), D[-1], color='crimson')
fig, ax = plt.subplots()
ax.set_prop_cycle(custom_cycler)
for i in range(len(Y) - 1):
ax.plot(St_Sp, Y[i])
ax.plot(St_Sp, Y[len(Y) - 1], color='crimson')
plt.show()
I have the following code. The beggining is quite long, but only serves to generate data. The problem happens with a few lines at the end.
##### Import packages
import numpy as np
import scipy.linalg as la
##### Initial conditions
N = 5
lamda = 7
mu = 2
a = 0.5
r = - np.log(a).copy()
St_Sp = np.arange(- N, N + 1)
Card = St_Sp.shape[0]
##### Define infintesimal generator
def LL(x, y):
if x == N or x == - N: re = 0
elif x - y == - 1: re = lamda
elif x - y == 1: re = mu
elif x - y == 0: re = - (mu + lamda)
else: re = 0
return re
def L(x):
return - LL(x, x)
##### Define function Phi
def Phi(x): return max(x, 0)
Phi = np.vectorize(Phi)
##### Define vector b
b = Phi(St_Sp).copy()
##### Define function Psi
def Psi(x): return L(x) / (L(x) + r)
Psi = np.vectorize(Psi)
##### Generate a Boolean vector whose all elements are False
d = np.array([0] * Card).astype(bool)
##### Define matrix A
A = np.zeros((Card, Card))
for i in range(Card):
for j in range(Card):
if (i != j) & (L(St_Sp[i]) != 0):
A[i, j] = LL(St_Sp[i], St_Sp[j]) / L(St_Sp[i])
elif (i != j) & (L(St_Sp[i]) == 0):
A[i, j] = 0
elif (i == j) & (Psi(St_Sp[i]) != 0):
A[i, j] = - 1 / Psi(St_Sp[i])
else: A[i, j] = 1
##### Row names of A
rows = np.arange(0, Card)
##### Define matrix B
B = np.zeros((Card, Card))
for i in range(Card):
for j in range(Card):
if i != j:
B[i, j] = LL(St_Sp[i], St_Sp[j])
else: B[i, j] = LL(St_Sp[i], St_Sp[j]) - r
##### Generate I_0
I = [np.array([1] * Card).astype(bool), d.copy()]
Z = b.copy()
index0 = np.matmul(B, Z) <= 0
index1 = ~ index0
##### Generate I_1
I = [index0, index1]
Z = b.copy()
if np.sum(I[1]) > 0:
order = np.concatenate((rows[I[1]], rows[~ I[1]]))
A1 = A[np.ix_(rows[I[1]], order)]
A2 = la.lu(A1)[2]
p = np.atleast_2d(A1).shape[0]
B1 = A2[:, range(p)]
B2 = - np.matmul(A2[:, p:], Z[I[0]])
print('Before being assigned new values, Z is \n', Z)
print('\n The index I[1] of elements of Z to be change \n', I[1])
M = la.solve_triangular(B1, B2, lower = False)
print('\n The values to be assigned to Z[I[1]] is \n', M)
Z[I[1]] = M
print('\n After being assigned new values, Z is \n', Z)
with result
Before being assigned new values, Z is
[0 0 0 0 0 0 1 2 3 4 5]
The index I[1] of elements of Z to be change
[False False False False False True True True True True False]
The values to be assigned to Z[I[1]] is
[2.08686055 2.88974949 3.40529229 3.88978577 4.41338306]
After being assigned new values, Z is
[0 0 0 0 0 2 2 3 3 4 5]
It's very weird to me that the command Z[I[1]] = M does not assign new values from M to the postion of Z indexed by I[1]. Could you please elaborate on why this problem arises and how to resolve it?
The datatype of your array Z is int, to the values are typecasted by python automatically, resulting in the interger values of int([2.08686055 2.88974949 3.40529229 3.88978577 4.41338306]) = [2 2 3 3 4 5].
If you want to change that behavour, you just need to add a line to change the type of your original array:
Z = Z.astype(float)
I have the following code that solves simultaneous linear equations by starting with the first equation and finding y when x=0, then putting that y into the second equation and finding x, then putting that x back into the first equation etc...
Obviously, this has the potential to reach infinity, so if it reaches +-inf then it swaps the order of the equations so the spiral/ladder goes the other way.
This seems to work, tho I'm not such a good mathematician that I can prove it will always work beyond a hunch, and of course some lines never meet (I know how to use matrices and linear algebra to check straight off whether they will never meet, but I'm not so interested in that atm).
Is there a better way to 'spiral' in on the answer? I'm not interested in using math functions or numpy for the whole solution - I want to be able to code the solution. I don't mind using libraries to improve the performance, for instance using some sort of statistical method.
This may be a very naive question from either a coding or maths point of view, but if so I'd like to know why!
My code is as follows:
# A python program to solve 2d simultaneous equations
# by iterating over coefficients in spirals
import numpy as np
def Input(coeff_or_constant, var, lower, upper):
val = int(input("Let the {} {} be a number between {} and {}: ".format(coeff_or_constant, var, lower, upper)))
if val >= lower and val <= upper :
return val
else:
print("Invalid input")
exit(0)
def Equation(equation_array):
a = Input("coefficient", "a", 0, 10)
b = Input("coefficient", "b", 0, 10)
c = Input("constant", "c", 0, 10)
equation_list = [a, b, c]
equation_array.append(equation_list)
return equation_array
def Stringify_Equations(equation_array):
A = str(equation_array[0][0])
B = str(equation_array[0][1])
C = str(equation_array[0][2])
D = str(equation_array[1][0])
E = str(equation_array[1][1])
F = str(equation_array[1][2])
eq1 = str(A + "y = " + B + "x + " + C)
eq2 = str(D + "y = " + E + "x + " + F)
print(eq1)
print(eq2)
def Spiral(equation_array):
a = equation_array[0][0]
b = equation_array[0][1]
c = equation_array[0][2]
d = equation_array[1][0]
e = equation_array[1][1]
f = equation_array[1][2]
# start at y when x = 0
x = 0
infinity_flag = False
count = 0
coords = []
coords.append([0, 0])
coords.append([1, 1])
# solve equation 2 for x when y = START
while not (coords[0][0] == coords[1][0]):
try:
y = ( ( b * x ) + c ) / a
except:
y = 0
print(y)
try:
x = ( ( d * y ) - f ) / e
except:
x = 0
if x >= 100000 or x <= -100000:
count = count + 1
if count >= 100000:
print("It\'s looking like these linear equations don\'t intersect!")
break
print(x)
new_coords = [x, y]
coords.append(new_coords)
coords.pop(0)
if not ((x == float("inf") or x == float("-inf")) and (y == float("inf") or y == float("-inf"))):
pass
else:
infinity_flag if False else True
if infinity_flag == False:
# if the spiral is divergent this switches the equations around so it converges
# the infinity_flag is to check if both spirals returned infinity meaning the lines do not intersect
# I think this would mostly work for linear equations, but for other kinds of equations it might not
x = 0
a = equation_array[1][0]
b = equation_array[1][1]
c = equation_array[1][2]
d = equation_array[0][0]
e = equation_array[0][1]
f = equation_array[0][2]
infinity_flag = False
else:
print("These linear equations do not intersect")
break
y = round(y, 3)
x = round(x, 3)
print(x, y)
equation_array = []
print("Specify coefficients a and b, and a constant c for equation 1")
equations = Equation(equation_array)
print("Specify coefficients a and b, and a constant c for equation 1")
equations = Equation(equation_array)
print(equation_array)
Stringify_Equations(equation_array)
Spiral(equation_array)