#!/usr/bin/env python
# coding: utf-8

# In[1]:


import numpy as np
np.random.seed(12345)
import matplotlib.pyplot as plt
plt.rc("figure", figsize=(10, 6))
np.set_printoptions(precision=4, suppress=True)


# In[2]:


import numpy as np

my_arr = np.arange(1_000_000)
my_list = list(range(1_000_000))


# In[3]:


get_ipython().run_line_magic('timeit', 'my_arr2 = my_arr * 2')
get_ipython().run_line_magic('timeit', 'my_list2 = [x * 2 for x in my_list]')


# In[4]:


import numpy as np
data = np.array([[1.5, -0.1, 3], [0, -3, 6.5]])
data


# In[5]:


data * 10
data + data


# In[6]:


data.shape
data.dtype


# In[7]:


data1 = [6, 7.5, 8, 0, 1]
arr1 = np.array(data1)
arr1


# In[8]:


data2 = [[1, 2, 3, 4], [5, 6, 7, 8]]
arr2 = np.array(data2)
arr2


# In[9]:


arr2.ndim
arr2.shape


# In[10]:


arr1.dtype
arr2.dtype


# In[11]:


np.zeros(10)
np.zeros((3, 6))
np.empty((2, 3, 2))


# In[12]:


np.arange(15)


# In[13]:


arr1 = np.array([1, 2, 3], dtype=np.float64)
arr2 = np.array([1, 2, 3], dtype=np.int32)
arr1.dtype
arr2.dtype


# In[14]:


arr = np.array([1, 2, 3, 4, 5])
arr.dtype
float_arr = arr.astype(np.float64)
float_arr
float_arr.dtype


# In[15]:


arr = np.array([3.7, -1.2, -2.6, 0.5, 12.9, 10.1])
arr
arr.astype(np.int32)


# In[16]:


numeric_strings = np.array(["1.25", "-9.6", "42"], dtype=np.string_)
numeric_strings.astype(float)


# In[17]:


int_array = np.arange(10)
calibers = np.array([.22, .270, .357, .380, .44, .50], dtype=np.float64)
int_array.astype(calibers.dtype)


# In[18]:


zeros_uint32 = np.zeros(8, dtype="u4")
zeros_uint32


# In[19]:


arr = np.array([[1., 2., 3.], [4., 5., 6.]])
arr
arr * arr
arr - arr


# In[20]:


1 / arr
arr ** 2


# In[21]:


arr2 = np.array([[0., 4., 1.], [7., 2., 12.]])
arr2
arr2 > arr


# In[22]:


arr = np.arange(10)
arr
arr[5]
arr[5:8]
arr[5:8] = 12
arr


# In[23]:


arr_slice = arr[5:8]
arr_slice


# In[24]:


arr_slice[1] = 12345
arr


# In[25]:


arr_slice[:] = 64
arr


# In[26]:


arr2d = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
arr2d[2]


# In[27]:


arr2d[0][2]
arr2d[0, 2]


# In[28]:


arr3d = np.array([[[1, 2, 3], [4, 5, 6]], [[7, 8, 9], [10, 11, 12]]])
arr3d


# In[29]:


arr3d[0]


# In[30]:


old_values = arr3d[0].copy()
arr3d[0] = 42
arr3d
arr3d[0] = old_values
arr3d


# In[31]:


arr3d[1, 0]


# In[32]:


x = arr3d[1]
x
x[0]


# In[33]:


arr
arr[1:6]


# In[34]:


arr2d
arr2d[:2]


# In[35]:


arr2d[:2, 1:]


# In[36]:


lower_dim_slice = arr2d[1, :2]


# In[37]:


lower_dim_slice.shape


# In[38]:


arr2d[:2, 2]


# In[39]:


arr2d[:, :1]


# In[40]:


arr2d[:2, 1:] = 0
arr2d


# In[41]:


names = np.array(["Bob", "Joe", "Will", "Bob", "Will", "Joe", "Joe"])
data = np.array([[4, 7], [0, 2], [-5, 6], [0, 0], [1, 2],
                 [-12, -4], [3, 4]])
names
data


# In[42]:


names == "Bob"


# In[43]:


data[names == "Bob"]


# In[44]:


data[names == "Bob", 1:]
data[names == "Bob", 1]


# In[45]:


names != "Bob"
~(names == "Bob")
data[~(names == "Bob")]


# In[46]:


cond = names == "Bob"
data[~cond]


# In[47]:


mask = (names == "Bob") | (names == "Will")
mask
data[mask]


# In[48]:


data[data < 0] = 0
data


# In[49]:


data[names != "Joe"] = 7
data


# In[50]:


arr = np.zeros((8, 4))
for i in range(8):
    arr[i] = i
arr


# In[51]:


arr[[4, 3, 0, 6]]


# In[52]:


arr[[-3, -5, -7]]


# In[53]:


arr = np.arange(32).reshape((8, 4))
arr
arr[[1, 5, 7, 2], [0, 3, 1, 2]]


# In[54]:


arr[[1, 5, 7, 2]][:, [0, 3, 1, 2]]


# In[55]:


arr[[1, 5, 7, 2], [0, 3, 1, 2]]
arr[[1, 5, 7, 2], [0, 3, 1, 2]] = 0
arr


# In[56]:


arr = np.arange(15).reshape((3, 5))
arr
arr.T


# In[57]:


arr = np.array([[0, 1, 0], [1, 2, -2], [6, 3, 2], [-1, 0, -1], [1, 0, 1]])
arr
np.dot(arr.T, arr)


# In[58]:


arr.T @ arr


# In[59]:


arr
arr.swapaxes(0, 1)


# In[60]:


samples = np.random.standard_normal(size=(4, 4))
samples


# In[61]:


from random import normalvariate
N = 1_000_000
get_ipython().run_line_magic('timeit', 'samples = [normalvariate(0, 1) for _ in range(N)]')
get_ipython().run_line_magic('timeit', 'np.random.standard_normal(N)')


# In[62]:


rng = np.random.default_rng(seed=12345)
data = rng.standard_normal((2, 3))


# In[63]:


type(rng)


# In[64]:


arr = np.arange(10)
arr
np.sqrt(arr)
np.exp(arr)


# In[65]:


x = rng.standard_normal(8)
y = rng.standard_normal(8)
x
y
np.maximum(x, y)


# In[66]:


arr = rng.standard_normal(7) * 5
arr
remainder, whole_part = np.modf(arr)
remainder
whole_part


# In[67]:


arr
out = np.zeros_like(arr)
np.add(arr, 1)
np.add(arr, 1, out=out)
out


# In[68]:


points = np.arange(-5, 5, 0.01) # 100 equally spaced points
xs, ys = np.meshgrid(points, points)
ys


# In[69]:


z = np.sqrt(xs ** 2 + ys ** 2)
z


# In[70]:


import matplotlib.pyplot as plt
plt.imshow(z, cmap=plt.cm.gray, extent=[-5, 5, -5, 5])
plt.colorbar()
plt.title("Image plot of $\sqrt{x^2 + y^2}$ for a grid of values")


# In[71]:


plt.draw()


# In[72]:


plt.close("all")


# In[73]:


xarr = np.array([1.1, 1.2, 1.3, 1.4, 1.5])
yarr = np.array([2.1, 2.2, 2.3, 2.4, 2.5])
cond = np.array([True, False, True, True, False])


# In[74]:


result = [(x if c else y)
          for x, y, c in zip(xarr, yarr, cond)]
result


# In[75]:


result = np.where(cond, xarr, yarr)
result


# In[76]:


arr = rng.standard_normal((4, 4))
arr
arr > 0
np.where(arr > 0, 2, -2)


# In[77]:


np.where(arr > 0, 2, arr) # set only positive values to 2


# In[78]:


arr = rng.standard_normal((5, 4))
arr
arr.mean()
np.mean(arr)
arr.sum()


# In[79]:


arr.mean(axis=1)
arr.sum(axis=0)


# In[80]:


arr = np.array([0, 1, 2, 3, 4, 5, 6, 7])
arr.cumsum()


# In[81]:


arr = np.array([[0, 1, 2], [3, 4, 5], [6, 7, 8]])
arr


# In[82]:


arr.cumsum(axis=0)
arr.cumsum(axis=1)


# In[83]:


arr = rng.standard_normal(100)
(arr > 0).sum() # Number of positive values
(arr <= 0).sum() # Number of non-positive values


# In[84]:


bools = np.array([False, False, True, False])
bools.any()
bools.all()


# In[85]:


arr = rng.standard_normal(6)
arr
arr.sort()
arr


# In[86]:


arr = rng.standard_normal((5, 3))
arr


# In[87]:


arr.sort(axis=0)
arr
arr.sort(axis=1)
arr


# In[88]:


arr2 = np.array([5, -10, 7, 1, 0, -3])
sorted_arr2 = np.sort(arr2)
sorted_arr2


# In[89]:


names = np.array(["Bob", "Will", "Joe", "Bob", "Will", "Joe", "Joe"])
np.unique(names)
ints = np.array([3, 3, 3, 2, 2, 1, 1, 4, 4])
np.unique(ints)


# In[90]:


sorted(set(names))


# In[91]:


values = np.array([6, 0, 0, 3, 2, 5, 6])
np.in1d(values, [2, 3, 6])


# In[92]:


arr = np.arange(10)
np.save("some_array", arr)


# In[93]:


np.load("some_array.npy")


# In[94]:


np.savez("array_archive.npz", a=arr, b=arr)


# In[95]:


arch = np.load("array_archive.npz")
arch["b"]


# In[96]:


np.savez_compressed("arrays_compressed.npz", a=arr, b=arr)


# In[97]:


get_ipython().system('rm some_array.npy')
get_ipython().system('rm array_archive.npz')
get_ipython().system('rm arrays_compressed.npz')


# In[98]:


x = np.array([[1., 2., 3.], [4., 5., 6.]])
y = np.array([[6., 23.], [-1, 7], [8, 9]])
x
y
x.dot(y)


# In[99]:


np.dot(x, y)


# In[100]:


x @ np.ones(3)


# In[101]:


from numpy.linalg import inv, qr
X = rng.standard_normal((5, 5))
mat = X.T @ X
inv(mat)
mat @ inv(mat)


# In[102]:


import random
position = 0
walk = [position]
nsteps = 1000
for _ in range(nsteps):
    step = 1 if random.randint(0, 1) else -1
    position += step
    walk.append(position)


# In[103]:


plt.figure()


# In[104]:


plt.plot(walk[:100])


# In[105]:


nsteps = 1000
rng = np.random.default_rng(seed=12345)  # fresh random generator
draws = rng.integers(0, 2, size=nsteps)
steps = np.where(draws == 0, 1, -1)
walk = steps.cumsum()


# In[106]:


walk.min()
walk.max()


# In[107]:


(np.abs(walk) >= 10).argmax()


# In[108]:


nwalks = 5000
nsteps = 1000
draws = rng.integers(0, 2, size=(nwalks, nsteps)) # 0 or 1
steps = np.where(draws > 0, 1, -1)
walks = steps.cumsum(axis=1)
walks


# In[109]:


walks.max()
walks.min()


# In[110]:


hits30 = (np.abs(walks) >= 30).any(axis=1)
hits30
hits30.sum() # Number that hit 30 or -30


# In[111]:


crossing_times = (np.abs(walks[hits30]) >= 30).argmax(axis=1)
crossing_times


# In[112]:


crossing_times.mean()


# In[113]:


draws = 0.25 * rng.standard_normal((nwalks, nsteps))


# In[114]: