综述

numpy：支持大量的维度数组与矩阵运算
ndarray：对象（存放同类型元素的多维数组）

• Numpy 常用的基本数据类型

np.bool_, np.bool8
np.int_, np.intc, np.intp, np.int8, np.int16, np.int32, np.int64
np.uint, np.uint8, np.uint16, np.uint32, np.uint64
np.float_, np.float16, np.float32, np.float64
np.complex_, np.complex64, np.complex128

• 字符串代码（每一个内建类型都有唯一定义它的字符串代码）

b布尔型 i(有符号）整型 u（无符号）整型
f浮点型 c复数浮点型
m时间间隔（timedelta） M日期时间（datetime）
O（python）对象
S,a（byte）字符串
U：Unicode
V：（void）原始数据

• 数据类型对象 dtype

dt = np.dtype(np.int32)
dt_1 = np.dtype('i8') # int8, int16, int32, int64 可以使用字符串 'i1','i2','i4','i8'
dt_2 = np.dtype('>f4') # 大端法（高位组放在最前面）
dt_3 = np.dtype([('name','S20'), ('age','), ("mark", '>f4')])  # 结构化数据类型

students = np.array([("lizhong", 25, 95), ("xiaohong", 19, 89.5), ('zhangjun', 30, 60)], dtype=dt_3)
print(students)
print(students['age'])
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• Ndarray attribute

a = np.arange(24).reshape(2,4,3)
print(a)
print(a.ndim, a.shape, a.size, a.dtype, a.itemsize)
print(a.flags)  # 内存信息
print(a.real, a.imag)
print(a.data)  
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1. Create Ndarray

• np.array()

a = np.array([[1,2,3],[4,5,6]], dtype=float, ndmin=3).reshape(3, 2)  # a.dtype=float64 
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• Create fixed ndarray

a = np.empty([3,2], dtype='i1', order='C')  # 随机填充
b = np.empty([2,2,3], dtype=[('x', "S1"), ("y",'>i4'), ('z', np.float32)], order='C')
c = np.zeros([4,5], dtype=float, order='F')  # 以0填充
d = np.ones([1,2,3], dtype=np.int16, order='F')  # 以1填充
e = np.eye(3)  # 对角线为1
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• Create Ndarray from exist list, tuple, buffer, iter

x = [(1,2,3),(4,5,6)]
y = np.asarray(x, dtype=np.int16, order="C")

buf = b'Hello World'
from_buf = np.frombuffer(buf, dtype='S1', count=-1, offset=0)

it = iter(range(6))
from_it = np.fromiter(it, dtype=float, count=-1).reshape(2,3)
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• Create Ndarray from range

ar = np.arange(0, 10, 2, dtype=float)  # 数值范围
li = np.linspace(1, 10, 10, endpoint=True, retstep=True, dtype=int)  # 等差数列
lg = np.logspace(1.0, 2.0, num=10, endpoint=True, base=10.0, dtype=None)  # 等比数列
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2 slice and index

• slice

a = np.arange(10)
sl = slice(2,7,2)  # [start, stop, step]
print(a[sl])  # print(a[2:7:2])

## （:）冒号 
b = np.array([[1,2,3],[3,4,5],[4,5,6]])
print(b[1:]) # b[1], b[2]
print("b[1]=", b[1])
print("b[2]=", b[2])

## 省略号（...）使得选择元组的长度与数组的维度相同
print(b[...,1])  # 第2列元素
print(b[1,...])  # 第2行元素
print(b[...,1:])  # 第2列及剩下的所有元素（第3列）
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• 数组索引

# 数组索引(0,0) (1,1) (2,0)
x = np.array([[1,2],[3,4],[5,6]])
y = x[[0,1,2],[0,1,0]]
print(y)

# 获取4x3数组中四个角的元素，行索引是[0.0]和[3,3].而列索引是[0.2]和[0,2]
x = np.arange(12).reshape(4,3)
rows = np.array([[0,0],[3,3]])
cols = np.array([[0,2],[0,2]])
y = x[rows, cols] # 2*2        y = x[[0,0,3,3],[0,2,0,2]] 1*4
print(y)

# 借助省略号（...）与索引数组组合
a = np.array([[1,2,3],[4,5,6],[7,8,9]])
b = a[1:3, 1:3]  # 第2,3行  第2,3列
c = a[1:3, [1,2]] # 第2,3行 第2,3列
d = a[...,1:] # 第2,3列，行与数组维度相同
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• 布尔索引

x = np.arange(12).reshape(4,3)
print(x[x>5])  # 获取大于5的元素
a = np.array([1, 2+6j, 5, 3.5+5j])
print(a[np.iscomplex(a)])
b = np.array([np.nan, 1, 2, np.nan, 3,4,5])
print(b[~np.isnan(b)])  # 过滤掉非复数元素
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• 花式索引（利用整数数组进行索引）

x = np.arange(32).reshape((8,4))
print(x[[4,2,1,7]]) # 顺序索引数组（第4,2,1,7行）
print(x[[-4,-2,-1,-7]]) # 传入倒序索引数组（第4,6,7,1行）
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3. Broadcast

对不同形状的数组进行数值计算的方式。

a = np.arange(12).reshape(4,3)
b = np.array([1,1,1])
c = np.tile(b, [4,1])  # 重复b的各个维度
print(a+b)
print(a+c)
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4. Iterable

a = np.arange(6).reshape(2,3)
for x in np.nditer(a):
    print(x, end=",")
for x in np.nditer(a.T):  # a与a.T的遍历顺序相同，由于在内存中的存储顺序相同
    print(x, end=",")
for x in np.nditer(a.T.copy(order='C')):  # 与a的遍历顺序不同，由于在内存中的存储顺序不一样
    print(x, end=",")
for x in np.nditer(a.T.copy(order="F")):
    print(x, end=",")
    
print() # 通过显示设置，强制nditer对象使用某种顺序
for x in np.nditer(a, order='C'):  
    print(x, end=",")
for x in np.nditer(a, order="F"):
    print(x, end=",")

print()# nditer 对象遍历权限 （read-only、read-write、write-only）
for x in np.nditer(a, op_flags=['readwrite']):
    x[...] = 2*x
print(a)
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• 外部循环
  b = np.arange(0, 60, 5).reshape(3,4)
  print(b)
  for x in np.nditer(b, flags=[‘external_loop’], order=“F”): # 迭代器将每列组合为一维数组
  print(x, end=“,”)

• 广播迭代
  c = np.array([1,2,3,4],dtype=int)
  for x,y in np.nditer([b, c]):
  print(“%d:%d” % (x, y), end=", ")

3. Ndarray Operations

3.1 修改数组形状

## reshape
a = np.arange(8).reshape(4, 2)
for row in a:
    print(row)

## flat:  A 1-D iterator over the array.
for element in a.flat:
    print(element)
print(a.T.flat[3]) # 6

## flatten:  Return a copy of the array collapsed into one dimension.
print(a.flatten())
print(a.flatten(order='F'))

## ravel:  Return a contiguous flattened array.  view of the array, modifications affect the original data
print(a.ravel())
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3.2 翻转数组

• np.transpose(a, axes=None)

Reverse or permute the axes of an array; returns the modified array.

a = np.arange(12).reshape(3,4)
print(np.transpose(a)) 
print(a.T)
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• np.rollaxis(a, axis, start=0)

Roll the specified axis backwards, until it lies in a given position.

a = np.arange(8).reshape(2,2,2)
print(a)
print(np.where(a==6))
print(a[1,1,0])

b = np.rollaxis(a, 2, 0)  # 将轴2 滚到轴0（宽度到深度）
print(b)
print(np.where(b==6))
print(b[0,1,1])

c = np.rollaxis(a, 2,1) # 将轴2 滚动到轴1（宽度到高度）
print(c)
print(np.where(c==6))
print(c[1,0,1])
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• np.swapaxes(a, axis1, axis2)

Interchange two axes of an array.

x = np.array([[[0,1],[2,3]],[[4,5],[6,7]]])
y = np.swapaxes(x, 2, 0) # 交换轴0（深度方向）到轴2（宽度方向）
print(y)
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3.3 修改数组维度

• broadcast()

Produce an object that mimics broadcasting.

x = np.array([[1],[2],[3]])
y = np.array([4,5,6])
b = np.broadcast(x,y) # 对y广播x

r,c = b.iters
print(next(r), next(c))
print(next(r), next(c))
print(b.shape)  # 3x3

b = np.broadcast(x, y)  # 若以上一步的广播结果+next后，结果不同
c = np.empty(b.shape)
c.flat = [u+v for (u,v) in b]
print(c)
print(x+y)  # built_in broadcasting
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• np.broadcast_to(array, shape, subok=False)

Broadcast an array to a new shape.

a = np.arange(4)
b = np.broadcast_to(a,(4,4))
print(a.shape, b.shape)  # (4,) (4, 4)
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• np.expand_dims(a, axis)

Insert a new axis that will appear at the axis position in the expanded array shape.

x = np.array(([1,2],[3,4]))
y = np.expand_dims(x, axis=0)
print(x.shape, y.shape)  # (2, 2) (1, 2, 2)
y = np.expand_dims(x, axis=1)
print(x.shape, y.shape)  # 2, 2) (2, 1, 2)
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• a.squeeze(axis=None)

Remove single-dimensional entries from the shape of a.

a = np.arange(6).reshape(1,2,3)
b = np.squeeze(a, axis=0)
print(a.shape, b.shape)  # (1, 2, 3) (2, 3)
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3.4 连接数组

• np.concatenate((a1, a2, ...), axis=0, out=None)

Join a sequence of arrays along an existing axis.

a = np.array([[1,2],[3,4]])
b = np.array([[5,6],[7,8]])
c = np.concatenate((a,b),axis=0)
d = np.concatenate((a,b),axis=1)
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• np.stack(arrays, axis=0, out=None)

Join a sequence of arrays along a new axis.

a = np.array([[1,2],[3,4]])
b = np.array([[5,6],[7,8]])
c = np.stack((a,b), 0)  # 沿轴0 堆叠两数组
d = np.stack((a,b), 1)
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• np.hstack(tup)

Stack arrays in sequence horizontally (column wise).

a = np.array([[1,2],[3,4]])
b = np.array([[5,6],[7,8]])
c = np.hstack((a,b))
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• np.vstack(tup):

Stack arrays in sequence vertically (row wise).

a = np.array([[1,2],[3,4]])
b = np.array([[5,6],[7,8]])
c = np.vstack((a,b))
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3.5 分割数组

• np.split(ary, indices_or_sections, axis=0)

Split an array into multiple sub-arrays as views into ary.

a = np.arange(9)
b = np.split(a,3) # 平均切分
c = np.split(a, [4, 7])  # 按指定位置分割

a = np.arange(16).reshape(4,4)
b = np.split(a, 2, 0) # 沿水平方向分割
c = np.split(a, 2, 1)  # 沿垂直方向分割
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• np.hsplit(ary, indices_or_sections)

Split an array into multiple sub-arrays horizontally (column-wise).

a = np.floor(10*np.random.random((2,6)))
np.hsplit(a, 3)
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• np.vsplit(ary, indices_or_sections)

Split an array into multiple sub-arrays vertically (row-wise).

b = np.arange(16).reshape(4,4)
np.vsplit(b, 2)
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3.6 add or remove elements

• np.resize(a, new_shape)

Return a new array with the specified shape.

 a=np.array([[0,1],[2,3]])
 print(np.resize(a, (2,3))
 print(np.resize(a, (1,4))
 print(np.resize(a, (2,4))
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• np.append(arr, values, axis=None)

Append values to the end of an array.

a = np.array([[1,2,3],[4,5,6]])
b = np.append(a, [7,8,9])  # 向数组添加元素
c = np.append(a, [[7,8,9]], axis=0)  # 列 添加元素
d = np.append(a, [[5,5,5], [7,8,9]], axis=1)  # 行 添加元素
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• np.insert(arr, obj, values, axis=None)

Insert values along the given axis before the given indices.

a = np.array([[1,2,3],[4,5,6]])
b = np.insert(a, 3, [11,12])
c = np.insert(a,1,[11], axis=0)  # 沿轴0 广播
d = np.insert(a,1,11, axis=1)  # 沿轴1 广播
a,b,c,d
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• np.delete(arr, obj, axis=None)

Return a new array with sub-arrays along an axis deleted.

a = np.arange(12).reshape(3,4)
b = np.delete(a, 5)
c = np.delete(a, 1, axis=1)  # 删除第二列
d = np.delete(a, np.s_[::2])
a,b,c,d
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• np.unique(ar, return_index=False, return_inverse=False, return_counts=False, axis=None)

Returns the sorted unique elements of an array.

a = np.array([5,2,6,2,7,5,6,8,2,9])
u,indics = np.unique(a, return_index=True)  # 去重后的数组，及在原数组中的索引
u,indics = np.unique(a, return_inverse=True)  # 去重后的数组，及原数组中元素在该数组中的索引
u[indics]  # 重构原数组
u,indics = np.unique(a, return_counts=True) # 去重后的数组，及在原数组中的数量
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4. 位运算

• bitwise_and，bitwise_or，invert，binary_repr

print(bin(13),bin(17))  # 0b1101 0b10001
print(np.bitwise_and(13,17))  # 1
print(np.bitwise_or(12,17))  # 29
print(np.invert(np.array([13], dtype=np.uint8)))  # [242]
print(np.binary_repr(13, width=8))  # 00001101
print(np.binary_repr(242, width=8))  # 11110010
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• left_shift，right_shift

print(np.left_shift(10,2))  # 40
print(np.right_shift(40,2))  # 10
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5. 字符串函数

定义在 numpy.char中

print(np.char.add(["hello", 'Google'],[" world", ' Search']))  # Return element-wise string concatenation for two arrays of str or unicode.
print(np.char.multiply("RUNOOB ",3))  # Return (a * i), that is string multiple concatenation,element-wise.

print(np.char.center("RUNOOB", 20, fillchar='*'))  # Return a copy of `a` with its elements centered in a string of length `width`.

print(np.char.capitalize('runoob'))  # Return a copy of `a` with only the first character of each element capitalized.
print(np.char.title("i like runoob"))  #  Title case words start with uppercase characters, all remaining cased characters are lowercase.

print(np.char.lower(["RUNoob","GOOgle"]))
print(np.char.upper(['runoob','facebook']))

print(np.char.split('i like runoob?'))
print(np.char.split('www.runoob.com', sep='.'))
print(np.char.splitlines('i\nlike\r\nrunoob?'))  # 以换行符作为分隔符来分割字符串
print(np.char.splitlines('i\rlike\n\rrunoob?'))  # "\n","\r","\r\n" 都可用作换行符

print(np.char.strip(["arunooba","admin","java"],"a"))  # 用于移除开头或结尾处的特定字符
print(np.char.join([':','-'],['runoob','google']))  # 通过指定分隔符来连接数组中的元素或字符串

print(np.char.replace('i like runoob','oo','cc'))  # 使用新字符串替换字符串中的所有子字符串

a = np.char.encode('runoob','cp500')
print(a)
print(np.char.decode(a, 'cp500'))
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6. 数学函数

• 三角函数

a = np.array([0, 30, 45, 60, 90])  # 角度
print(np.around(np.sin(a*np.pi/180), 1))  # 通过乘 np.pi/180 角度转化为弧度
print(np.around(np.cos(a*np.pi/180), 1))
print(np.tan(a*np.pi/180))
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• 反三角函数

a = np.array([0,30,45,60, 90])  # 角度
sin = np.sin(a*np.pi/180) 
inv = np.arcsin(sin)  # 返回值以弧度为单位
print(np.degrees(inv))  # 将弧度转换为角度

cos = np.cos(a*np.pi/180)
inv = np.arccos(cos)
print(np.degrees(inv))

tan = np.tan(a*np.pi/180)
inv = np.arctan(tan)
print(np.degrees(inv))
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• 舍入函数

a = np.array([1.0, 15.55, 123, 0.467,-2.532, -1.34])
np.around(a, decimals=1)  # 保留小数点后一位四舍五入
np.around(a, decimals=-1) # 小数点前一位四舍五入
np.floor(a)  # 向下取整
np.ceil(a)  # 向上取整
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• 算术函数

a = np.arange(9, dtype=np.float_).reshape(3,3)
b = np.array([10,10,10])
print(np.add(a,b))       # 广播相加
print(np.subtract(a,b))  # 广播相减
print(np.multiply(a, b)) # 广播相乘
print(np.divide(a,b))    # 广播相除
a,b

a = np.array([0.25, 1.33, 1, 100])
print(np.reciprocal(a))  # 返回逐个元素的倒数

a = np.array([2,3,4])
b = np.array([1,2,3])
print(np.power(a, 2))
print(np.power(a, b))

a = np.array([10, 20, 30])
b = np.array([3,5,7])
print(np.mod(a, b))
print(np.remainder(a,b))
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• 统计函数

# amax(a, axis=None, out=None, keepdims=, initial=, where=) 
## Return the maximum of an array or maximum along an axis.
a = np.array([[3,7,5],[8,4,3],[2,4,9]])
print(np.amax(a))  # 数组中最大值 9
print(np.amax(a, 1))  # 各行最大值 [7 8 9]
print(np.amax(a, 0))  # 各列最大值 [8 7 9]

# amin(a, axis=None, out=None, keepdims=, initial=, where=)
## Return the minimum of an array or minimum along an axis.
a = np.array([[3,7,5],[8,4,3],[2,4,9]])
print(np.amin(a))  # 数组中最小值 2
print(np.amin(a, 1)) # 各行最小值 [3 3 2]
print(np.amin(a, 0))  # 各列最小值 [2 4 3]

# ptp(a, axis=None, out=None, keepdims=)
##  Range of values (maximum - minimum) along an axis.
a = np.array([[3,7,5],[8,4,3],[2,4,9]])
print(np.ptp(a))          # 数组中（最大值-最小值）即9-2=7
print(np.ptp(a, axis=1))  # 各行（最大值-最小值） [4 5 7]
print(np.ptp(a, axis=0))  # 各列（最大值-最小值） [6 3 6]

# percentile(a, q, axis=None, out=None, overwrite_input=False, interpolation='linear', keepdims=False)   分位数值
a = np.array([[10,7,4],[3,2,1]])
print(np.percentile(a, 50))
print(np.percentile(a, 50, axis=1))  # 各行
print(np.percentile(a, 50, axis=0))  # 各列
print(np.percentile(a, 50, axis=1, keepdims=True))  # 保持维度不变

# median(a, axis=None, out=None, overwrite_input=False, keepdims=False)  中位数
a = np.array([[30,65,70],[80,95,10],[50,90,60]])
print(np.median(a))
print(np.median(a, axis=0)) # 轴0（列）的中位数
print(np.median(a, axis=1)) # 轴1（行）的中位数

# mean(a, axis=None, dtype=None, out=None, keepdims=)  算术平均值
a = np.array([[1,2,3],[3,4,5],[4,5,6]])
print(np.mean(a))
print(np.mean(a, axis=0))  # 轴0（列）算术平均值
print(np.mean(a, axis=1))  # 轴1（行）算术平均值

# average(a, axis=None, weights=None, returned=False)  加权平均值
a = np.array([1,2,3,4]).reshape(2,2)
np.average(a)
np.average(a, weights=[[4,3],[2,1]])
np.average(a, weights=[1,2], axis=0) # 轴0（列）加权平均值
np.average(a, weights=[2,1], axis=1) # 轴1（行）加权平均值

# std(a, axis=None, dtype=None, out=None, ddof=0, keepdims=)  标准差
a = np.array([1,2,3,4]).reshape(2,2)
print(np.std(a))
print(np.std(a, axis=0)) # 轴0（列）标准差
print(np.std(a, axis=1)) # 轴1（行）标准差

# var(a, axis=None, dtype=None, out=None, ddof=0, keepdims=)  方差
a = np.array([1,2,3,4]).reshape(2,2)
print(np.var(a))
print(np.var(a, axis=0))  # 轴0（列）方差
print(np.var(a, axis=1))  # 轴1（行）方差
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• 排序函数

# sort(a, axis=-1, kind=None, order=None)
a = np.array([[3,7],[9,1]])
print(np.sort(a))
print(np.sort(a, axis=0))  # 按轴0（列）排序
print(np.sort(a, axis=1))  # 按轴1（行）排序

dt = np.dtype([('name','S10'),("age", int)])  # 结构化数据类型
a = np.array([('raju',31),("anil",25),('ravi',17),("amar",27)], dtype=dt)
print(np.sort(a, order='name'))


# argsort(a, axis=-1, kind=None, order=None)
## Returns the indices that would sort an array.
x = np.array([3,1,2])
y = np.argsort(x)
y, x[y]  # 以排序后的顺序重构原数组


# lexsort(keys, axis=-1)
## Perform an indirect stable sort using a sequence of keys.
a = [1,5,1,4,3,4,4] # First column
b = [9,4,0,4,0,2,1] # Second column
ind = np.lexsort((b,a)) # Sort by a, then by b, Return indices 
print(ind)  # [2 0 4 6 5 3 1]
[(a[i],b[i]) for i in ind]  # [(1, 0), (1, 9), (3, 0), (4, 1), (4, 2), (4, 4), (5, 4)]


# sort_complex(a) 
##  Sort a complex array using the real part first, then the imaginary part.
print(np.sort_complex([1+2j, 2-1j, 3-2j, 3+2j, -1+3j]))  # [-1.+3.j  1.+2.j  2.-1.j  3.-2.j  3.+2.j]
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• 条件筛选函数

# partition(a, kth, axis=-1, kind='introselect', order=None)
##  Return a partitioned copy of an array.
a = np.array([3, 4, 2, 1])
print(np.partition(a, 3))  # [2, 1, 3, 4]
print(np.partition(a, (1, 3)))  # [1, 2, 3, 4]

# argpartition(a, kth, axis=-1, kind='introselect', order=None)
## Array of indices that partition `a` along the specified axis.
x = np.array([3, 4, 2, 1])
print(x[np.argpartition(x, 3)])
print(x[np.argpartition(x, (1, 3))])

# argmax(a, axis=None, out=None)
## Returns the indices of the maximum values along an axis.
a = np.array([[30, 40, 70],[80, 20, 10], [50,90,60]])
np.argmax(a)
np.argmax(a, axis=0) # 沿轴0（列）的最大值索引   第1列，第2行
np.argmax(a, axis=1) # 沿轴1（行）的最大值索引   第2行，第1列

# argmin(a, axis=None, out=None)
## Returns the indices of the minimum values along an axis.
np.argmin(a)
np.argmin(a, axis=0)
np.argmin(a, axis=1)
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# nonzero() 
## Return the indices of the elements that are non-zero.
a = np.array([[30,40,0],[0,20,10],[50,0,60]])
print(np.nonzero(a))
a[np.nonzero(a)]

# where(condition, [x, y])
## Return elements chosen from `x` or `y` depending on `condition`.
x = np.arange(9.).reshape(3,3)
y = np.where(x>3)
x[y]
np.where(x==6)

# extract(condition, arr)
## Return the elements of an array that satisfy some condition.
x = np.arange(9.).reshape(3,3)
condition = np.mod(x, 2)==0  # 定义条件，选择偶数
np.extract(condition, x)
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• 字节交换

E.g：data = 0x 00 12 34 56
大端模式：数据的高字节保存在内存的低地址中，数据的低字节保存在内存的高地址中。[00 12 34 56] （阅读习惯一直）
小端模式：数据的高字节保存在内存的高地址中，数据的高字节保存在内存的低地址中。[56 43 12 00]

• np.ndarray.byteswap()

将 Ndarray 中每个元素中的字节进行大小端转换。

a = np.array([1, -1, 256, 8755], dtype=np.int16)
print(a)
print(list(map(hex, a)))  # 以十六进制表示内存中的数据
a.byteswap(True)
print(a)
print(list(map(hex, a)))
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7. 副本和视图

• 赋值操作不产生副本

a = np.arange(6).reshape(2,3)
b = a
print(id(a))  # id 相同
print(id(b))
b[0,0] = 100  # 修改值影响
print(a)
print(b)
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• 视图和浅拷贝

a = np.arange(6).reshape(3,2)
b = a.view()
print(id(a))
print(id(b))  # id不同
b[0, 0] = 100  # 修改值影响
print(a)
print(b)
b.shape = 1,6
print(a)  # 修改维度不影响
print(b)
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• 切片创建视图

a = np.arange(12)
b = a[3:]
c = a[3:]  # 切片创建视图,，修改数据会影响到原始数组
b[1] = 123
c[2] = 234
print(id(b),id(c),id(a[3:]))  # id不同（区别于赋值引用）
b is c  # False
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• 副本和深拷贝

a = np.array([[10, 10], [2,3], [4,5]])
b = a.copy()  # 修改副本数据，不会影响原始数据
print(b is a)  # False
print(id(a), id(b))  # 不同
b[0, 0] = 100
a, b
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7. 矩阵库 Matrix

• ndarray 与 matrix 区别

ndarray 可以是任意维数据，mat只能是2维数据
矩阵乘法与逐项乘法不同

# ndarray的dot和a@b是矩阵乘法， a*b和multiply()是逐项相乘
a = np.array([[1, 2], [3, 4]])
b = np.array([[5, 6], [7, 8]])
print('dot =',np.dot(a, b)) # [[1*5+2*7=19  1*6+2*8=22], [3*5+4*7=43  3*6+4*8=50]] 矩阵乘法
print('@ =',a@b)
print('* =',a*b)
print('mul =', np.multiply(a,b), '\n')


# matrix的dot和c*d,c@d是矩阵乘法， multiply()是逐项相乘
c = np.mat([[1,2], [3,4]])
d = np.mat([[5,6], [7,8]])
print('dot =', np.dot(c, d))
print('* =', c*d)
print('@ =', c@d)
print('mul =', np.multiply(c, d))
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• Matrix 定义

import numpy.matlib as mb
a = mb.empty((2,2))  # mb.zeros(), mb.ones(), mb.eye(), mb.identity(), mb.rand(), 
print(a, type(a))

b = np.mat((2,3))
c = np.array([(2,3)])
print(b, type(b))
print(c, type(c))
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• 二者转换

import numpy.matlib as mb

a = np.mat('1,2;3,4')
print(a, type(a))
b = np.asarray(a)  # matrix->Ndarray
print(b, type(b))
c = np.asmatrix(b) # Ndarr
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8. 线性代数

内积（Inner product）和点积（dot product）的区别：

• 内积：一般是用在内积空间中的
• 点积：一般是用在欧几里得空间中的
• 欧几里得空间是内积空间的一种特殊情况。

• dot(a, b, out=None)

Dot product of two arrays. 两数组点积

# 1-D
a = np.array([1, 2, 3])
b = np.array([3, 2, 1])
print(np.dot(a, b))  # 向量内积 inner product of vectors

# 2-D
a = np.array([[0, 1], [2, 3]])
b = np.array([[4, 5], [6, 7]])
print(np.dot(a, b))  # E.q: np.matmul(a,b) or a@b    矩阵乘积法（与np.inner不同）

# 0-D
a = np.array([[0, 1], [1, 2]])
print(np.dot(a, 2))  # E.q: np.multiply(a, 2) or a*2
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• vdot(a, b)

Return the dot product of two vectors.

a = np.array([[0, 1], [2, 3]])
b = np.array([[4, 5], [6, 7]])
print(np.vdot(a, b))  # 0*4 + 1*5 + 2*6 + 3*7 = 38   对应项相乘
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• inner(a,b)

Inner product of two arrays.

a = np.array([[0, 1], [2, 3]])
b = np.array([[4, 5], [6, 7]])
print(np.inner(a, b))  # [[0*4+1*5  0*6+1*7], [2*4+3*5  2*6+3*7]   [[5 7],[23 33]]   对应项相乘
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• matmul()

a = np.array([[0, 1], [2, 3]])
b = np.array([[4, 5], [6, 7]])
print(np.dot(a, b))
print(np.matmul(a, b))  # 与 np.dot() 都是矩阵乘积法
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• linalg.det(a)

Compute the determinant of an array . 计算矩阵的行列式值

a = np.array([[1,2],[3,4]])
print(np.linalg.det(a))  # -2
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• lnalg.solve()

Solve a linear matrix equation, or system of linear scalar equations. 求解线性方程组

a = np.array([[3,1], [1,2]])
b = np.array([9,8])
x = np.linalg.solve(a, b)
print(x)  # array([2.,  3.])
## 3 * x0 + x1 = 9`` and ``x0 + 2 * x1 = 8`
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• linalg.inv()

Compute the (multiplicative) inverse of a matrix.

x = np.array([[1,2], [3,4]])
y = np.linalg.inv(x)
print(np.dot(x, y))
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9. IO

• save/load

a = np.array([1,2,3,4,5])
np.save('outfile.npy',a)
b = np.load('outfile.npy')
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• savez()

Save several arrays into a single file in uncompressed .npz format.

a = np.array([[1,2,3],[4,5,6]])
b = np.arange(0,1.0,0.1)
c = np.sin(b)
np.savez("runoob.npz", a, b, sin_array=c)  # c使用关键字参数
r = np.load("Runoob.npz")
r.files
# r['arr_0']
# r['arr_1']
# r["sin_array"]
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• savetxt(fname, X, fmt='%.18e', delimiter=' ', newline='\n', header='', footer='', comments='# ', encoding=None)

Save an array to a text file.

a = np.array([1,2,3,4,5])
np.savetxt('out.txt', a)
b = np.loadtxt('out.txt')

a = np.arange(0, 10, 0.5).reshape(4, -1)
np.savetxt('out_1.txt', a, fmt="%d", delimiter=",") # 保存为整数，以逗号分隔
b = np.loadtxt('out_1.txt', delimiter=",")  # load 时也要指定逗号分隔
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histogram() 数据的评率分布的图形表示

a = np.array([22,87,5,43,56,73,55,54,11,20,51,5,79,31,27])
hist, bins = np.histogram(a, bins=[0, 20, 40, 60, 80, 100])

tensor 与 ndarray 转换 （底层内存共享）

a = torch.arange(12, dtype=torch.float32).reshape(3,4) # tensor
b = a.detach().numpy() # tensor 转换为 ndarray
c = torch.from_numpy(b) # ndarray 转换为 tensor
a[0, 1] = 100
print(a, a.dtype)
print(b, b.dtype)
print(c, c.dtype)

a = np.ones((2,2), dtype=np.float32) # ndarray
b = torch.Tensor(a) # numpy 转换为 Tensor
c = b.numpy() # tensor 转换为 numpy
d = torch.tensor(a) # numpy 转换为 tensor 不共享内存
a[1, 0]=100
print(a, a.dtype)
print(b, b.dtype)
print(c, c.dtype)
print(d, d.dtype)

a = np.ones([2,3]) # float64
b = torch.Tensor(a) # ndarray 转换 torch torch.float32 (数据类型不同，此处进行拷贝，不共享内存)
c = torch.from_numpy(a) # 注意c的类型 torch.float64 共享内存
d = torch.tensor(a) # 无论什么类型，tensor()都会进行数据拷贝，不会共享内存
a[0,1] = 100
print(a, a.dtype)
print(b, b.dtype)
print(c, c.dtype)
print(d, d.dtype)

from IPython.core.interactiveshell import InteractiveShell
InteractiveShell.ast_node_interactivity = “all”

a.dtype
b.dtype
c.dtype
d.dtype