NumPy使用手记

前面一个NumPy系列基本上是抄书，没有多少具体的内容。最近做实验经常使用NumPy，确实感觉到向量计算的强大。这个系列开始，我记录在使用NumPy使用中的一些具体的技巧和注意事项。

1） 巧用 where函数

where函数是numpy的内置，也是一个非常有用的函数，提供了快速并且灵活的计算功能。

def f_norm_1(data, estimate):

residule = 0

for row_index in range(data.shape[0]):

for column_index in range(data.shape[1]):

if data[row_index][column_index] != 0:

residule += (data[row_index][column_index] - estimate[row_index][column_index]) ** 2

return residule

def f_norm_2(data, estimate)

return sum(where(data != 0, (data-estimate) **2, 0))

这两段代码完成同样的功能，计算两个矩阵的差，然后将残差进行平方，注意，因为我需要的是考虑矩阵稀疏性，所以不能用内置的norm，函数1是我用普通的python写的，不太复杂，对于规模10*10的矩阵，计算200次耗时0.15s，函数2使用了where函数和sum函数，这两个函数都是为向量计算优化过的，不仅简介，而且耗时仅0.03s,
快了有五倍，不仅如此，有同学将NumPy和matlab做过比较，NumPy稍快一些，这已经是很让人兴奋的结果。

本篇我们看看NumPy中最为基本的Array操作

>>> from numpy import *

创建一个矩阵

>>> a=array([[1,2,3],[4,5,6]])

>>> a.shape

(2, 3)

>>> b=arange(15);print b

[ 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14]

>>> b.reshape(3,5)

array([[ 0, 1, 2, 3, 4],

[ 5, 6, 7, 8, 9],

[10, 11, 12, 13, 14]])

可以看到，A是2行3列的矩阵。通过arange方法，可以得到一个1维的数组。然后我们可以通过reshape方法改变它的维度。

>>> c=zeros((4,5));print c

[[ 0. 0. 0. 0. 0.]

[ 0. 0. 0. 0. 0.]

[ 0. 0. 0. 0. 0.]

[ 0. 0. 0. 0. 0.]]

>>> d=ones((5,7));print d

[[ 1. 1. 1. 1. 1. 1. 1.]

[ 1. 1. 1. 1. 1. 1. 1.]

[ 1. 1. 1. 1. 1. 1. 1.]

[ 1. 1. 1. 1. 1. 1. 1.]

[ 1. 1. 1. 1. 1. 1. 1.]]

>>> e=add(c,arange(20).reshape(4,5))

>>> f=dot(e,d);print f

[[ 10. 10. 10. 10. 10. 10. 10.]

[ 35. 35. 35. 35. 35. 35. 35.]

[ 60. 60. 60. 60. 60. 60. 60.]

[ 85. 85. 85. 85. 85. 85. 85.]]

使用zeros可以生成一个零矩阵。同理，用ones可以生成值全部为1的矩阵。我选择了一个4*5的矩阵e，和一个5*7的矩阵d做点乘。最后得到f矩阵。再举一个更加明显的例子：

>>> a=arange(5);print a

[0 1 2 3 4]

>>> b=arange(5).reshape(5,1);print b

[[0]

[1]

[2]

[3]

[4]]

>>> print dot(a,b)

[30]

点积的效果更加明显了。

ndarray的几个常用属性：

· shape： 代表一个array的形态，是一个向量还是一个矩阵，抑或是一个更复杂的向量组。

· ndim： 代表这个array的维度

· size： 在array中拥有的元素数量

· itemsize： 这个array中每一个元素所需要占的字节数

· nbytes： 这个array的总字节数（=itemsize*size）

· real： 代表一个array中所有元素的实数部分

· imag： 同理，代表一个array中所有元素的虚数部分

· flat： 将这个array整理成一维的，可以索引的一系列的元素组合。它实际上是通过iterator实现的，我们可以通过for x in array.flat来取得到所有的元素

· T： 矩阵转置，同transpose()方法

一些比较有用的方法：

· tolist()： 将array转化成一个Python中的list对象

· item(*args)： 取得某一位置的元素

· dump(file)： 将这个对象序列化至文件。同cPickle中的dump作用

· dumps()： 将序列化的结果通过字符串加以输出

一些关于Array的形态操作：

· reshape()： 改变array的形态

· resize()： 也是改变array的形态。不同的是，resize是直接修改这个对象的，而reshape则会生成一个新的对象

· transpose()： 这个就是矩阵的转置操作啦

· swapaxes()： 将n个维度中任意两个维度（坐标轴）进行调换

· flatten()： 复制一个一维的array出来

还有一些关于Array的运算操作：

· max()：取得所有元素中的最大值

· min()：取得最小值。还有一点值得说，就是max、min这些函数都可以针对某一坐标轴（具体维度）进行运算，例如array.max(axis=0)，就在0坐标上求最大值

· sum()：求和

· cumsum()：求累计和

· prod()：求所有元素之积

· cumprod()：求累计积

· all()：如果所有元素都为真，那么返回真；否则返回假

· any()：只要有一个元素为真则返回真

· mean()：求平均数

Array高级操作

1. Vectorize函数

def t(x):
return x + 3
a1 = scipy.zeros((5,4))
a1
NumPy array, format: long
[[0 0 0 0]
[0 0 0 0]
[0 0 0 0]
[0 0 0 0]
[0 0 0 0]]
s = scipy.vectorize(t)
a2 = s(a1)
a2
NumPy array, format: long
[[3 3 3 3]
[3 3 3 3]
[3 3 3 3]
[3 3 3 3]
[3 3 3 3]]

2. NumPy和SciPy相互转化

import numpy
import scipy
a1 = zeros((4,6))
type(a1)
<type 'scipy.ndarray'>
a2 = numpy.asarray(a1)
type(a2)
<type 'numpy.ndarray'>
a3 = numpy.zeros((3,5))
type(a3)
<type 'numpy.ndarray'>
a4 = scipy.asarray(a3)
type(a4)
<type 'scipy.ndarray'>

NumPy 数学函数

Trigonometric functions¶

sin (x[, out])	Trigonometric sine, element-wise.
cos (x[, out])	Cosine elementwise.
tan (x[, out])	Compute tangent element-wise.
arcsin (x[, out])	Inverse sine elementwise.
arccos (x[, out])	Trigonometric inverse cosine, element-wise.
arctan (x[, out])	Trigonometric inverse tangent, element-wise.
hypot (x1, x2[, out])	Given two sides of a right triangle, return its hypotenuse.
arctan2 (x1, x2[, out])	Elementwise arc tangent of x1/x2 choosing the quadrant correctly.
degrees (x[, out])	Convert angles from radians to degrees. This is the same function as rad2deg but the latter is preferred because of the more descriptive name.
radians (x[, out])	Convert angles from degrees to radians. This function is the same as deg2rad, which is more descriptive..
unwrap (p[, discont, axis])	Unwrap by changing deltas between values to 2*pi complement.

Hyperbolic functions¶

sinh (x[, out])	Hyperbolic sine, element-wise.
cosh (x[, out])	Hyperbolic cosine, element-wise.
tanh (x[, out])	Hyperbolic tangent element-wise.
arcsinh (x[, out])	Inverse hyperbolic sine elementwise.
arccosh (x[, out])	Inverse hyperbolic cosine, elementwise.
arctanh (x[, out])	Inverse hyperbolic tangent elementwise.

Rounding¶

around (a[, decimals, out])	Evenly round to the given number of decimals.
round_ (a[, decimals, out])	Round an array to the given number of decimals.
rint (x[, out])	Round elements of the array to the nearest integer.
fix (x[, y])	Round to nearest integer towards zero.
floor (x[, out])	Return the floor of the input, element-wise.
ceil (x[, out])	Return the ceiling of the input, element-wise.

Sums, products, differences¶

prod (a[, axis, dtype, out])	Return the product of array elements over a given axis.
sum (a[, axis, dtype, out])	Return the sum of array elements over a given axis.
nansum (a[, axis])	Return the sum of array elements over a given axis treating Not a Numbers (NaNs) as zero.
cumprod (a[, axis, dtype, out])	Return the cumulative product of elements along a given axis.
cumsum (a[, axis, dtype, out])	Return the cumulative sum of the elements along a given axis.
diff (a[, n, axis])	Calculate the nth order discrete difference along given axis.
ediff1d (ary[, to_end, to_begin])	The differences between consecutive elements of an array.
gradient (f, *varargs)	Return the gradient of an N-dimensional array.
cross (a, b[, axisa, axisb, axisc, ...])	Return the cross product of two (arrays of) vectors.
trapz (y[, x, dx, axis])	Integrate along the given axis using the composite trapezoidal rule.

Exponents and logarithms¶

exp (x[, out])	Calculate the exponential of the elements in the input array.
expm1 (x[, out])	Return the exponential of the elements in the array minus one.
log (x[, out])	Natural logarithm, element-wise.
log10 (x[, out])	Compute the logarithm in base 10 element-wise.
log2 (x[, y])	Return the base 2 logarithm.
log1p (x[, out])	log(1 + x) in base e, elementwise.

Other special functions¶

i0 (x)	Modified Bessel function of the first kind, order 0.
sinc (x)	Return the sinc function.

Floating point routines¶

signbit (x[, out])	Returns element-wise True where signbit is set (less than zero).
frexp (x[, out1, out2])	Split the number, x, into a normalized fraction (y1) and exponent (y2)
ldexp (x1, x2[, out])	Compute y = x1 * 2**x2.

Arithmetic operations¶

add (x1, x2[, out])	Add arguments element-wise.
reciprocal (x[, out])	Return element-wise reciprocal.
negative (x[, out])	Returns an array with the negative of each element of the original array.
multiply (x1, x2[, out])	Multiply arguments elementwise.
divide (x1, x2[, out])	Divide arguments element-wise.
power (x1, x2[, out])	Returns element-wise base array raised to power from second array.
subtract (x1, x2[, out])	Subtract arguments element-wise.
true_divide (x1, x2[, out])	Returns an element-wise, true division of the inputs.
floor_divide (x1, x2[, out])	Return the largest integer smaller or equal to the division of the inputs.
fmod (x1, x2[, out])	Return the remainder of division.
mod (x1, x2[, out])	Returns element-wise remainder of division.
modf (x[, out1, out2])	Return the fractional and integral part of a number.
remainder (x1, x2[, out])	Returns element-wise remainder of division.

Handling complex numbers¶

angle (z[, deg])	Return the angle of the complex argument.
real (val)	Return the real part of the elements of the array.
imag (val)	Return the imaginary part of array.
conj (x[, out])	Return the complex conjugate, element-wise.

Miscellaneous¶

convolve (a, v[, mode])	Returns the discrete, linear convolution of two one-dimensional sequences.
clip (a, a_min, a_max[, out])	Clip (limit) the values in an array.
sqrt (x[, out])	Return the positive square-root of an array, element-wise.
square (x[, out])	Return the element-wise square of the input.
absolute (x[, out])	Calculate the absolute value element-wise.
fabs (x[, out])	Compute the absolute values elementwise.
sign (x[, out])	Returns an element-wise indication of the sign of a number.
maximum (x1, x2[, out])	Element-wise maximum of array elements.
minimum (x1, x2[, out])	Element-wise minimum of array elements.
nan_to_num (x)	Replace nan with zero and inf with large numbers.
real_if_close (a[, tol])	If complex input returns a real array if complex parts are close to zero.
interp (x, xp, fp[, left, right])	One-dimensional linear interpolation.