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. |
原帖：http://blog.csdn.net/leiowu1982/archive/2009/03/17/3998301.aspx
