2020-10-19 21:08:55

docs/da/061.md

@@ -4,7 +4,7 @@
 
 In [1]:
 
-```
+```py
 import numpy as np
 import numpy.linalg
 import scipy as sp
@@ -28,13 +28,13 @@ from scipy import linalg
 
 In [2]:
 
-```
+```py
 print "number of items in numpy.linalg:", len(dir(numpy.linalg))
 print "number of items in scipy.linalg:", len(dir(scipy.linalg))
 
 ```
 
-```
+```py
 number of items in numpy.linalg: 36
 number of items in scipy.linalg: 115
 
@@ -56,7 +56,7 @@ number of items in scipy.linalg: 115
 
 In [3]:
 
-```
+```py
 A = np.mat("[1, 2; 3, 4]")
 print repr(A)
 
@@ -65,7 +65,7 @@ print repr(A)
 
 ```
 
-```
+```py
 matrix([[1, 2],
         [3, 4]])
 matrix([[1, 2],
@@ -77,13 +77,13 @@ matrix([[1, 2],
 
 In [4]:
 
-```
+```py
 print repr(A.I)
 print repr(A.T)
 
 ```
 
-```
+```py
 matrix([[-2\. ,  1\. ],
         [ 1.5, -0.5]])
 matrix([[1, 3],
@@ -95,13 +95,13 @@ matrix([[1, 3],
 
 In [5]:
 
-```
+```py
 b = np.mat('[5; 6]')
 print repr(A * b)
 
 ```
 
-```
+```py
 matrix([[17],
         [39]])
 
@@ -115,13 +115,13 @@ matrix([[17],
 
 In [6]:
 
-```
+```py
 A = np.array([[1,2], [3,4]])
 print repr(A)
 
 ```
 
-```
+```py
 array([[1, 2],
        [3, 4]])
 
@@ -131,13 +131,13 @@ array([[1, 2],
 
 In [7]:
 
-```
+```py
 print repr(linalg.inv(A))
 print repr(A.T)
 
 ```
 
-```
+```py
 array([[-2\. ,  1\. ],
        [ 1.5, -0.5]])
 array([[1, 3],
@@ -149,14 +149,14 @@ array([[1, 3],
 
 In [8]:
 
-```
+```py
 b = np.array([5, 6])
 
 print repr(A.dot(b))
 
 ```
 
-```
+```py
 array([17, 39])
 
 ```
@@ -165,12 +165,12 @@ array([17, 39])
 
 In [9]:
 
-```
+```py
 print repr(A * b)
 
 ```
 
-```
+```py
 array([[ 5, 12],
        [15, 24]])
 
@@ -188,7 +188,7 @@ array([[ 5, 12],
 
 In [10]:
 
-```
+```py
 A = np.array([[1,2],[3,4]])
 
 print linalg.inv(A)
@@ -197,7 +197,7 @@ print A.dot(scipy.linalg.inv(A))
 
 ```
 
-```
+```py
 [[-2\.   1\. ]
  [ 1.5 -0.5]]
 [[  1.00000000e+00   0.00000000e+00]
@@ -213,7 +213,7 @@ print A.dot(scipy.linalg.inv(A))
 
 In [11]:
 
-```
+```py
 import time
 
 A = np.array([[1, 3, 5],
@@ -241,7 +241,7 @@ print "solve: {} s".format(time.time() - tic)
 
 ```
 
-```
+```py
 [-9.28  5.16  0.76]
 [  0.00000000e+00  -1.77635684e-15  -8.88178420e-16]
 inv and dot: 0.0353579521179 s
@@ -263,7 +263,7 @@ solve: 0.0284671783447 s
 
 In [12]:
 
-```
+```py
 A = np.array([[1, 3, 5],
               [2, 5, 1],
               [2, 3, 8]])
@@ -272,7 +272,7 @@ print linalg.det(A)
 
 ```
 
-```
+```py
 -25.0
 
 ```
@@ -287,7 +287,7 @@ print linalg.det(A)
 
 In [13]:
 
-```
+```py
 A = np.array([[1, 2],
               [3, 4]])
 
@@ -303,7 +303,7 @@ print linalg.norm(A,np.inf) # L inf norm 最大行和
 
 ```
 
-```
+```py
 5.47722557505
 5.47722557505
 6
@@ -350,7 +350,7 @@ $$ y_{i}=\sum_{j}c_{j}f_{j}\left(\mathbf{x}_{i}\right)+\epsilon_{i} $$
 
 In [14]:
 
-```
+```py
 c1, c2 = 5.0, 2.0
 i = np.r_[1:11]
 xi = 0.1*i
@@ -363,13 +363,13 @@ zi = yi + 0.05 * np.max(yi) * np.random.randn(len(yi))
 
 In [15]:
 
-```
+```py
 A = np.c_[np.exp(-xi)[:, np.newaxis], xi[:, np.newaxis]]
 print A
 
 ```
 
-```
+```py
 [[ 0.90483742  0.1       ]
  [ 0.81873075  0.2       ]
  [ 0.74081822  0.3       ]
@@ -387,14 +387,14 @@ print A
 
 In [16]:
 
-```
+```py
 c, resid, rank, sigma = linalg.lstsq(A, zi)
 
 print c
 
 ```
 
-```
+```py
 [ 4.87016856  2.19081311]
 
 ```
@@ -405,7 +405,7 @@ print c
 
 In [17]:
 
-```
+```py
 xi2 = np.r_[0.1:1.0:100j]
 yi2 = c[0]*np.exp(-xi2) + c[1]*xi2
 
@@ -608,7 +608,7 @@ gIuIRNT/AXU6OlSJKzNiAAAAAElFTkSuQmCC
 
 In [18]:
 
-```
+```py
 A = np.array([[1, 5, 2], 
               [2, 4, 1],
               [3, 6, 2]])
@@ -630,7 +630,7 @@ print linalg.norm(A.dot(v1)-l1*v1)
 
 ```
 
-```
+```py
 [ 7.95791620+0.j -1.25766471+0.j  0.29974850+0.j]
 [ 1\.  1\.  1.]
 3.23301824835e-15
@@ -660,7 +660,7 @@ $M \times N$ 矩阵 $\mathbf A$ 的奇异值分解为： $$ \mathbf{A=U}\boldsym
 
 In [19]:
 
-```
+```py
 A = np.array([[1,2,3],[4,5,6]])
 
 U, s, Vh = linalg.svd(A)
@@ -671,7 +671,7 @@ $\boldsymbol{\Sigma}$ 矩阵：
 
 In [20]:
 
-```
+```py
 M, N = A.shape
 Sig = linalg.diagsvd(s,M,N)
 
@@ -679,7 +679,7 @@ print Sig
 
 ```
 
-```
+```py
 [[ 9.508032    0\.          0\.        ]
  [ 0\.          0.77286964  0\.        ]]
 
@@ -689,13 +689,13 @@ print Sig
 
 In [21]:
 
-```
+```py
 print A
 print U.dot(Sig.dot(Vh))
 
 ```
 
-```
+```py
 [[1 2 3]
  [4 5 6]]
 [[ 1\.  2\.  3.]
@@ -715,7 +715,7 @@ $\mathbf P$ 是 $M \times M$ 的单位矩阵的一个排列，$\mathbf L$ 是下
 
 In [22]:
 
-```
+```py
 A = np.array([[1,2,3],[4,5,6]])
 
 P, L, U = linalg.lu(A)
@@ -728,7 +728,7 @@ print P.dot(L).dot(U)
 
 ```
 
-```
+```py
 [[ 0\.  1.]
  [ 1\.  0.]]
 [[ 1\.    0\.  ]
@@ -768,7 +768,7 @@ $\mathbf R$ 为上三角形矩阵，$\mathbf Q$ 是正交矩阵。
 
 In [23]:
 
-```
+```py
 A = np.mat('[1 3 2; 1 4 5; 2 3 6]')
 
 print A
@@ -781,7 +781,7 @@ print Z.dot(T).dot(Z.T)
 
 ```
 
-```
+```py
 [[1 3 2]
  [1 4 5]
  [2 3 6]]
@@ -814,14 +814,14 @@ print Z.dot(T).dot(Z.T)
 
 In [24]:
 
-```
+```py
 A = np.array([[1, 2], [3, 4]])
 
 print linalg.expm3(A)
 
 ```
 
-```
+```py
 [[  51.96890355   74.73648784]
  [ 112.10473176  164.07363531]]
 
@@ -835,12 +835,12 @@ print linalg.expm3(A)
 
 In [25]:
 
-```
+```py
 print linalg.expm2(A)
 
 ```
 
-```
+```py
 [[  51.9689562    74.73656457]
  [ 112.10484685  164.07380305]]
 
@@ -852,12 +852,12 @@ print linalg.expm2(A)
 
 In [26]:
 
-```
+```py
 print linalg.expm(A)
 
 ```
 
-```
+```py
 [[  51.9689562    74.73656457]
  [ 112.10484685  164.07380305]]
 
@@ -869,13 +869,13 @@ print linalg.expm(A)
 
 In [27]:
 
-```
+```py
 print A
 print linalg.logm(linalg.expm(A))
 
 ```
 
-```
+```py
 [[1 2]
  [3 4]]
 [[ 1\.  2.]