NumPy programmā Python | 2. komplekts (papildu)

NumPy programmā Python | 2. komplekts (papildu)
NumPy programmā Python | 1. komplekts (ievads) Šajā rakstā ir apskatītas dažas vairāk un nedaudz uzlabotas metodes, kas pieejamas NumPy.
    Sakraušana: Vairākus masīvus var sakraut kopā pa dažādām asīm.
      np.vstack: Masīvu salikšanai pa vertikālo asi. np.hstack: Masīvu salikšanai pa horizontālo asi. np.column_stack: Lai 1-D masīvus sakrautu kā kolonnas 2-D masīvos. np.concatenate: Masīvu sakraušana pa norādīto asi (ass tiek nodota kā arguments).
    Python
       import   numpy   as   np   a   =   np  .  array  ([[  1     2  ]   [  3     4  ]])   b   =   np  .  array  ([[  5     6  ]   [  7     8  ]])   # vertical stacking   print  (  'Vertical stacking:  n  '     np  .  vstack  ((  a     b  )))   # horizontal stacking   print  (  '  n  Horizontal stacking:  n  '     np  .  hstack  ((  a     b  )))   c   =   [  5     6  ]   # stacking columns   print  (  '  n  Column stacking:  n  '     np  .  column_stack  ((  a     c  )))   # concatenation method    print  (  '  n  Concatenating to 2nd axis:  n  '     np  .  concatenate  ((  a     b  )   1  ))   
    Output:
    Vertical stacking: [[1 2] [3 4] [5 6] [7 8]] Horizontal stacking: [[1 2 5 6] [3 4 7 8]] Column stacking: [[1 2 5] [3 4 6]] Concatenating to 2nd axis: [[1 2 5 6] [3 4 7 8]] 
    Sadalīšana: Sadalīšanai mums ir šādas funkcijas:
      np.hsplit: Sadaliet masīvu pa horizontālo asi. np.vsplit: Sadaliet masīvu pa vertikālo asi. np.array_split: Sadaliet masīvu pa norādīto asi.
    Python
       import   numpy   as   np   a   =   np  .  array  ([[  1     3     5     7     9     11  ]   [  2     4     6     8     10     12  ]])   # horizontal splitting   print  (  'Splitting along horizontal axis into 2 parts:  n  '     np  .  hsplit  (  a     2  ))   # vertical splitting   print  (  '  n  Splitting along vertical axis into 2 parts:  n  '     np  .  vsplit  (  a     2  ))   
    Output:
    Splitting along horizontal axis into 2 parts: [array([[1 3 5] [2 4 6]]) array([[ 7 9 11] [ 8 10 12]])] Splitting along vertical axis into 2 parts: [array([[ 1 3 5 7 9 11]]) array([[ 2 4 6 8 10 12]])] 
    Apraide: Termins apraide apraksta, kā NumPy aritmētisko darbību laikā apstrādā dažādu formu masīvus. Ievērojot noteiktus ierobežojumus, mazākais masīvs tiek "pārraidīts" lielākajā masīvā, lai tiem būtu saderīgas formas. Apraide nodrošina līdzekli masīva darbību vektorizēšanai, lai cilpa notiktu C, nevis Python. Tas tiek darīts, neveidojot nevajadzīgas datu kopijas, un parasti tiek nodrošināta efektīva algoritmu ieviešana. Ir arī gadījumi, kad apraide ir slikta ideja, jo tā izraisa neefektīvu atmiņas izmantošanu, kas palēnina aprēķinus. NumPy darbības parasti tiek veiktas pa vienam elementam, un diviem masīviem ir nepieciešama tieši tāda pati forma. Numpy apraides noteikums atvieglo šo ierobežojumu, ja masīvu formas atbilst noteiktiem ierobežojumiem. Apraides noteikums: Lai operācijā pārraidītu abu masīvu beigu asu izmēriem ir jābūt vienāda izmēra vai arī vienam no tiem ir jābūt viens . Let us see some examples:
     A(2-D array): 4 x 3 B(1-D array): 3 Result : 4 x 3    
     A(4-D array): 7 x 1 x 6 x 1 B(3-D array): 3 x 1 x 5 Result : 7 x 3 x 6 x 5   But this would be a mismatch:  
     A: 4 x 3 B: 4   The simplest broadcasting example occurs when an array and a scalar value are combined in an operation. Consider the example given below: Python   
       import   numpy   as   np   a   =   np  .  array  ([  1.0     2.0     3.0  ])   # Example 1   b   =   2.0   print  (  a   *   b  )   # Example 2   c   =   [  2.0     2.0     2.0  ]   print  (  a   *   c  )   
    Output:
    [ 2. 4. 6.] [ 2. 4. 6.] 
    We can think of the scalar b being stretched during the arithmetic operation into an array with the same shape as a. The new elements in b as shown in above figure are simply copies of the original scalar. Although the stretching analogy is only conceptual. Numpy is smart enough to use the original scalar value without actually making copies so that broadcasting operations are as memory and computationally efficient as possible. Because Example 1 moves less memory (b is a scalar not an array) around during the multiplication it is about 10% faster than Example 2 using the standard numpy on Windows 2000 with one million element arrays! The figure below makes the concept more clear: NumPy programmā Python | 2. komplekts (papildu) In above example the scalar b is stretched to become an array of with the same shape as a so the shapes are compatible for element-by-element multiplication. Now let us see an example where both arrays get stretched. Python
       import   numpy   as   np   a   =   np  .  array  ([  0.0     10.0     20.0     30.0  ])   b   =   np  .  array  ([  0.0     1.0     2.0  ])   print  (  a  [:   np  .  newaxis  ]   +   b  )   
    Output:
    [[ 0. 1. 2.] [ 10. 11. 12.] [ 20. 21. 22.] [ 30. 31. 32.]]  
    NumPy programmā Python | 2. komplekts (papildu)Dažos gadījumos apraide izstiepj abus masīvus, veidojot izvades masīvu, kas ir lielāks par kādu no sākotnējiem masīviem. Darbs ar datumu un laiku: Numpy has core array data types which natively support datetime functionality. The data type is called datetime64 so named because datetime is already taken by the datetime library included in Python. Consider the example below for some examples: Python
       import   numpy   as   np   # creating a date   today   =   np  .  datetime64  (  '2017-02-12'  )   print  (  'Date is:'     today  )   print  (  'Year is:'     np  .  datetime64  (  today     'Y'  ))   # creating array of dates in a month   dates   =   np  .  arange  (  '2017-02'     '2017-03'     dtype  =  'datetime64[D]'  )   print  (  '  n  Dates of February 2017:  n  '     dates  )   print  (  'Today is February:'     today   in   dates  )   # arithmetic operation on dates   dur   =   np  .  datetime64  (  '2017-05-22'  )   -   np  .  datetime64  (  '2016-05-22'  )   print  (  '  n  No. of days:'     dur  )   print  (  'No. of weeks:'     np  .  timedelta64  (  dur     'W'  ))   # sorting dates   a   =   np  .  array  ([  '2017-02-12'     '2016-10-13'     '2019-05-22'  ]   dtype  =  'datetime64'  )   print  (  '  n  Dates in sorted order:'     np  .  sort  (  a  ))   
    Output:
    Date is: 2017-02-12 Year is: 2017 Dates of February 2017: ['2017-02-01' '2017-02-02' '2017-02-03' '2017-02-04' '2017-02-05' '2017-02-06' '2017-02-07' '2017-02-08' '2017-02-09' '2017-02-10' '2017-02-11' '2017-02-12' '2017-02-13' '2017-02-14' '2017-02-15' '2017-02-16' '2017-02-17' '2017-02-18' '2017-02-19' '2017-02-20' '2017-02-21' '2017-02-22' '2017-02-23' '2017-02-24' '2017-02-25' '2017-02-26' '2017-02-27' '2017-02-28'] Today is February: True No. of days: 365 days No. of weeks: 52 weeks Dates in sorted order: ['2016-10-13' '2017-02-12' '2019-05-22'] 
    Lineārā algebra programmā NumPy: NumPy lineārās algebras modulis piedāvā dažādas metodes, lai piemērotu lineāro algebru jebkuram nelīdzenam masīvam. Jūs varat atrast:
    • masīva ranga noteicošā izsekošana utt.
    • savas vērtības vai matricas
    • matricas un vektoru reizinājums (punkts iekšējais ārējais utt. reizinājums) matricas kāpināšana
    • atrisiniet lineāros vai tenzoru vienādojumus un daudz ko citu!
    Consider the example below which explains how we can use NumPy to do some matrix operations. Python
       import   numpy   as   np   A   =   np  .  array  ([[  6     1     1  ]   [  4     -  2     5  ]   [  2     8     7  ]])   print  (  'Rank of A:'     np  .  linalg  .  matrix_rank  (  A  ))   print  (  '  n  Trace of A:'     np  .  trace  (  A  ))   print  (  '  n  Determinant of A:'     np  .  linalg  .  det  (  A  ))   print  (  '  n  Inverse of A:  n  '     np  .  linalg  .  inv  (  A  ))   print  (  '  n  Matrix A raised to power 3:  n  '     np  .  linalg  .  matrix_power  (  A     3  ))   
    Output:
    Rank of A: 3 Trace of A: 11 Determinant of A: -306.0 Inverse of A: [[ 0.17647059 -0.00326797 -0.02287582] [ 0.05882353 -0.13071895 0.08496732] [-0.11764706 0.1503268 0.05228758]] Matrix A raised to power 3: [[336 162 228] [406 162 469] [698 702 905]] 
    Let us assume that we want to solve this linear equation set:
     x + 2*y = 8 3*x + 4*y = 18   This problem can be solved using   linalg.atrisināt   method as shown in example below: Python   
       import   numpy   as   np   # coefficients   a   =   np  .  array  ([[  1     2  ]   [  3     4  ]])   # constants   b   =   np  .  array  ([  8     18  ])   print  (  'Solution of linear equations:'     np  .  linalg  .  solve  (  a     b  ))   
    Output:
    Solution of linear equations: [ 2. 3.] 
    Finally we see an example which shows how one can perform linear regression using least squares method. A linear regression line is of the form w1 x + w 2 = y, un tā ir līnija, kas samazina attāluma kvadrātu summu no katra datu punkta līdz līnijai. Tātad, ņemot vērā n datu pārus (xi yi), mūsu meklētie parametri ir w1 un w2, kas samazina kļūdu: NumPy programmā Python | 2. komplekts (papildu) Let us have a look at the example below: Python
       import   numpy   as   np   import   matplotlib.pyplot   as   plt   # x co-ordinates   x   =   np  .  arange  (  0     9  )   A   =   np  .  array  ([  x     np  .  ones  (  9  )])   # linearly generated sequence   y   =   [  19     20     20.5     21.5     22     23     23     25.5     24  ]   # obtaining the parameters of regression line   w   =   np  .  linalg  .  lstsq  (  A  .  T     y  )[  0  ]   # plotting the line   line   =   w  [  0  ]  *  x   +   w  [  1  ]   # regression line   plt  .  plot  (  x     line     'r-'  )   plt  .  plot  (  x     y     'o'  )   plt  .  show  ()   
    Output:
Tātad tas noved pie šīs NumPy apmācības sērijas noslēguma. NumPy ir plaši izmantota vispārējas nozīmes bibliotēka, kas ir daudzu citu skaitļošanas bibliotēku pamatā, piemēram, scipy scikit-learn tensorflow matplotlib opencv utt. Pamatzināšanas par NumPy palīdz efektīvi strādāt ar citām augstāka līmeņa bibliotēkām! Atsauces: Izveidojiet viktorīnu