how does multiplication differ for NumPy Matrix vs Array classes

Question

The numpy docs recommend using array instead of matrix for working with matrices  However  unlike octave  which I was using till recently     doesn t perform matrix multiplication  you need to use the function matrixmultipy    I feel this makes the code very unreadable   Does anybody share my views  and has found a solution

User · Answer

There is a situation where the dot operator will give different answers when dealing with arrays as with dealing with matrices. For example, suppose the following:

>>> a=numpy.array([1, 2, 3])
>>> b=numpy.array([1, 2, 3])

Lets convert them into matrices:

>>> am=numpy.mat(a)
>>> bm=numpy.mat(b)

Now, we can see a different output for the two cases:

>>> print numpy.dot(a.T, b)
14
>>> print am.T*bm
[[1.  2.  3.]
 [2.  4.  6.]
 [3.  6.  9.]]

User · Answer

This trick could be what you are looking for  It is a kind of simple operator overload   You can then use something like the suggested Infix class like this   a   np random rand 3 4  b   np random rand 4 3  x   Infix lambda x y  np dot x y   c   a  x  b

User · Answer

the key things to know for operations on NumPy arrays versus operations on NumPy matrices are    NumPy matrix is a subclass of NumPy array NumPy array operations are element-wise  once broadcasting is accounted for  NumPy matrix operations follow the ordinary rules of linear algebra   some code snippets to illustrate    gt  gt  gt  from numpy import linalg as LA  gt  gt  gt  import numpy as NP   gt  gt  gt  a1   NP matrix  4 3 5  6 7 8  1 3 13  7 21 9    gt  gt  gt  a1 matrix    4   3   5             6   7   8             1   3  13             7  21   9      gt  gt  gt  a2   NP matrix  7 8 15  5 3 11  7 4 9  6 15 4    gt  gt  gt  a2 matrix    7   8  15             5   3  11             7   4   9             6  15   4      gt  gt  gt  a1 shape  4  3    gt  gt  gt  a2 shape  4  3    gt  gt  gt  a2t   a2 T  gt  gt  gt  a2t shape  3  4    gt  gt  gt  a1   a2t           same as NP dot a1  a2t   matrix   127   84   85   89            218  139  142  173            226  157  136  103            352  197  214  393      but this operations fails if these two NumPy matrices are converted to arrays    gt  gt  gt  a1   NP array a1   gt  gt  gt  a2t   NP array a2t    gt  gt  gt  a1   a2t Traceback  most recent call last      File   lt pyshell 277 gt    line 1  in  lt module gt     a1   a2t    ValueError  operands could not be broadcast together with shapes  4 3   3 4     though using the NP dot syntax works with arrays  this operations works like matrix multiplication    gt  gt  NP dot a1  a2t  array   127   84   85   89           218  139  142  173           226  157  136  103           352  197  214  393      so do you ever need a NumPy matrix  ie  will a NumPy array suffice for linear algebra computation  provided you know the correct syntax  ie  NP dot    the rule seems to be that if the arguments  arrays  have shapes  m x n  compatible with the a given linear algebra operation  then you are ok  otherwise  NumPy throws   the only exception i have come across  there are likely others  is calculating matrix inverse   below are snippets in which i have called a pure linear algebra operation  in fact  from Numpy s Linear Algebra module  and passed in a NumPy array  determinant of an array    gt  gt  gt  m   NP random randint 0  10  16  reshape 4  4   gt  gt  gt  m array   6  2  5  2           8  5  1  6           5  9  7  5           0  5  6  7      gt  gt  gt  type m   lt type  numpy ndarray  gt    gt  gt  gt  md   LA det m   gt  gt  gt  md 1772 9999999999995   eigenvectors eigenvalue pairs    gt  gt  gt  LA eig m   array   19 703 0 j       0 097 4 198j    0 097-4 198j    5 103 0 j        array   -0 374 0 j     -0 091 0 278j  -0 091-0 278j  -0 574 0 j              -0 446 0 j      0 671 0 j      0 671 0 j     -0 084 0 j              -0 654 0 j     -0 239-0 476j  -0 239 0 476j  -0 181 0 j              -0 484 0 j     -0 387 0 178j  -0 387-0 178j   0 794 0 j          matrix norm    gt  gt  gt  gt  LA norm m  22 0227   qr factorization    gt  gt  gt  LA qr a1   array    0 5   0 5   0 5             0 5   0 5  -0 5             0 5  -0 5   0 5             0 5  -0 5  -0 5       array    6    6    6              0    0    0              0    0    0        matrix rank    gt  gt  gt  m   NP random rand 40  reshape 8  5   gt  gt  gt  m array    0 545   0 459   0 601   0 34    0 778            0 799   0 047   0 699   0 907   0 381            0 004   0 136   0 819   0 647   0 892            0 062   0 389   0 183   0 289   0 809            0 539   0 213   0 805   0 61    0 677            0 269   0 071   0 377   0 25    0 692            0 274   0 206   0 655   0 062   0 229            0 397   0 115   0 083   0 19    0 701     gt  gt  gt  LA matrix rank m  5   matrix condition    gt  gt  gt  a1   NP random randint 1  10  12  reshape 4  3   gt  gt  gt  LA cond a1  5 7093446189400954   inversion requires a NumPy matrix though    gt  gt  gt  a1   NP matrix a1   gt  gt  gt  type a1   lt class  numpy matrixlib defmatrix matrix  gt    gt  gt  gt  a1 I matrix    0 028   0 028   0 028   0 028             0 028   0 028   0 028   0 028             0 028   0 028   0 028   0 028     gt  gt  gt  a1   NP array a1   gt  gt  gt  a1 I  Traceback  most recent call last      File   lt pyshell 230 gt    line 1  in  lt module gt     a1 I    AttributeError   numpy ndarray  object has no attribute  I    but the Moore-Penrose pseudoinverse seems to works just fine   gt  gt  gt  LA pinv m  matrix    0 314   0 407  -1 008  -0 553   0 131   0 373   0 217   0 785             1 393   0 084  -0 605   1 777  -0 054  -1 658   0 069  -1 203            -0 042  -0 355   0 494  -0 729   0 292   0 252   1 079  -0 432            -0 18    1 068   0 396   0 895  -0 003  -0 896  -1 115  -0 666            -0 224  -0 479   0 303  -0 079  -0 066   0 872  -0 175   0 901      gt  gt  gt  m   NP array m    gt  gt  gt  LA pinv m  array    0 314   0 407  -1 008  -0 553   0 131   0 373   0 217   0 785            1 393   0 084  -0 605   1 777  -0 054  -1 658   0 069  -1 203           -0 042  -0 355   0 494  -0 729   0 292   0 252   1 079  -0 432           -0 18    1 068   0 396   0 895  -0 003  -0 896  -1 115  -0 666           -0 224  -0 479   0 303  -0 079  -0 066   0 872  -0 175   0 901

User · Answer

Function matmul  since numpy 1 10 1  works fine for both types and return result as a numpy matrix class   import numpy as np  A   np mat  1 2 3  4 5 6  7 8 9  10 11 12   B   np array np mat  1 1 1 1  1 1 1 1  1 1 1 1    print  A  type A   print  B  type B    C   np matmul A  B  print  C  type C     Output    matrix    1   2   3             4   5   6             7   8   9            10  11  12      lt class  numpy matrixlib defmatrix matrix  gt    array   1  1  1  1           1  1  1  1           1  1  1  1      lt type  numpy ndarray  gt    matrix    6   6   6   6            15  15  15  15            24  24  24  24            33  33  33  33      lt class  numpy matrixlib defmatrix matrix  gt     Since python 3 5 as mentioned early you also can use a new matrix multiplication operator   like  C   A   B   and get the same result as above

User · Answer

In 3 5  Python finally got a matrix multiplication operator  The syntax is a   b

User · Answer

Reference from http   docs scipy org doc scipy reference tutorial linalg html       the use of the numpy matrix class is discouraged  since it adds nothing that cannot be accomplished with 2D numpy ndarray objects  and may lead to a confusion of which class is being used  For example    gt  gt  gt  import numpy as np  gt  gt  gt  from scipy import linalg  gt  gt  gt  A   np array   1 2   3 4     gt  gt  gt  A     array   1  2               3  4     gt  gt  gt  linalg inv A  array   -2     1             1 5  -0 5     gt  gt  gt  b   np array   5 6     2D array  gt  gt  gt  b array   5  6     gt  gt  gt  b T array   5          6     gt  gt  gt  A b  not matrix multiplication  array    5  12          15  24     gt  gt  gt  A dot b T   matrix multiplication array   17          39     gt  gt  gt  b   np array  5 6    1D array  gt  gt  gt  b array  5  6    gt  gt  gt  b T   not matrix transpose  array  5  6    gt  gt  gt  A dot b    does not matter for multiplication array  17  39     scipy linalg operations can be applied equally to numpy matrix or to 2D numpy ndarray objects

User · Answer

A pertinent quote from PEP 465 - A dedicated infix operator for matrix multiplication   as mentioned by  petr-viktorin  clarifies the problem the OP was getting at            numpy provides two different types with different   mul   methods  For numpy ndarray objects    performs elementwise multiplication  and matrix multiplication must use a function call  numpy dot   For numpy matrix objects    performs matrix multiplication  and elementwise multiplication requires function syntax  Writing code using numpy ndarray works fine  Writing code using numpy matrix also works fine  But trouble begins as soon as we try to integrate these two pieces of code together  Code that expects an ndarray and gets a matrix  or vice-versa  may crash or return incorrect results   The introduction of the   infix operator should help to unify and simplify python matrix code

User · Answer

The main reason to avoid using the matrix class is that a  it s inherently 2-dimensional  and b  there s additional overhead compared to a  normal  numpy array  If all you re doing is linear algebra  then by all means  feel free to use the matrix class    Personally I find it more trouble than it s worth  though   For arrays  prior to Python 3 5   use dot instead of matrixmultiply   E g   import numpy as np x   np arange 9  reshape  3 3   y   np arange 3   print np dot x y    Or in newer versions of numpy  simply use x dot y   Personally  I find it much more readable than the   operator implying matrix multiplication       For arrays in Python 3 5  use x   y

[python] how does multiplication differ for NumPy Matrix vs Array classes?

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