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python for data science cheat sheet lists also see numpy arrays libraries python basics a is import libraries b nice import numpy data analysis machine learning learn more python for ...

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        Python For Data Science Cheat Sheet                                                               Lists                                                    Also see NumPy Arrays                    Libraries
                                      Python Basics                                                        >>> a = 'is'                                                                                    Import libraries
                                                                                                           >>> b = 'nice'                                                                                >>> import numpy                                        Data analysis        Machine learning
           Learn More Python for Data Science Interactively at  www.datacamp.com                           >>> my_list = ['my', 'list', a, b]                                                            >>> import numpy as np
                                                                                                           >>> my_list2 = [[4,5,6,7], [3,4,5,6]]                                                           Selective import
                                                                                                                                                                         Index starts at 0               >>> from math import pi                              Scientific computing       2D plotting
     Variables and Data Types                                                                               Selecting List Elements
           Variable Assignment                                                                               Subset                                                                                        Install Python
         >>> x=5                                                                                           >>> my_list[1]                                Select item at index 1
         >>> x                                                                                             >>> my_list[-3]                               Select 3rd last item
          5                                                                                                  Slice
                                                                                                           >>> my_list[1:3]                              Select items at index 1 and 2
          Calculations With Variables                                                                      >>> my_list[1:]                               Select items after index 0
         >>> x+2                Sum of two variables                                                       >>> my_list[:3]                               Select items before index 3                       Leading open data science platform       Free IDE that is included       Create and share 
                                                                                                           >>> my_list[:]                                Copy my_list                                              powered by Python                     with Anaconda         documents with live code, 
          7                                                                                                  Subset Lists of Lists                                                                                                                                                visualizations, text, ...
         >>> x-2                Subtraction of two variables                                               >>> my_list2[1][0]                            my_list[list][itemOfList]
          3                                                                                                >>> my_list2[1][:2]                                                                             Numpy Arrays                                                              Also see Lists
         >>> x*2                Multiplication of two variables                                                                                                                                            >>> my_list = [1, 2, 3, 4]
          10                                                                                                 List Operations                                                                               >>> my_array = np.array(my_list)
         >>> x**2               Exponentiation of a variable                                               >>> my_list + my_list                                                                           >>> my_2darray = np.array([[1,2,3],[4,5,6]])
          25
         >>> x%2                Remainder of a variable                                                    ['my', 'list', 'is', 'nice', 'my', 'list', 'is', 'nice']                                         Selecting Numpy Array Elements                                       Index starts at 0
          1                                                                                                >>> my_list * 2
         >>> x/float(2)          Division of a variable                                                    ['my', 'list', 'is', 'nice', 'my', 'list', 'is', 'nice']                                          Subset
          2.5                                                                                              >>> my_list2 > 4                                                                                >>> my_array[1]                                   Select item at index 1
          Types and Type Conversion                                                                        True                                                                                               2
                                                                                                             List Methods                                                                                    Slice
          str()     '5', '3.45', 'True'                                                                                                                                                                    >>> my_array[0:2]                                 Select items at index 0 and 1
                                                                  Variables to strings                                                                          Get the index of an item                      array([1, 2])
                                                                                                           >>> my_list.index(a)                                                                              Subset 2D Numpy arrays
          int()     5, 3, 1                                       Variables to integers                    >>> my_list.count(a)                                 Count an item
                                                                                                           >>> my_list.append('!')                              Append an item at a time                   >>> my_2darray[:,0]                               my_2darray[rows, columns]
          float()    5.0, 1.0                                     Variables to floats                      >>> my_list.remove('!')                              Remove an item                                array([1, 4])
                                                                                                           >>> del(my_list[0:1])                                Remove an item                              Numpy Array Operations
          bool()    True, True, True                              Variables to booleans                    >>> my_list.reverse()                                Reverse the list                           >>> my_array > 3
                                                                                                           >>> my_list.extend('!')                              Append an item                               array([False, False, False,  True], dtype=bool)
     Asking For Help                                                                                       >>> my_list.pop(-1)                                  Remove an item                             >>> my_array * 2
                                                                                                           >>> my_list.insert(0,'!')                            Insert an item                               array([2, 4, 6, 8])
    >>> help(str)                                                                                          >>> my_list.sort()                                   Sort the list                              >>> my_array + np.array([5, 6, 7, 8])
    Strings                                                                                                                                                                                                  array([6, 8, 10, 12])
        >>> my_string = 'thisStringIsAwesome'                                                                                                                                                               Numpy Array Functions
        >>> my_string                                                                                       String Operations                                                Index starts at 0             >>> my_array.shape                                       Get the dimensions of the array
        'thisStringIsAwesome'                                                                              >>> my_string[3]                                                                                >>> np.append(other_array)                               Append items to an array
         String Operations                                                                                 >>> my_string[4:9]                                                                              >>> np.insert(my_array, 1, 5) Insert items in an array
                                                                                                             String Methods                                                                                >>> np.delete(my_array,[1])                              Delete items in an array
        >>> my_string * 2                                                                                                                                                                                  >>> np.mean(my_array)                                    Mean of the array
          'thisStringIsAwesomethisStringIsAwesome'                                                          >>> my_string.upper()                                  String to uppercase                     >>> np.median(my_array)                                  Median of the array
        >>> my_string + 'Innit'                                                                             >>> my_string.lower()                                  String to lowercase                     >>> my_array.corrcoef()                                  Correlation coefficient
          'thisStringIsAwesomeInnit'                                                                        >>> my_string.count('w')                               Count String elements                   >>> np.std(my_array)                                     Standard deviation
        >>> 'm' in my_string                                                                                >>> my_string.replace('e', 'i') Replace String elements
          True                                                                                              >>> my_string.strip()                                  Strip whitespaces                                                               DataCamp
                                                                                                                                                                                                                                       Learn Python for Data Science Interactively
     Python For Data Science Cheat Sheet                                         Working with Different Programming Languages                                Widgets
                                                                                 Kernels provide computation and communication with front-end interfaces      Notebook widgets provide the ability to visualize and control changes 
                         Jupyter Notebook                                        like the notebooks. There are three main kernels:                            in your data, often as a control like a slider, textbox, etc. 
        Learn More Python for Data Science Interactively at  www.DataCamp.com                                                                                 You can use them to build interactive GUIs for your notebooks or to 
                                                                                                                   IRkernel              IJulia               synchronize stateful and stateless information between Python and 
                                                                                 Installing Jupyter Notebook will automatically install the IPython kernel.   JavaScript.
    Saving/Loading Notebooks                                                         Restart kernel                                Interrupt kernel
     Create new notebook                                                         Restart kernel & run                               Interrupt kernel &         Download serialized                                Save notebook 
                                                    Open an existing             all cells                                          clear all output           state of all widget                                with interactive 
   Make a copy of the                               notebook                      Restart kernel & run                              Connect back to a          models in use                                      widgets
   current notebook                                                               all cells                                         remote notebook
                                                     Rename notebook                                                                Run other installed                                                         Embed current 
                                                                                                                                    kernels                                                                     widgets
    Save current notebook                             Revert notebook to a 
    and record checkpoint                             previous checkpoint      Command Mode:
                                                     Download notebook as
   Preview of the printed                               - IPython notebook                                                                                                                                                     15
   notebook                                             - Python
                                                        - HTML
   Close notebook & stop                                - Markdown                                                                                                                                                          13   14
   running any scripts                                  - reST
                                                        - LaTeX                   1    2   3   4   5   6   7   8   9  10        11        12
                                                        - PDF
    Writing Code And Text
    Code and text are encapsulated by 3 basic cell types: markdown cells, code 
    cells, and raw NBConvert cells.
     Edit Cells                                                                Edit Mode:                                                                              1. Save and checkpoint        9. Interrupt kernel
                                                                                                                                                                       2. Insert cell below          10. Restart kernel
    Cut currently selected cells                         Copy cells from                                                                                               3. Cut cell                   11. Display characteristics
    to clipboard                                         clipboard to current                                                                                          4. Copy cell(s)               12. Open command palette
                                                                                                                                                                       5. Paste cell(s) below        13. Current kernel
    Paste cells from                                     cursor position         Executing Cells                                                                       6. Move cell up               14. Kernel status
    clipboard above                                                                                                                                                    7. Move cell down             15. Log out from notebook server
    current cell                                          Paste cells from       Run selected cell(s)                           Run current cells down                 8. Run current cell 
                                                          clipboard below                                                       and create a new one 
    Paste cells from                                      current cell                                                          below                     Asking For Help
    clipboard on top                                      Delete current cells  Run current cells down 
    of current cel                                                              and create a new one                                                        Walk through a UI tour
    Revert “Delete Cells”                                 Split up a cell from  above                                              Run all cells
    invocation                                            current cursor         Run all cells above the                           Run all cells below                                                     List of built-in keyboard 
                                                          position               current cell                                      the current cell        Edit the built-in                               shortcuts
    Merge current cell                                  Merge current cell       Change the cell type of                            toggle, toggle         keyboard shortcuts                              Notebook help topics
    with the one above                                  with the one below       current cell                                       scrolling and clear   Description of 
    Move current cell up                                Move current cell                toggle, toggle                             current outputs       markdown available                               Information on 
    Adjust metadata                                     down                             scrolling and clear                                              in notebook                                      unofficial Jupyter 
    underlying the                                      Find and replace                 all output                                                         Python help topics                             Notebook extensions
    current notebook                                    in selected cells        View Cells                                                                                                                IPython help topics
        Remove cell                                  Copy attachments of                                                                                    NumPy help topics
        attachments                                  current cell                 Toggle display of Jupyter                 Toggle display of toolbar     Matplotlib help topics                            SciPy help topics
     Paste attachments of                                  Insert image in        logo and filename                                                                                                         SymPy help topics
     current cell                                          selected cells                                                       Toggle display of cell     Pandas help topics
                                                                                                                                action icons:                                                              About Jupyter Notebook
     Insert Cells                                                                                                                    - None
                                                                                                                                     - Edit metadata
                                                 Add new cell below the              Toggle line numbers                             - Raw cell format
     Add new cell above the                                                          in cells                                        - Slideshow
     current one                                 current one                                                                         - Attachments                                      DataCamp
                                                                                                                                     - Tags
                                                                                                                                                                                Learn Python for Data Science Interactively
              Python For Data Science Cheat Sheet                                                                                                                                                                                                                                                Inspecting Your Array                                                                                                                                                                                                                                                               Subsetting, Slicing, Indexing                                                                                                                                                                                    Also see Lists
                                                                                                                                                                                                                                                                                                    >>> a.shape               Array dimensions                                                                                                                                                                                                                                           Subsetting
                                                                                                  NumPy Basics                                                                                                                                                                                      >>> len(a)                Length of array                                                                                                                                                                                                                                                                                                                                      1          2          3
                                                                                                                                                                                                                                                                                                    >>> b.ndim                Number of array dimensions                                                                                                                                                                                                                               >>> a[2]                       Select the element at the 2nd index
                               Learn Python for Data Science Interactively at  www.DataCamp.com                                                                                                                                                                                                     >>> e.size                Number of array elements                                                                                                                                                                                                                                   3
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  1.5          2          3
                                                                                                                                                                                                                                                                                                    >>> b.dtype               Data type of array elements                                                                                                                                                                                                                              >>> b[1,2]                     Select the element at row 0 column 2
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    4          5          6
                                                                                                                                                                                                                                                                                                    >>> b.dtype.name          Name of data type                                                                                                                                                                                                                                          6.0                           (equivalent to b[1][2])
                                                                                                                                                                                                                                                                                                    >>> b.astype(int)         Convert an array to a different type                                                                                                                                                                                                                       Slicing
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       >>> a[0:2]                     Select items at index 0 and 1
            NumPy                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        array([1, 2])                                                                              1          2          3
                                                                                                                                             2                                                                                                                                                    Asking For Help
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  1.5          2          3
             The NumPy library is the core library for scientific computing in                                                                                                                                                                                                                >>> np.info(np.ndarray.dtype)                                                                                                                                                                                                                                                            >>> b[0:2,1]                   Select items at rows 0 and 1 in column 1
             Python. It provides a high-performance multidimensional array                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               array([ 2.,  5.])                                                                          4          5          6
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  1.5          2          3
             object, and tools for working with these arrays.                                                                                                                                                                                                                                    Array Mathematics                                                                                                                                                                                                                                                                     >>> b[:1]                      Select all items at row 0
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    4          5          6
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         array([[1.5, 2., 3.]])               (equivalent to b[0:1, :])
                Use the following import convention:                                                                                                                                                                                                                                                      Arithmetic Operations                                                                                                                                                                                                                                                        >>> c[1,...]                   Same as [1,:,:]
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         array([[[ 3.,  2.,  1.],
                             >>> import numpy as np                                                                                                                                                                                                                                                  >>> g = a - b                          Subtraction                                                                                                                                                                                                                                          [ 4.,  5.,  6.]]])
                                                                                                                                                                                                                                                                                                       array([[-0.5,  0. ,  0. ],                                                                                                                                                                                                                                                      >>> a[ : :-1]                  Reversed array a 
                    NumPy Arrays                                                                                                                                                                                                                                                                              [-3. , -3. , -3. ]])                                                                                                                                                                                                                                                       array([3, 2, 1])
                       1D array                                                                    2D array                                      3D array                                                                                                                                            >>> np.subtract(a,b)                   Subtraction                                                                                                                                                                                                                                  Boolean Indexing
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       >>> a[a<2]                     Select elements from a less than 2
                                                                                                                                                                                                                                                                                                     >>> b + a                              Addition                                                                                                                                                                                                                                     array([1])                                                                                1          2          3
                           1            2            3                                   axis 1                                                                                                      axis 2                                                                                            array([[ 2.5,  4. ,  6. ],
                                                                                                                                                                                           axis 1                                                                                                             [ 5. ,  7. ,  9. ]])                                                                                                                                                                                                                                                       Fancy Indexing
                                                                                     axis 0                               1.5             2            3                                                                                                                                             >>> np.add(b,a)                        Addition                                                                                                                                                                                                                                   >>> b[[1, 0, 1, 0],[0, 1, 2, 0]]    Select elements (1,0),(0,1),(1,2) and (0,0)
                                                                                                                            4             5            6                               axis 0                                                                                                        >>> a / b                              Division                                                                                                                                                                                                                                     array([ 4. , 2. , 6. , 1.5]) 
                                                                                                                                                                                                                                                                                                       array([[ 0.66666667,  1.        ,  1.        ],                                                                                                                                                                                                                                 >>> b[[1, 0, 1, 0]][:,[0,1,2,0]]      Select a subset of the matrix’s rows
                                                                                                                                                                                                                                                                                                              [ 0.25      ,  0.4       ,  0.5       ]])                                                                                                                                                                                                                                  array([[ 4. ,5. , 6. , 4. ],           and columns
                                                                                                                                                                                                                                                                                                     >>> np.divide(a,b)                     Division                                                                                                                                                                                                                                           [ 1.5, 2. , 3. , 1.5],
             Creating Arrays                                                                                                                                                                                                                                                                         >>> a * b                              Multiplication                                                                                                                                                                                                                                     [ 4. , 5. , 6. , 4. ],
                                                                                                                                                                                                                                                                                                       array([[  1.5,   4. ,   9. ],                                                                                                                                                                                                                                                           [ 1.5, 2. , 3. , 1.5]])
             >>> a = np.array([1,2,3])                                                                                                                                                                                                                                                                        [  4. ,  10. ,  18. ]])                                                                                                                                                                                                                                               Array Manipulation
             >>> b = np.array([(1.5,2,3), (4,5,6)], dtype = float)                                                                                                                                                                                                                                   >>> np.multiply(a,b)                   Multiplication
             >>> c = np.array([[(1.5,2,3), (4,5,6)], [(3,2,1), (4,5,6)]],                                                                                                                                                                                                                            >>> np.exp(b)                          Exponentiation                                                                                                                                                                                                                           Transposing Array
                              dtype = float)                                                                                                                                                                                                                                                         >>> np.sqrt(b)                         Square root                                                                                                                                                                                                                            >>> i = np.transpose(b)          Permute array dimensions
                  Initial Placeholders                                                                                                                                                                                                                                                               >>> np.sin(a)                          Print sines of an array                                                                                                                                                                                                                >>> i.T                          Permute array dimensions
                                                                                                                                                                                                                                                                                                     >>> np.cos(b)                          Element-wise cosine 
             >>> np.zeros((3,4))                Create an array of zeros                                                                                                                                                                                                                             >>> np.log(a)                          Element-wise natural logarithm                                                                                                                                                                                                           Changing Array Shape
                                                                                                                                                                                                                                                                                                     >>> e.dot(f)                           Dot product                                                                                                                                                                                                                            >>> b.ravel()                    Flatten the array
             >>> np.ones((2,3,4),dtype=np.int16) Create an array of ones                                                                                                                                                                                                                               array([[ 7.,  7.],
             >>> d = np.arange(10,25,5)         Create an array of evenly                                                                                                                                                                                                                                     [ 7.,  7.]])                                                                                                                                                                                                                                                         >>> g.reshape(3,-2)              Reshape, but don’t change data
                                                spaced values (step value)                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           Adding/Removing Elements
             >>> np.linspace(0,2,9)             Create an array of evenly                                                                                                                                                                                                                                Comparison                                                                                                                                                                                                                                                                >>> h.resize((2,6))              Return a new array with shape (2,6) 
                                                spaced values (number of samples)                                                                                                                                                                                                                   >>> a == b                             Element-wise comparison                                                                                                                                                                                                                 >>> np.append(h,g)               Append items to an array
             >>> e = np.full((2,2),7)           Create a constant array                                                                                                                                                                                                                               array([[False,  True,  True],                                                                                                                                                                                                                                                >>> np.insert(a, 1, 5)           Insert items in an array
             >>> f = np.eye(2)                  Create a 2X2 identity matrix                                                                                                                                                                                                                                 [False, False, False]], dtype=bool)                                                                                                                                                                                                                                   >>> np.delete(a,[1])             Delete items from an array
             >>> np.random.random((2,2))        Create an array with random values                                                                                                                                                                                                                  >>> a < 2                              Element-wise comparison
             >>> np.empty((3,2))                Create an empty array                                                                                                                                                                                                                                 array([True, False, False], dtype=bool)                                                                                                                                                                                                                                         Combining Arrays
                                                                                                                                                                                                                                                                                                    >>> np.array_equal(a, b)               Array-wise comparison                                                                                                                                                                                                                   >>> np.concatenate((a,d),axis=0) Concatenate arrays
             I/O                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     array([ 1,  2,  3, 10, 15, 20])
                                                                                                                                                                                                                                                                                                         Aggregate Functions                                                                                                                                                                                                                                                       >>> np.vstack((a,b))             Stack arrays vertically (row-wise)
                        Saving & Loading On Disk                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     array([[ 1. ,  2. ,  3. ],
                                                                                                                                                                                                                                                                                                    >>> a.sum()                     Array-wise sum                                                                                                                                                                                                                                          [ 1.5,  2. ,  3. ],
                   >>> np.save('my_array', a)                                                                                                                                                                                                                                                       >>> a.min()                     Array-wise minimum value                                                                                                                                                                                                                                [ 4. ,  5. ,  6. ]])
                   >>> np.savez('array.npz', a, b)                                                                                                                                                                                                                                                  >>> b.max(axis=0)               Maximum value of an array row                                                                                                                                                                                                                  >>> np.r_[e,f]                   Stack arrays vertically (row-wise)
                   >>> np.load('my_array.npy')                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     >>> np.hstack((e,f))             Stack arrays horizontally (column-wise)
                                                                                                                                                                                                                                                                                                    >>> b.cumsum(axis=1)            Cumulative sum of the elements                                                                                                                                                                                                                   array([[ 7.,  7.,  1.,  0.], 
                      Saving & Loading Text Files                                                                                                                                                                                                                                                   >>> a.mean()                    Mean                                                                                                                                                                                                                                                    [ 7.,  7.,  0.,  1.]])
                                                                                                                                                                                                                                                                                                    >>> b.median()                  Median                                                                                                                                                                                                                                         >>> np.column_stack((a,d))       Create stacked column-wise arrays
                   >>> np.loadtxt("myfile.txt")                                                                                                                                                                                                                                                     >>> a.corrcoef()                Correlation coefficient                                                                                                                                                                                                                          array([[ 1, 10],
                   >>> np.genfromtxt("my_file.csv", delimiter=',')                                                                                                                                                                                                                                  >>> np.std(b)                   Standard deviation                                                                                                                                                                                                                                      [ 2, 15],
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            [ 3, 20]])
                   >>> np.savetxt("myarray.txt", a, delimiter=" ")                                                                                                                                                                                                                              Copying Arrays                                                                                                                                                                                                                                                                     >>> np.c_[a,d]                   Create stacked column-wise arrays
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      Splitting Arrays
             Data Types                                                                                                                                                                                                                                                                             >>> h = a.view()          Create a view of the array with the same data                                                                                                                                                                                                        >>> np.hsplit(a,3)               Split the array horizontally at the 3rd      
                >>> np.int64          Signed 64-bit integer types                                                                                                                                                                                                                                   >>> np.copy(a)            Create a copy of the array                                                                                                                                                                                                                               [array([1]),array([2]),array([3])]    index
                >>> np.float32         Standard double-precision floating point                                                                                                                                                                                                                     >>> h = a.copy()          Create a deep copy of the array                                                                                                                                                                                                                      >>> np.vsplit(c,2)               Split the array vertically at the 2nd index
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   [array([[[ 1.5,  2. ,  1. ],
                >>> np.complex        Complex numbers represented by 128 floats                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             [ 4. ,  5. ,  6. ]]]), 
                >>> np.bool           Boolean type storing TRUE and FALSE values                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     array([[[ 3.,  2.,  3.],
                >>> np.object         Python object type                                                                                                                                                                                                                                         Sorting Arrays                                                                                                                                                                                                                                                                              [ 4.,  5.,  6.]]])]
                >>> np.string_        Fixed-length string type                                                                                                                                                                                                                                   >>> a.sort()                 Sort an array                                                                                                                                                                                                                                                                                                                                                           DataCamp
                >>> np.unicode_       Fixed-length unicode type                                                                                                                                                                                                                                  >>> c.sort(axis=0)           Sort the elements of an array's axis                                                                                                                                                                                                                                                                                                     Learn Python for Data Science Interactively
            Python For Data Science Cheat Sheet                                                                                                                            Linear Algebra                                                                                                                                                                                                                                                               Also see NumPy
                                               SciPy - Linear Algebra                                                                                                         You’ll use the linalg and sparse modules. Note that  scipy.linalg contains and expands on  numpy.linalg. 
                  Learn More Python for Data Science Interactively at  www.datacamp.com                                                                                     >>> from scipy import linalg, sparse                                                                                                                                Matrix Functions
                                                                                                                                                                               Creating Matrices                                                                                                                                               Addition
                                                                                                                                                                           >>> A = np.matrix(np.random.random((2,2)))                                                                                                                        >>> np.add(A,D)                      Addition
        SciPy                                                                                                                                                              >>> B = np.asmatrix(b)                                                                                                                                             Subtraction
         The SciPy library is one of the core packages for                                                                                                                 >>> C = np.mat(np.random.random((10,5)))                                                                                                                          >>> np.subtract(A,D)                 Subtraction
                                                                                                                                                                           >>> D = np.mat([[3,4], [5,6]])                                                                                                                                     Division
         scientific computing that provides mathematical                                                                                                                     Basic Matrix Routines                                                                                                                                           >>> np.divide(A,D)                   Division
         algorithms and convenience functions built on the                                                                                                                                                                                                                                                                                    Multiplication
         NumPy extension of Python.                                                                                                                                           Inverse                                                                                                                                                        >>> np.multiply(D,A)                 Multiplication
                                                                                                                                                                            >>> A.I                        Inverse                                                                                                                           >>> np.dot(A,D)                      Dot product
                                                                                                                           Also see NumPy                                   >>> linalg.inv(A)              Inverse                                                                                                                           >>> np.vdot(A,D)                     Vector dot product
        Interacting With NumPy                                                                                                                                              >>> A.T                        Tranpose matrix                                                                                                                   >>> np.inner(A,D)                    Inner product
          >>> import numpy as np                                                                                                                                            >>> A.H                        Conjugate transposition                                                                                                           >>> np.outer(A,D)                    Outer product
          >>> a = np.array([1,2,3])                                                                                                                                         >>> np.trace(A)                Trace                                                                                                                             >>> np.tensordot(A,D)                Tensor dot product
          >>> b = np.array([(1+5j,2j,3j), (4j,5j,6j)])                                                                                                                        Norm                                                                                                                                                           >>> np.kron(A,D)                     Kronecker product
          >>> c = np.array([[(1.5,2,3), (4,5,6)], [(3,2,1), (4,5,6)]])                                                                                                                                                                                                                                                                         Exponential Functions
                                                                                                                                                                            >>> linalg.norm(A)             Frobenius norm                                                                                                                    >>> linalg.expm(A)                   Matrix exponential  
            Index Tricks                                                                                                                                                    >>> linalg.norm(A,1)           L1 norm (max column sum)                                                                                                          >>> linalg.expm2(A)                  Matrix exponential (Taylor Series)
                                                                                                                                                                            >>> linalg.norm(A,np.inf)      L inf norm (max row sum)                                                                                                          >>> linalg.expm3(D)                  Matrix exponential (eigenvalue 
         >>> np.mgrid[0:5,0:5]             Create a dense meshgrid                                                                                                            Rank                                                                                                                                                                                                                                                        decomposition)
         >>> np.ogrid[0:2,0:2]                                                 Create an open meshgrid                                                                      >>> np.linalg.matrix_rank(C)   Matrix rank                                                                                                                         Logarithm Function
         >>> np.r_[[3,[0]*5,-1:1:10j]     Stack arrays vertically (row-wise)                                                                                                                                                                                                                                                                 >>> linalg.logm(A)                   Matrix logarithm 
         >>> np.c_[b,c]                                            Create stacked column-wise arrays                                                                          Determinant                                                                                                                                                      Trigonometric Tunctions
            Shape Manipulation                                                                                                                                              >>> linalg.det(A)              Determinant                                                                                                                       >>> linalg.sinm(D)                   Matrix sine
                                                                                                                                                                              Solving linear problems                                                                                                                                        >>> linalg.cosm(D)                   Matrix cosine
         >>> np.transpose(b)           Permute array dimensions                                                                                                             >>> linalg.solve(A,b)          Solver for dense matrices                                                                                                         >>> linalg.tanm(A)                   Matrix tangent
         >>> b.flatten()                Flatten the array                                                                                                                   >>> E = np.mat(a).T            Solver for dense matrices                                                                                                           Hyperbolic Trigonometric Functions
         >>> np.hstack((b,c))          Stack arrays horizontally (column-wise)                                                                                              >>> linalg.lstsq(D,E)          Least-squares solution to linear matrix                                                                                           >>> linalg.sinhm(D)                  Hypberbolic matrix sine
         >>> np.vstack((a,b))          Stack arrays vertically (row-wise)                                                                                                                                                                                      equation                                                                      >>> linalg.coshm(D)                  Hyperbolic matrix cosine
         >>> np.hsplit(c,2)            Split the array horizontally at the 2nd index                                                                                           Generalized inverse                                                                                                                                           >>> linalg.tanhm(A)                  Hyperbolic matrix tangent
         >>> np.vpslit(d,2)                                                Split the array vertically at the 2nd index                                                      >>> linalg.pinv(C)             Compute the pseudo-inverse of a matrix                                                                                              Matrix Sign Function 
            Polynomials                                                                                                                                                                                                                                        (least-squares solver)                                                        >>> np.sigm(A)                       Matrix sign function
                                                                                                                                                                            >>> linalg.pinv2(C)            Compute the pseudo-inverse of a matrix                                                                                              Matrix Square Root
         >>> from numpy import poly1d                                                                                                                                                                                                                           (SVD)                                                                        >>> linalg.sqrtm(A)                  Matrix square root
         >>> p = poly1d([3,4,5])          Create a polynomial object                                                                                                          Creating Sparse Matrices                                                                                                                                         Arbitrary Functions
            Vectorizing Functions                                                                                                                                                                                                                                                                                                            >>> linalg.funm(A, lambda x: x*x)    Evaluate matrix function
         >>> def myfunc(a):                                                                                                                                                >>> F = np.eye(3, k=1)         Create a 2X2 identity matrix
                              if a < 0:                                                                                                                                    >>> G = np.mat(np.identity(2)) Create a 2x2 identity matrix                                                                                                          Decompositions
                     return a*2                                                                                                                                            >>> C[C > 0.5] = 0 
                   else:                                                                                                                                                   >>> H = sparse.csr_matrix(C)   Compressed Sparse Row matrix                                                                                                         Eigenvalues and Eigenvectors
                     return a/2                                                                                                                                            >>> I = sparse.csc_matrix(D)   Compressed Sparse Column matrix                                                                                                    >>> la, v = linalg.eig(A)       Solve ordinary or generalized 
         >>> np.vectorize(myfunc)         Vectorize functions                                                                                                              >>> J = sparse.dok_matrix(A)   Dictionary Of Keys matrix                                                                                                                                                                                                eigenvalue problem for square matrix
                                                                                                                                                                           >>> E.todense()                Sparse matrix to full matrix                                                                                                       >>> l1, l2 = la                 Unpack eigenvalues
            Type Handling                                                                                                                                                  >>> sparse.isspmatrix_csc(A)   Identify sparse matrix                                                                                                             >>> v[:,0]                      First eigenvector
        >>> np.real(c)              Return the real part of the array elements                                                                                                                                                                                                                                                               >>> v[:,1]                      Second eigenvector
        >>> np.imag(c)              Return the imaginary part of the array elements                                                                                           Sparse Matrix Routines                                                                                                                                         >>> linalg.eigvals(A)           Unpack eigenvalues
        >>> np.real_if_close(c,tol=1000) Return a real array if complex parts close to 0                                                                                     Inverse                                                                                                                                                           Singular Value Decomposition 
        >>> np.cast['f'](np.pi)            Cast object to a data type                                                                                                                                                                                   Inverse                                                                              >>> U,s,Vh = linalg.svd(B)      Singular Value Decomposition (SVD)  
                                                                                                                                                                           >>> sparse.linalg.inv(I)                                                                                                                                          >>> M,N = B.shape                 
            Other Useful Functions                                                                                                                                           Norm                                                                                                                                                            >>> Sig = linalg.diagsvd(s,M,N) Construct sigma matrix in SVD
        >>> np.angle(b,deg=True)   Return the angle of the complex argument                                                                                                >>> sparse.linalg.norm(I)       Norm                                                                                                                                LU Decomposition
        >>> g = np.linspace(0,np.pi,num=5) Create an array of evenly spaced values                                                                                          Solving linear problems                                                                                                                                          >>> P,L,U = linalg.lu(C)        LU Decomposition
                                                                                                                              (number of samples)                          >>> sparse.linalg.spsolve(H,I)  Solver for sparse matrices
        >>> g [3:] += np.pi                                                                                                                                                                                                                                                                                                                    Sparse Matrix Decompositions
        >>> np.unwrap(g)             Unwrap                                                                                                                                   Sparse Matrix Functions
        >>> np.logspace(0,10,3)     Create an array of evenly spaced values (log scale)                                                                                                                                                                                                                                                      >>> la, v = sparse.linalg.eigs(F,1)  Eigenvalues and eigenvectors
        >>> np.select([c<4],[c*2])  Return values from a list of arrays depending on                                                                                       >>> sparse.linalg.expm(I)       Sparse matrix exponential                                                                                                         >>> sparse.linalg.svds(H, 2)         SVD
                                                                                  conditions
        >>> misc.factorial(a)      Factorial       
        >>> misc.comb(10,3,exact=True)  Combine N things taken at k time                                                                                                   Asking For Help
        >>> misc.central_diff_weights(3)   Weights for Np-point central derivative                                                                                       >>> help(scipy.linalg.diagsvd)                                                                                                                                                                                              DataCamp
        >>> misc.derivative(myfunc,1.0)   Find the n-th derivative of a function at a point                                                                              >>> np.info(np.matrix)                                                                                                                                                                            Learn Python for Data Science Interactively
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