python-data-analysis/3-Numpy.slides.html at master · hsbarbosa/python-data-analysis · GitHub

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<h1 id="Numpy----multidimensional-data-arrays">Numpy -  multidimensional data arrays<a class="anchor-link" href="#Numpy----multidimensional-data-arrays">&#182;</a></h1><h2 id="Introduction">Introduction<a class="anchor-link" href="#Introduction">&#182;</a></h2><p>NumPy is the fundamental package for scientific computing with Python. It contains among other things:</p>
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<p>First, we need to import the Numpy module. Python has few different ways to import a module.</p>

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<div class=" highlight hl-ipython2"><pre><span class="kn">import</span> <span class="nn">numpy</span>
<span class="k">print</span> <span class="n">numpy</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">numpy</span><span class="o">.</span><span class="n">pi</span><span class="p">)</span>
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<pre>-1.0
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<div class=" highlight hl-ipython2"><pre><span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span>
<span class="k">print</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="p">)</span>
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<pre>-1.0
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<div class=" highlight hl-ipython2"><pre><span class="kn">from</span> <span class="nn">numpy</span> <span class="kn">import</span> <span class="o">*</span>
<span class="k">print</span> <span class="n">cos</span><span class="p">(</span><span class="n">pi</span><span class="p">)</span>
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<p>Even though the last one makes it simpler to use the module functions, importing all the objects of a module is not a good idea, especially for a large one like the numpy.</p>
<ul>
<li>The numpy namespace can conflict with the namespace of other modules (e.g., the math module) or user-defined functions </li>
<li>It polutes your variables namespace with hundreds of objects you probably are not going to use.</li>
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<div class=" highlight hl-ipython2"><pre><span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span>
<span class="k">print</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="p">)</span>
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<pre>-1.0
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<div class=" highlight hl-ipython2"><pre><span class="o">%</span><span class="k">who</span>
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<pre>np
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<div class=" highlight hl-ipython2"><pre><span class="kn">from</span> <span class="nn">numpy</span> <span class="kn">import</span> <span class="o">*</span>
<span class="k">print</span> <span class="n">cos</span><span class="p">(</span><span class="n">pi</span><span class="p">)</span>
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<pre>ALLOW_THREADS	 BUFSIZE	 CLIP	 ComplexWarning	 DataSource	 ERR_CALL	 ERR_DEFAULT	 ERR_DEFAULT2	 ERR_IGNORE
ERR_LOG	 ERR_PRINT	 ERR_RAISE	 ERR_WARN	 FLOATING_POINT_SUPPORT	 FPE_DIVIDEBYZERO	 FPE_INVALID	 FPE_OVERFLOW	 FPE_UNDERFLOW
False_	 Inf	 Infinity	 MAXDIMS	 MachAr	 ModuleDeprecationWarning	 NAN	 NINF	 NZERO
NaN	 PINF	 PZERO	 PackageLoader	 RAISE	 RankWarning	 SHIFT_DIVIDEBYZERO	 SHIFT_INVALID	 SHIFT_OVERFLOW
SHIFT_UNDERFLOW	 ScalarType	 True_	 UFUNC_BUFSIZE_DEFAULT	 UFUNC_PYVALS_NAME	 WRAP	 absolute	 add	 add_docstring
add_newdoc	 add_newdoc_ufunc	 add_newdocs	 alen	 all	 allclose	 alltrue	 alterdot	 amax
amin	 angle	 any	 append	 apply_along_axis	 apply_over_axes	 arange	 arccos	 arccosh
arcsin	 arcsinh	 arctan	 arctan2	 arctanh	 argmax	 argmin	 argpartition	 argsort
argwhere	 around	 array	 array2string	 array_equal	 array_equiv	 array_repr	 array_split	 array_str
asanyarray	 asarray	 asarray_chkfinite	 ascontiguousarray	 asfarray	 asfortranarray	 asmatrix	 asscalar	 atleast_1d
atleast_2d	 atleast_3d	 average	 bartlett	 base_repr	 binary_repr	 bincount	 bitwise_and	 bitwise_not
bitwise_or	 bitwise_xor	 blackman	 bmat	 bool8	 bool_	 broadcast	 broadcast_arrays	 busday_count
busday_offset	 busdaycalendar	 byte	 byte_bounds	 bytes_	 c_	 can_cast	 cast	 cdouble
ceil	 cfloat	 char	 character	 chararray	 choose	 clip	 clongdouble	 clongfloat
column_stack	 common_type	 compare_chararrays	 complex128	 complex256	 complex64	 complex_	 complexfloating	 compress
concatenate	 conj	 conjugate	 convolve	 copy	 copysign	 copyto	 corrcoef	 correlate
cos	 cosh	 count_nonzero	 cov	 cross	 csingle	 ctypeslib	 cumprod	 cumproduct
cumsum	 datetime64	 datetime_as_string	 datetime_data	 deg2rad	 degrees	 delete	 deprecate	 deprecate_with_doc
diag	 diag_indices	 diag_indices_from	 diagflat	 diagonal	 diff	 digitize	 disp	 divide
dot	 double	 dsplit	 dstack	 dtype	 e	 ediff1d	 einsum	 emath
empty	 empty_like	 equal	 errstate	 euler_gamma	 exp	 exp2	 expand_dims	 expm1
extract	 eye	 fabs	 fastCopyAndTranspose	 fft	 fill_diagonal	 find_common_type	 finfo	 fix
flatiter	 flatnonzero	 flexible	 fliplr	 flipud	 float128	 float16	 float32	 float64
float_	 floating	 floor	 floor_divide	 fmax	 fmin	 fmod	 format_parser	 frexp
frombuffer	 fromfile	 fromfunction	 fromiter	 frompyfunc	 fromregex	 fromstring	 full	 full_like
fv	 generic	 genfromtxt	 get_array_wrap	 get_include	 get_numarray_include	 get_printoptions	 getbuffer	 getbufsize
geterr	 geterrcall	 geterrobj	 gradient	 greater	 greater_equal	 half	 hamming	 hanning
histogram	 histogram2d	 histogramdd	 hsplit	 hstack	 hypot	 i0	 identity	 iinfo
imag	 in1d	 index_exp	 indices	 inexact	 inf	 info	 infty	 inner
insert	 int0	 int16	 int32	 int64	 int8	 int_	 int_asbuffer	 intc
integer	 interp	 intersect1d	 intp	 invert	 ipmt	 irr	 is_busday	 isclose
iscomplex	 iscomplexobj	 isfinite	 isfortran	 isinf	 isnan	 isneginf	 isposinf	 isreal
isrealobj	 isscalar	 issctype	 issubclass_	 issubdtype	 issubsctype	 iterable	 ix_	 kaiser
kron	 ldexp	 left_shift	 less	 less_equal	 lexsort	 linalg	 linspace	 little_endian
load	 loads	 loadtxt	 log	 log10	 log1p	 log2	 logaddexp	 logaddexp2
logical_and	 logical_not	 logical_or	 logical_xor	 logspace	 longcomplex	 longdouble	 longfloat	 longlong
lookfor	 ma	 mafromtxt	 mask_indices	 mat	 math	 matrix	 maximum	 maximum_sctype
may_share_memory	 mean	 median	 memmap	 meshgrid	 mgrid	 min_scalar_type	 minimum	 mintypecode
mirr	 mod	 modf	 msort	 multiply	 nan	 nan_to_num	 nanargmax	 nanargmin
nanmax	 nanmean	 nanmin	 nanstd	 nansum	 nanvar	 nbytes	 ndarray	 ndenumerate
ndfromtxt	 ndim	 ndindex	 nditer	 negative	 nested_iters	 newaxis	 newbuffer	 nextafter
nonzero	 not_equal	 np	 nper	 npv	 number	 obj2sctype	 object0	 object_
ogrid	 ones	 ones_like	 outer	 packbits	 pad	 partition	 percentile	 pi
piecewise	 pkgload	 place	 pmt	 poly	 poly1d	 polyadd	 polyder	 polydiv
polyfit	 polyint	 polymul	 polysub	 polyval	 power	 ppmt	 prod	 product
promote_types	 ptp	 put	 putmask	 pv	 r_	 rad2deg	 radians	 random
rank	 rate	 ravel	 ravel_multi_index	 real	 real_if_close	 rec	 recarray	 recfromcsv
recfromtxt	 reciprocal	 record	 remainder	 repeat	 require	 reshape	 resize	 restoredot
result_type	 right_shift	 rint	 roll	 rollaxis	 roots	 rot90	 round_	 row_stack
s_	 safe_eval	 save	 savetxt	 savez	 savez_compressed	 sctype2char	 sctypeDict	 sctypeNA
sctypes	 searchsorted	 select	 set_numeric_ops	 set_printoptions	 set_string_function	 setbufsize	 setdiff1d	 seterr
seterrcall	 seterrobj	 setxor1d	 shape	 short	 show_config	 sign	 signbit	 signedinteger
sin	 sinc	 single	 singlecomplex	 sinh	 size	 sometrue	 sort	 sort_complex
source	 spacing	 split	 sqrt	 square	 squeeze	 std	 str_	 string0
string_	 subtract	 sum	 swapaxes	 take	 tan	 tanh	 tensordot	 tile
timedelta64	 trace	 transpose	 trapz	 tri	 tril	 tril_indices	 tril_indices_from	 trim_zeros
triu	 triu_indices	 triu_indices_from	 true_divide	 trunc	 typeDict	 typeNA	 typecodes	 typename
ubyte	 ufunc	 uint	 uint0	 uint16	 uint32	 uint64	 uint8	 uintc
uintp	 ulonglong	 unicode0	 unicode_	 union1d	 unique	 unpackbits	 unravel_index	 unsignedinteger
unwrap	 ushort	 vander	 var	 vdot	 vectorize	 void	 void0	 vsplit
vstack	 where	 who	 zeros	 zeros_like
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<h2 id="Creating-numpy-arrays">Creating <code>numpy</code> arrays<a class="anchor-link" href="#Creating-numpy-arrays">&#182;</a></h2><p>In the <code>numpy</code> package the terminology used for vectors, matrices and higher-dimensional data sets is <em>array</em>.</p>
<p>There are a number of ways to initialize new numpy arrays, for example from</p>
<ul>
<li>a Python list or tuples</li>
<li>using functions that are dedicated to generating numpy arrays, such as <code>arange</code>, <code>linspace</code>, etc.</li>
<li>reading data from files</li>
</ul>
<h3 id="From-lists">From lists<a class="anchor-link" href="#From-lists">&#182;</a></h3><p>For example, to create new vector and matrix arrays from Python lists we can use the <code>numpy.array</code> function.</p>

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<div class=" highlight hl-ipython2"><pre><span class="c"># a vector: the argument to the array function is a Python list</span>
<span class="n">v</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">])</span>

<span class="n">v</span>
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<pre>array([1, 2, 3, 4])</pre>
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<div class=" highlight hl-ipython2"><pre><span class="c"># a matrix: the argument to the array function is a nested Python list</span>
<span class="n">M</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">]])</span>

<span class="n">M</span>
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<pre>array([[1, 2],
       [3, 4]])</pre>
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<p>The <code>v</code> and <code>M</code> objects are both of the type <code>ndarray</code> that the <code>numpy</code> module provides.</p>

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<div class=" highlight hl-ipython2"><pre><span class="nb">type</span><span class="p">(</span><span class="n">v</span><span class="p">),</span> <span class="nb">type</span><span class="p">(</span><span class="n">M</span><span class="p">)</span>
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<pre>(numpy.ndarray, numpy.ndarray)</pre>
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<p>The difference between the <code>v</code> and <code>M</code> arrays is only their shapes. We can get information about the shape of an array by using the <code>ndarray.shape</code> property.</p>

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<div class=" highlight hl-ipython2"><pre><span class="n">M</span><span class="o">.</span><span class="n">size</span>
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<pre>4</pre>
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<div class=" highlight hl-ipython2"><pre><span class="n">v</span><span class="o">.</span><span class="n">size</span>
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<pre>4</pre>
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<div class=" highlight hl-ipython2"><pre><span class="n">v</span><span class="o">.</span><span class="n">shape</span>
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<pre>(4,)</pre>
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<div class=" highlight hl-ipython2"><pre><span class="n">M</span><span class="o">.</span><span class="n">shape</span>
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<pre>(2, 2)</pre>
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<p>The number of elements in the array is available through the <code>ndarray.size</code> property:</p>

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<div class=" highlight hl-ipython2"><pre><span class="n">M</span><span class="o">.</span><span class="n">size</span>
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<pre>4</pre>
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<p>So far the <code>numpy.ndarray</code> looks awefully much like a Python list (or nested list). Why not simply use Python lists for computations instead of creating a new array type?</p>
<p>There are several reasons:</p>
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<li>Python lists are very general. They can contain any kind of object. They are dynamically typed. They do not support mathematical functions such as matrix and dot multiplications, etc. Implementating such functions for Python lists would not be very efficient because of the dynamic typing.</li>
<li>Numpy arrays are <strong>statically typed</strong> and <strong>homogeneous</strong>. The type of the elements is determined when array is created.</li>
<li>Numpy arrays are memory efficient.</li>
<li>Because of the static typing, fast implementation of mathematical functions such as multiplication and addition of <code>numpy</code> arrays can be implemented in a compiled language (C and Fortran is used).</li>
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<p>Using the <code>dtype</code> (data type) property of an <code>ndarray</code>, we can see what type the data of an array has:</p>

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<div class=" highlight hl-ipython2"><pre><span class="n">M</span><span class="o">.</span><span class="n">dtype</span>
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<pre>dtype(&apos;int64&apos;)</pre>
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<p>We get an error if we try to assign a value of the wrong type to an element in a numpy array:</p>

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<div class=" highlight hl-ipython2"><pre><span class="n">M</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="s">&quot;hello&quot;</span>
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<pre>
<span class="ansired">---------------------------------------------------------------------------</span>
<span class="ansired">ValueError</span>                                Traceback (most recent call last)
<span class="ansigreen">&lt;ipython-input-12-a09d72434238&gt;</span> in <span class="ansicyan">&lt;module&gt;</span><span class="ansiblue">()</span>
<span class="ansigreen">----&gt; 1</span><span class="ansiyellow"> </span>M<span class="ansiyellow">[</span><span class="ansicyan">0</span><span class="ansiyellow">,</span><span class="ansicyan">0</span><span class="ansiyellow">]</span> <span class="ansiyellow">=</span> <span class="ansiblue">&quot;hello&quot;</span><span class="ansiyellow"></span>

<span class="ansired">ValueError</span>: invalid literal for long() with base 10: &apos;hello&apos;</pre>
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<p>If we want, we can explicitly define the type of the array data when we create it, using the <code>dtype</code> keyword argument:</p>

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<div class=" highlight hl-ipython2"><pre><span class="n">M</span> <span class="o">=</span> <span class="n">array</span><span class="p">([[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">]],</span> <span class="n">dtype</span><span class="o">=</span><span class="nb">complex</span><span class="p">)</span>

<span class="n">M</span>
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<pre>array([[ 1.+0.j,  2.+0.j],
       [ 3.+0.j,  4.+0.j]])</pre>
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<p>Common type that can be used with <code>dtype</code> are: <code>int</code>, <code>float</code>, <code>complex</code>, <code>bool</code>, <code>object</code>, etc.</p>
<p>We can also explicitly define the bit size of the data types, for example: <code>int64</code>, <code>int16</code>, <code>float128</code>, <code>complex128</code>.</p>

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