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<h1 id="Numpy----multidimensional-data-arrays">Numpy - multidimensional data arrays<a class="anchor-link" href="#Numpy----multidimensional-data-arrays">¶</a></h1><h2 id="Introduction">Introduction<a class="anchor-link" href="#Introduction">¶</a></h2><p>NumPy is the fundamental package for scientific computing with Python. It contains among other things:</p>
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<li>a powerful N-dimensional array object</li>
<li>sophisticated (broadcasting) functions</li>
<li>tools for integrating C/C++ and Fortran code</li>
<li>useful linear algebra, Fourier transform, and random number capabilities</li>
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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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<pre>-1.0
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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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<div class=" highlight hl-ipython2"><pre><span class="o">%</span><span class="k">who</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">¶</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">¶</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('int64')</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">"hello"</span>
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<pre>
<span class="ansired">---------------------------------------------------------------------------</span>
<span class="ansired">ValueError</span> Traceback (most recent call last)
<span class="ansigreen"><ipython-input-12-a09d72434238></span> in <span class="ansicyan"><module></span><span class="ansiblue">()</span>
<span class="ansigreen">----> 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">"hello"</span><span class="ansiyellow"></span>
<span class="ansired">ValueError</span>: invalid literal for long() with base 10: 'hello'</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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