session-01_part-02_intro_to_numpy_and_matplotlib.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Numpy and Matplotlib #\n",
    "\n",
    "These are two of the most fundamental parts of the scientific python \"ecosystem\". Most everything else is built on top of them.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What did we just do? We _imported_ a package. This brings new variables (mostly functions) into our interpreter. We access them as follows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['In', 'Out', '_', '__', '___', '__builtin__', '__builtins__', '__doc__', '__loader__', '__name__', '__package__', '__spec__', '_dh', '_i', '_i1', '_i2', '_ih', '_ii', '_iii', '_oh', 'exit', 'get_ipython', 'np', 'quit']\n"
     ]
    }
   ],
   "source": [
    "# find out what is in our namespace\n",
    "print(dir())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['ALLOW_THREADS', 'AxisError', 'BUFSIZE', 'CLIP', 'ComplexWarning', 'DataSource', 'ERR_CALL', 'ERR_DEFAULT', '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', 'MAY_SHARE_BOUNDS', 'MAY_SHARE_EXACT', 'MachAr', 'ModuleDeprecationWarning', 'NAN', 'NINF', 'NZERO', 'NaN', 'PINF', 'PZERO', 'PackageLoader', 'RAISE', 'RankWarning', 'SHIFT_DIVIDEBYZERO', 'SHIFT_INVALID', 'SHIFT_OVERFLOW', 'SHIFT_UNDERFLOW', 'ScalarType', 'Tester', 'TooHardError', 'True_', 'UFUNC_BUFSIZE_DEFAULT', 'UFUNC_PYVALS_NAME', 'VisibleDeprecationWarning', 'WRAP', '_NoValue', '__NUMPY_SETUP__', '__all__', '__builtins__', '__cached__', '__config__', '__doc__', '__file__', '__git_revision__', '__loader__', '__name__', '__package__', '__path__', '__spec__', '__version__', '_distributor_init', '_globals', '_import_tools', '_mat', '_numpy_tester', 'abs', 'absolute', 'absolute_import', 'add', 'add_docstring', 'add_newdoc', 'add_newdoc_ufunc', 'add_newdocs', 'alen', 'all', 'allclose', 'alltrue', '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', 'bench', 'binary_repr', 'bincount', 'bitwise_and', 'bitwise_not', 'bitwise_or', 'bitwise_xor', 'blackman', 'block', 'bmat', 'bool', 'bool8', 'bool_', 'broadcast', 'broadcast_arrays', 'broadcast_to', 'busday_count', 'busday_offset', 'busdaycalendar', 'byte', 'byte_bounds', 'bytes0', 'bytes_', 'c_', 'can_cast', 'cast', 'cbrt', 'cdouble', 'ceil', 'cfloat', 'char', 'character', 'chararray', 'choose', 'clip', 'clongdouble', 'clongfloat', 'column_stack', 'common_type', 'compare_chararrays', 'compat', 'complex', 'complex128', 'complex256', 'complex64', 'complex_', 'complexfloating', 'compress', 'concatenate', 'conj', 'conjugate', 'convolve', 'copy', 'copysign', 'copyto', 'core', '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', 'division', 'divmod', 'dot', 'double', 'dsplit', 'dstack', 'dtype', 'e', 'ediff1d', 'einsum', 'einsum_path', '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', 'flip', 'fliplr', 'flipud', 'float', 'float128', 'float16', 'float32', 'float64', 'float_', 'float_power', 'floating', 'floor', 'floor_divide', 'fmax', 'fmin', 'fmod', 'format_float_positional', 'format_float_scientific', 'format_parser', 'frexp', 'frombuffer', 'fromfile', 'fromfunction', 'fromiter', 'frompyfunc', 'fromregex', 'fromstring', 'full', 'full_like', 'fv', 'generic', 'genfromtxt', 'geomspace', 'get_array_wrap', 'get_include', 'get_printoptions', 'getbufsize', 'geterr', 'geterrcall', 'geterrobj', 'gradient', 'greater', 'greater_equal', 'half', 'hamming', 'hanning', 'heaviside', 'histogram', 'histogram2d', 'histogramdd', 'hsplit', 'hstack', 'hypot', 'i0', 'identity', 'iinfo', 'imag', 'in1d', 'index_exp', 'indices', 'inexact', 'inf', 'info', 'infty', 'inner', 'insert', 'int', 'int0', 'int16', 'int32', 'int64', 'int8', 'int_', 'int_asbuffer', 'intc', 'integer', 'interp', 'intersect1d', 'intp', 'invert', 'ipmt', 'irr', 'is_busday', 'isclose', 'iscomplex', 'iscomplexobj', 'isfinite', 'isfortran', 'isin', 'isinf', 'isnan', 'isnat', 'isneginf', 'isposinf', 'isreal', 'isrealobj', 'isscalar', 'issctype', 'issubclass_', 'issubdtype', 'issubsctype', 'iterable', 'ix_', 'kaiser', 'kron', 'ldexp', 'left_shift', 'less', 'less_equal', 'lexsort', 'lib', 'linalg', 'linspace', 'little_endian', 'load', 'loads', 'loadtxt', 'log', 'log10', 'log1p', 'log2', 'logaddexp', 'logaddexp2', 'logical_and', 'logical_not', 'logical_or', 'logical_xor', 'logspace', 'long', 'longcomplex', 'longdouble', 'longfloat', 'longlong', 'lookfor', 'ma', 'mafromtxt', 'mask_indices', 'mat', 'math', 'matmul', 'matrix', 'matrixlib', 'max', 'maximum', 'maximum_sctype', 'may_share_memory', 'mean', 'median', 'memmap', 'meshgrid', 'mgrid', 'min', 'min_scalar_type', 'minimum', 'mintypecode', 'mirr', 'mod', 'modf', 'moveaxis', 'msort', 'multiply', 'nan', 'nan_to_num', 'nanargmax', 'nanargmin', 'nancumprod', 'nancumsum', 'nanmax', 'nanmean', 'nanmedian', 'nanmin', 'nanpercentile', 'nanprod', 'nanstd', 'nansum', 'nanvar', 'nbytes', 'ndarray', 'ndenumerate', 'ndfromtxt', 'ndim', 'ndindex', 'nditer', 'negative', 'nested_iters', 'newaxis', 'nextafter', 'nonzero', 'not_equal', 'nper', 'npv', 'numarray', 'number', 'obj2sctype', 'object', 'object0', 'object_', 'ogrid', 'oldnumeric', 'ones', 'ones_like', 'outer', 'packbits', 'pad', 'partition', 'percentile', 'pi', 'piecewise', 'pkgload', 'place', 'pmt', 'poly', 'poly1d', 'polyadd', 'polyder', 'polydiv', 'polyfit', 'polyint', 'polymul', 'polynomial', 'polysub', 'polyval', 'positive', 'power', 'ppmt', 'print_function', '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', 'result_type', 'right_shift', 'rint', 'roll', 'rollaxis', 'roots', 'rot90', 'round', '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', 'shares_memory', 'short', 'show_config', 'sign', 'signbit', 'signedinteger', 'sin', 'sinc', 'single', 'singlecomplex', 'sinh', 'size', 'sometrue', 'sort', 'sort_complex', 'source', 'spacing', 'split', 'sqrt', 'square', 'squeeze', 'stack', 'std', 'str', 'str0', 'str_', 'string_', 'subtract', 'sum', 'swapaxes', 'sys', 'take', 'tan', 'tanh', 'tensordot', 'test', 'testing', 'tile', 'timedelta64', 'trace', 'tracemalloc_domain', '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', 'unicode', 'unicode_', 'union1d', 'unique', 'unpackbits', 'unravel_index', 'unsignedinteger', 'unwrap', 'ushort', 'vander', 'var', 'vdot', 'vectorize', 'version', 'void', 'void0', 'vsplit', 'vstack', 'warnings', 'where', 'who', 'zeros', 'zeros_like']\n"
     ]
    }
   ],
   "source": [
    "# find out what's in numpy\n",
    "print(dir(np))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'1.14.2'"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# find out what version we have\n",
    "np.__version__"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The numpy documentation is crucial!\n",
    "\n",
    "http://docs.scipy.org/doc/numpy/reference/\n",
    "\n",
    "## NDArrays ##\n",
    "\n",
    "The core class is the numpy ndarray (n-dimensional array)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<img src=\"http://docs.scipy.org/doc/numpy/_images/threefundamental.png\"/>"
      ],
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import Image\n",
    "Image(url='http://docs.scipy.org/doc/numpy/_images/threefundamental.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# create an array from a list\n",
    "a = np.array([9, 0, 2, 1, 0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('int64')"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# find out the datatype\n",
    "a.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5,)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# find out the shape\n",
    "a.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tuple"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# what is the shape\n",
    "type(a.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# another array with a different datatype and shape\n",
    "b = np.array([[5, 3, 1, 9], [9, 2, 3, 0]], dtype=np.float64)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(dtype('float64'), (2, 4))"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# check dtype and shape\n",
    "b.dtype, b.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Important Concept__: The fastest varying dimension is the last dimension! The outer level of the hierarchy is the first dimension. (This is called \"c-style\" indexing.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## More array creation ##\n",
    "\n",
    "There are lots of ways to create arrays."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# create some uniform arrays\n",
    "c = np.zeros((9, 9))\n",
    "d = np.ones((3, 6, 3), dtype=np.complex128)\n",
    "e = np.full((3, 3), np.pi)\n",
    "e = np.ones_like(c)\n",
    "f = np.zeros_like(d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# create some ranges\n",
    "np.arange(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2.  , 2.25, 2.5 , 2.75, 3.  , 3.25, 3.5 , 3.75])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# arange is left inclusive, right exclusive\n",
    "np.arange(2, 4, 0.25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2.        , 2.10526316, 2.21052632, 2.31578947, 2.42105263,\n",
       "       2.52631579, 2.63157895, 2.73684211, 2.84210526, 2.94736842,\n",
       "       3.05263158, 3.15789474, 3.26315789, 3.36842105, 3.47368421,\n",
       "       3.57894737, 3.68421053, 3.78947368, 3.89473684, 4.        ])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# linearly spaced\n",
    "np.linspace(2, 4, 20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 10.        ,  12.91549665,  16.68100537,  21.5443469 ,\n",
       "        27.82559402,  35.93813664,  46.41588834,  59.94842503,\n",
       "        77.42636827, 100.        ])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# log spaced\n",
    "np.logspace(1, 2, 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((50, 100), (50, 100))"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# two dimensional grids\n",
    "x = np.linspace(-2 * np.pi, 2 * np.pi, 100)\n",
    "y = np.linspace(-np.pi, np.pi, 50)\n",
    "xx, yy = np.meshgrid(x, y)\n",
    "xx.shape, yy.shape  # Note that shape is an attribute of a numpy array !"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Indexing ##\n",
    "\n",
    "Basic indexing is similar to lists"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-6.283185307179586, 6.283185307179586, 5.775453161144872)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# get some individual elements of xx\n",
    "xx[0, 0], xx[-1, -1], xx[3, -5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((100,), (50,))"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# get some whole rows and columns\n",
    "xx[0].shape, xx[:, -1].shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(7, 10)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# get some ranges\n",
    "xx[3:10, 30:40].shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are many advanced ways to index arrays. You can read about them in the manual. Here is one example."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2500,)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# use a boolean array as an index\n",
    "idx = xx < 0\n",
    "yy[idx].shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5000,)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# the array got flattened\n",
    "xx.ravel().shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[0;31mDocstring:\u001b[0m\n",
       "a.ravel([order])\n",
       "\n",
       "Return a flattened array.\n",
       "\n",
       "Refer to `numpy.ravel` for full documentation.\n",
       "\n",
       "See Also\n",
       "--------\n",
       "numpy.ravel : equivalent function\n",
       "\n",
       "ndarray.flat : a flat iterator on the array.\n",
       "\u001b[0;31mType:\u001b[0m      builtin_function_or_method\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xx.ravel?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Array Operations ##\n",
    "\n",
    "There are a huge number of operations available on arrays. All the familiar arithemtic operators are applied on an element-by-element basis.\n",
    "\n",
    "### Basic Math ##"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "f = np.sin(xx) * np.cos(0.5 * yy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "At this point you might be getting curious what these arrays \"look\" like. So we need to introduce some visualization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.pcolormesh(f);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Manipulating array dimensions ##"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# transpose\n",
    "plt.pcolormesh(f.T);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "_We'll get into `matplotlib` later. If you're curious now, check the\n",
    "documentation: <https://matplotlib.org/>_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Modifying the shape of arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(50, 100)\n"
     ]
    },
    {
     "ename": "ValueError",
     "evalue": "cannot reshape array of size 5000 into shape (8,9)",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-28-141499b05982>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;31m# reshape an array (wrong size)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m \u001b[0mg\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mreshape\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0;36m8\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m9\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m~/miniconda3_20171008/envs/py3_std_course/lib/python3.6/site-packages/numpy/core/fromnumeric.py\u001b[0m in \u001b[0;36mreshape\u001b[0;34m(a, newshape, order)\u001b[0m\n\u001b[1;32m    255\u001b[0m            [5, 6]])\n\u001b[1;32m    256\u001b[0m     \"\"\"\n\u001b[0;32m--> 257\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0m_wrapfunc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'reshape'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnewshape\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0morder\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0morder\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    258\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    259\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/miniconda3_20171008/envs/py3_std_course/lib/python3.6/site-packages/numpy/core/fromnumeric.py\u001b[0m in \u001b[0;36m_wrapfunc\u001b[0;34m(obj, method, *args, **kwds)\u001b[0m\n\u001b[1;32m     50\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m_wrapfunc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mobj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmethod\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwds\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     51\u001b[0m     \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 52\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mgetattr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mobj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmethod\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwds\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     53\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     54\u001b[0m     \u001b[0;31m# An AttributeError occurs if the object does not have\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mValueError\u001b[0m: cannot reshape array of size 5000 into shape (8,9)"
     ]
    }
   ],
   "source": [
    "# reshape an array (wrong size)\n",
    "print(f.shape)\n",
    "g = np.reshape(f, (8, 9))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5000\n"
     ]
    }
   ],
   "source": [
    "# reshape an array (right size) and mess it up\n",
    "print(f.size)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "g = np.reshape(f, (200, 25))\n",
    "plt.pcolormesh(g);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# tile an array\n",
    "plt.pcolormesh(np.tile(f, (6, 1)));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Broadcasting ##\n",
    "\n",
    "Broadcasting is an efficient way to multiply arrays of different sizes\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<img src=\"http://scipy-lectures.github.io/_images/numpy_broadcasting.png\" width=\"720\"/>"
      ],
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Image(url='http://scipy-lectures.github.io/_images/numpy_broadcasting.png',\n",
    "      width=720)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(50, 100) (100,)\n",
      "(50, 100)\n"
     ]
    }
   ],
   "source": [
    "# multiply f by x\n",
    "print(f.shape, x.shape)\n",
    "g = f * x\n",
    "print(g.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(50, 100) (50,)\n"
     ]
    },
    {
     "ename": "ValueError",
     "evalue": "operands could not be broadcast together with shapes (50,100) (50,) ",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-34-10fa0d4ac112>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;31m# multiply f by y\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m \u001b[0mh\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mf\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      4\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mh\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mValueError\u001b[0m: operands could not be broadcast together with shapes (50,100) (50,) "
     ]
    }
   ],
   "source": [
    "# multiply f by y\n",
    "print(f.shape, y.shape)\n",
    "h = f * y\n",
    "print(h.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(50, 100)\n"
     ]
    }
   ],
   "source": [
    "# use newaxis special syntax\n",
    "h = f * y[:, np.newaxis]\n",
    "print(h.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.pcolormesh(g);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Reduction Operations ##\n",
    "\n",
    "_(Note that `.sum()`, `.mean()` etc. are **methods** defined for the numpy array class.)_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-3083.038387807155"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# sum\n",
    "g.sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.616607677561431"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# mean\n",
    "g.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.6402280119141424"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# std\n",
    "g.std()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# apply on just one axis\n",
    "g_ymean = g.mean(axis=0)\n",
    "g_xmean = g.mean(axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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oG53kr39ezrh7cVsGRzsG+eSvqli5JJ77b1yzqPcyg9hIJ6V5LnbVSp/dzCTYQ8Du6aPN7Npff7e1WYk8dOdGDrT0c9+jVYv2MrVjYJyP/M9+YiLDeOTuzZbdC2auLi9K48jJQU4NGTsDSZyfBHsI2FXXxZKEKIrSrbVl7ELcsHYpX3rval6o7uTrzx0J+PWHxt185Kf7GRxz88jdm8lMMvf5pYHkf/J7XWbHmJYEu815vD5er+vm8qJUSx3wEAh/ddkyPnJpPo+80cCDzx8N2MrUgVE3H/3pfmo7h3j4Q6WsyUwMyHWtYvXSBFJiI+SQaxMz9ynGYsEOtg4wOO4JmTbMu33pvasZd3t5+NUTdAyO82/vW7+gqYht/WPc/cg+mnpGeejOjSHx3uLdHA7F5UWp7K7rxufTOGy0utYuZMRuc7tqu1AKS51tGkhhDsU3bl3H328v5onKNv7qZ+UMjrvnda2a9kHe9/CbdAyM89OPbubG9faeAXMh24rT6BmZpObkoNGliHMISLArpW5QSh1TSh1XSn0uENcUgfH68W7WZyXissFujvOllOK+7UX82/vW8cbxbrZ/+zWeOdg+69bM6KSHf3v+KDf/1+toNI/du5VLCkPzB6Wf//St3dJnN6UFB7tSKgz4PvAeYDXwAaWU9TegtoGRCQ8HW/rZGuIh5Pf+zbk8ce8lZCRE8alfV/GXP9nHm8e7cXvPfZbnwJibxytaufY/dvGDV0+wY1MWz33qclYuSQhy5eaTHj/1Mn6PHJdnSoHosW8Bjmut6wGUUo8CtwA1Abj2Oxxo6aexe4Qdm7ICfWlbKm/qw+PTbC1MMboU09iQk8RTH7+UX73VxIMvHOMvfvwWidHhXL0yndzpfdN9WlPV3M/e+h48Ps2KjHh+87Gttl61Ox9bC1N4vKIVt9dn2y0UAql/dJI/HO7gyhVpLE1c3FlUgQj2LODMI2xagYve/UFKqXuAewByc3PndaOnqtr4bUUrt2zMDLkZHvOx50QPToeiLM9ldCmmEuZQ/OXWfN5Xms2u2m521nTyx6Od9I3+qfdekBbLX19ewLWrM9iUkyQvCM9ha0EKP9/TxNut/ZTmyQ+9mRzrGOLzTxzif/9qiyWC/Vxf8Wc1L7XWPwJ+BFBWVjaveWfZrmiGJjwMjLlJigndnvFs7anvYUNOErGRMvnpXGIinNywdgk3rF1idCmWdFHB1JPgnhM9Euyz0Dy9j31uEE7UCsTzUyuQc8avs4H2AFz3LP6/kGbZ6H9GQ+NuDrcNsLVA2jBicSTHRrBySbz02WeppXcUhyIoi9kCEez7gSKl1DKlVARwJ/BMAK57Fv+ueRLsMytv7MMr/XWxyLYWplDe2Cfb+M5Cc+8oSxOjg/I+YsF30Fp7gE8ALwBHgN9orasXet1zyXFJsM/WnvoeIsIclEp/XSyirQUpTHh8HGjuN7oU02vuHQ1KGwYCNI9da/17rXWx1rpQa/31QFzzXGIjnaTGRciZi7Ow50QPG3OTbL1NrzDeRctSUAppx8xCc++YtYI9mHKSY2TEPoOBMTfV7dJfF4svMSacNZkJ7DkhwX4ho5MeuocngnYIi+WCPTc5hpbeMaPLMLV9Db34NFwswS6C4OJlKVQ19y/63vdW1to3lVk5MmI/txxXDG39Y3jOs1pQTLVhIpwONuUmGV2KCAFbC1OY9PqobJLj8s6nuSd4Ux3BgsGemxyD16c5OSCb/J/P3voeSnNd0l8XQbFlWTIONfV1J84tmHPYwYLBniNz2S9ocNzNkY5BWf4ugiY+KpzVmQnsa+w1uhTTau4dJS7SiSsmPCj3s1ywy1z2C6to6kNrJNhFUG3OT6aquZ9Jj7RIz6Wld5RsV3TQtkKxXLAvSYgiPExJsJ/H/oZenA4l/XURVFvyk5nw+DjcPmB0KaYUzDnsYMFgD3Mosl0y5fF89jf2siYrkZgI2R9GBE9Z/tQT4v4Gace8m9aalj4J9hnlJMfQKsF+lnG3l4MtA2zJl9WmIrjS4iMpSI1lv/TZz9I1PMG42xe0Oexg1WB3RcuI/RwOtQ0w6fWxOV/66yL4yvJd7G/sw+cLzKHhduFfKR+sOexg0WDPTY6hb9Q977Mr7Wrf9GOwBLswwub8ZAbG3NSdGja6FFMJ9lRHsHCwA7JnzLvsb+ylKD0upM83Fcbxz8SSaY/v1NwzhlKQFYTtev0sGew5Euxn8fo0FY19bJZpjsIguckxpMdHUi7B/g7NvaMsSYgK6oJBSwa7zGU/29GOQYYmPGyWF6fCIEopNi9Llpkx79LSOxrU/jpYNNgTosJJigmXzcDOsF/668IEtuQn0z4wTmufDLr8WvpGT58lESyWDHaY2gxMRux/sr+xj8zEKLKD/AUkxJnKpp8YZdrjlHG3l47B8aC+OAULB/vU9r0S7DC1AGJ/Y6/014XhVi5JID7Syb4G2ekRoK1/DK0hNyV4L07BwsGekxxDS98oXpkzS2vfGKeGJiiTY/CEwcIcik15LqqaJdjhT+8BpRUzS/kpMbi9mpMD0mevnP4mKs2TEbswXlmei2OdQwyMyTqTpu4RAPJTY4N6X8sGe17K1F9UU4+0Y8ob+4iNCGPFknijSxGC0jwXWsOBFjngurFnarvelCCvLbFwsE892jT2jBhcifEqmvrYlOsizBGcLUGFuJANOUk41NTXZahr6hkhNzkmaNv1+lk22JckRBHhdIT8iH14wsPRjkFKpL8uTCIu0snKJQlUNMnMmKaeUfJTgz9TzbLB7nAo8pJjaOwO7RH7wZZ+fBp5cSpMpSzfxYHm/pA+m9jrm9qu1982DibLBjtM9dlDfS57eWMfSsFGOVhDmEhpnouRSS/HOoeMLsUw7f1juL2a/CBu1+tn6WDPT4mhsWcErUN3ymNFcx8rMuJJiArOWYpCzEZJ7tQTZCj32f1tYhmxz1Feaizjbh+nhiaMLsUQPp+mqqmPUmnDCJPJdkWTkRAZ0sHun9iRL8E+N/5HnFDts9edGmZowiPBLkxHKUVpniukg72pZ4SocAfp8ZFBv7fFgz2057KXT886kGAXZlSS66K1b4zOwXGjSzFEY88oecmxOAyYhmzpYF+aGIXToUJ2LntFUx+pcRFB32BIiNnwDzhCddTe1DMS1HNOz2TpYHeGOchJjgnZEXvldH892IsfhJiNNZmJRDodlDeGXrD7fHpqDrsE+/zkTc+MCTXdwxM09oyenn0ghNlEOB2sz048vZdRKOkcGmfC4zNkRgzYINjzU2Jp6hkNuSmPVc1T+3DIilNhZiW5LqrbBxh3e40uJagau6e6CEbMiAEbBHteSgzDEx56RiaNLiWoKpv7cDoU67ISjS5FiPPalOvC7dVUtw8YXUpQNU13EfKkFTM/f5oZE1rtmMqmPtZkJgT1gFwh5qokb2pFtP8JM1Q09owSHqbITAruARt+lg/207s8dofOC1SP18fbrQNskv66MLn0+CiyXdEh12dv6hkhJznGsB1XLR/s2a4YHCq0RuxHO4YYc3ulvy4soSTXRWVT6I3Yjeqvgw2CPcLpIMsVTVMIbQbmH/2UyMZfwgJKcpPoGBynvT80TjvTWtPcM2JYfx1sEOwAecmxNIbQXPbKpj7S4yPJMqh/J8Rc+J8sQ6Ud0z08yciklzwDFw7aI9hTYkKqFVPZ3M+m3CRZmCQsYeWSBCKdjpBpx5yeERPkc07PtKBgV0rdoZSqVkr5lFJlgSpqrvJTYukfddM/av8pj93DEzT3ysIkYR2htlCpodu4XR39FjpiPwzcBuwKQC3ztmz6J+OJLvuP2mVhkrCiUFqoVN89gtOhyHYZ1ypdULBrrY9orY8Fqpj5KkibCvb6rmGDK1l8sjBJWFEoLVSq7xomNyWG8DDjOt1Bu7NS6h6lVLlSqryrqyug185JjsHpUKcfgexMFiYJKwqlhUoN3SMUpMYZWsOMwa6Uekkpdfgc/90ylxtprX+ktS7TWpelpaXNv+JzCA9zkJsSQ73NWzGyMElYVagsVPL6NI09oxSmGddfB3DO9AFa6+3BKGShClLjqO+2dytGFiYJKyvJdbGvodfoMhZVW98Ykx7f6fawUWwx3RGgMG1qLrvXZ99dHv2jnU05sjBJWM+mEFiodGJ6cLnM7K2YC1FK3aqUagW2As8ppV4ITFlzV5AWy6THR1uffb9oqpr7SYuPNPRtuxDz5Z+ia+c+u78dbOkRu9b6Sa11ttY6UmudobW+PlCFzZX/J+QJG7djKpv7KJGFScKiVi2dXqhk4z57fdcwCVFOUmIjDK3DNq0Y/0/IBpu+QO0enqCpZ1RenArLinA6WJdl74VKDd0jFKTFGT74sk2wp8RGkBDltO0L1AP+hUkS7MLCSvJcVLcNMuGx50Kl+q4Rw9swYKNgV0pRkBZn2ymPsjBJ2EFJbhKTXh/V7YNGlxJwIxMeOgbHKTBwjxg/2wQ7TLVj7Bzsq5YmEB0hC5OEdflbiZVN9mvH+BdIFqQZOyMGbBbshWlxdAyOMzLhMbqUgPIvTJL914XVZSREkZUUTVWL/WbGnJje0kRaMQHmfwSy29YCxzqHGJ2UhUnCHjblJlFlwxF7fdcIShm7q6OfrYJ9WZp/l0d7vUCtnH5xuilHgl1Y36ZcF+0D43QMjBtdSkDVd4+QlRRtin2cbBXs+SmxKGW/EXtVcx+pcRHkJMvCJGF9/pZilc2mPTZ0D5uivw42C/ao8DCykqJt9wK1qrmfTbkuw+fGChEIazITibDZQiWtNQ1dI6aYEQM2C3aYeiNtp7nsvSOTNHSPsElenAqbiHA6WJuZcLrFaAedgxOMTHpN8eIU7BjsqbE0dI2gtT02A/M/rpbKwiRhI6V5Lg61DdhmoZL/kB+j92H3s12wF6bFMjLppXNwwuhSAqKiaWph0vpsGbEL+yjJdTHpsc9CpRPd5tj8y89+wZ4+9ROz7tSQwZUERmVzH6szZWGSsBf/1F27LFQ63jlEbEQYSxOjjC4FsGGwF2fEA1Dbaf0+u8fr42DLgOwPI2wnI8FeJyrVdg6zPCPeNBMcbBfsqXGRJMdGUNdp/RG7nJgk7Kwk10VFU58t3ofVnRqiON0c/XWwYbADFKXHUWuDYK+YfkwtlWAXNlSa56JzcIJ2iy9U6h2ZpHt48nS3wAxsGezFGfHUdQ5bfiRQ2dxHRkIkmSbp2wkRSCU22RDMP4gsypAR+6IqzohjaHoLTSuraOqjNE8WJgl7Wrk0nujwsNNPplblb/vKiH2RLU+3/gvUU4PjtPaNyYtTYVvhYQ425CRafmuB2s5h4iOdppkRAzYN9uLpRyIrv0D1zxaQF6fCzkpyXVS3DzI2ad2FSrWdQyzPMP44vDPZMthT4iJJiY2gzsIj9oqmPiKcDtZkJhhdihCLpjTPhcenebvVutsLHD81THG6edowYNNgh6kXGbUWXqRU2dzPuqxEIp2yMEnY1+kTlSy6b0zP8AQ9I5OmenEKNg724ox4jlt0ZsyEx8uh1gGZ5ihsLzk2goLUWMu+QPW/xzPTi1OwcbAXZcQzNOHhpAXnyB5uG2TS65Oj8ERIKMlzUdlszYVK/q1LJNiDxL8KzIoLlcobewEoy082uBIhFt/mfBe9I5PUW/CAnNrOIeKjnGQkRBpdyjvYN9inf4Ja8QXq/sY+lqXGkhpnri8WIRZDad7UAMY/oLGS2s5hik20R4yfbYPdFRtBalyk5UbsPp+moqmXMumvixBRmBaLKyac/Y3W6rNrranrHDo9vdpMbBvsMDWfvfaUtUbs9d3D9I262SxtGBEilFKU5SdbbsTePTxJ36ibIpNNdQTbB3s8xzuHLPVSxj9qKcuXEbsIHZvzXTT2jNI1ZJ0DcupMuEeMn62DvSgjjpFJL239Y0aXMmvljX2kxEawzCSH4goRDP6JAhVN1hm115pwjxg/Wwf7ium/8KMnrdNnL2/qpSxfNv4SoWVtZiKRToel+uxHO4ZIigknPd58kxxsHewrlyagFNSctMa5iqcGx2nqGZX+ugg5EU4HG3OSLNVnrzk5yJrMBFMOwmwd7HGRTvJTYqluHzC6lFkpb/L31yXYRejZnJ/M4fZBRic9RpcyI7fXx9GOIVYvNedeTrbWflaRAAARU0lEQVQOdoDVmQmWOQl9f2MvUeGy8ZcITWX5Lrw+zQEL7BtzomuYSY+PNZmJRpdyTrYP9jWZCbT2jTEw6ja6lBmVN/axKcdFeJjt/1mEOEtJngulsESfvbptarBo1kGY7RPE/xPV7H324QkP1e0DbJZpjiJEJUSFs3JJAuUWmBlTc3KQqHAHBWnmm+oIIRDs/h6Y2fvsVc19+DSUSn9dhLDN+S4qmvpwe31Gl3JB1e0DrFySQJjDfC9OIQSCPS0+kvT4SGpM3mffW99DmEPJVgIipF20LIXRSS+H28w7ENNaU9M+yGqTtmFggcGulPqWUuqoUuptpdSTSilT7jO7xgIvUPfW97I+O5HYSKfRpQhhmIsKpp5Y99abtx3T2jfG4LjHtP11WPiIfSewVmu9HqgFPr/wkgJvTWYix7uGGXeb81zF0UkPb7f2c3FBitGlCGGo1LhIitLjeKuhx+hSzsvf1jXrjBhYYLBrrV/UWvsnne4FshdeUuCtyUzA69Om3emxsqkft1dLsAsBXFyQwv6GXjwm7bPXtA/iULByifm2EvALZI/9o8AfAni9gPH3wszajpH+uhB/cnFBCiOTXg6b9Pu1un2QwrQ4osLNex7xjMGulHpJKXX4HP/dcsbHfBHwAL+8wHXuUUqVK6XKu7q6AlP9LOW4YoiPdJp2Zsze+h7prwsx7U99dnO2Y6rbB03dX4dZBLvWervWeu05/nsaQCl1F3Aj8EF9gf1xtdY/0lqXaa3L0tLSAvcZzILDoVhl0heoo5MeDkp/XYjT/H12MwZ7z/AEHYPjpu6vw8JnxdwA/BNws9Z6NDAlLY41mQkcPTmE12euvdmlvy7E2czaZ/cvdLT8iH0G/wXEAzuVUgeUUj8MQE2LYk1mImNuLw0mOzDX318vlf66EKddVJBsyj67/6nfzHPYARbU1NVaLw9UIYttbdbUP8Shtn6Wp5tnGfDe+h7WZSUSJ/11IU67aNnUE+ze+h425phnecyh1gGykqJJiokwupQLsv3KU7+i9HjiIp1UNpln5zjprwtxbmnxkSw3YZ+9srmPEgs8XYdMsIc5FBtzkqhoMs/OcX/qr8v+MEK828UFyexv6DXNvjHt/WOcHBinNNc8TxDnEzLBDlCSm8TRjkFGJsyxkf/u412Ehyk5MUmIc7i0MJWRSS8HW8zxlF3ZPDUolBG7yWzKc+HTcLDVHF8ou2q7Kc1zyfx1Ic7hksJUHAp21QZ33cv5VDb1ExXuYJVJT006U0gFe0nO1E/aKhOc0HJqaJwjJwfZVhzcOf1CWEViTDgbc5LYVddtdCnA1Ih9fVaSJQ7CMX+FAZQYE05hWqwp+uxvHJ/6Yt1WJMEuxPlcXpTG26399I9OGlrHuNtLdfsAm/LM31+HEAt2gNI8F1XNfVxgkWxQ7KrtJjk2wrSH4QphBtuKU/FpeOO4sbNjqtsHcHs1pbnm769DCAZ7Sa6LvlG3oQuVfD7N7rpuLlueisOkJ7AIYQYbspOIj3Kyu87YPrv/Kd8KL04hFIN9+h+m0sA++9GOIbqHJ6S/LsQMnGEOLi1MZXddt6FP2ZVN/eQmx5AaF2lYDXMRcsG+PC2O+CinoX32XdOjj8uLUg2rQQiruLw4lbb+MU50GfOUrbWeWphkgfnrfiEX7A6HYlPuVJ/dKLvruliREU9GQpRhNQhhFf4JBka1Y9r6xzg1NGGp/ZxCLthhaqHSsc4hhsbdQb/32KSX/Q19MloXYpZykmPIT4lht0HTHv1t200WeXEKIRvsLrSGAwasaNvb0MOk1yf9dSHmYFtxGntO9DDhCf65xZVNfcREhJn6KLx3C81gz3PhdCj2nAj+FKqXj3QSHR7GlmWyjYAQs3XlijTG3F5Dvmf3nOihJNeF0wILk/ysU2kAxUU6Kcl1Bf3RzufT7Kzp5IriNFOflyiE2VxSmEpMRBgv1nQG9b6dg+Mc6xxiW7G1WqchGewwNSPlcPsAPcMTQbvnwdZ+OgcnuG5NRtDuKYQdRIWHceWKNHbWdOIL4ilo/sHf5RZbIR66wV6chtbwRhAf7V6s6STMobhmpQS7EHN1/ZoldA1NUBXEd2O767pIjYu0VH8dQjjY12Ulkhgdzu4g7hz3YnUHFxckkxgTHrR7CmEXV65Ix+lQvFjTEZT7+Xya1+u62VaUilLWWiEessEe5lBctjx4K9qOnxrmRNcI169Zsuj3EsKOEqPD2VqYwovVnUH5nq05OUjPyCSXW6y/DiEc7DDVZ+8YHOf4qeFFv5d/lLF9lbRhhJiv69YsoaF7JCjfs/7++qXLJdgt5bLpRULB2O/5xepO1mcnkpkUvej3EsKurp0eGAVjdszuui5WLU0gPd56K8RDOtizXTEUpMUu+lLljoFxDrT0SxtGiAVakhjFxpwkXqhe3D776KSH8sY+tll0hXhIBztM7UOxt35xV7T52zDXrZY2jBALdd2aDN5uHaCtf2zR7vFWQy+TXp/lpjn6hXywX16UyrjbR0Xj4m0K9tvKNlYuiWd5etyi3UOIUHHT+kwAnqxsXbR77K7tJtLpoCzfOvvDnCnkg/3ighQinI5Fe7Sr6xziYEs/t5dmW27KlBBmlJMcw8UFyTxe0boos2O01rxY08HWwhTLrhAP+WCPjXSyfVU6v3v7JG6vL+DXf6yiFadDceumrIBfW4hQdUdpDo09o+xfhCftiqY+WvvGuHlDZsCvHSwhH+wAOzZm0TMyyevHAzs7xu318URlG1evTCfFIievCGEF71m3hLhIJ4+VtwT82k8daCMq3MF1Fp7sIMHO1Iq2xOhwnq5qC+h1XzvWRffwBHeU5QT0ukKEupgIJ+9dt5TnDp1kZMITsOtOenz87u2TXLd66geHVUmwAxFOB3+2bikvVHcG9IvksYoWUuMiuHKFNd+sC2Fmd5RlMzrp5feHTgbsmrtqu+gfdbNjk3XbMCDBftqtm7IYc3vZGaCFDz3DE7x85BQ7NmYRbqF9nIWwitI8F8tSY3msInCzY5480EZybIRlpzn6SeJMK8tzkZUUzVMHAtOOebKqDY9PSxtGiEWilOL20mz2NfTS0L3wg66Hxt28VNPJe9cttfxgzNrVB5DDobh5Yya767rpXuAe7RMeLz/e3cCW/GRWWGy7TyGs5I6ybCKdDn7w6vEFX+uF6k4mPD522GAGmwT7GW7dlIXXp3lqgS9Rf7O/hY7BcT51TVGAKhNCnEt6fBQf2JLLE5VttPSOLuhav61oJTc5hpLcpABVZxwJ9jMUZ8SzJT+Z/95dz7h7flsMTHi8PPzqCUrzXFy6PCXAFQoh3u3eKwtxOBTff2X+o/b9jb3sqe/hLy7KtcVCQgn2d/n0dcV0Dk7wi71N8/rzj1e0cnJgnPuuKbLFF4gQZpeREMUHNufweEXrvEbtWmv+/YVjpMZF8uGteYtQYfBJsL/LxQUpXLY8lR+8emLOUx8nPT4efuUEm3KTuNyiu8IJYUV/c2UhDqV4+NUTc/6zb57o4a2GXj5+VSExEdadu34mCfZz+PR1xfSMTPKzPY1z+nOPVbTQ1j8mo3UhgmxpYjTv35zD4xUtcxq1a6359ovHWJo41au3Cwn2cyjJdXH1ynT+32v1DI67Z/Vn6ruG+cZzR9iSn8wVxdaeAyuEFd17ZSERYQ7ue7Rq1vs+vXqsi8rmfj55dZFlN/w6Fwn28/j0tcUMjLn59gvHZvzYcbeXv/1lJRFOB9+9c6OM1oUwQGZSNN9833oqm/t58PmjM3788ISHf/3DEXKTY7ijLDsIFQbPgoJdKfVVpdTbSqkDSqkXlVLWXod7hrVZidx9ST4/29PED1+7cN/uy89Uc7RjiP94/0Y5+k4IA920IZMPb83jv3c38OIFtuIed3u55+flnOga4Su3rLH8gqR3W+hn8y2t9Xqt9Ubgd8D9AajJNO6/cTU3bcjkm384yqP7ms/6fZ9P85PXG3h0fwsfv6qQq1akG1ClEOJMX3zvKtZlJfIPjx3kQEv/Wb/v8fq479Eq3jzRw7duX8+VNvy+XdArYK314Bm/jAUCv+u9gRwOxbfv2MDgmJsvPHmIkwPjXLEijXVZiVQ29fG1545wqG2AK4rT+PvtxUaXK4QAIp1hPPzBEm77wZvs+P4b3LYpi8/csILYSCcVjX383/4WXqju5P4bV3Nbib1aMH5qoSeQKKW+DnwYGACu0lrPeDJ0WVmZLi8vX9B9g2l00sPH/reC3XVT+7VHOh1MeHwsTYziszes4JYNWTgc0lcXwkyGxt18/5UTPPJ6AwBunw+tITxMcd81RXziauutDFdKVWity2b8uJmCXSn1EnCuHee/qLV++oyP+zwQpbX+l/Nc5x7gHoDc3NzSpqb5LQAyUtfQBPsbe9nX0MuSxCju2ppPdIR93qQLYUctvaP85PUGkmLC2bIsmU05Lst+3wYs2OdwwzzgOa312pk+1mojdiGEMIPZBvtCZ8Wc+SxzMzDzHCMhhBCLaqHrZ7+plFoB+IAm4G8WXpIQQoiFWOismPcFqhAhhBCBYa9Z+UIIISTYhRDCbiTYhRDCZiTYhRDCZiTYhRDCZgK2QGlON1Wqi6npkYGWCnQvwnWDxer1g/U/B6vXD9b/HKxePyze55CntZ7xwAdDgn2xKKXKZ7Mqy6ysXj9Y/3Owev1g/c/B6vWD8Z+DtGKEEMJmJNiFEMJm7BbsPzK6gAWyev1g/c/B6vWD9T8Hq9cPBn8OtuqxCyGEsN+IXQghQp4tg10p9Uml1DGlVLVS6kGj65kPpdQ/KqW0UirV6FrmSin1LaXU0emDzp9USiUZXdNsKKVumP66Oa6U+pzR9cyFUipHKfWKUurI9Nf9fUbXNF9KqTClVJVS6ndG1zJXSqkkpdTj01//R5RSW42ow3bBrpS6CrgFWK+1XgP8u8ElzZlSKge4Fjj7BG1r2Ams1VqvB2qBzxtcz4yUUmHA94H3AKuBDyilVhtb1Zx4gH/QWq8CLgY+brH6z3QfcMToIubpIeB5rfVKYAMGfR62C3bgXuCbWusJAK31KYPrmY/vAJ/FooeDa61f1Fp7pn+5F7DCicFbgONa63qt9STwKFMDBEvQWp/UWldO/+8hpgIly9iq5k4plQ28F/ix0bXMlVIqAdgG/ARAaz2pte43ohY7BnsxcLlS6i2l1GtKqc1GFzQXSqmbgTat9UGjawmQjwJ/MLqIWcgCWs74dSsWDEYApVQ+sAl4y9hK5uW7TA1qfEYXMg8FQBfwP9OtpB8rpWKNKGShJygZ4kIHbDP1ObmYehzdDPxGKVWgTTT9Z4b6vwBcF9yK5m42h5wrpb7IVIvgl8GsbZ7UOf4/03zNzJZSKg74LfB3WutBo+uZC6XUjcAprXWFUupKo+uZBydQAnxSa/2WUuoh4HPAPxtRiOVorbef7/eUUvcCT0wH+T6llI+pfRu6glXfTM5Xv1JqHbAMOKiUgqkWRqVSaovWuiOIJc7oQv8GAEqpu4AbgWvM9EP1AlqBnDN+nQ20G1TLvCilwpkK9V9qrZ8wup55uBS4WSn1Z0AUkKCU+oXW+kMG1zVbrUCr1tr/pPQ4U8EedHZsxTwFXA2glCoGIrDIhkJa60Na63Stdb7WOp+pL5QSs4X6TJRSNwD/BNystR41up5Z2g8UKaWWKaUigDuBZwyuadbU1EjgJ8ARrfV/GF3PfGitP6+1zp7+2r8T+KOFQp3p79OW6XOgAa4BaoyoxZIj9hk8AjyilDoMTAJ3WWTEaCf/BUQCO6efPPZqrU190LnW2qOU+gTwAhAGPKK1rja4rLm4FPhL4JBS6sD0//cFrfXvDawpFH0S+OX04KAe+IgRRcjKUyGEsBk7tmKEECKkSbALIYTNSLALIYTNSLALIYTNSLALIYTNSLALIYTNSLALIYTNSLALIYTN/H+LPKUToRhVXwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, g_ymean);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(g_xmean, y);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Key concepts from this notebook\n",
    "\n",
    "- importing a module\n",
    "- inspecting the namespace\n",
    "- ndarrays\n",
    "- different ways of creating frequently used arrays\n",
    "- indexing\n",
    "- math with arrays\n",
    "- basic plotting (will be covered in detail later!)\n",
    "- broadcasting\n",
    "- reductions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Resources for Matlab users\n",
    "\n",
    "- [Numpy for matlab users from the Numpy docs](https://docs.scipy.org/doc/numpy/user/numpy-for-matlab-users.html)\n",
    "- [Matplotlib is heavily inspired by the MATLAB plotting syntax](https://matplotlib.org/users/pyplot_tutorial.html)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "*This notebook is based on a notebook from the [CC BY-NC 4.0 licensed](https://creativecommons.org/licenses/by/4.0/) course notes on [research computing by Ryan Abernathey et al.](https://rabernat.github.io/research_computing/).  The original notebook was downloaded from <https://raw.githubusercontent.com/rabernat/research_computing/master/content/lectures/python/numpy_and_matplotlib.ipynb> on 2018-02-21.  To track modifications relative to this original version, please check the history of <https://git.geomar.de/edu/python-intro-201804/>.*"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}