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"source": [
"# Week I - Key Python Features for Coding Numerical Simulations"
]
},
{
"cell_type": "markdown",
"id": "3b25ff85",
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"source": [
"\n",
"## Dynamic typing\n",
"\n",
"Python is dynamically typed (opposed to static language such as C, C++, Fortran), hence:\n",
"\n",
"* Types are set on the values, not on the names, of the variables.\n",
"* Types do not need to be known before variables are actually used: variable types are checked at run time!\n",
"* Variable names can change types if their values are changed\n",
"\n",
"### Example"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "31e48d1a",
"metadata": {
"scrolled": true
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"outputs": [],
"source": [
"def inspect(x):\n",
" print('This object is: {}'.format(type(x)))\n",
" print('x = {}'.format(x))\n",
" return type(x)\n",
"\n",
"x = 2 \n",
"inspect(x)\n",
"\n",
"x = 3.2\n",
"inspect(x)\n",
"\n",
"x = 'Hello!'\n",
"inspect(x)\n"
]
},
{
"cell_type": "markdown",
"id": "5d367e84",
"metadata": {},
"source": [
"\n",
"## Shared references\n",
"\n",
"Python is *reference counted*, so variables names are just references to the underlying values. How many times a reference is used and what are its related names is counted internally.\n",
"Notably, multiple names can reference to the same object: **shared references**\n",
"\n",
"### Examples\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "bec4246d",
"metadata": {},
"outputs": [],
"source": [
"x = 5\n",
"y = x\n",
"print(id(x))\n",
"print(id(y))"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "200cf2c6",
"metadata": {},
"outputs": [],
"source": [
"help(id)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "7c3cf0da",
"metadata": {},
"outputs": [],
"source": [
"x = 3\n",
"print(id(x))\n",
"print(id(y))"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "70780769",
"metadata": {},
"outputs": [],
"source": [
"y = 4\n",
"print(id(x))\n",
"print(id(y))"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "7e674fbb",
"metadata": {},
"outputs": [],
"source": [
"x = ['a','b','c']\n",
"y = x\n",
"print(id(x))\n",
"print(id(y))"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "ebe8fe75",
"metadata": {},
"outputs": [],
"source": [
"x[1] = 'w'\n",
"print(x)\n",
"print(y)\n",
"print(id(x),id(y))"
]
},
{
"cell_type": "markdown",
"id": "2e3fbef4",
"metadata": {},
"source": [
"## Mutability\n",
"\n",
"In Python, data types can be either mutable or immutable:\n",
"\n",
"* **mutable** types allow values to change after creation, such as *lists, dictionaries, sets*\n",
"* **immutable** types are static and cannot change values, such as *int, float, bool, str, tuples*\n",
"\n",
"### Examples"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "e9e2d5e7",
"metadata": {},
"outputs": [],
"source": [
"lis = ['a','b','c']\n",
"tup = ('a','b','c')\n",
"print(lis)\n",
"print(id(lis),id(tup))\n",
"lis[2] = 'zz'\n",
"print(lis)\n",
"print(id(lis))\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "eba371b0",
"metadata": {},
"outputs": [],
"source": [
"try:\n",
" tup[2] = 'zz'\n",
"except TypeError as err:\n",
" print('Forbidden!',err)"
]
},
{
"cell_type": "markdown",
"id": "4ad9adbc",
"metadata": {},
"source": [
"\n",
"## Integers and Floats in Python\n",
"\n",
"Several numerical datatypes are available in Python, such as:\n",
"* *int*: integers, with unlimited precision!\n",
"* *float*: floating points, (usually) implemented with 'double' in C (check with sys.float_info)\n",
"* *complex*: two floats (get with z.real and z.imag)\n",
"\n",
"Other relevant numeric datatypes:\n",
"* *fractions.Fraction*, rational number arithmetics \n",
"* *decimal.Decimal*, floats with user-definable precision\n",
"\n",
"Numpy has its own datatypes, here some of the most relevant:\n",
"* np.half, np.single, np.double, np.longdouble (depends on platform!)\n",
"* np.float16 (alias of np.half), np.float32 (alias of np.single), np.float64 (alias of np.double), np.float128 (alias np.longdouble - existence depends on the platform!)\n",
"\n",
"For more details on extended precision, beyond 64 bits, check out https://numpy.org/doc/stable/user/basics.types.html#extended-precision"
]
},
{
"cell_type": "markdown",
"id": "e620a8e6",
"metadata": {},
"source": [
"-------------"
]
},
{
"cell_type": "markdown",
"id": "ec8f18da",
"metadata": {},
"source": [
"\n",
"### Week 1, Exercise - Underflow, overflow and machine precision\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "330ee8d6",
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"\n",
"def check_underflow_limit(float_type):\n",
" '''\n",
" Returns the underflow limit\n",
" '''\n",
" a = float_type(1.0)\n",
" while a>float_type(0.0):\n",
" under = a\n",
" a = a/float_type(2.0)\n",
" print('The calculated underflow limit is:{}'.format(under))\n",
"\n",
"def check_overflow_limit(float_type):\n",
" '''\n",
" Returns the overflow limit\n",
" '''\n",
" a = float_type(1.0)\n",
" while a!=float_type('Inf'):\n",
" over = a\n",
" a = a*float_type(2.0)\n",
" print('The calculated overflow limit is:{}'.format(over))\n",
"\n",
"def check_machine_precision(float_type):\n",
" '''\n",
" Returns machine precision\n",
" '''\n",
" eps = float_type(1.0)\n",
" while (float_type(1.0)+eps!=float_type(1.0)):\n",
" eps = eps/float_type(2.0)\n",
" print('The calcuated machine precision is:{}'.format(float_type(2)*eps))\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "121931e7",
"metadata": {},
"outputs": [],
"source": [
"for ft in [float,np.float16,np.float32,np.float64,np.longdouble]:\n",
" print(str(ft))\n",
" check_underflow_limit(ft)\n",
" check_overflow_limit(ft)\n",
" check_machine_precision(ft)\n",
" print('---------------')\n",
" #Compare with numpy results\n",
" print(np.finfo(ft))"
]
}
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