Lec_01_Python_intro_I.ipynb

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    "# Physics 300 \n",
    "## Computational Physics I (Fall 2018)\n",
    "## BPB-248, Mon/Wed 02:30 - 03:45 pm \n",
    "\n",
    "|Instructor| Prof. Qiang Zhu|\n",
    "|--|-------------------------------|\n",
    "|Email | qiang.zhu@unlv.edu|\n",
    "|Website|http://www.physics.unlv.edu/~qzhu/|\n",
    "|Office| BPB 232|\n",
    "|Office hours | Mon/Wed 03:45 - 05:00 pm |\n",
    "\n",
    "\n",
    "\n",
    "# 1 Python Basics\n",
    "## 1.1 Python Installation\n",
    "\n",
    "## Conda\n",
    "The best way set-up an scientific Python environment is to use the cross-platform package manager conda from Continuum Analytics. First download and install miniconda http://conda.pydata.org/miniconda.html or Anaconda (see below). Next, to install the required libraries for these notebooks, simply run:\n",
    "    \n",
    "    $ conda install jupyter spyder numpy scipy sympy matplotlib cython\n",
    "\n",
    "After you installed jupyter, you could run it from the anaconda terminal\n",
    "\n",
    "    $ jupyter notebook\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "hello, this is physics 300\n"
     ]
    }
   ],
   "source": [
    "#get started\n",
    "print(\"hello, this is physics 300\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1.2 Variables and types\n",
    "    Variable names in Python can contain alphanumerical characters a-z, A-Z, 0-9 and some special characters such as _. \n",
    "    Normal variable names must start with a letter.\n",
    "    By convention, variable names start with a lower-case letter, and Class names start with a capital letter.\n",
    "    In addition, there are a number of Python keywords that cannot be used as variable names. \n",
    "    $ and, as, assert, print......\n",
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# variable assignments\n",
    "#The assignment operator in Python is =. \n",
    "#Python is a dynamically typed language, different from C/C++, no need to specify the type of a variable\n",
    "\n",
    "x = '' #[] {}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " <class 'str'>\n"
     ]
    }
   ],
   "source": [
    "print(x, type(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "12 <class 'int'>\n"
     ]
    }
   ],
   "source": [
    "my_variable = 12\n",
    "print(my_variable, type(my_variable))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.0 1.0\n"
     ]
    }
   ],
   "source": [
    "# Fundamental Variables and types\n",
    "# integers\n",
    "# float\n",
    "# bollean\n",
    "# complex\n",
    "a = 1\n",
    "c = True\n",
    "d = 1+1.0j\n",
    "b = 2.0\n",
    "B = 1.0\n",
    "print(b, B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 <class 'int'>\n",
      "2.0 <class 'float'>\n",
      "True <class 'bool'>\n",
      "(1+1j) <class 'complex'>\n"
     ]
    }
   ],
   "source": [
    "print(a, type(a))\n",
    "print(b, type(b))\n",
    "print(c, type(c))\n",
    "print(d, type(d))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Quiz: \n",
    "    1, how to find the real and imaginary part for a complex variable\n",
    "    2, why do we need to set different types of variables for interger and float, instead of using just complex type?\n",
    "    3, how to define the variables in other languages like Matlab, C, C++, Java?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "complex_number = 1+1.0j"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "complex_number)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1.3 Operators and comparisons\n",
    "\n",
    "    Most operators and comparisons in Python work as one would expect:\n",
    "\n",
    "    Arithmetic operators +, -, *, /, // (integer division), '**' power\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3 -1 2 0.5 0 2\n",
      "False False True\n"
     ]
    }
   ],
   "source": [
    "x, y = 1, 2\n",
    "print(x+y, x-y, x*y, x/y, x//y, y**x)\n",
    "print(x>y, x==y, x<y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = 1\n",
    "y = 2\n",
    "x, y = 1, 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.8414709848078965 0.5403023058681398\n"
     ]
    }
   ],
   "source": [
    "# Advanced functions? sin, cos\n",
    "from math import sin, cos, tan, asin\n",
    "print(sin(x), cos(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import math"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
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     "text": [
      "Help on module math:\n",
      "\n",
      "NAME\n",
      "    math\n",
      "\n",
      "MODULE REFERENCE\n",
      "    https://docs.python.org/3.6/library/math\n",
      "    \n",
      "    The following documentation is automatically generated from the Python\n",
      "    source files.  It may be incomplete, incorrect or include features that\n",
      "    are considered implementation detail and may vary between Python\n",
      "    implementations.  When in doubt, consult the module reference at the\n",
      "    location listed above.\n",
      "\n",
      "DESCRIPTION\n",
      "    This module is always available.  It provides access to the\n",
      "    mathematical functions defined by the C standard.\n",
      "\n",
      "FUNCTIONS\n",
      "    acos(...)\n",
      "        acos(x)\n",
      "        \n",
      "        Return the arc cosine (measured in radians) of x.\n",
      "    \n",
      "    acosh(...)\n",
      "        acosh(x)\n",
      "        \n",
      "        Return the inverse hyperbolic cosine of x.\n",
      "    \n",
      "    asin(...)\n",
      "        asin(x)\n",
      "        \n",
      "        Return the arc sine (measured in radians) of x.\n",
      "    \n",
      "    asinh(...)\n",
      "        asinh(x)\n",
      "        \n",
      "        Return the inverse hyperbolic sine of x.\n",
      "    \n",
      "    atan(...)\n",
      "        atan(x)\n",
      "        \n",
      "        Return the arc tangent (measured in radians) of x.\n",
      "    \n",
      "    atan2(...)\n",
      "        atan2(y, x)\n",
      "        \n",
      "        Return the arc tangent (measured in radians) of y/x.\n",
      "        Unlike atan(y/x), the signs of both x and y are considered.\n",
      "    \n",
      "    atanh(...)\n",
      "        atanh(x)\n",
      "        \n",
      "        Return the inverse hyperbolic tangent of x.\n",
      "    \n",
      "    ceil(...)\n",
      "        ceil(x)\n",
      "        \n",
      "        Return the ceiling of x as an Integral.\n",
      "        This is the smallest integer >= x.\n",
      "    \n",
      "    copysign(...)\n",
      "        copysign(x, y)\n",
      "        \n",
      "        Return a float with the magnitude (absolute value) of x but the sign \n",
      "        of y. On platforms that support signed zeros, copysign(1.0, -0.0) \n",
      "        returns -1.0.\n",
      "    \n",
      "    cos(...)\n",
      "        cos(x)\n",
      "        \n",
      "        Return the cosine of x (measured in radians).\n",
      "    \n",
      "    cosh(...)\n",
      "        cosh(x)\n",
      "        \n",
      "        Return the hyperbolic cosine of x.\n",
      "    \n",
      "    degrees(...)\n",
      "        degrees(x)\n",
      "        \n",
      "        Convert angle x from radians to degrees.\n",
      "    \n",
      "    erf(...)\n",
      "        erf(x)\n",
      "        \n",
      "        Error function at x.\n",
      "    \n",
      "    erfc(...)\n",
      "        erfc(x)\n",
      "        \n",
      "        Complementary error function at x.\n",
      "    \n",
      "    exp(...)\n",
      "        exp(x)\n",
      "        \n",
      "        Return e raised to the power of x.\n",
      "    \n",
      "    expm1(...)\n",
      "        expm1(x)\n",
      "        \n",
      "        Return exp(x)-1.\n",
      "        This function avoids the loss of precision involved in the direct evaluation of exp(x)-1 for small x.\n",
      "    \n",
      "    fabs(...)\n",
      "        fabs(x)\n",
      "        \n",
      "        Return the absolute value of the float x.\n",
      "    \n",
      "    factorial(...)\n",
      "        factorial(x) -> Integral\n",
      "        \n",
      "        Find x!. Raise a ValueError if x is negative or non-integral.\n",
      "    \n",
      "    floor(...)\n",
      "        floor(x)\n",
      "        \n",
      "        Return the floor of x as an Integral.\n",
      "        This is the largest integer <= x.\n",
      "    \n",
      "    fmod(...)\n",
      "        fmod(x, y)\n",
      "        \n",
      "        Return fmod(x, y), according to platform C.  x % y may differ.\n",
      "    \n",
      "    frexp(...)\n",
      "        frexp(x)\n",
      "        \n",
      "        Return the mantissa and exponent of x, as pair (m, e).\n",
      "        m is a float and e is an int, such that x = m * 2.**e.\n",
      "        If x is 0, m and e are both 0.  Else 0.5 <= abs(m) < 1.0.\n",
      "    \n",
      "    fsum(...)\n",
      "        fsum(iterable)\n",
      "        \n",
      "        Return an accurate floating point sum of values in the iterable.\n",
      "        Assumes IEEE-754 floating point arithmetic.\n",
      "    \n",
      "    gamma(...)\n",
      "        gamma(x)\n",
      "        \n",
      "        Gamma function at x.\n",
      "    \n",
      "    gcd(...)\n",
      "        gcd(x, y) -> int\n",
      "        greatest common divisor of x and y\n",
      "    \n",
      "    hypot(...)\n",
      "        hypot(x, y)\n",
      "        \n",
      "        Return the Euclidean distance, sqrt(x*x + y*y).\n",
      "    \n",
      "    isclose(...)\n",
      "        isclose(a, b, *, rel_tol=1e-09, abs_tol=0.0) -> bool\n",
      "        \n",
      "        Determine whether two floating point numbers are close in value.\n",
      "        \n",
      "           rel_tol\n",
      "               maximum difference for being considered \"close\", relative to the\n",
      "               magnitude of the input values\n",
      "            abs_tol\n",
      "               maximum difference for being considered \"close\", regardless of the\n",
      "               magnitude of the input values\n",
      "        \n",
      "        Return True if a is close in value to b, and False otherwise.\n",
      "        \n",
      "        For the values to be considered close, the difference between them\n",
      "        must be smaller than at least one of the tolerances.\n",
      "        \n",
      "        -inf, inf and NaN behave similarly to the IEEE 754 Standard.  That\n",
      "        is, NaN is not close to anything, even itself.  inf and -inf are\n",
      "        only close to themselves.\n",
      "    \n",
      "    isfinite(...)\n",
      "        isfinite(x) -> bool\n",
      "        \n",
      "        Return True if x is neither an infinity nor a NaN, and False otherwise.\n",
      "    \n",
      "    isinf(...)\n",
      "        isinf(x) -> bool\n",
      "        \n",
      "        Return True if x is a positive or negative infinity, and False otherwise.\n",
      "    \n",
      "    isnan(...)\n",
      "        isnan(x) -> bool\n",
      "        \n",
      "        Return True if x is a NaN (not a number), and False otherwise.\n",
      "    \n",
      "    ldexp(...)\n",
      "        ldexp(x, i)\n",
      "        \n",
      "        Return x * (2**i).\n",
      "    \n",
      "    lgamma(...)\n",
      "        lgamma(x)\n",
      "        \n",
      "        Natural logarithm of absolute value of Gamma function at x.\n",
      "    \n",
      "    log(...)\n",
      "        log(x[, base])\n",
      "        \n",
      "        Return the logarithm of x to the given base.\n",
      "        If the base not specified, returns the natural logarithm (base e) of x.\n",
      "    \n",
      "    log10(...)\n",
      "        log10(x)\n",
      "        \n",
      "        Return the base 10 logarithm of x.\n",
      "    \n",
      "    log1p(...)\n",
      "        log1p(x)\n",
      "        \n",
      "        Return the natural logarithm of 1+x (base e).\n",
      "        The result is computed in a way which is accurate for x near zero.\n",
      "    \n",
      "    log2(...)\n",
      "        log2(x)\n",
      "        \n",
      "        Return the base 2 logarithm of x.\n",
      "    \n",
      "    modf(...)\n",
      "        modf(x)\n",
      "        \n",
      "        Return the fractional and integer parts of x.  Both results carry the sign\n",
      "        of x and are floats.\n",
      "    \n",
      "    pow(...)\n",
      "        pow(x, y)\n",
      "        \n",
      "        Return x**y (x to the power of y).\n",
      "    \n",
      "    radians(...)\n",
      "        radians(x)\n",
      "        \n",
      "        Convert angle x from degrees to radians.\n",
      "    \n",
      "    sin(...)\n",
      "        sin(x)\n",
      "        \n",
      "        Return the sine of x (measured in radians).\n",
      "    \n",
      "    sinh(...)\n",
      "        sinh(x)\n",
      "        \n",
      "        Return the hyperbolic sine of x.\n",
      "    \n",
      "    sqrt(...)\n",
      "        sqrt(x)\n",
      "        \n",
      "        Return the square root of x.\n",
      "    \n",
      "    tan(...)\n",
      "        tan(x)\n",
      "        \n",
      "        Return the tangent of x (measured in radians).\n",
      "    \n",
      "    tanh(...)\n",
      "        tanh(x)\n",
      "        \n",
      "        Return the hyperbolic tangent of x.\n",
      "    \n",
      "    trunc(...)\n",
      "        trunc(x:Real) -> Integral\n",
      "        \n",
      "        Truncates x to the nearest Integral toward 0. Uses the __trunc__ magic method.\n",
      "\n",
      "DATA\n",
      "    e = 2.718281828459045\n",
      "    inf = inf\n",
      "    nan = nan\n",
      "    pi = 3.141592653589793\n",
      "    tau = 6.283185307179586\n",
      "\n",
      "FILE\n",
      "    /Users/qiangzhu/miniconda3/lib/python3.6/lib-dynload/math.cpython-36m-darwin.so\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(math)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "welcomeUNLV\n"
     ]
    }
   ],
   "source": [
    "# we can also do string calculations!\n",
    "str1 = 'welcome' \n",
    "str2 = 'UNLV'\n",
    "print(str1+str2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1.4 Compound types\n",
    "\n",
    "## Strings\n",
    "## List\n",
    "## Dictionaries (_after-class study_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Welcome to Physics 300 <class 'str'>\n"
     ]
    }
   ],
   "source": [
    "Strings = \"Welcome to Physics 300\"\n",
    "print(Strings, type(Strings))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['Welcome to Physics 300'] <class 'list'>\n"
     ]
    }
   ],
   "source": [
    "Lists = ['Welcome to Physics 300']\n",
    "print(Lists, type(Lists))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "Strings."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Quiz: What are the differences?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# a few more tricks\n",
    "# len(Strings)\n",
    "# dir(Strings), check its attributes\n",
    "# help(Strings.replace)\n",
    "#dir(Strings)\n",
    "#help(Strings.isalpha)\n",
    "#dir(Lists)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['Welcome to Physics 300', 2]\n"
     ]
    }
   ],
   "source": [
    "# Lists are very similar to strings, except that each element can be of any type.\n",
    "# You can do different types of operations on List\n",
    "# List is like an array, you can call its elements according to index\n",
    "# You can call one element, and many element as well\n",
    "\n",
    "Lists.append(2)\n",
    "print(Lists)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# for loops\n",
    "In python, we can visit the list by for loop. The most common is the for loop, which is used together with iterable objects, such as lists. The basic syntax is:\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "1\n",
      "complete\n",
      "2\n",
      "4\n",
      "complete\n",
      "3\n",
      "9\n",
      "complete\n"
     ]
    }
   ],
   "source": [
    "for x in [1,2,3]:\n",
    "    print(x)\n",
    "    print(x**2)\n",
    "    print('complete')\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "true\n"
     ]
    }
   ],
   "source": [
    "x=3\n",
    "y=3\n",
    "if (x>=y):\n",
    "    print(\"true\")    \n",
    "else:\n",
    "    print(\"false\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "cycle-----------:  0 nm\n",
      "cycle-----------:  1 nm\n",
      "cycle-----------:  2 nm\n",
      "cycle-----------:  3 nm\n",
      "cycle-----------:  4 nm\n",
      "cycle-----------:  5 nm\n",
      "cycle-----------:  6 nm\n",
      "cycle-----------:  7 nm\n",
      "cycle-----------:  8 nm\n",
      "cycle-----------:  9 nm\n"
     ]
    }
   ],
   "source": [
    "i = 0\n",
    "while True:\n",
    "    print(\"cycle-----------: \", i, 'nm')\n",
    "    #i = i + 1 works\n",
    "    #i++ not work\n",
    "    i+=1\n",
    "    if i == 10:\n",
    "        break"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercise\n",
    "In 1888 Johannes Rydberg published his famous formula for the wavelengths $\\lambda$ of the emissioon lines of the hydrogen atom \n",
    "\n",
    "\n",
    "$$\\frac{1}{\\lambda} = R (\\frac{1}{m^2} - \\frac{1}{n^2})$$\n",
    "\n",
    "Where $R$ is the Rydberg constant = 1.097 $\\times$ $10^{-2} \\text{nm}^{-1}$, $m$ and $n$ are positive integers. For a given value of $m$, $\\lambda$ is given for this formula for all $n>m$ series, the first three series are known as the Lyman, Belmer and Paschen series, named after their discoverers. Can you write a code to compute the first three series for the first five lines?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "ename": "SyntaxError",
     "evalue": "Missing parentheses in call to 'print' (<ipython-input-40-cfbc5703203b>, line 14)",
     "output_type": "error",
     "traceback": [
      "\u001b[0;36m  File \u001b[0;32m\"<ipython-input-40-cfbc5703203b>\"\u001b[0;36m, line \u001b[0;32m14\u001b[0m\n\u001b[0;31m    print m, n, 1/m**2, 1/n**2\u001b[0m\n\u001b[0m          ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m Missing parentheses in call to 'print'\n"
     ]
    }
   ],
   "source": [
    "R = 1.097e-2\n",
    "for m in [1,2,3]:\n",
    "    print(\"Series for m = \", m)\n",
    "    for k in [1,2,3,4,5]:\n",
    "        n = m + k\n",
    "        #invlambda = R*(1.0/m**2 - 1/n**2)\n",
    "        invlambda = R*(1.0/m**2 - 1/n**2)\n",
    "        #print(1lambda) # variable names should not start with number\n",
    "\n",
    "        #print(\"n=\",n, \"  \", 1/invlambda, \"nm\")\n",
    "        #print(n, 1/invlambda, \"nm\")\n",
    "        \n",
    "        print       m, n, 1/m**2, 1/n**2 #only works for python 2\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "ename": "SyntaxError",
     "evalue": "invalid syntax (<ipython-input-34-c2e965a75d58>, line 1)",
     "output_type": "error",
     "traceback": [
      "\u001b[0;36m  File \u001b[0;32m\"<ipython-input-34-c2e965a75d58>\"\u001b[0;36m, line \u001b[0;32m1\u001b[0m\n\u001b[0;31m    lambda=2\u001b[0m\n\u001b[0m          ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n"
     ]
    }
   ],
   "source": [
    "lambda=2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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