Tools for ProgModX

Note that the package is in development and may undergo frequent updates

Install with python -m pip install pmxutils for windows and python3 -m pip install pmxutils for unix/linux

• Mathtools
  • construct
  • advConstruct
  • computeList
  • newton
  • isInbetween
  • rectangleIntegral
  • trapezoidIntegral
  • simpsonIntegral
  • euler
  • lemma
• Other
  • profile
  • loading
    • start
    • stop
    • animate

• construct(expression, var=x)

  Returns a function computing the given expression

  • expression - The mathematical expression to compute, type = string
  • var - The variable used in the mathematical expression, defaults tp 'x', type = string

• advConstruct(expression, *args, constants = {})

  Returns a function computing the given expression

  • expression - The mathematical expression to compute, type = string
  • args - Any number of individual arguments naming the variables used in the expresion, type = string
  • constants - A dictionary with any numerical constants in the expression, type = dict

• computeLists(function, low, high, step=1)

  Returns a touple of two lists containing x values inbetween low and high, and the computed results for y. In the format of (x_list, y_list)

  • low - The lower end of the function limit, type = number
  • high - The upper end of the function limit, type = number
  • function - The mathematical expression to use for y value computation, type = string or function from construct
  • step - The step size in the x value list, defaults to '1', type = number

• newton(function, derivative, low, high, tolerance=1e-8, rounding = 3, iterations = 1000)

  Uses Newtons way of finding the root of a function, using the function and its derivative, within the given limits.Returns None if it can't find a solution that satisfies the tolerance after the defined number of terations

  • function - The target mathematical expression, type = string or function from construct
  • derivative - The derivative of the target mathematical expression, type = string or function from construct
  • low - The lower end of the are which should be checked for roots, type = number
  • high - The upper end of the are which should be checked for roots, type = number
  • tolerance - The tolerance for error to speed up computation, defaults to '1e-8', type = number
  • rounding - Rounds the x value for the root to the specified amount of decimals, defaults to '3', type = number
  • iterations - The number of tries, after which the function will end early

• isInbetween(number, low, high)

  Returns True if number is inbetween limOne and limTwo, returns False otherwise

  • number - The number to be checked, type = number
  • low - The lower limit for which the number is checked, type = number
  • high - The upper limit for which the number is checked, type = number

• rectangleIntegral(function, low, high, n)

  Returns the numerically calculated integral of the function f inbetween a and b using n rectangles

  • function - The function to integrate, type = string or function from construct
  • low - The low end of the area to be computed, type = number
  • high - The high end of the area to be computed, type = number
  • n - The number of rectangles to use, type = int

• trapezoidIntegral(function, low, high, n)

  Returns the numerically calculated integral of the function f inbetween a and b using n trapezoids

  • function - The function to integrate, type = string or function from construct
  • low - The low end of the area to be computed, type = number
  • high - The high end of the area to be computed, type = number
  • n - The number of trapezoids to use, type = int

• simpsonIntegral(function, low, high, n)

  Returns the numerically calculated integral of the function inbetween low and high using n quadratic splines

  • function - The function to integrate, type = string or function from construct
  • low - The low end of the area to be computed, type = number
  • high - The high end of the area to be computed, type = number
  • n - The number of quadratic splines to use, type = int

• euler(functionDerivative, low, high, y0, n)

  Returns a numpy array x, containing the x values of the function, and an array F, containing the computed values for the antiderivative function of the given function functionDerivative inbetween low and high with N steps

  Only supports functions with one variable

  • functionDerivative - The derivative of the goal function, type = string or function from construct
  • low - The low end of the function to be computed, type = number
  • high - The high end of the area to be computed, type = number
  • y0 - The initial value of the goal function
  • n - The number of computations to perform

• lemma(a, b)

  Returns the greatest common denominator of a and b using the lemma algorithm

  • a - The first number
  • b - The second number

• profile(function)

  Time profiler. Prints out the elapsed time during function execution

  • function - The function to profile, type = function

Loading class

• start(flavor="loading")

  Starts a loading sequence

  • flavor - The message to be displayed during loading, defaults to 'loading', type = string

• stop()

  Stops the loading sequence

• animate()

  DO NOT USE, internal function