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| -rw-r--r-- | Functions/README.md | 89 |
1 files changed, 43 insertions, 46 deletions
diff --git a/Functions/README.md b/Functions/README.md index 8e881b3..c8805c2 100644 --- a/Functions/README.md +++ b/Functions/README.md @@ -1,11 +1,11 @@ # Functions This directory contains the functions written throught the course. -* days.m -* falsePositive.m -* heun.m -* luFactor.m -* simpson.m -* spacialMatrix.m +- days.m +- falsePositive.m +- heun.m +- luFactor.m +- simpson.m +- spacialMatrix.m --- @@ -14,12 +14,12 @@ Function to count the total days elapsed in a year according to a given date. The syntax of the function is `days(<months>, <days>, <leap>)` where `<months>` is a integer (1-12). `<days>` is an integer from 1-31 and `<leap>` accounts for leap years. ### Input -* `months` - month number (1-12). Example: `8` represents August. -* `days` - day number of the month. -* `leap` - indicates if the year is a leapyear or a regular year. `0` for regular and `1` for leap year. +- `months` - month number (1-12). Example: `8` represents August. +- `days` - day number of the month. +- `leap` - indicates if the year is a leapyear or a regular year. `0` for regular and `1` for leap year. ### Output -* `nd` - number of days elapsed in the year. +- `nd` - number of days elapsed in the year. ### Example: `days(8,4,0)` represents August 8th in a regular year (non-leap year). @@ -31,18 +31,18 @@ Function finds the root of an anonymous function using the false position method Synopsis: `[root, fx, ea, iter] = falsePosition(func, xl, xu, es, maxit, varargin)`. ### Input -* `func` - the function being evaluated. -* `xl` - lower bound guess. -* `xu` - upper bound guess. -* `es` - desired relative error (default 0.0001%) -* `maxit` - maximum number of iterations (default 200) -* `varargin` - any additional parameters used by the function +- `func` - the function being evaluated. +- `xl` - lower bound guess. +- `xu` - upper bound guess. +- `es` - desired relative error (default 0.0001%) +- `maxit` - maximum number of iterations (default 200) +- `varargin` - any additional parameters used by the function ### Output -* `root` - estimated root location. -* `fx` - function evaluated at root location. -* `ea` - approximated relative error (%). -* `iter` - number of iterations performed. +- `root` - estimated root location. +- `fx` - function evaluated at root location. +- `ea` - approximated relative error (%). +- `iter` - number of iterations performed. ### Notes: Known issue: the output of `iter` needs fixing. The output is incorrect. @@ -54,16 +54,16 @@ Uses the heun method to integrate an ODE. Synopsis: `[t,y] = Heun(dydt,tspan,y0,h)`. ### Input -* `dydt` -the differential equation of interest (must be anonymous function). -* `tspan` - the initial and final values of the independent variable as a vector with length=2 [ti,tf]. -* `y0` - the initial value of the dependent variable. -* `h` - step size. -* `es` - stopping criterion (%), optional (default = 0.001). -* `maxit` - maximum iterations of corrector, optional (default = 50). +- `dydt` -the differential equation of interest (must be anonymous function). +- `tspan` - the initial and final values of the independent variable as a vector with length=2 [ti,tf]. +- `y0` - the initial value of the dependent variable. +- `h` - step size. +- `es` - stopping criterion (%), optional (default = 0.001). +- `maxit` - maximum iterations of corrector, optional (default = 50). ### Output -* `t` - vector of independent variable values -* `y` - vector of solution for dependent variable +- `t` - vector of independent variable values +- `y` - vector of solution for dependent variable ### Notes: This function needs some working on to compute a correct solution when using multiple steps with an irregular step size at the end. @@ -76,12 +76,12 @@ Performs LU decomposition with pivoting. Synopsis: `[L, U, P] = luFactor(A)`. ### Input -* `A` - a coefficient matrix. +- `A` - a coefficient matrix. ### Output -* `L` - lower triangular matrix, with 1's along the diagonals. -* `U` - upper triangular matrix. -* `P` - the permutation matrix. +- `L` - lower triangular matrix, with 1's along the diagonals. +- `U` - upper triangular matrix. +- `P` - the permutation matrix. ### Notes: Be cautious when using this function on bigger matrices. The `L` variable is known to be incorrect. @@ -93,39 +93,36 @@ Evaluates the integral of two vectors by Simpsons 1/3 rule. Synopsis: `[I] = Simpson(x, y)` ### Input -* `x` - the vector of equally spaced independent variable. -* `y` - the vector of function values with respect to x. +- `x` - the vector of equally spaced independent variable. +- `y` - the vector of function values with respect to x. ### Output -* `I` - numerical calculated integral. +- `I` - numerical calculated integral. ### Notes: -The current state of this function is **deprecated**. The algorithm fails compute the correct trapeziodal rule given 2 data points as well as 3 data points. Thus, failing to solve real problem. Pull requests are welcomed. +The current state of this function is --deprecated--. The algorithm fails compute the correct trapeziodal rule given 2 data points as well as 3 data points. Thus, failing to solve real problem. Pull requests are welcomed. --- ## [specialMatrix.m](specialMatrix.m) - -# specialMatrix.m Function returns a special matrix A with the following criteria: - The value of each element in the first row is the number of the column. - The value of each element in the first column is the number of the row. - The rest of the elements each has a value equal to the sum of the element above it and element to the left. - The function returns a sensible error if the user does not input exactly two arguments. - Synopsis: `[root, fx, ea, iter] = falsePosition(func, xl, xu, es, maxit, varargin)`. ## Input -* `func` - the function being evaluated. -* `xl` - lower bound guess. -* `xu` - upper bound guess. -* `es` - desired relative error (default 0.0001%) -* `maxit` - maximum number of iterations (default 200) -* `varargin` - any additional parameters used by the function +- `func` - the function being evaluated. +- `xl` - lower bound guess. +- `xu` - upper bound guess. +- `es` - desired relative error (default 0.0001%) +- `maxit` - maximum number of iterations (default 200) +- `varargin` - any additional parameters used by the function ## Output -* `A` - special matrix with the appropriate rules +- `A` - special matrix with the appropriate rules ## Notes: This function has not much of a practical application, rather a very good exercise for beginners to get started with the basics of matrix manipulation and user-defined functions. |