From e55e41b76a740fdca3976459af65fccc2bf53b06 Mon Sep 17 00:00:00 2001
From: Terrell <tet12002@ad.engr.uconn.edu>
Date: Tue, 3 Oct 2017 11:01:28 -0400
Subject: [PATCH] HW2

---
 HW2/bisect.m         | 37 +++++++++++++++++++++++++++++++++++++
 HW2/falsepos.m       | 39 +++++++++++++++++++++++++++++++++++++++
 HW2/mod_secant.m     | 30 ++++++++++++++++++++++++++++++
 HW2/powerline_plot.m | 17 +++++++++++++++++
 4 files changed, 123 insertions(+)
 create mode 100644 HW2/bisect.m
 create mode 100644 HW2/falsepos.m
 create mode 100644 HW2/mod_secant.m
 create mode 100644 HW2/powerline_plot.m

diff --git a/HW2/bisect.m b/HW2/bisect.m
new file mode 100644
index 0000000..47ee7ec
--- /dev/null
+++ b/HW2/bisect.m
@@ -0,0 +1,37 @@
+function [root,fx,ea,iter]=bisect(func,xl,xu,es,maxit,varargin)
+% bisect: root location zeroes
+% [root,fx,ea,iter]=bisect(func,xl,xu,es,maxit,p1,p2,...):
+% uses bisection method to find the root of func
+% input:
+% func = name of function
+% xl, xu = lower and upper guesses
+% es = desired relative error (default = 0.0001%)
+% maxit = maximum allowable iterations (default = 50)
+% p1,p2,... = additional parameters used by func
+% output:
+% root = real root
+% fx = function value at root
+% ea = approximate relative error (%)
+% iter = number of iterations
+if nargin<3,error('at least 3 input arguments required'),end
+test = func(xl,varargin{:})*func(xu,varargin{:});
+if test>0,error('no sign change'),end
+if nargin<4||isempty(es), es=0.0001;end
+if nargin<5||isempty(maxit), maxit=50;end
+iter = 0; xr = xl; ea = 100;
+while (1)
+  xrold = xr;
+  xr = (xl + xu)/2;
+  iter = iter + 1;
+  if xr ~= 0,ea = abs((xr - xrold)/xr) * 100;end
+  test = func(xl,varargin{:})*func(xr,varargin{:});
+  if test < 0
+    xu = xr;
+  elseif test > 0
+    xl = xr;
+  else
+    ea = 0;
+  end
+  if ea <= es || iter >= maxit,break,end
+end
+root = xr; fx = func(xr, varargin{:});
\ No newline at end of file
diff --git a/HW2/falsepos.m b/HW2/falsepos.m
new file mode 100644
index 0000000..2d010c8
--- /dev/null
+++ b/HW2/falsepos.m
@@ -0,0 +1,39 @@
+function [root,fx,ea,iter]=falsepos(func,xl,xu,es,maxit,varargin)
+% bisect: root location zeroes
+% [root,fx,ea,iter]=bisect(func,xl,xu,es,maxit,p1,p2,...):
+% uses bisection method to find the root of func
+% input:
+% func = name of function
+% xl, xu = lower and upper guesses
+% es = desired relative error (default = 0.0001%)
+% maxit = maximum allowable iterations (default = 50)
+% p1,p2,... = additional parameters used by func
+% output:
+% root = real root
+% fx = function value at root
+% ea = approximate relative error (%)
+% iter = number of iterations
+if nargin<3,error('at least 3 input arguments required'),end
+test = func(xl,varargin{:})*func(xu,varargin{:});
+if test>0,error('no sign change'),end
+if nargin<4|isempty(es), es=0.0001;end
+if nargin<5|isempty(maxit), maxit=50;end
+iter = 0; xr = xl; ea = 100;
+while (1)
+  xrold = xr;
+  xr = (xl + xu)/2;
+  % xr = (xl + xu)/2; % bisect method
+  xr=xu - (func(xu)*(xl-xu))/(func(xl)-func(xu)); % false position method
+  iter = iter + 1;
+  if xr ~= 0,ea = abs((xr - xrold)/xr) * 100;end
+  test = func(xl,varargin{:})*func(xr,varargin{:});
+  if test < 0
+    xu = xr;
+  elseif test > 0
+    xl = xr;
+  else
+    ea = 0;
+  end
+  if ea <= es | iter >= maxit,break,end
+end
+root = xr; fx = func(xr, varargin{:});
\ No newline at end of file
diff --git a/HW2/mod_secant.m b/HW2/mod_secant.m
new file mode 100644
index 0000000..b74f181
--- /dev/null
+++ b/HW2/mod_secant.m
@@ -0,0 +1,30 @@
+function [root,ea,iter]=mod_secant(func,dx,xr,es,maxit,varargin)
+% newtraph: Modified secant root location zeroes
+% [root,ea,iter]=mod_secant(func,dfunc,xr,es,maxit,p1,p2,...):
+%   uses modified secant method to find the root of func
+% input:
+%   func = name of function
+%   dx = perturbation fraction
+%   xr = initial guess
+%   es = desired relative error (default = 0.0001%)
+%   maxit = maximum allowable iterations (default = 50)
+%   p1,p2,... = additional parameters used by function
+% output:
+%   root = real root
+%   ea = approximate relative error (%)
+%   iter = number of iterations
+if nargin<3,error('at least 3 input arguments required'),end
+if nargin<4 || isempty(es),es=0.0001;end
+if nargin<5 || isempty(maxit),maxit=50;end
+iter = 0;
+while (1)
+  xrold = xr;
+  dfunc=(func(xr+dx)-func(xr))./dx;
+  xr = xr - func(xr)/dfunc;
+  iter = iter + 1;
+  if xr ~= 0 
+    ea = abs((xr - xrold)/xr) * 100;
+  end
+  if ea <= es || iter >= maxit, break, end
+end
+root = xr;
\ No newline at end of file
diff --git a/HW2/powerline_plot.m b/HW2/powerline_plot.m
new file mode 100644
index 0000000..9e20645
--- /dev/null
+++ b/HW2/powerline_plot.m
@@ -0,0 +1,17 @@
+cat_cable = @(T) T/10.*cosh(10./T*30)+30-T/10-35;
+[root,fx,ea,iter] = falsepos(cat_cable,100,1000,0.00001,10000);
+[root1,fx1,ea1,iter1] = bisect(cat_cable,100,1000,0.00001,10000);
+[root2,ea2,iter2] = mod_secant(cat_cable,100,1000,0.00001,10000);
+
+%define T
+T = root2;
+
+%plotting the shape of the powerline
+x = -10:0.1:50;
+y = T/10.*cosh(10./T*x)+30-T/10;
+%setDefaults
+plot(x,y)
+title('Final Powerline Shape')
+xlabel('distance (m)')
+ylabel('height (m)')
+print('figure01','-dpng')
\ No newline at end of file