re-organized files

1 files changed, 39 insertions, 0 deletions

diff --git a/Functions/simpson.m b/Functions/simpson.m
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+++ b/Functions/simpson.m
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+function [I] = Simpson(x, y)
+% Numerical evaluation of integral by Simpson's 1/3 Rule
+% Inputs
+%   x = the vector of equally spaced independent variable
+%   y = the vector of function values with respect to x
+% Outputs:
+%   I = the numerical integral calculated
+
+%Error cheching
+if length(x)~=length(y), error('The vectors need to be of equal lengths'),end
+if length(x)==1, error('Vectors must be at least 2 data points long'),end
+if range(x(2:end)-x(1:end-1))~=0, error('The x vector needs to be equally spaced'), end
+%Error  Errorchecking END
+
+lower_bound=min(x);
+interval=length(x)-1;
+if rem(interval,2)==0
+	trap_rule=0;
+	upper_bound=max(x);
+else 
+	warning('Odd number of intervals. Applying Trapezoidal rule on last interval')
+	trap_rule=1;
+	upper_bound=x(end-1);
+end
+
+if length(x)==2
+	I=(upper_bound-lower_bound)*(y(1)+y(2))/2;
+else
+	h=(upper_bound-lower_bound)/interval;
+	SumOdd=sum(y(1:2:end))-y(end-1);
+	SumEven=sum(y(2:2:end))-y(end-2);
+	I=(upper_bound-lower_bound)*(y(1)+4*SumOdd+2*SumEven+y(end))/(3*interval);
+end
+
+if trap_rule==1 & length(x)~=2
+	I_trap=(max(x)-upper_bound)*(y(upper_bound)+y(max(x)))/2;
+	I=I+I_trap;
+end
+end
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