cumsimps
Cumulative Simpson's numerical integration
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Syntax
z = cumsimps(y) z = cumsimps(x,y) z = cumsimps(...,dim)
Description
z = cumsimps(y) computes an approximation of the cumulative integral of y via the Simpson's rule (with unit spacing). To compute the integral for spacing different from one, multiply z by the spacing increment.
For vectors, cumsimps(y) is a vector containing the cumulative integral of y. For matrices, cumsimps(y) is a matrix the same size as x with the cumulative integral over each column. For N-D arrays, cumsimps(y) works along the first non-singleton dimension.
z = cumsimps(x,y) computes the cumulative integral of y with respect to x using the Simpson's method. x and y must be vectors of the same length, or x must be a column vector and y an array whose first non-singleton dimension is length(x). cumsimps operates across this dimension.
z = cumsimps(x,y,dim) or cumsimps(y,dim) integrates along dimension dim of y. The length of x must be the same as size(y,dim).
Examples
Let us define by pdf the following probability density function of a normal distribution:
The exact related cumulative density function is given by:
Let us compare cumsimps(x,pdf) with cdf with mean = 0, variance = 1 and x = -5:0.5:5
mu = 0; sigma = 1;
x = -5:0.5:5;
pdf = 1/sqrt(2*pi)*exp(-(x-mu).^2/2/sigma^2);
cdf = 0.5*(1+erf((x-mu)/sigma/sqrt(2)));
plot(x,cumsimps(x,pdf),x,cdf,'o')
This example uses two complex inputs:
z = exp(1i*pi*(0:100)/100); ct = cumtrapz(z,1./z); ct(end)
ans = 0.0000 + 3.1411i
See also
About the author
Damien Garcia, Eng., Ph.D. Assistant professor, Department of radiology CRCHUM, University of Montreal Hospital Montreal, QC, Canada Damien.Garcia.REMOVE-THIS@BiomeCardio.com