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intg
definite integral
Calling Sequence
[v,err]=intg(a,b,f [,ea [,er])
Arguments
- a,b
real numbers
- f
external (function or list or string)
- ea, er
real numbers
- ea
absolute error required on the result. Default value: 1.d-14
- er
relative error required on the result. Default value: 1.d-8
- err
estimated absolute error on the result.
Description
intg(a,b,f)
evaluates the definite integral from
a
to b
of f(t)dt
.
The function f(t)
should be continuous.
The evaluation hopefully satisfies following claim for accuracy:
abs(I-v)<= max(ea,er*abs(I))
where I stands for the
exact value of the integral.
f
is an external :
If f
is function its definition must be as
follows y = f(t)
If f
is a list the list must be as follows:
list(f,x1,x2,...)
where f
is a
function with calling sequence f(t,x1,x2,...)
.
If f
is a string it refers to a the name of a
Fortran function or a C prodedure with a given calling sequence:
In the fortran case the calling sequence should be double
precision function f(x)
where x
is also a
double precision number.
In the C case the calling sequence should be double
f(double *x)
.
Examples
// Function written in the Scilab language function y=f(x),y=x*sin(30*x)/sqrt(1-((x/(2*%pi))^2)),endfunction exact=-2.5432596188; I=intg(0,2*%pi,f) abs(exact-I) // Function with an argument written in the Scilab language function y=f1(x, w),y=x*sin(w*x)/sqrt(1-((x/(2*%pi))^2)),endfunction I=intg(0,2*%pi,list(f1,30)) abs(exact-I) // Function written in Fortran (a Fortran compiler is required) // define a Fortran function cd TMPDIR; F=[' double precision function ffun(x)' ' double precision x,pi' ' pi=3.14159265358979312d+0' ' ffun=x*sin(30.0d+0*x)/sqrt(1.0d+0-(x/(2.0d+0*pi))**2)' ' return' ' end']; mputl(F,TMPDIR+'/ffun.f') // compile the function l=ilib_for_link('ffun','ffun.f',[],'f'); // add the function to the working environment link(l,'ffun','f') // integrate the function I=intg(0,2*%pi,'ffun') abs(exact-I) // Function written in C (a C compiler is required) // define a C function C=['#include <math.h>' 'double cfun(double *x)' '{' ' double y,pi=3.14159265358979312;' ' y=*x/(2.0e0*pi);' ' return *x*sin(30.0e0**x)/sqrt(1.0e0-y*y);' '}']; mputl(C,TMPDIR+'/cfun.c') // compile the function l=ilib_for_link('cfun','cfun.f',[],'c'); // add the function to the working environment link(l,'cfun','c') // integrate the function I=intg(0,2*%pi,'cfun') abs(exact-I)
Used Functions
The associated routines can be found in SCI/modules/differential_equations/src/fortran directory :
dqag0.f and dqags.f from quadpack
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