# clenshaw_curtis_rule

clenshaw_curtis_rule, an Octave code which generates a Clenshaw Curtis quadrature rule based on user input.

The rule is written to three files for easy use as input to other programs.

The standard Clenshaw Curtis quadrature rule is used as follows:

```        Integral ( A <= x <= B ) f(x) dx
```
is to be approximated by
```        Sum ( 1 <= i <= order ) w(i) * f(x(i))
```

### Usage:

clenshaw_curtis_rule ( order, a, b, 'filename' )
where
• order is the number of points in the quadrature rule;
• a is the left endpoint;
• b is the right endpoint;
• filename specifies the output filenames: namefile_w.txt, filename_x.txt, and filename_r.txt, containing the weights, abscissas, and interval limits.

### Languages:

clenshaw_curtis_rule is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version.

### Related Data and Programs:

alpert_rule, an Octave code which can set up an alpert quadrature rule for functions which are regular, log(x) singular, or 1/sqrt(x) singular.

ccn_rule, an Octave code which defines a nested clenshaw curtis quadrature rule.

chebyshev1_rule, an Octave code which can compute and print a gauss-chebyshev type 1 quadrature rule.

chebyshev2_rule, an Octave code which can compute and print a gauss-chebyshev type 2 quadrature rule.

gegenbauer_rule, an Octave code which can compute and print a gauss-gegenbauer quadrature rule.

gen_hermite_rule, an Octave code which can compute and print a generalized gauss-hermite quadrature rule.

gen_laguerre_rule, an Octave code which can compute and print a generalized gauss-laguerre quadrature rule.

hermite_rule, an Octave code which can compute and print a gauss-hermite quadrature rule.

jacobi_rule, an Octave code which can compute and print a gauss-jacobi quadrature rule.

laguerre_rule, an Octave code which can compute and print a gauss-laguerre quadrature rule.

legendre_rule, an Octave code which can compute and print a gauss-legendre quadrature rule.

line_felippa_rule, an Octave code which returns the points and weights of a felippa quadrature rule over the interior of a line segment in 1d.

patterson_rule, an Octave code which computes a gauss-patterson quadrature rule.

power_rule, an Octave code which constructs a power rule, that is, a product quadrature rule from identical 1d factor rules.

quadrature_rules_clenshaw_curtis, a dataset directory which contains quadrature rules for integration on [-1,+1], using a clenshaw curtis rule.

truncated_normal_rule, an Octave code which computes a quadrature rule for a normal probability density function (pdf), also called a gaussian distribution, that has been truncated to [a,+oo), (-oo,b] or [a,b].

### Reference:

1. Milton Abramowitz, Irene Stegun,
Handbook of Mathematical Functions,
National Bureau of Standards, 1964,
ISBN: 0-486-61272-4,
LC: QA47.A34.
2. Philip Davis, Philip Rabinowitz,
Methods of Numerical Integration,
Second Edition,
Dover, 2007,
ISBN: 0486453391,
LC: QA299.3.D28.
3. Arthur Stroud, Don Secrest,