octave_rule, an Octave code which computes a quadrature rule which estimates the integral of a function f(x), which might be defined over a one dimensional region (a line) or more complex shapes such as, a circle, a triangle, a quadrilateral, a polygon, or a higher dimensional region, and which might include an associated weight function w(x).
The information on this web page is distributed under the MIT license.
octave_rule is available in a C version and a C++ version and a Fortran77 version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.
alpert_rule, an Octave code which sets up an Alpert quadrature rule for functions which are regular, log(x) singular, or 1/sqrt(x) singular.
annulus_rule, an Octave code which computes a quadrature rule for estimating integrals of a function over the interior of a circular annulus in 2D.
ccn_rule, an Octave code which defines a Clenshaw Curtis Nested (CCN) quadrature rule.
chebyshev1_rule, an Octave code which computes a Gauss-Chebyshev type 1 quadrature rule.
chebyshev2_rule, an Octave code which computes a Gauss-Chebyshev type 2 quadrature rule.
circle_rule, an Octave code which computes a quadrature rule for the unit circle in 2D, to approximate integrals of f(x,y) over the circumference of the circle of radius 1 and center (0,0).
clenshaw_curtis_rule, an Octave code which defines a Clenshaw Curtis quadrature rule.
cube_arbq_rule, an Octave code which returns quadrature rules, with exactness up to total degree 15, over the interior of the symmetric cube in 3D, by Hong Xiao and Zydrunas Gimbutas.
cube_felippa_rule, an Octave code which returns the points and weights of a Felippa quadrature rule over the interior of a cube in 3D.
disk_rule, an Octave code which computes a quadrature rule over the interior of a disk of radius R centered at the origin.
disk01_positive_rule, an Octave code which computes a quadrature rule over the interior of the unit positive disk in 2D, with radius 1 and center (0,0).
disk01_rule, an Octave code which computes quadrature rules over the interior of the unit disk in 2D, with radius 1 and center (0,0).
filon_rule, an Octave code which uses Filon's method to approximate integrals including an oscillatory factor of sin(k*x) or cos(k*x).
gegenbauer_rule, an Octave code which computes a Gauss-Gegenbauer quadrature rule.
gen_hermite_rule, an Octave code which returns a generalized Gauss-Hermite quadrature rule.
gen_laguerre_rule, an Octave code which returns a generalized Gauss-Laguerre quadrature rule.
gl_fast_rule, an Octave code which carries out the rapid computation of the K-th value and weight of an N-point Gauss-Legendre quadrature rule, by Ignace Bogaert.
hermite_rule, an Octave code which returns a Gauss-Hermite quadrature rule for estimating the integral of a function with density exp(-x^2) over the interval (-oo,+oo).
hexagon_lyness_rule, an Octave code which computes one of 13 Lyness quadrature rules over the interior of the unit hexagon.
hexagon_stroud_rule, an Octave code which returns one of four Stroud quadrature rules over the interior of the unit hexagon.
hexahedron_jaskowiec_rule, an Octave code which returns a symmetric Jaskowiec quadrature rule for the hexahedron, with exactness up to total degree 21.
hexahedron_witherden_rule, an Octave code which returns a symmetric Witherden quadrature rule for the hexahedron, with exactness up to total degree 11.
jacobi_rule, an Octave code which returns a Gauss-Jacobi quadrature rule.
kronrod_rule, an Octave code which computes a Gauss and Gauss-Kronrod pair of quadrature rules of arbitrary order, by Robert Piessens, Maria Branders.
laguerre_rule, an Octave code which returns a Gauss-Laguerre quadrature rule for estimating the integral of a function with density exp(-x) over the interval [0,+oo).
lattice_rule, an Octave code which approximates M-dimensional integrals using lattice rules.
legendre_fast_rule, an Octave code which uses a fast algorithm to compute a Gauss-Legendre quadrature rule for estimating the integral of a function with density rho(x)=1 over the interval [-1,+1].
legendre_rule, an Octave code which returns a Gauss-Legendre quadrature rule for estimating the integral of a function with density rho(x)=1 over the interval [-1,+1].
line_fekete_rule, an Octave code which estimates the location of N Fekete points, for polynomial interpolation or quadrature, over the interior of a line segment in 1D.
line_felippa_rule, an Octave code which returns a Felippa quadrature rule over the interior of a line segment in 1D.
line_ncc_rule, an Octave code which computes a Newton Cotes Closed (NCC) quadrature rule, using equally spaced points, over the interior of a line segment in 1D.
line_nco_rule, an Octave code which computes a Newton Cotes Open (NCO) quadrature rule, using equally spaced points, over the interior of a line segment in 1D.
patterson_rule, an Octave code which returns a Gauss-Patterson quadrature rule of order 1, 3, 7, 15, 31, 63, 127, 255 or 511.
power_rule, an Octave code which constructs a power rule, that is, a product quadrature rule from identical 1D factor rules.
prism_jaskowiec_rule, an Octave code which returns symmetric quadrature rules, with exactness up to total degree 20, over the interior of a prism with triangular base, by Jan Jaskowiec, Natarajan Sukumar.
prism_witherden_rule, an Octave code which returns a symmetric Witherden quadrature rule for a prism with triangular base, with exactness up to total degree 10.
product_rule, an Octave code which constructs a product quadrature rule from distinct 1D factor rules.
pyramid_felippa_rule, an Octave code which returns a Felippa quadrature rule for approximating integrals over the interior of a pyramid in 3D.
pyramid_jaskowiec_rule, an Octave code which returns symmetric quadrature rules, with exactness up to total degree 20, over the interior of a pyramid in 3D, by Jan Jaskowiec, Natarajan Sukumar.
pyramid_rule, an Octave code which computes a conical product quadrature rule over the interior of the unit pyramid in 3D;
pyramid_witherden_rule, an Octave code which returns a Witherden quadrature rule, with exactness up to total degree 10, over the interior of a pyramid.
quad_rule, an Octave code which defines 1-dimensional quadrature rules.
quad_fast_rule, an Octave code which rapidly defines certain quadrature rules for 1D domains.
quadrilateral_witherden_rule, an Octave code which returns a symmetric Witherden quadrature rule for the quadrilateral, with exactness up to total degree 21.
simplex_gm_rule, an Octave code which defines Grundmann-Moeller quadrature rules over the interior of a triangle in 2D, a tetrahedron in 3D, or a simplex in M dimensions.
sphere_lebedev_rule, an Octave code which computes Lebedev quadrature rules on the surface of the unit sphere in 3D.
square_arbq_rule, an Octave code which returns quadrature rules, with exactness up to total degree 20, over the interior of the symmetric square in 2D, by Hong Xiao and Zydrunas Gimbutas.
square_felippa_rule, an Octave code which returns a Felippa quadrature rule over the interior of a square in 2D.
square_minimal_rule, an Octave code which returns almost minimal quadrature rules, with exactness up to total degree 55, over the interior of the symmetric square in 2D, by Mattia Festa and Alvise Sommariva.
square_symq_rule, an Octave code which returns symmetric quadrature rules, with exactness up to total degree 20, over the interior of the square in 2D, by Hong Xiao and Zydrunas Gimbutas.
tetrahedron_arbq_rule, an Octave code which returns quadrature rules, with exactness up to total degree 15, over the interior of a tetrahedron in 3D, by Hong Xiao and Zydrunas Gimbutas.
tetrahedron_felippa_rule, an Octave code which returns a Felippa quadrature rule for approximating integrals over the interior of a tetrahedron in 3D.
tetrahedron_jaskowiec_rule, an Octave code which returns quadrature rules, with exactness up to total degree 20, over the interior of a tetrahedron in 3D, by Jan Jaskowiec, Natarajan Sukumar.
tetrahedron_keast_rule, an Octave code which defines a Keast quadrature rule, with exactness degrees 0 through 8, over the interior of a tetrahedron in 3D.
tetrahedron_ncc_rule, an Octave code which defines Newton-Cotes closed (NCC) quadrature rules over the interior of a tetrahedron in 3D.
tetrahedron_nco_rule, an Octave code which defines Newton-Cotes open (NCO) quadrature rules over the interior of a tetrahedron in 3D.
tetrahedron_witherden_rule, an Octave code which returns a symmetric Witherden quadrature rule for the tetrahedron, with exactness up to total degree 10.
triangle_dunavant_rule, an Octave code which defines Dunavant rules for quadrature over the interior of a triangle in 2D.
triangle_fekete_rule, an Octave code which defines a Fekete rule for interpolation or quadrature over the interior of a triangle in 2D.
triangle_felippa_rule, an Octave code which returns a Felippa quadrature rule for approximating integrals over the interior of a triangle in 2D.
triangle_lyness_rule, an Octave code which returns a Lyness-Jespersen quadrature rule over the interior of a triangle in 2D.
triangle_ncc_rule, an Octave code which defines a Newton-Cotes Closed (NCC) quadrature rule over the interior of a triangle in 2D.
triangle_nco_rule, an Octave code which defines a Newton-Cotes Open (NCO) quadrature rule over the interior of a triangle in 2D.
triangle_symq_rule, an Octave code which returns symmetric quadrature rules, with precision up to 50, over the interior of a triangle in 2D, by Hong Xiao and Zydrunas Gimbutas.
triangle_twb_rule, an Octave code which generates a quadrature rule over the interior of a triangle in 2D, determined by Taylor, Wingate, and Bos.
triangle_wandzura_rule, an Octave code which defines a Wandzura rule for quadrature over the interior of a triangle in 2D.
triangle_witherden_rule, an Octave code which returns a symmetric Witherden quadrature rule for the triangle, with exactness up to total degree 20.
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].
wedge_felippa_rule, an Octave code which returns a Felippa quadrature rule for approximating integrals over the interior of the unit wedge in 3D.