cpp_rule, a C++ 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.
cpp_rule is available in a C version and a C++ version..
alpert_rule, a C++ code which sets up an Alpert quadrature rule for functions which are regular, log(x) singular, or 1/sqrt(x) singular.
annulus_rule, a C++ code which computes a quadrature rule for estimating integrals of a function over the interior of a circular annulus in 2D.
ccn_rule, a C++ code which defines a Clenshaw Curtis Nested (CCN) quadrature rule.
chebyshev1_rule, a C++ code which computes a Gauss-Chebyshev type 1 quadrature rule.
chebyshev2_rule, a C++ code which computes a Gauss-Chebyshev type 2 quadrature rule.
circle_rule, a C++ 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, a C++ code which defines a Clenshaw Curtis quadrature rule.
cube_arbq_rule, a C++ 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, a C++ code which returns the points and weights of a Felippa quadrature rule over the interior of a cube in 3D.
disk_rule, a C++ code which computes a quadrature rule over the interior of a disk of radius R centered at the origin.
disk01_rule, a C++ code which computes quadrature rules over the interior of the unit disk in 2D, with radius 1 and center (0,0).
filon_rule, a C++ code which uses Filon's method to approximate integrals including an oscillatory factor of sin(k*x) or cos(k*x).
gegenbauer_rule, a C++ code which computes a Gauss-Gegenbauer quadrature rule.
gen_hermite_rule, a C++ code which returns a generalized Gauss-Hermite quadrature rule.
gen_laguerre_rule, a C++ code which returns a generalized Gauss-Laguerre quadrature rule.
gl_fast_rule, a C++ 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, a C++ 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).
hexahedron_jaskowiec_rule, a C++ code which returns a symmetric Jaskowiec quadrature rule for the hexahedron, with exactness up to total degree 21.
hexahedron_witherden_rule, a C++ code which returns a symmetric Witherden quadrature rule for the hexahedron, with exactness up to total degree 11.
jacobi_rule, a C++ code which returns a Gauss-Jacobi quadrature rule.
kronrod_rule, a C++ code which computes a Gauss and Gauss-Kronrod pair of quadrature rules of arbitrary order, by Robert Piessens, Maria Branders.
laguerre_rule, a C++ 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, a C++ code which approximates M-dimensional integrals using lattice rules.
legendre_fast_rule, a C++ 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, a C++ 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, a C++ 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, a C++ code which returns a Felippa quadrature rule over the interior of a line segment in 1D.
line_ncc_rule, a C++ 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, a C++ code which computes a Newton Cotes Open (NCO) quadrature rule, using equally spaced points, over the interior of a line segment in 1D.
monte_carlo_rule, a C++ code which uses a random number generator (RNG) to create a dataset of N random M-dimensional points, regards it as a quadrature rule for the unit hypercube, and writes out three files of information.
patterson_rule, a C++ code which returns a Gauss-Patterson quadrature rule of order 1, 3, 7, 15, 31, 63, 127, 255 or 511.
power_rule, a C++ code which constructs a power rule, that is, a product quadrature rule from identical 1D factor rules.
prism_jaskowiec_rule, a C++ 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, a C++ code which returns a symmetric Witherden quadrature rule for a prism with triangular base, with exactness up to total degree 10.
product_rule, a C++ code which constructs a product quadrature rule from distinct 1D factor rules.
pyramid_felippa_rule, a C++ code which returns a Felippa quadrature rule for approximating integrals over the interior of a pyramid in 3D.
pyramid_jaskowiec_rule, a C++ 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, a C++ code which computes a conical product quadrature rule over the interior of the unit pyramid in 3D;
pyramid_witherden_rule, a C++ code which returns a Witherden quadrature rule, with exactness up to total degree 10, over the interior of a pyramid.
quad_rule, a C++ code which defines 1-dimensional quadrature rules.
quadrilateral_witherden_rule, a C++ code which returns a symmetric Witherden quadrature rule for the quadrilateral, with exactness up to total degree 21.
sandia_rules, a C++ code which produces 1D quadrature rules of Chebyshev, Clenshaw Curtis, Fejer 2, Gegenbauer, generalized Hermite, generalized Laguerre, Hermite, Jacobi, Laguerre, Legendre and Patterson types.
simplex_gm_rule, a C++ 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, a C++ code which computes Lebedev quadrature rules on the surface of the unit sphere in 3D.
square_arbq_rule, a C++ 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, a C++ code which returns a Felippa quadrature rule over the interior of a square in 2D.
square_minimal_rule, a C++ 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, a C++ 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, a C++ 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, a C++ code which returns a Felippa quadrature rule for approximating integrals over the interior of a tetrahedron in 3D.
tetrahedron_jaskowiec_rule, a C++ 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, a C++ code which defines a Keast quadrature rule, with exactness degrees 0 through 8, over the interior of a tetrahedron in 3D.
tetrahedron_ncc_rule, a C++ code which defines Newton-Cotes closed (NCC) quadrature rules over the interior of a tetrahedron in 3D.
tetrahedron_nco_rule, a C++ code which defines Newton-Cotes open (NCO) quadrature rules over the interior of a tetrahedron in 3D.
tetrahedron_witherden_rule, a C++ code which returns a symmetric Witherden quadrature rule for the tetrahedron, with exactness up to total degree 10.
triangle_dunavant_rule, a C++ code which defines Dunavant rules for quadrature over the interior of a triangle in 2D.
triangle_fekete_rule, a C++ code which defines a Fekete rule for interpolation or quadrature over the interior of a triangle in 2D.
triangle_felippa_rule, a C++ code which returns a Felippa quadrature rule for approximating integrals over the interior of a triangle in 2D.
triangle_lyness_rule, a C++ code which returns a Lyness-Jespersen quadrature rule over the interior of a triangle in 2D.
triangle_ncc_rule, a C++ code which defines a Newton-Cotes Closed (NCC) quadrature rule over the interior of a triangle in 2D.
triangle_nco_rule, a C++ code which defines a Newton-Cotes Open (NCO) quadrature rule over the interior of a triangle in 2D.
triangle_symq_rule, a C++ 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, a C++ code which generates a quadrature rule over the interior of a triangle in 2D, determined by Taylor, Wingate, and Bos.
triangle_wandzura_rule, a C++ code which defines a Wandzura rule for quadrature over the interior of a triangle in 2D.
triangle_witherden_rule, a C++ code which returns a symmetric Witherden quadrature rule for the triangle, with exactness up to total degree 20.
truncated_normal_rule, a C++ 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, a C++ code which returns a Felippa quadrature rule for approximating integrals over the interior of the unit wedge in 3D.