f77_rule, a Fortran77 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.
f77_rule is available in a C version and a C++ version and a Fortran77 version and a Python version.
ccn_rule, a Fortran77 code which defines a Clenshaw Curtis Nested (CCN) quadrature rule.
circle_rule, a Fortran77 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 Fortran77 code which defines a Clenshaw Curtis quadrature rule.
cube_arbq_rule, a Fortran77 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 Fortran77 code which returns the points and weights of a Felippa quadrature rule over the interior of a cube in 3D.
disk_rule, a Fortran77 code which computes a quadrature rule over the interior of a disk of radius R centered at the origin.
disk01_rule, a Fortran77 code which computes quadrature rules over the interior of the unit disk in 2D, with radius 1 and center (0,0).
filon_rule, a Fortran77 code which uses Filon's method to approximate integrals including an oscillatory factor of sin(k*x) or cos(k*x).
hermite_rule, a Fortran77 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).
kronrod_rule, a Fortran77 code which computes a Gauss and Gauss-Kronrod pair of quadrature rules of arbitrary order, by Robert Piessens, Maria Branders.
laguerre_rule, a Fortran77 code which returns a Gauss-Laguerre quadrature rule for estimating the integral of a function with density exp(-x) over the interval [0,+oo).
legendre_fast_rule, a Fortran77 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 Fortran77 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 Fortran77 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 Fortran77 code which returns a Felippa quadrature rule over the interior of a line segment in 1D.
line_ncc_rule, a Fortran77 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 Fortran77 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 Fortran77 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 Fortran77 code which returns a Gauss-Patterson quadrature rule of order 1, 3, 7, 15, 31, 63, 127, 255 or 511.
power_rule, a Fortran77 code which constructs a power rule, that is, a product quadrature rule from identical 1D factor rules.
product_rule, a Fortran77 code which constructs a product quadrature rule from distinct 1D factor rules.
pyramid_felippa_rule, a Fortran77 code which returns a Felippa quadrature rule for approximating integrals over the interior of a pyramid in 3D.
pyramid_rule, a Fortran77 code which computes a conical product quadrature rule over the interior of the unit pyramid in 3D;
quad_rule, a Fortran77 code which defines 1-dimensional quadrature rules.
simplex_gm_rule, a Fortran77 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 Fortran77 code which computes Lebedev quadrature rules on the surface of the unit sphere in 3D.
square_arbq_rule, a Fortran77 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 Fortran77 code which returns a Felippa quadrature rule over the interior of a square in 2D.
square_symq_rule, a Fortran77 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 Fortran77 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 Fortran77 code which returns a Felippa quadrature rule for approximating integrals over the interior of a tetrahedron in 3D.
triangle_felippa_rule, a Fortran77 code which returns a Felippa quadrature rule for approximating integrals over the interior of a triangle in 2D.
triangle_symq_rule, a Fortran77 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.
truncated_normal_rule, a Fortran77 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 Fortran77 code which returns a Felippa quadrature rule for approximating integrals over the interior of the unit wedge in 3D.