gaussLobattoQuadrature

Gauss-Lobatto Quadrature

@safe pure nothrow @nogc

size_t

(

)

(

scope T[] x

scope T[] w

scope T[] work

const T alpha = 0

const T beta = 0

)

Parameters

x T[]: (out) user-allocated quadrature nodes in ascending order length of N
w T[]: (out) user-allocated corresponding quadrature weights length of N
work T[]: (temp) user-allocated workspace length of greate or equal to N ^^ 2
alpha T: (optional) parameter '> -1'
beta T: (optional) parameter '> -1'

Return Value

Type: size_t

0 on success, xSTEQR LAPACK code on numerical error.

Examples

import mir.math.common;

auto n = 7;
auto x = new double[n];
auto w = new double[n];
auto work = new double[n ^^ 2];

gaussLobattoQuadrature(x, w, work);

static immutable xc =
   [-1,
    -sqrt(5.0 / 11 + 2.0 / 11 * sqrt(5.0 / 3)),
    -sqrt(5.0 / 11 - 2.0 / 11 * sqrt(5.0 / 3)),
     0.        ,
    +sqrt(5.0 / 11 - 2.0 / 11 * sqrt(5.0 / 3)),
    +sqrt(5.0 / 11 + 2.0 / 11 * sqrt(5.0 / 3)),
     1];

static immutable wc =
   [1.0 / 21,
    (124.0 - 7 * sqrt(15.0)) / 350,
    (124.0 + 7 * sqrt(15.0)) / 350,
    256.0 / 525,
    (124.0 + 7 * sqrt(15.0)) / 350,
    (124.0 - 7 * sqrt(15.0)) / 350,
    1.0 / 21];

foreach (i; 0 .. n)
    assert(x[i].approxEqual(xc[i]));
foreach (i; 0 .. n)
    assert(w[i].approxEqual(wc[i]));

The OpenD Programming Language

gaussLobattoQuadrature

Parameters

Return Value

Examples

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