From 1501659215a20a14fa589c5a60d7fe0135c72b22 Mon Sep 17 00:00:00 2001 From: "Documenter.jl" Date: Fri, 1 Nov 2024 22:33:35 +0000 Subject: [PATCH] build based on bfb9927 --- dev/.documenter-siteinfo.json | 2 +- dev/index.html | 2 +- 2 files changed, 2 insertions(+), 2 deletions(-) diff --git a/dev/.documenter-siteinfo.json b/dev/.documenter-siteinfo.json index 510592c..5b30fd3 100644 --- a/dev/.documenter-siteinfo.json +++ b/dev/.documenter-siteinfo.json @@ -1 +1 @@ -{"documenter":{"julia_version":"1.11.1","generation_timestamp":"2024-11-01T22:32:44","documenter_version":"1.7.0"}} \ No newline at end of file +{"documenter":{"julia_version":"1.11.1","generation_timestamp":"2024-11-01T22:33:31","documenter_version":"1.7.0"}} \ No newline at end of file diff --git a/dev/index.html b/dev/index.html index a9417ea..d646ac5 100644 --- a/dev/index.html +++ b/dev/index.html @@ -1,2 +1,2 @@ -ClenshawCurtisQuadrature.jl Documentation · ClenshawCurtisQuadrature.jl
GitHub

ClenshawCurtisQuadrature.jl Documentation

ClenshawCurtisQuadrature.interpolate — Method
interpolate(taus::AbstractVector{<:Real}, N::Integer; recursive::Bool = false)

Compute a matrix of Chebyshev polynomials of the first kind $T_n(\tau)$ for $\tau=taus$ and $n = 0,1,...,N$.

Arguments

  • taus::AbstractVector{<:Real}: The points at which to evaluate the Chebyshev polynomials.
  • N::Integer: The polynomial degree.
  • recursive::Bool: If true, use the recursive formula to compute the Chebyshev polynomials within the domain [-1,1]. If false, use the trigonometric formulation. Default is false.

Returns

  • Ts: A matrix of Chebyshev polynomial values at the given values of tau.

Description

This function computes the value of the N+1 Chebyshev polynomials at the given points in the domain [-1,1]. If the input taus is a scalar, it is converted to a vector. The function then computes the unweighted Chebyshev polynomial values at each tau.

source
ClenshawCurtisQuadrature.clenshaw_curtis_nested_ivpd — Method
clenshaw_curtis_nested_ivpd(N::Integer, M::Integer, d::Integer)

Compute the Clenshaw-Curtis quadrature and Chebyshev basis function matrices for a d-th order integral.

Arguments

  • N::Integer: The polynomial degree.
  • M::Integer: The sampling degree. Must bes greater than or equal to the polynomial degree. This is equal to the total number of function sampling points minus 1.
  • d::Integer: The integral order.

Returns

  • A: The Least Squares Operator matrix.
  • P: The Quadrature Matrix.
  • T: The Chebyshev Matrix.

Description

This function computes the Clenshaw-Curtis quadrature matrices and the basis function vectors a. It first generates the Chebyshev polynomials and the Least Squares Operator matrix using the lsq_chebyshev_fit function. Then, it calculates the Constants of Integration, and constructs the S matrix. Finally, it computes the Clenshaw Curtis Quadrature matrix.

source
ClenshawCurtisQuadrature.clenshaw_curtis_ivpi — Method
clenshaw_curtis_ivpi(N::Integer, M::Integer)

Compute the Clenshaw-Curtis quadrature and Cebyshev basis function matrices for a first order initial value problem.

Arguments

  • N::Integer: The polynomial degree.
  • M::Integer: The sampling degree. Must bes greater than or equal to the polynomial degree. This is equal to the total number of function sampling points minus 1.

Returns

  • A: The Least Squares Operator matrix.
  • Ta: The "acceleration" Chebyshev Matrix.
  • P1: The Quadrature Matrix for acceleration to velocity.
  • T1: The "Velocity" Chebyshev Matrix.

Description

This function computes the Clenshaw-Curtis quadrature matrices and the basis function vectors a. It first generates the Chebyshev polynomials and the Least Squares Operator matrix using the lsq_chebyshev_fit function. Then, it calculates the "Velocity" Constants of Integration, and constructs the S matrices for "velocity". Finally, it computes the Clenshaw Curtis Quadrature matrices for acceleration to velocity.

source
ClenshawCurtisQuadrature.clenshaw_curtis_ivpii — Method
clenshaw_curtis_ivpii(N::Integer, M::Integer)

Compute the Clenshaw-Curtis quadrature and Cebyshev basis function matrices for a second order initial value problem.

Arguments

  • N::Integer: The polynomial degree.
  • M::Integer: The sampling degree. Must bes greater than or equal to the polynomial degree. This is equal to the total number of function sampling points minus 1.

Returns

  • A: The Least Squares Operator matrix.
  • Ta: The "acceleration" Chebyshev Matrix.
  • P1: The Quadrature Matrix for acceleration to velocity.
  • T1: The "Velocity" Chebyshev Matrix.
  • P2: The Quadrature Matrix for velocity to position.
  • T2: The "Position" Chebyshev Matrix.

Description

This function computes the Clenshaw-Curtis quadrature matrices and the basis function vectors a. It first generates the Chebyshev polynomials and the Least Squares Operator matrix using the lsq_chebyshev_fit function. Then, it calculates the "Position" and "Velocity" Constants of Integration, and constructs the S matrices for "velocity" and "position". Finally, it computes the Clenshaw Curtis Quadrature matrices for acceleration to velocity and velocity to position.

Example

```julia N = 5 M = 5 A, Ta, P1, T1, P2, T2 = clenshawcurtisivpii(N, M)

source
+ClenshawCurtisQuadrature.jl Documentation · ClenshawCurtisQuadrature.jl
GitHub

ClenshawCurtisQuadrature.jl Documentation

ClenshawCurtisQuadrature.interpolate — Method
interpolate(taus::AbstractVector{<:Real}, N::Integer; recursive::Bool = false)

Compute a matrix of Chebyshev polynomials of the first kind $T_n(\tau)$ for $\tau=taus$ and $n = 0,1,...,N$.

Arguments

  • taus::AbstractVector{<:Real}: The points at which to evaluate the Chebyshev polynomials.
  • N::Integer: The polynomial degree.
  • recursive::Bool: If true, use the recursive formula to compute the Chebyshev polynomials within the domain [-1,1]. If false, use the trigonometric formulation. Default is false.

Returns

  • Ts: A matrix of Chebyshev polynomial values at the given values of tau.

Description

This function computes the value of the N+1 Chebyshev polynomials at the given points in the domain [-1,1]. If the input taus is a scalar, it is converted to a vector. The function then computes the unweighted Chebyshev polynomial values at each tau.

source
ClenshawCurtisQuadrature.clenshaw_curtis_nested_ivpd — Method
clenshaw_curtis_nested_ivpd(N::Integer, M::Integer, d::Integer)

Compute the Clenshaw-Curtis quadrature and Chebyshev basis function matrices for a d-th order integral.

Arguments

  • N::Integer: The polynomial degree.
  • M::Integer: The sampling degree. Must bes greater than or equal to the polynomial degree. This is equal to the total number of function sampling points minus 1.
  • d::Integer: The integral order.

Returns

  • A: The Least Squares Operator matrix.
  • P: The Quadrature Matrix.
  • T: The Chebyshev Matrix.

Description

This function computes the Clenshaw-Curtis quadrature matrices and the basis function vectors a. It first generates the Chebyshev polynomials and the Least Squares Operator matrix using the lsq_chebyshev_fit function. Then, it calculates the Constants of Integration, and constructs the S matrix. Finally, it computes the Clenshaw Curtis Quadrature matrix.

source
ClenshawCurtisQuadrature.clenshaw_curtis_ivpi — Method
clenshaw_curtis_ivpi(N::Integer, M::Integer)

Compute the Clenshaw-Curtis quadrature and Cebyshev basis function matrices for a first order initial value problem.

Arguments

  • N::Integer: The polynomial degree.
  • M::Integer: The sampling degree. Must bes greater than or equal to the polynomial degree. This is equal to the total number of function sampling points minus 1.

Returns

  • A: The Least Squares Operator matrix.
  • Ta: The "acceleration" Chebyshev Matrix.
  • P1: The Quadrature Matrix for acceleration to velocity.
  • T1: The "Velocity" Chebyshev Matrix.

Description

This function computes the Clenshaw-Curtis quadrature matrices and the basis function vectors a. It first generates the Chebyshev polynomials and the Least Squares Operator matrix using the lsq_chebyshev_fit function. Then, it calculates the "Velocity" Constants of Integration, and constructs the S matrices for "velocity". Finally, it computes the Clenshaw Curtis Quadrature matrices for acceleration to velocity.

source
ClenshawCurtisQuadrature.clenshaw_curtis_ivpii — Method
clenshaw_curtis_ivpii(N::Integer, M::Integer)

Compute the Clenshaw-Curtis quadrature and Cebyshev basis function matrices for a second order initial value problem.

Arguments

  • N::Integer: The polynomial degree.
  • M::Integer: The sampling degree. Must bes greater than or equal to the polynomial degree. This is equal to the total number of function sampling points minus 1.

Returns

  • A: The Least Squares Operator matrix.
  • Ta: The "acceleration" Chebyshev Matrix.
  • P1: The Quadrature Matrix for acceleration to velocity.
  • T1: The "Velocity" Chebyshev Matrix.
  • P2: The Quadrature Matrix for velocity to position.
  • T2: The "Position" Chebyshev Matrix.

Description

This function computes the Clenshaw-Curtis quadrature matrices and the basis function vectors a. It first generates the Chebyshev polynomials and the Least Squares Operator matrix using the lsq_chebyshev_fit function. Then, it calculates the "Position" and "Velocity" Constants of Integration, and constructs the S matrices for "velocity" and "position". Finally, it computes the Clenshaw Curtis Quadrature matrices for acceleration to velocity and velocity to position.

Example

```julia N = 5 M = 5 A, Ta, P1, T1, P2, T2 = clenshawcurtisivpii(N, M)

source