| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=8), | , | dimension(:) | :: | x | the mesh on which the function points are provided |
|
| real(kind=8), | , | dimension(:) | :: | f | the function points |
|
| real(kind=8) | :: | x_i | the point at which the function value is desired |
the value at point x_i
find a linearly interpolated value of a function \(f\left(x\right)\) at point \(x_{i}\) given values of the function in \(\vec{f}\) at points \(\vec{x}\)
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=8), | intent(in), | dimension(:,:) | :: | M | The matrix |
|
| real(kind=8), | intent(in), | dimension(:) | :: | v | The vector |
|
| real(kind=8), | intent(out), | dimension(:), allocatable | :: | outv | The result |
multiply a matrix \(\mathbb{M}\) and a vector \(\vec{v}\) and get result \(\vec{outv}\)
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=8), | intent(in), | dimension(:,:) | :: | A | The matrix \(\mathbb{A}\) to be inverted |
|
| real(kind=8), | intent(out), | dimension(:) | :: | x | The vector solution \(\vec{x}\) |
|
| real(kind=8), | intent(in), | dimension(:) | :: | b | The vector \(\vec{b}\) with the boundary conditions |
solve the equation \(\mathbb{A}\vec{x} = \vec{b}\) for \(\vec{x}\) using Gauss-Seidel method