Math

linspace(start, stop, n)

Python linspace function

heaviside(x)

Heaviside step function

fortsign(x, y)

Fortran sign function

mat_split(m)

Split matrix into row vectors

This function can be used for building physics-informed neural networks.

central_diff(y, x)

Central difference

central_diff(y, dx)

central_diff!(dy, y, x)

Central difference

central_diff!(dy, y, dx)

upwind_diff(y, x; stream)

Upwind difference

upwind_diff(y, dx; stream)

upwind_diff!(dy, y, x; stream)

Upwind difference

upwind_diff!(dy, y, dx; stream)

unstruct_diff(u, x, nx; mode)

Finite difference for pseudo-unstructured mesh

unstruct_diff(u, x, nx, dim; mode)

lgwt(N, a, b)

Gauss Legendre integral for fast spectral method

Arguments

• N: number of quadrature points,
• a, b: integral range

extract_last(a, idx; mode)

Extract subarray except the last column