# Compact.f90

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## Overview

*Author: Ignis*
@brief High-order compact finite difference scheme solver.

This module handles the generation of tridiagonal/pentadiagonal matrices,
LU decomposition calculations, and tridiagonal solver operations for periodic
and non-periodic boundary conditions.

## API Index

- [Module: `Compact`](#compact)
- [Subroutine: `ludcmp`](#ludcmp)
- [Subroutine: `ludcmp_allocate`](#ludcmp_allocate)
- [Subroutine: `ludcmp_deallocate`](#ludcmp_deallocate)
- [Subroutine: `ludcmp_testalloc`](#ludcmp_testalloc)
- [Subroutine: `ludcmp_calculate`](#ludcmp_calculate)
- [Subroutine: `test_nonp_lud1`](#test_nonp_lud1)
- [Subroutine: `test_nonp_lud2`](#test_nonp_lud2)
- [Subroutine: `test_p_lud1`](#test_p_lud1)
- [Subroutine: `test_p_lud2`](#test_p_lud2)
- [Subroutine: `nonp_lud`](#nonp_lud)
- [Subroutine: `p_lud`](#p_lud)
- [Subroutine: `stdlu`](#stdlu)
- [Subroutine: `ptdlu`](#ptdlu)
- [Subroutine: `rhs1np`](#rhs1np)
- [Subroutine: `dfnonp`](#dfnonp)
- [Subroutine: `dfp`](#dfp)
- [Subroutine: `ptdslv`](#ptdslv)
- [Subroutine: `d2fp`](#d2fp)
- [Subroutine: `tdslv`](#tdslv)
- [Subroutine: `d2fnonp`](#d2fnonp)

---

## API Reference

### [Module] `Compact`

*Author: Ignis*
@brief High-order compact finite difference scheme solver.

This module handles the generation of tridiagonal/pentadiagonal matrices,
LU decomposition calculations, and tridiagonal solver operations for periodic
and non-periodic boundary conditions.

---

### [Subroutine] `ludcmp`

```fortran
subroutine ludcmp(nx, ny, nz, xp, yp, zp)
```

Entry point for LU decomposition calculations.

Prepares the workspace allocations and runs the decomposition calculation for all three directions.

- ` nx `: Grid size in x-direction.
- ` ny `: Grid size in y-direction.
- ` nz `: Grid size in z-direction.
- ` xp `: Periodic flag for x-direction (0 = periodic, other = non-periodic).
- ` yp `: Periodic flag for y-direction (0 = periodic, other = non-periodic).
- ` zp `: Periodic flag for z-direction (0 = periodic, other = non-periodic).

---

### [Subroutine] `ludcmp_allocate`

```fortran
subroutine ludcmp_allocate(nx, ny, nz, xp, yp, zp)
```

*No description provided.*

---

### [Subroutine] `ludcmp_deallocate`

```fortran
subroutine ludcmp_deallocate(xp, yp, zp)
```

*No description provided.*

---

### [Subroutine] `ludcmp_testalloc`

```fortran
subroutine ludcmp_testalloc()
```

*No description provided.*

---

### [Subroutine] `ludcmp_calculate`

```fortran
subroutine ludcmp_calculate(nx, ny, nz, xp, yp, zp)
```

*No description provided.*

---

### [Subroutine] `test_nonp_lud1`

```fortran
subroutine test_nonp_lud1(xx, coef)
```

*No description provided.*

---

### [Subroutine] `test_nonp_lud2`

```fortran
subroutine test_nonp_lud2(xx, coef)
```

*No description provided.*

---

### [Subroutine] `test_p_lud1`

```fortran
subroutine test_p_lud1(xx, coef1, coef2)
```

*No description provided.*

---

### [Subroutine] `test_p_lud2`

```fortran
subroutine test_p_lud2(xx, coef1, coef2)
```

*No description provided.*

---

### [Subroutine] `nonp_lud`

```fortran
subroutine nonp_lud(xyz, xx)
```

*No description provided.*

---

### [Subroutine] `p_lud`

```fortran
subroutine p_lud(xyz, xx)
```

*No description provided.*

---

### [Subroutine] `stdlu`

```fortran
subroutine stdlu(a, n, l)
```

*No description provided.*

---

### [Subroutine] `ptdlu`

```fortran
subroutine ptdlu(a, n, l, w)
```

*No description provided.*

---

### [Subroutine] `rhs1np`

```fortran
subroutine rhs1np(n, h, x, dx, nd)
```

*No description provided.*

---

### [Subroutine] `dfnonp`

```fortran
subroutine dfnonp(n, h, x, dx, nd, dir)
```

*No description provided.*

---

### [Subroutine] `dfp`

```fortran
subroutine dfp(n, h, x, dx, nd, dir)
```

*No description provided.*

---

### [Subroutine] `ptdslv`

```fortran
subroutine ptdslv(r, n, l, w, nd)
```

*No description provided.*

---

### [Subroutine] `d2fp`

```fortran
subroutine d2fp(n, h, x, dx, nd, dir)
```

*No description provided.*

---

### [Subroutine] `tdslv`

```fortran
subroutine tdslv(r, n, l, nd)
```

*No description provided.*

---

### [Subroutine] `d2fnonp`

```fortran
subroutine d2fnonp(n, h, x, dx, nd, dir)
```

*No description provided.*

---