numpy-numerical-analysis

name	numpy-numerical-analysis
version	1.0.0
description	NumPy for matrix operations, FFT, linear algebra, and numerical computations in marine engineering
type	reference
author	workspace-hub
category	data
tags	["numpy","numerical-analysis","matrix-operations","fft","linear-algebra","engineering"]
platforms	["python"]
capabilities	[]
requires	[]

Numpy Numerical Analysis

When to Use This Skill

Use NumPy numerical analysis when you need:

• Matrix operations - 6DOF equations of motion, mass matrices, stiffness matrices
• FFT analysis - Frequency domain analysis, spectral density, response spectra
• Linear algebra - Solve linear systems, eigenvalue analysis, matrix decomposition
• Array operations - Efficient computations on large datasets
• Numerical integration - Time-stepping, ODE solvers
• Signal processing - Filtering, windowing, convolution

Avoid when:

• Symbolic mathematics needed (use SymPy)
• Sparse matrices dominate (use SciPy sparse)
• GPU acceleration required (use CuPy or JAX)
• Distributed computing needed (use Dask)

Complete Examples

Example 1: 6DOF Time-Domain Simulation

import numpy as np
import plotly.graph_objects as go

def simulate_6dof_vessel_motion(
    mass_matrix: np.ndarray,
    damping_matrix: np.ndarray,
    stiffness_matrix: np.ndarray,
    force_time_series: np.ndarray,
    time: np.ndarray

*See sub-skills for full details.*
### Example 2: RAO Calculation from FFT

```python
def calculate_rao_from_time_series(
    wave_elevation: np.ndarray,
    vessel_response: np.ndarray,
    dt: float
) -> tuple[np.ndarray, np.ndarray]:
    """
    Calculate Response Amplitude Operator (RAO) from time series.

    RAO(ω) = |Response(ω)| / |Wave(ω)|

*See sub-skills for full details.*
### Example 3: Mooring Stiffness Matrix

```python
def calculate_mooring_stiffness_matrix(
    num_lines: int,
    pretension: float,
    fairlead_radius: float,
    fairlead_depth: float,
    line_azimuth: np.ndarray,
    weight_per_length: float
) -> np.ndarray:
    """

*See sub-skills for full details.*
### Example 4: Statistical Analysis of Extremes

```python
def extreme_value_statistics(
    data: np.ndarray,
    method:  = 
) -> :
    
    Convolve impulse response  force time series.

    Response() = ∫ h() * F() dτ

*See sub-skills  full details.*



- **NumPy Documentation**: https://numpy.org/doc/
- **NumPy  MATLAB Users**: https://numpy.org/doc/stable/user/numpy--matlab-users.html
- **Linear Algebra**: https://numpy.org/doc/stable/reference/routines.linalg.html
- **FFT Module**: https://numpy.org/doc/stable/reference/routines.fft.html
- **SciPy ()**: https://scipy.org/

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**Use this skill   numerical computations  DigitalModel!**



- [ Array Creation  Operations ()]()
- [ 6DOF Equations of Motion]()
- [ FFT  Frequency Analysis]()
- [ Linear Algebra Operations]()
- [ Numerical Integration]()
- [ Use Vectorization ()]()