W4
===
[](https://pypi.python.org/pypi/w4/)
[](https://pypi.python.org/pypi/w4/)
This package provides the [W4
method](https://doi.org/10.1016/j.apnum.2022.08.019) for nonlinear root finding, inspired by the [R implementation](https://github.com/ramiromagno/w4).
Install
-------
create a virtual environment, activate it and upgrade pip:
```bash
python3 -m venv .venv
source .venv/bin/activate
pip install -U pip
```
install from pypi:
```bash
pip install w4
```
or from github repo:
```bash
pip install git+https://github.com/gmagno/w4
```
Usage
-----
```python
import numpy as np
from w4.w4 import w4
from w4.xy import Decomposition
x0: np.ndarray = np.array([0.5, 5.0])
def f(x: np.ndarray) -> np.ndarray:
return np.array([x[0] ** 2 + x[1] ** 2 - 4, x[0] ** 2 * x[1] - 1])
def fa(x: np.ndarray) -> np.ndarray:
return np.array(
[abs(x[0] ** 2) + abs(x[1] ** 2) + abs(-4), abs(x[0] ** 2 * x[1]) + abs(-1)]
)
def jac(x: np.ndarray) -> np.ndarray:
return np.array([[2 * x[0], 2 * x[1]], [2 * x[0] * x[1], x[0] ** 2]])
solution: np.ndarray = w4(
x0=x0, f=f, fa=fa, jac=jac, decomposition=Decomposition.LU, trace=True
)
print(solution)
```
Output:
```bash
[( 0, 7.26495726e-01, 0.5 , 5. )
( 1, 7.26495726e-01, 0.51413317, 4.46733668)
( 2, 6.69713968e-01, 0.52954179, 3.8709697 )
( 3, 5.84735305e-01, 0.54795009, 3.34463474)
( 4, 4.83432079e-01, 0.57024824, 2.91997823)
( 5, 3.77502437e-01, 0.5956425 , 2.59451865)
( 6, 2.78389751e-01, 0.6222772 , 2.3546681 )
( 7, 1.94497674e-01, 0.64795729, 2.18404118)
( 8, 1.29477634e-01, 0.67078251, 2.06671229)
( 9, 8.27001827e-02, 0.68957129, 1.98864688)
(10, 5.10336293e-02, 0.70398283, 1.93831422)
(11, 3.06148582e-02, 0.7143608 , 1.90680022)
(12, 1.79468274e-02, 0.7214358 , 1.88758697)
(13, 1.03240723e-02, 0.7260406 , 1.87614544)
(14, 5.84768757e-03, 0.72892454, 1.86946918)
(15, 3.35778195e-03, 0.73067466, 1.8656404 )
(16, 1.98478537e-03, 0.7317098 , 1.86347648)
(17, 1.14937826e-03, 0.73230941, 1.86226842)
(18, 6.54505913e-04, 0.73265086, 1.86160094)
(19, 3.67583154e-04, 0.73284262, 1.86123535)
(20, 2.04087865e-04, 0.73294908, 1.86103659)
(21, 1.12232060e-04, 0.73300761, 1.86092922)
(22, 6.12220725e-05, 0.73303954, 1.86087154)]
```
Tests
-----
clone repo:
```bash
git clone https://github.com/gmagno/w4
cd w4
```
create virtual environment and install dependencies
```python
python3 -m venv .venv
source .venv/bin/activate
pip install -U pip
pip install -r requirements_dev.txt
```
run tests:
```bash
make test
```
Raw data
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"description": "W4\n===\n\n[](https://pypi.python.org/pypi/w4/)\n\n[](https://pypi.python.org/pypi/w4/)\n\nThis package provides the [W4\nmethod](https://doi.org/10.1016/j.apnum.2022.08.019) for nonlinear root finding, inspired by the [R implementation](https://github.com/ramiromagno/w4).\n\nInstall\n-------\n\ncreate a virtual environment, activate it and upgrade pip:\n\n```bash\npython3 -m venv .venv\nsource .venv/bin/activate\npip install -U pip\n```\n\ninstall from pypi:\n\n```bash\npip install w4\n```\n\nor from github repo:\n\n```bash\npip install git+https://github.com/gmagno/w4\n```\n\nUsage\n-----\n\n```python\nimport numpy as np\nfrom w4.w4 import w4\nfrom w4.xy import Decomposition\n\nx0: np.ndarray = np.array([0.5, 5.0])\n\ndef f(x: np.ndarray) -> np.ndarray:\n return np.array([x[0] ** 2 + x[1] ** 2 - 4, x[0] ** 2 * x[1] - 1])\n\ndef fa(x: np.ndarray) -> np.ndarray:\n return np.array(\n [abs(x[0] ** 2) + abs(x[1] ** 2) + abs(-4), abs(x[0] ** 2 * x[1]) + abs(-1)]\n )\n\ndef jac(x: np.ndarray) -> np.ndarray:\n return np.array([[2 * x[0], 2 * x[1]], [2 * x[0] * x[1], x[0] ** 2]])\n\nsolution: np.ndarray = w4(\n x0=x0, f=f, fa=fa, jac=jac, decomposition=Decomposition.LU, trace=True\n)\n\nprint(solution)\n```\n\nOutput:\n\n```bash\n[( 0, 7.26495726e-01, 0.5 , 5. )\n ( 1, 7.26495726e-01, 0.51413317, 4.46733668)\n ( 2, 6.69713968e-01, 0.52954179, 3.8709697 )\n ( 3, 5.84735305e-01, 0.54795009, 3.34463474)\n ( 4, 4.83432079e-01, 0.57024824, 2.91997823)\n ( 5, 3.77502437e-01, 0.5956425 , 2.59451865)\n ( 6, 2.78389751e-01, 0.6222772 , 2.3546681 )\n ( 7, 1.94497674e-01, 0.64795729, 2.18404118)\n ( 8, 1.29477634e-01, 0.67078251, 2.06671229)\n ( 9, 8.27001827e-02, 0.68957129, 1.98864688)\n (10, 5.10336293e-02, 0.70398283, 1.93831422)\n (11, 3.06148582e-02, 0.7143608 , 1.90680022)\n (12, 1.79468274e-02, 0.7214358 , 1.88758697)\n (13, 1.03240723e-02, 0.7260406 , 1.87614544)\n (14, 5.84768757e-03, 0.72892454, 1.86946918)\n (15, 3.35778195e-03, 0.73067466, 1.8656404 )\n (16, 1.98478537e-03, 0.7317098 , 1.86347648)\n (17, 1.14937826e-03, 0.73230941, 1.86226842)\n (18, 6.54505913e-04, 0.73265086, 1.86160094)\n (19, 3.67583154e-04, 0.73284262, 1.86123535)\n (20, 2.04087865e-04, 0.73294908, 1.86103659)\n (21, 1.12232060e-04, 0.73300761, 1.86092922)\n (22, 6.12220725e-05, 0.73303954, 1.86087154)]\n```\n\nTests\n-----\n\nclone repo:\n\n```bash\ngit clone https://github.com/gmagno/w4\ncd w4\n```\n\ncreate virtual environment and install dependencies\n\n```python\npython3 -m venv .venv\nsource .venv/bin/activate\npip install -U pip\npip install -r requirements_dev.txt\n```\n\nrun tests:\n\n```bash\nmake test\n```\n\n\n",
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