feat: add lapack/base/dgttrf

[aayush0325]

Description

What is the purpose of this pull request?

This pull request:

• adds lapack/base/dgttrf

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No.

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• Read, understood, and followed the contributing guidelines.

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[stdlib-bot]

Coverage Report

Package	Statements	Branches	Functions	Lines
lapack/base/dgttrf	$\color{green}438/438$ $\color{green}+100.00\%$	$\color{green}29/29$ $\color{green}+100.00\%$	$\color{green}3/3$ $\color{green}+100.00\%$	$\color{green}438/438$ $\color{green}+100.00\%$

The above coverage report was generated for the changes in this PR.

[aayush0325]

/stdlib update-copyright-years

[aayush0325]

import numpy as np
from scipy.linalg.lapack import dgttrf

n = 9
dl = np.array([3.0] * 8, dtype=np.float64)
d = np.array([1.0] * 9, dtype=np.float64)
du = np.array([4.0] * 8, dtype=np.float64)

dl, d, du, du2, ipiv, info = dgttrf(dl, d, du)

testing all values against the scipy implementation.

[aayush0325]

ready for a review!

[aayush0325]

this PR is being used as an example in contributing FAQs (PR #6157) mentioning this here as a reminder to update the link in that doc to redirect to the merged package.

cc @anandkaranubc @ShabiShett07

[aayush0325]

I've updated the tests to use deepEqual instead of isApprox

[aayush0325]

import numpy as np
from scipy.linalg.lapack import dgttrf

DL = np.array([1, 1])
D = np.array([2, 3, 1])
DU = np.array([1, 1])

DL_o, D_o, DU_o, DU2_o, IPIV_o, info = dgttrf(DL, D, DU)

np.set_printoptions(precision=20, suppress=True)
print(info)
print(DL_o)
print(D_o)
print(DU_o)
print(DU2_o)
print(IPIV_o)

DL = np.array([3, 3, 3, 3, 3, 3, 3, 3])
D = np.array([1, 1, 1, 1, 1, 1, 1, 1, 1 ])
DU = np.array([4, 4, 4, 4, 4, 4, 4, 4])

DL_o, D_o, DU_o, DU2_o, IPIV_o, info = dgttrf(DL, D, DU)

np.set_printoptions(precision=20, suppress=True)
print(info)
print(DL_o)
print(D_o)
print(DU_o)
print(DU2_o)
print(IPIV_o)

this is what i've used to write the fixtures