feat: add `lapack/base/dgtts2`

[aayush0325]

Description

What is the purpose of this pull request?

This pull request:

• adds lapack/base/dgtts2

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No.

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• [x] Read, understood, and followed the contributing guidelines.

---

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[stdlib-bot]

Coverage Report

Package	Statements	Branches	Functions	Lines
lapack/base/dgtts2	$\color{green}660/660$ $\color{green}+100.00\%$	$\color{green}38/38$ $\color{green}+100.00\%$	$\color{green}5/5$ $\color{green}+100.00\%$	$\color{green}660/660$ $\color{green}+100.00\%$

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 dgttrs

DL_T3 = np.array([0.25, 0.26666667]) 
D_T3 = np.array([4.0, 3.75, 3.73333333])
DU_T3 = np.array([1.0, 0.73333333])
DU2_T3 = np.array([0.0]) 
IPIV_T3 = np.array([1, 2, 3])

B_T3 = np.array([
    [7.0, 8.0, 7.0],  
    [2.0, 3.0, 4], 
    [1.0, 1.5, 2.0]
], dtype=np.float64)

X_T3, info = dgttrs(DL_T3, D_T3, DU_T3, DU2_T3, IPIV_T3, B_T3)

np.set_printoptions(precision=20, suppress=True)
print(X_T3.flatten(order='F'))

column-major, no transpose, nrhs > 1

[aayush0325]

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

DL_T3 = np.array([0.25, 0.26666667]) 
D_T3 = np.array([4.0, 3.75, 3.73333333])
DU_T3 = np.array([1.0, 0.73333333])
DU2_T3 = np.array([0.0]) 
IPIV_T3 = np.array([1, 2, 3])

B_T3 = np.array([
    [7.0, 8.0, 7.0],  
    [2.0, 3.0, 4], 
    [1.0, 1.5, 2.0]   
], dtype=np.float64)

X_T3, info = dgttrs(DL_T3, D_T3, DU_T3, DU2_T3, IPIV_T3, B_T3, trans='T')

np.set_printoptions(precision=20, suppress=True)
print(X_T3.flatten(order='F'))

column-major, transpose, nrhs > 1

[aayush0325]

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

DL_T3 = np.array([0.25, 0.26666667]) 
D_T3 = np.array([4.0, 3.75, 3.73333333])
DU_T3 = np.array([1.0, 0.73333333])
DU2_T3 = np.array([0.0]) 
IPIV_T3 = np.array([1, 2, 3])

B_T3 = np.array([
    [7.0, 2.0, 1.0], 
    [8.0, 3.0, 1.5],
    [7.0, 4.0, 2.0] 
], dtype=np.float64)

X_T3, info = dgttrs(DL_T3, D_T3, DU_T3, DU2_T3, IPIV_T3, B_T3)

np.set_printoptions(precision=20, suppress=True)
print(X_T3.ravel(order='C'))

row-major, no transpose, nrhs > 1

[aayush0325]

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

DL_T3 = np.array([0.25, 0.26666667]) 
D_T3 = np.array([4.0, 3.75, 3.73333333])
DU_T3 = np.array([1.0, 0.73333333])
DU2_T3 = np.array([0.0]) 
IPIV_T3 = np.array([1, 2, 3])

B_T3 = np.array([
    [7.0, 2.0, 1.0], 
    [8.0, 3.0, 1.5],  
    [7.0, 4.0, 2.0] 
], dtype=np.float64)

X_T3, info = dgttrs(DL_T3, D_T3, DU_T3, DU2_T3, IPIV_T3, B_T3, trans='T')

np.set_printoptions(precision=20, suppress=True)
print(X_T3.ravel(order='C'))

row-major, transpose, nrhs > 1

[aayush0325]

*     Determine the number of right-hand sides to solve at a time.
*
      IF( NRHS.EQ.1 ) THEN
         NB = 1
      ELSE
         NB = MAX( 1, ILAENV( 1, 'DGTTRS', TRANS, N, NRHS, -1, -1 ) )
      END IF
*
      IF( NB.GE.NRHS ) THEN
         CALL DGTTS2( ITRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB )
      ELSE
         DO 10 J = 1, NRHS, NB
            JB = MIN( NRHS-J+1, NB )
            CALL DGTTS2( ITRANS, N, JB, DL, D, DU, DU2, IPIV, B( 1,
     $                   J ),
     $                   LDB )
   10    CONTINUE
      END IF
*
*     End of DGTTRS

I've used dgttrs from scipy to test my implementation for dgtts2 because under the hood dgttrs is just a wrapper over dgtts2. did this because i couldn't find the scipy implementation for dgtts2

https://github.com/aayush0325/lapack/blob/master/SRC/dgttrs.f#L208

[aayush0325]

/stdlib merge