feat: add lapack/base/dgtts2

[aayush0325]

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• adds lapack/base/dgtts2

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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]

I was able to get the exact results by bumping up the precision to 20 places of decimals in my python code. putting it down below for reference

[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]

LDB should be compared to nrhs instead of N here as the dimensions of B are (LDB, nrhs)

while N is being used to represent the dimensions of A

[aayush0325]

/stdlib merge