Fix least squares solver

[lilkeet]

Solves #683.
Not enough memory was being allocated for the iwork array which caused Lapack to sometimes write past the end of the sequence.
The natural log was used instead of binary log which was fine for certain tensor shapes since floor(ln(n)) == floor(log2(n)) for certain small n.
From Lapack's documentation:

!>          LWORK is INTEGER
!>          The dimension of the array WORK. LWORK must be at least 1.
!>          The exact minimum amount of workspace needed depends on M,
!>          N and NRHS. As long as LWORK is at least
!>              12*N + 2*N*SMLSIZ + 8*N*NLVL + N*NRHS + (SMLSIZ+1)**2,
!>          if M is greater than or equal to N or
!>              12*M + 2*M*SMLSIZ + 8*M*NLVL + M*NRHS + (SMLSIZ+1)**2,
!>          if M is less than N, the code will execute correctly.
!>          SMLSIZ is returned by ILAENV and is equal to the maximum
!>          size of the subproblems at the bottom of the computation
!>          tree (usually about 25), and
!>             NLVL = MAX( 0, INT( LOG_2( MIN( M,N )/(SMLSIZ+1) ) ) + 1 )
!>          For good performance, LWORK should generally be larger.
!>
!>          If LWORK = -1, then a workspace query is assumed; the routine
!>          only calculates the optimal size of the array WORK and the
!>          minimum size of the array IWORK, and returns these values as
!>          the first entries of the WORK and IWORK arrays, and no error
!>          message related to LWORK is issued by XERBLA.

[gemini-code-assist]

Summary of Changes

Hello @lilkeet, I'm Gemini Code Assist¹! I'm currently reviewing this pull request and will post my feedback shortly. In the meantime, here's a summary to help you and other reviewers quickly get up to speed!

This pull request addresses a critical issue in the least squares solver's memory allocation for the iwork array by correcting the nlvl parameter calculation. By switching from natural logarithm to binary logarithm as specified by Lapack's documentation, the solver now accurately determines the required workspace, preventing potential memory overflows and ensuring robust operation.

Highlights

• Corrected nlvl calculation: The calculation for nlvl (level of recursion) in the gelsd function was updated to use the binary logarithm (log2) instead of the natural logarithm (ln), aligning with Lapack's documentation for optimal workspace allocation.
• Resolved iwork array memory allocation: The previous incorrect nlvl calculation could lead to insufficient memory allocation for the iwork array, potentially causing Lapack to write past allocated memory. This fix ensures correct memory provisioning.

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[gemini-code-assist]

Code Review

This pull request addresses a critical bug in the gelsd wrapper for the least squares solver. The calculation for nlvl was incorrectly using the natural logarithm (ln) instead of the binary logarithm (log2), which is specified by the LAPACK documentation. This error could lead to insufficient memory allocation for the iwork array, risking memory corruption. The submitted change corrects the formula by using log2, which is the proper fix for this issue. The change is accurate and effectively resolves the bug.

[mratsim]

Excellent catch, thanks!