SRC/slalsd.f(3)

🌸 SRC/slalsd.f(3) — Library Functions Manual 🌸

okay bestie, welcome to the manual page for SRC/slalsd.f 💖. This is the Library Functions Manual moment where slalsd pulls up with singular value decomposition energy and solves a least-squares problem. iconic behavior, honestly ✨

💖 NAME 💖

SRC/slalsd.f

✨ SYNOPSIS ✨

Functions/Subroutines

subroutine slalsd (uplo, smlsiz, n, nrhs, d, e, b, ldb, rcond, rank,
    work, iwork, info)
    SLALSD uses the singular value decomposition of A to solve the least
    squares problem.

🎀 Function/Subroutine Documentation 🎀

subroutine slalsd (character uplo, integer smlsiz, integer n, integer nrhs,
    real, dimension( * ) d, real, dimension( * ) e, real, dimension( ldb, *
    ) b, integer ldb, real rcond, integer rank, real, dimension( * ) work,
    integer, dimension( * ) iwork, integer info)

SLALSD uses the singular value decomposition of A to solve the least squares problem. 🫶

🌟 Purpose 🌟

okay so SLALSD uses the singular value decomposition of A to solve the least squares problem of finding X to minimize the Euclidean norm of each column of A*X-B, where A is N-by-N upper bidiagonal, and X and B are N-by-NRHS. The solution X overwrites B. periodt 💅

The singular values of A smaller than RCOND times the largest singular value are treated as zero in solving the least squares problem; in this case a minimum norm solution is returned. The actual singular values are returned in D in ascending order ✨.

💅 Parameters 💅

• UPLO — CHARACTER*1. = 'U': D and E define an upper bidiagonal matrix. = 'L': D and E define a lower bidiagonal matrix.
• SMLSIZ — INTEGER. The maximum size of the subproblems at the bottom of the computation tree.
• N — INTEGER. The dimension of the bidiagonal matrix. N >= 0.
• NRHS — INTEGER. The number of columns of B. NRHS must be at least 1.
• D — REAL array, dimension (N). On entry D contains the main diagonal of the bidiagonal matrix. On exit, if INFO = 0, D contains its singular values.
• E — REAL array, dimension (N-1). Contains the super-diagonal entries of the bidiagonal matrix. On exit, E has been destroyed. 💀 bestie, E does not survive this — that’s the documented exit condition, no cap.
• B — REAL array, dimension (LDB,NRHS). On input, B contains the right hand sides of the least squares problem. On output, B contains the solution X.
• LDB — INTEGER. The leading dimension of B in the calling subprogram. LDB must be at least max(1,N).
• RCOND — REAL. The singular values of A less than or equal to RCOND times the largest singular value are treated as zero in solving the least squares problem. If RCOND is negative, machine precision is used instead. For example, if diag(S)*X=B were the least squares problem, where diag(S) is a diagonal matrix of singular values, the solution would be X(i) = B(i) / S(i) if S(i) is greater than RCOND*max(S), and X(i) = 0 if S(i) is less than or equal to RCOND*max(S).
• RANK — INTEGER. The number of singular values of A greater than RCOND times the largest singular value.
• WORK — REAL array, dimension at least (9*N + 2*N*SMLSIZ + 8*N*NLVL + N*NRHS + (SMLSIZ+1)**2), where NLVL = max(0, INT(log_2 (N/(SMLSIZ+1))) + 1).
• IWORK — INTEGER array, dimension at least (3*N*NLVL + 11*N).
• INFO — INTEGER. = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. > 0: The algorithm failed to compute a singular value while working on the submatrix lying in rows and columns INFO/(N+1) through MOD(INFO,N+1).

👑 Author 👑

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

🫶 Contributors: 🫶

Ming Gu and Ren-Cang Li, Computer Science Division, University of California at Berkeley, USA

Osni Marques, LBNL/NERSC, USA

Definition at line 171 of file slalsd.f.

💫 Author 💫

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mwah 💋 — that’s the whole page, bestie: LAPACK Version 3.12.0, SRC/slalsd.f(3), no cap 🎀✨