CLALSD(3)

💖 clalsd.f(3) — Library Functions Manual 💖

okay bestie, welcome to clalsd.f(3) from the Library Functions Manual — the header path is literally /home/abui...RC/clalsd.f(3), and this whole page is about one very specific linear-algebra slay. 🫶✨

📛 NAME 📛

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/clalsd.f

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

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

💅 Function/Subroutine Documentation 💅

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

CLALSD uses the singular value decomposition of A to solve the least squares problem. Iconic. No cap.

🌟 Purpose 🌟

CLALSD 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.

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 — UPLO is CHARACTER*1. = 'U': D and E define an upper bidiagonal matrix. = 'L': D and E define a lower bidiagonal matrix.
• SMLSIZ — SMLSIZ is INTEGER. The maximum size of the subproblems at the bottom of the computation tree.
• N — N is INTEGER. The dimension of the bidiagonal matrix. N >= 0.
• NRHS — NRHS is INTEGER. The number of columns of B. NRHS must be at least 1.
• D — D is 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 — E is REAL array, dimension (N-1). Contains the super-diagonal entries of the bidiagonal matrix. On exit, E has been destroyed.
• B — B is COMPLEX 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 — LDB is INTEGER. The leading dimension of B in the calling subprogram. LDB must be at least max(1,N).
• RCOND — RCOND is 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 — RANK is INTEGER. The number of singular values of A greater than RCOND times the largest singular value.
• WORK — WORK is COMPLEX array, dimension (N * NRHS).
• RWORK — RWORK is REAL array, dimension at least:

(9*N + 2*N*SMLSIZ + 8*N*NLVL + 3*SMLSIZ*NRHS +
MAX( (SMLSIZ+1)**2, N*(1+NRHS) + 2*NRHS ),

where

NLVL = MAX( 0, INT( LOG_2( MIN( M,N )/(SMLSIZ+1) ) ) + 1 )

• IWORK — IWORK is INTEGER array, dimension (3*N*NLVL + 11*N).
• INFO — INFO is 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 178 of file clalsd.f.

👑 Author 👑

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LAPACK Version 3.12.0, from /home/abui...RC/clalsd.f(3) — the footer doesn’t show a separate date, so this is the source/version sign-off, bestie. ✨💖🎀🦋🌸