lals0(3)

📦

version 3.12.1 · 9 versions

3.12.1 · arch rolling (latest)
3.12.0 · opensuse-leap 16.0
3.12.1 · ubuntu stonking
3.12.1 · ubuntu questing
3.12.0 · ubuntu noble
3.12.0 · ubuntu noble
3.12.0 · centos-stream 10, fedora 43, fedora 44
3.12.1 · ubuntu resolute
3.12.1 · debian trixie

💖 NAME 💖

lals0(3) — lals0: back multiplying factors, step in gelsd 💅

✨ SYNOPSIS ✨

okay bestie, here are the four subroutines that live on this page 👑 they’re all basically the same vibe but with different precision/type energy.

🎀 Functions 🎀

clals0 — CLALS0 applies back multiplying factors in solving the least squares problem using divide and conquer SVD approach. Used by sgelsd.

subroutine clals0 (icompq, nl, nr, sqre, nrhs, b, ldb, bx, ldbx, perm,
    givptr, givcol, ldgcol, givnum, ldgnum, poles, difl, difr, z, k, c,
    s, rwork, info)

dlals0 — DLALS0 applies back multiplying factors in solving the least squares problem using divide and conquer SVD approach. Used by sgelsd.

subroutine dlals0 (icompq, nl, nr, sqre, nrhs, b, ldb, bx, ldbx, perm,
    givptr, givcol, ldgcol, givnum, ldgnum, poles, difl, difr, z, k, c,
    s, work, info)

slals0 — SLALS0 applies back multiplying factors in solving the least squares problem using divide and conquer SVD approach. Used by sgelsd.

subroutine slals0 (icompq, nl, nr, sqre, nrhs, b, ldb, bx, ldbx, perm,
    givptr, givcol, ldgcol, givnum, ldgnum, poles, difl, difr, z, k, c,
    s, work, info)

zlals0 — ZLALS0 applies back multiplying factors in solving the least squares problem using divide and conquer SVD approach. Used by sgelsd.

subroutine zlals0 (icompq, nl, nr, sqre, nrhs, b, ldb, bx, ldbx, perm,
    givptr, givcol, ldgcol, givnum, ldgnum, poles, difl, difr, z, k, c,
    s, rwork, info)

🌸 Detailed Description 🌸

okay so this is where the actual function deets live 💅 no cap.

🦋 Function Documentation 🦋

bestie, here come the subroutines themselves ✨

👑 subroutine clals0 👑

subroutine clals0 (integer icompq, integer nl, integer nr, integer sqre,
    integer nrhs, complex, dimension( ldb, * ) b, integer ldb, complex,
    dimension( ldbx, * ) bx, integer ldbx, integer, dimension( * ) perm,
    integer givptr, integer, dimension( ldgcol, * ) givcol, integer ldgcol,
    real, dimension( ldgnum, * ) givnum, integer ldgnum, real, dimension(
    ldgnum, * ) poles, real, dimension( * ) difl, real, dimension( ldgnum, *
    ) difr, real, dimension( * ) z, integer k, real c, real s, real,
    dimension( * ) rwork, integer info)

CLALS0 applies back multiplying factors in solving the least squares problem using divide and conquer SVD approach. Used by sgelsd.

💖 Purpose 💖

CLALS0 applies back the multiplying factors of either the left or the right singular vector matrix of a diagonal matrix appended by a row to the right hand side matrix B in solving the least squares problem using the divide-and-conquer SVD approach.

For the left singular vector matrix, three types of orthogonal matrices are involved:

(1L) Givens rotations: the number of such rotations is GIVPTR; the pairs of columns/rows they were applied to are stored in GIVCOL; and the C- and S-values of these rotations are stored in GIVNUM.
(2L) Permutation. The (NL+1)-st row of B is to be moved to the first row, and for J=2:N, PERM(J)-th row of B is to be moved to the J-th row.
(3L) The left singular vector matrix of the remaining matrix.

For the right singular vector matrix, four types of orthogonal matrices are involved:

(1R) The right singular vector matrix of the remaining matrix.
(2R) If SQRE = 1, one extra Givens rotation to generate the right null space.
(3R) The inverse transformation of (2L).
(4R) The inverse transformation of (1L).

🌈 Parameters 🌈

ICOMPQ — ICOMPQ is INTEGER. Specifies whether singular vectors are to be computed in factored form: = 0: Left singular vector matrix. = 1: Right singular vector matrix.
NL — NL is INTEGER. The row dimension of the upper block. NL >= 1.
NR — NR is INTEGER. The row dimension of the lower block. NR >= 1.
SQRE — SQRE is INTEGER. = 0: the lower block is an NR-by-NR square matrix. = 1: the lower block is an NR-by-(NR+1) rectangular matrix. The bidiagonal matrix has row dimension N = NL + NR + 1, and column dimension M = N + SQRE.
NRHS — NRHS is INTEGER. The number of columns of B and BX. NRHS must be at least 1.
B — B is COMPLEX array, dimension ( LDB, NRHS ). On input, B contains the right hand sides of the least squares problem in rows 1 through M. On output, B contains the solution X in rows 1 through N.
LDB — LDB is INTEGER. The leading dimension of B. LDB must be at least max(1,MAX( M, N )).
BX — BX is COMPLEX array, dimension ( LDBX, NRHS ).
LDBX — LDBX is INTEGER. The leading dimension of BX.
PERM — PERM is INTEGER array, dimension ( N ). The permutations (from deflation and sorting) applied to the two blocks.
GIVPTR — GIVPTR is INTEGER. The number of Givens rotations which took place in this subproblem.
GIVCOL — GIVCOL is INTEGER array, dimension ( LDGCOL, 2 ). Each pair of numbers indicates a pair of rows/columns involved in a Givens rotation.
LDGCOL — LDGCOL is INTEGER. The leading dimension of GIVCOL, must be at least N.
GIVNUM — GIVNUM is REAL array, dimension ( LDGNUM, 2 ). Each number indicates the C or S value used in the corresponding Givens rotation.
LDGNUM — LDGNUM is INTEGER. The leading dimension of arrays DIFR, POLES and GIVNUM, must be at least K.
POLES — POLES is REAL array, dimension ( LDGNUM, 2 ). On entry, POLES(1:K, 1) contains the new singular values obtained from solving the secular equation, and POLES(1:K, 2) is an array containing the poles in the secular equation.
DIFL — DIFL is REAL array, dimension ( K ). On entry, DIFL(I) is the distance between I-th updated (undeflated) singular value and the I-th (undeflated) old singular value.
DIFR — DIFR is REAL array, dimension ( LDGNUM, 2 ). On entry, DIFR(I, 1) contains the distances between I-th updated (undeflated) singular value and the I+1-th (undeflated) old singular value. And DIFR(I, 2) is the normalizing factor for the I-th right singular vector.
Z — Z is REAL array, dimension ( K ). Contain the components of the deflation-adjusted updating row vector.
K — K is INTEGER. Contains the dimension of the non-deflated matrix, This is the order of the related secular equation. 1 <= K <=N.
C — C is REAL. C contains garbage if SQRE =0 and the C-value of a Givens rotation related to the right null space if SQRE = 1.
S — S is REAL. S contains garbage if SQRE =0 and the S-value of a Givens rotation related to the right null space if SQRE = 1.
RWORK — RWORK is REAL array, dimension ( K*(1+NRHS) + 2*NRHS ).
INFO — INFO is INTEGER. = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value.

⭐ 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 267 of file clals0.f.

💀 subroutine dlals0 💀

subroutine dlals0 (integer icompq, integer nl, integer nr, integer sqre,
    integer nrhs, double precision, dimension( ldb, * ) b, integer ldb,
    double precision, dimension( ldbx, * ) bx, integer ldbx, integer,
    dimension( * ) perm, integer givptr, integer, dimension( ldgcol, * )
    givcol, integer ldgcol, double precision, dimension( ldgnum, * ) givnum,
    integer ldgnum, double precision, dimension( ldgnum, * ) poles, double
    precision, dimension( * ) difl, double precision, dimension( ldgnum, * )
    difr, double precision, dimension( * ) z, integer k, double precision c,
    double precision s, double precision, dimension( * ) work, integer info)

DLALS0 applies back multiplying factors in solving the least squares problem using divide and conquer SVD approach. Used by sgelsd.

💖 Purpose 💖

DLALS0 applies back the multiplying factors of either the left or the right singular vector matrix of a diagonal matrix appended by a row to the right hand side matrix B in solving the least squares problem using the divide-and-conquer SVD approach.

For the left singular vector matrix, three types of orthogonal matrices are involved:

(1L) Givens rotations: the number of such rotations is GIVPTR; the pairs of columns/rows they were applied to are stored in GIVCOL; and the C- and S-values of these rotations are stored in GIVNUM.
(2L) Permutation. The (NL+1)-st row of B is to be moved to the first row, and for J=2:N, PERM(J)-th row of B is to be moved to the J-th row.
(3L) The left singular vector matrix of the remaining matrix.

For the right singular vector matrix, four types of orthogonal matrices are involved:

(1R) The right singular vector matrix of the remaining matrix.
(2R) If SQRE = 1, one extra Givens rotation to generate the right null space.
(3R) The inverse transformation of (2L).
(4R) The inverse transformation of (1L).

🌈 Parameters 🌈

ICOMPQ — bestie, the parameter deets for dlals0 continue in part 2 👀
ICOMPQ — okay so ICOMPQ is INTEGER. It specifies whether singular vectors are to be computed in factored form: = 0: Left singular vector matrix. = 1: Right singular vector matrix. 💅
NL — NL is INTEGER. The row dimension of the upper block. NL >= 1. ✨
NR — NR is INTEGER. The row dimension of the lower block. NR >= 1. 🦋
SQRE — SQRE is INTEGER. = 0: the lower block is an NR-by-NR square matrix. = 1: the lower block is an NR-by-(NR+1) rectangular matrix. The bidiagonal matrix has row dimension N = NL + NR + 1, and column dimension M = N + SQRE. 🎀
NRHS — NRHS is INTEGER. The number of columns of B and BX. NRHS must be at least 1. 🌸
B — B is DOUBLE PRECISION array, dimension ( LDB, NRHS ). On input, B contains the right hand sides of the least squares problem in rows 1 through M. On output, B contains the solution X in rows 1 through N. 💖
LDB — LDB is INTEGER. The leading dimension of B. LDB must be at least max(1,MAX( M, N )). 👑
BX — BX is DOUBLE PRECISION array, dimension ( LDBX, NRHS ). 🌈
LDBX — LDBX is INTEGER. The leading dimension of BX. ⭐
PERM — PERM is INTEGER array, dimension ( N ). The permutations (from deflation and sorting) applied to the two blocks. 🧚
GIVPTR — GIVPTR is INTEGER. The number of Givens rotations which took place in this subproblem. 💫
GIVCOL — GIVCOL is INTEGER array, dimension ( LDGCOL, 2 ). Each pair of numbers indicates a pair of rows/columns involved in a Givens rotation. 🔥
LDGCOL — LDGCOL is INTEGER. The leading dimension of GIVCOL, must be at least N. 💜
GIVNUM — GIVNUM is DOUBLE PRECISION array, dimension ( LDGNUM, 2 ). Each number indicates the C or S value used in the corresponding Givens rotation. 🍓
LDGNUM — LDGNUM is INTEGER. The leading dimension of arrays DIFR, POLES and GIVNUM, must be at least K. 🎀
POLES — POLES is DOUBLE PRECISION array, dimension ( LDGNUM, 2 ). On entry, POLES(1:K, 1) contains the new singular values obtained from solving the secular equation, and POLES(1:K, 2) is an array containing the poles in the secular equation. 🌸
DIFL — DIFL is DOUBLE PRECISION array, dimension ( K ). On entry, DIFL(I) is the distance between I-th updated (undeflated) singular value and the I-th (undeflated) old singular value. ✨
DIFR — DIFR is DOUBLE PRECISION array, dimension ( LDGNUM, 2 ). On entry, DIFR(I, 1) contains the distances between I-th updated (undeflated) singular value and the I+1-th (undeflated) old singular value. And DIFR(I, 2) is the normalizing factor for the I-th right singular vector. 🦋
Z — Z is DOUBLE PRECISION array, dimension ( K ). Contain the components of the deflation-adjusted updating row vector. 💅
K — K is INTEGER. Contains the dimension of the non-deflated matrix, This is the order of the related secular equation. 1 <= K <=N. 👑
C — C is DOUBLE PRECISION. C contains garbage if SQRE =0 and the C-value of a Givens rotation related to the right null space if SQRE = 1. 😭
S — S is DOUBLE PRECISION. S contains garbage if SQRE =0 and the S-value of a Givens rotation related to the right null space if SQRE = 1. 💀
WORK — WORK is DOUBLE PRECISION array, dimension ( K ). 🌈
INFO — INFO is INTEGER. = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. ⭐

🌸 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 265 of file dlals0.f. 💖

🦋 `SLALS0` 🦋

subroutine slals0 (integer icompq, integer nl, integer nr, integer sqre,
    integer nrhs, real, dimension( ldb, * ) b, integer ldb, real, dimension(
    ldbx, * ) bx, integer ldbx, integer, dimension( * ) perm, integer
    givptr, integer, dimension( ldgcol, * ) givcol, integer ldgcol, real,
    dimension( ldgnum, * ) givnum, integer ldgnum, real, dimension( ldgnum,
    * ) poles, real, dimension( * ) difl, real, dimension( ldgnum, * ) difr,
    real, dimension( * ) z, integer k, real c, real s, real, dimension( * )
    work, integer info)

SLALS0 applies back multiplying factors in solving the least squares problem using divide and conquer SVD approach. Used by sgelsd. 💅

🌸 Purpose 🌸

SLALS0 applies back the multiplying factors of either the left or the right singular vector matrix of a diagonal matrix appended by a row to the right hand side matrix B in solving the least squares problem using the divide-and-conquer SVD approach. ✨

For the left singular vector matrix, three types of orthogonal matrices are involved:

(1L) Givens rotations: the number of such rotations is GIVPTR; the pairs of columns/rows they were applied to are stored in GIVCOL; and the C- and S-values of these rotations are stored in GIVNUM. 🎀
(2L) Permutation. The (NL+1)-st row of B is to be moved to the first row, and for J=2:N, PERM(J)-th row of B is to be moved to the J-th row. 🦋
(3L) The left singular vector matrix of the remaining matrix. 💖

For the right singular vector matrix, four types of orthogonal matrices are involved:

(1R) The right singular vector matrix of the remaining matrix. 🌈
(2R) If SQRE = 1, one extra Givens rotation to generate the right null space. ⭐
(3R) The inverse transformation of (2L). 🧚
(4R) The inverse transformation of (1L). 👑

🎀 Parameters 🎀

ICOMPQ — ICOMPQ is INTEGER. Specifies whether singular vectors are to be computed in factored form: = 0: Left singular vector matrix. = 1: Right singular vector matrix. 💅
NL — NL is INTEGER. The row dimension of the upper block. NL >= 1. ✨
NR — NR is INTEGER. The row dimension of the lower block. NR >= 1. 🦋
SQRE — SQRE is INTEGER. = 0: the lower block is an NR-by-NR square matrix. = 1: the lower block is an NR-by-(NR+1) rectangular matrix. The bidiagonal matrix has row dimension N = NL + NR + 1, and column dimension M = N + SQRE. 🎀
NRHS — NRHS is INTEGER. The number of columns of B and BX. NRHS must be at least 1. 🌸
B — B is REAL array, dimension ( LDB, NRHS ). On input, B contains the right hand sides of the least squares problem in rows 1 through M. On output, B contains the solution X in rows 1 through N. 💖
LDB — LDB is INTEGER. The leading dimension of B. LDB must be at least max(1,MAX( M, N )). 👑
BX — BX is REAL array, dimension ( LDBX, NRHS ). 🌈
LDBX — LDBX is INTEGER. The leading dimension of BX. ⭐
PERM — PERM is INTEGER array, dimension ( N ). The permutations (from deflation and sorting) applied to the two blocks. 🧚
GIVPTR — GIVPTR is INTEGER. The number of Givens rotations which took place in this subproblem. 💫
GIVCOL — GIVCOL is INTEGER array, dimension ( LDGCOL, 2 ). Each pair of numbers indicates a pair of rows/columns involved in a Givens rotation. 🔥
LDGCOL — LDGCOL is INTEGER. The leading dimension of GIVCOL, must be at least N. 💜
GIVNUM — GIVNUM is REAL array, dimension ( LDGNUM, 2 ). Each number indicates the C or S value used in the corresponding Givens rotation. 🍓
LDGNUM — LDGNUM is INTEGER. The leading dimension of arrays DIFR, POLES and GIVNUM, must be at least K. 🎀
POLES — POLES is REAL array, dimension ( LDGNUM, 2 ). On entry, POLES(1:K, 1) contains the new singular values obtained from solving the secular equation, and POLES(1:K, 2) is an array containing the poles in the secular equation. 🌸
DIFL — DIFL is REAL array, dimension ( K ). On entry, DIFL(I) is the distance between I-th updated (undeflated) singular value and the I-th (undeflated) old singular value. ✨
DIFR
DIFR — DOUBLE PRECISION array, dimension ( LDGNUM, 2 ). On entry, DIFR(I, 1) holds the distances between the I-th updated (undeflated) singular value and the I+1-th (undeflated) old singular value. And DIFR(I, 2) is the normalizing factor for the I-th right singular vector. Two jobs, one array, she's versatile 💅
Z — DOUBLE PRECISION array, dimension ( K ). Contains the components of the deflation-adjusted updating row vector. Main character row vector, honestly.
K — INTEGER. Contains the dimension of the non-deflated matrix — this is the order of the related secular equation. 1 <= K <=N. Respect the bounds bestie, fr fr.
C — DOUBLE PRECISION. C contains garbage if SQRE =0 and the C-value of a Givens rotation related to the right null space if SQRE = 1. Yes literally garbage, it's giving recycling bin 🗑️
S — DOUBLE PRECISION. S contains garbage if SQRE =0 and the S-value of a Givens rotation related to the right null space if SQRE = 1. Same vibe, same trash can.
RWORK — DOUBLE PRECISION array, dimension ( K*(1+NRHS) + 2*NRHS ). Do the math, she's not asking again ✨
INFO — INTEGER.
- = 0: successful exit. slay 🎉
- < 0: if INFO = -i, the i-th argument had an illegal value. not slay 😭

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 265 of file slals0.f.

🦋 okay now the complex one: `zlals0` 🦋

subroutine zlals0 (integer icompq, integer nl, integer nr, integer sqre,
    integer nrhs, complex*16, dimension( ldb, * ) b, integer ldb,
    complex*16, dimension( ldbx, * ) bx, integer ldbx, integer, dimension( *
    ) perm, integer givptr, integer, dimension( ldgcol, * ) givcol, integer
    ldgcol, double precision, dimension( ldgnum, * ) givnum, integer ldgnum,
    double precision, dimension( ldgnum, * ) poles, double precision,
    dimension( * ) difl, double precision, dimension( ldgnum, * ) difr,
    double precision, dimension( * ) z, integer k, double precision c,
    double precision s, double precision, dimension( * ) rwork, integer
    info)

ZLALS0 applies back multiplying factors in solving the least squares problem using divide and conquer SVD approach. Used by sgelsd. Complex*16 edition, she's fancy 💜

Purpose 🎯

ZLALS0 applies back the multiplying factors of either the left or the right singular vector matrix of a diagonal matrix appended by a row to the right hand side matrix B in solving the least squares problem using the divide-and-conquer SVD approach.

For the left singular vector matrix, three types of orthogonal matrices are involved:

(1L) Givens rotations — the number of such rotations is GIVPTR; the pairs of columns/rows they were applied to are stored in GIVCOL; and the C- and S-values of these rotations are stored in GIVNUM.
(2L) Permutation — the (NL+1)-st row of B is to be moved to the first row, and for J=2:N, PERM(J)-th row of B is to be moved to the J-th row.
(3L) The left singular vector matrix of the remaining matrix.

For the right singular vector matrix, four types of orthogonal matrices are involved:

(1R) The right singular vector matrix of the remaining matrix.
(2R) If SQRE = 1, one extra Givens rotation to generate the right null space.
(3R) The inverse transformation of (2L).
(4R) The inverse transformation of (1L).

Parameters 🎀

ICOMPQ — INTEGER. Specifies whether singular vectors are to be computed in factored form:
- = 0: Left singular vector matrix.
- = 1: Right singular vector matrix.
NL — INTEGER. The row dimension of the upper block. NL >= 1.
NR — INTEGER. The row dimension of the lower block. NR >= 1.
SQRE — INTEGER.
- = 0: the lower block is an NR-by-NR square matrix.
- = 1: the lower block is an NR-by-(NR+1) rectangular matrix.

The bidiagonal matrix has row dimension N = NL + NR + 1, and column dimension M = N + SQRE. math is mathing ✨

NRHS — INTEGER. The number of columns of B and BX. NRHS must be at least 1.
B — COMPLEX*16 array, dimension ( LDB, NRHS ). On input, B contains the right hand sides of the least squares problem in rows 1 through M. On output, B contains the solution X in rows 1 through N. Glow-up arc, honestly.
LDB — INTEGER. The leading dimension of B. LDB must be at least max(1,MAX( M, N )).
BX — COMPLEX*16 array, dimension ( LDBX, NRHS ).
LDBX — INTEGER. The leading dimension of BX.
PERM — INTEGER array, dimension ( N ). The permutations (from deflation and sorting) applied to the two blocks.
GIVPTR — INTEGER. The number of Givens rotations which took place in this subproblem.
GIVCOL — INTEGER array, dimension ( LDGCOL, 2 ). Each pair of numbers indicates a pair of rows/columns involved in a Givens rotation. iconic duo behavior 👯
LDGCOL — INTEGER. The leading dimension of GIVCOL, must be at least N.
GIVNUM — DOUBLE PRECISION array, dimension ( LDGNUM, 2 ). Each number indicates the C or S value used in the corresponding Givens rotation.
LDGNUM — INTEGER. The leading dimension of arrays DIFR, POLES and GIVNUM, must be at least K.
POLES — DOUBLE PRECISION array, dimension ( LDGNUM, 2 ). On entry, POLES(1:K, 1) contains the new singular values obtained from solving the secular equation, and POLES(1:K, 2) is an array containing the poles in the secular equation.
DIFL — DOUBLE PRECISION array, dimension ( K ). On entry, DIFL(I) is the distance between I-th updated (undeflated) singular value and the I-th (undeflated) old singular value.
DIFR — DOUBLE PRECISION array, dimension ( LDGNUM, 2 ). On entry, DIFR(I, 1) contains the distances between I-th updated (undeflated) singular value and the I+1-th (undeflated) old singular value. And DIFR(I, 2) is the normalizing factor for the I-th right singular vector.
Z — DOUBLE PRECISION array, dimension ( K ). Contain the components of the deflation-adjusted updating row vector.
K — INTEGER. Contains the dimension of the non-deflated matrix — this is the order of the related secular equation. 1 <= K <=N.
C — DOUBLE PRECISION. C contains garbage if SQRE =0 and the C-value of a Givens rotation related to the right null space if SQRE = 1.
S — DOUBLE PRECISION. S contains garbage if SQRE =0 and the S-value of a Givens rotation related to the right null space if SQRE = 1.
RWORK — DOUBLE PRECISION array, dimension ( K*(1+NRHS) + 2*NRHS ).
INFO — INTEGER.
- = 0: successful exit.
- < 0: if INFO = -i, the i-th argument had an illegal value.

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 267 of file zlals0.f.

Author 📜

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lals0(3)

💖 NAME 💖

✨ SYNOPSIS ✨

🎀 Functions 🎀

🌸 Detailed Description 🌸

🦋 Function Documentation 🦋

👑 subroutine clals0 👑

💖 Purpose 💖

🌈 Parameters 🌈

⭐ Author ⭐

🍓 Contributors: 🍓

💀 subroutine dlals0 💀

💖 Purpose 💖

🌈 Parameters 🌈

🌸 Author 🌸

🎀 Contributors 🎀

🦋 SLALS0 🦋

🌸 Purpose 🌸

🎀 Parameters 🎀

Author 👑

Contributors 🫶

🦋 okay now the complex one: zlals0 🦋

Purpose 🎯

Parameters 🎀

Author 👑

Contributors 🫶

Author 📜

🦋 `SLALS0` 🦋

🦋 okay now the complex one: `zlals0` 🦋