SRC/dlasd2.f(3)

📦

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🌸 NAME 🌸

SRC/dlasd2.f — bestie, this is the Library Functions Manual page for the dlasd2 subroutine. It’s giving “LAPACK internals, but make it understandable” 💅✨

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

Here’s the whole call, copied exactly because we do not mess with signatures:

subroutine dlasd2 (nl, nr, sqre, k, d, z, alpha, beta, u, ldu, vt, ldvt,
           dsigma, u2, ldu2, vt2, ldvt2, idxp, idx, idxc, idxq, coltyp, info)

One-line vibe: DLASD2 merges the two sets of singular values together into a single sorted set. Used by sbdsdc. No cap, that’s literally its whole synopsis 🫶

💅 Function/Subroutine Documentation 💅

Okay so this is the full signature with all the types and dimensions. Do not lose your place, bestie — it’s long but iconic:

subroutine dlasd2 (integer nl, integer nr, integer sqre, integer k, double
       precision, dimension( * ) d, double precision, dimension( * ) z, double
       precision alpha, double precision beta, double precision, dimension(
       ldu, * ) u, integer ldu, double precision, dimension( ldvt, * ) vt,
       integer ldvt, double precision, dimension( * ) dsigma, double precision,
       dimension( ldu2, * ) u2, integer ldu2, double precision, dimension(
       ldvt2, * ) vt2, integer ldvt2, integer, dimension( * ) idxp, integer,
       dimension( * ) idx, integer, dimension( * ) idxc, integer, dimension( *
       ) idxq, integer, dimension( * ) coltyp, integer info)

Description: DLASD2 merges the two sets of singular values together into a single sorted set. Used by sbdsdc. 💖

🔥 Purpose 🔥

Okay, here’s the tea: DLASD2 merges the two sets of singular values together into a single sorted set. Then it tries to deflate the size of the problem. Deflation can happen in two ways: when two or more singular values are close together, or if there is a tiny entry in the Z vector. For each such occurrence, the order of the related secular equation problem is reduced by one. And yes — DLASD2 is called from DLASD1 👑

🌈 Parameters 🌈

NL — INTEGER. The row dimension of the upper block. Constraint: NL >= 1.
NR — INTEGER. The row dimension of the lower block. Constraint: 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 N = NL + NR + 1 rows and M = N + SQRE >= N columns.
K — INTEGER. Contains the dimension of the non-deflated matrix. This is the order of the related secular equation. 1 <= K <=N.
D — DOUBLE PRECISION array, dimension(N). On entry, D contains the singular values of the two submatrices to be combined. On exit, D contains the trailing (N-K) updated singular values — those which were deflated — sorted into increasing order.
Z — DOUBLE PRECISION array, dimension(N). On exit, Z contains the updating row vector in the secular equation.
ALPHA — DOUBLE PRECISION. Contains the diagonal element associated with the added row.
BETA — DOUBLE PRECISION. Contains the off-diagonal element associated with the added row.
U — DOUBLE PRECISION array, dimension(LDU,N). On entry, U contains the left singular vectors of two submatrices in the two square blocks with corners at (1,1), (NL, NL), and (NL+2, NL+2), (N,N). On exit, U contains the trailing (N-K) updated left singular vectors — those which were deflated — in its last N-K columns.
LDU — INTEGER. The leading dimension of the array U. LDU >= N.
VT — DOUBLE PRECISION array, dimension(LDVT,M). On entry, VT**T contains the right singular vectors of two submatrices in the two square blocks with corners at (1,1), (NL+1, NL+1), and (NL+2, NL+2), (M,M). On exit, VT**T contains the trailing (N-K) updated right singular vectors — those which were deflated — in its last N-K columns. In case SQRE =1, the last row of VT spans the right null space.
LDVT — INTEGER. The leading dimension of the array VT. LDVT >= M.
DSIGMA — DOUBLE PRECISION array, dimension (N). Contains a copy of the diagonal elements (K-1 singular values and one zero) in the secular equation.
U2 — DOUBLE PRECISION array, dimension(LDU2,N). Contains a copy of the first K-1 left singular vectors which will be used by DLASD3 in a matrix multiply (DGEMM) to solve for the new left singular vectors. U2 is arranged into four blocks. The first block contains a column with 1 at NL+1 and zero everywhere else; the second block contains non-zero entries only at and above NL; the third contains non-zero entries only below NL+1; and the fourth is dense.
LDU2 — INTEGER. The leading dimension of the array U2. LDU2 >= N.
VT2 — DOUBLE PRECISION array, dimension(LDVT2,N). VT2**T contains a copy of the first K right singular vectors which will be used by DLASD3 in a matrix multiply (DGEMM) to solve for the new right singular vectors. VT2 is arranged into three blocks. The first block contains a row that corresponds to the special 0 diagonal element in SIGMA; the second block contains non-zeros only at and before NL +1; the third block contains non-zeros only at and after NL +2.
LDVT2 — INTEGER. The leading dimension of the array VT2. LDVT2 >= M.
IDXP — INTEGER array, dimension(N). This will contain the permutation used to place deflated values of D at the end of the array. On output, IDXP(2:K) points to the nondeflated D-values and IDXP(K+1:N) points to the deflated singular values.
IDX — INTEGER array, dimension(N). This will contain the permutation used to sort the contents of D into ascending order.
IDXC — INTEGER array, dimension(N). This will contain the permutation used to arrange the columns of the deflated U matrix into three groups: the first group contains non-zero entries only at and above NL, the second contains non-zero entries only below NL+2, and the third is dense.
IDXQ — INTEGER array, dimension(N). This contains the permutation which separately sorts the two sub-problems in D into ascending order. Note that entries in the first hlaf — yes, that’s the source’s spelling 😭 — of this permutation must first be moved one position backward; and entries in the second half must first have NL+1 added to their values.
COLTYP — INTEGER array, dimension(N). As workspace, this will contain a label which will indicate which of the following types a column in the U2 matrix or a row in the VT2 matrix is: 1 : non-zero in the upper half only; 2 : non-zero in the lower half only; 3 : dense; 4 : deflated. On exit, it is an array of dimension 4, with COLTYP(I) being the dimension of the I-th type columns.
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 Huan Ren, Computer Science Division, University of California at Berkeley, USA

Definition at line 266 of file dlasd2.f.

💖 Author 💖

Generated automatically by Doxygen for LAPACK from the source code.

That’s the whole page, bestie! The footer vibes are LAPACK Version 3.12.0 for SRC/dlasd2.f(3) — no separate date in that footer, just those details, and honestly I’m obsessed with the consistency 💅✨

📦 where this page comes from

arch rolling: lapack-doc 3.12.1-2 · custom
💖 girlified by deepseek-ai/DeepSeek-V4.1-Flash-1017 on 2026-11-04: a language model's rewrite of the original, under its terms