lasd3(3)

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lasd3 💅✨ — D&C step: secular equation

okay bestie, pull up a chair because this one is from the Library Functions Manual (section 3, we're fancy) and it's literally the divide-and-conquer era of your life. it's lasd3, and it comes in a double precision flavor and a real flavor, because of course it does. 💖

NAME 🌸

lasd3 — lasd3: D&C step: secular equation. that's it, that's the whole name, no notes. 🎀

SYNOPSIS ✨

Functions 🦋

subroutine dlasd3 (nl, nr, sqre, k, d, q, ldq, dsigma, u, ldu, u2, ldu2, vt, ldvt, vt2, ldvt2, idxc, ctot, z, info) — DLASD3 finds all square roots of the roots of the secular equation, as defined by the values in D and Z, and then updates the singular vectors by matrix multiplication. Used by sbdsdc.
subroutine slasd3 (nl, nr, sqre, k, d, q, ldq, dsigma, u, ldu, u2, ldu2, vt, ldvt, vt2, ldvt2, idxc, ctot, z, info) — SLASD3 finds all square roots of the roots of the secular equation, as defined by the values in D and Z, and then updates the singular vectors by matrix multiplication. Used by sbdsdc.

real ones know: same name, same dance, one is DOUBLE PRECISION and one is REAL. pick your fighter. 💅

Detailed Description 🫶

(the page literally drops the heading and moves straight on — no extra prose here, bestie. we go directly to the function docs. ✨)

Function Documentation 💖

`subroutine dlasd3` 🎀

subroutine dlasd3 (integer nl, integer nr, integer sqre, integer k, double
    precision, dimension( * ) d, double precision, dimension( ldq, * ) q,
    integer ldq, double precision, dimension( * ) dsigma, double precision,
    dimension( ldu, * ) u, integer ldu, double precision, dimension( ldu2, *
    ) u2, integer ldu2, double precision, dimension( ldvt, * ) vt, integer
    ldvt, double precision, dimension( ldvt2, * ) vt2, integer ldvt2,
    integer, dimension( * ) idxc, integer, dimension( * ) ctot, double
    precision, dimension( * ) z, integer info)

DLASD3 finds all square roots of the roots of the secular equation, as defined by the values in D and Z, and then updates the singular vectors by matrix multiplication. Used by sbdsdc.

Purpose 🔥

DLASD3 finds all the square roots of the roots of the secular equation, as defined by the values in D and Z. It makes the appropriate calls to DLASD4 and then updates the singular vectors by matrix multiplication. DLASD3 is called from DLASD1.

(i know, it's giving very much "called from" and "makes the appropriate calls to" — the girlies love a call graph 😭)

Parameters 🌈

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 N = NL + NR + 1 rows and M = N + SQRE >= N columns.

K — K is INTEGER. The size of the secular equation, 1 =< K = < N. (yes that's the exact inequality as printed, don't come for me 💀)
D — D is DOUBLE PRECISION array, dimension(K). On exit the square roots of the roots of the secular equation, in ascending order. ✨
Q — Q is DOUBLE PRECISION array, dimension (LDQ,K).
LDQ — LDQ is INTEGER. The leading dimension of the array Q. LDQ >= K.
DSIGMA — DSIGMA is DOUBLE PRECISION array, dimension(K). The first K elements of this array contain the old roots of the deflated updating problem. These are the poles of the secular equation. (poles! iconic. no cap.)
U — U is DOUBLE PRECISION array, dimension (LDU, N). The last N - K columns of this matrix contain the deflated left singular vectors.
LDU — LDU is INTEGER. The leading dimension of the array U. LDU >= N.
U2 — U2 is DOUBLE PRECISION array, dimension (LDU2, N). The first K columns of this matrix contain the non-deflated left singular vectors for the split problem.
LDU2 — LDU2 is INTEGER. The leading dimension of the array U2. LDU2 >= N.
VT — VT is DOUBLE PRECISION array, dimension (LDVT, M). The last M - K columns of VT**T contain the deflated right singular vectors.
LDVT — LDVT is INTEGER. The leading dimension of the array VT. LDVT >= N.
VT2 — VT2 is DOUBLE PRECISION array, dimension (LDVT2, N). The first K columns of VT2**T contain the non-deflated right singular vectors for the split problem.
LDVT2 — LDVT2 is INTEGER. The leading dimension of the array VT2. LDVT2 >= N.
IDXC — IDXC is INTEGER array, dimension ( N ). The permutation used to arrange the columns of U (and rows of VT) into three groups:
1. the first group contains non-zero entries only at and above (or before) NL +1;
2. the second contains non-zero entries only at and below (or after) NL+2;
3. and the third is dense.

The first column of U and the row of VT are treated separately, however.

The rows of the singular vectors found by DLASD4 must be likewise permuted before the matrix multiplies can take place.

CTOT — CTOT is INTEGER array, dimension ( 4 ). A count of the total number of the various types of columns in U (or rows in VT), as described in IDXC. The fourth column type is any column which has been deflated.
Z — Z is DOUBLE PRECISION array, dimension (K). The first K elements of this array contain the components of the deflation-adjusted updating row vector. 🫶
INFO — INFO is INTEGER.
- = 0: successful exit.
- < 0: if INFO = -i, the i-th argument had an illegal value.
- > 0: if INFO = 1, a singular value did not converge. 😭

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 📌

Definition at line 214 of file dlasd3.f.

`subroutine slasd3` 💜

subroutine slasd3 (integer nl, integer nr, integer sqre, integer k, real,
    dimension( * ) d, real, dimension( ldq, * ) q, integer ldq, real,
    dimension( * ) dsigma, real, dimension( ldu, * ) u, integer ldu, real,
    dimension( ldu2, * ) u2, integer ldu2, real, dimension( ldvt, * ) vt,
    integer ldvt, real, dimension( ldvt2, * ) vt2, integer ldvt2, integer,
    dimension( * ) idxc, integer, dimension( * ) ctot, real, dimension( * )
    z, integer info)

SLASD3 finds all square roots of the roots of the secular equation, as defined by the values in D and Z, and then updates the singular vectors by matrix multiplication. Used by sbdsdc.

Purpose 🔥

SLASD3 finds all the square roots of the roots of the secular equation, as defined by the values in D and Z. It makes the appropriate calls to SLASD4 and then updates the singular vectors by matrix multiplication. SLASD3 is called from SLASD1.

(spot the pattern? D-prefix calls DLASD4 and DLASD1, S-prefix calls SLASD4 and SLASD1. consistency ate. 💅)

Parameters 🌈

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 N = NL + NR + 1 rows and M = N + SQRE >= N columns.

K — K is INTEGER. The size of the secular equation, 1 =< K = < N.
D — D is REAL array, dimension(K). On exit the square roots of the roots of the secular equation, in ascending order. ⭐
Q — Q is REAL array, dimension (LDQ,K).
LDQ — LDQ is INTEGER. The leading dimension of the array Q. LDQ >= K.
DSIGMA — DSIGMA is REAL array, dimension(K). The first K elements of this array contain the old roots of the deflated updating problem. These are the poles of the secular equation.
U — U is REAL array, dimension (LDU, N). The last N - K columns of this matrix contain the deflated left singular vectors.
LDU — LDU is INTEGER. The leading dimension of the array U. LDU >= N.
U2 — U2 is REAL array, dimension (LDU2, N). The first K columns of this matrix contain the non-deflated left singular vectors for the split problem.
LDU2 — LDU2 is INTEGER. The leading dimension of the array U2. LDU2 >= N.
VT — VT is REAL array, dimension (LDVT, M). The last M - K columns of VT**T contain the deflated right singular vectors.
LDVT — LDVT is INTEGER. The leading dimension of the array VT. LDVT >= N.
VT2 — VT2 is REAL array, dimension (LDVT2, N). The first K columns of VT2**T contain the non-deflated right singular vectors for the split problem.
LDVT2 — LDVT2 is INTEGER. The leading dimension of the array VT2. LDVT2 >= N.
IDXC — IDXC is INTEGER array, dimension (N). The permutation used to arrange the columns of U (and rows of VT) into three groups:
1. the first group contains non-zero entries only at and above (or before) NL +1;
2. the second contains non-zero entries only at and below (or after) NL+2;
3. and the third is dense.

The first column of U and the row of VT are treated separately, however.

The rows of the singular vectors found by SLASD4 must be likewise permuted before the matrix multiplies can take place.

CTOT

(…and that's where part 1 runs out, bestie — CTOT's description rolls in with part 2. 🫶✨)

CTOT — okay so this one is an INTEGER array, dimension (4). It’s a count of the total number of the various types of columns in U (or rows in VT), as described in IDXC. The fourth column type is any column which has been deflated. deflated columns have main character energy too 💅
Z — REAL array, dimension (K). The first K elements of this array contain the components of the deflation-adjusted updating row vector. deflation-adjusted updating row vector is such a mouthful but we respect it ✨
INFO — INTEGER, bestie, and here’s the vibe check:
- = 0: successful exit. slay, we love a clean exit ✅
- < 0: if INFO = -i, the i-th argument had an illegal value. oop, illegal value alert 🚨
- > 0: if INFO = 1, a singular value did not converge. not the convergence we wanted 😭

💖 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 214 of file slasd3.f. the receipts are right there, periodt 📜

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code. yes bestie, the docs generated themselves-ish 💅

And that’s the page, babes! Signing off from LAPACK Version 3.12.0, page lasd3(3) — no date listed in this footer, but the source/version is right there. Mwah 💋✨

📦 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

lasd3(3)

lasd3 💅✨ — D&C step: secular equation

NAME 🌸

SYNOPSIS ✨

Functions 🦋

Detailed Description 🫶

Function Documentation 💖

subroutine dlasd3 🎀

Purpose 🔥

Parameters 🌈

Author 👑

Contributors: 🌟

Definition 📌

subroutine slasd3 💜

Purpose 🔥

Parameters 🌈

💖 Author 💖

🫶 Contributors 🫶

🌈 Author 🌈

`subroutine dlasd3` 🎀

`subroutine slasd3` 💜