SRC/dlaed9.f(3)

SRC/dlaed9.f(3) is the page title, bestie, and it's living in the Library Functions Manual. It's giving dense-matrix secular-equation energy, and we're gonna read every single parameter like the main characters they are. 💅

✨ NAME ✨

SRC/dlaed9.f — that's the name. Iconic, short, to the point. 🎀

🌟 SYNOPSIS 🌟

🧚 Functions/Subroutines 🧚

Here's the signature, copied exactly because we do not mess with code in this group chat:

   subroutine dlaed9 (k, kstart, kstop, n, d, q, ldq, rho, dlambda, w, s,
       lds, info)

DLAED9 is used by DSTEDC. It finds the roots of the secular equation and updates the eigenvectors. It's used when the original matrix is dense. No cap, that's the whole synopsis vibe. 💖

💖 Function/Subroutine Documentation 💖

Here's the full typed-out version, again exactly:

   subroutine dlaed9 (integer k, integer kstart, integer kstop, integer n,
       double precision, dimension( * ) d, double precision, dimension( ldq, *
       ) q, integer ldq, double precision rho, double precision, dimension( * )
       dlambda, double precision, dimension( * ) w, double precision,
       dimension( lds, * ) s, integer lds, integer info)

DLAED9 is used by DSTEDC. It finds the roots of the secular equation and updates the eigenvectors. Used when the original matrix is dense. 💖

💫 Purpose 💫

Okay so DLAED9 finds the roots of the secular equation — the one defined by the values in D, Z, and RHO — between KSTART and KSTOP. It makes the appropriate calls to DLAED4, then stores the new matrix of eigenvectors for use in calculating the next level of Z vectors. Literally the glow-up pipeline. ✨

🎀 Parameters 🎀

• K — K is INTEGER; the number of terms in the rational function to be solved by DLAED4. K >= 0. 🧮
• KSTART — KSTART is INTEGER.
• KSTOP — KSTOP is INTEGER; the updated eigenvalues Lambda(I), KSTART <= I <= KSTOP, are to be computed. 1 <= KSTART <= KSTOP <= K.
• N — N is INTEGER; the number of rows and columns in the Q matrix. N >= K (delation may result in N > K). 🫶
• D — D is DOUBLE PRECISION array, dimension (N); D(I) contains the updated eigenvalues for KSTART <= I <= KSTOP.
• Q — Q is DOUBLE PRECISION array, dimension (LDQ,N).
• LDQ — LDQ is INTEGER; the leading dimension of the array Q. LDQ >= max( 1, N ).
• RHO — RHO is DOUBLE PRECISION; the value of the parameter in the rank one update equation. RHO >= 0 required. 💅
• DLAMBDA — DLAMBDA 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. 🌀
• W — W is DOUBLE PRECISION array, dimension (K); the first K elements of this array contain the components of the deflation-adjusted updating vector.
• S — S is DOUBLE PRECISION array, dimension (LDS, K); will contain the eigenvectors of the repaired matrix which will be stored for subsequent Z vector calculation and multiplied by the previously accumulated eigenvectors to update the system. ✨
• LDS — LDS is INTEGER; the leading dimension of S. LDS >= max( 1, K ).
• INFO — INFO is INTEGER; = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. > 0: if INFO = 1, an eigenvalue did not converge. 💀

👑 Author 👑

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

🫶 Contributors: 🫶

Jeff Rutter, Computer Science Division, University of California at Berkeley, USA.

Definition at line 154 of file dlaed9.f.

🌸 Author 🌸

Generated automatically by Doxygen for LAPACK from the source code.

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Cute footer sign-off, bestie: LAPACK Version 3.12.0, source SRC/dlaed9.f(3), and the date slot is blank on this page — no invented dates, just vibes. 💖🎀